FAMILIAR LECTURES ON
SCIENTIFIC SUBJECTS








FAMILIAR LECTURES ON
SCIENTIFIC SUBJECTS
BY SIR JOHN  F. W. HERSCHEL, BART., K. H.;
M.A.; D.C.L.; F.R.S. L AND E.; HON. M.R.I.A; F.R.A.S.; M.C.U.P.S.
MEMBER OF THE INSTITUTE OF FRANCE; AND
CORRESPONDENT, ASSOCIATE, HONORARY OR ORDINARY MEMBER OF VARIOUS OTHER
ACADEMIES AND INSTITUTIONS
NEW YORK:
GEORGE ROUTLEDGE & SONS,
416 Broome Street.
PHILADELPHIA: J. B. LIPPINCOTT & Co.
LONDON:
ALEXANDER STRAHAN & Co., AND GEORGE ROUTLEDGE & SONS.
1871.








PR E F ACE.
HE three first lectures in the following
collection-on Earthquakes and Volcanoes, on the Sun, and on Cometswere delivered by the Author to a village audience, in the school-house of the parish
of Hawkhurst, in Kent, his place of residence.
They were subsequently printed as contributions
to the pages of that excellent and useful periodical, Good lWords, in which they were followed
by those " On the Weather and Weather Prophets," "On Celestial Measurings and Weighings," and " On Light," the latter assuming in its
progress the dimensions of a little elementary




vi                  PREFACE.
treatise, adapted for the perusal of non-mathematical readers. On the completion of this, it was
suggested by the publisher of that work to collect
and reprint them together,-a proposal the more
welcome, as it afforded an opportunity for bringing together several other pieces of a somewhat
similar character, some of which, though not
properly characterized as " Lectures," it seemed
desirable to reproduce.  More especially, it appeared to the Author an imperative duty to let
no opportunity pass of recalling the attention of the
public to the great question of the proposed abandonment of our national system  of weights and
measures, and adoption in its stead of the metrical system of the French, with its unit, the metre,
in place of the English yard, which has been so
actively, and, in his opinion, so mischievously
urged on Parliament; the agitation in favour of
which only sleeps for the present, in the view of
allowing the public mind to familiarize itself with
the idea under a Permissive Act,-to be assuredly
brought forward again with renewed activity, and
under a more intense and prolonged pressure (to
be met by a more concentrated and determined
resistance), on no distant occasion.




PREFACE.                  Vii
No apology will be considered necessary for reproducing the little piece " On the Absorption of
Light," the thirteenth in order of this collection.
Though it does not pretend to anticipate any of
the later experimental researches, and the reasonings grounded on them  for concluding the conversion of motion into heat, electricity, and magnetism,-it is, nevertheless, a step (though a small
one) in that direction, by showing that a state of
apparent rest in a material body is not incompatible with the internal propagation ad ifinitlum
within it of movement impressed on it from without. It is very conceivable that the internal or
atomic organization of ponderable matter may be
such as to concentrate and localize, in its individual
molecular groups, the broken-up and dispersed
undulations caused by any external shock; and so
preserve them from attaining that final state of
complete mutual counteraction which  is there
contemplated.
Some slight alterations in the wording, and
additions (not in every instance unimportant) to
the matter of the several Essays here reproduced,
have been made; as well as, here and there, some
numerical corrections.  In particular, the last little




viii                  PREFACE.
piece, "On the Estimation  of" Skill in TargetShooting," has for one of its objects the correction
of an error in one of the Author's former works,
while, at the same time, calling attention to a
subject generally, and even nationally, interesting.
COLLINGWOOD, unrze 8, 1866




CONTENTS.
PAGE
PREFACE,....              Vii
I. ABOUT VOLCANOS AND EARTHQUAKES,..   I
II. THE SUN,.....  47
III. ON COMETS,.....         9
IV. THE WEATHER AND WEATHER PROPHETS,..  42
V. CELESTIAL MEASURINGS AND WEIGHINGS,.. 176
VI. ON LIGHT.  PART I.-REFLEXION-REFRACTIONDISPERSION-COLOUR-ABSORPTION,.. 219
VII. ON LIGHT. PART II.-THEORIES OF LIGHT-INTERFERENCES-DIFFRACTION,...268
VIII. ON LIGHT. PART III.-DOUBLE REFRACTION —POLARIZATION,..... 34
IX. ON SENSORIAL VISION,... 400
X. THE YARD, THE PENDULUM, AND THE METRE,. 419
XI. ON ATOMS. A DIALOGUE,. ~. 452
XII. ON THE ORIGIN OF FORCE,..             460
XIII. ON THE ABSORPTION OF LIGHT BY COLOURED MEDIA,
VIEWED IN CONNEXION WITH THE UNDULATORY
THEORY,..... 476
XIV. ON THE ESTIMATION OF SKILL IN TARGET-SHOOTING, 495








LECTURE L
ABOUT VOLCANOS AND EARTHQUAKES.
PURPOSE in this Lecture to say something
about volcanos and earthquakes.  It is a
subject I have thought a good deal about,
and seen a little of, for though I have
never been so fortunate as to have seen a volcano
in eruption, or to have been shaken out of my bed
by an earthquake, still I have climbed the cones of
Vesuvius and Etna, hammer in hand and barometer on
back, and have wandered over and geologized among,
I believe, nearly all the principal scenes of extinct volcanic activity in Europe, those of Spain excepted.
(2.) Every one knows that a volcano is a mountain
that vomits out fire, and smoke, and cinders, and melted
lava, and sulphur, and steam, and gases, and all kinds
of horrible things; nay, even sometimes mud, and boiling water, and fishes; and everybody has heard or read
of the earth opening, and swallowing up man and beast,




2      ABOUT VOLCANOS AND EARTHQUAKES.
and houses and churches; and closing on them with a
snap, and smashing them to pieces; and then perhaps
opening again, and casting them out with a food of
dirty water from  some river or lake that had been
gulped down with them.  Now, all this, and much
more, is literally true, and has happened over and over
again; and when we have imagined it all, we shall have
formed a tolerably correct notion of some at least of
these visitations. And perhaps some may have been
tempted to ask why and how it is that God has permitted this fair earth to be visited with such destruction.
It can hardly be for the sins of men: for when these
things occur they involve alike the innocent and the
guilty; and besides, the volcano and the earthquake
were raging on this earth with as much, nay greater
violence, thousands and thousands of years before man
ever set his foot upon it. But perhaps, on the other
hand, it may have occurred to some to ask themselves
whether it is not just possible that these ugly affairs are
sent among us for some beneficent purpose; or at all
events that they may form part and parcel of some great
scheme of providential arrangement which is at work for
good, and not for ill. A ship sometimes strikes on a
rock, and all on board perish; a railway train runs into
another, or breaks down, and then wounds and contusions are the order of the day; but nobody doubts that
navigation and railway communication are great blessings. None of the great natural provisions for producing good are exempt in their workings from producing
occasional mischief. Storms disperse and dilute pesti



ABOUT VOLCANOS AND EARTHQUAKES.            3
lential vapours, and lightnings decompose and destroy
them; but both the one and the other often annihilate
the works of man, and inflict upon him sudden death.
Well, then, I think I shall be able to show that the volcano and the earthquake, dreadful as they are, as local
and temporary visitations, are in fact unavoidable (I had
almost said necessary) incidents in a vast system of
action to which we owe the very ground we stand upon,
the very land we inhabit, without which neither man,
beast, nor bird would have a place for their existence, and
the world would be the habitation of nothing but fishes.
(3.) Now, to make this clear, I must go a little out
of my way and say something about the first principles
of geology.  Geology does not pretend to go back to
the creation of the world, or concern itself about its
primitive state, but it does concern itself with the
changes it sees going on in it now, and with the evidence of a long series of such changes it can produce in
the most unmistakable features of the structure of our
rocks and soil, and the way in which they lie one on
the other. As to what we SEE.going on.-We see everywhere, and along every coast-line, the sea warring
against the land, and everywhere overcoming it; wearing
and eating it down, and battering it to pieces; grinding
those pieces to powder; carrying that powder away, and
spreading it out over its own bottom, by the continued
effect of the tides and currents.  Look at our chalk
cliffs, which once, no doubt, extended across the Channel to the similar cliffs on the French coast. What
do we see   Precipices cut down to the sea-beach,




4      ABOUT VOLCANOS AND EARTHQUAKES.
constantly  hammered by the waves and  constantly
crumbling: the beach itself made of the flints outstanding after the softer chalk has been ground down and
washed away; themselves grinding one another under
the same ceaseless discipline; first rounded into pebbles,
then worn into sand, and then carried out farther and
farther down the slope, to be replaced by fresh ones
from the same source.
(4.) Well: the same thing is going on everywhere, round
every coast of Europe, Asia, Africa, and America. Foot
by foot or inch by inch, month by month or century by
century, dozen everything MUST go. Time is as nothing
in geology. And what the sea is doing the rivers are
helping it to do. Look at the sand-banks at the mouth
of the Thames. What are they but the materials of our
island carried out to sea by the stream? The Ganges
carries away from the soil of India, and delivers into
the sea, twice as much solid substance zeekly as is contained in the great pyramid of Egypt. The Irawaddy
sweeps off from Burmah 62 cubic feet of earth in every
second of time on an average, and there are 86,400 seconds in every day, and 365 days in every year; and so on
for the other rivers. What has become of all that great
bed of chalk which once covered all the weald of Kent,
and formed a continuous mass from Ramsgate and Dover
to Beechy Head, running inland to Madamscourt Hill and
Seven Oaks? All clean gone, and swept out into the
bosom of the Atlantic, and there forming other chalkbeds. Now, geology assures us, on the most conclusive
and undeniable evidence, that ALL our present land, all




ABOUT VOLCANOS AND EARTHQUAKES.             5
our continents and islands, have been formed in this way
out of the ruins of former ones.  The old ones which
existed at the beginning of things have all perished, and
what we now stand upon has most assuredly been, at one
time or other, perhaps many times, the bottom of the sea.
(5.) Well, then, there is power enough at work, and it
has been at work long enough, utterly to have cleared
away and spread over the bed of the sea all our present
existing continents and islands, had they been placed
where they are at the creation of the world; and from
this it follows, as clear as demonstration can make it,
that without some process of renovation or restoration to
act in antagonism to this destructive work of old Neptune, there would not now be remaining a foot of dry
land for living thing to stand upon.
(6.) Now, what is this process of restoration? Let
the volcano and the earthquake tell their tale. Let the
earthquake tell how, within the memory of man-under
the eyesight of eye-witnesses, one of whom (Mrs Graham)
has described the fact —the whohl coast line of Chili,
for ioo miles about Valparaiso, with the mighty chain
of the Andes-mountains to which the Alps shrink into
insignificance-was hoisted at one blow (in a single
night, Nov. 19, A.D. 1822) from two to seven feet above
its former level, leaving the beach below the old low watermark high and dry; leaving the shell-fish sticking on
the rocks out of reach of water; leaving the seaweed
rotting in the air, or rather drying up to dust under
the burning sun of a coast where rain never falls. The
ancients had a fable of Titan hurled from heaven and




6      ABOUT VOLCANOS AND EARTHQUAKES.
buried under Etna, and by his struggles causing the
earthquakes that desolated Sicily. But here we have an
exhibition of Titanic forces on a far mightier scale. One
of the Andes upheaved on this occasion was the gigantic
mass of Aconcagua, which overlooks Valparaiso. To
bring home to the mind the conception of such an effort,
we must form a clear idea of what sort of mountain this
is. It is nearly 24,000 feet in height. Chimborazo, the
loftiest of the volcanic cones of the Andes, is lower by
2500 feet; and yet Etna, with Vesuvius at the top of it,
and another Vesuvius piled on that, would litte more than
surpass the midway height of the snow-covered portion of
that cone, which is one of the many chimneys by which
the hidden fires of the Andes find vent.  On the occasion I am speaking of, at least Io,ooo square miles of
country were estimated as having been upheaved, and
the upheaval was not confined to the land, but extended
far away to sea, which was proved by the soundings off
Valparaiso, and along the coast, having been found considerably shallower than they were before the shock.
(7.) Again, in the year 1819, in an earthquake in
India, in the district of Cutch, bordering on the Indus,
a tract of country more than fifty miles long and sixteen
broad was suddenly raised ten feet above its former
level. The raised portion still stands up above the unraised, like a long perpendicular wall, which is known by
the name of the" Ullah Bund," or "God's Wall."  And
again, in I538, in that convulsion which threw up the
Monte Nuovo (New Mountain), a cone of ashes 450
feet high, in a single night; the whole coast of Pozzuoli,




ABOUT VOLCANOS AND EARTHQUAKES.                 7
near Naples, was raised twenty feet above its former
level, and remains so permanently upheaved to this day.
And I could mention innumerable other instances of the
same kind.'*
(8.) This, then, is the manner in which the earthquake
does its work; and it is always at weork.  Somewhere or
other in the world, there is perhaps not a day, certainly
not a month, without an earthquake.  In those districts
of South and Central America, where the great chain of
volcanic cones is situated-Chimborazo, Cotopaxi, and
a long list with names unmentionable, or at least unpronounceable-the inhabitants no more think of counting
earthquake shocks than we do of counting showers of
rain. Indeed, in some places along that coast, a shower
is a greater rarity.  Even in our own island, near Perth,
a year seldom  passes without a shock, happily, witlin
the records of history, never powerful enough to do any
mischief.
(9.) It is not everywhere that this process goes on by
fits and starts.  For instance, the northern gulfs, and
borders of the Baltic Sea, are steadily shallowing: and
the whole mass of Scandinavia, including  Norway,
Sweden, and Lapland, is rising out of the sea at the
average rate of about two feet per century.  But as this
fact (which is perfectly well established by reference to
ancient high and low water-marks) is not so evidently
connected with the action of earthquakes, I shall not
further refer to it just now. All that I want to show is,
* Not that earthquakes always raise the soil; there are plenty
of instances of subsidence, etc.




8      ABOUT VOLCANOS AND EARTHQUAKES.
that there is a great cycle of changes going on, in which
the earthquake and volcano act a very conspicuous part,
and thatp art a restorative and conservative one; in opposition to the steadily destructive and levelling action of
the ocean waters.
(Io.) How this can happen; what can be the origin ot
such an enormous power thus occasionally exerting
itself, will no doubt seem very marvellous-little short,
indeed, of miraculous intervention-but the mystery,
after all, is not quite so great as at first it seems. We
are permitted to look a little way into these great secrets
of nature; not far enough, indeed, to clear up every
difficulty, but quite enough to penetrate us with admiration of that wonderful system of counterbalances and
compensations; that adjustment of causes and consequences, by which, throughout all nature, evils are made
to work their own cure; life to spring out of death; and
renovation to tread in the steps and efface the vestiges
of decay.
(ii.) The key to the whole affair is to be found in the
central heat of the earth. This is no scientific dream,
no theoretical notion, but a fact established by direct
evidence up to a certain point, and standing out from
plain facts as a matter of unavoidable conclusion, in a
hundred ways.
(12.) We all know that when we go into a cellar out of
a summer sun, it feels cool; but when we go into it out
of a wintry frost it is warm. The fact is, that a cellar,
or a well, or any pit of a moderate depth, has always,
day and night, summer and winter, the same degree of




ABOUT VOLCANOS AND EARTHQUAKES.             9
warmth, the same fervnerature, as it is called: and that
always and everywhere is the same, or nearly the same,
as the average warmth of the climate of the place.
Forty or fifty feet deep in the ground, a thermometer
here, in this spot,* would always mark the same degree,
49~ that is, or seventeen degrees above the freezing
point. Under the equator, at the same depth, it always
stands at 84~, which is our hot summer heat, but which
there is the average heat of the whole year. And this is
so everywhere.  Just at the surface, or a few inches
below it, the ground is warm in the daytime, cool at
night: at two or three feet deep the difference of day
and night is hardly perceptible, but that of summer and
winter is considerable.  But at forty or fifty feet this
difference also disappears, and you find a perfectly fixed,
uniform degree of warmth, day and night; summer and
winter; year after year.
(13.) But when we go deeper, as, for instance, down
into mines or coal-pits, this one broad and general fact is
always observed,-everywhere, in all countries, in all
latitudes, in all climates, wherever there are mines, or
deep subterranean caves,-the deeper you go, the hotter
the earth is found to be. In one and the same mine,
each particular depth has its own particular degree of
heat, which never varies: but the lower always the hotter;
and that not by a trifling, but what may well be called
an astonishingly rapid rate of increase,-about a degree of
the thermometer additional warmth for every go feet of
additional depth, which is about 580 per mile!-so that,
* At Hawkhurst in Kent.




IO     ABOUT VOLCANOS AND EARTHQUAKES.
if we had a shaft sunk a mile deep, we should find in the
rock a heat of io5~, which is much hotter than the
hottest summer day ever experienced in England.
(I4.) It is not everywhere, however, that it is worth
while to sink a shaft to any great depth; but borings for
water (in what are called Artesian wells) are often made
to enormous depths, and the water always comes up hot;
and the deeper the boring, the hotter the water. There
is a very famous boring of this sort in Paris, at La
Grenelle.  The water rises from a depth of I794 feet,
and its temperature is 82~ of our scale, which is almost
that of the equator. And, again, at Salzwerth, in Oeynhausen, in Germany, in a boring for salt-springs 2144
feet deep, the salt water comes up with a still higher
heat, viz., 9i~. Then, again, we have natural hot-water
springs, which rise, it is true, from depths we have no
means of ascertaining; but which, from  the earliest
recorded times, have always maintained the same heat.
At Bath, for instance, the hottest well is 117~ Fahr. On
the Arkansas River, in the United States, is a spring of
I80~; which is scalding hot; and that out of the neighbourhood of any volcano.
(15.) Now, only consider what sort of a conclusion
this lands us in. This globe of ours is 8000 miles in
diameter; a mile deep on its surface is a mere scratch.
If a man had twenty greatcoats on, and I found under
the first a warmth of 60~ above the external air, I should
expect to find 60~ more under the second, and 60~ more
under the third, and so on; and, within all, no man, but
a mass of red-hot iron. Just so with the outside crust of




ABOUT VOLCANOS AND EARTHQUAKES.            It
the earth. Every mile thick is such a greatcoat, and at
20 miles depth, according to this rate, the ground must
be fully red-hot; and at no such very great depth beyond,
either the whole must be melted, or only the most in-.
fusible and intractable kinds of material, such as our fireclays and flints, would present some degree of solidity.
(16.) In short, what the icefloes and icebergs are to
the polar seas, so we shall come to regard our continents
and mountain-ranges in relation to the ocean of melted
matter beneath.  I do not mean to say there is no solid
central mass; there may be one, or there may not, and,
upon the whole, I think it likely enough that there iskept solid, in spite of the heat, by the enormous pressure; but that has nothing to do with my present argument.  All that I contend for is this,-Grant me a sea
of liquid fire, on which we are all floating,-land and
sea; for the bottom of the sea, anyhow, will not come
nearly down to the lava level.  The sea is probably
nowhere more than five or six miles deep, which is far
enough above that level to keep its bed from becoming
red-hot.
(i7.) Well, now, the land is perpetually wearing down,
and the materials being carried out to sea. The coat
of heavier matter is thinning off towards the land, and
thickening over all the bed of the sea.  What must
happen?  If a ship float even on her keel, transfer
weight from the starboard to the larboard side, will she
continue to float even? No, certainly.  She will heel
over to larboard.  Many a good ship has gone to the
bottom  in this way.  If the continents be lightened.




12     ABOUT VOLCANOS AND EARTHQUAKES.
they will rise; if the bed of the sea receive additional
weight, it will sink. The bottom of the Pacific is sinking, in point of fact. Not that the Pacific is becoming
deeper. This seems a paradox; but it is easily explained.
The whole bed of the sea is in the act of being pressed
down by the laying on of new solid substance over its bottom.
The new bottom then is laid upon the old, and so the
actual bed of the ocean remains at or nearly at the same
distance from the surface water.  But what becomes of
the islands?  They form  part and parcel of the old
bottom; and Dr Darwin has shown, by the most curious
and convincing proofs, that they are sinking, and have
been sinking for ages, and are only kept above water-by
what, think you3 By the labours of the coral insects,
which always build up to the surface!
(I8.) It is impossible but that this increase of pressure
in some places and relief in others must be very unequal in their bearings. So that at some place or other
this solid floating crust must be brought into a state of
strain, and if there be a weak or a soft part, a crack will
at last take place. When this happens, down goes the
land on the heavy side, and up on the light side. Now
this is exactly what took place in the earthquake which
raised the Ullah Bund in Cutch. I have told you of a
great crack drawn across the country, not far from the
coast line; the inland country rose ten feet, but much of
the sea-coast, and probably a large tract in the bed of
the Indian Ocean, sank considerably below its former
level. And just as you see when a crack takes place in
ice, the water oozes up; so this kind of thing is always,




ABOUT VOLCANOS AND EARTHQUAKES.           13
or almost always, followed by an upburst of the subterranean fiery matter.   The earthquake of Cutch wa;
terminated by the outbreak of a volcano at the town,f
Bhooi, which it destroyed.
(I9.) Now where, following out this idea, should we
naturally expect such cracks and outbreaks to happen.
Why, of course, along those lines where the relief of
pressure on the land side is the greatest, and also its
increase on the sea side; that is to say, along or in the
neighbourhood of the sea-coasts, where the destruction
of the land is going on with most activity. Well, now,
it is a remarkable fact in the history of volcanos, that
there is hardly an instance of an active volcano at any
considerable distance from the sea-coast. All the great
volcanic chain of the Andes is close to the western
coast line of America.  Etna is close to the sea; so is
Vesuvius; Teneriffe is very near the African coast;
Mount Erebus is on the edge of the great Antarctic
continent.  Out of 225 volcanos which are known to
have been in actual eruption over the whole earth
within the last i50 years, I remember only a single
instance of one more than 320 miles from the sea, and
even that is on the edge of the Caspian, the largest of
all the inland seas-I mean Mount Demawend in Persia.
(20.) Suppose from this, or from any other cause, a
crack to take place in the solid crust of the earth. Don't
imagine that the melted matter below will simply ooze
up quietly, as water does from under an ice-crack.  No
such thing. There is an element in the case we have
not considered: steam and condensed gases. We all




14     ABOUT VOLCANOS AND EARTHQUAKES.
know what happens when a crack takes place in a highpressure steam-boiler, with what violence the contents
escape, and what havoc takes place.  Now there is no
doubt that among the minerals of the subterranean
world, there is water in abundance, and sulphur, and
many other vaporizable substances, all kept subdued
and repressed by the enormous pressure. Let this pressure be relieved, and forth they rush, and the nearer
they approach the surface the more they expand, and
the greater is the explosive force they acquire; till at
length, after more or fewer preparatory shocks, eac.h
accompanied with progressive weakening of the overlying strata, the surface finally breaks up, and forth rushes
the imprisoned power, with all the awful violence of a
volcanic eruption.
(21.) Certainly a volcano does seem to be a very bad
neighbour; and yet it affords a compensation in the extraordinary richness of the volcanic soil, and the fertilizing quality of the ashes thrown out. The flanks or
Somma (the exterior crater of Vesuvius)  are covered
with vineyards producing wonderful wine, and whoever
has visited Naples, will not fail to be astonished at the
productiveness of the volcanized territory as contrasted
with the barrenness of the limestone rocks bordering on
it. There you will see the amazing sight (as an English
farmer would call it) of a triple crop growing at once
on the same soil; a vineyard, an orchard, and a cornfield all in one. A magnificent wheat crop, five or six
feet high, overhung with clustering grape-vines swinging
from one apple or pear tree to another in the most iuxu



ABOUT VOLCANOS AND EARTHQUAKES.            15
riant festoons!  When I visited Somma, to see the
country where the celebrated wine, the Lacryma Christi,
is grown, it was the festival of the Madonna del Arco.
Her church was crowded to suffocation with a hot and
dusty assemblage of the peasantry. The fine impalpable
volcanic dust was everywhere; in your eyes, in your
mouth, begriming every pore; and there I saw what I
shall never forget.  Jammed among the crowd, I felt
something jostling my legs.  Looking down, and the
crowd making way, I beheld a line of worshippers crawling on their hands and knees from  the door of the
church to the altar, licking the dusty pavement all the
way with their tongues, positively applied to the ground
and ro mistake. No trifling dose of Lacryma would be
required to wash down what they must have swallowed
on that journey, and I have no doubt it was administered
pretty copiously after the penance was over.
(22.) Now I come to consider the manner in which
an earthquake is propagated from place to place; how it
travels, in short. It runs along the earth precisely in
the same manner, and according to the same mechanical
laws as a wave along the sea, or rather as the waves of
sound run along the air, but quicker. The earthquake
which destroyed Lisbon ran out from thence, as from a
centre, in all directions, at a rate averaging about twenty
miles per minute, as far as could be gathered from a
comparison of the times of its occurrence at different
places; but there is little doubt that it must have been
retarded by having to traverse all sorts of ground, for a
blow or shock of any description is conveyed through the




I6     ABOUT VOLCANOS AND EARTHQUAKES.
substance on which it is delivered with the rapidity of
sound in that substance. Perhaps it may be new to many
who hear me to be told that sound is conveyed by water,
by stone, by iron, and indeed by everything, and at a different rate for each. In air it travels at the rate of about
1140 feet per second, or about I3 miles in a minute.  In
water much faster, more than four times as fast (4700
feet).  In iron ten times as fast (II,400 feet), or about
130 miles in a minute, so that a blow delivered endways
at one end of an iron rod, I30 miles long, would only
reach the other after the lapse of a minute, and a
pull at one end of an iron wire of that length, would
require a minute before it would be felt at the other.
But the substance of the earth through which the shock
is conveyed is not only far less elastic than iron, but it
does not form a coherent, connected body; it is full of
interruptions, cracks, loose materials, and all these tend
to deaden and retard the shock: and putting together all
the accounts of all the earthquakes that have been exactly observed, their rate of travel may be taken to vary
from as low as 12 or I3 miles a minute to 70 or 80:
but perhaps the low velocities arise from oblique waves.
(23.) The way, then, that we may conceive an earthquake to travel is this,-I shall take the case which is
most common, when the motion of the ground to-andfro is horizontal.  How far each particular spot on the
surface of the ground is actually pushed from its place
there is no way of ascertaining, since all the surrounding
objects receive the same impulse almost at the same instant of time, but there are many indications that it is




ABOUT VOLCANOS AND EARTHQUAKES.             17
often several yards. In the earthquake of Cutch, which
I have mentioned, trees were seen to flog the ground
with their branches, which proves that their stems must
have been jerked suddenly away for some considerable
distance and as suddenly pushed back; and the same
conclusion follows from the sudden rise of the water ot
lakes on the side where the shock reaches them, and its
fall on the opposite side; the bed of the lake has been
jerked away for a certain distance from under the water
and pulled back.
(24.) Now, suppose a row of sixty persons, standing
a mile apart from each other, in a straight line, in the
direction in which the shock travels; at a rate, we will
suppose, of sixty miles per minute: and let the ground
below the first get a sudden and violent shove, carrying
it a yard in the direction of the next.  Since this shock
will not reach the next till after the lapse of one second
of time, it is clear that the space between the two will be
shortened by a yard, and the ground-that is to say, not
the mere loose soil on the surface, but the whole mass of
solid rock below, down to an unknown depth-compressed, or driven into a smaller space.  It is this compression that carries the shock forwards. The elastic
force of the rocky matter, like a coiled spring acts both
ways; it drives back the first man to his old place, and
shoves the second a yard nearer to the third; and so on.
Instead of men place a row of tall buildings, or columns,
and they will tumble down in succession, the base flyiing
forwards, and leaving the tops behind to drop on the
soil on the sidefrom which the shock came.  This is
B




18     ABOUT VOLCANOS AND EARTHQUAKES.
just what was seen to happen in Messina in the great
Calabrian earthquake.  As the shock ran along the
ground, the houses of the Faro were seen to topple
down in succession; beginning at one end and running
on to the other, as if a succession of mines had been
sprung. In the earthquake in Cutch, a sentinel standing
at one end of a long straight line of wall, saw the wall
bow forward and recover itself; not all at once, but with
a swell like a wave running all along it with immense
rapidity.  In this case it is evident that the earthquake
wave must have had its front oblique to the direction of
the wall (just as an obliquely-held ruler runs along the
edge of a page of paper while it advances, like a wave of
the sea, perpendicularly to its own length).
(25.) In reference to extinct volcanos, I may just
mention that any one who wishes to see some of the
finest specimens in Europe may do so by making a
couple of days' railway travel to Clermont, in the department of the Puy de Dome in France.  There he will
find a magnificent series of volcanic cones, fields of ashes,
streams of lavas, and basaltic terraces or platforms,
proving the volcanic action to have been continued for
countless ages before the present surface of the earth
was formed; and all so clear that he who runs may read
their lesson. There can there be seen a configuration
of surface quite resembling what telescopes show in the
most volcanic districts of the moon. Let not my hearers
be startled: half the moon's face is covered with unmistakable craters of extinct volcanos.
(26.) Many of the lavas of Auvergne and the Puy d:




ABOUT VOLCANOS AND EARTHQUAKES.           19
Dome are basaltic; that is, consisting of columns placed
close together; and some of the cones are quite complete, and covered with loose ashes and cinders, just as
Vesuvius is at this hour.
(27.) In the study of these vast and awful phenomena
we are brought in contact with those immense and rude
powers of nature which seem to convey to the imagination the impress of brute force and lawless violence; but
it is not so. Such an idea is not more derogatory to the
wisdom and benevolence that prevails throughout all the
scheme of creation than it is in itself erroneous.  In
their wildest paroxysms the rage of the volcano and the
earthquake is subject to great and immutable laws:
they feel the bridle and obey it. The volcano bellows
forth its pent-up overplus of energy, and sinks into long
and tranquil repose;  The earthquake rolls away, and
industry, that balm which nature knows how to shed
over every wound, effaces its traces, and festoons its
ruins with flowers. There is mighty and rough work to
be accomplished, and it cannot be done by gentle means.
It seems, no doubt, terrible, awful, perhaps harsh, that
twenty or thirty thousand lives should be swept away in
a moment by a sudden and unforeseen calamity; but we
must remember that sooner or later every one of those
lives must be called for, and it is by no means the most
sudden end that is the most afflictive. It is well too that
we should contemplate occasionally, if it were only to
teach us humility and submission, the immense energies
which are everywhere at work in maintaining the system
of nature we see going on so smoothly and tranquilly




20     ABOUT VOLCANOS AND EARTHQUAKES.
around us, and of which these furious outbreaks, after all.
are but minute, and for the moment unbalanced surpluses in the great account.  The energy requisite to
overthrow a mountain is as a drop in the ocean compared with that which holds it in its place, and makes it
a mountain.  Chemistry tells us that the forces constantly in action to maintain a single grain of water in
its habitual state; when only partially and sparingly let
loose in the form of electricity, would manifest themselves as a powerful flash of lightning.*  And we learn
from optical science that in even the smallest element of
every material body, nay, even in zhal t e we call empty
space, there are forces in perpetual action to which even
such energies sink into insignificance.  Yet, amid all
this, nature holds her even course: the flowers blossom;
animals enjoy their brief span of existence; and man has
leisure and opportunity to contemplate and adore, secure
of the watchful care which provides for his well-being
at every instant that he is permitted to remain on earth.
ON THE HISTORY OF EARTHQUAKES AND VOLCANOS.
(28.) The first great earthquake of which any very
distinct knowledge has reached us is that which occurred
in the year 63 after our Saviour, which produced great
destruction in the neighbourhood  of Vesuvius, and
shattered the cities of Pompeii and Herculaneum upon
the Bay of Naples, though it did not destroy them.
This earthquake is chiefly remarkable as having been
* Faraday: "Experimental Researches in Electricity," ~ 853.




ABOUT VOLCANOS AND EARTHQUAKES.           21
the forerunner and the warning (if that warning could
have been understood) of the first eruption of Vesuvius
on record. which followed sixteen years afterwards in
the year 79. Before that time none of the ancients had
any notion of its being a volcano, though Pompeii itself
is paved with its lava. The crater was probably filled,
or at least the bottom  occupied, by a lake; and we
read of it as the stronghold of the rebel chief Spartacus,
who, when lured there by the Roman army, escaped
with his followers by clambering up the steep sides by
the help of the wild vines that festooned them. The
ground since the first earthquake in 63 had often been
shaken by slight shocks, when at length, in August 79,
they became more numerous and violent, and, on the
night preceding the eruption, so tremendous as to
threaten everything with destruction.  A morning of
comparative repose succeeded, and the terrified inhabitants of those devoted towns no doubt breathed more
freely, and hoped the worst was over; when, about one
o'clock in the afternoon, the Elder Pliny, who was
stationed in command of the Roman fleet at Misenum in
full view of Vesuvius, beheld a huge black cloud ascending from the mountain, which, " rising slowly always
higher," at last spread out aloft like the head of one of
those picturesque flat-topped pines which form such an
ornament of the Italian landscape.  The meaning of
such a phenomenon was to Pliny and to every one a
mystery. We know now too well what it imports, and
they were not long left in doubt.  From  that cloud
descended stones, ashes, and pumice; and the cloud




22     ABOUT VOLCANOS AND EARTHQUAKES.
itself lowered down upon the surrounding  country,
involving land and sea in profound darkness, pierced by
flashes of fire more vivid than lightning. These, with
the volumes of ashes that began to encumber the soil,
and which covered the sea with floating pumice-stone;
the constant heaving of the ground; and the sudden
recoil of the sea, form a picture which is wonderfully
well described by the Younger Pliny.  His uncle, animated by an eager desire to know what was going on,
and to afford aid to the inhabitants of the towns, made
sail for the nearest point of the coast and landed; but
was instantly enveloped in the dense sulphureous vapour
that swept down from  the mountain, and perished
miserably.
(29.) It does not seem that any lava flowed on that
occasion. Pompeii was buried under the ashes; Herculaneum by a torrent of mud, probably the contents of
the crater, ejected at the first explosion. This was most
fortunate. We owe to it the preservation of some of
the most wonderful remains of antiquity. For it is -not
yet much more than a century ago that, in digging a
well at Portici near Naples, the Theatre of Herculaneum
was discovered, some sixty feet under ground,-then
houses, baths, statues, and, most interesting of all, a
library, full of books; and those books still legible, and
among them the writings of some ancient authors which
had never before been met with, but which have now
been read, copied, and published, while hundreds and
hundreds, I am  sorry to say, still remain unopened.
Pompeii was not buried so deep; the walls of some of




ABOUT VOLCANOS.AND EARTHQUAKES.    23
the buildings appeared among the modern vineyards;
and led to excavations, which were easy, the ashes being
light and loose. And there you now may walk through
the streets, enter the houses, and find the skeletons of
their inmates, some in the very act of trying to escape.
Nothing can be more strange and striking.
(30.) Since that time Vesuvius has been frequently
but very irregularly in eruption. The next after Pompeii was in the year 202, under Severus: and in 472
occurred an eruption so tremendous that all Europe was
covered by the ashes, and even Constantinople thrown
into alarm. This may seem to savour of the marvellous;
but before I have done, I hope to show that it is
not beyond what we know of the power of existing
volcanos.
(3I.) I shall not, of course, occupy attention with a
history of Vesuvius, but pass at once to the eruption of
1779,-one of the most interesting on record, from the
excellent account given of it by Sir William Hamilton,
who was then resident at Naples as our Minister, and
watched it throughout with the eye of an artist as well
as the scrutiny of a philosopher.
(32.) In I767, there had been a considerable eruption, during which Pliny's account of the great pine-like,
flat-topped, spreading mass of smoke had been superbly
exemplified; extending over the Island of Capri, which
is twenty-eight miles from Vesuvius.  The showers of
ashes, the lava currents, the lightnings, thunderings, and
earthquakes were very dreadful; but they were at once
brought to a close when the mob insisted that the head




24     ABOUT VOLCANOS AND EARTHQUAKES.
of St Januarius should be brought out and shown to the
mountain; and when this was done, all the uproar
ceased on the instant, and Vesuvius became as quiet
as a lamb!
(33.) He did not continue so, however, and it would
have been well for Naples if the good Saint's head could
have been permanently fixed in some conspicuous place
in sight of the hill-for from that time till the year I779
it never was quiet. In the spring of that year it began
to pour out lava; and on one occasion, when Sir William Hamilton approached too near, the running stream
was on the point of surrounding him; and the sulphureous vapour cut off his retreat, so that his only mode of
escape was to walk across the lava, which, to his astonishment, and, no doubt, to his great joy, he found
accompanied with no difficulty, and with no more inconvenience than what proceeded from the radiation of heat
on his legs and feet from the scorine and cinders with
which the external crust of the lava was loaded; and
which in great measure intercepted and confined the
glowing heat of the ignited mass below.
(34.) In such cases, and when cooled down to a
certain point, the motion of the lava-stream is slow and
creeping; rather rolling over itself than flowing like a
river; the top becoming the bottom, owing to the toughness of the half-congealed crust. When it issues, however, from any accessible vent, it is described as perfectly
liquid, of an intense white heat, and spouting or welling
forth with extreme rapidity.  So Sir Humphry Davy
described it in an eruption at which he was present 




ABOUT VOLCANOS AND EARTHQUAKES.            25
and so Sir William Hamilton, in the eruption we arc
now concerned with, saw it " bubbling utp violently"
from one of its fountains on the slope of the volcano,
" with a hissing and crackling noise, like that of an artificial firework; and forming, by the continual splashing
up of the vitrified matter, a sort of dome or arch over
the crevice from which it issued," which was all, internally, " red-hot like a heated oven."
(35.) However, as time went on, this quiet mode of
getting rid of its contents would no longer suffice, and
the usual symptoms of more violent action-rumbling
noises and explosions within the mountain; puffs or
smoke from its crater, and jets of red-hot stones and
ashes —continued till the end of July, when they increased to such a degree -as to exhibit at night the most
beautiful firework imaginable.  The eruption came to
its climax from the 5th to the ioth of August, on the
former of which days, after the ejection of an enormous
volume of white clouds, piled like bales of the whitest
cotton, in a mass exceeding four times the height and
size of the mountain itself; the lava began to overflow
the rim of the crater, and stream in torrents down the
steep slope of the cone.  This was continued till the
8th, when the great mass of the lava would seem to have
been evacuated, and no longer repressing by its weight
the free discharge of the imprisoned gases, allowed
what remained to be ejected in fountains of fire, carried
up to an immense height in the air. The description of
one of these I must give in the picturesque and vivid
words of Sir William Hamilton himself.  " About nine




20     ABOUT VOLCANOS AND EARTHQUAKES.
o'clock," he says, on Sunday the 8th of August, " there
was a loud report, which shook the houses at Portici
and its neighbourhood to such a degree, as to alarm the
inhabitants and drive them out into the streets. Many
windows were broken, and as I have since seen, walls
cracked by the concussion of the air from that explosion.....In one instant a fountain of liquid transparent
fire began to rise, and gradually increasing, arrived
at so amazing a height, as to strike every one who
beheld it with the most awfiul astonishment.  I shall
scarcely be  credited  when  I assure  you  that, to
the best of my judgment, the height of this stupendous column  of fire could not be less than three
times that of Vesuvius itself; which, you know, rises
perpendicularly near 3700 feet above  the level of
the sea."  (The height by my own measurement in
1824 is 3920 feet).  "Puffs of smoke, as black as can
possibly be imagined, succeeded one another hastily,
and accompanied the red-hot, transparent, and liquid
lava, interrupting its splendid brightness here and there
by patches of the darkest hue.  Within these puffs of
smoke, at the very moment of their emission from the
crater, I could perceive a bright but pale electrical fire
playing about in zigzag lines.  The liquid lava, mixed
with scorime and stones, after having mounted, I verily
believe at least Io,ooo feet, falling perpendicularly on
Vesuvius, covered its whole cone, part of that of Somma,
and the valley between them. The falling matter being
nearly as vivid and inflamed as that which was continually issuing fresh from  the crater, formed with it ore




ABOUT VOLCANOS AND EARTHQUAKES.           27
complete body of fire, which could not be less than two
miles and a half in breadth, and of the extraordinary
height above mentioned; casting a heat to the distance
of at least six miles around it. The brushwood of the
mountain of Somma was soon in a flame, which, being
of a different tint from the deep red of the matter thrown
out from the volcano, and from the silvery blue of the
electrical fire, still added to the contrast of this most
extraordinary scene. After the column of fire had continued in full force for nearly half an hour, the eruption ceased at once, and Vesuvius remained sullen and
silent.'
(36.) The lightnings here described arose evidently in
part from the chemical activity of gaseous decompositions going forward, in part to the friction of steam, and
in part from the still more intense friction of the dust,
stones, and ashes encountering one another in the air, in
analogy to the electric manifestations which accompany
the dust storms in India.
(37.) To give an idea of the state of the inhabitants
of the country when an explosion is going on, I will make
one other extract:-" The mountain of Somma, at the
foot of which Ottaiano is situated, hides Vesuvius from
its sight: so that till the eruption became considerable
it was not visible to them. On Sunday night, when the
noise increased, and the fire began to appear above the
mountain of Somma, many of the inhabitants of the town
flew to the churches; and others were preparing to quit
the town, wnen a sudden violent report was heard, soon
after which they found themselves involved in a thick




28     ABOUT VOLCANOS AND EARTHQUAKES.
cloud of smoke and minute ashes; a horrid clashing
noise was heard in the air; and presently fell a deluge
of stones and large scorie, some of which scoriae were
of the diameter of seven or eight feet, and must have
weighed more than one hundred pounds before they
were broken by their falls, as some of the fragments
of them which I picked up in the streets still weighed
upwards of sixty pounds. When these large vitrified
masses either struck against each other in the air or fell
on the ground they broke in many pieces, and covered a
large space around them with vivid sparks of fire, which
communicated their heat to everything that was combustible.  In an instant the town and country about it was
on fire in many parts; for in the vineyards there were
several straw-huts, which had been erected for the watchmen of the grapes, all of which were burnt.  A great
magazine of wood in the heart of the town was all in a
blaze: and had there been much wind, the flames must
have spread universally, and all the inhabitants would
have infallibly been burnt in their houses, for it was impossible for them to stir out. Some who attempted it
with pillows, tables, chairs, tops of wine casks, etc., on
their heads, were either knocked down or driven back to
their close quarters, under arches and in the cellars of the
houses.  Many were wounded, but only two persons
have died of the wounds they received from this dreadful volcanic shower. To add to the horror of the scene,
incessant volcanic lightning was writhing about the black
cloud that surrounded them, and the sulphureous smell and
heat would scarcely allow them to draw their breath.'




ABOUT VOLCANOS AND EARTHQUAKES.            29
(38.) The next volcano I shall introduce is Etna, the
grandest of all our European volcanos. I ascended it in
I824, and found its height by a very careful barometric
measurement to be I0,772 feet above the sea, which, by
the way, agrees within some eight or ten feet with
Admiral Smyth's measurement.
(39.) The scenery of _Etna is on the grandest scale.
Ascending: from Catania you skirt the stream of lava
which destroyed a large part of that city in 1669, and
which ran into the sea, forming a jetty or breakwater
that now gives Catania what it never had before, the
advantage of a harbour. There it lies as hard, rugged,
barren, and fresh-looking as if it had flowed but yesterday.  In many places it is full of huge caverns; great
air-bubbles, into which one may ride on horseback (at
least large enough) and which communicate, in a succession of horrible vaults, where one might wander and
lose one's self without hope of escape. Higher up, near
Nicolosi, is the spot from which that lava flowed. It is
marked by two volcanic cones, each of them a considerable mountain, called the Monti Rossi, rising 300 feet
above the slope of the hill, and which were thrown up
on that occasion. Indeed, one of the most remarkable
features of LEtna is that of its flanks bristling over with
innumerable smaller volcanos.  For the height is so
great that the lava now scarcely ever rises to the top of
the crater; for before that, its immense weight breaks
through at the sides. In one of the eruptions that happened in the early part of this century, I forget the date,
but I think it was in 1819, and which was described to




30     ABOUT VOLCANOS AND EARTHQUAKES.
me on the spot by an eye-witness-the Old Man of the
Mountain, Mario Gemellaro-the side of -Etna was
rent by a great fissure or crack, beginning near the top,
and throwing out jets of lava from openings fourteen or
fifteen in number all the way down, so as to form a row
of fiery fountains rising from different levels, and all
ascending nearly to the same height: thereby proving
them all to have originated in the great internal cistern
as it were, the crater being filled up to the top level.
(40.) From the summit of ZEtna extends a view of
extraordinary magnificence.  The whole of Sicily lies at
your feet, and far beyond it are seen a string of lesser
volcanos; the Lipari Islands, between Sicily and the
Italian coast; one of which, Stromboli, is always in
eruption, unceasingly throwing up ashes, smoke, and
liquid fire.
(4I.) But I must not linger on the summit of ~Etna.
We will now take a flight thence, all across Europe, to
Iceland  a wonderful land of frost and fire.  It is full of
volcanos, one of which, HECLA, has been twenty-two
times in eruption within the last 800 years. Besides
Hecla, there are five others, from which in the same
period twenty eruptions have burst forth, making about
one every twenty years.  The most formidable of these
was that which happened in I783, a year also memorable as that of the terrible earthquake in Calabria.  In
May of that year, a bluish fog was observed over the
mountain called Skaptar Jokul, and the neighbourhood
was shaken by earthquakes. After a while a great pillar
of smoke was observed to ascend from it, which dark



ABOUT VOLCANOS AND EARTHQUAKES.           31
ened the whole surrounding district, and which descended
in a whirlwind of ashes. On the ioth of May, innumerable fountains of fire were seen shooting up through the
ice and snow which covered the mountain; and the
principal river, called the Skapta, after rolling down a
flood of foul and poisonous water, disappeared. Two
days after, a torrent of lava poured down into the bed
which  the river had deserted.  The river had run
in a ravine, 600 feet deep and 200 broad.  This
the lava entirely filled; and not only so, but it overflowed the surrounding country, and ran into a great
lake, from which it instantly expelled the water in an explosion of steam. When the lake was fairly filled, the
lava again overflowed and divided into two streams, one
of which covered some ancient lava fields; the other reentered the bed of the Skapta lower down; and presented the astounding sight of a cataract of liquid fire
pouring over what was formerly the waterfall of Stapafoss.
This was the greatest eruption on record in Europe. It
lasted in its violence till the end of August, and closed
with a violent earthquake; but for nearly the whole
year a canopy of cinder-laden cloud hung over the
island; the Faroe Islands, nay, even Shetland and the
Orkneys, were deluged with the ashes; and volcanic
dust and a preternatural smoke, which obscured the sun,
covered all Europe as far as the Alps, over which it could
not rise.  It has been surmised that the great Fireball of August I8, 1783, which traversed all England
and the Continent, from the North Sea to Rome, by far
the greatest ever known (for it was more than half a




32     ABOUT VOLCANOS AND EARTHQUAKES.
mile in diameter), was somehow  connected with the
electric excitement of the upper atmosphere produced
by this enormous discharge of smoke and ashes. The
destruction of life in Iceland was frightful: gooo men,
II,ooo cattle, 28,000 horses, and I9o,ooo sheep perished; mostly by suffocation.  The lava ejected has
been computed to have amounted in volume to more
than twenty cubic miles.
(42.) We shall now proceed to still more remote regions, and describe, in as few words as may be, two immense eruptions,-one in Mexico, in the year 1759; the
other in the island of Sumbawa in the Eastern Archipelago, in 1815.
(43.) I ought to mention, by way of preliminary, that
almost the whole line of coast of South and Central
America, from Mexico southwards as far as Valparaisothat is to say, nearly the whole chain of the Andes-is
one mass of volcanos. In Mexico and Central America
there are two and twenty, and in Quito, Peru, and Chili,
six and twenty more, in activity; and nearly as many
more extinct ones, any one of which may at any moment
break out afresh. This does not prevent the country
from being inhabited, fertile, and well cultivated. Well:
in a district of Mexico celebrated for the growth of the
finest cotton, between two streams called Cuitimba and
San Pedro, which furnished water for irrigation, lay the
farm and homestead of Don Pedro de Jurullo, one of
the richest and most fertile properties in that country.
He was a thriving man, and lived in comfort as a large
proprietor, little expecting the mischief that was to be



ABOUT VOLCANOS AND EARTHQUAKES.            33
fall him.  In June 1759, however, a subterranean noise
was heard in this peaceful region. Hollow sounds of the
most alarming nature were succeeded by frequent earthquakes, succeeding one another for fifty or sixty days; but
they (lied away, and in the beginning of September everything seemed to have returned to its usual state of tranquillity.  Suddenly, on the night of the 28th of September, the horrible noises recommenced.  All the inhabitants fled in terror; and the whole tract of ground, from
three to four square miles in extent, rose up in the form
of a bladder to a height of upwards of 500 feet! Flames
broke forth over a surface of more than half a square
league, and through a thick cloud of ashes illuminated
by this ghastly light, the refugees, who had ascended a
mountain at some distance, could see the ground as if
softened by the heat, and swelling and sinking like an
agitated sea. Vast rents opened in the earth, into which
the two rivers I mentioned precipitated themselves, but so
far from quenching the fires, only seemed to make them
more furious. Finally, the whole plain became covered
with an immense torrent of boiling mud, out of which
sprang thousands of little volcanic cones called Hornitos,
or ovens.  But the most astonishing part of the whole
was the opening of a chasm vomiting out fire, and redhot stones,. and ashes, which accumulated so as to form
" a range of six large mountain masses, one of which is
upwards of 600o feet in height above the old level, and
which is now known as the volcano of Jorullo,  It is
continually burning; and for a whole year continued to
throw up an immense quantity of ashes, lava, and fragc




34     ABOUT VOLCANOS AND EARTHQUAKES.
ments of rock. The roofs of houses at the town or village of Queretaro, upwards of 140 miles distant, were
covered with the ashes.  The two rivers have again
appeared, issuing at some distance from  among the
hornitos, but no longer as sources of wealth and fertility,
for they are scalding hot, or at least were so when Baron
Humboldt visited them  several years after the event.
The ground even then retained a violent heat, and the
hornitos were pouring forth columns of steam twenty
or thirty feet high, with a rumbling noise like that of
a steam-boiler.
(44.) The Island of Sumbawa is one of that curious
line of islands which links on Australia to the southeastern corner of Asia.  It forms, with one or two
smaller volcanic islands, a prolongation of Java, at that
time, in I8I5, a British possession, and under the government of Sir Stamford Raffles, to whom we owe the
account of the eruption, and who took a great deal
of pains to ascertain all the particulars. Java itself, I
should observe, is one rookery of volcanos, and so are
all the adjoining islands in that long crescent-shaped
line I refer to.
(45.) On the Island of Sumbawa is the volcano of
Tomboro, which broke out into eruption on the 5th of
April in that year; and I can hardly do better than
quote the account of it in Sir Stamford Raffles' own
words:(46.) "Almost every one," says this writer, "is acquainted with the intermitting convulsions of Etna and
Vesuvius as they appear in the descriptions of the poet,




ABOUT VOLCANOS AND EARTHQUAKES.            35
and the authentic accounts of the naturalist; but the
most extraordinary of them can bear no comparison, in
point of duration and force, with that of Mount Tomboro
in the Island of Sumbawa! This eruption extended perceptible evidences of its existence over the whole of the
Molucca Islands, over Java, a considerable portion of
the Celebes, Sumatra, and Borneo, to a circumference of
iooo statute miles from its centre" (i.e., to iooo miles'
distance), "by tremulous motions and the report of explosions. In a short time the whole mountain near the
Sang'ir appeared like a body of liquid fire, extending itself in every direction.  The fire and columns of flame
continued to rage with unabated fury, until the darkness,
caused by the quantity of falling matter, obscured it at
about eight P.M. Stones at this time fell very thick at
Sang'ir, some of them as large as two fists, but generally
not larger than walnuts.  Between nine and ten P.M.,
ashes began to fall, and soon after a violent whirlwind
ensued, which blew down nearly every house of Sang'ir,
carrying the roofs and light parts away with it.  In the
port of Sang'ir, adjoining Sumbawa, its effects were
much more violent, tearing up by the roots the largest
trees, and carrying them  into the air, together with
men, horses, cattle, and whatsoever came within its
influence. This will account for the immense number
of floating trees seen at sea.   The sea rose nearly
twelve feet higher than  it had  ever been  known
to do before, and completely spoiled the only small
spots of rice land in Sang'ir, sweeping away houses and
everything within its reach. The whirlwind lasted about




36     ABOUT VOLCANOS AND EARTHQUAKES.
an hour.  No explosions were heard till the whirlwind
had ceased at about eleven P.M. From midnight till the
evening of the IIth, they continued without intermission; after that time their violence moderated, and they
were heard only at intervals; but the explosions did not
cease entirely until the I5th of July.  Of all the villages
round Tomboro, Tempo, containing about forty inhabitants, is the only one remaining,  In Pekate no vestige
of a house is left; twenty-six of the people, who were at
Sumbawa at the time, are the whole of the population
who have escaped. From the best inquiries, there were
certainly not fewer than 12,000 individuals in Tomboro
and Pekate at the time of the eruption, of whom five or
six survive. The trees and herbage of every description,
along the whole of the north and west of the peninsula,
have been completely destroyed, with the exception of a
high point of land near the spot where the village of
Tomboro stood. At Sang'ir, it is added, the famine
occasioned by this event was so extreme, that one of
the rajah's own daughters died of starvation."
(47.) I have seen it computed that the quantity of
ashes and lava vomited forth in this awful eruption
would have formed three mountains the size of Mont
Blanc, the highest of the Alps; and if spread over the
surface of Germany, would have covered the whole of
it two feet deep! The ashes did actually cover the
whole island of Tombock, more than Ioo miles distant,
to that depth, and 44,000 persons there perished by
starvation, from the total destruction of all vegetation.
(48.) The mountain Kirauiah in the island of Owyhee,




ABOUT VOLCANOS AND EARTHQUAKES.            37
one of the Sandwich Isles, exhibits the remarkable
phenomenon of a lake of molten and very liquid lava
always filling the bottom of the crater, and always in a
state of terrific ebullition: rolling to and fro its fiery
surge and flaming billows-yet with this it is content,
for it would seem that at least for a long time past there
has been no violent outbreak so as to make what is
generally understood by a volcanic eruption. Volcanic
eruptions are almost always preceded by earthquakes, by
which the beds of rock, that overlie and keep down the
struggling powers beneath, are dislocated and cracked,
till at last they give way, and the strain is immediately
relieved.  It is chiefly when this does not happen, when
the force below is sufficient to heave up and shake the
earth, but not to burst open the crust, and give vent to
the lava and gases, that the most destructive effects are
produced.  The great earthquake of November I, 1755,
which destroyed Lisbon, was an instance of this kind,
and was one of the greatest, if not the very greatest on
record; for the concussion extended over all Spain and
Portugal-indeed, over all Europe, and even into Scotland-over North Africa, where in one town in Morocco
8ooo or io,ooo  people  perished.  Nay, its effects
extended even across the Atlantic to Madeira, where it
was very violent; and to the West Indies.  The most
striking feature about this earthquake was its extreme
suddenness. All was going on quite as usual in Lisbon
the morning of that memorable day; the weather fine
and clear; and nothing whatever to give the population
of that great capital the least suspicion of mischief. All




38     ABOUT VOLCANOS AND EARTHQUAKES.
at once, at twenty minutes before ten A.M., a noise was
heard like the rumbling of carriages under ground; it
increased rapidly and became a succession of deafening
explosions like the loudest cannon.  Then a shock,
which, as described by one writing from  the spot,
seemed to last but the tenth part of a minute; and down
came tumbling palaces, churches, theatres, and every
large public edifice, and about a third or a fourth part oi
the dwelling houses.  More shocks followed in rapid
succession, and in six minutes from the commencement
6o,ooo persons were crushed in the ruins! Here are
the simple but. expressive words of one J. Latham, who
writes to his uncle in London.  "I was on the river
with one of my customers going to a village three miles
off. Presently the boat made a noise as if on the shore
or landing, though then in the middle of the water. I
asked my companion if he knew what was the matter.
He stared at me, and looking at Lisbon, we saw the
houses falling, which made him say,' God bless us, it is
an earthquake!' About four or five minutes after, the
boat made a noise as before-; and we saw the houses
tumble down on both sides of the river."  They then
landed and made for a hill; whence they beheld the sea
(which had at first receded and laid a great tract dry)
come rolling in, in a vast mountain wave fifty or sixty
feet high, on the land, and sweeping all before it. Three
thousand people had taken refuge on a new stone quay
or jetty just completed at great expense.  In an instant
it was turned topsy-turvy; and the whole quay, and
every person on it, with all the vessels moored to it,




ABOUT VOLCANOS AND EARTHQUAKES.           39
disappeared, and not a vestige of them ever appeared
again. Where that quay stood, was afterwards found a
depth of ioo fathoms (600 feet) water. It happened to
be a religious festival, and most of the population were
assemibled in the churches, which fell and crushed them.
That no horror might be wanting, fires broke out in
innumerable houses where the wood-work had fallen on
the fires; and much that the earthquake had spared was
destroyed by fire. And then too broke forth that worst
of all scourges, a lawless ruffian-like mob, who plundered,
burned, and murdered in the midst of all that desolation
and horror. The huge wave I have spoken of swept the
whole coast of Spain and Portugal.  Its swell and fall
was ten or twelve feet at Madeira.  It swept quite
across the Atlantic, and broke on the shores of the West
Indies.  Every lake and firth in England and Scotland
was dashed for a moment out of its bed, the water not
partaking of the sudden shove given to the land, just as
when you splash a flat saucerful of water, the water
dashes over on the sidefrom which the shock is given.
(49.) One of the most curious incidents in this earthquake was its effect on ships far out at sea, which would
lead us to suppose that the immediate impulse was in
the nature of a violent blow or thrust upwards, under the
bed of the ocean. Thus it is recorded that this upward
shock was so sudden and violent on a ship, at that time
forty leagues from Cape St Vincent, that the sailors on
deck were tossed up into the air to a height of eighteen
inches. So also, on another occasion in 1796, a British
ship eleven miles from land near the Philippine Islands




40     ABOUT VOLCANOS AND EARTHQUAI(ES,
was struck upwards from below with such force as to unship and split up the main-mast.
(5o.) Evidences of a similar sudden and upward explosive action are of frequent occurrence among the
extinct volcanos of Auvergne and the Vivarais, where in
many instances the perforation of the granitic beds which
form the basis or substratum of the whole country appears to have been effected at a single blow, accompanied with little evidence of disturbance of the surrounding rocks-much in the same way as a bullet will
pass through a pane of glass without starring or shattering it.  In such cases it would seem as if water in a
liquid state had suddenly been let in through a fissure
upon a most intensely heated and molten mass beneath,
producing a violent but local explosion, so instantaneous
as to break its way through the overlying rocks, without
allowing time for them  to bend or crumple, and so displace the surrounding masses
(5i.) The same kind of upward bounding movement
took place at Riobamba in Quito in the great earths
quake of February 4, 1797, which was connected with
an eruption of the volcano of Tunguragua.  That earth.
quake extended in its greatest intensity over an oval
space of 120 miles from south to north, and 60 from
east to west, within which space every town and village
was levelled with the ground; but the total extent of
surface shaken was upwards of 500 miles in one direction (from  Puna to Popayan), and 400 in the other.
Quero, Riobamba, and several other towns, were buried
under fallen mountains, and in a very few minutes




ABOUT VOLCANOS AND EARTHQUAKES.           41
30,000 persons were destroyed.  At Riobamba, however, after the earthquake, a great number of corpses
were found to have been tossed across a river, and
scattered over the slope of a hill on the other side.
(52.) The frequency of these South American earthquakes is not more extraordinary than the duration of
the shocks.  Humboldt relates that on one occasion,
when travelling on mule-back with his companion
Bonpland, they were obliged to dismount in a dense
forest, and throw themselves on the ground: the earth
being shaken uninterruptedly for upwards of a quarter
of an hour with such violence that they could not keep
their legs.
(53.) One of the most circumstantially described earthquakes on record is that which happened in Calabria
on the 5th of February 1783; I should say began then,
for it may be said to have lasted four years. In the
year 1783, for instance, 949 shocks took place, of which
50I were great ones, and in 1784, I5I shocks were felt,
98 of which were violent. The centre of action seemed
to be under the towns of Monteleone and Oppido. In
a circle twenty-two miles in radius round Oppido every
town and village was destroyed within two minutes by
the first shock, and within one of seventy miles' radius
all were seriously shaken and much damage done.
The whole of Calabria was affected, and even across
the sea Messina was shaken, and a great part of
Sicily.
(54.) There is no end of the capricious and out-of-theway accidents and movements recorded in this Calabrian




42     ABOUT VOLCANOS AND EARTHQUAKES.
earthquake.  The ground undulated like a ship at sea.
People became actually sea-sick, and to give an idea of
the undulation (just as it happens at sea), the scud of
the clouds before the wind seemed to be fitfully arrested
during the pitching movement when it took place in the
same direction, and to redouble its speed in the reverse
movement.  At Oppido many houses were swallowed
up bodily. Loose objects were tossed up several yards
into the air. The flagstones in some places were found
after a severe shock all turned bottom upwards. Great
fissures opened in the earth, and at Terra Nova a mass
of rock 200 feet high and 400 in diameter travelled four
miles down a ravine. All landmarks were removed, and
the land itself, in some instances, with trees and hedges
growing on it, carried bodily away and set down in
another place. Altogether about 40,ooo people perished
by the earthquakes, and some 20,000 more of the epidemic diseases produced by want and the effluvia of the
dead bodies.
(55.) Volcanos occasionally break forth at the bottom
of the sea, and, when this is the case, the result is usually
the production of a new island. This, in many cases,
disappears soon after its formation, being composed of
loose and incoherent materials, which easily yield to the
destructive power of the waves.  Such was the case with
the Island  of Sabrina, thrown up, in I8II, off St
Michaels, in the Azores, which disappeared almost as
soon as formed, and in that of Pantellaria, on the
Sicilian coast, which resisted longer, but was gradually
washed into a shoal, and at length has, we believe, col



ABOUT VOLCANOS AND EARTHQUAKES.              43
pletely disappeared.'  In numerous other instances, the
cones of cinders and scoriae, once raised, have become
compacted and bound together by the effusion of lava,
hardening into solid stone, and thus, becoming habitual
volcanic vents, they continue to increase in height and
diameter, and assume the importance of permanent volcanic islands. Such has been, doubtless, the history of
those numerous insular volcanos which dot the ocean
in so many parts of the world, such as Teneriffe, the
Azores, Ascension, St Helena, Tristan d'Acunha, etc.
In some cases the process has been witnessed from its
commencement, as in that of two islands which arose in
the Aleutian group, connecting Kamtschatka with North
America, the one in I796, the other in 18I4, and which
both attained the elevation of 3000 feet.
(56.) Besides these evident instances of eruptive action,
there is every reason to believe that enormous floods of
lava have been, at various remote periods in the earth's
history, poured forth at the bottom of seas so deep as to
repress, by the mere weight of water, all outbreak oI
steam, gas, or ashes; and reposing perhaps for ages in a
liquid state, protected from the cooling action of the
water on their upper surface by a thick crust of congealed stony matter, to have assumed a perfect level; and,
at length, by slow cooling, taken on that peculiar columnar structure which we see produced in miniature in
* Such an event is at this moment in progress (March 1866),
close to the island of Santorini, in the bay of Thera, ir the Greek
Archipelago: itself, with the adjacent Kaimeni Islands, products of
the same kind.




44     ABOUT VOLCANOS AND EARTHQUAKES.
starch by the contraction or shrinkage, and consequent
splitting, of the material in drying; and resulting in those
picturesque and singular landscape-features called basaltic
colonnades: when brought up to day by sudden or
gradual upheaval, and broken into cliffs and terraces by
the action of waves, torrents, or weather. Those grand
specimens of such colonnades which Britain possesses
in the Giant's Causeway of Antrim, and the cave of
Fingal in Staffa, for instance, are no doubt extreme outstanding portions of such a vast submarine lava-flood
vwhich at some inconceivably remote epoch occupied the
whole intermediate space; affording the same kind of
evidence of a former connexion of the coasts of Scotland
and Ireland as do the opposing chalk cliffs of Dover and
Boulogne of the ancient connexion of France with
Britain.  Here and there a small basaltic island, such
as that of Rathlin, remains to attest this former continuity, and to recall to the contemplative mind that sublime antagonism between sudden violence and persevering effort, which the study of geology impresses in every
form of repetition.
(57.) There exists a very general impression that earthquakes are preceded and ushered in by some kind of
preternatural, and, as it were, expectant calm in the
elements; as if to make the confusion and desolation
they create the more impressive.  The records of such
visitations which we possess, however striking some particular cases of this kind may appear, by no means bear
out this as a general fact, or go to indicate any particular
phase of weather as preferentially accompanying their




ABOUT VOLCANOS AND EARTHQUAKES.            45
occurrence.  This does not prevent, however, certain
conjunctures of atmospheric or other circumstances from
exercising a determining influence on the times of their
occurrence.  According to the view we have taken of
their origin (viz., the displacement of pressure, resulting
in a state of strain in the strata at certain points, gradually increasing to the maximum they can bear without
disruption), it is the last ounce which breaks the camel's
back.  Great barometrical fluctuation, accumulating atmospheric pressure for a time over the sea, and relieving it over the land; an unusually high tide, aided by
long-continued and powerful winds, heaping  up the
water; nay, even the tidal action of the sun and moon
on the solid portion of the earth's crust,-all these
causes, for the moment combining, may very well suffice
to determine the instant of fracture, when the balance
between the opposing forces is on the eve of subversion.
The last-mentioned cause may need a few words of explanation. The action of the sun and moon, though it
cannot produce a tide in the solid crust of the earth,
tends to do so, and, were it fluid, would produce it.  It
therefore, in point of fact, does bring the solid portions
of the earth's surface into a state alternately of strain and
compression.  The effective part of their force, in the
present case, is not that which aids to lift or topress the
superficial matter (for t/at, acting alike on the continents
and on the bed of the sea, would have no influence), but
that which tends to produce lateral displacement; or
what geometers call the tcangentia/lforce. This of necessity brings the whole ring of the earth's surface, which




46      ABOUT VOLCANOS AND EARTHQUAKES.
at any instant has the acting luminaryon its horizon, into
a state of strain; and the whole area over which it is
nearly vertical, into one of compression. We leave this
point to be further followed out, but we cannot forbear
remarking, that the great volcanic chains of the world
have, in point of fact, a direction which this cause of disruption would tend rather to favour than to contravene.




LECTURE II.
THE SUN.
HE subject I have chosen for this Lecture is
perhaps an ambitious one; for it is no less
than an attempt to convey to my hearers
some faint impression of the vastness and
grandeur of the most magnificent object in natureof that glorious body which occupies the centre of our
planetary system, and on which not only our own globe,
but all the other planets, many of them of far greater
magnitude and possibly too of greater importance in
the scale of being than our own; depend in the most
immediate manner for the fulfilment of those conditions
without which animated existence and organic life are
impossible-THE SUN.  There is a poem  of Byron's
entitled "Darkness," which begins thus:" I had a dream which was not all a dream,
The bright sun was extinguish'd, and the earth
Did wander darkling in th' eternal space
Rayless and pathless,"




48                    THE SUN.
and so on: describing, or trying to describe, the horrors
of that desolation which would ensue.  They are assembled and piled on one another in this powerful
poem with the hand of a master of the horrible; and
in the end everybody goes mad, fights with everybody
else, and dies of starvation.
(2.) But there would not be time for fighting or starvation. In three days from the extinction of the sun
there would, in all probability, not be a vestige of animal or vegetable life on the globe; unless it were among
deep-sea fishes and the subterranean inhabitants of the
great limestone caves.  The first forty-eight hours would
suffice to precipitate every atom of moisture from the
air in deluges of rain and piles of snow, and from that
moment would set in a universal frost such as Siberia
or the highest peak of the Himalayas never felt-a temperature of between two and three hundred degrees
below the zero of our thermometers. This is no fanciful
guess-work.  Professor Tyndall has quite recently shown
that it is entirely to the moisture existing in the air
that our atmosphere owes its power of confining, and
cherishing as it were the heat which is always endeavouring to radiate away from the earth's surface into
space.  Pure air is peifectly transparent to terrestrial
heat-so that but for the moisture present in the atmosphere, every night would place the earth's surface as it
were in contact with that intense cold which we are
certain exists in empty space: a degree of cold which
from several different and quite independent lines of inquiry we are sure is not less than 230 degrees of Fah



THE SUN.                     49
renheit's thermometer below the zero of that scale.  No
animal or vegetable could resist such a frost for an hour,
any more than it could live for an hour in boiling water.
Such a frost exists, no doubt, over the dark half of the
moon, which has no atmosphere, neither air nor vapour,
and in all probability quite as violent an extreme of heat,
a boiling temperature at least, over the bright half; so
that we may pretty well make up our minds as to that
half of the moon at least which we see, being uninhabited;
while on the other hand, if it would not lead too far
away from our immediate subject, I think it might be
shown on admissible principles, that Venus and Mercury, in spite of their nearness to the sun, and possibly
also Jupiter and Saturn, in spite of their remoteness,
may have climates in which animal and vegetable life
such as we see them here, might be maintained.
(3.) But it is with the sun itself that we are now concerned.  What I am going to say about the sun will
consist of a series of statements so enormous in all
their proportions, that I dare say, before I have done,
some of my hearers will almost think me mad, or intending to palm  on them  a string of rhodomontades,
like some of the mythical stories of the Hindus.  And
yet there is nothing more certain in modern science
than the truth of some of -the most extravagant of these
statements; and, wild as they may seem to those who
for the first time hear them, they, appear not only not
extravagant, but actually dwarfed into littleness by the
still vaster revelations of that science respecting the scale
of the visible universe; in every part of which when we
D




50                    THE SUN.
come to measure in figures either the magnitude or
the minuteness of its mechanisms, we find our arithmetic almost breaking down in the attempt, and numbers of ten or twenty places of figures, as it were tossed
about like dust, and turning up on every occasion.
(4.) To come then to our subject.  The first and
most important office the sun has to perform in our
system is to keep it together, to keep its members from
parting company, from seceding, and running off into
outer darkness, out of the reach of the genial influence
of his beams. Were the sun simply extinguished, the
planets would all continue to circulate round it as they
do at present, only in cold and darkness; but were it
annililated, each would from  that moment set forth
on a journey into infinite space in the direction in
which it happened  then to be moving; and wander
on, centuries after centuries, lost in that awful abyss
which separates us from the stars, and without making
any sensible approach even to the nearest of them in
many hundreds or even thousands of years. The power
by which the sun is enabled to perform this office-to
gather the planets round its hearth and to keep them
there-is the same in kind  (though very different in
intensity) with that which when a stone is thrown up
into the air draws it down again to the earth. As to
the manner in which this is effected by the weight of
the stone, or its tendency to fall straight down, acting
to turn or draw it out of its right-lined course oblique
to the surface, and oblige it to move in a curve,-with
the explanation of that we have here nothing to do.




THE SUN.                     $5
That belongs to mechanics, and we must take it for
granted. But in order to understand how it is possible
to pass from this familiar case that we see every day
before our eyes, to that of a. vast globe like the earth
revolving in an orbit about the sun, it will be necessary to enlarge the scale of our ideas of magnitude.
We must try to conceive a similar degree of command
and control exercised over such a mass as our globe,
and over the much greater masses of the remote planets,
by the sun as a central body; hardly moved from its
place, while as it were swinging all the others round
it.  And for this purpose it is necessary to possess
some distinct conception of what sort of a body the
sun really is-of its size-of its distance from us-of
its weight or mass-and of the proportion it bears to
the other bodies, the earth included, which circulate
round it.
(5.) It is strange what crude ideas people in general
have about the size of very distant objects.  I was reading only the other day a letter to the Times giving an account of a magnificent meteor. The writer described it as
round, about the size of a cricket-bazl, and apparenM/y about
Ioo yards offi   Many persons spoke of the tail of the
great comet of 1858 as being several yards long, without
at all seeming aware of the absurdity of such a way of
talking. The sun or the moon may be covered by a threepenny piece held at arm's length: but it takes a house,
or a church, or a great tree to cover it on a near horizon,
and a hill or a mountain on a distant one; so that it
must be at least as large as any of these objects.  Among




52                    THE SUN.
the ancient Greek philosophers there was a lively dispute
as to the real size of the sun. One maintained that it
was "precisely as large as it looks to be," a thoroughly
Greek way of getting out of a difficulty. All the best
thinkers among them, however, clearly saw that it must
be a very large body.  One of them  (Anaxagoras) went
the length of saying that it might be as large as all Greece,
for which he got laughed at.  But he was outbid by
Anaximander, who said it was twenty-eight times as large
the earth.  What would Anaximander or the scoffer of
Anaxagoras have said, could he have known what we now
know, that, seen from the same distance as the sun, the
territory of Greece would have been absolutely invisible;
and that even the whole earth, if laid upon it, would not
cover more than one thirteen-thousandth part of its apparent surface,-less in proportion, that is to say, than a
single letter in the broad expanse of type which meets
the reader's eye when a closely-printed volume with a
large page and small type lies open before him.*
(6.) My object in this notice is not to put before my
audience, except in one single instance, any connected
chain of reasoning and deduction; or to show how, from
the principles of abstract science combined with observation, the results I have to state have been obtained.
This would lead me a great deal too far, and would require not one but a whole series of such lectures.  What I
e The original type and page of " Gcod Words" were here referred to, in which this lecture first appeared in print: each page of
which contains about 6000 letters. The pages which now lie open
before the eye of the reader contain, together, only about 2600




THE SUN.                      53
aim at is to convey to their minds, as matters of fact,
what those results are in the case of the sun, and to enable them to form a conception of it as a reality. Still it
is reasonable for any one to ask how it is possible to
prove such a statement, for instance, as that just made:
and as the kind of process by which our conclusions as
to the size and mass of the sun are arrived at may be
put in a few words, it will not be amiss to give a sketch
of it.
(7.) The first step towards ascertaining the real size of
the sun is to determine its distance. Now, the simplest
way to find the distance of an object which cannot be
got at, is to measure what is called a base line from the
two ends of which it can be seen at one and the same
moment, and then to measure with proper instruments
the angles at the base of the triangle formed by the distant object and the two ends of the base. Geography
and surveying in modern times have arrived at such perfection, that we know the size and form of the earth we
stand upon to an extreme nicety.  It is a globe a little
flattened in the direction of the poles,-the longer diameter, that across the equator, being 7925 miles and five
furlongs, and the shorter, or polar axis, 7899 miles and
one furlong; and in these measures it is pretty certain
that there is not an error of a quarter of a mile. And
knowing this, it is possible to calculate with quite as much
exactness as if it could be measured, the distance in a
straigiat line between any two places whose geographical
positions on the earth's surface are known. Now there
are two astronomical observatories very remote from one




54                    THE SUN.
another; the one in the northern hemisphere, the other
in the southern, viz., at Hammerfest in Norway, and at
the Cape of Good Hope, both very nearly on the same
meridian, so that the sun, or the moon, or any other
heavenly body attains its greatest altitude above the horizon of each (or as astronomers express it, passes the
meridian of each) very nearly at the same time.  Supposing then that this, its- meridian altitude, is carefully observed at each of these two stations on the same day; it
is easy to find, by computation, the angles included between each of the two lines of direction in which it was
seen from  the two places, and their common line of
junction; so that taking this latter line for the base of a
triangle, of which the two sides are the distances of the
object from either place, those two sides can thence be
calculated by the very same process of computation which
is employed in geographical surveying to find the distance
of a signal from observations at the ends of a measured
base. Now, the distance between Hammerfest and the
Cape in a straight line is nearly 6300 miles, and owing
to the situations of the two places in latitude, the triangle
in question is always what a land surveyor would call a
favourable one for calculation: so that, with so long a base,
we may reasonably expect to arrive at a considerably
exact knowledge of its sides,-after which a little additional calculation will readily enable us to conclude the
distance of the object observed from the earth's centre.
(8.) When the moon is the object observed, this expectation is found to be justified. The triangle in question, though a long one, is not extravagantly so.  Its




THE SUN.                       55
sides are found to be, each about thirty-eight times the
length of the base, and the resulting distance of the moon
from the earth's centre about thirty diameters of the
latter, or more exactly sixty times and a quarter its
radius, that is to say, 238,100  (say 240,000) miles,
which is rather under a quarter of a million-so that,
speaking roughly, we may consider the moon's orbit
round the earth as a circle about half a million of miles
across. In the case of the sun, however, it is otherwise.
The sides of our triangle are here what may be called
extravagantly out of proportion to its base; and the
result of the calculation is found to assign to the sun a
distance very little short of four hundred times that
already found for the moon-being in effect no less than
23,984 (in round numbers 24,000) radii, or I2,000
diameters of the earth, or in miles 94,880,700 or about
95,000oo000ooo.*
(9.) When so vast a disproportion exists between the
distance of an object and the base employed to measure
it, a very trifling error in the measured angles produces a
great one in the result. Happily, however, there exists
another and a very much more precise method, though
far more refined in principle, by which this most important element can be determined; viz., by observations of
the planet Venus, at the time of its " transit " (or visible
passage) across the sun's disc. It would lead us too far
aside from  our purpose to explain this, however, at
* These numbers and all the subsequent statements in miles are
too large by about I mile in 3I.  See Lecture III. on Comets,
~9.




g5                    THE SUN.
length.  The necessary observations were made at the
time of the last " transit" in i769, and will no doubt be
repeated on the next occasion of the same kind, in 1874.'
(ro.) From the distance of the sun so obtained, and
from its apparent size (or, as astronomers call it, its
angular diameter), measured very nicely by delicate
instruments called micrometers, the real diameter of the
sun has been calculated at 882,o00 miles, which I suppose may be taken as exact to a few odd thousands.
(ii.) Now, only let us pause a little, and consider
among what sort of magnitudes we are landed.  It runs
glibly over the tongue to talk of a distance of 9,000,000o
of miles, and a globe of 88o,ooo miles in diameter, but
such numbers hardly convey any distinct notion to
the mind.  Let us see what kind of conception we can
get of them  in other ways.  And first then, as to the
distance.  By railway, at an average rate of 40 miles an
hour one might travel round the world in 26 days and
nights.  At the same rate it would take 270 years and
more to get to the sun.  The ball of an Armstrong ioopounder leaves the gun with a speed of about 400 yards
per second.  Well, at the same rate of transit it would
be more than thirteen years and a quarter in its journey
to reach the sun; and the sound of the explosion (supposing it conveyed through the interval with the same
speed that sound travels in our air), would not arrive
till half a year later.  The velocity of sound, or of any
* The distance above stated is that which results from this more
precise mode of procedure. See this explained in Lecture V.,
~I7.




THE SUN.                     57
other impulse conveyed along a steel bar, is about sixteen times greater than in air. Now, suppose the sun
and the earth connected by a steel bar. A blow struck
at one end of the bar, or a pull applied to it, would not
be delivered-would not begin to be felt-at the sun till
after a lapse of 313 days.  Even light, the speed of
which is such that it would travel round the globe in less
time than any bird takes to make a single stroke of his
wing, requires seven minutes and a half to reach us from
the sun.
(I2.) The illustration of the distance of the sun which
I have just mentioned, by supposing it connected with
the earth by a steel bar, will serve to give us some notion
of the wonderful connexion which that mystery of mysteries, gravitation, establishes between them. The sun
drazes or pulls the earth towards it. We know of no
material way of communicating a pull to a distant object
more immediate, more intimate, than grappling it with
bonds of steel; and how such a bond would suffice we
have just seen.  But the pul on the earth which the sun
makes is instantaneous, or at all events incomparably
more rapid in its transmission across the interval than
any solid connexion would produce, and even demonstrably far more rapid than the propagation of light
itself.*
(I3.) Let me now try to convey some sort of palpable
notion of the size of the sun itself.  On a circle six feet
in diameter, representing a section of it through the
centre, a similar section of the earth would be about
* See note at the end of this lecture.




58                    THE SUN.
represented by a fourpenny-piece, and a distance of a
thousand miles by a line of less than one-twelfth of an
inch in length. A circle concentric with it, representing
on the same scale the size of the moon's orbit about the
earth, would have for its diameter only thirty-nine inches
and a quarter, or very little more than half the sun's.
Imagine, now, if you can, a globe concentric with this
earth on which we stand; large enough not only to fill
the whole orbit of the moon, but to project beyond it on
all sides into space almost as far again on the outside!
A spangle, representing the moon, placed on the circumference of its orbit so represented, would require to be
only a sixth part of an inch in diameter.
(I. ) It is nothing to have the size of a giant without
the strength of one. The sun retains the planets in their
several orbits by a powerful mechanical force, precisely
as the hand of a slinger retains the stone which he whirls
round till the proper moment comes for letting it go.
The stone pulls at the string one way, the controlling
hand at the centre of its circle the other. Were the
string too weak, it would break, and the stone, preinaturely released, would fly off in a tangential direction. If a
mechanist were told the weight of the stone (say a pound),
the length of the string (say a yard, including the motion
of the hand), and the number of turns made by the stone
in a certain time (say sixty in a minute, or one in a
second), lie would be able to tell precisely what ought to
be the strength of the string so asjust not to break; that
is to say, what weight it ought at least to be able to lift
without breaking.  In the case I have mentioned, it




THE SUN.                     59
ought to be capable of sustaining 3 lb. io oz. 386 grs.
If it be weaker it will break. And this is the force or
effort which the hand must steadily exert, to draw the
stone in towards itself, out of the direction in which it
would naturally proceed if let go; and to keep it revolving in a circle at that distance.
(I5.) Now, what the string does to the stone in the
sling, that, in the case of the sun retaining the earth in
its orbit,, is done-that same office is performed-that
effort (in some mysterious way which the human mind is
utterly incapable of comprehending) is exerted-that
pull communicated; in an instant of time, and so far as
we can discover, without any material tie; by the force
of gravitation.  We know the time the earth takes to
revolve about the sun. It is a year; of so many days,
hours, minutes and seconds; and we know its distance
-95,0o0,000 of miles, which may easily be turned into
yards.  Well, now, suppose a stone or a lump of lead of
a ton weight to be tied to the sun by a string, and slung
round it in such a circle and in such a time.  Then,
on the very same principles, and by the same rules of
arithmetic, one may calculate the amount of pull, or
tension of the string, and it will be found to come out
T lb. 6 oz. 5I grs.
(i6.) We all know what sort of lifting power-what
amount of muscular force-it takes to sustain a pound
weight.  Multiply this by 2240 and you have the muscular effort necessary to sustain a ton. It would require
three or four strong horses straining with all their might.
Well, now, it is one of the peculiarities of this mysterious




60                     THE SUN.
power of gravitation, that its intensity-the energy of its
pull-is less and less as the distance of the thing pulled
is greater: and that in a higher proportion.  At double
the distance, the force of the pull is not halved, but
quartered: at triple, it is not a third part, but a ninth.
There are mountains in the world five miles high; that
is to say, whose summits are five miles farther from the
centre of the earth than the sea-level.  If a ton of lead
were carried up to the top of such a mountain, though
it would still balance another ton, or 2240 weights of a
pound each on the scales, then and there; yet it would
not require so great an effort, such an exertion of muscular force, to raise and sustain it by five pounds and a
half. Now, fancy it removed to a height of 94,900,ooo
miles from the earth's surface, and estimating by the
same rule its apparent weight, you will find, if you make
the calculation, that it would not require more effort to sustain it from  falling, than would suffice to lift one thirtyseventh part of a grain from the surface of the earth.
(I7.) This, then, one thirty-seventh part of a grain, is
the force which the earth, placed where the sun is, would
exert onour lump of lead.  But we have seen that to
retain such a lump in such an orbit requires a pull of i
lb. 6 oz. 51 grs.  Of course, then, the earth, so placed,
would be quite inadequate to retain it from flying off.
To do this would require as many earths to pull it as
there are thirty-seventh parts of a grain in i lb. 6 oz.
5i grs.: that is to say, by an easy sum  in arithmetic,
356,929; or in round numbers, 360,000.  Now, this is
equivalent to saying, that to do the work which the sun




THE SUN.                      6I
coes upon each individual ton of matter which the earth
consists of, it must pull it as if (mind I say as if) it were
made up of 360,000 earths.  And this is what is meant
by saying, that the mass or quantity of gravitating
matter constituting the sun is 360,000 times as great as
the mass or quantity of such matter in the earth.
(i8.) Thus, now, you see, we have weighed as well as
measured the sun, and the comparison of the two results
leads to a very remarkable conclusion.  In point of size,
the globe of the sun, being in diameter   o times that of
the earth, occupies in bulZ, the cube of that number, or
1,33 I,00  times the amount of space.  The disproportion
in bulk, then, is much greater than the disproportion in
weight,-very nearly four times greater: so that you see,
comparatively speaking, and of course on an average of
its whole mass, the sun consists of much Zighzter materials
than the earth. And in this respect it agrees with all the
four great exterior planets, Jupiter, Saturn, Uranus, and
Neptune; while all the others-Mercury, Venus, and
Mars-agree much more nearly with the earth, and seem
to form a quite distinct and separate family.
(I9.) From this calculation of the mass of the sun, and
from its diameter, we are enabled to calculate the pressure which any heavy body placed on its surface would
exercise upon it, or what power it would require to lift
it off. It is very nearly thirty times the power required
to lift the same mass here on earth. A pound of lead,
for instance, transported to the sun's surface, could not
be raised from it by an effort short of what would lift
thirty pounds here.   A  man could no more stand




62                      THE SUN.
upright there, than he could here on earth with twentynine men on his shoulders.  He would be squeezed as
flat as a pancake by his own weight.
(20.) Giant Size and Giant Strength are ugly qualities
without beneficence. But the sun is the almoner of the
Almighty, the delegated dispenser to us of light and
warmth, as well as the centre of attraction; and as such,
the immediate source of all our comforts, and indeed
of the very possibility of our existence on earth.  Even
the very coals which we burn, owe their origin to the
sun's influence, being all of vegetable materials, the remains of vast forests which have been buried and preserved in that form for the use of man, millions of ages
before he was placed on the earth; and which, but for
the solar light and heat, would have had no existence.-*
Indeed, the theory of heat which is now gaining ground
would almost go to prove that it is the actual identical
heat which the sun put into the coal, while in the form
of living vegetation, that comes out again when it is
burnt as coal in our grates and furnaces; so that, after
all, Swift's idea of extracting sunbeams out of cucumbers,
which he attributes to his Laputan philosophers, may
not be so very absurd.t
* See the treatise on Astronomy, by the author of this paper, in
"Lardner's Cabinet Cyclopsdia," published in I833. Stevenson
(the celebrated engineer) has more recently drawn attention to this
fact.
t Not more so at least than some of his other Laputan speculations;
such as calcining ice into gunpowder: or moving vast locomotive
masses by magnetism, both which feats have, in a somewhat altered
form of expression, been accomplished (as in the explosion of potassium when laid on ice, and the movement of a ship by electro-mag



THE SUN.                       63
(21.) But how shall I attempt to convey to you any
conception of the scale on which the great work of
warming and lighting is carried on in the sun    It is
not by large words that it can be done.  All "wordpainting" must break down, and it is only by bringing
before you the consideration of great facts in the simplest language, that there is any chance of doing it. In
the very outset here is the greatest fact of all-the enormous waste, or what appears to us to be waste-the excessive, exorbitant prodigality of diffusion of the sun's
light and heat.  No doubt it is a great thing to light
and warm the whole surface of our globe. Then look at
such globes as Jupiter and Saturn and the others. This,
as you will soon see, is something astounding; but then
look what a trifling space they occupy in the whole
sphere of diffusion around the sun.  Conceive that little
globe of the earth, such as we have described it in comparison with our six feet sphere, removed I2,000 of its
own diameters, that is to say, 210 yards from the centre
of such a sphere (for that would be the relative size of
its orbit)! why, it would be an invisible point, and would
require a strong telescope to be seen at all as a thing
having size and shape. It occupies only the 75,oooth
part of the circumference of the circle which it describes
about the sun.  So that 75,000 of such earths at that
distance, and in that circle placed side by side, would
netism); or than his plan for writing books by the concourse of accidental letters, and selection of such combinations as form syllables,
words, sentences, &c., which has a close parallel in the learned
theories of the production of the existing races of animals by natural
selection.




64                    THE SUN.
all be equally well warmed and lighted,-and, then, that
is only in one plane! But there is the whole sphere of
space above and below, unoccupied; at any single point
of which if an earth were placed at the same distance,
it would receive the same amount of light and heat.
Take all the planets together, great and small; the light
and heat they receive is only one 227 millionth part of
the whole quantity thrown out by the sun.  All the rest
escapes into free space, and is lost among the stars; or
does there some other work that we know nothing about.
Of the small fraction thus utilized in our system, the
earth takes for its share only one Ioth part, or less than
one 2000 millionth part of the whole supply.
(22.) Now, then, bearing in mind this huge preliminary
fact to start with, let us see what amount of heat the
earth does receive from the sun.  The earth is a globe;
and therefore, taken on an average, it is constantly receiving as much, both of light and heat, as a flat circle
8000ooo miles in diameter, held perpendicularly to receive
it. Now, that section is 50,000,ooo square miles, so that
there falls at every instant on the whole earth 5o,ooo,ooo
times as much heat as falls on a square mile of the hottest
desert under the equator at noonday with a vertical sun
and with not a cloud in the sky-and in fact nearly a
third more; for more than a quarter of the sun's heat is
absorbed in the air in the clearest weather, and never
reaches the ground.  Now, we all know that in those
countries it is much hotter than we like to keep our
rooms by fires.  I have seen the thermometer four inches
deep in the sand in South Africa rise to  59~ Fahrenheit:




THE SUN.                     65
and I have cooked a beef-steak and boiled eggs hard
by simple exposure to the sun in a box covered with a
pane of window-glass, and placed in another box so
covered.
(23.) From a series of experiments I made there, I
ascertained that the direct heat of the sun, received on a
a surface capable of absorbing and retaining it, is competent to melt an inch in thickness of ice in 2 13m, and
from this I was enabled to calculate how much ice would
be melted per hour by the heat actually thrown on a
square mile exposed at noon under the equator, and the
result is 58,360,0oo lb., or in round numbers, 260ooo
tons, and this vast mass, has to be multiplied 50 millionfold to give the effect produced on a diametral section of
our globe.
(24.) And, now, let us endeavour to form some kind of
estimate of the temperature; that is to say, the degree or
intensity of the heat at the actual surface of the sun.  By
a calculation, with which I will not trouble you, it turns
out to be more than go,ooo times greater than the intensity of sunshine here on our globe at noon and under
the equator-a far greater heat than can be produced in
the focus of any burning-glass; though some have been
made powerful enough to melt, not only silver and gold,
but even platina, and, indeed, all metals which resist the
greatest heats that can be raised in furnaces.
(25.) Perhaps the best way to convey some sort of
conception of it, will be to state the result of certain experiments and calculations recently published; which is
this —that the heat thrown out FROM EVERY SQUARE YARD
E




66                    THE SUN.
of the sun's surface is equal to that which would be produced by burning on that square yard six tons of coal
per hour, and keeping up constantly to that rate of consumption-which, if used to the greatest advantage, would
keep a 63,000 horse steam-engine at work.-And this,
mind, on each individual square yard of that enormous
surface which is 12,000 times that of the whole surface
of the earth!
(26.) Let me say something now of the light of the sun.
The means we have of measuring the intensity of light
are not nearly so exact as in the case of heat-but this at
least we know-that the most intense lights we can produce artificially, are as nothing compared surface for surface with the sun.-The most brilliant and beautiful light
which can be artificially produced is that of a ball of
quicklime kept violently hot by a flame of mixed ignited
oxygen and hydrogen gases playing on its surface. Such
a ball, if brought near enough to appear of the same size
as the sun does, can no more be looked at without hurt
than the sun-but if it be held between the eye and the
sun, and both so enfeebled by a dark glass as to allow of
their being looked at together-it appears as a black
spot on the sun or as the black outline of the moon in
an eclipse, seen thrown upon it. It has been ascertained
by experiments which I cannot now describe, that the
brightness, the intrinsic splendour, of the surface of such
a lime-ball is only one 146th part of that of the sun's
surface. That is to say, that the sun gives out as much
light as 146 balls of quicklime each the size of th/e szun, and
each heated over all its surface in the way I have de



TIIE SUN.                       67
scribed, which is the most intense heat we can raise, and
in which platina melts like lead.
(27.) On the benefits which the sun's light confers on
us it cannot be necessary to say much; only one thing,
I think, may not be known to all who may read these
pages, viz., that it is not only by enabling us to see that
it is useful, but that it is quite as necessary as its heat
to the life and well-being both of plants and animals.
Animals, indeed, may live some time in complete darkness, but they grow unhealthy; lose strength and pine
away; while plants very quickly lose their green colour;
turn white or pale yellow; lose all their peculiar scent and
flavour; refuse to flower; and at last rot and die off.
What I have now to say about the light of the sun is of
quite a different nature.
(28.) The sun's light, as we all know, is purely white.
If the sun sometimes looks yellow or red, it is because it is
seen through vapours, or smoke, or a London fog of smoke
and vapour mixed.  It has been seen blue;* but when
high up, in a clear sky, it is quite white.  The whiteness
of snow, of a white cloud, of white paper, is the whiteness
of the sun's light which falls upon them. Whatever reflects the rays of the sun without choice or preference, appears
rwh/ie.  Whatever does not do so appears coloured; and
if it does not reflect them at all-black. Now I must
explain what I mean by saying-" without choice or pre* This has been denied by Arago. But I have a description of
the phlenomenon by an eye-witness, accompanied with a coloured
drawing, which leaves no doubt on my mind of the reality of the fact.
It was after a hurricane at Barbadoes.




68                     THE SUN.
ference."  Every ray of light which comes from the sun is
not a simple but a compound thizg.  Here, again, I must
explain.  The air we breathe is not a simple but a compound thing.  It is separable at least into four distinct
things, as different from  one another as any four things
you can name.  Well, then, so of a ray or beam  of the
sun; it may be separated, split, subdivided, not into four,
but into many hundreds, nay, thousands, of perfectly distinct rays or things, or rather of three distinct sorts or
species of rays; of which one sort affects the eyes as
light; one the sense of feeling and the thermometer as
heat; and one the chemical composition of everything
it falls upon; and which produces all the effects of photography.  Each of these three classes (and I believe there
are several more, indeed I have proved the existence of
one more) consists of absolutely innumerable species or
sorts; every one of which is separated from every other
by a boundary line, as sharp and as distinct as that which
separates Kent and Sussex on a map.  A ray of light is
a world in miniature, and if I were to set down all that
experiment has revealed to us of its nature and constitution, it would take more volumes than there are pages
in the manuscript of this lecture.
(29.) When the sun's light is allowed to pass through
a small hole in a dark place, the course of the ray or
sunbeam may be traced through the air (by reason of the
small fine dust that is always floating in it), as a straight
line or thread of light of the same apparent size, or very
nearly so, from the hole to the opposite wall. But if in
the course of such a beam, be held at any point the edge




THE SUN.                      69
of a clear angular polished piece of glass called a prism,
the course of the beam from that place will be seen to
be bent aside in a direction towards the thicker part of
the glass-and not only so bent or refracted, but spread
out to a certain degree, so that the beam in its further
progress grows continually broader, the light being dispersed, into a flat fan-shaped plane: and if this be received on white paper; instead of a single white spot
which the unbroken beam  would have formed on it,
appears a coloured streak; the colours being of exceeding vividness and brilliancy, and following one another
in a certain fixed order-graduating from a pure crimson
red at the end least remote from the original direction
(or least deviated), through orange, yellow, green, and
blue, to a faint and rather rosy violet. This beautiful
phoenomenon-the Prismatic Spectrum, as it is calledstrikes every one who sees it for the first time in a high
degree of purity, with wonder and delight; as I once
had the gratification of witnessing in the case of that
eminent artist the late Sir David Wilkie, who, strange to
say, had never seen a " Spectrum" till I had the pleasure
of showing him one; and whose exclamations, though a
man habitually of few words, I shall not easily forget. I
shall not attempt to give any account of the theory of
this prismatic dispersion of the sunbeam; but an illustration of it may be found in a very familiar and primitive
operation-the winnowing of wheat.  Suppose I had a
sieve full of mixed grains and other things-shot, for
instance; wheat grains; sand; chaff; feathers; and
that I flung them all out across a side wind, and noticed




70                    THE SUN.
where they fell. The shot would fall in one place, the
wheat in another, the sand in another, the chaff in
another, and the feathers anywhere-nowhere; but none
of them in the straight direction in which they were
originally tossed.  All would be deviated; and if you
marked the places of each sort, you would find them all
arranged in a certain order-that of their relative lightness-in a line on the ground, oblique to the line of their
projection.  You would have separated and assorted
them, and formed a spectrum, so to speak, on the
ground; or a picture of what had taken place in the
process; which would in effect have been the perfornance of a mechanical analysis of the contents of your
basket.
(30.) Bearing always in mind that it is an illustration
of a series of facts, not a theoretical explanation of a
natural process, which is here intended; I will now proceed to observe that the analogy of this case to that of
the prismatic analysis of a sunbeam may be pursued still
further.  If the original contents of the basket had been
all of one material, such as sand, consisting of a mixture
of particles of every gradation of coarseness and fineness;
from small pebbles down to impalpable dust; the trace
upon the ground, the sand spectrum, however long,
would be uninterrupted: the coarsest particles lying at
one end; the finest at the other; and every intermediate
size in every intermediate place.  On the other hand, in
the case first supposed, and supposing the shot to differ
inter se in respect of size within certain limits; the wheat
grains again within certain other; the sand within other;




THE SUN,                     71
and so on; they would be found after projection all indeed lying in a line, but that line an interrupted oneconsisting first of shot occupying a certain length; then
an interval; then wheaten grains to a certain extentanother interval-then sand, chaff, and so on. Now this
is by no means an inapt though a coarse representation
of the constitution of the Prismatic Spectrum. When it
is formed by an extremely pure prism, and with certain
precautions (which need not here be detailed) to ensure
the perfect purity of its colours, it is found to be disconztizzuous: that is to say, not a simple streak like a riband
of paper coloured from end to end by tints graduating
insensibly from  red to violet, but like such a riband
marked, across its breadth, by perfectly black lines of
exceeding delicacy, yet some wider some narrower than
others; and where these lines are, the paper is not illuminated at all. Into these spaces (for narrow as they
are, they have each a certain breadth) none of the light
dispersed by the prism  falls. These lines, be it also
observed, are not occasional or accidental, but permanent; and belong to the sun's light as szuch.  They
divide the spectrum into compartments as the boundary
lines between counties on a map divide the soil into
regions; and each individual of these compartments
differs in other qualities besides colour from its neighbours on either side; much as contiguous regions of a
country differ in soil and cultivation as well as in climate.
It is as if our assorted grains were distinguished not
only by being coloured according to their respective
sizes, but each particular size and weight distinguished




72                    THE SUN.
also by differences in the material of which they consisted.
(3I.) Every observer who has examined the spectrum
with more care than the last, has added to the number
of these lines. Dr Wollaston first noticed two or three
of the most conspicuous.  Fraunhofer registered and
fixed the places of some thirty or forty more; and later
observers have mapped down with all the precision of a
geographical survey, not less than two thousand of them.
The knowledge of them, and the precise measurement of
their distances from one another, has proved most valuable in a great many lines of scientific enquiry, and most
particularly in Optics and Chemistry; and, quite recently,
has been the means of revealing facts respecting the constitution of the sun itself, which one would have supposed
it impossible for man ever to have become acquainted
with.  One word more on these lines-for we must husband time, as there remains a great deal more ground
to go over.  I have said that they are not occasionaf, but
belong to the sun's light as such. But they may be considered as in some sort accidental as regards the sun-for
the light of each of the stars when thrown into a spectrum, is found to have a different system of these "fixed
lines."  And what is more, the light of every flame has
its peculiar lines, which indicate the nature of the burning substance. And in this way there seems to arise a
possibility that by studying these lines carefully, as ex
hibited by terrestrial flames and other sources of artificial
light, we may come to a knowlege of what the sun and
stars are made of. This is what men of science are now




THE SUN.                     73
very busily occupied about, and it seems to have been
rendered at least highly probable-I do not say that it
has been proved-that a great many of the chemical
elements of this our earth exist in the sun-such as, for
instance, iron, soda, magnesia, and some others. We
cannot here state the extraordinary facts on which this
conclusion rests. But the conclusion itself is not so absolutely strange and startling as it may at first appear.
The analysis of meteorolites, which there can be no doubt
have come to the earth from very remote regions of the
Planetary spaces, has, up to the present time, exhibited
no new chemical element-so that a community of
nature, at least as regards material constitution, between
our earth and the rest of the bodies of our system, is at
all events no unexpected, as it is, in itself, no unreasonable conclusion.
(32.) Not that it is meant, by anything above said, to
imply that the light of the sun is that of any flame, in the
usual sense of the word.  A late celebrated French philosopher, M. Arago, indeed, considered that he had
proved it to be so by certain optical tests. But in the
first place his proof is vitiated by an enormous oversight;
and the thing, besides, is a physical impossibility. The
light and heat of the sun cannot possibly arise from the
burning offuel, so as to give out what we call flame. If
it be the sun's substance that burns (I mean consumes),
where is the oxygen to come from l and what is to become
of the ashes, and other products of combustion? Even
supposing the oxygen supplied from the material, as in
the cases of gunpowder, Bengal light, or gun cotton, still




74                     THE SUN.
the chemical products have to be disposed of.  In the
case of gun cotton, it has been calculated that, if the sun
were made of it so condensed as only to burn on the
surface, it would burn out, at the rate of the sun's expenditure of light and heat, in eight thousand years. Anyhow-fire, kept up by fuel and air, is out of the question.
There remain only three possible sources of them, so far
as we can perceive-electricity, friction, and vital action.
The first of these was suggested by the late Sir William
Herschel in I80o; the second, at least as a possibility,
though without indicating any mode by which the necessary friction could arise, by myself, in a work* published
in 1I33.  The theory at present current of it is founded
on what may not unfairly be considered a further development of this idea, the friction being supposed to arise
from  meteoric matter circulating round the sun, and
gradually subsiding into it, and either tearing up its surface, or ploughing into its atmosphere. But on this we
cannot dilate, as nothing has been hitherto said about
the appearance of the sun in telescopes, and the strange
phenomena its surface, so examined, exhibits.
(33.) One of the earliest applications of the telescope
was to turn it on the sun.  And the first fruits of this
application (which originated about the same time in
the year i611, with Harriot in England, Galileo in Italy,
and Fabricius and Scheiner in Germany), was the dis*'Lardner's Cabinet Cyclopedia," Astronomy, s. 337, p. 212.
Aristotle was earlier in making this suggestion: but such random
guesses as those of the ancients can hardly merit the name of scientific suggestions.




THE SUN.                     75
covery of black spots on its surface, which, when watched
from day to day, were found to change their situation on
its disc, in a certain regular manner; coming in, or
making their first appearance on the eastern edge or
border of the disc: i.e., on the left-hand side of the sun
when seen at noonday; and going off, or disappearing
at the west, or on the right-hand side.  It very soon
became evident that, whatever these spots might be, they
adhered: to the body of the sun, and that their apparent
motions could only be accounted for by a real motion of
rotation of the sun on an axis nearly, but not quite, perpendicular to the ecliptic.  By following out this indication by careful observation and calculation, it has become
known that the sun does so rotate; that the time
occupied in a single rotation is very nearly 25 days 7
hours 48 minutes; that the axis of rotation is about 7~
inclined to a line perpendicular to the ecliptic, its direction in space being that of a line pointing nearly to the
star r (tau), in the constellation of the Dragon; in consequence of which on and about the i th of June, the
spots appear to pass across the sun in straight lines, from
the apparent northern to the apparent southern hemisphere of the sun, and the reverse on and about the I2th
of December, while at intervening times, their course
across the sun is a flattened elliptical or oval curve; a
necessary consequence of their real motion being in a
circle much inclined to the line of sight. Their ellipses
are most open on the I ith of March, and the I3th of September; on the former of which days we get the best view of
the south pole of the sun, and on the latter of the north.




76                   THE SUN.
(34.) But here comes the strange part of their history.
These spots are not permanent marks on the sun's
surface.  They come and go. They begin as small dim
specks; grow to be great blotches; and then dwindle
away.  Sometimes they are large enough to be seen
without a telescope, when the sun is near setting or just
risen, so as to have its dazzling splendour mitigated by
the vapours of the horizon, and admit of being looked
at steadily.  Many instances of such appearances are
recorded, some very remarkable ones, long before the
invention of the telescope. Two were so seen by my
son, Mr A. Herschel, in London, in November, i86I,
who sent me a drawing of them, which I found verified
on comparison with a drawing taken from the telescope
on the same day, by a very assiduous observer in my immediate neighbourhood.
(35.) Ever since the first discovery of the solar spots,
they have been watched with great interest, and it has
been ascertained that they do not make their appearance
indiscriminately upon every part of the globe of the
sun. At or near either of its poles they never appear;
and very rarely indeed on its equator, or on any part of
its body beyond the 4oth degree of latitude-understanding that term on the sun in the same acceptation which
geographers attach to it on our own globe.  They
mainly frequent two zones or belts parallel to its equator;
bearing very nearly the same relation to that great circle
of its sphere which the regions on our own globe in
which the trade winds prevail, bear to the equatorial
region of the earth-extending, that is to say, to some




TItE SUN.                      77
25~ or 300 of north, and not quite so far, or in such
abundance in south latitude; with a comp5aratively spotless intermediate belt, of five or six degrees broad between them, answering to our region of equatorial calms.
The resemblance is so striking as most strongly to suggest
some analogy in the causes of the two phenomena-and
it has been suggested that as our trade winds originate in
a greater influx of heat from  without, on and near the
equator, than at the poles, combined with the earth's
rotation on its axis: so the maculiferous belts of the sun
may owe their origin, to a less * equatorial efflux of heat,
combined with the axial rotation of that luminary.+
There is another extremely remarkable feature in the
appearance and disappearance of these spots. I have
said that they are not pernmanent.  Sometimes, indeed,
but rarely, one and the same spot lasts long enough, after
disappearing at the western edge of the sun, to come
round again and reappear at the eastern; and it has
happened that a spot has lasted long enough to reappear
four or five times; but for the most part this is not the
case.  But as regards the number of spots which appear
on the sun at different times, there is the greatest possible difference.   Sometimes it is quite spotless; at
others the spots swarm upon it: and as many as fifty or
sixty spots or groups, large and small, have been seen at
once, arranged in two belts.
(36.) Now, it has lately been ascertained by a careful
* Misprinted greater in the original lecture as it appeared in
Good Words.
t "Results of Astronomical Observations at the Cape of Good
Hope," by the author, p. 434




78                    THE SUN.
comparison of all the recorded observations of the spots,
that the periods of their scarcity and abundance succeed
one another at regular intervals of a trifle more than five
years and a half: so that in eleven years and one-tenth,
or nine times in a century, the sun passes through all its
states of purity and spottiness. Thus, for instance, in
the present century, the years 1800, 1811, 1822, 1833,
1844, i855-6 were years in which the sun exhibited few
or no spots, while in the years i80o, i8r6, 1827, 1838,
1849, i860, the spots have been remarkably abundant
and large. Several attempts have been made to connect
this with periodical variations in the weather, with hot
and cold years-wet and dry ones-years of good and
bad harvests, etc.; but though I believe there is some
such connexion, it is so overlaid and, as it were, masked
by the multitude of causes which act to produce what
we call the prevalent weather of a season, that nothing
satisfactory has been made out. But there are two classes
of phenomena or facts which occur here on earth which
certainly do stand in very singular accordance with the
appearance and disappearance of the sun's spots. The
first is that splendid and beautiful appearance in the sky
which we call the Aurora or Northern lights; and which,
by comparison of the recorded displays, have been ascertained to be much more frequent in the years when the
spots are abundant, and extremely rare in those years
when the sun is free from spots. The other is a class of
facts not so obvious to common observation, but of very
great importance to us; because it is connected with the
history and theory of the mariner's compass, and with




THE SUN.                      79
the magnetism of the earth; which we all know to be
the cause of the compass needle pointing to the north.
This is only a rough way of speaking.   It does iw.
point to the north, but very considerably to the west of
north, and that, not always alike.  Three centuries ago
it pointed nearly as much east as now west of north.
From  year to year the change is very perceptible; and.
what is more, at every hour of the day there is a sma!
but perfectly distinct movement to and fro, eastward ani
westward, of its average direction.  But besides this, tli
compass needle is subject to irregular, sudden, and capricious variations-jerking, as it were, aside, and oscillating backwards and forwards without any visible cause
of disturbance. And, what is still more strange; these
disturbances and jerks sometimes go on for many hours
and even days, and often at the same instants of time,
over very large regions of the globe; and in some
remarkable instances, over the whole earth-the same
jerks and jumps occurring at the same moments of time
(allowance made for the difference of longitude). These
occurrences are called magnetic storms, and they invariably accompany great displays of the Aurora; and are
very much more frequent when the sun is most spotted,
and rarely or never witnessed in the years of few spots.
(37.) The last four years' have been remarkable for
spots, and there occurred on the ist September I859, an
appearance on the sun which may be considered an
epoch, if not in the sun's history, at least in our know* This lecture was delivered about the end of z861.




80                    THE SUN.
ledge of it.  On that day great spots were exhibited;
and two observers, far apart and unknown to each other,
were viewing them with powerful telescopes; when suddenly, at the same moment of time, both saw a strikingly
brilliant luminous appearance, like a cloud of light far
brighter than the general surface of the sun, break out
in the immediate neighbourhood of one of the spots,
and sweep across and beside it. It occupied about five
minutes in its passage, and in that time travelled over a
space on the sun's surface which could not be estimated
at less than 35,000 miles.
(38.) A magnetic storm was in progress at the time.
From the 28th of August to the 4th of September many
indications showed the earth to have bee-n in a perfect
convulsion of electro-magnetism.  When one of the
observers I have mentioned had registered his observation; he bethought himself of sending to Kew, where
there are self-registering magnetic instruments always at
work, recording by photography at every instant of the
twenty-four hours the positions of three magnetic needles
differently arranged. On examining the record for that
day, it was found that at that very moment of time (as if
the influence had arrived with the light) all three had
made a strongly marked jerk from their former positions.
By degrees, accounts began to pour in of great Auroras
seen on the nights of those days; not only in these latitudes, but at Rome; in the West Indies; on the tropics
within I8~ of the equator (where they hardly ever appear), nay, what is still more striking, in South America
and in Australia; where, at Melbourne, on the night of




THE SUN.                     8r
the 2d of September the greatest Aurora ever seen there
made its appearance. These Auroras were accompanied
with unusually great electro-magnetic disturbances in
every part of the world. In many places the telegraphic
wires struck work. They had too many private messages
of their own to convey.  At Washington and Philadelphia, in America, the telegraph signal-men received
severe electric shocks.  At a station in Norway the
telegraphic apparatus was set fire to; and at Boston, in
North America, a flame of fire followed the pen of Bain's
electric telegraph, which, as my hearers perhaps know,
writes down the message upon chemically  prepared
paper.
(39.) I must now proceed to tell you what the telescope has revealed to us as to the nature and magnitude
of these spots. And here again, the closer we look, the
more the wonder increases.  The spots were at first
supposed to be clouds of black smoke floating over the
great fiery furnace beneath,-then great lumps of fresh
coal laid on; then comets fallen in to feed the fire; then
tops of mountains standing up above a great surging
ocean of melted matter.  They are none of all these
things; they are not clouds floating above the light, nor
protuberances sticking up above the general surface;
they are regions in which, by the action of some most
violent cause, the bright, luminous clouds, or what at all
events we may provisionally call clouds, which float in
the sun's atmosphere, are for a time cleared off; and
through the irregular vacuities thus created, allow us to
see perhaps thousands or tens of thousands of miles
F




82                    THE SUN.
below them, first, a layer of what we may consider real
clouds, which appear comparatively dark, as if they were
not self-luminous, but were seen only by the reflected
light of the upper layer of bright ones; secondly, through
other openings in this first layer, a second still darker
layer, independent of the first, and probably still thousands of miles below that, and reached by some-but
very little — light from above; and thirdly, through
again other openings, what at present we must consider
to be the body of the sun itself-at some vast and immeasurable depth still lower-and emitting so little
light in comparison as to appear quite black, though that
does not prevent its being in as vivid a state of fiery
glare as a white-hot iron; when we remember what has
been said of the lime light appearing black against the
light of the sun's surface. And it is a fact, that when
Venus, and Mercury pass across the sun, and are seen
as round spots on it, they do really appear sensibly
blacker than the blackest parts of the spots.
(40.) The sun then has an atmosphere, and in that
atmosphere float at least three layers of something, that,
for want of a better word, we must call clouds. The
two nearest the body are not luminous. They cannot
possibly be clouds of wfeatey vapour, such as we have in
our air, for water in a non-transparent state could not
exist at that heat; but they may be what perhaps we
might call smokes, that is to say, clouds in which the
metals or their oxides and the earths exist in the same
intermediate form that water does in our clouds.  The
third or upper layer of luminous clouds, or, as it is called,




THE SUN.                      83
"the photosphere," is a sort of thing that three or four
years ago we might be said to know nothing at all about;
I mean as to its nature and constitution; but within
that time a most wonderful discovery has been made by
Mr Nasmyth.  According to his observations, made
with a very fine telescope of his own making, the bright
surface of the sun consists of separate, insulated, individual objects or things, all nearly or exactly of one certain definite size and shape, which is more like that of
a willow leaf, as he describes them, than anything else.
These leaves or scales are not arranged in any order
(as those on a butterfly's wing are), but lie crossing one
another in all directions, like what are called spills in
the game of spillikins; except at the borders of a spot,
where they point for the most part inwards towards the
middle of the spot, presenting much the sort of appearance that the small leaves of some water-plants or seaweeds do at the edge of a deep hole of clear water. The
exceedingly definite shape of these objects; their exact
similarity one to another; and the way in which they lie
across and athwart each other (except where they form a
sort of bridge across a spot, in which case they seem to
affect a common direction, that, namely, of the bridge
itself),-all these characters seem quite repugnant to
the notion of their being of a vaporous, a cloudy, or a
fluid nature. Nothing remains but to consider them as
separate and independent sheets, flakes, or scales, having
some sort of solidity. And these flakes, be they what
they may, and whatever may be said about the dashing
of meteoric stones into the sun's atmosphere, etc., are




84                    THE SUN.
evidently the immediate sources of the solar light and heat,
by whatever mechanism or whatever processes they may
be enabled to develop and, as it were, elaborate these
elements from the bosom of the non-luminous fluid in
which they appear to float. Looked at in this point of
view, we cannot refuse to regard them as organisms of
some peculiar and amazing kind; and though it would
be too daring to speak of such organization as partaking
of the nature of life, yet we do know that vital action is
competent to develop both heat, light, and electricity.
These wonderful objects have been  seen by others
as well as by Mr Nasmyth, so that there is no room to
doubt of their reality. To be seen at all, however, even
with the highest magnifying powers our telescopes will
bear when applied to the sun, they can hardly be less
than a thousand miles in length, and two or three
hundred in breadth.
(41.) Next as to the actual size of the spots themselves: the distance of the sun is so vast, that a single
second of angular measure on its surface as seen from
the earth corresponds to 460 miles; and since, to present a distinguishableform, so as to allow of a certainty,
for instance, that it is round or square, in the best telescopes, an object must present a surface of at least a
second in diameter, it follows that to be seen at all so as
to make out its shape, a spot must cover an area of not
less than two hundred thousand square miles.  Now,
spots of not very irregular, and what may be called a compact form, of two minutes in extent, covering, that is to
say, an area of between seven and eight hundred millions




TTHE SUN.                    85
of square miles, are by no means uncommon. One spot
which I measured in the year I837 occupied no less than
three thousand seven hundred and eighty mnillions, taking
in all the irregularities of its form; and the black space
or'         umbra" in the middle of one, which was very nearly
round, would have allowed the earth to drop through
it, leaving a thousand miles clear of contact on every
side: and many instances of much larger spots than
these are on record. What are we to think, then, of the
awful scale of hurricane and turmoil and fiery tempest
which can in a few days totally change the form of such
a region, break it up into distinct parts-open up great
abysses in one part, such as that I have just described,
and fill up others beside them   As to the forms of the
spots, they are so conspicuously irregular as to defy description.
(42.) But we must proceed, for there are more wonders yet to relate.  Far beyond the photosphere, or
brilliant surface of the sun, extends what perhaps may
be considered as its true atmosphere. This can only
be seen at all in the rare opportunities afforded by total
eclipses of the sun. Everybody knows that an eclipse of
the sun is caused by the moon coming between it and
us. Now, by an odd coincidence, it so happens that
the sun being 400 times farther off than the moon, is
also ALMOST exactly, but a trifle less than 400 times as
large in diameter; so that when the centre of the moon
comes exactly in the line with the centre of the sun it
appears to cover it, and a very little more, so as to project on all sides a very little beyond it. Now, as the




86                    THE SUN.
moon is opaque (or not transparent), it completely stops
all the light from every part of the bright disc of the sun,
so long as the total eclipse continues, which is sometimes
as much as two or three minutes; and then are witnessed,
what at no other time can be seen, viz., certain wonderful appearances of rose-coloured masses of light projecting, as it were, from the dark edge of the moon, for the
most part like knobs, or cones, or long ranged ridges
of what would seem to be mountains, rising from it; but
sometimes like clouds or flaring flag-shaped masses of
red light, some of which have been seen quite detatched
from all connexion with the moon's border.  That they
belong to the sun, however, and not the moon, is evident
from the fact that the moon in its progress over the sun's
face gradually hides those to which it is approaching, and
discloses those which belong to that side of the sun
which the moon is going to leave; for I should mention
that they are seen irregularly placed all round the edge
of the sun.
(43.) Now, what are these singular lights?  Flames
they certainly are not; clouds of some sort it is extremely probable that they are, of most excessively thin
and filmy vapour, floating in a transparent atmosphere
which must for that purpose extend to a very considerable height above the luminous surface of the sun. We
are all familiar with the beautiful appearance of those
thin vapoury clouds which appear in our own atmosphere
at sunset.  But these solar clouds must be almost infinitely thinner and more unsubstantial, since even in that
intense illumination they are only seen when the sun




THE SUN.                    87
itself is hidden; and when it is remembered that the
head of the comet of 1843 was seen at noon-day within
two or three degrees of the sun by the naked eye.
(44.) Then, again, as to the magnitude of these cloudy
masses, it must be enormous. Some of them have projected or stood out from the edge of the sun to a distance
calculated at no less than forty or fifty thousand miles.
They have now been observed in three great eclipses,
that of 1842, I851, and I859; on which last occasion
they were photographed in Spain by Mr De la Rue,
under such circumstances as left no possibility of doubting their belonging to the sun. I dwell upon this, because there is another luminous appearance seen about
the moon in total eclipses of the sun, which can only be
referred to vapours of excessive tenuity, existing at an
immense height in our own atmosphere; and which surrounds the disc of the moon like a glory, or corona, as it
is called.  By the accounts of all who have witnessed
a total eclipse of the sun, it is one of the most awful
natural phaenomena. An earthquake has " rolled unheededly away" during a battle, but an eclipse has on more
than one occasion either stopped the combat or so paralyzed one of the parties with terror, as to give the others
who were prepared for it an easy victory: and I may as
well add that two very remarkable battles in ancient
history, the one on the 28th May, B.c. 585, the other the
g9th May, B.C. 557, which were in progress during total
eclipses, have had the years and days of their occurrence
thereby fixed by calculation with a certainty which belongs to no other epochs in ancient chronology.




88                    THE SUN.
(45.) There is only one more point which my limits
will allow me to touch upon.  I will go back to my original metaphor.  Our giant may be a huge giant and a
strong giant, and a good-natured giant, but if he be a
sluggard he is no giant worth the name. We have seen
that he is a little slow to turn on his axis and roll himself
round in his nest. But take him in his relation to the
outer world, he is lively enough; he "rejoices as a giant
to run his course;" and vindicates his credit as a swift
runner with a vengeance! Hitherto I have only spoken
of the sun as a sun, the centre of our system; and, as
such, regarded by us as immovable.  Even in this
capacity he is not quite fixed.  If he pulls the planets,
they pull him and each other; but such family struggles
affect him  but little.  They amuse /tem, and set them
dancing rather oddly; but don't disturb him. As all the
gods in the ancient mythology hung dangling from and
tugging at the golden chain which linked them to the
throne of Jove; but without power to draw him from his
seat: so if all the planets were in one straight line, and
exerting their joint attractions, the sun, leaning a little
back as it were to resist their force, would not be displaced by a space equal to his own radius; and the fixed
centre, or, as an engineer would call it, the centre of
gravity of our system, would still lie within the sun's
globe.
(46.) But the sun has another and, so far as we can
judge, a much vaster part in creation to perform than to
sit still as the quiet patriarch of a domestic circle.
He is up and active as a member of a community like




THE SUN                      89
himself. The sun is not only a sun, he is a STAR also,
and that but a small one in comparison with individual
stars (one of which, Sirius, would make two or three
hundred of him); and among these glorious compeers he
moves on a path which is just beginning to become
known to us; though in what orbit, or for what purpose,
will never be given to man to know.  Yet we do knowalmost to a nicety-the direction in which that path is
leading; and the rate of his travel (though this is less
exactly determined). Still this rate, at the very lowest
estimate, cannot be taken under four or five hundred
thousand miles a day; and yet this speed, vast as it is,
in the 2000 years which separate us from the observations
of Hipparchus (who made the first catalogue of the stars),
would not suffice to carry it (and of course our system
along with it) over one sixtieth part of the distance which
now  separates it from  the very nearest of the stars.
When we travel through a diversified country, we become
aware of our change of situation by the different grouping and presentation of the objects around us.  But
though travelling at this amazing rate through space,
successive generations of mankind witness no change in
the order and arrangement of the stars; and Hipparchus,
were he to come once more among us, would recognize
the old familiar forms of his constellations; and, without
better means of observation than he then possessed,
would be unable to detect, with certainty, any change in
their appearance; though we, who are better provided
in that respect, are enabled to do so.
(47.) Such, then, is the scale of things with which we




90                       THE SUN.
become familiar when we contemplate the sun. In what
has been said, it will be perceived that I have been more
anxious to dwell upon facts than theories, and rather to
supply the imaginations of my audience with materials for
forming a just conception of the stupendous magnificence
of this member of God's creation, than to puzzle them
with physical and mathematical reasonings and arguments.
NOTE ON ~ 12.-The effect of any supposed small loss of time in
the transmission of the sun's attractive force on the earth across the intervening space, may be very easily made intelligible without going
through any abstruse calculation. The pull exerted on the earth
would be delivered there, not in the direction of the line joining the
sun and earth at the instant of its arrival, but of that which did join
them when it left the sun. Its action on the earth would therefore
be oblique to their actual line of junction, or to what is called the
radius vector of the orbit-tending, not towards the seun, but towards
a point somewhat ii advance of it-(i.e., lying from it in the direction in space of the region towards which the earth is moving).
This force then being resolved in radial and tangential directions
would produce, in the former, a force directed to the sun differing
by a mere infinitesimal from its direct gravity-and in the latter, one
always accelerating the earth in its orbit, and which, however minute,
must of necessity result in a continually progressive increase of the
major axis, and therefore of the length of the year. Supposing the
transmission of gravity to be performed with the speed only of light
-the inclination of the line of pull to the radius vector would be
20" 25 (the exact value of the coefficient of aberration), and the
accelerating tangential force thence resulting would amount to
I-Ioi88th part of the sun's direct attraction, a force whose effects
would become evident in a very few years-to say nothing of the
centuries elapsed since the first determination of the length of the
year.




LECTURE IIL
ON COMETS.
HE subject of comets, about which I now propose to say something, is one that has of late
naturally drawn to it a good deal of inquiry
and general interest, by reason of the unusually magnificent spectacles of this description which
have within the last few years been exhibited to us.* In
itself it is perhaps not one of the best adapted for
popular discussion  and familiar explanation of this
nature, because there are so many things in the history of
comets unexplained, and so many wild and extravagant
notions in consequence floating about in the minds of
even well-informed persons, that the whole subject has
rather, in the public mind, that kind of dreamy indefinite interest that attaches to signs and wonders than
any distinct, positive, practical bearing. The fact is,
that, though much is certainly known about comets, there
* This lecture was delivered on February I4, I859.




92                   ON COMETS.
is a great deal more about which our theories are quite
at fault; and, in short, that it is a subject rather calculated to show us the extent of our ignorance than to
make us vain of our knowledge, and to cause us to exclaim with Hamlet, " There are more things in heaven
and earth, Horatio, than are dreamt of in our philosophy."   This; the sublimity of the spectacle they
afford; and the universal interest they inspire, make the
appearance of a great comet an occasion for the imaginations of men to break loose from  all restraint of
reason, and luxuriate in the strangest conceptions.. I
have received letters about the comets of the last few
years, enough to make one's hair stand on end at the
absurdity of the theories they propose, and at the
ignorance of the commonest laws of optics, of motion, of
heat, and of general physics they betray in their writers.
This is always the case whenever a great comet appears,
only that in the later instances one feature of the general
commotion of mind  they inspire has been wanting.
Thanks to the prevalence of juster notions of the constitution of the universe, and of the relation in which
man  stands to its Author; countries calling  themselves civilized appear not to have been disgraced by
any of those panic terrors, or thought it necessary to
propitiate Heaven by any of those superstitious extravagances, about which we read on several former
occasions.  Even at Naples, which seems to be almost
the lowest point of Europe in the scale of intellectual and social progress, I have not heard that it was
thought necessary to liquefy the blood of St Januarius,




ON COMETS.                      93
or to carry his bones about the streets on account of
any of these later great comets.
(2.) When we look through nature and observe the
manifest indications of design which every point of it exhibits, it would be very presumptuous in us to assert that
comets are of no use, and serve no purpose in our system.
Hitherto, however, no one has been able to assign any
single point in which we should be a bit better or worse
off, materially speaking, if there were no such thing as
a comet.  Persons, even thinking persons, have busied
themselves with conjectures: such as that they may serve
for fuel for the sun (into which, however, they never
fall), or that they may cause warm  summers-which
is a mere fancy-or that they may give rise to epidemics,
or potato-blights, and so forth.  But I need hardly say
this is all wild talking, as my readers will. be better
able to judge when I shall have stated a few things which
are known for certain about them.  But there is a use,
and a very important one, of a purely intellectual kind.
which they have amply fulfilled; and who shall say that
it has not been desigzned that such should be the case?
They have afforded some of the sublimest and most
satisfactory verifications of our astronomical theoriesthey have furnished  us with  a proof amounting to
demonstration of the existence of a repulsive force*
directed (under certain circumstances, and acting on
certain forms of matter) from  the sun as well as of that
* See on this subject my "Results of Astronomical Observations
at the Cape of Good Hope," p. 407, et se., where the existence of
such a repulsive force is clearly demonstrated.




94                   ON. COMETS.
great and general attractive force which keeps the planets
in their orbits-and they have actually informed us of
the weight of one of the planets which could not have
been determined with any exactness if a comet had not
on one occasion passed very near to it.
(3.) The ancients believed comets to be much of the
same nature as meteors or shooting stars-either in the
earth's atmosphere-not far above the clouds; or, at all
events, much lower than the moon-or else as a species
of vapours or exhalations raised up from the earth by
the sun's heat, or by some other unknown cause; but
they never for a moment dreamed of their forming part
and parcel of that vast system  of planetary bodies circulating about the sun, of which in fact they had hardly
any distinct notions.  In ancient history, however,
several very remarkable comets stand recorded. One
is mentioned by the Greek philosopher Aristotle in 371
B.C., with a tail extending over a third part of the sky.
Many great comets are recorded at even more ancient
dates in the Chinese annals: for that strange people kept
an official record of all the remarkable stars, meteors,
and other celestial appearances, for more than a thousand years before the Christian era, and what is stranger
still, that record has been handed down to us and seems
dependable.  A great comet was seen close to the sun
62 years before Christ, during a total eclipse-and one
which appeared in the year 43 B.c., soon after the
murder of Julius Caesar at Rome, was seen by all the
assembled people in full daylight. Such a thing, though
very uncommon, is by no means singular-it has hap



ON COMETS.                      95
pened several times, and in one case quite recently; for
the great comet of 1843 was seen at noonday quite close
to the sun both in Nova Scotia and at Madrid, and before sunset at the Cape of Good Hope.*  Of course it
is only the brightest part, or the head of a comet that
can ever.be so seen. The faint light of the tail has no
chance of contending against broad daylight.
(4.) Before the invention of telescopes the appearance
of a comet was a rare occurrence, because only a small
proportion of them can ever be seen by the naked eye,
and of them again only a small portion are considerable
enough to attract much attention-but since that discovery it has been ascertained that they are very numerous-hardly a year passes without one; and very often
two, three, and in one year, 1846, no less than eight were
observed.  Taking only two a year on an average as
visible if looked for in a telescope, and considering that
at least as many must occur in such situations that we
could not expect to see them-in the 6000 years of recorded history there must have been between twenty and
thirty thousand comets, great and small. A great comet,
however, hardly occurs on an average oftener than once
in fifteen or twenty years, or even yet more rarely;
* At Halifax, in the first mentioned colony, my informant saw a
nstmber of persons-natives of the place- hale and sturdy men,
gathered in a group and gazing full on the sun, which, when he attempted to do, dazzled and almost blindedhim. He was compelled
to desist, and inquire what they were looking at, and how they
could do so without being blinded. " Blinded!" was the reply"Load bless you, it does not hurt us;-what, can't you see it-that
thing up by the sun?"




96                    ON COMETS.
though, as sometimes happens in matters of pure accident and in the run of chances, it is not very unfrequent
(and we have lately seen it remarkably exemplified) for
two or even three very great comets to follow each other
in rapid succession.  Thus the great comet of i680 was
followed in 1682 by two other very conspicuous ones, of
which we shall have more to say presently.
(5.) When a comet is first discovered in a telescope it is
for the most part seen only as a small, faint, round, or oval
patch of foggy, or, as it is called, nebulous light, somewhat
brighter in the middle.  By degrees it grows larger and
brighter, and at the same time more oval, and at length
begins to throw out a " tail" that is to say a streak of light
extending always in a directionfrom the sun, or in the continuation of a line supposed to be drawn from the place of
the sun below the horizon to the head of the comet above
it.  As time goes on, night after night the tail grows
longer and brighter, the "head," or nebulous mass from
which the tail seems to spring also increases, and within
it begins to be seen what is called a "z nucleus" or kernel,
a sort of rounded, misty lump of light dying off rapidly
into a haziness called the " coma " or hair.  Within this,
but, often a good deal out of the centre, there is seen
with a good telescope and a high magnifying power a
very small spark or pellet of light which may or may not
be the solid body of the comet, and which is the real
nucleus.  What in an indifferent telescope looks like a
rather large puffy ball, more or less oval, is certainly not
a solid substance.  All the while the comet is getting
every evening nearer and nearer to the place of the sun,




ON COMETS.                     97
and is therefore seen for a shorter time after sunset-or
before sunrise, as the case may be-(for quite as many
comets are seen in the morning before sunrise as in the
evening after sunset).  At last it approaches so near the
sun as to rise or set very nearly at the same time, and so
ceases to be seen except it should be so very bright and
so great a comet as to be visible in presence of the sun.
(6.) When this has taken place, however, the comet is
by no means to be considered as dead and buried. After
a time it reappears, having passed by the sun, or perhaps
before or behind it, and got so far away on the other side
as to rise before the sun or set after him.  If it first
appeared after sunset in the west, it will now reappear in
the east before sunrise.  And what is very remarkable,
its shape and size are usually totally different after its
reappearance from what they were before its disappearance. Some, indeed, never reappear at all.  The path
they pursue carries them into situations where they could
not be seen by the same spectators who saw them before.
Others-like those which appeared in 1858 and I86I,
without altogether disappearing as if swallowed up by the
sun-after attaining a certain maximum  or climax of
splendour and size die away, and at the same time move
southward, and are seen, as that of I858 was (on the
i ith of October for the first time), in the southern hemisphere, the faded remnants of a brighter and more glorious existence of which we here witnessed the grandest
display.  And on the other hand ye here receive as it
were many comets from the southern sky, whose greatest
display the inhabitants of the southern parts of the earth
G




98                  ON COMETS.
only have witnessed. It also very often happens that a
comet, which before its disappearance in the sun's rays
was but a feeble and insignificant object, reappears magnified and glorified, throwing out an immense tail and
exhibiting every symptom of violent excitement, as if set
on fire by a near approach to the source of light and heat.
Such was the case with the great comet of I68o-and
that of 1843, both of which, as I shall presently take
occasion to explain, really did approach extremely near
to the body of the sun, and must have undergone a very
violent heat. Other comets, furnished with beautiful and
conspicuous tails before their immersion in the sun's
rays, at their reappearance are seen stripped of that appendage, and altogether so very different that, but for a
knowledge of their courses, it would be quite impossible
to identify them as the same bodies. This was the case
with the beautiful comet of 1835-6, one of the most remarkable comets in history. Some, on the other hand,
which have escaped notice altogether in their approach
to the sun burst upon us at once in the plenitude of their
splendour, quite unexpectedly, as did that of the year
I86I.
(7.) I come now to speak of the paths described by
comets in the sky among the stars (which I need hardly observe keep always the same relative situations one among
the other, and stand as landmarks, among which comets,
planets, the moon and the sun pursue, or seem to us to
pursue, their destined courses). Now we all know that the
sun, moon, and planets, keep to certain high roads, like
bl);:ten tracks in the sky, from which they never deviate




ON COMETS.                      99
beyond definite and narrow limits assignable by calculation.  With comets it is far otherwise.  They are wild
wanderers, and care nothing for beaten tracks.  A comet
is just as likely to appear in any one region of the starry
heavens as in any other.  They are no respecters of
boundaries.  The first time a comet is seen, no one can
tell where it may next day be.  The next observation
still leaves a great uncertainty as to its future course.
The third nails it.  After three good observations, carefully made, of its place, we can thence foretell where it
will go.  Meanwhile, such is the variety of which their
paths are susceptible, that for a very long time their
movements were considered to be altogether capricious
and unaccountable-creatures of chance-governed by
no laws.  Now the case is different.  Most persons will
remember that the comet of 1858 passed on the 5th of
October of that year close to a very brilliant star, Arcturus, which shone through its tail at a very little distance
from its root or outspring from the head.  Well! within
a very short time from the first appearance of that comet,
while yet it was but a faint object, it was known to calculating persons that it wozldpass over Arcturus-the
day-the hour-nay, almost the minute when the nucleus
of the comet would be closest to the star were predicted
-and the prediction was exactly verified.  How  this
could happen I must now proceed to explain; but before
I do so, I must premise that my hearers are not to be
startled if I use some words that are not familiar to many
oi them, and ask for a little more of their attention than
if I were merely telling some amusing story.  What I am




100                 ON COMETS.
going to say will be already well known to a portion of
them, but will be quite new to many,-and I will try to
put it in' such a way as shall not only be clearly intelligible, but shall stick by them, and become part and parcel
of their minds and thoughts henceforward-and I am
mistaken if many of this class of hearers (provided they
will give me the attention the thing requires) do not rise
from the perusal of this brief statement with much larger
and higher conceptions of the magnificent system  we
belong to than they commenced it with.
(8.) The sun, as we all know, or may have heard, stands
immovable, or nearly immoyable, in the centre of our
system, and all the planets, including the earth, circulate
or revolve round it, each in its own time and at its own
proper distance.  These distances, for each planet, stand
to each other in relations of proportional magnitude,
which have become, by a long course of astronomical
observation and calculations, known to us with extreme
exactness, so that if the exact distance of any one of the
planets from the sun, or the exact interval between any
two of their orbits, can anyhow be ascertained in miles,
yards, or feet, the dimensions of all the rest in similar
units of measure may thence be derived.  Supposing,
for instance, we knew.exactly the interval between the
orbits of the earth and Mars, then if we would know the
respective distances of the several planets in their order
from the sun, it would only be necessary to multiply
that interval, in the case of Mercury, by the decimal
fraction 07392; in that of Venus by I'3812; of the
Earth by I'9095; of Mars by 2'9095; of Jupiter by




ON COMETS.                    IOI
9'9349; of Saturn by I82I146; of Uranus by 36-6293;
and of Neptune, the most distant of the known planets,
by 57'355I.*
Now the interval between the earth's orbit and that
of Mars (or the distance between that planet and the
earth when they approach nearest) has quite recently
been ascertained by a concerted system of observation,
made during the past year, in which the astronomers in
all the principal observatories of the globe have borne a
part, and of which the final result has only within these
few weeks become known.  From these observations, so
far as they have as yet been conmmunicated and reduced,t
it has been concluded that the interval in question is
607I diameters of the earth, and as we know to a great
nicety, by actual measurement of the earth's circumference, that its diameter is 79I21 miles, we are enabled
at once to reduce the distance  so obtained into miles
(which gives 48,036,200 miles), and thence, as above indicated, to derive the earth's distance from the sun,
which comes out 91,718,000, or about 92 millions of
miles; and in the same way we may obtain the numerical
dimensions in miles of the orbits of all the other planets,
as also the sun's actual diameter, which appears to be
852,600 miles.
(9.) Such of our readers as may take the trouble to compare the distances and dimensions here set down with
* We consider in this and what follows, the orbits as circles, which
is quite sufficient for purposes of illustration.
t Some time will probably elapse before our whole series can be
collected and finally reduced.




102                  ON COMETS.
those stated in my paper on the sun in the last lecture,
will not fail to observe that they are materially smallerby one thirtieth part of their respective amounts.  The
numbers there stated are in accordance with the state of
our knowledge accepted at the time when that lecture
was delivered, which rested for its basis on observations made upon Venus at the time of her transit across
the sun's disc in the year I769-observations by which
the nearest distance of the orbits of Venus and the earth
was concluded in terms of the earth's diameter, on the
same general principle, though by a somewhat more refined and circuitous process, as that from which the
least distance of Mars has just now been derived. As
the circumstances of this earlier determination (delicacy
of instruments and means of observation alone excepted)
were much more favourable to exactness, astronomers
would have hesitated in accepting the more recent conclusion in preference to the former, were it not for the
support and corroboration it derives from another determination, also quite recent (though somewhat prior in
point of date), depending on a direct measurement of
the velocity of light by a peculiarly ingenious and delicate
process invented and executed by M. Foucault. To explain the nature of this process here would lead me too
far away from the immediate object of this discourse, from
which, indeed, the whole of what is above said on the
distance of the sun and planets would be justly considered as a digression were it not in some sort obligatory on every one to account for a departure from
numerical statements once made.  Suffice it therefore




ON COMETS.                    I03
to say that the velocity of light so concluded was found
to be somewhat less (and that by about one 3oth part)
of that which had been hitherto received (192,000 miles
per second) and which was concluded from the observed
fact of its traversing the diameter of the earth's orbit in
I6m. 26sec. of time, and very considerably less than that
before obtained by M. Fizeau, with a less perfect apparatus, and a less delicate and refined system of procedure.
Now it will not fail to be remarked, that the time (I6m26se') remaining unaltered, and the velocity dimintished
by one 30th, the distance traversed (the diameter of the
orbit) in that time will also be diminished by the same
aliquot fraction, so that there is a coincidence between
the two corrections of the sun's distance, which, coming
simultaneously, from such very different sources, cannot
but lead to their acceptance, at least provisionally, and
until the recurrence of that grand phoenomenon, the
transit of Venus, which will take place in the year I874,
shall put an end to all uncertainty on the subject of the
true numerical dimensions of our system.
(io.) Bearing now these dimensions in mind, let us
construct in imagination a figure consisting of concentric
circles, to represent the orbits of the planets. Taking
the largest, that of Neptune, as 30 feet in diameter, then
will that of Uranus measure a little more than I9 feet
across, of Saturn somewhere less than io, of Jupiter rather
more than 5, of Mars about i8 inches, and of the earth a
foot, while the enormous body of the sun will stand represented in the centre of all by a pellet of very little more
than one-ninth of an inch in diameter-the orbits of




104                 ON COMETS.
Mercury and Venus by circles of 41 and 9 inches respectively-that of the moon above the earth by one 15th of
an inch, and the globe of the earth itself by a dot barely
the thousandth part of an inch in size.
(ii.) Strictly speaking, the orbits are not circles-they
are slightly oval, or, as it is called, elliptic in form, and
the sun does not occupy their common centre, but what
is called the focus of each; that is to say, one of the two
pins round which an ellipse may be described by carrying a pencil round them  confined by a looped string
encircling them both.  The planetary orbits, moreover,
all lie nearly in one plane, or very slightly inclined to
that in which the earth performs its annual revolution,
which is called the plane of the ecliptic-the angle at
which the plane of each orbit meets and cuts this, being
called its inclinzaion to the ecliptic.  They all circulate
the same way round the sun, and the farther they are
from the sun the slower they move-so that while the
earth goes round it in 365 days, Mercury occupies only
88 in its revolution, while Neptune requires no less than
i68 years to complete one of his circuits.
(12.) When we come to the comets, however, we find a
very different state of things. A comet, it is true, moves
round the sun as his centre of motion: not, however, in
a circle, or any approach to a circle, but (with a very
few, and those highly remarkable exceptions) in an immensely elongated, or, as it is termed, a very eccentric
ellipse.  In consequence, the nearest distances to which
they approach the sun bear almost universally an exceedingly small proportion to those they attain when most




ON COMETS.                  o10
remote, that is to say, at the two extremities of their
elliptic orbits, or what are termed their perihelion and
aphelion.  By far the great majority approach it at their
perihelion near enough to arrive within the earth's orbit
-very many within that of Venus, or even of Mercury
-and not a few attain an extreme proximity to the
actual surface of the sun, while on the other hand only
four or five among the vast number of recorded comets
(those of I747, 1826, I835, I847) have failed to arrive
within twice the earth's distance, or within the orbits of
those small planets called asteroids; and one only has
had a perihelion distance exceeding four times the earth's
distance (that of 1729), still falling short of the orbit of
Jupiter.  Probably, however, a comet, which should
always remain outside of the latter planet's orbit, would
have no chance of ever being seen by us. As to the
extreme distances to which they recede from the sun, it
is only in comparatively few instances that it can be even
estimated-their ellipses being in general so elongated
as to be undistinguishable from that extreme and limiting form which is called a parabola, which never returns
into itself at all. The form of this curve is that which a
stone thrown into the air describes, or which a jet of
water thrown up obliquely by a smooth round pipe
assumes in the air, being very much curved or bent
about the point which is called the vertex, and less and
less so in the ascending and descending branches.
(I3.) Comets, we have said, are wild wanderers, and
despise beaten tracks. No way confined, as the planets
are, to move in planes nearly coincident with the ecliptic,




I06                  ON COMETS.
they cut across it at every possible angle, and, as nearly
as can be ascertained (with exception of one small class
of comets), quite indifferently as to the degree of their
inclination, or to the direction of the longer axes or longest dimensions of their orbits in space; so that there is
no region of space, however situated either in direction
or distance from the sun, which a comet may not visit.
Neither do they conform to that other universal planetary rule of circulation round the sun in one direction.
Retrograde comets, or those whose motion is opposite to
that of the planets, are as common as direct ones, or
those which conform to the planetary rule. Here again,
however, there is a small class in which a tendency to
conformity is exhibited, co-extensive with that above
noticed, which affects a certain proximity to the ecliptic.
But of this we shall have occasion to speak more at
large.
(i 4.) It is only when all the particulars which determine
geometrically the situation and the form of the orbit of
a comet, its nearest distance from  the sun, and the
direction in which it is moving,-or what are called the
elements of its orbit,-that it can be ascertained whether
it has ever been seen before, and whether we are to
expect ever to see it again; and that its future course,
while it remains invisible, can be predicted with certainty. These elements are technically calledi. The perihelion distance, or nearest approach to the
sun.
2. The eccentricity of its ellipse, or whether the orbit
be sensibly a parabola.




ON COMETS.                   I07
3. The inclination of its plane to the ecliptic.
4. The longitude of its node, or the direction of the
line in which its plane intersects the ecliptic,
which is called the line of its nodes.
5. The longitude cf its perihelion, or, which comes to
the same thing, the angle which the axis of the
orbit makes with the line of nodes.
6. The exact moment when the comet passed through
its perihelion, or was nearest to the sun.
7. The  direction of its motion (direct or retrograde).
(I5.) It is natural to ask how all these particulars ever
can be known; and to this the answer is-By the same
system of observation and calculation combined, by which
we have come to know the form and dimensions of the
orbits of the planets, their times of revolution round the
sun, and their situation in space.
( 6.) I believe it was Tycho Brahe, a celebrated Danish
astronomer, who first rose to the conception that comets
are beyond the moon, and not mere exhalations.  The
appearance of a great comet in I577 set him thinking
about it, and he was led by his observations and reasonings on them to a certain knowledge of the fact of its
being much more remote than our own satellite; and he
was therefore led to conjecture that the motions of
comets had reference rather to the sun as their centre
than the earth. The elliptic form of the planetary orbits
was not then known, and Tycho accordingly supposed
that comets moved about the sun in perfect circles.
Borelli, a Neapolitan mathematician, suggested the idea




108                  ON COMETS.
of a long ellipse or parabola as the possible form of a
comet's orbit; and Dirfel, a German astronomer in
I68I, upon a careful consideration of all the observations of the great comet of i680, came to the positive
conclusion that that comet did really move in a parabolic
orbit with the sun in its focus. This was an immense
step; but neither Dirfel nor any one else could at that
time give any account of the reason why this should be
the case, or in what manner the comet was made to conform its sweep through space in so singular a way to the
sun.
(I7.) The wonderful discoveries of Sir Isaac Newton
made all this clear.  He first showed that the sun controls
the movements of these wanderers by the very same force
acting according to the very same law which retains the
planets in their paths-that marvellous law of gravitation-the same power which draws a stone thrown from
the hand back to the earth (in a parabolic curve)which keeps the moon from flying off, and holds her to
us as a companion-which keeps the planets in their
circles, or rather ellipses, about the sun-and which we
now know holds together several of the stars in couples,
circulating one about the other.
(18.) The great comet of i680, which occurred while
Newton was brooding over these grand ideas which
broke upon the world like the dawn of a new day in his
"Principia," afforded him a beautiful occasion to test
the truth of his gravitation theory by the most extreme
case which could be proposed. The planets were tame
and gentle things to deal with. A little tightening of




ON COMETS.                    109
the rein here and a little relaxation there, as they careered round and round, would suffice perhaps to keep
them  regular, and guide them  in their graceful and
smooth evolutions.  But here we had a. stranger from
afar-from  out beyond the extremest limits of our system-dashing in, scorning all their conventions, cutting
across all their orbits, and rushing like some wild infuriated thing close up to the central sun, and steering
short round it in a sharp and violent curve with a speed
(for such it was) of 1,200,000 miles an hour at the
turning poiht, and then going off as if curbed by the
guidance of a firm  and steady leading rein, held by a
powerful hand, in a path exactly similar to that of its
arrival, with perfect regularity and beautiful precision;
in conformity to a rule which required not the smallest
alteration in its wording to make it applicable to such
a case.  If anything could carry conviction to men's
minds of the truth of a theory, it was this. And it (lid
so.  I believe that Newton's explanation of the motions
of comets, so exemplijfed, was that which stamped his
discoveries in the minds of men with the impress of
reality beyond all other things.
(19.) This comet was perhaps the most magnificent ever
seen.  It appeared from November i68o to March i68I.
In its approach to the sun it was not very bright, but
began to throw out a tail when about as far from the sun
as the earth.  It passed its perihelion on December 8and when nearest was only one-sixth part of the sun's
diameter from his surface-one fifty-fourth part of an inch
on the conventional scale of our imaginary figure, and at




IIO                 ON COMETS.
that moment had the astonishing speed I have just mentioned.  NIow observe one thing. The distance from the
sun's centre was about one i6oth part of our distance
from it. All the heat we enjoy on this earth comes from
the sun. Imagine the heat we should have to endure it
the sun were to approach us or we the sun to 4 —th part
of its present distance.  It would not be merely as if
60o suns were shining on us all at once, but I6o times
60, according to a rule which is well known to all
who are conversant with such matters.  Now that is
25,600. Only imagine a glare 25,600 times fiercer than
that of an equatorial sunshine at noonday with the sun
vertical. And again, only conceive a light 25,600 times
more glaring than the glare of such a noonday! In such
a heat there is no solid substance we know of which
would not run like water-boil-and be converted into
smoke or vapour.  No wonder it gave evidence of violent excitement-coming from the cold region outside
the planetary system, torpid and icebound; already when
arrived even in our temperate region it began to show
signs of internal activity-the head had begun to develop
and the tail to elongate till the comet was for a time lost
sight of. No human eye beheld the wondrous spectacle
it must have offered on the 8th December. Only four
days afterwards, however, it was seen: and its tail, whose
direction was reversed and which (observe) could not
possibly be the same tail it had before-(for it is not to
be conceived as a stick brandished round, or a flaming
sword, but fresh matter continually streaming forth),-its
tail I say had already lengthened to an extent of about




ON COMETS.                    III
go millions of miles, so that it must have been shot out
with immense force in a direction from the sun, a force
far greater than that with which the sun acted on and controlled the head of the comet itself, which, as the reader
will have observed, took from November  o to December 8,
or 28 days, to fall to the sun from the same distance, and
that with all the velocity it had on November I o to start
with.
(20.) All this is very mysterious. We shall never perhaps
quite understand it, but the mystery will be at all events
a little diminished when we shall have described some of
the things which are seen to be going on in the heads
of comets under the excitement of the sun's action, and
when calming and quieting down afterwards. At present, however, we must get on with another part of our
subject.
(21.) Only two years after this appeared another brilliant comet, and our countryman, Edmund Halley, following Newton's example and employing his system of
calculation, computed its orbit, assuming (which simplifies the calculation very much) that orbit to be a parabola.  He found its path to be very different from that
of Newton's comet.  Instead of nearly grazing the surface of the sun, its nearest approach to it was about 55
millions of miles, or about half-way between the orbits of
Mercury and Venus.  The plane of its motion, too, was
much less inclined to that of the planets' orbit or the
ecliptic-viz., about 173, and its motion was not direct,
as Newton's was, but retrograde.
(22.) Halley was encouraged by the good agreement of




112                  ON COMETS.
his calculations with the observed places of this comet
to collect observations of former comets, and endeavour to make out their paths, or, as we now express
it, to determine the elements of their orbits. With incredible labour he calculated the orbits of twenty-four
remarkable comets, and among them  he found two
whose "elements" agreed in a:remarkable manner with
those of his first comet-both great comets, viz., one.
observed by Appian in I53I, and one by Kepler in
i6o7, and he noticed also this fact, this remarkable approximate coincidence-from 153I to 1607 is 76 years,
and from I6o7 to 1682 75 years.  This led him to suspect that all three were one and the same comet, returning periodically; and guided by this idea he was led to
examine the records of history for comets of earlier date.
Among them, three turned up-in the years 1305, I380,
1456-and when all these years are arranged in a series,
you see that the intervals are alternately 75 and 76
years. This confirmed him in his impression of its periodical return; and emboldened him to predict its return
about the end of I758 or beginning of I759.  You will
observe that he allowed more than an average length of
the period (77 years) for the fulfilment of his prediction.
He had a reason for this.  He ascertained that in coming back it would pass near the planet Jupiter, which is
a large and massive planet, and Newton's discoveries had
already taught him to contemplate the possibility of some
disturbance of its motion from the attraction of such a
body, and even enabled him to perceive that it would
act to retard the return or prolong the period.  Such




ON COMETS.                     113
disturbances do really exist, and have often very considerable effects on the return of comets.   This very
comet, in the table of its returns set down in the note
below,* offers some striking examples.  There occurs, for
instance, I378 A.D. and not I380 set down for one of the
epochs of its appearance, with 78 years interval between
that and 1456. The fact is that Halley was mistaken in
supposing either the comet of 1305 or that of I380 to be
the same with that in question.  That comet really appeared in 1378, but thatfact  alley had no means of knowing.  It has very lately come to light on searching the
Chinese annals.  And the same annals have informed us
of no less than six other still more ancient appearances
of this selfsame comet, the earliest in the iith year before our Saviour.  And this, it must be allowed, greatly
tends to increase our confidence in those venerable records of Chinese  history.   All this apparent irregularity is owing to the action mainly of Jupiter, which is
a general disturber of comets, and gives a vast deal of
trouble to  calculators, as I shall. soon  explain; and
Saturn is not without a finger in the pie.
(23.) This prediction of Halley's, as the time for its
accomplishment drew near, created a great sensation-all
the astronomers furbished up their telescopes, and all
the mathematicians set to work to calculate.   The
mutual actions of the planets in that long interval had
been well studied, and it was clearly ascertained that
* A.D. 451, July 3; 760, June I; 1378, Nov. 8; I456, June 8;
153I, Aug. 24; 1607, Oct. 26; I682, Sept. 14; 1759, March 12;
1835, Nov. 15.
H




114                 ON COMETS.
Halley was right in his conjecture about Jupiter, and
that in fact the return of the comet would be delayed by
the attraction of that planet 518 days, and by that of
Saturn ioo more, and that it would make its next closest
approach to the sun within a month one way or another
of the I3th of April 1759.
(24.) All the astronomers of Europe were looking out
for it, eager to seize it on its first coming within the range
of human vision.  They were all disappointed of their
prize.  It was carried off by a Saxon farmer of the name
of Palitzch, an astronomer of Nature's own creating,
who was always watching the heavens,-without telescopes, without knowledge,-simply from the profound
interest their aspect inspired him with.  He it was who
first caught sight of it, on the I3th December I758.  It
was taken up by others and regularly observed.  It
passed its perihelion on the I3th of March, just within
the limit of possible uncertainty the mathematicians had
allowed for their calculations.
(25.) This was certainly a very great and signal triumph.
It was repeated, with every circumstance that could
make it decisive or give it notoriety, in the year I835,
the epoch of the next appearance of "Halley's Comet."
The calculation of the planetary perturbations (as the
disturbances they cause in each other's motions are
called) had then been brought to great perfection. The
passage through the perihelion was predicted by M.
Pontecoulant to take place  on the I2th November,
and by Rosenberger between the IIth and i6th.  In
point of fact, it happened on the I5th. And this time,




ON COMETS.                    115
too, the astronomers were not- beaten by the farmers,
Their telescopes were from day to day pointed right on
the spot where it would be sure to appear-which was
advertised all over the world in the almanacs; and it
was caught at the earliest possible moment, and pursued
till it faded away into a dim mist.
(26.) When lost to European astronomers (for, like
those of 1858 and I86I, it ran southwards), Mr Maclear
and myself received it in the southern hemisphere; and
it was fortunate we did so; for, extraordinary as were the
appearances it presented on its approach to the sun, they
vere if possible surpassed by those it exhibited afterwards; and the whole series of its phaenomena has given
us more insight into the interior xconomy of a comet and
the forces developed in it by the sun's action, than anything before or since.
(27.) When first it was seen, it presented the usual aspect
of a round misty spot, and by degrees threw out a tail,
which was never very long or brilliant, and which to the
naked eye or in a low-magnifying telescope appeared
like a narrow, straight streak of light, terminating in a
bright head; which in a telescope of small power appeared capped with a kind of crescent; but in one of
great power exhibited the appearance of jets, as it were,
of flame, or rather of luminous smoke, like a gas fanlight.  These varied from  day to day, as if wavering
backwards and forwards, and as if they were thrown out
of particular parts of the internal nucleus or kernel,
which shifted round, or to and fro, by their recoil, like a
squib not heldfast. The bright smoke of these jets, how



ii6                 ON COMETS.
ever, never seemed to be able to get far out towards the
sun, but always to be driven back and forced into the
tail, as if by the action of a violent wind setting against
them,-alwaysfrom the sun,-so as to make it clear that
this tail is neither more nor less than the accumulation
of this sort of luminous vapour darted off in the first
instance TOWARDS the sun, as if it were something raised
up, and, as it were, exploded by the sun's heat, out of
the kernel, and then immediately and forcibly turned
back and repelledfrom the sun.
(28.) As this comet approached the sun, its tail, far
from increasing, diminished; and between the middle of
November and the 2Ist of January, strange to say, both
head (that is coma) and tail were altogether destroyed,
or at least rendered invisible. On the 2Ist of January
the comet was actually seefi like a small star without any
tail or any haziness, and was only known not to be a star
by being exactly in its calculated place, and by its not
being there next night. After that its head seemed to
form again round this star, and grew rapidly and visibly
from night to night, putting on appearances which could
not be clearly apprehended without elaborate figures.
This growth of the comet was so very rapid, that in the
interval of 17 days from the time I first saw it as a round
body its real bulk had increased to 74 times the size it
then had-and at the same rate it continued to swell
out, not, however, preserving a round form, but growing
longer in proportion to its breadth as if it intended to
develop a new tail. But this it never did —the dilatation
or swelling out continued, and at one time it had exactly




ON COMETS.                    I17
the appearance of a ground glass lamp-the light always
becoming fainter and fainter, till it at last seemed to pass
away from  view from  mere faintness.  All this while,
however, there was a sort of smaller and much brighter
interior comet visible, with a tail-like appendage, which
seemed to be as it were a conducting channel by which
the matter of the newly-forming head was gradually retreating back into the centre.
(29.) The discovery of the periodical return of Halley's
comets forms an epoch in the history of their bodies.
Since that time a great many more have been ascertained to return at regular intervals. I will mention some
of the most remarkable cases of this kind.
(30.) In I770 a comet appeared which proved rebellious
to the then adopted system of calculation, which set out
with assuming the orbit to be a parabola. It very soon
appeared, by'the calculations of M. Lexell, that the real
orbit was an ellipse, and that not a very eccentric one.
In fact, all the observations were perfectly consistent with
an ellipse nearly coincident with the plane of the earth's
orbit, of such dimensions as that the extreme excursion
from  the sun would carry it over a little beyond the
orbit of Jupiter, and its nearest approach would bring it
within that of Venus-the time of its revolution being
51 years. Here was quite a new fact. All other comets
then known had run out to limits far beyond our system
-since even Halley's, with its period of 76 years at its
greatest distance from the sun, passed very far beyond
the orbit of Saturn, the most distant planet then known,
and in fact beyond the two since discovered, Uranus and




118                 ON COMETS.
Neptune.  But here we seemed to have quite a sort of
tame comet keeping within bounds, and within call. Of
course its return was watched for with eagerness, but
alas! it never made its appearance again. At its next
return in 1776 this was well accounted for, as owing to
the relative situations of the earth, sun, and comet, it
could not have been visible; but at the next, in 178I,
the earth was favourably situated, since 5- years would
place the sun in the opposite part of its orbit; but I 
years in the same, and the calculators for a time were
puzzled.  The solution of the enigma was a very strange
one.  The poor comet had got bewildered.  It had
plunged headlong into the immediate sphere of Jupiter's
attraction-had intruded, an uninvited guest, into his
family circle-actually nearer to him than his fourth
satellite, and into a situation where Jupiter's attraction
for it was two hundred times that of the sun.  Of course
its course was for a time commanded entirely by this
new centre of motion, and the comet was completely
diverted from its former orbit.
(31.) So far all was clear enough.  But people began
to ask how, with so short a:period, and being a tolerably
large comet, it had never been seen before 2  Here again
Lexell called Jupiter to the rescue. As he had taken
away, so it turned out he had given. Jupiter, it will be
borne in mind, comes round to the same point of his
orbit in Ii years and io months; two of the comet's revolutions would occupy iI years and 3 months, so that
tracing back the comet two revolutions in its ellipse, and
Jupiter rather less than one in his circle from the place




ON COMETS.                    119
of their final rencontre, which took place in I779, it is
clear they could not have been far asunder in 1767, 3
years before it became visible; and in fact, on executing
the calculations necessary, it was clearly proved that
before I767 this unhappy comet had been revolving in
a totally different orbit of much greater dimensions, and
was actually siezed upon then and there by Jupiter,
flung as it were inwards-and then after making two
visits to the sun, again seized on, and thrown off into
space, into an orbit of 20 years' period, where perhaps
it may be quietly circulating to this day.  Jupiter, in
fact, is a regular stumbling-block in the way of comets.
(32.) This is a strange history-but it proved a very
instructive one.. The comet passed, as I have said,
through the system  of Jupiter's satellites.  N ow  the
motions of these bodies have been studied with a degree
of care and precision quite remarkable by reason of their
furnishing one of the means for ascertaining the longitudes of places.  And if the comet had been a heavy
massive body, its attraction must have produced some
sensible disturbance in their motions. But no, not a
trace of anything of the kind was detected.  One and
all of them pursued their courses with the very same
precision and regularity as if nothing had happened.
The conclusion is irresistible.  Tha]t comet at least had
no sensible weight or mass-it was a mere bunch of
vapours.
(33.) Another very remarkable periodical comet is that
of Encke, which makes its circuit about the sun in I200
days, or about 3 years and 4 months, in the same




I20                  ON COMETS.
direction as the planets.  It is but a small one, being
seldom visible without a telescope.  Its orbit was first
computed on its appearance in I795 (when it was discovered by Miss C. Herschel), and again in 1805 and
1819.  Upon this last occasion M. Encke, an eminent
computist, found that its motion could not be explained
without supposing it to move in an ellipse of the last
period I have mentioned-and on searching back into
the records of comets he found those two I have just
named, which agreed perfectly, and proved to have been
really the same.
(34.) Since that time it has been re-observed on every
subsequent revolution in'22,'25,'29,'32,'35,'38,'42,'45,'48,'5 I,'55, and is always announced in the almanacs
as a regular member of our system. Its nearest approach
to the sun brings it just within the orbit of Mercury, and
on one occasion that planet happened to be so very near
it on its arrival, that it produced a pretty considerable
disturbance of the comet.  But here, too, as in the case
of Lexell's comet, not the smallest perceptible effect was
produced by the comet on the planet; and thus two
valuable pieces of information were gained.  First; Astronomers were enabled to estimate the mass or weight
of that small planet better than by any other means; and
secozndly; It was proved that this comet also has no perceptible weight-and is also a mere puff of vapour, or
something as unsubstantial.
(35.) There is another strange fact which this comet
has revealed.  Its successive revolutions are each a little
shorter than the last-a small fraction of a day, it is true,




ON COMETS.                    121
but still unquestionably made out. This has been held to
prove that the comet is by very slow degrees approaching
the sun, and will at last fall into it-as if it moved in a
space not quite empty, and were in some very slight
degree resisted in its motion.  I cannot quite reconcile
myself to this opinion, and I think I have perceived
another explanation of the fact, which I have given elsewhere; but to state this would lead me too far, and i
must now go on to relate one of the strangest and most
uncouth facts of this strange cometic history.
(36.) On the 27th February I826, Professor Biela, an
Austrian astronomer of Josephstadt, discovered a small
comet.  When its motions were carefully studied it was
found by M. Clausen, another of those indefatigable
German computists, that it revolved in an elliptic orbit
in a period of 6 years and 8 months. On looking back
into the list of comets, it proved to be identical with
comets that had been observed in I772, 1805, and
perhaps in I8I8. Its return was accordingly predicted,
and the prediction verified with the most striking exactness.  And this went on regularly till its appearance
(also predicted) in 1846.  In that year it was observed
as usual, and all seemed to be going on quietly and comfortably, when behold! suddenly on- the I3th of January
it split into two distinct comets! each with a head and
coma and a little nucleus of its own.  There is some
little contradiction about the exact date.  Lieutenant
Maury, of the United States Observatory of Washington,
reported officially on the I 5t/ having seen it double on the
I 3t/, but Professor Wichmann, who saw it double on the




122                  ON COMETS.
I/51z, avers that he had a good view of it on the I4th,
and remarked nothing particular in its appearance. Be
that as it may, the comet from a single became a double
one.  What domestic troubles caused the secession it is
impossible to conjecture, but the two receded farther
and farther from  each other up to a certain moderate
distance, with some degree of mutual communication and
a very odd interchange of light-one day one head being
brighter and another the other-till they seem to have
agreed finally to part company. The oddest part of the
story, however, is yet to come.  The year I852 brought
round the time for their reappearance, and behold! there
they both were, at about the same distance from each
other, and both visible in one telescope.
(37.) The orbit of this comet very nearly indeed intersects that of the earth on the place which the earth occupies on the 3oth of November.  If ever the earth is to
be swallowed up by a comet, or to swallow up one, it will
be on or about that day of the year.  In the year 1832
we missed it by a month.  The head of the comet enveloped that point of our orbit, but this happened on the
29th of October, so that we escaped that time.  Had a
meeting taken place, from what we know of comets, it is
most probable that no harm would have happened, and
that nobody would have known anything about it.'
* It would appear that we are happily relieved from the dread of
such a collision. It is now (Feb. I866) over due! Its orbit has
been recomputed and an ephemeris calculated. Astronomers have
been eagerly looking out for its reappearance for the last two
months, when, according to all former experience, it ought to have




ON COMETS.                      I23
(38.) The number of comets whose periodical return
has been calculated is pretty considerable. Altogether
about 36; and of these there are 5 which revolve in
periods of from 70 to 80 years, and several of the rest in
short periods from 3 to 7 years; and it is a very remarkable feature in their history that all the comets of short
period, and three out of the five of those of the larger
ones specified, revolve in the same direction round the
sun as the planets, and have their orbits inclined at no
very large angles to the ecliptic.
(39.) Of comets not periodical, I have already mentioned that most remarkable one of I680, but several
others deserve special notice. That of I744 was a truly
wonderful object.  It is described, and has been depicted,
with six tails spread out like an immense fan-extending
30~ from the head-which is fully the extent of the tail of
the comet of 1858; and the appearance of its head when
viewed through a telescope exhibited the same sort of
jets of luminous smoke, the same curved envelopes and
arches as'I have already described, showing the same
kind of excitement by the sun's heat, and the same
action driving the vapour back into the tail.
(40.) The comet of I843 was still more remarkable.
Many of my hearers, I dare say, remember its immense
been conspicuously visible-but without success! giving rise to the
strangest theories. At all events it seems to have fairly disappeared,
and that without any such excuse as in the case of Lexell's, the preponderant attraction of some great planet. Can it have come into
contact or exceedingly close approach to some asteroid as yet undiscovered; or, peradventure, plunged into and got bewildered among
the ring of meteorolites, which astronomers more than suspect?




124                  ON COMETS.
tail, which stretched half-way across the sky after sunset
in March of that year.  But its head, as we here saw it,
was not worthy such a tail. Farther south, however, it
was seen in great splendour.  I possess a picture by Mr
Piazzi Smythe, Astronomer-Royal of Edinburgh, of its
appearance at the Cape of Good Hope, which represents
it with an immensely long, brilliant, but very slender and
forked tail. Of all the comets on record, that approached
nearest the sun-indeed, it was at first supposed that it
had actually grazed the sun's surface, but it proved to
have just missed by an interval of not more than 80,ooo
miles-about a third of the distance of the moon from
the earth, which (in such a matter) is a very close shave
indeed to get clear off. There seems very considerable
reason to believe that this comet has figured as a great
comet on many occasions in history, and especially in
the year I668, when just such a comet, with the same
remarkable peculiarity, of a comparatively feeble head
and an immense train, was seen at the same season of
the year, and in the very same situation among the stars.
Thirty-five years has been assigned with considerable
probability as its period of return, but it cannot be regarded as quite certain. (It will of course be understood
that the return of a great comet to the neighbourhood of
the sun by no means implies that it should be a conspicuous one, as seen from the earth. The phase of its
greatest development may be, and is, indeed, more likely
than not to be, ill-timed, as regards the relative situations
of the earth and sun, for its exhibition as a great celestial phenomenon.)




ON COMETS.                   125
(41.) Another great comet which has assumed a sort of
historical and political importance is that which appeared in A.D. I556.  According to the account of
Gemma, it would not seem to have been a very large
one, as he assigns to it a tail of only four degrees long.
Its head, however, equalled Jupiter in brightness, and in
size was estimated at about one-third or one-half of the
diameter of the moon.  It appeared about the end of
February, and on the I6th of March is described by
Ripamonte as a really terrific object.  Terrific indeed
it might well have been to the mind of a prince prepared
by the most abject superstition to receive its appearance
as a warning of approaching death, and as specially sent,
whether in anger or in mercy, to detach his thoughts
from earthly things, and fix them on his eternal interests. Such was its effect on the Emperor Charles V.,
whose abdication of the imperial throne is distinctly
ascribed by many historians to this cause, and whose
words on the occasion of his first beholding it have
even been recordedHis ergo indiciis me mena ofca " v c "
the language and the metrical form of which exclamation
afford no ground for disputing its authenticity, when the
habits and education of those times are fairly considered.
This comet has been supposed to be periodical, and to
return in 29I years, on the ground of the prior appearance of great comets in the years 975 and 1264 (at intervals, that is, of 289 and 292 years respectively), and
the general agreement of their orbits, so far as could be




126                 ON COMETS.
made out from the imperfect records we possess of their
courses, with that of the comet in question. The next
return, on this supposition, would have fallen about the
year I846 or I847.  It did not, however, appear at that
epoch, nor in any subsequent year up to the present
time, although, from some very elaborate calculations by
Mr Hind and Professor Bomme (too elaborate, it would
appear, to have been bestowed on the imperfect records
we possess of its previous history) it should have been
delayed by planetary perturbations for several. years beyond that date, and even so late as to the year 1858
or i860.
(42.) Accordingly, when the three great comets, whose
arrival in and since the year I858 has so surprised and
delighted the astronomical world, made their successive
appearances, there were few persons at all acquainted
with cometary history whose first impression was not
that of the return of " Hind's Comet," as it had grown
to be called, from the eminent calculator and mathematician who had bestowed so much pains on it. This,
however, it is needless to observe, was not the case.
Neither of them  had ever been seen before, nor can
either of them ever be expected to appear again, unless
to a posterity which may look back on our record of
them as we do on those ancient Chinese annals already
spoken of.  Of these, by far the most magnificent
in point of mere display, as well as the most interesting, when contemplated in a physical point of view,
was that of i858 (the fifth of that year), or Donati's
comet, as it is now called, from the astronomer of that




ON COMETS.                   I27
name, who first observed it at Florence on the 2d of
June, at which time it appeared only as a round misty
patch or "nebula."  This was about a month after it
had passed from the southern to the northern side of
the plane of the earth's orbit: and that of the comet
being very highly inclined (63~) to the ecliptic; its perihelion lying also on the north side of that plane; its
motion being retrograde, and the earth accordingly advancing to meet it;-all these favourable circumstances
concurring, it so happened that our nearest proximity to
it occurred only six days after its "perihelion passage"
or time of nearest approach to the sun, which took place
on the 29th of September, and in a situation with respect
to the sun every way advantageous to obtaining a good
view of it. Accordingly, with the.exception of the comet
of Halley in I835, no comet on record has been watched
with such assiduity, or been more thoroughly scrutinized.
A resume of all the observations of it has been recently
published by Professor Bond, forming the third volume
of the "Annals of the Observatory of Harvard College,
in the United States," in which its appearance in every
stage of its progress is represented in a series of engravings, which in point of exquisite finish and beauty of
delineation leave far behind everything hitherto done in
that department of astronomy.
(43.) It was not till the I4th of August, or 73 days after
its first discovery, that it began to throw out a tail, and
to become a conspicuous object. Very soon after this,
its first appearance; a slight but perceptible curvature
was perceived in the tail, which, on the i6th of Sep



128                  ON COMETS.
tember, had become unmistakable, and continued to
increase in amount.as the latter extended in apparent
dimension, till it assumed at length that superb aigrettelike form, like a tall plume wafted by the breeze, which
has never probably formed so conspicuous a feature in
any previous comet. To a certain extent, it is a common
enough feature in the tails of comets, and is usually regarded as conveying the idea of their moving in a
resisting medium;-in a space, that is to say, not quite
empty, as smoke is left behind a moving torch.  But
this is a very gross and inadequate conception of the
peculiarity in question.  The resistance of the "ether,"
such  as the phenomena of Encke's comet already
noticed, may be supposed to indicate, is far too infinitesmally small to be competent to produce any perceptible deviation from  straightness.  Nor is it at all
necessary to resort to any such explanation of the fact.
Such an appearance would naturally arise from a combination of the motion the matter of the tail had (in
participation with that of the nucleus) with the impulse
given it by the sun-each particle of it describing, from
the moment of quitting the head, an orbit quite different
from  that of the latter; being necessarily, under the
influence of the repulsive force directed from the sun, a
curve of the form  called by geometers an hyperbola,
nearly approaching to a straight line, and having its convexity turned towards the sun: the visible form of the.tail (be it observed) being, not the perspective view of
such an orbit, but that of the portion of space containing, for the time being, all those particles, each describ



ON COMETS.                      129
ing its own independent orbit, and each reflecting to the
eye its quota of the solar light.*
(44.) A very striking feature in Professor Bond's engravings, which he describes as frequently and certainly
observed in America, and which did not pass wholly
unnoticed in Europe, consists in the appearance of one,
and on some nights two, excessively faint, narrow, and
perfectly straight rays of light, or " secondary tails," starting off from the main tail on its preceding or anterior
side (that towards which the comet was advancing, and
which side was always the brightest, sharpest, and best
defined) in the direction of tangents to its curvature
at points very near the head, and extending on some
nights (on the 4th, 5th, and 6th of October) to a much
greater length than the primary or more luminous tail.
These appearances were presented from  the 28th September to the IIth of October with more or less distinctness. They are peculiarly instructive, as they clearly
indicate an analysis of the cometic matter by the sun's repulsive action-the matter of the secondary  tails being
evidently darted off with incomparably greater velocity
(indicating an incomparably greater intensity of repulsive
energy) than that which went to form  the primary one.
The primary tail also presented another feature, frequently, indeed almost always, observed in comets, viz.,
* Some anomalous appearances in the early development of the
tail in this comet, which was slightly curved, even when the earth
was in the plane of the orbit, can by no means be regarded as
fatal to this explanation of the general phlnoqmenor, as they might
have originated in a lateral direction of projection of the caudal
matter from the nucleus in ipso nhotius iniiio.
I




130                  ON COMETS.
its separation, behind the head, into two main streams
with comparative darkness between them.  This would
be a natural and necessary optical consequence of the
tail consisting of a hollow, conical envelope, streaming
off on all sides around from the head, and presenting to
the eye therefore a much greater thickness of luminous
matter at its edges than at its middle. But in this comet
the separation, when viewed through powerful telescopes,
was singularly sharp; and appeared as a clear, narrow,
straight cut, or dark chink, originating close to the nucleus
(as, indeed, on that explanation of the fact it ought).
And this brings me to treat of the appearances presented
by the head and nucleus under the inspection of powerful telescopes.
(45.) All considerable comets which have been examined with anything like what would in these days be regarded'as apowel;fzdtelescope, have presented the appearance of a nucleus of more or less definable and condensed
light, sometimes having a much brighter and almost
stellar point in or near its centre, and at some distance,
in the direction of the sun,'a capping of light sometimes
quite separated, as if some transparent atmosphere
sustained it-more frequently connected by those fanlike jets of " flame," such as we have mentioned in the
case of Halley's comet, and putting on the aspect of a
"sector," or fan, opening out into a widening arc, and
bounded internally by two crescents springing from the
nucleus. Donati's comet exhibited this feature in perfection; not,'however, without striking variations and
individual peculiarities. There was the same appearance




ON COMETS.                    131
with low magnziyingjpowers of an envelope surrounding
a nucleus in the general way above described, but the
connexion was singularly varied, as if several jets of
luminous (or illuminated) matter had been issuing from
various parts of the nucleus, giving rise, by their more or
less oblique presentation to the eye, to exceedingly
varied appearances-sometimes like the spokes of a
wheel or the radial sticks of a fan, sometimes blotted
by patches of irregular light, and sometimes interrupted
by equally irregular blots of darkness.  From the 24th
September to the ioth October, however, there were
seen to form no less than three distinct caps or envelopes
in front of the nucleus, each separated from that below
it by a more or less distinct comparatively dark interval.  These Professor Bond appears to consider as having been thrown off in intermittent succession, as if the
forces of ejection had been temporarily exhausted, and
again and again resumed a phase of activity; the peculiar
action by which the matter of the envelopes was ultimately driven into the tail (or, as we conceive it, an
analysis of that matter performed by solar action, the
levitating portion of it being hurried off-the gravitatizn
remaining behind in the form of a transparent, gaseous,
non-reflective medium), taking place, not on the surface
of the nucleus, but at successively higher levels.  Meanwhile, and especially from the 7th to the ioth of October,
that is to say, when the full effect of the perihelion action
had been endured, the nucleus and its adjacent sector
offered every appearance of most violent, and, so to
speak, angry excitement, evidenced by the complicated




132                   ON COMETS.
structure and convolutions of the jets issuing from it.
From  this time, to its final disappearance, the violence
of action gradually calmed down, while the comet itself went southwards, and at length vanished from our
horizon.
(46.) An idea of the actual dimensions of this comet
may be formed from the measurements taken by Professor
Bond on the 2d October, which, combined with the distance of the comets from  the earth at that date afford
the following results, viz.:Miles.
Diameter of the bright internal pellet or nucleus,.  I,600
Distance from its centre to the summit of the
first envelope,....     7,500
Distance to that of the second envelope,.      3,200
Bieadth of the brightest part of the tail where it
seemed (to the naked eye) to issue from the
comet,...            o,ooo0
to which it may be added that the actual length of the
tail, when at its greatest development, could not have
been less than 30 millions of miles, and those of the
faint streaks or secondary tails 34 or 35 millions.
(47.) The comet of I861, which burst suddenly on us in
its full splendour on the 3oth of June in that year (though
it had been seen for seven weeks before in the southern
hemisphere), was considered by those who saw it at its
first appearance to surpass in brightness even that of
1858, and was remarkable for the extreme breadth and
diffusion of its tail when first seen, arising from the circumstance of the earth having been then situated nearly
in its prolongation. Indeed, it is not impossible that on
that day we actually traversed some portion of it, our




ON COMETS.                  I33
distance from the head being then only about I3,000,000
miles, and more than one observer having noticed and
been much struck with an unusual and general brightness,
like an auroral light not confined to the neighbourhood
of the comet, but spreading over the whole sky. The
most remarkable peculiarity of this comet, however, consisted in the enormous length which one side of its tail
attained between the 2d and the 4th of July, extending
in a perfectly straight but feeble ray from near the star
Alpha in the Great Bear, to and beyond that designated
by the same letter in Ophiuchus, or over 75 degrees in
angular measure, contrasting strikingly with the stunted
development and bushy aspect of the opposite branch.
Its head, when viewed with good telescopes, exhibited
the same general. phaenomena of luminous jets and
crescent-like emanations as its predecessor, but much
less complex and varied. Owing to the great inclination
of its orbit, this comet, coming to us from the southern
side of the ecliptic, soared high above it on the northern
side and remained long and conspicuously visible as a
cricuvpolar object, the whole of its diurnal course being
above our horizon.  Not so its successor of 1862, whose
orbit being but slightly inclined to our own, its motion
retrograde (or meeting the earth), its perihelion distance
almost exactly equal to our distance from the sun, and
its passage through the perihelion occurring at a time
when the earth was not very remote from that point, it
passed us closely and swiftly, swelling into importance,
and dying away with unusual rapidity.  The phenomena
exhibited by its nucleus and head were on this account




T34                   ON COMETS.
peculiarly interesting and instructive, it being only on
very rare occasions that a comet can be closely inspected
at the very crisis of its fate, so as to witness the actual
effect of the sun's rays on it.  In this instance, the pouring forth of the cometic matter from the singularly bright
and highly condensed, almost planetary nucleus, took
place in a single compact stream, which after attaining a
short distance, equal to rather less than a diameter of
the nucleus itself, was so suddenly broken up and dispersed as to give, on the.first inspection, the impression
of a double nucleus.  The direction of this jet varied
considerably from day to day, but always declined more
or less in one direction from the exact direction from the
sun.  So far as I am aware. the formation of an envelope
disjoined from the head was not witnessed in this comet.
(48.) And now, I daresay, all my hearers are ready to
ask  After all what is the tail of a comet? Is it material
substance in the first place?  To this I answer unhesitatingly, Yes! Donati's comet has given a decisive proof
on that point.  There is a criterion by which, when it is
observed, it can be positively asserted that the light by
which anything is seen has been reflected from  a material substance.  The light reflected, when it exhibits
that peculiar property in which this criterion consists is
said, to be polarized. The direct light of the sun or that
of a candle is not polarized, but when reflected at a particular angle on any surface but a metallic one, it is, and
if it is polarized, we may be sure that it is not direct
light thrown out'by the object seen, but borrowed or indirect light. No matter at present what this polarization




ON COMETS.                      I35
is, all I wish to convey is, that there is a simple enough
experiment which everybody who  understands optics
knows how to make, which ifthe result be of a certain kind,
the reflection of the light is demonstrated-(the converse, be it observed, does not hold good)-in an instant,
by merely looking through a small instrument contrived
on purpose.  Now, Mr Airy, the present astronomerroyal, a person who is not only an excellent astronomer,
but who stands very high as an authority on this especial
branch of optics, applied this test to the light of the
comet's tail on the 27th September, and found it polarized.  The tail then shone by reflected light, and there
was also another particular indication or character of the
polarization impressed, which the same trial afforded, and
which enabled him to say positively that the light had
been reflected from some source of light agreeing in
situation with the sun.
(49.) The tail of the comet then was material substance.*
But now, only conceive what must be the thinness, the
almost spiritual lightness of a vapour or fog, which, occupying such an enormous space, would not extinguish
* I applied the same test to the comet of 1862. There are various
modes of making the trial.  Mine was by looking at the comet
through an achromatized doubly refracting prism, and turning the
prism round in its own plane. I could perceive no alternate maxima
and minima of brightness in the images. But in this case it is the
positive result which is conclusive. Everything depends in the first
instance on the relative situations of the objects and the eye. And,
moreover, the light of the comet of 1862 was far inferior to that of
Donati's, rendering the experiment pro tanto more delicate-and it
is very possible that to septuagenarian eyes, indications of partial
polarization might escape observation.




136                 ON COMETS.
the stars shining through it.  Arcturus was noway dimmed
when it shone through the very middle of the brightest
part of the tail of that comet. But I have already stated
that that part measured go,ooo miles, and as this part of
the tail was no doubt round, as thick as broad, the star's
light must have shone through go,ooo miles of this mist.
Now, every one must have noticed that the steam puff of
a railway carriage completely obscures the sun, much
more a star. You cannot see the sun through it. Well,
then: there must have been less substance in the line of
90,0ooo miles of tail between the eye and star than in the
line of a few yards of steam smoke penetrated by the
eye in the other case.
(50.) If you look at a filmy cloud at sunset, though not
thick enough to hide a star, you see it bright with vivid
golden light by reflection from  the sun.  How much
more then if it were much nearer to the sun, and much
more strongly illuminated. Such a cloud is penetrated
with light through its whole thickness and reflects it
equally from its interior and exterior.  Just so in the
almost infinitely more thin texture of a comet-even in
the densest part of the head it cannot be compared to
the lightest cloud so far as substance goes.  In Biela's
comet very minute stars have been seen by myself
through a part of the head at least 50,000 miles in thickness, which a fog a few yards thick would have extinguished. A solid body of a round shape would exhibit
phases like the moon, and would appear sometimes as a
half moon, sometimes as a crescent, and sometimes as a
full moon-but the heads of comets show no such appear



ON COMETS.                    137
ances. Of course I do not mean to deny that that very
minute brilliant point which some are said to have exhibited, may not be a solid body-but it must be a very
small one-perhaps not a tenth or a hundredth part the
size of the moon; and, indeed, if there be not some little
solid mass, it seems impossible to conceive how the observations of a loose bundle of smoke, rolling and careering about, could ever be represented by any calculation.
Certain it is, that what appears to be the central point of
a comet, is that point (and no other is) which conforms
rigorously to the laws of solar gravitation, and moves
strictly in a parabolic or elliptic orbit.
(5 i.) There is a very curious feature common to all the
comets which have little or no tail, and which circulate
about the sun in short periods; such as that of Encke,
in which it has been especially observed. As they approach the sun, so far from dilating in size, they contract, —  mean in their real bulk, orat least their visible
bulk,-and on receding from the sun they grow again to
their former size.  The only possible explanation  of
this is, that a portion of their substance is evaporated by
the heat-that is to say, converted from the state of fog
or cloud into that of invisible transparent vapour. Perhaps I ought to explain what is the difference.  Take
the case of a light cloud in a clear sky when the sun
shines on it.  If you watch it attentively, you will very
often see it grow thinner and thinner, and at last disappear altogether. It has been converted from mist to
invisible valpour. The material substance, the watery
particles are there, but they have passed into another




138                 ON COMETS.
form  of existence, in which, like the air itself, they are
invisible.  As the comet then gets heated a portion is
actually vaporized-and  the vapour condenses as it
cools again.  The whole substance of the comet of
Halley, as you have heard, was so evaporated in I835-6,
all but what I suppose must have been really its solid
body; that star which I have already mentioned, which
was seen on the 22d January I836: and all that curious
process that went on afterwards, no doubt was that of the
re-condensation of the evaporated matter, and its gradual
re-absorption into and close around the body.
(52.) There is still one point in the history of comets
which I have not touched upon, or but slightly.  Comparatively only a few of the great number of comets which
have been observed, and of which the orbits have been
calculated, have been seen more than once-the great
majority once seen, seem lost for ever. What becomes
of them, is a very natural question. The answer to this
is, that the time of the periodical return of a comet
depends entirely on the distance to which it may run out
from the sun.  Now we know of nothing to interfere
with or disturb the motion of a comet, once clear of the
planetary system, between the farthest planet and the
nearest fixed star; and that interval is so immense that
the imagination is lost in attempting to conceive it. The
farthest planet we know of is only 30 times the distance
of the earth from the sun.  Halley's comet in its elliptic orbit of 75 years, goes only a little beyond that, or to
about 36 times the earth's distance.  Donati's comet, if
the computists are right, will return in 2Ioo years, and




ON COMETS.                   139
will have gone out to a distance 238 times the earth's
distance from the sun, or nearly 80 times the distance of
the planet: Neptune.. But this is still hardly the thousandth part of the distance to the very nearest fixed star
-and supposing the elliptical orbit of a comet should be
so long as to carry it out only half-way to the nearest
star-its return to the sun would require upwards of  1
millions of years from its last appearance. Few of those
who saw the last-mentioned comet pass over Arcturus,
had any idea of the enormous distance at which the star
really was behind the comet: and Arcturus is by no
means the nearest star.
(53.) I think, from what I have said, you will perceive
that there is in the history of comets matter enough both
to encourage inquiry and to check presumption. Looking
to the amount of our positive knowledge of them-knowledge acquired by centuries of observation, and by the
conspiring efforts within the last two centuries of the
profoundest thought and the most persevering labour of
which man is capable, we may reasonably enough congratulate ourselves on what has been done, and while we
can afford to look back with an indulgent smile on the
unfledged and somewhat puerile attempts of the ancient
mind to penetrate their secret, we may as reasonably
look forward to the revelations they will afford, as time
rolls on, of facts and laws of which at present we have no
idea.  This may, and ought to inspire confidence of the
powers of man to penetrate always deeper and deeper
into the secrets of nature. But, on the other hand, here,
as on every other occasion, we find that the last and




140                   ON COMETS.
greatest discoveries only land us on the confines of a
wider and more wonderfully diversified view of the universe; and have now, as we always shall have, to acknowledge ourselves baffled and bowed down by the
infinite which surrounds us on every side.
(54.) Beyond all doubt, the widest and most interesting
prospect of future discovery which their study holds out
to us, is that distinction between gravitating and levitating
matter, that positive and unrefutable demonstration of
the existence in nature of a repulsive force, co-extensive
with but enormously more powerful than the attractive
force we call gravity, which the phenomena of their tails
afford.  This force cannot possibly be of the nature of
electric or magnetic forces.* These forces are especially
polar in their action between particle and particle-a
magnet, or an electrified particle, of indefinitely minute
dimensions-so minute as the discrete particles which go
to form a comet's tail, could by no possibility be either
attracted or repelled, as such, by a body, however powerfully magnetized or electrified, placed at the distance of
the sun. It might have a direction given to its magnetic
or electric axis, but its centre of gravity would not be
~ This and much of what follows may seem inconsistent with
what is said in my "Results of Ast. Obs., &c., at the Cape of
Good Hope," p. 409, and note thereon. To a certain extent it
is so, and to that extent it is a recommendation, but I am here
speaking only of that portion of the matter of the comet whose
chemical union may be considered as completely overcome, and
whose levitating or negative constituent is fairly driven off, never
to return. That which may be conceived to remain behind may
conform under the circumstances of the case to the dynamical
relations there indicated.




ON COMETS.                   141
affected one way or- the other.  The attraction on one
of its sides would precisely equal the repulsion on the
other.  The separation of one portion of the matter of
a comet from the other by the action of the sun, which
we see, unmistakably, operated at and near the perihelion passage (a separation which the late Sir William
Herschel certainly had in mind, though perhaps somewhat indistinctly, when he spoke of a comet visiting our
system  for the first time as consisting of "unperihelioned" matter in contradistinction to those which he considered to have lost their tails by the effect of repeated
appulses, and to consist mainly of perihelioned matter)
-this separation I can only conceive, as I have ventured to express it above, as an analysis of the materials: analogous to that analysis or rather disunion by
the action of heat which St Clair Deville has lately shown
to take place between the constituents of water at high
temperatures. In this latter case the chemical affinity is so
weakened that the mere difference of difficulty in traversing an earthenware tube suffices to set them free of one
another.  How much more so, then, were the one constituent of a chemical compound subject to a powerful
repulsion from a centre which should attract the other,
and with it by far the larger mass of the total comet.
Might not, under such circumstances, the mere ordinary
action of the sun's heat sufficiently weaken their bond of
union: and might not the residual mass, losing at every
return to the perihelion more and more of its levitating
constituents, at length settle down into a quiet, sober,
unexcitable denizen of our system?




LECTURE IV.
THE WEATHER, AND WEATHER PROPHETS,
" Varium et mutabile semper."
HERE is an ugly look about the sky, and
I   m [  the wind is getting up, and Fitzroy's stormsignals were hoisted yesterday evening and
are up now. We shall have a gale. I am
afraid we must put off our boating for to-day anyhow;"
said my friend A-    to his wife the other day; " there
may be nothing in it; but we should look very silly to
come home half-drowned in the face of a warning."
(2.) And it was well the lady took the advice. It was
but a pleasure party after all. But the fishermen to
whom the loss of a day was a serious matter, put off.
Not that they altogether pooh-pooh'd the inverted cone
and drum: but they reckoned on twenty-fours' law at
least, and suffered for their miscalculation. One boat
came on shore in fragments, several suffered damage,
and all agreed it would have been wiser to have stayed
at home.




THE WEATHER, AND WEATHER PROPHETS.   143
(3.) An occurrence like this took place at one of our
southern watering-places not far from hence, a few days
ago; and the gale which followed was one of the precursors of that far more fearful one which has just (apparently) blown itself out;* part and parcel, no doubt, of
that great periodical phaenomenon whose recurrence
under the name of " the November atmospheric wave,"
is beginning to be recognized as one of the features of
our European weather table-a vast and considerably
well-defined atmospherical disturbance; peculiar, it
would seem, to this portion of the globe, though originating, as we shall see reason to believe, in the opposite
hemisphere; and of which the gale of the Royal Charter
(October 25, I859); the great Crimean hurricane of
disastrous memory (November 14, I855); and the still
more awful storm  of December 8, (N.S.) 1703, the
greatest which has ever swept this'island,-may be
considered as shadowing out the beginning, middle, and
end.
(4-) The actual barometric fluctuation to which the
epithet has been affixed by Mr Birt, who first drew
attention to one of its most peculiar features, is, however, confined to narrower limits of time; and refers to
one great billow or mountainous breaker (so to speak) of
air, which sweeps in November across the whole North
Atlantic and the European continent from N.W. to S.E.;
preceded and followed by sudden and violent subor* This was written on the morning of the 2d of November I863,
after a night of most terrific storm.




144   THE WEATHER, AND WEATHER PROPHETS.
dinate fluctuations, embracing in their whole extent and
in different years the longer period referred to.*
(5.) Meteorology, so far as prediction of the weather'
is concerned (which most persons consider, very erroneously, to be its only practical object), may be regarded
as a science still in its infancy; though if such be the
case, to judge from the voluminous nature of its records,
and the multitude of books which have been written
on it, its maturity, if ever attained, would promise to be
gigantic indeed; were it ntt that the progress of all
real science is towards compression and condensation,
and its whole aim  to supersede the endless detail of
individual cases by the announcement of easily remembered and readily applicable laws. Most of the indications of the " weatherwise," from Aratus down to Foster,
have hitherto been little more than what, in the language
of Mr Mill, would be called  " simple connotations."
The condor is circling in the sky: therefore a lion is
devouring a horse below.  The sheep turn their tails to
the south-west: thzeefore there will be a gale of wind
from  that quarter.  The " Rainbow  in the morning,"
&c.  The " Evening red and the morning gray," &c.,
&c.  All such connotations have their value in an absolute ignorance of causes and modes of action: but it is
only by the study of these that we learn what to connote.
And there is no doubt, that since, after an immense
* This is the direction of the progress of the wave. That of the
wind during the gales which accompany it is at right angles to that
direction, or from S.W. to N.E.: in analogy (?) to the- traniverse
rotation of the etherial molecules in the propagation of a circularly
polarized ray of light.




THE WEATHER, AND WEATH'ER PROPHETS.   145
amount of persevering labour bestowed on daily and
hourly records of the weather, an insight (and no inconsiderable one) has been gained into the causes which
determzine it, and the sequence of phaenomena which
exhibit them in action; a style of connotation has commenced, which is already bearing practical fruit, in the
form of telegraphic warnings of approaching bad weather,
of positive value and interest. There can be no better
proof of this, than in the fact that the example set by
our own Admiralty in the establishment of a system of
coast weather signals, has already been followed to a
certain extent in Holland, and is in course of being so
in France.  Nations are perhaps not overready in following up the improvements of their neighbours; but
at all events, they are remarkably slow in adopting each
other's practical blunders.
(6.) The indications of the coming weather which
experience has shown to be in any degree dependable,
have been embodied by Admiral Fitzroy in a sort of
code of instructions or " forecasts," which have been
so very extensively circulated by his praiseworthy zeal,
aided by the powerful means at his disposal. that we do
not consider it necessary to recapitulate them.  They
rely mainly on the indications of the barometer and
thermometer, together with the observation of the direction and force of the wind at the time and place, and ot
its immediately previous course; all these particulars
being regarded not per se, but as in connexion with
each other; their indications not being absolute, but
relative: so that a rise in the barometer, coupled in one
K




146   TIHE WEATHER, AND WEATHER PROPHETS.
case with a rise, and in another with a fall in the thermometer, may indicate, under given, or, as the case may
be, differing circumstances of wind; widely different or
even opposite features in the character of the approaching weather.  It is to be borne in mind, however, most
carefully, that all such indications are to be received as
valid (piro lanto) only for a very brief interval in advance;
and that the " weather-prophet" who ventures his predictions on the great scale, is altogether to be distrusted.
A lucky hit may be made; nay, some rude approach to
the perception of " a cycle of seasons" may possibly be
attainable. But no person in his senses would alter his
plans of conduct for six months in advance in the most
trifling particular, on the faith of any special prediction
of a warm or a cold, a wet or a dry, a calm or a stormy
summer or winter. Of all the minor or simply connotative
indications of the coming weather (as distinct from
those which connect themselves with our knowledge of
causes), the only one in which we place the slightest
reliance is that the appearance of "anvil-shaped clouds"'
is very likely to be speedily followed by a gale of wind.
(7.) The moon is often appealed to as a great indicator of the weather, and especially its changes as taken
in conjunction with some existing state of wind or sky.
As an attracting body causing an " aerial tide," it has
of course an effect, but one utterly insignificant as a
meteorological cause; and the only effect distinctly
connected with its position with regard to the sun which
can be reckoned upon with any degree of certainty, is its
tendency to clear the sky of cloud, and to produce not




THE WEATHER, AND WEATHER PROPHETS.  147
only a serene, but a calm night, when so near the full as
to- appear round to the eye-a tendency of which we
have assured ourselves by long continued and registered
observation.  This, however, is more than a " simple
connotation.   The effect in question, so far as the
clearance of the sky is concerned, is traceable to a distinct physical cause, the warmth radiated from its highly
heated surface; though why the effect should not continue
for several nights after the full, remains problematic.
(8.) Lunar prognostics about the weather may be
classed under three several heads,-viz., ist, Simple
connotations of the appearance of halos, coronas, lunar
rainbows, and." a watery" moon, as prognostics of wet.
No doubt they do indicate the presence of vapour, passing into cloud, in the higher regions of the air (in that of
the rainbow, actual rain not far away), and so may be
put on a par with the indications which may sometimes
be gathered from the behaviour of birds, especially such
as fly high, and make long excursions, and which may:convey to us some notion of their cogitations as to the
coming weather; which are perhaps more likely to be:right than our own, as founded on a wider range of perception..2d, Purely arbitrary laws or rules founded on
the hour of the day or night at which the changes of the
moon take place. There is (or was a few years ago, for
we believe the race is dying out) hardly a small farmer
or farm-labourer who had not some faith in certain "weather-tables" in the "Farmer's Almanac," ascribed (we
need hardly say falsely) to the late Sir W. Herschel, and
which went on this principle.  Others, again, pressed




148   THE WEATHER, AND WEATHER PROPHETS.
into the service the great and recondite names of APoGEE and PERIGEE; and professed to determine the character of the lunation from her proximity at new or full to
these mysterious points of her orbit. Both the one and
other rule utterly break down when brought to the tests
of long-continued and registered experience.  Others,
again, drew their prognostic for the whole lunation from
the character of the weather during the first quarter.
Such was the rule said to have been implicitly adhered
to by the late Marshal Bugeaud in the planning of any
military expedition whose success was likely to be any
way dependent on weather:" Primus, secundus, tertius, nullus,
Quartus, aliquis,
Quintus, sextus, qualis;
Tota Luna talis."
(9.) 3dly, A more ambitious form of lunar prediction
was that of the late eminent meteorologist (for such, this
one crotchet excepted, he certainly was), Luke Howard;
who took great account of the moon's declination as
influencing the averages of rainfall, and of the height of
the barometer. Still more so was his weather-cycle of
nineteen years, the period of the circulation of the nodes
of the moon's orbit; in the course of which the absoluze
maximum of north declination occurs when the ascending
node is in the spring equinox, and the moon go~ in
advance of the node in her orbit, and that of south in
the reversed circumstances-the intermediate situations
of the node corresponding to the absolute minima of each.
These situations, according to the declination theory,




THE WEATHER, AND WEATHER PROPHETS.  149
ought to bring round a periodical increase and diminution in the average rainfalls and barometric heights.
Like the others, however, when compared on any extended scale with recorded facts, this results in no
establishment of any positive conclusion.
(io.) A small monthly depression in the average temperature arising from the nocturnal radiation consequent
on the cloudless state of the sky about the full moon,
would seem  almost a necessary consequence of that
phsenomenon.
(II.) The causes by.which that " various and mutable
thing" which we call THE WEATHER are produced are in
themselves few and simple enough; but the physical
laws which determine their actions are numerous and
complex; and the results, in consequence, so mutually
interwoven, and the momentary conditions of their action so dependent on the state of things induced by
their previous agency, that it is no wonder it should
be next to impossible to trace each specific cause (acting as it has done through all past.time) direct to its
present effect.  Yet from  this very complexity results
that sort of regulated casualty-that apparently accidental, yet limited departure and excursion on either
side from a monotonous medium-that exceeding variety
of climate, which renders our globe a fit habitation for
such innumerable diversities of incompatible life-and
that general equilibrium in each which secures to every
species, and to each individual of them all, its due share
in the distribution of heat, moisture, and wholesome
air:-considerations, these, which are not lost on those




150   THE WEATHER, AND WEATHER PROPHETS.
who believe that they can trace in nature the, operation
of motive and design as distinct from a mere necessity
arising out of the nature of things and the so-called
conservation of vis viva.
(12.) Let us take our globe as we find it-revolving on
its axis in twenty-four hours; and carried round the sun
in an orbit oblique to its equator in a year; which is
divided into two somewhat unequal halves (if such an
expression may be pardoned) from  equinox to equinox
by its unequal angular motion in a slightly elliptic orbit;
thus giving rise to unequal summers and winters in the
two hemispheres:  its surface very unequally divided
between land and sea-the land mainly congregated
upon one half of it, and that half principally belonging
to the northern hemisphere; and so distributed as effectually to'bar all free circulation of the ocean in the direction of the diurnal rotation (or round the equator), and
allow but a restricted one in that at right angles to it (or
across the poles): thus compelling whatever circulation
does exist, to take place within three great basins or
semi-land-locked areas, and a vast southern expanse into
which all the three.open; and within each of which
a system  of circulation is kept up by the action of the
winds; its course being determined partly by the sinuosities of their shores, partly by the inequalities of their
bottoms, and partly by the rotation of the earth itself.
(T3.) We have, besides, to consider the globe as enitirely and deeply covered by an atmosphere of mixed
gases-highly elastic, very dilatable by heat, and of
extreme mobility: expanding itself in virtue of its elas



THE WEATHER, AND WEATHER PROPHETS.   15r
ticity out into space, far above the tops of the highest
mountains; yet, in virtue of its compressibility, so condensed (comparatively) in its lower strata as that onethird of its total ponderable mass lies within a mile of
altitude above the sea-level-nearly one-half within two,
and nearly two-thirds within five miles; within which
latter limit the whole would be contained, were it everywhere of the same density as on the surface: so that
only about one-third of its total mass is free to range,
unimpeded'by the crests of the highest Himalaya; and
not much more'than two-fifths can entirely clear the
range of the Andes without pressure a tergo.  In consequence, when driven in the state of WIND over these or
other mountain ranges, it is thrown up into vast ripples
or waves, which are propagated thenceforward onwards
overindefinite areas of land or sea, and become no
doubt the origin of a great part of those casual fluctuations of the barometer which give so much trouble to
meteorologists.
(I4.) This aerial ocean is not of the same temperature
throughout, even in the same climate and over the same
tract of country.  It is everywhere warmer near the
ground, colder aloft: and at very great heights a most
intense cold always prevails; more intense than that of
our severest winters. Hence the snow which covers the
summits of lofty mountains even in the hottest climates.
This relation between the temperatures existing below
and aloft is not subverted by any amount of mutual
admixture of the strata, such as. internal movements or
ascending currents would produce.  On the contrary,




152   THE WEATI-IER, AND WEATHER PROPHETS.
paradoxical as it may appear, such ascensional movemlents are the primary cause of this state of things; in
consequence of the habitudes of air with respect to heat
when compressed or expanded, according to a mode of
action well understood by meteorologists, which we need
not stop here to explain, as the reader will readily collect
it for himself from what follows.
(i5.) As the air aloft is colder than below, so also is
it drier. Every one considers that he knows the distinction between damp and dry air; but many are not
aware that all air contains some moisture, in the form of
transparent invisible vapour; or that in summer and
winter on two days, both which would in common parlance be pronounced dry ones, there is more than twice
as much moisture present in an equal bulk of air in the
summer, as in the winter day.  In this state of invisible
vapour which water is always assuming (throwing itself
off in that.form from its surface whenever exposed, and
the more copiously the warmer it is), the air is its general
recipient and distributor. The mechanism by which it
is enabled to do so on the great scale is exceedingly
curious.  We shall endeavour to exhibit it, as it were in
action-not so much with a view to affording a coup-d'eil
of the whole of meteorology, as with that of rendering
in some degree more intelligible than at present it seems
to be, that great phaenomenon of the November storms,
with the mention of which we began this lecture, which
has never been satisfactorily explained.
(i6.) Looking at our globe as revolving under the
warming influence of the sun, whose rays at noon fall on




THE WEATHIER, AND WEATHER PROPHETS.   X53
it with little obliquity in tropical regions, while their
incidence on those near the poles is always very oblique,
and during the half of each year null; it is obvious that
its surface must be very unequally warmed. The cook,
to use a homely illustration, knows full well that, however good her fire, the two ends of her joint will be
under-roasted when the middle is done brown; unless
she apply a couple of concave reflectors on her spit to
throw some of the lateral heat upon them. As a matter
of fact, no one needs to be told that it is so; and that
the intertropical regions of the globe are very hot, and
the polar, habitually very cold. The average annual
temperature at the equator is about 84~ Fahr., while in
the colder regions near the' North Pole it is as low as
5~ Fahr., or 27~ below freezing. The difference would
be much greater were there no sea, or even were the
whole surface initially moist soil.  Whatever that initial
moisture, it would soon dry qo from the warmer portions,
to settle down in snow or hoar frost on the colder; after
which the dried portions would grow hotter and hotter.
Every one knows what a cooling power there is in the
evaporation of water. So long as a vestige of moisture
were present, the temperature of the soil could never, at
at all events exceed, however it might fall short of, that
of boiling water: but when once completely dried off,
there would no longer be a limit to the possible increase
of temperature; since there would then be no circulation
or return of moisture to the part once dried.  How this
circulation is kept up under the existing circumstances
is what we must now explain: and first of all how it




154   THE WEATIER, AND WEATH-ER PROPHETS.
happens that in the course of ages the whole ocean has
not been transferred by this sort of distillatory process
from the tropics to the poles; leaving the former dry,
and piling the latter with mountainous accumulations of
ice.  Were the Polar regions of the globe occupied
by land instead of by sea, there is every reason to believe that such would be the case. As it is, the contrary
arrangement prevails, and the Polar snows fall upon
these seas or upon their frozen surfaces, and form floating masses of ice, which are partly broken up and drifted
away, and partly melted in situ by currents of water perpetually streaming in against and beneath them  from
warmer regions, and thus become restored to the general
ocean.
(I7.) But what, it will be asked of course, produces
these warm  currents? And how is the water of which
that snow consists, and all the rain which falls and feeds
the rivers that restore it to the sea, raised into the air,
and distributed over the world, and thrown down again
indiscriminately over all its surface?  Common sense
assures us-that all the rain, &c., which falls from  the
skies must have originated in the sea, and must (if the
present state of things is to endure) find its way back to
it.  But how is it done?  And, in the first place, where
are we to look for the motive power?  To this the
answer presents itself at once.  In the sun's heat.  Any
of our readers who will take the trouble to refer to Lect.
II., ~ 23, will find that the amount of solar heat which
actually reaches the surface of our globe would suffice to
melt an inch in thickness of ice in two hours thirteen




THE WEATHER, AND WEATHER PROPHETS.   155
minutes on a surface perpendicularly exposed to it; and
from  this he will have no difficulty in calculating the
depth of water over the whole area of the globe, land
and sea, per annum, which it would suffice to convert
into vapour if wholly expended in so doing.  This he
will find to amount, as nearly as may be, to nine feet.*
Meteorologists, collecting the registers of "rainfall" in
all regions of the globe, and comparing and calculating
on their indications, have come to the conclusion that
taking one region with another, the quantity of water
actually precipitated from  the air per annum, in the
forms of rain, hail, snow, and dew, would suffice to
cover.the whole of its surface to a depth of five feet.
Remains the equivalent of four feet, expended in warming
the soil;; which is partly radiated away, and partly communicated to the air, thus going to maintain the average
temperature, according to its climatic distribution.  And
as solely expended on this last-mentioned object, we
have to reckon fully one-third of the sun's total radiation, or one-half of that already accounted for, which is
absorbed by the air, or rather by the moisture in it,
before reaching the earth.  The joint effect of these
two portions is, as we have seen, to maintain the air in
* We will make the calculation for him. An inch of ice melted
in 2 hours I3 minutes over a great circle of the globe perpendicularly exposed to the sun, corresponds to a quarter of an inch in
that time over the whole surface (which is four great circles), or,
per annum, to 987'75 inches; or to nine-tenths of this, or 890 inches
of water raised I35~ Fahr. in temperature; or (taking the initial
temperature of the water evaporated on an average at 60~ Fahr.) to.
Io8 inches or 9 feet heated I 12~ to convert it into steam.




156   THE WEATHER, AND WEATHER PROPHETS.
the equatorial region of the earth habitually hotter by
about 80~ Fahr. on an average of all seasons and hours,
than the Polar.
(i8.)  Hot air under equal barometric pressure is
lighter than cold. The equatorial portion of the atmosphere, then, in comparison with the polar, is dilated
upwards; the only direction in which the lateral pressure
it experiences will permit it to dilate. Hence, the external form of the atmosphere, and of each of its upper
strata, instead of conforming in exact parallelism to the
spherical* form of the globe on which it reposes, as the
laws of equilibrium would require; are unduly elevated,
and bulged out, equatorially, into elliptic forms, a state
of things inconsistent with repose.   The prominent
portion rests, in fact, either way, on a slope, and being
unsupported laterally, fowzs down on either side-that is,
from the equator towards the poles. In so doing, however, it deserts its place, and ceases to contribute by its
weight to the total pressure on the equatorial region;
while at the same time it goes to add to the weight incumbent on the polar. Thus the hydrostatic equilibrium
of pressure is subverted, and air is pressed inwards towards the equator from the poles below, to make good
the efflux aloft. A circulation is established in each
hemisphere by inferior currents of air running in on both
sides towards the equator and superior ones setting outwards, all around the globe, from  the equator towards
the poles. Both these, were the earth at rest, would
* We neglect the spheroidal form of the earth, which in meteorology is never worth considering.




THE WEATHER, AND WEATHER PROPHETS.   157
follow the directions of meridians, but are converted by
its rotation on its axis and the gradual diminution of the
rotatory velocity in advancing from the equator to the
poles, into relatively oblique currents. The upper or outward follow precisely the reverse direction to the lower
or inward, and being drawn downwards, and are ultimately
brought down to the sea level, in their approach towards
the poles to supply the void which would otherwise be
left by the withdrawal of air below.*  They thus become
surface winds, prevalent in the regions beyond the tropics
from about 30 of latitude either way.
(I9.) In the view thus taken of the great and permanent system  of winds known as the " trades" and
" anti-trades," it will be observed that we have been
careful to regard them as resulting not so much from the
immediate (and diurnally intermittent) action of the sun,
as in a certain established gradation of climatic temperature, the result of its action on the whole earth's
surface continued through successive ages.  Were the
sun extinguished, the system  of the trade winds would
continue to subsist, though with diminishing intensity,
so long as the equator continued in any degree warmer
than the poles.
(20.) By the action of the trade winds which occupy
* Those of our readers who are not already familiar with the
nature of this transformation, and who would wish to follow it out
more closely, are referred (as well as for every other matter of detail
in similar cases, precluded by our limits) to the article Meteorology,
in the " Encyclopaedia Britannica," or to the same article published separately by (A. & C. Black, Edinburgh) the editors of
that work.




158   THE WEATHER, AND WEATHER PROPHETS,
the intertropical region, and a little more, and which,
though differing as to north and south, conspire in their
general easterly character, the surface of the equatorial
ocean is driven westward, and directed full against the
two great barriers (the west coasts of America and Asia),
and divided northward and southward into streams or
currents which in their progress, after issuing from
tropical latitudes, receive a direction, by reason of the
rotation of the earth, corresponding to that of the antitrade winds.  These also, beginning about the same
latitudes to descend to the sea level and strike on the
ocean, aid their further progress, and carry them, or
portions of them, far northward and southward into the
Polar Seas, there to perform the work above assigned to
them  of melting the ice, and so keeping up the total
amount of the ocean-water; besides mitigating, to a
great extent, the severity of the cold on the coasts in
high latitudes on which they strike; of which we have a
familiar example in the warming influence of the celebrated Gulf-stream.
(21.) The steady and equalized agency by which the
great system of the permanent winds and oceanic currents is kept up, which we have just described, contrasts.
itself strongly with the violent and, as it may almost in
comparison be called, impulsive action of the sun on
and around the point of the globe over which, for the
moment, it happens to be vertical; and which corresponds to that portion of the solar energy which is
directly employed in producing evaporation. The nature
of this process we have now to explain.




THE WEATHER, AND WEATHER PROPHETS.   159
(22.) When water is converted into invisible vapour,
it occupies between sixteen and seventeen hundred
times its original volume, and becomes much lighter
than air-as light, indeed, as the ordinary coal gas with
which balloons are filled, so that if enclosed in a similar
envelope it would rise in the air like a balloon. Being
free, however, it mixes with the air, and that not merely
by a simple chance-medley confusion, but by a peculiar
self-diffusive energy arising from its inherent elasticity;
by which the particles of every one species of gas or
vapour struggle to interpenetrate, and needle, as it were,
their way among those of every other. These latter oppose
to them no elastic pressure, but that simple resistance to
jostling which an inert body of any other kind might do,
-which feathers, for instance, might oppose to air, introduced and struggling to diffuse itself among them.
Of course they will be pushed from their places in the
struggle, both laterally and vertically, and thus arises
over the whole region in which the vapour is in course
of production, a pressure on the air both outwards and
upwards.  The former, however, cannot be effective in
removing air bodily to any great distance horizontally,
for the simple reason that to do so it would.have to
shove aside the whole surrounding a6rial atmosphere, and
to crowd it upon that which is beyond. while there is
room in a vertical direction for an indefinite removal,
and the upward pressure is also aided by the lightness of
the up-struggling vapour, which therefore rises rapidlynot without dratgging, u/ with it a great deal of air.  The
consequence is to establish, immediately under the sun,




I60   THE WEATHER, AND WEATIER PROPHETS.
at whatever part of the globe it happens to be vertical,
and at which there is a supply of moisture, and for
a very large space around it; what may be likened
to a vast up-surging fountain of air and vapour throwing itself up with an impetus; breaking up and bulging outwards the immediately incumbent aerial strata
very far above their natural levels.; and introducing
at the same time into the air a great quantity of vapour, as well as withdrawing, by direct transfer, from the
lower atmosphere, a great deal of air; which of course
has to be supplied by in-draft along the surface of the
earth.
(23.) The process now described, is in a great many
of its features similar to that gentler one previously
stated: and as it always takes place at some point
or other of the intertropical region, it conspires with
and locally exaggerates its result so far as the transfer
and circulation of air and the production of winds is
concerned.  As regards the vapour, a large portion is
very speedily deprived of its elasticity and ascensional
power, and reduced to the state of visible cloud, collecting and descending in rain.  This is a consequence
partly of its arrival in a colder region, but mainly of the
property which all gases and all vapours alike possess,
of absorbing and rendering latent a large quantity of
heat as they expand in volume, and so becoming, ipso
facto, colder.  Both the air and the vapour do so expand
as they rise, by reason of the diminution of pressure they
experience.  The air indeed retains its elastic state as
air, however cold it may become; and therefore merely




THE WEATHER, AND WEATHER PROPHETS.  16I
takes its place in its new situation as very cold air, without further tendency to rise.  But the vapour so chilled
loses its vaporous state, and condenses in the manner
above stated; leaving only so much uncondensed as can
remain vaporous under thzat temperature and pressure. This
is the origin of those continual and violent tropical rains
which always accompany the vertical sun, and its near
neighbourhood, and of which we feel the influence,
though slightly, in our wet Julys.  The vapour being
thus arrested in its upward progress, the whole of the
evaporatory process we have just described, however
tumultuous in its origin, is confined to what may be considered comparatively the lower strata of the atmosphere.
But these become in this manner saturated with moisture; and when carried into the general circulation, convey it either as cloud or as invisible vapour to the
farthest regions of the earth.
(24.) Besides the evaporation produced by the direct
action of the sun, a vast amount of moisture is taken up
by the air immediately from the sea and land over which
it passes in its indraft towards the Equator as a tradewind.  Corning from a colder region to a warmer, and
acquiring heat as it advances, its capacity for receiving
and retaining moisture in an invisible state is continually
increasing; and hence, even during the absence of the
sun in the night hours, it is constantly absorbing moisture; which it carries along with it, and delivers, as
a contribution of its own collecting, into the general
ascending mass, to be handed over in the returning
upper current into the circulation.  Hence it arises that
L




162   THE WEATHER, AND WEATHER PROPHETS.
the regions of the earth habitually swept by the trad2winds abound in sandy deserts and arid wastes.  When,
however, in the progress of that circulation, it descends
again to the earth, and becomes a surface-wind (assuming the character of an "anti-trade"), it finds itself in
precisely reversed circumstances. It is now travelling
from  a warmer to a colder region.   Saturated  with
moisture in the warmer, and  parting with the heat
which alone enabled it to retain it, its vapour condenses.
Clouds already formed thicken, and descend in rain,
and fresh ones are continually forming, to fall in snow
at a further stage of its progress; till all the superfluous
moisture is thus successively drained off, and it is prepared to re-assume, while starting on a fresh circuit, the
character of a drying wind.
(25.) We have here the origin of that generally observed difference of character between our two most
prevalent winds-the S.W. and the N.E.  The former is
our "anti-trade," that which from our geographical position we are chiefly entitled to expect, and which, in
point of fact, is of far the most frequent occurrence.
Its prevailing characters are warmth, moisture, cloud
and rain, as well as persistence and strength.  In the
former of these characters it is strongly reinforced by the
circumstance of its accompanying across the Atlantic the
Gullf-stream, which, in fact, it helps to drift upon our
w.stern coasts, and which, retaining  a  considerable
amount of the equatorial heat, sends up along its whole
course a copious supply of vapour, in addition to that
with which the air above it is already loaded: and this




.THE WEATHER, AND WEATHER PROPHETS.   163
it is which gives to our west coasts, and to that of Ireland, their moist and rainy climate-double, and more
than double, the amount of rain falling annually on the
coasts exposed to its full influence, as compared with
the eastern coast; which it does not reach until drained
of its excess of humidity.
(26..) The characters of our North-east winds (for
such as are in common parlance called Easterly winds
are almost always such) are the reverse of these in every
particular. They are cold, dry, and hence often spoken
of as cutling, from their parching effect on the skin; and,
as a natural consequence, for the most part accompanied
with a clear sky. They are seldom of very long continuance, and may be regarded rather as casual winds, except
in the spring; when the advance of the sun to the north
of the equator begins to call into action a northern
indraft-to push to the northward the limit of the northeast trades, and to unsetlle by its intrzlsion /the line of
demarcation betzzeen te wind-zones which ifs long conlinuance in extreme south latitude, near the winler solstice, had
allowed to lake up/, and rest in, its extreme sozuternmost
position. To this opposition of characters we may add,
that the South-west wind is generally accompanied with
a lower, and that of the North-east with a higher than
average barometric pressure; a connexion partially, but
not entirely, accounted for by the lightness of warm and
moist air as compared with cold and dry; and which is
the origin of those indications of the weather (fair,
settled fair rain, mr ch rain, &cc., &c.) which we find
inscribed opposite to the divisions of the scale of inches




164   THE WEATHER, AND WEATHER PROPHETS.
in our ordinary barometers. When the North-east wind
brings snow, as it very frequently does, it is not by the
precipitation of its own moisture; but by its intrusion as a
cold wind into a warmer atmosphere charged with moisture, and ready to deposit it under any cooling influence.
(27.) Complementary to the phenomenon just mentioned of a tendency to North-easterly wind in the
spring, i.e., to the production of a lull or temporary
intermittence in the regular South-west current, and the
substitution for it of its opposite; may be considered that
aggravation of its intensity which takes place subsequent
to the autumnal equinox; exaggerated, however, and
thrown later into the season, viz., into November, by the
conspiring action of several distinct causes, which we
will now proceed to explain.
(28.) As the sun in its annual course traverses the
northern and southern halves of the ecliptic, it creates
summer in the one hemisphere, simultaneously with
winter in the other; and the balance of aerial expansion
and aqueous evaporation is alternately struck in favour
of each. As a necessary consequence, a large amount
both of air and of aqueous vapour carrying air along
with it, is alternately driven over from one hemisphere
to the other. The only course which the elements so
transferred can pursue, is by passing in the higher
regions of the atmosphere across that medial line where
the two superior out-flowing currents separate on their
courses towards either pole-in other words, by joining
with, and reinforcing the " anti-trade" current on that
side of the equator toewards which they are propelled.




THE WEATHER, AND WEATHER PROPHETS.   165
Now this cause of reinforcement cannot begin to be felt
until the sun, having passed the equinoctial, has advanced considerably towards the other solstice. In the
case of the northern anti-trade, the effect in question is
rendered still more sensible by the great preponderance
of sea in the southern hemisphere as compared with the
northern; and the much greater quantity of vapour
raised by the summer sun on that side of the equator.
And besides all this, it will be remembered that all the
air which had been dragged across the equator into the
southern hemisphere by transferred vapour during the
continuance of our northern summer, and there as it
were imprisoned, is now released; and returns, necessarily by the same course, and contributes to reinforce
the northern anti-trades.
(29.) There is a special cause, too, arising from the
geographical position of Britain and north-west Europe,
in relation to the South American continent, which is
probably not uninfluential in producing or aggravating
this disturbance.  If we trace on a map the course of
the wind which reaches our island from the south-west,
we shall find that it has its origin on the coast of Guiana,
between the fiftieth and sixtieth degrees of west longitude. This also is nearly about the point where the
medial line between the north and south trades, in its
average position, intersects the South American coast.
Here the South American continent is comparatively
narrow, but south of this it expands in longitude, and
between the fifth and fifteenth degrees of south latitude
has an average breadth of between 30~ and 40~.




I66   THE WEATHER, AND WEATHER PROPHETS.
(30.) In the view we have taken of the production of
the trades, the immediate verticality of the sun acts as a
disturbing force.  In its passage from solstice to solstice
it causes an annual fluctuation or oscillation to and fro
of this medial line, and of the northern and southern
limits of the wind-zones; which, where those limits cross
the ocean, is but of moderate amount, because the
medium temperature of the intertropical seas varies but
little with the seasons.  But where they cross extensive
tracts of land, their oscillations to and fro may become
very considerable, owing to the high temperature which
the land is capable of acquiring. Now in this case, so
soon as the autumnal equinox is passed, the vertical sun
enters on the full breadth of this vast continental tract;
and commences throwing up torrents of vapour and intensely heated air, the latter being far in excess of what
it would be over an equal area of sea; while at the same
time, owing to the sun's then rapid motion in declination, the limits of the wind-zones retreat southward, and
their regularity is disturbed and broken; which cannot
but give rise to great temporary confusion and disturbance in the winds themselves. As to the " atmospheric
wave" which recurs periodically at this season, it results
most probably from the operation of the more general of
the causes above mentioned, by which a large amount of
extraneous air and vapour is thrown into the atmosphere
of the Northz Pacifc, causing the south-west wind. of that
ocean to sweep with increased force up the western
slope of that vast range of lofty mountains which fringes
the North American continent; and to be thrown up




THE WEATHER, AND WEATHER PROPHETS.   I67
along the whole length of that range into a broad swell,
propagated onwards as a wave across America and the
North Atlantic into Europe.  No merely local action,
and no casual conjunction of circumstances, can be considered  competent to produce  so extensive and so
regularly recurring an effect.  A  mere inspection of
Admiral Fitzroy's interesting compendium of the state of
the barometer, &c., &c., over the area occupied by our
island and the neighbouring continental coasts, as recorded from  day to day in the Timnes, will suffice to
satisfy any one of its occurrence in former years, and to
show that its character has been (so far at least, Nov.
21) fully maintained in the present (1864).
(31.) If we are ever to make any material progress in
the prediction of the weather beyond " forecasts" of a
few hours, or it may be a whole day in advance, it can
only be by the continued study of such of its phases as
recur periodically, or of such as manifest a periodicity of
event, as distinct from that of times and seasons, with a
view to connecting them  with their efficient physical
causes. Of this latter description we have an example
of one, and of its successful reduction under the domain
of philosophical reasoning, in  the law  of the rotation of the winds.  That the winds in their changes,
in a general way, " follow the sun," i.e., have a tendency to veer in the same direction round the compass card with the sun's apparent diurnal course in
the heavens (from  east round  by south, west, and
north in the northern hemisphere, and reversely in the
southern), in continual succession back to the original




168   THE WEATHER, AND WEATHER PROPHETS.
point-has been surmised from  very early times; but
until lately, rather as a matter of occasional remark,
agreeing on the whole with the general impressions of
casual observers, than as a meteorological law of universal applicability. As such, however, it has now taken
its place among ascertained facts; verified by the registered movements of the wind-vane at every station where
continuous observation is made; and connected by the
researches of M. Dove with that great fact which underlies so many other phaenomena-the rotation  of the
earth on its axis.*   Nothing apparently can be more
capricious than the shifting and veering of a weathercock on a gusty day, and to any one who watches its
leaps to and fro for a few hours, it may well be a matter
of surprise to be told that with anything like a fair exposure, the preponderance of its movement is sure to be in
one direction-if not in a week or two, at all events on
the long average, and in a great majority of cases before
the expiration of a month.  Thus it appears from  the
record kept at the Observatory at Greenwich, in which
every change of the wind's direction is noted by a piece
of mechanism  attached to the vane and traced on a
table by a pencil-that in the thirteen years elapsed
from the beginning of I849 to the end of i86I, the vane
made I66 complete revolutions more in the direction
* For the reasoning by which this connexion is made, and for
the mode in which any casual advance and retreat of a body of air
over an extensive but limited tract of country is transformed by
this cause into a relative gyration, the reader is referred to the
works already cited in a former note.




THE WEATHER, AND WEATHER PROPHETS.   I69
above indicated than in the opposite, on a comparison
of the sums of all its angular movements either way-or
on an average, nearly thirteen revolutions per annum.
In all this interval, two years only, 1853 and i86o, gave
a contrary result, and that only to the total amount of
two revolutions in excess the wrong way in each. And
of these the year i860 was in many points an abnormal
one in respect of stormy weather. Nothing can convey
a better idea of the disappointment to which all meteorological predictions, even though founded on just principles, and supported by extensive inductions, are liable,
than this example. Still there remains a decided balance
of probabilities in favour of a change of wind occurring in
this rather than in a contrary direction on any specified
occasion.  A  continuous circuit round the horizon in
the contrary direction would certainly be in a high degree improbable.
(32.) On the other hand we have an instance of the
failure of a distinctly periodical cause (as to all appearance it would seem  fairly entitled to be considered
a priori), to exhibit itself in any cognizable periodical
effect on the seasons, in that curious recurrence of a
spotted state of the sun's surface which takes place every
eleven years (see Lecture II., ~ 36). Looking to the sun
as the great source of all meteorological action, it might
most reasonably be expected that such indications of an
activity of some sort going on in its very photospherein the actual visible laboratory of its light and heatwould correspond to some difference in its supply of
both; which, recurring periodically at stated intervals,




ri0   TiIE WEATIIER, AND WEATHER PROPHETS.
must, one wc Id think, manifest itself in some effect or
other on oui weather and climates.  Such, however,
does not yet appear to be the case. The most obvious
consequence would seem  to be a periodical return of
olt and cold years, which, however, the average registered temperatures of successive years in different places
have not borne out.  Yet, after all, it is possible that
meteorologists may here have been on a wrong scent,
and that increased emission of heat from the sun may
make itself felt, not so much in any material increase
of the average annual temperature, as in an increased
generation of vapour from the ocean; in a much more
copious and immediate rainfall in the equatorial regions
of the globe, and in a sensible increase of it over the
whole earth's surface: but especially in a more cloudy
state of the general atmosphere, consequent on the introduction of a larger amount of vapour into it; and in an
increased tendency to atmospheric disturbance and barometric fluctuation.  No one who has watched with disappointment the rapid upcast of cloud on a calm morning commencing with unclouded sunshine, which blots
the prospect of a glorious summer day, and who has
seen the same change take place day after day, often for
weeks in succession, can have failed to be struck by that
self-induced interposition of a veil between the sun and
the earth's surface which mitigates the ardour of his
beams and tempers them to the requirements of animal
and vegetable life. The increased heat, or by far the
greater part of it, may be expended in re-evaporating the
upper suiface of this zery cloud, and, by so doing, simply




THE WEATHER, AND WEATHER PROPHETS.   17I
extending the limits of the vaporous atmosphere and
maintaining the higher regions of the air in a state
of increased humidity.  And this is the way in which
we conceive it possible the planets Venus and Mercury
(as we have before hinted in our Lecture on the Sun,
but without further explanation) may be maintained at a
degree of superficial temperature not incompatible with
even terrestrial forms of life. Their climate, to be sure,
would have little to recommend it to our tastes; as
it would probably afford small relief from a perpetual
succession of cloudy days and rainy nights.
(33.) Is it in any degree within the power of man to
alter the weather.  A strange question, it may seem at
first sight to propose! but by no means so absurd a one
as it may appear.  The total amount of annual rainfall
over any district, is an element of its weather and its
climate of the last importance; and when we look over
the registers of rainfalls which are now so assiduously
kept in almost every part of England and other civilized
countries, it is impossible not to be struck by its very
great local diversity; even in neighbouring places, whose
general similarity of situation as regards wind-exposure
and surface configuration would seem  to preclude any
material difference on an average of years in their reception of rain; if really indifferent in its choice whzere
to fall. There is evidently something distinct from mere
local situation which determines this element of climate;
and we must look for it in the nature of the surface of
the districts, and its relations to heat and moisturerelations which the operations of man on the soil itself,




172   THE WEATHER, AND WEATHER PROPHETS.
and his selection of the kind of vegetation with which it
shall be habitually clothed, place to a great extent
within his power. It is chiefly in his clearance or allowance of arborescent vegetation, and in his artificial
drainage of the soil over extensive districts for agricultural purposes, that his influence on these relations is
perceptible.  The total rainfall, and (which is perhaps
as regards weather and climate of even more importance) the frequency of showers on an extensive wellwooded tract, or one entirely covered by forests, ought,
on every theoretical view of the causes which determine
rain, to be greater than on the same tract denuded of
trees. The foliage of trees defends the soil beneath and
around them  from the sun's direct rays, and disperses
their heat in the air, to be carried away.by winds, and
thus prevents the ground -from becoming heated in the
summer; while, on the other hand, a heated surface-soil
reacts by its radiation on the clouds as they pass over it,
and thus prevents many a refreshing shower, which they
would otherwise deposit, or disperses them altogether.
So again of drainage:-by carrying away rapidly the
surface-water down to the rivulet, and so hurrying it
away to the ocean, it not only cuts off a great deal of
the supply of local evaporation, which is a material
element in the amount of rainfall, but by:causing the
surface to dry more rapidly under the sun's influence,
it allows it also to become more heated; and so to con-.
spire with the action of the denudation of trees to prevent
rain.- Evidence is not wanting to corroborate this d
priori view of the matter. The rainfall over large regions




THE WEATHER, AND WEATHER PROPHETS.   173
of North America is said to be gradually diminishing,
and the climate otherwise altering, in consequence of the
clearance of the forests; while, on the other hand, under
the beneficent influence of a largely increased cultivation
of the palm  in Egypt, rain is annually becoming more
frequent.  Lakes are cited in what was formerly Spanish
America whose water supply (derived of course from atmospheric sources) had been so largely diminished, owing
to the denudation of the country under the Spanish regime, as to contract their area, and leave large tracts of
their shores dry; which, now that the vegetation is again
restored, are once more covered by their waters. Even
in our own southern counties complaints are beginning
to be heard of a diminution of water supply, partly, it is
said, owing to  gradually decreasing rainfall from  the
universal clearance of timber,' though chiefly perhaps
attributable to robbing the springs of their supply by
draining-a  practice  beneficial no  doubt to agriculture, if used  with  caution  and  in  moderation, but
of which the consequences, if carried to excess, may ere
long be very  severely felt, in  rendering large tracts of
* On the other hand, forests, owing to the immense evaporation
from their foliage which must be supplied from the soil beneath,
have a direct tendency to drain that jzsoil  wards, and so throw its
moisture into the air. This has been well pointed out and strongly
insisted on by M. le Marechal Vaillant, in "Les Mondes," T. 8,
p. 674. As a matter of fact, it seems pretty distinctly proved by
the collection of data laboriously accumulated by Mr Symondsthat the annual average rainfall is decreasing over the whole of the
British Isles, and more especially along a line running nearly S.W.
— N.E. from Cornwall to the Wash. (Symond's Report of British
Association, 1865.)




174   THE WEATHER, AND WEATHER PROPHETS.
country uninhabitable in summer from  mere want of
water.
(34.) To return to our prognostics.  We would
strongly recommend any of our readers whose occupations lead them to attend to the " signs of the weather,"
and who, from hearing a particular weather adage often
repeated, and from noticing themselves a few remarkable
instances of its verification, have " begun to put faith in
it," to commence keeping a note-book, and to set down
without bias all the instances which occur to them  of
the recognized antecedent, and the occurrence or nonoccurrence of the expected consequent, not omitting
also to set down the cases in which it is left undecided;
and after so collecting a considerable number of instances (not less than a hundred), proceed to form his
judgment on a fair comparison of the favourable, the
unfavourable, and the undecided cases: remembering
always that the absence of a majority one way or the
other would be in  itself an improbability, and that,
therefore, to have any weight, the majority  should
be a very decided one, and that not only in itself,
but in reference to the neutral instances.  We are
all involuntarily much more strongly impressed by the
fulfilment than by the failure of a prediction, and it
is only when thus placing ourselves face to face with
fact and experience, that we can fully divest ourselves of
this bias. Any one before whose eyes these pages may
pass, for instance, who may feel disposed to give our
dictum respecting the clearance of the sky under the influence of the full moon (we will not say through a hun



THE WEATHER, AND WEATHER PROPHETS.  175
dred lunations, but throughout the year 1864) a fair trial
of the kind, should record the state of the sky as to cloud
on three successive nights of each lunation —that on
which the full moon occurs, and those immediately preceding and succeeding it, from an hour before the rise
of the moon, and thence hourly to as late an hour of the
night as his usual habits will allow-noting the strength
and direction of the wind, and accompanying his memoranda in every instance with a note of the day and hour
at which the observation it refers to was made.




LECTURE V.
CELESTIAL MEASURINGS AND WEIGHINGS.
" Omnia in numero, pondere, et mensura."
HERE are epochs in the history of every great
operation, and in the course of every undertaking, to which the co-operations of successive generations of men have contributed
(especially such as have received their increments at
various and remote periods of history); when it becomes
desirable to pause for a while, and, as it were, to take
stock; to review the progress made and estimate the
amount of work done: not so much for complacency, as
for the purpose of forming a judgment of the efficiency
of the methods resorted to, to do it; and to lead us to
inquire how they may yet be improved, if such improvement be possible; to accelerate the furtherance of.the
object; or to ensure the ultimate perfection of its attainment.  In scientific, no less than in material or social
undertakings, such pauses and resumles are eminently
useful; and are sometimes forced on our consideration




CELESTIAL MEASURINGS AND WEIGHINGS.   177
by a conjuncture of circumstances, which almost of necessity obliges us to take a cozu-d'wil of the whole subject,
and make up our minds, not only as to the validity of
what is done, but of the manner in which it has been
done; the methods employed; the direction in which
we are henceforth to proceed, and the probability of
further progress.
(2.) The subject to which  this lecture is devoted
affords an instance of a conjuncture of this kind.  We
have already had occasion incidentally, in Lect. III.
~ 9, to call attention to the  change which it has
been found necessary to make (at present of a provisional rather than a definitive character) in our estimate of the distance of the sun-a change, implying
of course the necessity of a proportionate alteration in
all those statements of the dimensions of our system,
such as the diameters of the planetary orbits; of the sun
and the planets themselves; and the distances of their
satellites from the primary, and even the estimate of the
masses of all these bodies and the dimensions of the
cometary orbits: all those elements, in short, which
assume directly or indirectly the mean distance of the
sun as their unit of scale. There is reason to believe,
too, that the distance of the moon (our knowledge of
which does not assume that of the sun as known) has
been somewhat misestimated, and that an alteration
(though not nearly to so great a proportional extent),
bringing our nearest celestial neighbour into somewhat
closer proximity than heretofore supposed, is required.
(3.) The dimensions and figure of the earth itself too,
M




I78   CELESTIAL MEASURINGS AND WEIGHINGS.
as concluded from the immense series of great Trigonometrical Surveys carried  on now  during nearly two
centuries, have quite recently, and in two distinct and
independent quarters,* undergone a fresh, and most
searching and elaborate inquiry.  And the conclusion
from both is, that our knowledge on this point is not
likely to be improved in any material degree by any
further operations of the kind; at least until the time,
probably yet far distant, when the Australian Continent
shall have become easily and conveniently traversable
from North to South, and when the wastes of Patagonia
and Terra del Fuego shall afford to future geodesists the
opportunity of winning a hard-earned distinction. Till
then (and most probably then also), we must rest satisfied
with the conclusions arrived at,-conclusions, be it observed, which have disclosed a numerical relation of
singular simplicity between our British unit of measure
and the length of the earth's polar axis.
(4.) Moreover, in ignorance probably of this last-mentioned fact, and therefore with too gratuitous a contempt
for our national and time-honoured standards, and too
hasty a preference for the apparently more scientifically,
and certainly more symmetrically, constructed system of
our continental neighbours, an agitation is and has for
some time been going on, headed by persons of considerable influence, and strongly, no doubt, though we
think unduly, impressed with the  advantage of the
change; with the object of abolishing in toto our British
* By Gen. de Schubert (Mem. Imp. Acad. Petersburg, I859),
and Capt. A. R. Clarke, R.E. (Mem. R.A.S., I86o).




CELESTIAL MEASURINGS AND WEIGHINGS.   179
system of weights and measures, and introducing in its
stead the French metrical system.  A  bill was introduced in the session of 1863 into Parliament with this
avowed object: and though withdrawn, after passing the
second reading, has been reintroduced in the present
(1864), and reached the same stage, with every prospect
of being passed.*  It is true that the change immediately
proposed is permissive, not compulsory: but there can
be no doubt that the attempt, if successful, will be followed up at no distant period by the introduction of a
compulsory measure; one whose effect on the habits,
feelings, and interests of nine hundred and ninety-nine
out of a thousand persons in the whole community, this
is not the proper place to dilate upon.
(5.) As civilization extends, wants and desires of a
higher order than material gratifications  arise; and
among them that of extending knowledge for the sake of
knowing, the craving after a larger grasp, a clearer insight, a more complete conception in all its relations of
the wondrous universe of which we form a part.  Such
desires, when accompanied with the means of their gratification, are included by the author of a recent work of
much interest on the subject of wealth (under the somewhat inappropriate title of Plutologyt), among those
* It has passed, and is now the law of the land.  So far there is
no actual harm done, beyond unsettling opinions and creating uneasiness; but we trust the common sense of the nation will repudiate
any attempt to carry out to its designed completion a measure so
thoroughly retrograde.
t By Professor Hearn, of Melbourne University, Australia. The
title ought to have been Aphnology. Aphnos, or Aphenos (acpvos,




I80   CELESTIAL MEASURINGS AND WEIGHINGS.
sources of positive enjoyment which are not less real
because they are intellectual, or less valuable because
they cannot be appropriated or bartered in exchange:
but which yet cannot be attained by mere intellectual
aspiration or effort; but require for their production and
dissemination appliances and means of a refined character, and combinations of a recondite kind; such as only
an advanced stage of material as well as intellectual progress can furnish. Such a piece of intellectual wealth is
the solution of that great enigma (such, at least, in all
former time) of the distance of the stars,-a problem
which has yielded, at length, to the delicacy and refinement of astronomical observation, during the lapse of
the last thirty years; combined with and acting through
the marvels of mechanical skill and workmanship which
are now obtainable.  That distance is now no longer
the hazy and absolutely indefinite matter of conjecture
which it was (to go no farther back) in the time of Newton, or even in the middle of the last century.  Of some,
at least, of them it can be said with every reasonable
assurance of probability, that their distance is known
within an eighth or a ninth part of the truth, one way or
the other; and of several, that we can arrange them in
order of distance, nearer and more remote, with little or
no presumption of mistake. A stepping-stone is thus laid
for another upward struggle towards the infinite-to the
nebula, the remotest objects of which we have any knowafevos, Gr.), expresses wzeealih in its largest sense of general abund.
ance and well-being. Ploutos (rXouvros, Plutus), riches, in the more
restricted sense of the precious metals, or, at the utmost, of exchangeable value.




CELESTIAL MEASURINGS AND WEIGHINGS.   IS8
ledge: though the stride is here too vast, as it may seem,
for the limited faculties of man ever to take. Nor can
it be said that man is dwarfed and humiliated by such
attempts:-that they teach him  nothing but his own insignificance, and so are the reverse of ennobling. The
greatness of nature is not synonymous with the littleness
of man.  That only is little which cannot rise to great
conceptions.
(6.) Enough, perhaps, has been said to justify an
attempt to lay before our readers the actual state of our
positive knowledge of these subjects; of the methods by
which it has been attained; and of the history of their
development; and to give them  a distinct conception
of the several links which connect the British slandard
inch with the distances of the fixed stars, and of the sort
of intermediate units we have to deal with in the inquiry.
It fortunately happens that we shall not need for our purpose anyresort to abstruse considerations, or have occasion
for any illustrations which are not of the simplest kind.
(7.) In every country having the slightest pretensions
to civilization there is preserved, with more or less care,
some rod, bar, ruler, or other standard, the material incorporation of the national idea of the most ordinary
unit of length; and its representative, when it is required
to test the correctness of one in vulgar use, or to multiply
and disseminate copies of itself for purposes of ordinary
mensuration.  Thus, among the Jews, we find (Exodus
xxx. 2) the cubit'. identified as equal to either of the
* This cubit is presumed to be identical with the Egyptian cubit,
still preserved, of the Nilometer.




182   CELESTIAL MEASURINGS AND WEIGHINGS.
sides, or to half the height of the altar of incense. And
the same is true of similar representatives of the most
commonly received units of weight and measure of
capacity.  What the original type might be, which such
standard professed to represent, matters little.  The
inhabitants of a nation might agree to use for their unit
of length the foot of one of their ancient heroes, or the
hundredth part of the height of their principal church,
or the hundred thousandth part of the extreme breadth
of their country from sea to sea.  But as these objects
could never be appealed to for the settlement of any
practical dispute between man and man, or to convict
the user of any fraudulent measure, a material and producible object must exist in some safe custody, carefully
preserved, or safe in its received sanctity, from damage;
and authoritatively declared, and generally believed to
be, rigorously equal in length to its prototype; and to
have been, at some period, however remote, ascertained
to be so by some appropriate process of comparison; or,
at all events, by the exact copying of some former and
lost standard so compared.  And from the moment of
such authoritative declaration, the length of this material
representative necessarily becomes the real and /legal
unit of length.  The hero may turn out, on a close and
irreverent scrutiny of history, to have been a purely
mythical personage; the church may have been consumed by fire; the breadth of the land diminished by the
encroachments of the sea: but so long as the standard
remains uninjured by rough usage, and secured from loss
by a sufficient multiplication of authentic copies, its




CELESTIAL MEASURINGS AND WEIGHINGS.  IS3
practical utility is unimpaired by such mishaps; and
should it be really damaged or lost, public opinion readily
transfers the same reverence to its legitimate successor.
(8.) The history of our existing " Imperial" standard
is not quite so simple.  It is the successor of one
destroyed by fire in 1834: not, however, being copied
or even having been immediately compared with its predecessor; but recovered by the evidence of an assemblage of other standards which had, at various times, been
compared with that and with each other.  And that
again had been derived, not by direct copying and exact
equalizing with its predecessor the then "reputed Exchequer Standard," but by a somewhat similar process,
from all the best evidence that could be procured of a
former state of things. The ultimate prototype is either
to be referred to the age of Henry I., who is said "to
have settled the yard by the length of his own arm," or
to the more ancient foot of twelve inches, "each the
length of three barleycorns from the middle of the ear,
laid end to end." The point is not of the slightest importance, now that we are assured from the number and
exactness of the copies taken; their wide distribution;
and the precautions taken to ensure their preservation;
that it is scarcely in the power of accident to deprive us
of a perfectly "legitimate" successor in the sense in
which we have above used the term.
(9.) To measure lengths of many miles (to say nothing
of the breadth of a country or of a kingdom), by the
simple repetition and laying end to end of yaid measures
(supposed' exactly equal), would not only be intolerably




I84   CELESTIAL MEASURINGS AND WEIGHINGS.
tedious but impracticable, except on a'carefully-levelled
plain free from all obstructions.  Nevertheless, when the
object is to measure any large tract of country, or to construct a chart of a territory by what is called a "  ri'gfonometrical Survey," it is indispensable to lay down and
measure, no matter at what cost of time and labour,
some one such very long line, as a "base line;" and to
mark its two extremities in some very distinct and permanent manner: so that their linear distance (a large
multiple of the original standard unit) shall not only be
exactly known, but shall be capable of being appealed
to for all future time, or at least till the whole work is
completed, as a new and larger unit, "the length of te
base," to which all other distances in the survey are temporarily referred.  These, being subsequently reduced
by calculation to multiples and fractions of the original
unit, all the dimensions of the territory become finally
known in yards, feet, and inches.  For the purpose of
measuring such a base, the ground must be cleared and
reduced to perfect horizontality (or any slight inclination exactly taken account of), and the intended base
line allineated by placing a telescope a little beyond one
of its proposed extremities, so as to command them
both, and as it were to fore-shorten its whole length into
one point, the intersection  of two wires in its focus.
Anything seen in the telescope to the right or left of
this point, or above or below it, is out of the line.
(io.) Whenever lengths are to be added by the repetition of one and the same unit, there is always a possibility of error arising from imperfect juxta-positions




CELESTIAL MEASURINGS AND WEIGHINGS.  185
And the oftener the unit is repeated (when it once becomes wearisome), the greater is the difficulty of keeping
up the necessary attention, and the greater therefore the
amount of error to be feared in each case. To diminish
this source of accumulating error (besides the saving of
time), it is desirable to diminish the number and increase
the nicety of these juxtapositions.  Hence the utility and
convenience of creating an intermediate unit or set of
such units or "Base-measuring bars," and of devising
some means of juxtaposing or laying them end to end,
without the derangement of one by the small shock
arising from the contact (however delicately performed)
of its successor. These bars should not be so long as to
prevent their being conveniently manageable, yet long
enough to diminish greatly the requisite number of thein
repetitions. The bars now actually used for this purpose are miracles of ingenious contrivance and delicate
workmanship.  They are self-col;pensating for changes of
/emperature; that is to say, the two fine dots which mark
the two extremities of the measure remain exactly at the
same distance from each other whatever be the temperature of the bars, which are compound ones of two differently expansible metals combined on a principle devised
by the late Lieutenant Drummond.  And their repetition
is performed, not by driving the end of one against the
other, or by laying dot against dot, but by focussing a
detached microscope on the more advanced dot, removing the bar and bringing the other dot under the microscope to occupy the exact position in the centre of its
field (marked by a cross wire) which its predecessor




136   CLI ES'TIAL MEASURINGS AND WEIGHINGS.
did.* Thus the bar has been moved forward by its exact
length in the air, as it were, without touching anything.
Arrived at the end of the base, a dot is made and adjusted under the terminal microscope on a gold or
platina plate let into a solid block of stone already prepared —the starting point having been a similar one
similarly fixed at the other end.
(ii.) The base measured, the " Trizangulation" commences.  This is founded on the universally known fact
that when two angles of a triangle are known, a knoxwledge of the length of the side between them leads by
exact rules of calculation to that of the other two; accordingly, at the two extremities of the base, and centrally over the dots which mark them, are placed delicately divided instruments called theodolites, competent
to the measurement of angles to an extreme nicety. The
telescopes of these being pointed so as to look down the
throats of each other, it is clear that both must be
directed along the base line, and if then turned on some
one object at a distance considerably greater from either
than they are from each other, that object becomes the
summit of a triangle, the inclinations of whose sides to
the base is measured.  Its distance from  either end of
the base then can be calculated.  Thenceforward either
of those sides becomes available as a new and longer
base.  And thus the survey may go on, throwing out
In actual practice the procedure is a little more complex, but
the principle is the same; and it is only intended here to convey to
the uninitiated a general notion of the sort of niceties which have
to be attended to.




CELESTIAL MEASURINGS AND WEIGHINGS.   187
new triangles on all sides, of larger and larger dimensions; till the whole surface of a kingdom or a continent
becomes covered with a.network of them, all whose
angular points are precisely determined.  The strides
so taken, moderate at first, become gigantic at last:
steeples, towers, obelisks, mountain cairns, and snowy
peaks, becoming in turn the stepping-stones for further
progress; the distances being only limited by the range
of distinct visibility of objects through the haze of the
atmosphere.  Even this is extended by artificial means
-by Bengal lights at night and by the use of the "heliotrope," a contrivance of the celebrated Gauss for reflecta strong sunbeam from station to station; by the use of
which, stations 90 or Ioo miles distant have been brought
into direct connexion.
(12.) If the earth's surface were a plane such a process
might be continued ad infinitum.  The general roundness
of the earth, however, has been recognized as a fact from
very early ages; and indeed it is scarcely possible for
any thinking person, with ever so slight an acquaintance
with the most elementary geometry, not to be aware of
it.  It was not, however, till about some three centuries
before our era, that something like just notions of its
actual size were entertained: unless we admit (an opinion
which has found strenuous defenders) that this important
datum was already exactly known to the ancient Egyptians 180o  years previously;* a fact, if true, all memory
* The height of the great pyramid from base to apex is (was) contained exactly 270,000 times in the circumference of some one diametrical section of the earth.




188   CELESTIAL MEASURINGS AND WEIGHINGS.
of which had perished in the. lapse of that interval. The
Chaldean astronomers at the later epoch above mentioned are reported to have arrived at an estimate not
very remote from the truth. But the first estimate which
has been handed down to us, accompanied with a statement of the process by which it was arrived at, is that of
Eratosthenes (B.c. 250); who, measuring the shadow
cast by a vertical rod on the day of the summer solstice
at Alexandria, and coupling it with the fact reported to
him, that at Syene in Upper Egypt on the same day,
the bottom  of a well received the full sunshine, concluded a difference of latitude between the two places,
equal to one 5oth part of the circumference of a meridian.
Hence, imagining the two places to lie pretty nearly
north and south of one another, he concluded the circumference of the earth to be fifty times the distance
from Alexandria to Syene, which on the most probable
interpretation of his estimate of that distance in the
itinerary measures of the time, affords an approximation
to what we now know to be the truth, by no means contemptible; falling within about a sixth part of the real
circumference, and if the deviation of the mutual direction of the places from the true meridian be allowed for,
within much less.
(I3.) Thus we see that with very coarse and rude
means of observation and measurement, it is not difficult
to arrive at what may be termed a respectable estimate
(as contrasted with a mere guess) of the size of our own
globe; which is our first step outwards into those distant
regions which will next engage our attention.  We need




CELESTIAL MEASURINGS AND WEIGHINGS.  189
not, therefore, dwell on a multitude of intermediate
attempts between that epoch and the year I669, when
Picard, under the auspices of the then newly constituted
French Academy of Sciences, took up the subject in a
truly scientific manner, and with means and appliances
of a higher order. They all turned, of course, as every
such estimate must do, on the more or less precise
measurement of the length of a degree or a certain number
of degrees of latitude on the earth's surface.  But the step
which this measure of Picard inaugurated, is distinguished
by the abandonment of the old methods of ascertaining
such length (viz. by simply measuring it as an itinerary
distance by rods, or measuring chains, or by rolling
wheels self-registering their own revolutions); and substituting for it the infinitely more precise one, which consists in the very careful measurement of a base line; the
extension from it, northward and southward, of a series
of triangles, as above described; the ascertaining, by
accurate astronomical observations, the latitudes of the
extreme points; and the taking account of the deviation
from the true meridian of their mutual direction, by a
systematic process of calculation, grounded also on the
astronomical determination of their bearings.   From
that to the present time, this process (in which consists
"geodesy" as distinct from mere mensuration and surveying) has been generally adopted; with continual improvement of the instruments used; increasing accuracy in all
the requisite astronomical observations; and the adoption of a more and more perfect and refined system of
computation for the "reduction" of the observations and




190   CELESTIAL MEASURINGS AND WEIGHINGS.
calculation of the sides of the triangles, considered as lying
not on a plane, but on a spaerical surface, and ultimately
(as we shall see) on a spheroidal one.  It is not our
object to dwell on these details, or to describe more
minutely any one of the many operations of the kind
which have been carried out or are still in progress in
France, England, America, Prussia, Austria, Italy (but
more especially and on the vastest scale in the Russian
and in our own Indian Empire), and in the southern
hemisphere at the Cape of Good Hope.  We are only
concerned here with the final conclusions arrived at, and
with the reasons on which they rest, and these are:ist. The length of a degree of the meridian, in whatever region of the earth it is measured, is very nearly the
same, nowhere varying from a general average by more
than about one 200th part of its amount.  And from
this it follows that the figure of the earth approaches
exceedingly near to that of an exact sphere. For the
length of such a degree is a measure of the curvature of
the surface, it being evident that were any one to travel
southward  till the meridian  altitude of a star was
increased by one degree, he must have arrived at a
place where the surface on which he stands is just
one degree inclined to that at his starting point: so that
in walking on he is at that moment pursuing a course
deviating by one degree from the direction of his outset.
Now this deviation from a strazight course is our idea of
curvateure. The curvature of each geographical meridian
then is very nearly the same everywhere.  In other
words, the earth is very nearly a sphere. The average




CELESTIAL MEASURINGS AND WEIGHINGS.   191
length of a degree of its circumference is 364,578 English feet; or very nearly as many thousand feet as there
are days in a year.
2d. Though  nearly, the  degrees are  not precisely
equal.  In all geographical longitzudes the degrees of latitude are found to increase in length in going from  the
equator towards the poles.  An increase in the length of
a degree indicates a less amount of curvature.  The
earth's surface is therefore less curved, or less convexthat is, flatter —as we approach its poles on all sides
from  the equator.  Its form  then is elliptical, or oblaze,
and its polar diameter somewhat shorter than its equatorial.  From  the most recent calculations (those of Captain Clarke, founded on a general assemblage of all the
measured arcs) it results that the difference of these two
diameters is one 292d part of the former.
3d. That the length of its polar diameter is 4I,707,796
British imperial standard feet, which is within a single
furlong of 500,500,000 such inches.
(I4.) Hence it follows, that if we were to increase all
our imperial standard measures, each by one precise thoz,sandt part,* and designate the measures so increased by
the epithet geovmetrical instead of inperial, a geometrical
inch would be the exact 5oo,ooo,oooth part; a rod of
fifty szuch inches the exact io,ooo,oooth part of. the
earth's polar axis; and one of twenty-five such (which
might be called A GEOMETRICAL CUBIT) the io,ooooooth
I have before me for ordinary use two foot rules, both bought
at respectable shops, and not the worse for wear, which differ by
more than this amount.




192   CELESTIAL MEASURINGS AND WVTEIGHINGS.
part of its polar semi-axis: that is to say, if we disregard
so insignificaht an error as a furlong upon 8000 miles,
or one part in 64,000.
(I5.) It follows, moreover (as may be verified by any
one who will make the calculation), that if we consent
to disregard so trifling an error as one part in 8000; one
cubic geometrical foot of distilled water at our standard
temperature weighs exactly iooo of our actual imperial
ounces, and is exactly filled by ioo of our actual imperial half-pints.*
(16.) Having thus exhibited the connexion between
our ordinary measures of len,_h, weight, and capacity,
and the dimensions of the globe we inhabit (a connexion
of singular felicity, when we consider the simplicity of
the numerical relations), we are prepared to take a further step, and, by using the diameter of the earth itself
as a base-line, carry on the same principle of triangulation into our solar and planetary system.  In this, the
natural unit —that to which astronomers have agreed
with one accord to refer all its dimensions —is the mean
or average distance of the earth from the sun, or the
semi-axis of the ellipse which it describes about that
luminary.
(17.) The way in which a knowledge of this distance
is obtained being very fully described in our Lectures on
"The Sun" and on " Comets," t it is unnecessary to re* The deviation of the actuzal French litre and gramme from
their true theoretical values, is more than three times as great, being one part in 2730.
t A very unfortunate erratum exists in one of the numbers in p.




CELESTIAL MEASURINGS. AND WEIGHINGS.   193
peat the explanations there given.  The use which may
be made of Venus as a stepping-stone on the way
towards the great centre of our system, however, is
there rather alluded to than explained; so that a few
words on this subject will not be out of place here.
The interval between Venus and the earth when near
est, is not more than one-fourth of the sun's distance,
and its angular displacement when seen from opposite
extremities of a diameter of our globe, therefore, four
times as great as the sun's. Venus, however, is invisible
in this situation, except on those very rare occasions
(occurring at intervals alternating between eight years
and upwards of a century) on which it passes between
us and the sun, and is seen as a round black spot on its
disc.  In this state of things the face of the sun itself
serves as a screen onl which the planet is seen projected;
and its circular outi.:;  serves as a celestial line of reference,. across which the planet is seen to" transit," as it
would across wires fixed in the focus of a telescope; or
rather as it would across the circular outline of what
astronomers call a "ring micrometer."  The sun itself is
thus transformed for the time into an astronomical instrument of that description, freed by nature from  all
the sources of fluctuation and instability which affect our
instruments.  And the whole observation is reduced to
determining the precise moments of time at which the
foremost and hindmost borders of the planet cross this
479, col. I, line 52, of this last-mentioned Lecture as printed originally in "Good Words' -For I6,071, read 6,071. All the other
numbers are right, as they there stand.
* *   ~  "                               ^




194   CELESTIAL MEASURINGS AND WEIGHINGS.
ring (which they do in a very leisurely manner), leaving
the apparent displacement of the planet on the sun's disc
to subsequent calculation, on a comparison of reports
from all the points of observation selected. One-fourth
of the advantage arising. from its proximity, it is true, is
lost,. by the sun itself sharing to that extent in the displacement- of the planet; but enough remains to give
this a superiority over every other method of measuring
the sun's distance.
(18.) Taking as the general conclusion for that distance which we must at present rest in, that assigned in
our article last cited, viz., 9I,7 18,oo   imperial (or
91,626,282 geometrical) miles, we find it equivalent to
23,222 polar semi-diameters of the earth, or ten million
times that number of GEOMETRICAL CUBITS of twenty-five
geometrical inches each.
(19.) Our next step is to the fixed stars, within whose
sphere modern science has at length made good a footing, secure, though somewhat unsteady for the present.
In conformity with the same principle of procedure, we
here rest for our base of operations on our last and
greatest accessible measured length, viz., the diameter of
the earth's annual orbit, a base line of I83,000,000 miles,
which, as the orbit is very nearly circular, presents itself
(in some situation or other across it) perpendicularly to
a line joining the sun and any selected star, so as to be
seen unforeshortened from  the star.  As the earth at
half-yearly intervals passes alternately from one to the
other extremity of such a diameter, the visual line by




CELESTIAL MEASURINGS AND WEIGHINGS.  195
which the star is seen will undergo a semi-annual displacement to and fro to the amount of the apparent (angular) breadth of the orbit as it would be seen by a spectator in the star. And this, in its equivalent form of
annual displacement, is the angle astronomers have to
measure for the purpose in question. One would naturally suppose that so enormous a magnitude would be
something conspicuous from any distance short of the
fabulous; and that here at least we should have something to deal with palpable to very moderate means of
observation. Pent up and "chafing within the narrow
limit of the world" the astronomer in his measurement
of the sun's distance might complain, in the words which
the poet puts into the mouth of the great conqueror of
antiquity, of restricted elbow-room. Using the world
itself as a means of transport, and thus enabled to commence anew on so vast a scale, he might expect to find
" ample room  and verge enough" for his operations.
Quite the contrary! The earth itself seen from the sun
would appear as large as the globe of Saturn at its medium
distance does to us-a very conspicuous object in a
moderately good telescope.  A globe large enough to
fill the ear/th's or-bi rounzd the sun would appear to a
spectator placed in the nearest fixed star, hardly larger
than the third satellite of Jupiter, as seen from the earth;
which requires a very good telescope to be perceived to
have any size at all.
(20.) Two methods only have been devised by which
this annual or p-a/lactic displacement (as it is technically




I96   CELESTIAL MEASURINGS AND WEIGHINGS.
called by astronomers)'* can be ascertained.  The first
consists in determining the exact situation which its
direction in space holds at all times of the year in relation to some plane, and to some line in that plane which
we have reason to consider as fixed; or at all events of
whose movements (exceedingly small in amount) we can
render an exact account. Such a plane is that in which
the earth revolves round the sun, or the ecliptic, and such
a line that of the equinoxes, and the astronomical process
employed is that by which the two elements technically
called the longitude and latitude of the star are determined.
This is in effect the process by which all celestial charts
are constructed and catalogues of stars made. Only for
this purpose the observations require to be made with
the very best instruments; with the minutest attention to
everything which can affect their precision; and with the
most rigorous application of an innumerable host of "corrections," some large, some small, but of which the
smallest, neglected or erroneously applied, would be
quite sufficient to overlay and conceal from  view the
minute quantity we are in search of. To give some idea
of the delicacies which have to be attended to in this inquiry, it will suffice to mention that the stability not only
of the instruments used and the masonry which supports
them, but of the very rock itself on which it is founded,
is found to be subject to annual fluctuations capable of
seriously affecting the result.  So that it is only when
after a series of observations continued for several years
* What is technically called parallax, is only the half of the total
annual apparent displacement.




CELESTIAL MEASURINGS AND WEIGHINGS.  197
it is found that one star appears to be subject to a regularly recurring annual displacement, such as that which
the earth's orbital motion might cause, and others in its
near neighbourhood show no signs of it, we can accept
the double conclusion that the one is and the others are
not at a measurable distance.
(2.) As the ancients had no knowledge of the earth's
motion, so they could have had no conception of this
annual displacement of the stars or of their" parallax."
Tycho Brahe who rejected the Copernican system, might
perhaps have been led to do so from his not having been
able to perceive any such displacement of the pole star,
hich, from the rudeness of his means of observation, he
could not possibly have done. Much more lately, in the
latter years of the 17th and beginning of the i8th centuries, the attention of many eminent astronomers was
drawn, in consequence of the improvements then introduced in the construction of astronomical instruments,
to a regularly recurring annual displacement of certain
stars observed by them to a very considerable amount,
which was at first supposed to be parallax, but which
proved to be what is now called " aberration," and to be
common to all the stars; and when this was recognized
finally by Bradley as a result of the motion of light, the
idea of a measurable " parallax" was abandoned in despair; to be revived again by Dr Brinkley in I8Io; who
from his observations with a very fine circle in the Royal
Observatory of Dublin thought he had detected a parallax of i" in the bright star Lyra (corresponding to an
annual displacement of 2"). This however proved to be




198   CELESTIAL MEASURINGS AND WEIGHINGS.
illusory; and it was not till the year 1839 that Mr Henderson, having returned from filling the situation of Astronomer Royal at the Cape of Good Hope, and discussing a series of observations made there with a large
"mural circle " of the bright star a Centauri, was enabled
to announce as a positive fact the existence of a measurable parallax for that star: a result since fully confirmed
with a very trifling correction by the observations of his
successor, Sir T. Maclear.
(22.) The parallax thus assigned to a Centauri is so
very nearly a whole second in amount (o"98) that we
may speak of it as such.  It corresponds to a distance
from the sun of 206,265 times that of the sun from the
earth, which, as we have already seen, is itself 23,222
polar semi-axes of the latter, thus making a total of
4,789,880,ooo  such  semi-axes  (or Io,ooo;ooo times
that number of geometrical  cubits), equivalent to
I8,918,,ooo,000,oo    (nearly nineteen billions) of British
statute miles. Its near neighbour a of the same constellation and other stars adjacent exhibit no such
annual displacement, and  are therefore beyond the
reach of our measurement.  Such, then, is the length
of the sounding-line with which we have first touched
bottom  in the attempt to fathom  the great abyss of the
sidereal heavens.  At such a distance, the vast globe
filling the earth's orbit, above spoken of, would be
covered from sight by a human hair held at twenty-five
feet from the eye.*
(23.) The other mode in which this great question
* Supposing the pupil reduced to a point.




CELESTIAL MEASURINGS AND WEIGHINGS.   I99
has been approached is to select for inquiry bright stars,
which have in their immediate vicinity, so near as to be
seen with them at the same time in the same telescope,
two or three other very much smaller ones; and without
troubling ourselves to determine their absolute places in
the heavens (so throwing overboard the enormous difficulties which, as we have seen, that determination to a
sufficient precision presents), confine ourselves to what
may be called a microscopic examination and mapping
down of the relative distances and situations of these
stars inter se. Repeating this at all seasons of the year,
we are enabled to ascertain whether the large star maintains steadily the same invariable position among the
smaller ones; or is affected by any movements of which
they do not partake.  There is a general frimal facie
probability that the brighter stars are nearer than very
faint ones: and, near objects being more displaced than
distant ones by the spectator's change of place; the
large star in the case supposed would appear, by the
effect of parallax, to move to and fro among the smaller
ones; or rather to describe annually a minute ellipsis
among them, the exact counterpart, equal in size and
similar in the situation of its longer and shorter diameters, to that into which the earth's orbit itself would
be seen projected by the effect of perspective from the
star.  Now no casual movement, or one arising from
any other physical cause, could be mistaken for such a
motion as this. For, not to mention the completion of
the revolution in an exact year, the two diameters of
the ellipse ought to stand to each other in a certain defi



200   CELESTIAL MEASURINGS AND WEIGHINGS.
nite and calculable proportion known beforehand; and,
moreover, the longer ought to be situated in a parallel of
latitude, and the shorter in a circle of longitude passing
through the star.
(24.) There is a star, the 6ist of Flamsteed's list, of
those in the Constellation Cygnus-a star far, however,
from  conspicuous for its brightness; being only of the
fifth magnitude; but which, for a reason presently to be
mentioned, was suspected to be nearer than the generality of the stars.  This star was subjected by the late
Professor Bessel to the examination above described
between the years I834 and 1838, and the result of his
examination (made public by a singular coincidence a
few days before the announcement of Professor Henderson's discovery) was such as to leave no doubt of the
reality of its parallax, to the amount (as slightly corrected by a further continuance of his observations) of
o" 35.  Later astronomers,* going over the same ground,
with more perfect instruments and improved practice in
this very delicate process of observation, have found
a somewhat larger result-stated by one at 0o'57, and
by another at 0"'5Iso that we may take it at o"'54,
corresponding to somewhat less than twice the distance
of a Centauri; or to 374,320 solar distances, which
light would require about eight years and four months
to travel over.
(25.) It cannot be supposed that results like these
would be accepted without undergoing the most severe
scrutiny and receiving confirmation from further and
* Messrs Auwers and 0. Struve.




CELESTIAL MEASURINGS AND WEIGHINGS.  201
continued observation.  They have received it, and
(with exception of those subsequent corrections in the
numerical values which we have noticed and included
in the above statement) they remain intact, and rank
among the well-established facts of astronomy. Moreover, numerous other stars have been subjected to examination, some by one, some by the other method.
And the result is not a little surprising. Up to the present time, out of all the stars examined, only a very few
exhibit any distinctly measurable amount of parallax.
The list hitherto accumulated consists only of about ten
or at most a dozen. Of these cc Centauri, in the southern hemisphere, is the nearest.  It is a fine star of the
first magnitude, the third or fourth in brightness of all
the sidereal host.  This is our next neighbour.  On the
other hand, Sirius, the brightest of all the stars, and
Lyra (next to Sirius, one of the four most conspicuous
stars in our hemisphere) stand low in the order of proximity.  This, of course, only proves that among the
stars there exists a very wide range of absolute brightness, but by no means invalidates the strong d priori
reasons for admitting distance as a very important element in determining their relative apparent brightness.
(26.) But how, it will be asked, came such a seemingly insignificant object as this No. 61 to be selected
for examination at all, to the exclusion or postponement
of so many more conspicuous? We reply, by reason of
its large apparent proper motion.  None of the stars we
see maintains quite the same relative situation among its
compeers.  It would be strange if it did.  Unless nailed




202   CELESTIAL MEASURINGS AND WEIGHINGS.
to the celestial vault and carried round with it, such a
thing is not to be supposed.  In the total absence then
of any information as to the velocity or direction of the
real motions, we can only presume that such as appear
to move fastest are nearest.  The fact may be otherwise,
but such at least is the primifacie presumption.  Now,
while the stars in general exhibit an annual apparent
proper motion averaging less than a second per annum,
these two 6i Cygni and a Centauri, are carried annually
from their places, by movements apparently rectilineal
of 5'3 and 3"'6 respectively: motions which would carry
them away from their places through a space equal to
the moon's apparent diameter in 339 and 499 years respectively. In point of fact, we find that they are nearer,
so that a part at least of their great apparent motions is
owing to proximity.
(27.) Such a uniformly progressive change of place
complicates apparently, but not really, the microscopic
process we have described. Being accurately known by
long continued observation, both in amount and direction; its effect in displacing the star among its neighbours is easily taken account of and allowed for. The
combination of these two motions, the one real and
rectilinear, and the other apparent and elliptic, will be
readily understood from  the accompanying diagram,
where ab, be, cd represent the former continued for
three years; e, f, g, the ellipses described in those years
in virtue of the latter in the direction of the arrows; and
h i k the sort of undulating line apparently described in
virtue of them both going on together.




CELESTIAL MEASURINGS AND WEIGHINGS.  203
(28.) But, besides this, the two stars in question are
remarkable in another way. They are both conspicuous
DOUBLE STARS, and have been long watched with especial
ue                   y
Fig. i.
interest by reason of the two individuals of which each
respectively consists standing to each other in the relation of sun and planet, or planet and satellite. Not only
do they keep close company with each other in their
journey through space by a common  roper motion; but
while so journeying together they revolve about each
other or about their common centre of gravity in regular
elliptic orbits, under the influence of that very same law
of gravitation which retains the planets in their circulation round the sun.  They are, therefore, at the same
distance from us, and therefore both equally and similarly apparently displaced by parallax; so that each of
them, microscopically watched, appears to describe the
same minute annual parallactic ellipse above spoken of.
This must not be confounded with the elliptic orbit the
two stars describe about each other.  That is on a far
larger scale, and requires many years for its completion.




204  CELESTIAL MEASURINGS AND WEIGHINGS.
It is to the dimensions of these and similar orbits described byothers of those wonderful bodies, the double
stars, about each other, that we have now to turn our
attention: thus opening another chapter in the history
0Fig 
Fig a,
of sidereal mensuration. The mode in which these two
elliptic movements, the larger real, and the smaller apparent or parallactic, are combined together or superposed, and the sort of undulating line apparently described by either star in consequence, will easily be
understood by a glance at Fig. 2.
(29.) Assiduous observation, aided by a powerful and
not very complicated system of calculation, has enabled
astronomers to assign in a great many instances with
considerable precision the trueforms of these orbits as
distinguished from those in which, by the effect of perspective (owing to their oblique presentation to our
sight), they aeppear; to state the amount of that obliquity;




CELESTIAL MEASURINGS AND WEIGHINGS.   205
the situation in space of the planes in which they revolve;
and the number of years required to complete their revolutions.  Among them  occurs every variety of form
(always elliptic), from  the nearly circular one of the
planetary, to the long ellipsis of the cometary orbits;
every variety of oblique presentation, from a plane passing nearly or quite edgeways through the eye of the
spectator to one nearly perpendicular to the visual line;
and every length of period, from thirty years up to many
centuries. The only element about which in the great
majority of cases we are left in complete uncertainty, is
the actual size of the orbit, which cannot become known
till the distance of the star is ascertained.  For our present purpose then we must confine our attention to those
of which at present the distance is known.  The two
just spoken of present a striking contrast.  The revolution of the two stars of a Centauri is performed in about
seventy-eight years.  Their orbit is a very elongated
ellipse, decidedly cometary in its character; and its presentation to our sight so nearly edgeways, that the two
stars at present almost occult or cover one another;
though when at their greatest distance from each other,
they would appear, if viewed perpendicularly, nearly
thirty seconds apart.  The other requires about 514
years for a complete revolution.  Its orbit is nearly
circular, and its presentation to our view nearly perpendicular: so that we see the distance between the two
stars unforeshortened; and so seen it measures almost
exactly sixteen seconds, or a little less than the average
apparent diameter of the globe of Saturn. Now we have




206   CELESTIAL MEASURINGS AND WEIGHINGS.
already seen that in the former case the distance between
the earth and sun would appear under an angle of I" and
in the latter 0"'54, whence it is easy to conclude that the
mean distances of the stars from each other, or the semiaxes of their orbits, are, in the former case about 15, and
in the latter about 293 times that distance. The former
orbit would be contained between those of.Saturn and
Uranus: the latter is about the size of that of Neptune.
(30.) In such orbits, then, gyrating round each other
-not in the subordinate relation of sun and planet, but
as compeers in dignity and on the equal footing of regal
splendour; communicating to each other we know not
what benefits, and bound on we know not what errand,.
-are these wonderful sidereal couples journeying onward
through space at the respective rates of 920,000 and
2,500,000 miles per diem  at the very least: for such
would be their proper motions were we sure that they are
not foreshortened by oblique presentation to our line of
sight!
(31.) An interesting, and what to many of our readers will probably appear a very unexpected, conclusion
follows from this determination of the distance of these
stars, conjoined with the knowledge so obtained of the
periodic times of their orbital motion. It enables us to
wzeigh them; that is, to state in numbers the proportion
which the total ponderable mass or aliount of gravitating
matter of the two stars of either couple bears to that of
the sun, and therefore as a necessary consequence to that
of our own globe, and ultimately (if we choose to luxuriate in the long array of figures in which such a calcu



CELESTIAL  MEASURINGS AND WEIGHINGS.   207
lation would land us) to our British standard ounce, of
which this our globe is equivalent to about 2I0 quadrillions.'
(32.) It is an  elementary proposition  in  physical
astronomy that the time in which two masses so connected into a system by their mutual attraction, revolve
about each other in elliptic orbits, depends only on the
sum  of their masses or weights, and on the lelngth of the
elliptic relative orbit, and not at all on its breadth, and is
therefore the same as if the orbit were circular, i.e., as
if the two masses were retained constantly at the same distance from each other, viz., that which we have called their
mean distance; and which mean distances, as we have seen
in the cases before us, are respectively in round numbers
fifteen and thirty times that of the sun from the earth.
(33.) It is an equally elementary conclusion from the
theory of gravitation, and was long since demonstrated
by Newton, that, so far as the time of revolution is concerned, it is unimportant in what proportions the sum of
the masses.or the entire ponderable matter of the system
is distributed between the two, the distance being unaltered.  That time, therefore, would remain unaltered,
* Adopting that nomenclature which calls I followed by 6 ciphers
a million, by 12 a billion, by I8 a trillion, and by 24 a quadrillion.
For the weight of our globe in tons (5852 trillions), see Herschel's
" Physical Geography," 2d edit. sect. 5. The elastic forces with
which Mr Bailey, in his repetitions of the celebrated " Cavendish
Experiment" (from which this estimate of the weight of our globe
is concluded) compared that weight, varied from less than one
29,oooth part of a grain in some experiments to one 2500th in
others! The result, however, being corroborated in various ways,
is received without hesitation.




208  CELESTIAL MEASURINGS AND WEIGHINGS.
if all the ponderable matter but a single pound were collected in one of them, and that pound circulated about
it as the earth does about the sun.  Here, then, we have
the case stated over again, with only the difference of
times and distances, which, in our Lecture on "The
Sun," already referred to, ~ 16, 17, served us to show how
we might arrive at a knowledge of the sun's mass, and to
calculate that mass.  Substitute in the. reasoning there
explained for one year 78 or 514 years, and for the sun's
distance respectively fifteen and thirty times that distance;
and the result, in place of the mass of the sun, will furnish us with the total or joint masses of the two stars in
the one or the other of these two sidereal combinations or
"binary systems" respectively.  We shall not trouble
our readers with the calculation: suffice it to state the
result, viz., that the joint mass in question in the former
pair (that in the Centaur), is about  -, -a little more
than half that of the sun, or equal to 198,000 earths;
and in the latter (in the Swan), about l-  of the sun,
equivalent to 36,000 earths.'(34.) Beyond the distances of these two remarkable
sidereal combinations, our grasp becomes less and less
assured as we push forward into space.  Remarkably
enough, Sirius and Arcturus, the two brightest stars
visible in our hemisphere, stand barely within the limits
of any estimation approaching to certainty,-the former
being between six and seven, the latter about eight,
times the distance of our nearest neighbour in the Centaur. At the distance thus assigned to Sirius, our sun (if
any faith can be placed in photometry) would appear as




CELESTIAL MEASURINGS AND WEIGHINGS.  209
a star hardly of the sixth magnitude-invisible, therefore,
or but barely discernible to the ordinary unassisted eye;
and it would require four hundred such suns concentred
into one to send us the light which that superb star
actually does; supposing none lost or extinguished in
traversing so enormous a distance: a journey which it
would take more than twenty years to accomplish! We
speak here only of the proportion between the  /izts of
the two bodies; but this can give no indication of that
between either their magnitudes or their weights or
masses, since the intrinsic splendour of the surface of the
one may, for anything we can tell, exceed that of the
other in any proportion. As to the proportion between
the masses, however, a very unexpected prospect of being able to ascertain it ere many years  shall have
elapsed; and even of forming something like a rude
estimate of it already, has quite recently opened to us:
the history of which may serve to show what persevering
industry will accomplish in apparently the most hopeless
lines of inquiry.
(35.) Sirius, as the most conspicuous of the stars, has
been watched by all astronomers with the utmost assiduity as the principal of the great landmarks of their
science; the chief of their list of "fundamental stars;"
those to which every observer of necessity resorts to test
the stability of his instruments; the rates of his clocks;
and every condition which gives precision to his observations. It has long been known, like most and probably all the other stars, not to be absolutely fixed in the
heavens: but subject to what we have above described
0




210  CELESTIAL MEASURINGS AND WEIGHINGS.
as a Cproper motion," or slow progressive movement
pr(oper to itself as an individual: smaller indeed than
those already specified in its apparent amount, but by
no means inconsiderable, being sufficient to displace it
by about two minutes in angle or one-fifteenth part of
the apparent diameter of the moon per cenzury: corresponding at the distance of the star to no less:an amount
of actual linear travel than I,9oo,ooo miles per diem.
This movement, in the absence of all apparent reason to
the contrary, was of course presumed to be uniform and
rectilineal; but as instruments improved, as observations
became more exact, and their calculation more scrupulous and refined, this became at first doubtful, and at
length demonstrably incorrect.  Not to dwell on the
steps of the proof, it became apparent that the visible
path of the star, mapped down from year to year and
from  century to century, is not a straight line, but is
affected by a small and regularly recurring undulation,
alternately carrying it to a small distance above and
below the medial line, similar to those represented in
Fig. I: the performance of one complete undulation
occupying about 491 years, and the excursions to and
fro on either side of the medial line being about onesixtieth part of the linear distance passed over in the
same interval.
(36.) It was impossible to ascribe this phenomenon
(as in the case of our star in the Swan) to parallax.
Were this its origin, the undulations (as above explained)
would be annual, instead of extending over a period of
nearly fifty years; and moreover that cause of apparent




CELESTIAL MEASURINGS AND WEIGHINGS.  211
motion was taken account of in the investigation, in a
manner we need not here explain.  The only other, and
in the then state of knowledge a very obvious, way of
accounting for it, was to ascribe these anomalous movements to the attraction of an unseen companion; in other
words, to consider Sirius as in reality a " double star;"
its companion being either a non-luminous body, and in
the nature rather of a planet than an associated sun; or,
if luminous, so feebly so as to be lost in the rays of Sirius
itself, which, in powerful telescopes, is of dazzling brightness.  Accordingly, Professor'Peters,'to whom we owe
this interesting investigation, proceeded (by steps which
we could not possibly make clear to our readers, and
which indeed only experts in mathematical calculation
can follow) to compute the relative orbit of the pair on
the theory of gravitation, and thence to ascertain,-not
their mutual distance from  each other (for that necessarily then remained uncertain) but that of Sirius itself
from  their common centre of gravity.  For this he found
an apparent angular measure, of 2"'4, corresponding to
about I6~ times the distance of the earth from the sun;
and calculating on his final result, the observed anomalous deviations from uniform rectilinear motion were
found to be satisfactorily accounted for.
(37.) It is now time, however, to mention what, to
render our explanation more simple, we have hitherto
kept out of view, viz., that all the foregoing calculations
were directed only to that part of the "proper motion"
of Sirius which carries it in the direction of a parallel to
the earth's equator, or, as it is technically called, "in




212  CELESTIAL MEASURINGS AND WEIGHINGS.
right ascension." If that movement were coincident in
direction with such a parallel, there would remain nothing further to explain. But such is not the case. It
is oblique; and may therefore be regarded as composed
of two movements,-the one along that parallel (in right
ascension), the other perpendicular to it, or, as it is
technically called, "in declination." Now these movements admit of a distinct and separate examination, and
it is clear that, if both do not agree in indicating the
same kind of undulation and the same identical period,
the explanation so afforded of what may be called one
half of the phmenomenon is at variance with that of the
other.  Mr Peters left this other half untouched; but
very recently that also has been examined by an American computist, Mr Safford, on the same principles; and
the result is that the orbital motion, which accounts for'the one set of movements, gives at the same time a sufficiently satisfactory explanation of the other.
(38.) Here, then, we are furnished with another example like that afforded by the grand discovery of the
planet Neptune by the calculations of Adams and Leverrier. The existence of a celestial body not seen and not
before known to exist, has been revealed to us and its
orbit computed, by the simple application of mathematical calculation grounded upon observed irregularities
in the movements of one already well known.
(39.) The parallel of the cases promises to be still
closer.  Neptune, as is well known, was immediately
sought and found in the place assigned to it by the calculation. In January 1862, Mr Alvan Clark, an eminent




CELESTIAL MEASURINGS AND WEIGHINGS.  213
optician of New York, turning on Sirius a fine telescope
of his own construction, noticed extremely near to it a
minute star which had eluded all former observation.
This may be the body in question. There is even some
reason to suppose it is.  Its apparent situation is stated
to be at least not such as to be incompatible with such
a connexion.  Its real existence has been verifed, and its
apparent distance from Sirius measured, and found to be
about seven seconds; corresponding (if seen unforeshortened) to about forty-seven times the distance of
the sun from the earth.
(40.) Another beautiful specimen of these binary sidereal systems is presented by the star No. 70 in Flamsteed's list of those in the constellation Ophiuchus, and
therefore cited as 70 Ophiuchi. The ellipse described
by the stars of this pair (the one a star of the fourth, the
other of the sixth, magnitude) has been determined with
much care and every probability of considerable precision. The period of their mutual circulation may be
stated at about ninety-six years, and the semiaxis of their
mutual ellipse in angular measure at 4"'8.  Of this elegant couple the parallax has been ascertained by M.
Kriiger, from observations made in I858 and 1859, at
o"'I6.  And from  these data he concludes in the very
same way:-First, their distance from  our own system
(I,272,000 semi-diameters of the earth's orbit); secondly, the mean distance of the stars from each other
(302 such semi-diameters, so that here also their relative
orbit is nearly equal to that of Neptune); and, thirdly,
the total mass (equivalent to 3- times that of the sun).




214  CELESTIAL MEASURINGS AND WEIGHINGS.
(4I.) Shall we spread our wings for a farther flight-to
the region of the nebulae? For such an excursion we are
hardly yet prepared.  Our present reach extends, as we
have seen, only to a very few of our nearest neighbours
among the stars; a class of bodies which we have every
reason to believe form with our own sun a system-to us
a universe —but which, removed to the distance of the
nebulae, would appear perhaps as one of them.  Moreover, it is not wings, but a resting-place for the sole of
our foot that we want. If we knew in what orbit the sun
itself is moving (for that it moves is certain, and with no
trifling speed), and if human observations were to endure
till it had completed half a circuit in that vast orbit-then
indeed we should have established a new base line from
whose extremities the parallax of'the nearest nebula
might become sensible. Failing this, we must rest content with such probable indications as we can glean from
other sources.
(42.) There is one which can hardly fail to strike any
one who does not reject altogether from his philosophy
the consideration of design and purpose in the construction of the frame of nature.  In their orbits round the
sun, the earth and other planets carry round with them
satellites retained in their orbits by gravitation to their
primaries.  These orbits, though very sensibly disturbed
by the sun's attraction, are yet in no case so much so as
to hazard in the smallest degree the stability of these
miniature planetary systems, or in the lapse of even indefinite ages to produce any very material change in
their relations to their primaries or to each other. The




CELESTIAL MEASURINGS AND WEIGHINGS.  2I5
enormous distance which separates the sun from  the
nearest fixed star affords a still more complete guarantee
against the possibility of any disturbance of the planetary movements by their attraction, and may not unnaturally be considered as so intended. A continuance
of the same system of precaution (if we may venture on
the use of such a word) against external influence, into
the mutual relations of sidereal systems might therefore
lead us to expect that the intervals between them would
at least bear some very large proportion to the extent of
each. That there exist instances of nebula which appear
to be bound together by a kind of companionship similar
to that of the double stars, does not in the least invalidate
this as a general conclusion.  Here, however, figures
avail us nothing.  Nor can it be necessary, after what
has been already said, to stimulate our imaginations to
any further effort to grasp and comprehend distances
and magnitudes inconceivable by man.  Suffice it that
in the dim glimpse thus caught of an immensity of material existence stretching outward by steps continually
more and more gigantic, we carry with us not a mere
general impression, but a well-founded  conviction
grounded on an induction from observed facts of measurement and computation, that the same mechanical
laws at least; the same relation between matter, force,
and motion as those we see in action around us, prevail
in the uttermost regions of space; and regulate, there as
here, the evolutions of the systems disseminated through
it. In the endless variety of combination exhibited
among the double stars too (to say nothing of a multi



216  CELESTIAL MEASURINGS.AND WEIGHINGS.
tude of other phaenomena, less clearly in1tellZg-ible, which
the sidereal heavens present, and to which our subject
has not led us to refer), we trace the same inexhaustible
fecundity of design realized and embodied in the same
unity of workmanship which in this our planetary system
we find luxuriating in so surprising a variety of forms,
magnitudes, and mutual relations among its primaries,
satellites, rings, comets, and asteroids.
(43.) Is the material universe finite or infinitel The
question is as old as Aristotle; and the answer, though
uznalzsweerable, never yet convinced mortal man.   A
material universe must consist of material objects, each
individual of which, being a really existing thing, must
possess that attribute of all real existing things, place.
Every two objects then, be they where they will at any
certain moment of time, mark ltwo defZiife places, and the
distance  between them, or the straight line joining
them, has two definite terminations.  It is not therefore
infinite in length, but finite, ie., terminated.  Now an
assemblage of objects, every two of which are distant
from each other by a finite interval, cannot be infinite in
extent.   The speculation is unprofitable  enough in
itself, and the difficulty it involves turns on the mental
substitution of a positive and conceivable notion of " the
infinite " for the purely negative and utterly inconceivable
one which it carries with it into all matters where the
term is employed in its logical sense. -Our only reason
for at all alluding to it is, that to zis, practically speaking, the material universe lust be regarded as infinite:
seeing that we can perceive no reason which can place




CELESTIAL MEASURINGS AND WEIGHINGS.   217
any bounds to the further extension of that principle of
systematic subordination which we have already traced
to a certain extent; and which combines in its fullest
conception a unity of plan and singleness of result with
an unlimited multiplicity of subordinated individuals,
groups, systems, and families of systems. Thus it by no
means follows that all those objects which stand classed
under the general designation of " nebul " or " clusters
of stars," and of which the number already known
amounts to upwards of five thousand, are objects (looked
upon from this point of view) of the same order.  Among
those dim and mysterious existences, which only a practised eye, aided by a powerful telescope, can pronounce
to be somethzizg differentfrom minute stars, may, for anything we can prove to the contrary, be included systems
of a hizh/er order than that which comprehends all our
nebulae (properly such) reduced by immensity of distance
to the very last limit of visibility.  And this conception,
we may remark, affords something like a reasonable
answer to those who have assumed an inperf7ect trassparency of the celestial spaces, on the ground that, but
for some such cause, the whole celestial vault ought to
blaze with solar splendour, seeing that in no direction of
the visual ray, if continued far enough, would it fail to
meet with a star.  Such would no doubt be the case
were all space occupied by stars disseminated through it
uniformly, i.e., so that the same number of stars should
in every region be comprised in the same space.  But no
such consequence would follow were the law of sidereal
distribution such as we have been here describing: a




218  CELESTIAL MEASURINGS AND WEIGHINGS.
position, however, with whose demonstration (founded
on the very elementary properties of a decreasing geometrical progression) we shall not trouble our readers.
(44.) Such a speculation as this just mentioned may
possibly appear irrelevant. But it must be remembered
that it is LIGHT, and thefree communication of it from the
remotest regions of the universe, which alone can give, and
does fully give us, the assurance of a uniform and allpervading energy-a mechanism almost beyond conception complex, minute, and powerful, by which that
influence, or rather that movement, is propagated.
Our evidence of the existence of gravitation fails us
beyond the region of the double stars, or leaves us at
best only a presumption amounting to moral conviction
in its favour. But the argument for a unity of design
and action afforded by light stands unweakened by distance, and is co-extensive with the universe itself.




LECTURE VI.
ON LIGHT.
PART I. REFLEXION-REFRACTION-DISPERSIONCOLOUR-ABSORPTION.
N a conversation held some years ago by the
author of these pages with his lamented
friend, Dr Hawtrey, Head-Master and late
Provost of Eton College, on the subject of
Etymology, I happened to remark that the syllable Ur
or Or must have had some very remote origin, having
found its way into many languages, conveying the sense
of something absolute, solemn, definite, fundamental, or
of unknown antiquity, as in the German words Ur-alt
(primeval), Ur-satz (a fundamental proposition), Ur-thezl
(a solemn judgment)-in the Latin Oriri (to arise),
Origo (the origin), Aurora (the dawn)-in the Greek
"o0os (a boundary, a mountain, the extreme limit of
our vision, whence our horizon),'Oc&a  (to see),'O`4Os
(straight, just, right), "Ox0o0 (an oath or solemn sanction),'Racl (the seasons, the great natural divisions of time),
&c. "You are right," was his reply, "it is the oldest of




220                 ON LIGHT.
all words; the first word ever recorded to have been
pronounced.  It is the Hebrew for LIGHT (tYq AOR)."
(2.) Assuredly there is something in the phrenomena
of Light; in its universality; in the high office it performs in creation; in the very hypotheses which have
been advanced as to its nature; which powerfully suggests the idea of the funclamental, the primeval, the antecedent and superior in point of rank and conception to
all other products or results of creative power in the
physical world.  "It is LIGHT," as we took occasion to
observe at the conclusion of the last lecture (not without reference to this very consideration), "and the free
communication of it from the remotest regions of the
universe, which alone can give, and does fully give us,
the assurance of a uniform and all-pervading energya MECHANISM almost beyond conception complex, minute, and powerful, by which that influence, or rather
that movement, is propagated.  Our evidence of the
existence of gravitation fails us beyond the region of the
double stars, or leaves us at best only a presumption
amounting to moral conviction in its favour. But the
argument for a unity of design and action afforded by
light stands unweakened by distance, and is co-extensive
with the universe itself."'
(3.) What we propose in the following lecture is to
make intelligible, in as simple language and form as the
nature of the subject will admit, the grounds of this
assertion.  In some of its features it is too complex
and abstruse to be thoroughly followed out by any one
* "Celestial Measurings and Weighings," p. 218.




ON LIGHT.                    221
not familiar with some of the mqst intricate departments
of mathematical science.  In explaining such features
(when unavoidable), without prejudice to the strictness
of mathematical reasoning adducible and held to. be
conclusive and satisfactory by those who have mastered
it, we must have recourse to analogies more or less close
with processes we see going on in nature; and which,
whether perfectly understood or not in their mozdus operandi, we, at all events, perceive to consist in a sequence
of events, comprehensible in themselves and arising
naturally and familiarly one out of another. There are
many phenomena of polarized light which admit of being so, as it were, shadowed forth to the mind of a
beginner as analogous to things familiar enough.  In
such cases, though the analogy may be imperfect, or
even altogether incompetent to stand for an explanation, the phaenomenon is sometimes so neatly conveyed
to the intellect, that by generalizing to the extreme all
the terms.used in describing the one, it is very conceivable that the cardinal feature of the other-that which
dominates its whole explanation-may be included.
Even if not so, the object is so far answered, that the
student remains possessed of a mental picture which
will not allow him to forget its prototype. And it is
not a compendium of Optics, or an essay on Vision, or
an account of telescopes, microscopes, or other optical
instruments, that he has here to expect.  Nothing of the
kind could by possibility be comprised within such limits
as a contributor to a work of this kind must necessarily
observe.  Suffice it to convey to his apprehension some




222                 ON LIGHT.
idea of at least the general nature of the mechanism by
which it seems now agreed, with hardly a dissentient
voice, that the peculiar communication between distant
objects which we call light is effected; and by which, or
by some mechanism of a nature still more recondite, and
at present perhaps beyond our conception of possibility,
it must be so.
(4.) That we see, is proof of a communication of some
sort between the eye and the thing seen. That we cannot see in the dark, is proof that such communication is
not the mere act of the eye. And that one object is
capable of impressing a photographic picture of itself on
another, is proof that the eye, though essential to seeing,
has nothing whatever to do with the process by which
such communication is performed.  And furthermore,
the immense variety and extent of the chemical agencies
of light as displayed in its action both on organic and
on inorganic matter, revealed to us by the late discoveries in photography, assign to it a rank among natural
agents of the highest and most universal character; and
have even rendered it exceedingly probable, if they have
not actually demonstrated, that vision itself is nothing
but the mental perception of a chemical change wrought
by its action on the material tissue of the retina of the
eye.
(5.) At all events, it is not by any sympathy, or absolute direct relation between the eye and the object, that
the latter is seen. The intermediate space, and indeed
all space, is concerned in the process.  An object is not
seen unless it be in a certain state, which we call " lumin



ON LIGHT.                     223
ous:" a state either natural to it, as'in the flame of
a candle or the sun; or induced, by being placed in presence of another luminous object, as when a sheet of
white paper is laid in the sun or before a candle. Nor
is it then seen if a screen of metal or any of the class of
substances called "opake" be interposed anywhere in
the direct straight line of communication; while on the
other hand, when so hidden from direct vision, it may
be rendered visible "by reflexion" from a polished sur
face held at a fitting angle, anywhere out of that direct
line, provided only such surface be not similarly screened
either from  the object or from the eye.  Thus we learn
two. things:-First,. that the line of unzinerrzupted luminous communication is a straight one; and, secondly, that
any point whatever in a sphere of indefinite radius surrounding a luminous object (in other words, in infinite
space) may become included in the line of indirect or
deflected  luminous communication between  any two
places.  7Te agency, whatever its nature, is there and
ready, requiring only a fitting arrangement of material
and tangible substances to make it available.
(6.).Light, though the cause of vision, is itself invisible.  A sunbeam, indeed, is said to be seen when it
traverses a dark room through a hole in the shutter-or
when in a partially clouded sky luminous bands or rays
are observed as if darted through openings in the clouds,
diverging from  the place (unseen) of the sun as the
vanishing point of their parallel lines seen in perspective.
But the thing seen in such cases is not the light, but the
innumerable particles of floating dust or smoky vapour




224                  ON LIGHT.
which catch and reflect a small portion of it, as when in
a thick fog the bull's-eye of a lanthorn seems to throw
out a broad diverging luminous cone, consisting in
reality of the whole illuminated portion of the fog.  The
moon is seen in virtue of the sun's light thrown upon it.
Where the moon is not we see nothing, though we are
very sure that when in the course of its revolution it
shall arrive in the place we are looking at, we shall see
it, and that if our eyes could be transferred to the moon's
place, wherever it may be in the firmament (if not
eclipsed), we should from it see the sun. There then,
at all times, is the light of the sun, but not visible as a
thing.'It exists as an agency. What is true of the sun
is no doubt equally so of a star; so that when we look
out on a dark night, though we are sure that all space is
continually being crossed in every direction by the lines
of its communication, along all which it is active; and in
particular, that all the dark space immediately around
us (outside of the earth's shadow) is, so to speak, flooded
with the sun's light, we yet perceive only darkness,
except where our line of vision encounters a star.
(7.) What then is LIGHT   or, in other words, what is
the nature of that communication by which not only
information is conveyed to our intellectual and perceptive being; but chemical and various other changes
are operated even on inorganic matter by processes
originating as it would seem in sources situate in the
most distant regions of space (for, be it observed, it has
been clearly proved that the light of the stars does produce photographic effects powerful enough to imprint




ON LIGHT.                    225
their images permanently on surfaces duly prepared to
receive them).  Is there any physical mode of conveyance by which, reasoning from what we see in cases
which we are able to analyze, we can imagine either a
material agent to be bodily transported, or a movement
propagated, or an influence wafted, from place to place,
so as to render a rational and consistent. account of the
phaenomena of light, or so. at least as, generalized, and
(so to speak) sublimated in modes not inconsistent with
the known properties of matter, to do so 1
(8.) One feature is common to all ordinary physical
modes of communication.  The transmission from place
to place, be it of what it may-of a letter by post, a
gunshot, a sound, a wave, a tremor, or a shock even of
an earthquake —occupies time.  It has a zelocity: sometimes a very great, but anyhow a measurable one.  Is
this the case with light. The answer, from all ordinary
experience, would be in the negative. But this is only
because the velocity in question is so great that the
longest distances to which we can send a flash of light
and receive it back again by reflexion is traversed in an
interval of time too short to be perceived as an interval,
so that the reflexion ayppears to-be simultaneous with the
direct flash.  It is otherwise when we bring to bear on
the question the ingenious combinations and delicate
appliancqs of modern science.  The telescope enables
us to become eye-witnesses in the way of astronomical
observation of events which take place at distances in
space almost inconceivably greater than any we carn
measure here on earth  at times calculable beforehand.
P




226                   ON LIGHT.
And in the way of experiment, the contrivances of
clock-work enable us to register the subdivisions of what
we call " an instant" into hundreds, nay, thousands, of
equal and exactly measurable portions-applying, so to
speak, a microscope to time, and estimating, by undeniable calculation, portions of it utterly eluding all our
powers of perception. The question has been asked in
both these modes, by astronomical observation and
by direct physical experiment, and the answer, from
each, has been affirmative; and from  both agreeing,
in a manner which may well be considered wonderful.
(g.) The planet Jupiter is attended by four satellites
which revolve round it in orbits very nearly circular,
and whose dimensions, forms, and situations with respect
to that of the planet itself are now perfectly well known.
The periodical times of their respective revolutions are
also ascertained with extreme precision, and all the particulars of their motions have been investigated with
extraordinary care and perseverance.  The three interior
of them are so near the planet and the planes of their
orbits so little inclined to that in which it revolves
round the sun, that they pass through its shadow, and
therefore undergo eclipse, at every revolution. These
eclipses have been assiduously observed ever since the
discovery of the satellites, and their times of occurrence
registered.  As they afford a means of determining the
longitudes of places, the pjrediction beforehand of the
exact times of their occurrence becomes an object of
great importance: and it is evident enough that, all the




ON LIGHT.                    227
particulars of their motions being known (as well as of
that of the planet itself, and therefore of the size and
situation of its shadow), there would be no difficulty in
making such prediction (starting from the time of some
one observed eclipse of each as an epoch); provided
always each eclipse were seen at the identical moment when
it actually happSened.  Moreover, on that supposition, the
times recorded of all the subsequent eclipses ought to
agree with the times so predicted. This, however, proved
not to be the case.  The observed times were sometimes earlier, sometimes later than the predicted; not,
however, capriciously, but according to a regular law of
increase and decrease in the amount of discordance, the
difference either way increasing to a maximum,-then
diminishing, vanishing, and passing over to a maximum
the other way, and the total amount of fluctuation to
and fro being about 16m 27s. Soon after this discrepancy between the predicted and observed times of
eclipse was noticed, it was suggested that such a disagreement would necessarily arise if the transmission of
light were not instantaneous. This suggestion was converted into a certainty by Roemer, a Danish astronomer,
who ascertained that they always happened earlier than
their calculated time when the earth in the course of its
annual revolution approached nearest to Jupiter, and
later when receding farthest: so that in effect the extreme difference of the errors or total extent of fluctuation-the I6m 27s in question-is no other than the
time taken by light to travel over the diameter of the
earth's orbit, that being the extreme difference of the




228                   ON LIGHT.
distances of the two planets at different points of their
respective revolutions.  At present, in our almanacs a
due allowance of time for the transmission of light at
this rate, assuming a uniform velocity, is m'ade in the
calculation of these eclipses; and the discrepancy in
question between the observed and predicted times has
ceased to exist.
(io.) Taking the diameter of the earth's orbit, as concluded from  the sun's observed parallax,* at 24,000
diameters of the earth itself, and the latter diameter
at 79251 miles,+ this gives a velocity of I92,700 miles
per second.
(ii.) So vast a speed seemed at first incredible; to
some indeed even more so than an instantaneous communication.  The one might be conceived as the result
of some sort of spiritual communication: the other
seemed, in those days, to transcend all imaginable limits
of mere physical agency. But it soon received a very
unexpected confirmation from Dr Bradley's discovery of
the ABERRATION of light: to conceive which, let any
one imagine a long tube held perpendicularly, at perfect
rest, while a falling body (a drop, suppose of a shower of
rain), descending also perpendicularly, should pass down
its axis.  If it entered at the centre of its upper orifice,
it would issue at that of the lower; and, judging from
this indication alone, and knowing the tube to be exactly
vertical, a spectator would truly conclude from  it that
the descent of the drop was so also. Supposing him and
* See p. I96. note.
t This is the equatorial diameter.




ON LIGHT.                   229
the tube, however, to be carried along uniformly in any
direction by a movement unperceived by himself, the
hinder part of it would advance to meet the falling drop;
which would, if the movement in advance were sufficiently rapid, cause it to strike against it; or if not, to
emerge at the lower end so far behind the centre as that
movement had carried the tube during the time of its
passage from end to end. And this deviation would
obviously bear the same proportion to the length of the
tube that the velocity of the falling drop bore to that of
the tube's advance. Judging, then, from this indication
alone, if unaware of his own motion; he would conclude'he fall of the drop to be inclined backward from the
perpendicular by a certain angle-but if, suspecting it,
he should reverse his movement, and travel with equal
speed the contrary way, he would find an equal deviation in the contrary direction, and would thus arrive at
the certainty that it was to the motion of himself and the
tube, and not to any real obliquity in the fall of the
drop, that this apparent deviation was owing. And by
measuring its angular amount (which would be easy by
the help of the marks left by two drops in the opposite
circumstances on a screen at the lower end of the tube,
and comparing it with the length of the latter), this angle,
which might be called the Aberration (from perpendicularity) of the apparent line of fall, would inform him of
the proportion his own velocity bore to that of the drop
in its passage, and, the former being known, would enable
him to estimate the latter.
(I2.) All this is a paraphrase of the astronomical pha.




230                  ON'LIGHT,
nomenon in question.  The rain-drop is the light; the
tube, a telescope; the screen at its lower end, a micrometer; and the two  opposite  directions of the
observer's motion, the two tangents at opposite sides of
the earth's orbit at right angles to the situation of a star
as viewed from  either.  And the angle in question is
what astronomers call their " Constant of Aberration "a very minute one indeed, but perfectly well measurable
-amounting to about a third of a minute (20" 45), from
which it results that the velocity of light is about ten
thousand (more exactly o1,089) times that of the earth
in its orbit, which we know to be very nearly I9 miles
(I8'923) per second, which gives I90,860 miles per
second for the velocity of light.
(I3.) Two different experimental processes for measureing this velocity have been devised and executed-the
one by M. Fizeau, of the Parisian Academy of Sciences;
the other by M. Leon Foucault, recently and most deservedly elected into the same illustrious body; the
inventor of that elegant instrument, the Gyroscope.
Both depend on the principle that the impression left on
the eye by any luminous object persists for a sensible,
though very minute, time (about the tenth of a second);
so that an object presented to the sight by successive
glimpses only, following each other more frequently than
ten times in a second, is seen continuously. If only
just so frequent, a fluttering is perceived; but this
diminishes as the rapidity of presentation is increased:
and when much more frequent, distinct and perfectly
uninterrupted vision is produced.  In M. Fizeau's ex



ON LIGIT.                     23K
periment (which is the simplest in its conception and
explanation), these glimpses are obtained by looking
through an opening in a screen corresponding exactly
in size and shape to one of the intervals between the
teeth of a metallic wheel which is made to revolve before
the opening, so that as the teeth pass in succession, they
intercept the light so long as they cover it; but allow it
to pass when, in place of a tooth, an interval is presented
before the eye.  Imagine such a wheel, screen, and
opening, the wheel being at rest in the last-described
situation; and through another such an opening in the
same screen, corresponding exactly in size, shape, and
situation to another of the intervals between the teeth,
let a sunbeam be directed outwards, in a direction parallel to the axis of the wheel, by a highly-polished
reflector, so as to strike upon another such reflector so
placed at some considerable and measured distance from
the wheel, that the light shall be reflected back again by
this second mirror. By slightly inclining and properly
adjusting this it may be made to return, not to the orifice
from which it issued, but to the other behind which the
eye of the observer is placed.  In this state of things,
when all is at rest, he will see the reflected light; but if
the wheel be turned slowly round, a tooth will come before the first reflector in place of an opening, and intercept the light-then another opening, another tooth, and
so on, producing successive glimpses of light separated
by dark intervals.
(r4.) If the motion of the wheel be gradually accelerated, so that more than ten teeth pass before the orifice




232                   ON LIGHT.
in a second of time, these glimpses run together into
continuous vision; and if considerably more numerous
(suppose fifty or sixty per second), the light is perceived
steadily as if the wheel were at perfect rest only, however (if the intervals between the teeth be exactly equal
to the breadths of the latter), of half the brilliancy, seeing that only half the quantity of light will have entered
the eye in the same time.  The motion of the wheel
still continuing to be accelerated, however, when it has
attained a certain very great rapidity the light is gradually perceived to grow feebler and at length altogether
disappears.  This happens when the velocity of rotation
is such as to bring a tooth of the wheel precisely to
cover the whole of the orifice in the screen into which
the returning beam  should be delivered at the very
moment of its arrival, so closing it up altogether; that
is to say, when the rotation is just so rapid as to carry
each tooth over its own breadth during the time taken
by the light to go and return.  When this happens,
suppose the acceleration of the wheel to cease, and its
motion to be maintained uniform.  Then by counting
the turns made per minute by the driving-handle of the
train of wheel-work, or otherwise registering its speed 3
and knowing (from the construction of the train) how
many turns of the wheel correspond to one of the driver,
as also how many teeth it carries, the exact duration of
this interval, no matter how minute, can be exactly
computed, so that the time and the space run over by
the light in that time both become known.
(I5.) If the rotation be now still further accelerated,




ON LIGHT.                      231
the light begins to reappear, and gradually increases to
its former brightness, in which state of things the obstructing tooth has been carried, in that same interval oi
time, quite clear of the opening, and the next notch
brought exactly opposite to it.  With yet increased
speed, the light again vanishes, again reappears, and so
on alternately, as the second, third, or fourth tooth or
notch is successively brought before the opening; and
on comparing the velocities of rotation corresponding,
they are found to increase in arithmetical progression;
which obviously ought to be the case. In M. Fizeau's
experiments,- the distance between the reflector and the
revolving wheel was about 8600 metres, thus giving for
the whole distance travelled over by the light going and
returning 17,200 metres, or about io3 miles; and for
the time occupied in its journey, hardly more than the
I8,oooth part of a second. A velocity of 96,000oo miles
per second was assigned by him  as their final result,
exceeding by about one-sixtieth part that resulting from
the astronomical observations.
(I6.) The experiments of M. Foucault, however,
leave no doubt that this last result is too great.  In
these experiments, instead of measuring these minute
intervals of time by the rotation of a toothed wheel, a
revolving reflector was employed in pursuance of an
idea suggested by Mr Wheatstone, and applied by him
* The actual details of this experiment, as executed by M.
Fizeau, were somewhat more complicated. Telescopes were used,
&c.  For clearness of explanation, we have reduced the whole
process to its simplest form of expression.




234                   ON LIGHT.
to measure the velocity of electricity. Without figures,
and without much more verbal detail than would be
compatible with our limits, it would be impossible to
give a clear conception of the conduct of this delicate
and refined experiment.  Suffice it to state, as its ultimate result, a velocity of 185,I72 miles per second.'
As there are other and independent reasons for believing that the sun's distance has been over-rated by about
one-thirtieth in our estimate of 12,000 diameters of the
earth, and that, in consequence, the velocity of light
deduced from  the phenomenon of aberration ought to
be diminished  in the same proportion  (which would
reduce it to 186,300 miles per second), we are authorized to conclude that in estimating this velocity at
I86,ooo miles we are within a thousand miles of the
truth.
(I7.) The form of experiment proposed and executed
by M. Foucault has this great advantage over the other,
-that it can be carried out within much smaller limits
of distance. A few yards of travel suffices for the determination of this enormous speed.  And this makes it
possible to compare the velocity of light in its passage
through air and water, and other transparent liquidswith this remarkable result, that the rate is found to be
slower in the denser medium; a result of the utmost
importance, as we shall presently see, as a crucial fact in
deciding between the claims of the two great rival
theories of light to be received as valid.
* 298 millions'of metres. See Comnzes Rendus de' Institut,
Sept. 22, I86o.




ON LIGHT.                     235
(I8.) Before we can give any intelligible account of
these theories, however, it is necessary to enter a little
more particularly into the modes by which a ray of light
may be deflected from its rectilinear path, and the laws
of such deflection. By this expression we understand
nothing more than that the line of communication between
the illuminating and illuminated object is, in some way
or other rendered circuitous.  It is so natural to speak of
light as a thing, and of its line of communication as the
path along which that thing, be it what it may, travels,
that we are apt to forget that (except on one hypothesis
as to its nature, viz., that it is, actually, a material substance, bodily transported from place to place) this form  of
expression is purely metaphorical, and that by a ray
nothing more is meant than the mathematical line, be it
straight or bent, between two points, standing to each
other in the relations of illuminating and illuminated
along which the communication is kept up-the test
being, that an opake body being placed anywhere in
that line, the illumination ceases.   Such a circuitous
line of communication may be established, independent
of and in addition to the direct rectilinear one, by placing anywhere in space any material object whatever,
provided there be no opake body interposed between
it and either of the two points; and this in two different
modes.  In the one the whole path of the ray, both before and after its deflection, is outside of the deflecting
body.  In this case the light is said to be "rejfected: " if
at a smooth and polished surface, regularly, if at a rough
one, irregularly; in which case the light is said to be




236                  ON LIGHT.
"scattered."  In the other mode the path of the ray,
subsequent to the point where it first encounters the
deflecting body, is wholly or partly within it, and the
light is said to be "refracted,' or "transmitted."
(I9.) The first law observed. in every case, whether of
direct or circuitous illumination, is gathered from ordinary and universal experience.  The illuminating and
illuminated points are mutually interchangeable.  By
whatever path, however circuitous, light is conveyed from
A to B, by the same it can be conveyed from  B to A.
This condition alone suffices to determine the path, and
to fix the situation of the point at which its flexure takes
place by rlefexioz, when the light is "incident" on any
polished surface, whether plane or curved. That point
(P) must be so situated on the surface, that the two lines
joining it and the illuminating and illuminated points (A,
B) shall there make equal angles with the surface, the
three points (A, B, P) all lying in one plane with a perpendicular to the surface.  For, ist, except the anzgles were
equal, the two directions (PB, PA) would not be similarly
related to the surface at the point of incidence; so that
in reversing the path of the ray, the physical condition
which determined the obliquity of the incident ray to the
surface in proceeding from A to B, to be greater or less
than that of the reflected, would have to be reversed in
the passage of light from B to A. And similarly, if the
reflected ray lay in a plane to the right or left of that in
which the perpendicular and the incident one were contained, the physical condition which determined it to
deviate to the one side or to the other of that plane, would




ON LIGHT.                      237
in like manner have to be reversed on interchanging the
illuminating and illuminated points. On neither supposition could the same intrinsic law  of communication
carry the ray from A through P, to B, and from B, through
P, to A. This, then, is the law of regular reflexion, commonly expressed by saying that the angle of incidence is
equal to that of refexion and lies in the same plane with it.
(20.) If the reflecting surface be a plane, there will be
only one point in it which fulfils these conditions. Thus
a perfectly polished flat surface of silver, free from
scratches, or that of still water, sends no light to the eye
from a candle, and is in fact invisible, except at this one
point so determined whence the light is reflected to the
eye, and in the direction of which from the eye the reflected candle is seen.  With curved surfaces, as well
as with those. we designate as "rough" or " unpolished,"
the case is different. In all surfaces of this last-mentioned description the microscope reveals to us such irregularities, such innumerable and abruptly broken facets,
protuberances and hollows, as to satisfy us that in every,
the most minute, visible portion of such a surface, places
must occur in which the condition of equal inclination of
the two lines in question to the actual surface, as it exists
in those laces, is satisfied-so that a ray there reflected
may reach an eye however situated.  By such rays, and
by others which have entered into the substance of the
object and been there internally reflected or otherwise
bent, in a manner presently to be explained, all surfaces
not self-luminous become visible as objects, being seen by
rays "scattered" from them in every possible direction.




238                    ON LIGHT.
(2I.) It is to this power of "scattering" the incident
light in all directions, then, that surfaces owe their visi-.bility, and that by its aid we are enabled to trace the
course of a ray of light itself as if it were a visible thing.
Thus a sunbeam  passing through a small hole and received on smoke is seen, and on a white screen moved
rapidly to and fro behind it, appears as a straight luminous line or beam, by the momentary persistence of the
sensation caused in the eye at every successive point of
its motion; and so, after reflexion or refraction, may its
subsequent course be rendered matter of ocular inspection.  A pleasing and elegant experiment is to hold a
common reading-glass (or even a spectacle-glass) in the
sun, and to move rapidly to and fro behind it a white
paper, when the course of the refracted light, converging
from all parts of the glass to the " focus," will be seen in
the air as a solid luminous cone, having the glass for
its base and the focus for its apex.
(22.) The reflexion of light, whether "regular" or
" scattered," is, except under very peculiar circumstances
to be presently noticed, only partial; so that the reflected image of an  object is seen fainter and less
luminous than the object itself directly viewed.  This is
perceptible in an ordinary looking-glass; yet more so
when the reflecting surface is still water, or unsilvered
glass.   The most rfeflective substances  are the white
metals —such as silver, speculum-metal, steel, or. quicksilver: transparent or semi-transparent bodies being
much inferior in respect of this quality. If the substance
on which the light falls be of the kind called opake, the




ON LIGHT.                      239
reflected is the only portion which can be rendered sensible to sight or otherwise traced.  But if transparent, a
very remarkable phaenomenon occurs. The incident ray
is, as it were, split or subdivided at'the point where it
meets the surface of the body; one portion pursuing its
subsequent course outside of it, as a reflected ray, in the
manner above described; the other within it, undergoing what is called " eufraction,', being bent aside fiom its
former direction at its point of entry, after which it pursues a straight course within the substance or "medium."
(23.) If the "refracting medium" be a liquid, a glass,
a jelly, or any substance in which no indications of
inequality of internal texture can be discovered-no
signs of lamination or " grain" shown by a greater tendency to split or " cleave" in one direction more than
another, this intromitted portion is sinzgle.  The whole of
the refracted light pursues its course from  the point of
its entry as one ray. The same is also the case when
the refracting medium  belongs to the class of bodies
called " crystallized," or which present a definite " cleavage;" provided the " primitive form" of their crystals
be either a cube, a regular octohedron, or a rhomboidal
dodecahedron, such as rock-salt, alum, or garnet.  In
all other transparent crystals the intromitted portion of
the light divides itself from the moment of its entry into
two distinct rays, pursuing different courses, and presenting the phenomenon known under the name of "' double
refraction,"  such  substances being  called  " doublyrefractive media," of which the substance called Iceland
Spar, or crystallized carbonate of lime, offers a beautiful




240                  ON LIGHT.
example.  And here we may pause for a moment to
observe that at this point we already find ourselves introduced to an assemblage of relations between light and
material objects, which divide the whole universe of such
objects, infinite as they are in variety, into classes, characterized by their habitudes with respect to light in its
reflexion from and passage through them.  The importance of this remark will grow upon us as we advance
further into the subject, and come to perceive that the
classification of bodies according to their " optical properties" stands in direct connexion with their most
intimate peculiarities of mechanical structure and chemical constitution; and brings us, so to speak, into contact with all those more recondite properties and reactions of the ultimate particles of bodies which constitute
the domain of molecular physics.
(24.) Confining ourselves now to the case where.the
refraction is single, the rule which determines the course
of the refracted ray is as follows. Suppose at the " point
of incidence" (i.e., where the ray first enters the medium)
a line be drawn perpendicular to the surface.  Then,
first, the refracted ray will lie in the same plane which
contains both the incident ray and this perpendicular;
and, secondly, the ray will be so bent at that point that
the exterior and interior portions shall make with the
perpendicular, not equal angles as would be the case
were there no flexure, but angles so related that their
sines (not the angles) shall bear to each other a certain
invariable proportion, whatever be the angles themselves, or whatever be the obliquity of the incident ray




ON LIGHT.                    241
to the surface.  As it is quite essential to the understanding of what follows that this, " the law of ordinary
refraction," should be clearly apprehended, we will illustrate it by a figure. Let A c B be a section of the surface
D
R          M
3   C __/_____A
~ E      Q
Fig. r.
by the plane in which the ray D c, incident at c, and
P c Q the line perpendicular to the surface at c, both lie,
andc E the refracted ray.  Taking c for a centre, with
any radius, c M, describe a circle cutting the incident
and refracted rays in M andN, from which points draw
M R, N s perpendicular to P c Q. Then will these two
lines be to each other, in one and the same invariable
proportion, whatever be the inclination'of the original
ray D c to the surface, or to the perpendicular c P.
This latter inclination is what is understood by the
"angle of incidence," and the corresponding inclination
(to the perpendicular Q c P) of the refracted ray, by " he
angle of refraction,"
Q




242                    ON LIGHT.
(25.) It is evident from what we said in the last paragraph, that according to the greater or less disproportion
between the lines M R, N s, on the diagram there given,
or the sines of the two angles of incidence and refraction,
the greater or less will be the amount of bending (or
angle of deviation, as it is called) of the ray at its point of
transmission, for one and the same degree of obliquityas also that for one and the same medium, the deviation
increases with the angle of incidence (though not roportionally to it) being nil when the ray enters perpendicularly, and a maximum  when just grazing the surface.
If in any case M R be greater than N s, or the " ratio of the
sines" be one of " greater inequality," the bending will be
oowtards the perpendicular; if less, or if that ratio be one
" of less inequality,"from it; as indicated by the course
of the dotted ray in the figure. If the former be the case
in any instance, as in that where a ray passes out of air
into water, the latter will happen in the reverse case, as
where it passes out of water into air: that is to say, in
optical language, " out of a denser medium into a rarer."
This follows, from the general fact that the illuminating
and illuminated points are convertible, or that a ray can
always return by the path of its arrival, so that the refraction of a ray out of any medium  into air is performed according to the same rule of the sines, only
reversing the terms of the proportion; or in other words,
regarding what was the angle of incidence in the one
case as that of refraction in the other and vice versd.
Numerically expressed, this reversal of the terms of a
proportion, or ratio, is equivalent to inverting the numer



ON LIGHT.                      243
ator and denominator of the fraction expressing it,-so
that, for instance, in the passage of light out of water
into air, the "law of the sines" is expressed in the same
general terms, but the "refractive index" (by which is
meant the number expressing the proportion in question)
has to be changed into its numerical reciprocal.  In the
case supposed, when light passes out of air into water,
the proportion of the sines is that of I336 to iooo, or
almost exactly 4 to 3; and the "refractive index" is
accordingly expressed by the fraction 4, or the almost
exactly equivalent decimal I'336.  In the reversed case,
then, when the transmission is out of water into air, it
will be  — o'75, or more precisely o0749.
(26.) As a matter of experiment, it is found that between transparent media, or substances capable of being
traversed by light, there exists a very wide diversity in
this ratio of the sines of the two angles in question, oi
in the numerical values of the "refractive indices."
Thus when light passes out of air into the less refractive
species of plate-glass, the index instead of. is  or I'5
into sulphur (which in its crystalline form is transparent),
2'0; and into diamond, or the mineral called octohedrite, 2'5.  In fact, each particular transparent substance, solid, liquid, orgaseous, has its own peculiar, and,
so to speak, characteristic index of refraction, which is
found to stand in relation to its physical habitudes in
many other respects, especially with its chemical composition, and its state'of aggregation and density.
(27.) Even common air, in respect of a vacuum, has
its refractive index —viz.,  o0003-the effect of which is




244                   ON LIGHT.
perceived in the phaenomenon of astronomical refraction,
by which the sun or moon is rendered visible when
actually sunk below the level of the true horizon.
(28.) From what is above stated, it is easy to see that
when a ray is transmitted through a sheet or plate of any
substance (as a window-glass) with parallel surfaces, its
course after emergence will be'parallel to its original
direction, so that though displaced laterally, its direction
in space is unchanged, which is the reason we see objects
in their proper directions through a window.  If the surface at which it emerges be not parallel to that through
which it enters, this exact restoration of the original
direction will not take place; and as we judge of the
situation of an object only by the direction in which its
light ultimately enters the eye, anything seen through a
transparent substance whose surfaces are so inclined,
will appear shifted in angular position. Any transparent
substance so formed of polished plane surfaces inclined
to each other, is called in optics "a prism;" and the
angle at which the two planes in question meet, or
would meet if extended, its "refractive angle." If such
a prism-of glass, for instance-be held before the eye
with its refractive angle vertical, and to the left, an
object seen through it will appear deviated or shifted to
the left of its true situation, the ray (as a slight consideration  will show) being  bent towards the thicker
part of the prism.  Arid thus by a very simple calculation, with which we. shall not trouble our readers, from
the angular amount of deviation caused by a prism of
any medium  whose refracting angle is measured, can




ON LIGHT.                     245
the  "refractive index"  of that medium  be  ascertained.
Fig. 2.
(29.) When refraction takes place out of any one transparent medium into any other in close and perfect contact with it-such contact as exists, for instance, between a fluid and a solid that it wets, or between two
fluids of different specific gravities, which do not mix,
resting the one on the other-experiment shows that, so
far as the mere direction of the refracted ray is concerned,
it is the same as if the two media were separated by an
exceedingly thin film of air.  In that case, the same perpendicular being common to both surfaces at the point
of contact, the angle of refraction out of the first medium
is the same with that of incidence on the second. And
from this it results that the proportion of the sine of internal incidence on the surface of the first to that of




246                   ON LIGHT.
internal refraction at that of the second, or the "relative
index of refraction," is constant for the same media, and
is equal to the quotient of their respective absolute refractive indices.  Thus, if the first medium  be water,
and the second be plate-glass, whose respective absolute
indices are 4 and -, the relative index, or that out of
water into glass, will be E divided by I or  — =  I25.
(30.) A very curious result follows from what has been
said,-viz., that though light can pass out of a rarer
medium  into a denser, whatever be' the obliquity of
incidence, even when the incident ray but just as it
were grazes the surface, yet the converse is not the case.
For every denser medium, there is a limit of obliquity,
beyond which transmission into a rarer cannot take
place.  The ray is zcwholy ref7ectet  without undergoing
any diminution of brightness whatever; observing the
same law of equality between the angles of incidence
and reflexion, as in the case of ordinary reflexion on a
mirror.  The brightness of the reflexion, however, far
surpasses anything that can be obtained from the most
brilliant looking-glass or metallic mirror, being equal to
that of the object directly seen.   The effect is very
striking, and is easily seen by immersing a small rod
obliquely in a glass tumbler of water, and viewing the
under surface of the water from  below  upwards at a
moderate obliquity.  The reflexion of the rod is seen
without the smallest diminution of brightness.  It is
thus that fishes see the bottom of their pond reduplicated by internal reflexion on the distant parts of its
surface.  The rationale is simple enough.  If two angles




ON LIGHT.                    247
always have their sines in a fixed proportion, the greater
may increase up to a right angle, but the less cannot:
since the contrary would require the sine of the greater
to exceed the radius of the circle.
(3I.) Within this limit, when the angle of incidence
is such as to admit of the transmission of the ray, the
reflexion is less than total. The incident beam is subdivided; a part only is transmitted, the rest undergoes
reflexion. The total amount of incident light is divided
between them, but very unequally, and the more so the
less the difference between the refractive indices of the
media; or, in optical language, between their "'refractive densities."  Thus, when light passes at a perpendicular incidence out of air into water, only 2 per cent.
of the whole incident beam is reflected; when into plateglass, about 4 per cent., but when out of water into such
glass, the amount of reflected light is less than ~ per
cent.  At oblique incidences, the reflexion is more
copious, increasing in intensity as the obliquity increases, until the incident light but just grazes the
surface.
(32.) The laws of reflexion and refraction being known,
it is the part of geometry to follow them  out in the
several cases where light is incident on plane, spherical,
or any other curved surfaces, reflecting or refracting,
and thus to deduce the various theorems and propositions which the practical optician has need of for the
construction of his mirrors, lenses, prisms, telescopes,
and microscopes.  All these, as beside our present purpose, we pretermit, confining ourselves entirely to the




248                  ON LIGHT.
physical properties of light, and the theories which have
been advanced for their explanation.  This need not
prevent us, however, from appealing to the effects produced by such instruments, especially such as are in
most common use, and as can hardly be other than
familiar to most of our readers, such as magnifying
glasses (or lenses), telescopes, &c.   It requires no
knowledge of geometry, for instance, or any acquaintance with its application to theoretical optics, to enable
any one to form a perfectly just conception of the mode
in which the eye enables him to see, when his attention
is called to a photographic picture, and lie sees it impressed on its ground by the rays of light collected and
brought to a focus by that assemblage of convex and
concave lenses in a camera obscura which the photographer uses for the purpose.  The dissection of an
eye shows it to be such an assemblage, and the picture
it produces may be actually seen at the back of the
eye of an  animal recently killed, by removing the
opake leathery coat which envelopes it, and disclosing
the retina.  How the nerves of that tissue, indeed, convey to the mind the perception of colour and form, is,
and will probably ever remain, a mystery; but is no
more so in the case of vision than of any other of the
senses; from which vision differs only in its transcendent
refinement and the elaborate structure of that most
wonderful of all optical instruments by which form, as
well as colour and brightness, is brought within its range.
The latter qualities are probably perceived by animals
unprovided with eyes, such as the proteus anguinus, which




ON LIGHT.                    249
inhabits dark caves, and whose delicate skin is evidently
and painfully affected by the light; but to convey the
perception of form, a picture must be produced, and in
its own peculiar manner.
(33.) We are now prepared to understand the mode
in which colour originates. This, to the ancients, was
always a mystery.  The light of the sun, and of ordinary
daylight, which is only that of the sun dispersed and
reflected backwards and forwards among the clouds, is
white, or nearly so. Nevertheless, when we look through
a red glass, or view a green leaf, it conveys to the mind
the perception of those colours.  How is this? If it be
by light only that we see, and if that light convey to us
absolutely none of the material elements of the bodies
from which we receive it, how comes it that it excites in
us such various and perfectly distinct sensations? The
light itself must have either acquired or parted with
something in its passage through or reflexion from the
coloured body.  Supposing, for instance, light to be a
substance; it may have taken up some excessively
minute portion of the object and introduced it to the
direct contact of our nerves.  In that case the sense of
colour would be assimilated to those of taste or smell.
Or it may have undergone analysis, and colour would
then arise from a deficiency of something existing in the
sun's light,'and the relative redundancy of some other
portion.  In this view, light would be regarded, not as a
simple, but a compound substance, or a mixture of so
many simple ones as would suffice to explain all the
observed differences of tint.  On the other hand, if light




250                   ON LIGHT.
be a movement, or an influence, we must admit in that
movement or influence a similar capacity for analysis or
composition, or else have recourse to some unknown
modification of the one or the other, leaving the phmenomenon as unexplained as before.  There may, for
instance, be a great variety of such movements, all
luminiferous, but not all alike; and some may be destroyed, or some exaggerated, in the act of reflexion or
transmission.
(34.) The key to this mystery, up to a certain point,
was furnished by Newton, in his analysis of white light
by prismatic refraction. A full account of the manner
in which that analysis is performed, of the phlenomena
it presents, and of the nature and subdivisions of the
" Prismatic spectrum," is given in our lecture on " The
Sun," ~ 29, to which,' to avoid repetition, we refer our
readers. Let us, however, consider what kind of general
theoretical interpretation we are entitled to put on this
analysis. Now, the first and most obvious conclusion is,
that the phmnomenon we have to deal with, is not what
in the accuracy of modern scientific language is understood by the term " analysis." It is the separation and
redistribution (according to degrees of a certain quality
common to all its elements-viz., that of REFRANGIBILITY) of a mixture, rather than the dialysis of a true
compolud.  The simile by which we there illustrated it
is so far exact. A glacier moraine might be redistributed
by tidal action over the floor of the Ocean; the great
blocks left in situ, or little moved-the smaller forming
shingle, gravel beds, sandstones, or incoherent muddy




ON LIGHT.                      251
deposits, with every possible intermediate gradation of
size.  But if in all this series any particular size were
found entirely and universally deficient, throughout the
whole series of formations traceable to that source, we
should conclude, not that a mass of that size is an impossibility in rerurum naturd, but that owing to some unknown cause in the nature of a previous sifting, every
pebble or grain of that size had been already separated,
or otherwise arrested in lilmin   and might expect elsewhere to find it in the case of some other series of
geological formations.  So it is with the sun's light.
Certain definite and marked degrees of refranzgibiliy are
wanting in its spectrum, indicated by the dark lines
which cross it. But if absent in solar light, they exist in
the light of flames, and of other luminous sources, which
in their turn are again deficient in other degrees which
yet abound in the.solar rays.   Refrangibility, then,
taken as a property of light generally, is a quality susceptible of indefinite gradation, from the one extreme of
the spectrum to the other.
(35.) If we limit our consideration  to some one
medium-glass, for instance-we find each particular
degree of refrangibility associated, first, with a determinate and invariable index of refraction, which determines its place in the spectrum by determining the
amount of deflexion it shall undergo in passing through
the prism; and, secondly, with an equally determinate
and invariable tint in the scale of " prismatic colour,"
the red corresponding to the least and the violet to the
greatest refractive index.  The truth of these proposi



252                   ON LIGHT
tions is easily tested on any one ray of the spectrum
insulated from the rest by intercepting all the others.
The ray so insulated, whatever its tint, is no longer
separated or " dispersed" by subsequent refraction into
a new spectrum.  It preserves its tint unaltered, and
conforms to the " rule of the sines" in its flexure, as if
no other colour or refrangibility existed.  Hence we
might be led to conclude; as Newton himself did, that
between these two qualities —refrangibility and colouran absolute and invariable connexion exists.  This,
however, is not the case. The propositions in question
cannot be  generalized.  When  different media are
examined, we find that not only does the same colour
correspond to different degrees of refrangibility, or to
different absolute values of the refractive index in each,
but that the same change of colour does not correspond
in different media to the same proportionale change of
the refractive index; and that, in short, taking the
" scale of colour" in all its gradations, from red, through
orange, yellow, green, blue, and indigo, to the least perceptible violet, and that feeble tint beyond the violet
which can hardly be called a colour, but'which is most
nearly expressed by the term lavender, as a guide,-each
particular medium  distributes these rays through its
spectrum, though always in the same order of succession, yet in other respects according to a law peculiar to
itself: thus indicating both a total amount of dispersion
and a scale of acion dependent on the physical properties of the medium, and in some sort as it were personal
to each.  This power which a transparent medium has




ON LIGHT.                      253
of separating the differently-coloured rays and spreading
them over an angular space greater or less in proportion
to the total deviation of some one ray, taken as a standard, from its former course, is called in optics the " dispersive power" of the medium.  It differs very widely in
different media, and in consequence, the lengths of the
spectra which they produce, corresponding to one and
the same mean or average refraction, differ accordingly.
Thus, for example, the total lengths of the spectra produced by prisms of fluorspar, water, diamond, flint glass,
and oil of cassia (the mean refractions being the same),
are to each other in the proportions of the numbers 22,
35, 38, 48, and I39.
(36.) This quality of dispersion stands in very distinct relation to the chemical constitution of the refracting medium.  Thus it is found that all the compounds
of lead, whether in liquid solution, natural or artificial
crystals, or glasses into which that metal enters largely,
possess very high dispersive powers; while those into
which strontia enters exhibit remarkably low ones.  It
is on this property of lead that the formation of highly
dispersive glasses, to imitate the brilliant colours of gems,
and to give the vivid prismatic colours of the pendants
of chandeliers by candle-light, depends, as well as that far
more important application which, by the combination
of two glasses of different dispersive powers, the one con-'
taining lead, the other none, enables the optician to
effect refraction without producing colour, and so to construct that admirable instrument, the achromatic telescope.
(37.) Not only are the total lengths of the spectra pro



254                   ON LIGHI.
duced by different media different for the same mean
amount of refraction, but within those lengths the distribution of the several colours differs, the spaces occupied by the several tints differing very considerably in
proportion to each other and to the whole.  Thus, in
the spectrum  formed by flint-glass, and most other of
the highly dispersive media, the green is situated nearer
to the red than to the violet end of the spectrum, while
in that formed by muriatic ("'hydrochloric") acid the
reverse is the case.
(38.) By the reunion of all the coloured prismatic
rays (which may be effected by an equal and contrary
refraction of the whole spectrum through a prism of the
same material reversely placed), white light is reproduced.  And hence we conclude that colour is not a
superinduced but an inherent quality of the luminous rays.
Again, if we exclude from this reunion any portion of
the spectrum, the reconstituted beam is coloured: and if
the rays so excluded be not extinguished, but diverted
aside, and  themselves collected  and  reunited  into
another and  separate beam  (which  may easily  be
effected, with a little management, by one skilled in experimental optics), this will also be coloured, but with a
tint conplementary to that of the first.  Between the
tints so arising is always found to prevail that beautiful
and, so to speak, harmonious contrast which is so effective in the ornamental arts, where one colour is said to
set-off another, or show it to the greatest advantage.
Thus, crimson or pink  is complementary to  green,
scarlet or orange to blue, yellow to purple, &c. The




ON LIGHT.                    255
relation to each other of these complementary colours
is curiously and strikingly illustrated by the spontaneous
production within the eye itself of the tint complementary to any vivid colour, which takes place when, after
gazing steadfastly on an area so coloured, on a white
ground, and strongly illuminated, the gaze is suddenly
transferred to a uniformly white surface. There is seen
on it, though only for a few moments, a picture or optical image of an area similar in form and size, but tinted
with the complementary hue, which fades quickly away.
This curious and beautiful experiment, which requires no
apparatus to exhibit, and which any one may try in a
moment, is exceedingly illustrative of the mode in which
the sensation of colour is produced. It proves that, in
the nervous tissue which receives and feels the picture
within the eye, there are nerves individually and exclusively sensitive to each of the coloured rays, or at all
events to each of those primary colours (if such there
be) by whose mixture all colours are compounded.
When white light falls on a portion of the retina wholly
or partially deadened or fatigued by the excitement of
the nerves appropriate to one set of rays, the sensibility
of the others being left unexhausted; that other portion
will be for a time proportionably more sensitive to the
remaining rays: so that under the stimulus of white light
an undue preponderance is temporarily given to their
influence, and the sensation of the complementary tint
is conveyed to the mind.  This is only one of innumerable instances of the wonderful adaptation of that most
astonishing organ to the performance of its office of con.




256                  ON LIGHT.
veying to us information not only of the forms and situations of objects, but of all that multitude of their physical
properties which stand in relation to colour, both those
which ordinary experience teaches and which science
reveals.
(39.) Lastly, by thus reuniting into one beam rays
going to form distant portions of the spectrum, and excluding the rest, we find that it is possible to produce a
compound beam which shall excite directly in the eye,
or illuminate a screen with any one of the innumerable
Varieties of tint which we observe in nature; and what
is especially remarkable, the same tint, or one undistinguishable from  it to ordinary eyes, is producible by
very different combinations of the prismatic rays; while
yet there exist individuals, and these not unfrequent,
who are perfectly capable of discriminating (in many
cases) between such compound tints, and who even
declare them to be widely different. To such cases of
what is called, though improperly, "colour-blindness,"
we shall presently have occasion to recur.
(4o.) The consideration of these facts has given rise
to a speculation which, if not demonstrable, has at least
a high degree of plausibility, and which, at all events,
has never yet been disproved,-viz., that there is no
real connexion between COLOUR and REFRANGIBILITY,
but that there exist three inherently distinct species of
lZiht, each competent per se to excite the sensation of
one of three PRIMARY COLOURS, by whose mixture all
compound tints are produced, white consisting of their
totality, and black being the exponent of their entire




ON LIGHT.                    257
absence. That, moreover, each of them has a spectrum
of its own, over the whole length of which it is distributed according to its own peculiar law of intensity,
and from whose superposition on the same ground results the prismatic spectrum, coloured as we see it.
The annexed figure will convey a better conception of
/':-.
X O     g o   t      i     v
Fig. 3.
this than any lengthened description, where A B represents the length of the total spectrum wherewith each
of the three is co-extensive, and where the curved lines
marked R, G, B, severally express, by the height to
which they rise on any one point in A B, the intensity
in its own spectrum  of each of the primary colours;
while the dotted curve, whose ordinate or height corresponding to any point is the sum  of those of the
other curves, will of course express the joint intensity
or degree of illumination in the visible spectrum.
(4I.) In this view  of the  subject, the prismatic
colours, with the exception of the extreme red, are all
more or less mixed tints, and this agrees well with its
general aspect, in which the red and indigo-blue are
the'only full and pure tints, the green being by no
means a saturated or full green, and the violet having
a strong dash of purplish-red in it...




258                   ON LIGHT.
(42.) The three primary colours assumed  in the
above figure are red, green, and blue, each in its highest
degree of purity and undilution, for it will be readily
apprehended that while the admixture of any one, in
however small a proportion, will produce a rich though
a mixed tint, that of both the others tends to dilution.
The only three colours which answer all the experimental conditions, are these three.  This may seem
contrary to the experience of the artist, who from his
habitual practice in mixing the colours he uses (all of
them without exception compound tints), would name
yellow, in place of green, as the intermediate primary.
The reason is obvious.  In all the yellows which he
uses there is a large admixture of red with green, and
in all his blues more or less green. When mixed, then,
there is sure to be a preponderance of green, while the
red goes to neutralize a portion of the other two, and
so to dilute the outstanding green. On the other hand,
the direct mixture of the prismatic yellow  and blue, in
whatever proportions, can no-how be made to produce green,
as Professor Maxwell's, M. Helmholz's, and my own
experiments* have distinctly proved; while that of the
prismatic green and red does produce yellow.  This
will be better understood when we come to speak of
the absorption of coloured light.
(43.) Since at each point of a compound spectrum
so constituted, all the three primary elements, in whatever proportion mixed, have one and the same degree
of refrangibility, it is evident that the compound tint
* See " Notices of the Royal Society," vol. x. p. 52.




ON LIGHT.                    259
arising from their mixture cannot be separated by any
subsequent refraction into its components.
(44.) In persons who are what is called " colourblind," the eye is sensible to all the rays of the prismatic
spectrum  as light, though even in that respect the red
rays appear comparatively deficient in power to stimulate
the nerves of vision, so that all colours, into which a
large proportional admixture of primary red enters, are
described by them  as sombre tints.  But besides this,
two of the primary coloured rays, the red and the green,
appear to excite in their nerves sensations of colour
nearly or exactly similar. Their vision is therefore, in
fact, dichrormic; all their compound colours are resolvable into two elements only instead of three.  Red
they do not distinguish from  green.  The scarlet coat
of the soldier and the turf on which he is exercisedthe ripe cherries and the green leaves among which
they hang-are to them  undistinguishable by colour,
though from  constantly hearing them  so spoken of,
they habitually speak of the fruit as red and the leaves
as green.  Their sensation of blue is probably the same
as in normal vision; though whether that excited by
their other colour, be such as a normal-eyed person
would  call red, yellow, green, or something  quite
different from either, we have no means of ascertaining, nor can they give us any information.  The face
of nature must appear, however, to them  far inferior
in splendour and variety to that which we behold;
and if there be, as is asserted, here and there an individual totally destitute of the sensation of difference




260                   ON LIGHT.
of colour, it must present to his eyes what we should
be disposed to call a hideous monotony-light and
shade only revealing the forms of objects as in an engraving.  Yet what we never knew  we never miss.
There may, and not improbably do, exist beings:in
other spheres, if not here on earth, whose vision is
sensitive to those rays of the spectrum which extend
far beyond the violet or its lavender prolongation, and
which we know  at present only by their powerful
photographic activity, and by their agency in producing
that singular species of phosphorescence in certain
media to which Professor Stokes has given the name
of Fluorescence.  By these properties, the solar spectrum is proved to be prolonged far beyond its visible
limits at its most refracted extremity; as it is by ot/er
invisible rays OF HEAT, which have been traced up to
nearly an equal distance beyond the extreme red in
the opposite direction.* All, however, whether of heat
or chemical influence, conform  each for itself, and according to its own special "refractive index," to the
same general law of the sines, as well as to every other
of those singular and complicated  relations of the
luminous rays, we shall hereafter have to describe;
and both the one and the other extending into and
thinning out as it were in the luminous region, just
as we have described the spectra of the primary colours
into those of each other.  Such, and so wondrously
complex a compound is a sunbeam!
* See my paper in the Phil. Trans. R. S. I842, "On the Action
of the Solar Rays on Vegetable Colours."




ON LIGHT.                      2 61
(45.) The analysis into its prismatic elements of the
colour of any natural object, is readily performed by
examining through the refracting angle of a prism  of
perfectly colourless glass a rectilinear band or strip of
the colour to be analysed, so narrow as to have scarcely
any apparent breadth, and to appear as little more than
a coloured line.   Placing this on a perfectly black
ground, parallel to the refracting edge of the prism, and
illuminating it as strongly as possible, it will be seen
dilated into a spectrum, or broad riband of colour, exhibiting of course those coloured rays only which belong
to the composition of the tint examined. An. exceed-.ngly convenient arrangement for this purpose is to
fasten across one end of a hollow square tube of metal
or pasteboard blackened within, of about an inch square
and twelve or fourteen inches long, a metal plate having
in it a very narrow slit parallel to one side, quite straight,
and very cleanly and sharply cut.  At the other end
within the tube is to be fixed a small prism of highly
dispersive colourless flint glass, having its refracting
angle parallel to the slit, and so placed that when the
tube is directed to the sky, or rather to a white cloud,
the slit shall be seen dilated into a clear and distinct
prismatic spectrum. In this of course all the prismatic
colours will be seen in their due order.  But if, instead
of this, any coloured object-as the leaf of a flower, for
instance, or a coloured paper, strongly illuminated by
direct sunshine (if necessary, concentred on it by a lens,
so, however, as not to scorch the object by the heat of
its focus),-be placed sonear to the slit as completely to




262                   ON LIGHT.
occupy its whole area and suffer no ray to enter it which
does not come from some part of the coloured surface;
the spectrum  will be seen deficient in all those rays
which the object does not reflect, and which belong to
its complementary colour.  The use of this little instrument, at once simple, portable, and inexpensive, will be
found to afford an inexhaustible source of amusement
and interest. To the florist, on a bright sunny morning,
the analysis of the tints of flowers and leaves, or the
hues of a butterfly's wing, and of every variety of coloured
object;-to the water-colour painter, the study of the
prismatic composition of his (so fancied) simple washes
of colour and the effects of their mixture and superposition;-to the oil painter, that of the various brilliantly coloured powders which mixed with oil form the
material of his artistic creations, are all replete with
interest and instruction.
(46.) If instead of a reflected colour we would examine a transmitted one, as in the case of a coloured
glass, or some natural transparent coloured product,-if
in the form of a plate or lamina, it may be laid over the
slit, and when directed to any bright white light (as that
of a white cloud), its spectrum  will be exhibited-if a
coloured flame, the slit may be placed close to it, but if
a liquid, it will be preferable to make it its own prism
by enclosing it in a hollow prism formed of plates of
glass cemented'together, when the differences arising
from difference of the thickness of the medium traversed
by therefracted rays will be more easily studied.
(47.) The colours of transparent media-such as




ON LIGHT.                    263
coloured glasses, crystals, resins, and liquids-depend
upon the greater or less facility with which the several
coloured rays are transmitted through their substance.
There is no medium  known, not even air or the purest
water, which allows all the coloured rays to pass through
it with equal facility. Independent of the partial reflexion which takes place at the surfaces of entry and
emergence, a portion greater or less according to the
nature of the medium, is always stifled, or as it is called
in optical language, " absorbed." and this absorptive
action is exerted unequally on the differently refrangible
rays; so that when a beam of white light is incident on
any such medium, it will be found at its emergence
deficient in some one or more of the elements of colour,
and will therefore have a tint complementary to that of
the absorbed portion. Supposing, as is most probable
in itself, and agrees with the general tenor of the facts,
that an equal per-cenzagte of the light of any specified
colour which arrives at any depth within the medium is
absorbed in traversing an equal additional thickness of
it, the intensity of the coloured ray so circumstanced
would diminish in geometrical, as the thickness traversed
increases in arithmetical progression.  The more absorbable any prismatic colour, then, the more quickly will it
become so much reduced in proportion to the rest as to
exercise no perceptible colorific action on the eye. And
thus it is found that in looking through different thicknesses of one and the same coloured glass or liquid, the
tint does not merely become deeper and fuller, but
changes its character.  Thus a solution of sap-green, or




264                   ON LIGHT.
of muriate of chromium, in small thicknesses is green —
in great ones red; tincture of violets, and that species of
rich blue glass which is coloured with cobalt, in like
manner are red when we look through a great thickness,
but beautifully blue when thin; and so in a multitude of
other cases. Those who paint in water colours are well
aware of what importance it is to effect the tint they aim
at by a single wash of their colour. A second application of the very same liquid, after allowing the first to
dry, does not simply heighten the colour, but changes the
tint, a circumstance which those who practise that fascinating art will do well to bear in mind.
(48.) When white light is transmitted successively
through two or more coloured media whose scales of
absorption differ materially, the residual beam, or that
which struggles through after passing their successive
ordeal, will consist of those rays only whose transmission is favoured by all the media. Hence it will follow,
first; that the final tint, or that of the beam ultimately
emergent, will most probably be very different not only
from  that exhibited by either of them  separately, but
from that which mig-ht be expected to arise from a union
or blending of their tints, and which would arise were we
to unite together distinct luminous beams having those
tints; and, secondly, that all such successive transmissions tend to produce  sombre tints, and ultimately
complete blackness; inasmuch as each successive transmission destroys (or absorbs) a greater or less proportion
of the total illuminating power of the original beam.
Thus when colour is produced on white paper by the




ON LIGHT.                    265
laying on of successive washes of diferent transparent
colours, the tendency is to produce, first, a tint very
remote from that expected to result from their union; and
secondly, becoming more and more muddy and sombre,
the greater the number of such heterogeneous layers of
colour.  Hence the maxim in water-colour painting, to
secure brilliancy by using only a single wash of colour,
if possible, to produce the required effect.  The painter
should never forget that his notion of colour (as compared with that of the photologist) is a negative one.
He operates solely by the destruction of light, and his
aim  should always be to destroy as little as possible.
His direct action (unknown to himself) is upon the tint
complementary to that which he aims at producing.
(49.) Each particular coloured medium  has its own
peculiar and specific scale of absorptive action, differing
inter se in the most singular and capricious manner. In
many, indeed in most cases, the spectrum viewed through
such a thickness as to give a strong colour to common
daylight, in place of being seen as a continuous band of
graduating colour, is broken up into distinct coloured
spaces, more or less intense, and more or less welldefined, separated by dark intervals. This is particularly
the case with coloured gases or vapours. Thus the red
vapour of nitrous gas, especially when its absorptive
action is intensified by heat, breaks up the spectrum
into a succession of narrow spaces, alternately dark and
bright, from one end to the other.
(50.) When coloured flames are examined with such a
" spectroscope" as above described, the phenomena are




266                    ON LIGHT,
no less varied, and in the highest degree characteristic.
The presence in the flame of each particular chemical
element determines the presence in its light of some one
or more coloured rays of defnile refrangibility and colour,
producing often in its spectrum  the appearance of a
definite line of coloured light out of all proportion
brighter than the rest. Thus the presence of soda in
any flaming  body is characterized by a narrow  and
exceedingly vivid line of yellow light. So completely
characteristic are these lines of the chemical elements to
which they bear relation, that no less than four new
metals, Thallium, Rubidium, Caesium, and Indium owe
their first discovery to the observation of definite spectral
lines of their appropriate colour, produced by their
presence in quantities too minute to be rendered sensible in any other manner.*
(5I.) It is impossible in the compass of a lecture like
the present, to do more than notice with extreme brevity
these remarkable classes of phmenomena, and that only
as bearing upon the general'object we have in view.
They prove in the most convincing manner the close
and intimate relation in which LIGHT stands to MATTER.
It enters into the interior of the hardest and least penetrable bodies, and thereout brings us information of an
* In reference to what is now called "Spectrum Analysis," in a
chemical point of view, I may be here allowed to call attention to a
passage in my "Treatise on Light," published in I827 (Encyc.
Metrop., vol. iv.):-" The colours thus communicated by the different bases to flame, afford in many cases a ready and neat way of
detecting extremely minute quantities of them."-Article, " Light,"
~ 524.)




ON LIGHT.                    267
almost infinite variety of particulars as to their intimate
nature and constitution (and, as we shall see further on,
of their internal structure, and the mechanism by which
they are held together as bodies), which by no other
means we can obtain: information which at present we
are only imperfectly able to interpret, but whose import,
from year to year, and almost from week to week, is
becoming better understood.   Its language in this
respect bears no distant similitude to that of a series
of ancient inscriptions in some unknown tongue and
character. A single sentence once developed by some
happy and unmistakable concurrence of evidence, affords
a clue to others, which in their turn become the stepping-stones of further progress. By the one are revealed
the histories of ages long buried in oblivion, and of the
phases of human thought and action under circumstances
bearing little analogy to anything we now see around us:
by the other we are admitted a step nearer to the perception of the intimate working of those powers which
maintain the material universe as it stands, and the laws
they observe.




LECTURE VIL
ON LIGHT.
PART II.-THEORIES OF LIGHT-INTERFERENCESDIFFRACTION.'WO theories only, entitled to any consideration
1   as rational and intelligible explanations of
the phenomena of Light, have been advanced-the one proposed by Sir Isaac
Newton, commonly known as the "Corpuscular;" the
other by Christian Huyghens, as the "Undulatory"
theory.  According to the former, light consists in
" Corpuscules," or excessively minute material particles
darted out in all directions from the luminous body,
in virtue of some violent repulsive power, or other energetic form of internal action, acting under such circumstances, and under such laws, as to give them all the
same initial velocity which they retain unchanged in their
progress through space, as well as their initial direction
according to the general laws of motion (to all which
they implicitly conform), until they meet with some material body by whose action their course is changed. All




ON LIGHT.                     269
this, and all subsequent changes of direction and velocity, are held, on this theory, to be effected by attractive
or repulsive powers resident in the bodies on which the
light-corpuscules fall (or, which comes to the same thing,
in the corpuscules themselves), and from which they are
either reflected, if the repulsive powers be too strong to
permit their penetration; or in which they are refracted,
if they are able to enter and make their way among the
particles of the refracting body. Colour, according to
this theory, is accounted for by specific diversity among
the luminous particles; and difference of refrangibility,
by differences in the intrinsic energy of the acting forces
as determined by the specific nature of the molecules,
or, which comes to the same, by a-difference of proportion between their moving force and their inertia. This
is one of the many weak points of the theory. It runs
counter to the only analogy which  the observation
of nature furnishes. It is as if the sun should be supposed to attract a planet of lead and one of cork with
different accelerating forces; or as if, here on earth, a
lump of platina and a lump of iron should be supposed
to acquire different velocities in falling through the same
space. It runs counter, too, to the original assumption,
that when first emitted from a luminous body, in their
passage through empty space, all the coloured particles
move with equal velocities, and. have therefore been
equally accelerated by the emitting forces.  That they do
so, we know from astronomical observation. The Aberration of all the coloured rays is the same. Were it not
so, every star seen through a highly magnifying telescope




270                  ON LIGHT.
ought to appear as drawn out into a short, coloured
spectrum in a certain definite direction.  Light requires
forty-two minutes to reach the earth from Jupiter at its
mean distance.  Supposing the rays of one end of the
spectrum-the violet, for instance-to travel faster than
those at the other (the red), a satellite undergoing
eclipse by immersion in the shadow of the planet ought
to change colour before extinction, from white to redthe last-emitted red rays lagging behind the violet on
their journey to the earth; while at its reappearance a
blue colour ought to be first perceptible.
(53.)  Among the stars are many which vary periodically in brightness, and some of them undergo complete
extinction.  As light takes several years to travel from
the stars, the difference in the times of arrival for any
sensible difference of velocity would amount to many
days, and would be quite sufficient to tinge the disappearing and reappearing star with the hues belonging to
opposite ends of the spectrum.  No such thing, however, is observed. Most of them retain their whiteness;
and though some do assume a deep-red colour when undergoing extinction, or when at their minimum of splendour, it is not changed to blue at their reappearance, oi
on their commencing augmentation of brightness.
(54.) The reflexion and refraction of light are, as we
have stated, accounted for on this theory by supposing
the particles of all material bodies, besides the attractive
force of gravitation, to be endowed with other forces,
both attractive and repulsive-the latter extending to a
greater distance than the former, so as to constitute an




ON LIGHT.                    271
attractive and a repulsive sphere one within the otherthe particles of light being repelled while passing through
the outer or repulsive sphere, and attracted when arrived
within the internal or attractive one. These forces are
supposed immensely energetic, and to decrease with such
excessive rapidity as to be absolutely insensible at any,
the very smallest, distance appretiable to our senses.  In
virtue of this repulsive force, the surface of any material body may be conceived as coated (metaphorically
speaking) with a film of repulsive power, off which, as
from  an elastic cushion, the luminous particles may be
imagined to rebound: in which case, according to the
known laws of elastic rebound, the angle of reflexion
(perfect elasticity being supposed) would be equal to
that of incidence, and the velocities before and after reflexion equal.
(55.) Reflexion, then, is easily and readily explained
on this theory.  In fact, it is explained too well.  For it
will be at once asked, how, on such suppositions, there
can be such a thing as partial reflexion.  Since all the
luminous particles of a ray arrive at (suppose) a plane
surface in the same direction and with the same velocity;
whatever happens to one, the repulsive force being the
same, must happen to all. This is another weak point of
the corpuscular theory; and to escape from the difficulty
so created, it becomes necessary to supplement the
original hypothesis of luminozus particles with another,
converting those particles into mechanisms of a peculiar
nature, of which the simplest conception that can be
formed is to suppose them  as it were minute magntds




272                   ON LIGHT.
having attractive and repulsive poles, and during their
progress through space revolving round their own centres
about axes not coincident with the direction of their
motion. - Under such circumstances it is clear that some
might arrive at the reflecting surface with the attractive
pole foremost-others with the repulsive.  The former
would be attracted, and escape the reflective action; the
latter repelled, and therefore subjected to it. Or, without making any supposition as to the sort of mechanism
by which such a result might be attained, we might content ourselves with assuming, as Newton (the framer of
this hypothesis) did, that the particles of light, throughout their whole progress through space, pass periodically
through a succession of alternating physical states-or,
as he called them, "fits "-" of easy reflexion and easy
transmission:" the only objection to such a form of
statement being, that it conveys no clear physical conception to the mind.
(56.) The particles so escaping reflexion are conceived
to have penetrated within the limit of the repulsive, and
to have entered that of the attractive forces, while yet at
some inconceivably minute distance outside of the actual
surface of the medium.  Their movement of approach
therefore to the surface is accelerated by the attractive
force whose resultant direction is perpendicular to the
surface, and when they have arrived wit/zin the medium
so far that all further action ceases (by the counteraction
of equal and opposite forces on all sides) each of them
will have undergone the total amount of acceleration
due to the attractive force —in the direction of thatforce,




ON LIGHT.                     273
i.e., at right angles to the surface.  Its velocity estimated in this direction will therefore be greater within
the medium  than without-while that parallel to the
surface remains unchanged: the force in that direction
being nil. The direction of the motion therefore will
be more highly inclined to the surface within the medium
than. without, in the same manner and for the very same
reason, that the path of a projectile shot obliquely downwards from the top of a hill makes a greater angle with
the horizon when it reaches the ground than it did in the
commencement of its descent.  And the conclusion, on
strict dynamical principles, is the same in both cases.
Supposing the initial velocity of projection the same, the
sines of the angles made by the direction of the motion
with the vertical or perpendicular to the surface, at the
beginning, and at the end of the descent (i.e., in the case
of light, those of the angles of incidence and refraction),
will be to each other in an invariable proportion, the
total heigZht of the descent being the same.  Thus we see
that the law of refraction is satisfactorily accounted for,
on the corpuscular hypothesis; and that, on that theory,
the velocity is greater in the interior of a refracting
medium  than in empty space; and the more so, the
greater the refractive power.
(57.) Let us now see'in what sort of conclusion we are
landed as to the intensity of the forces we have pressed
into our service. To consider only the reflective force,
we have this to guide us-that, supposing the incidence
perpendicular, and the light therefore reflected back by
the path of its arrival, that force must have been sufficiS




274                   ON LIGHT.
ently great to destroy the whole velocity of the luminous
particle, and to generate an equal one in the opposite
direction, in the time occupied by the particle in traversing forwards and backwards the thickness of our stratum
of reflecting force. Now the velocity of light, as we have
seen, is 86,ooo0 miles per second. To destroy and reproduce this velocity in a projectile shot directly upwards,
by the force of gravity on the earth, supposed uniform or
undiminished by distance, would require its action to be
continued for 706 days, or very nearly two years, while
the same effect has to be produced by the reflecting force
(also supposed uniform), in that inappretiable instant of
time in which the act of reflection is performed-a time
which would be extravagantly overrated at the billionth/
part of a second. After this we need hardly trouble our
readers with any estimation of the intensity of the refracting forces.  The sturdiest philosophy may fairly
be staggered at such a postulate as the foundation of a
physical theory.
(58.) According to the "undulatory theory" light consists in an undulatory or vibratory movement propagated
through an elastic medium pervading all space, not even
excepting what is occupied,. or seems to be occupied, by
what we call material bodies-that is, such as have weighzt,
and which, to us, constitute the visible and tangible universe of things.  It therefore resembles sound, which is
not a travelling entity, but a propagated motion in the air,
analogous to the tremulous movement which runs from
* A billion is a million times a million. The French milliard is
a thousand millions.




ON LIGHT.                    275
end to end of a stretched cord, or to the waves which appear to travel along the surface of water; though in reality
such a wave is only an advancing form, the real movement of the watery particles being vertically up an d down.
Colour in this view of the subject is analogous to tone, or
pitch, in music (if it be supposed to depend solely on refrangibility). As the frequency of the vibrations which
reach the ear from a sounding-string determines the pitch
of the musical note it yields, so the frequency of the undulations of this elastic medium or luminiferous "ether,"
as it is called, determines to the nerves of the eye the
colour of the light.  Or in that view of colour which
considers all but three primary hues composite, it must
on. this theory be assimilated to a difference analogous to
quality in a musical tone-as, for instance, between the
sounds of a violin, a flute, and a trumpet, only much
more decided and strongly characterized.
(59.) As sound spreads through the air with equal rapidity in all directions, and may be considered as propagated
from its origin as a spherical shell continually enlarging,
soin this theory must light be regarded as the movement of a WAVE in the ether, running out spherically in
all directions from the luminous point, whose situation
with respect to the eye, or to any other point on which
the wave may strike, is judged of as the centre of the
sphere-i.e., as lying in a line perpendicular to its surface.  A ray of light then, in this theory, is a purely
imaginary line from such point, perpendicular to the
general surface, or front of the wave, and has no other
meaning.  The wave, not the ray, is the primary object




276                   ON LIGHT.
of contemplation. If the point where the luminous excitement originates be near, the perpendiculars from it
to the wave-surface diverge conically; but if so far remote that the portion of that surface at the eye may be
regarded as sensibly plane, they are to all sense parallel,
as in the case of light emanating from the stars or the
sun.
(60.) The reflection of light in this theory is in exact
analogy with that of any other undulatory movement.
We cannot see the waves of sound, but those on smooth
water are easily followed and their reflexion made matter
of ocular inspection.  Drop a small pebble into still
water, and a wave will be seen to spread out in an enlarging ring, Let this be done near the perpendicular
and smooth side of any large. tank or pond, or near a
board held vertically in the water, and the ring will be
seen on reaching the board to be reflected, and will
thence spread back over the surface, still enlarging, as
the segment of another ring whose centre might be supposed as far on the land side of the reflecting surface as
the place where the pebble was dropped was in reality
on the water side. If several pebbles be dropped in
succession, or a regular up-and-down movement given
to the water at that point, a continued series of circular
waves will be generated and reflected,-the reflected
waves running out and intersecting the direct exactly as
if they originated in two distinct centres. What in water
is seen to be a reflected wave, in air we recognize as an
echo. And in the fact that a sound, though partially reflected as such from a window, a board partition, or a




ON LIGHTT.                   27
wall, isheard, though with diminished intensity, on the
other side,-we have the analogue to the partial reflexion
of a beam of light at a transparent surface; and on the
other hand, in the deadening of sound in passing through
woolly or puffy substances, while it is transmitted with
exceeding sharpness and distinctness through compact
solids or through water, we have the parallel to the
absorption of light in some media, and its copious transmission through others.
(6I.) The explanation of refraction on the undulatory
theory is exceedingly simple.  Suppose a plane wave to
sweep obliquely along the surface B E of a medium
capable of propagating within it the luminiferous undulation, and let it be supposed at equal intervals of time
a./;'"x
Fig. 4.
(successive seconds, for instance) to assume successive
positions B b, c c, D d, E e, arriving in succession at
equidistant points B C D E of the surface.  So soon as




278                  ON LIGHT.
any point in the surface is struck by the wave it will be
set in undulatory motion and propagate from it a movement which will run out spherically from that point in
all directions with such (uniform) velocity as belongs
to the luminous undulation in the medium. When, therefore, the wave has reached the position E e, E will just
have begun to move; the internal wave propagated from
D will have travelled during one second, from c two,
from  B three seconds,-and the motion, in virtue of
these, respectively, will have extended to the surfaces of
spheres about those points as centres, having radii in
the proportions I, 2, 3, so that a plane passing through
E, which touches one of them, will touch them all, and
the same is true for all points intermediate between
these.  Such a plane will define the limit up to which the
movement has reached within the medium  when the exterior wave has the position E e, and will, therefore, be
the front of a plane wave advancing within it.  If the
velocity of the undulation within the medium  be the
same as without, D 0, c N, B M, the radii of our spheres
will be equal to E H, E G, E F, the spaces run over in
one, two, three seconds outside, and the touching plane
E O N M will evidently be a continuation of the exterior
plane wave e E.  In this case, then, there is no refraction, the direction of the interior ray B M being the same
as A B, perpendicular to the exterior wave. But suppose
the velocity within the medium less than that without.
In that case the radii of our spheres D R, C Q, B P, will
be less than D, c N, B M, and in a constant proportion.
The plane E P touching them  all then, or the front of




ON LIGHT.                     279
the interior wave will be inclined at a less angle B E P to
the surface than B E M, or its equal E B F,-and the sines
of these angles to a common radius E B are evidently in
the proportion to each other of P B to B M, or of the velocity of light in the medium to the velocity out of it.  Now,
as the ray is perpendicular to the wave, the inclination of
the latter to the surface is the same as that of the former
to the perpendicular, and thus these angles are respectively identical with those of refraction and incidence.
(62.) To such of our readers as may find a difficulty in
following out this reasoning, the following familiar illustration will convey a full conception of its principle.
Imagine a line of soldiers in march across a tract of
country divided by a straight boundary line into two
regions, the one smooth, level, and well adapted for
marching, the other difficult, rough, and in which from
its nature the same progress cannot be made in the same
time. Suppose, moreover, their line of front oblique to
the line of demarcation between the two regions, so that
the men shall arrive at it in succession, and not simultaneously.  Each man, then, from  the moment he has
stepped across this line, will find himself unable to make
the same progress as before.  He will be therefore unable to keep line with that part of the troop which is
still on the better ground, but must of necessity lag behind; and that, by the greater space, the longer he
travels. Since each man on his reaching-the line of division experiences the same difficulty: if they will not
break line and straggle, but persist in still marching in.
line and keeping up their connexion, it will follow of




280                   ON LIGHT.
necessity that the front of their line must to a certain extent fall back and make an obtuse angle at its point of
junction with that of the unimpeded line. Thus, in our
figure, B E will represent the line of division between the
two regions, B b the advancing front of the troop when
the first man arrives at that line, E e that of the portion
stillon the good ground after some time elapsed, and
EP that of the other portion who have been unable to
keep up to the same rate of march.  And as the necessity of keeping step and not crossing ea.ch other's line
of march will oblige each man to step out rigzt in fron;
(i.e., at right angles to the new frontage), the progre3s,
B P, made by the first man after crossing the line, will be
perpendicular to E P, and will be to what he would have
made (BM) had it not been for the retardation, in the
proportion of his new to his former velocity of march.
(63.) Thus then we see that when light passes (in this
theory) out of what is called a rarer medium  into a
denser, or when the angle of refraction is less than that.
of incidence, the velocity of.propagation of the undulatory
movement is diminisihed, while on the corpuscular doctrine
it is increased, and vice versa.  Thus, too, we see that on
the undulatory hypothesis the connexion between refrangibility and velocity within the refracting medium is imzediate  and absolute, and consequently that it being certain, as we have shown, that light of all refrangibilities
travels equally fast in wlhat we call empty space (i.e.,
through the ether alone), it follows with equal certainty
that in material media the more refrangible rays are propagated slower than the less so; and all, more slowly than




ON LIGHT.                    281
in free space. In other words, this amounts to supposing the elastic force of the ether either to be enfeebled
in the interior of material bodies, or else that the movements of its particles are in some eway or other clogged or
burthened by some sort of connexion with or adhesion
to the material molecules among which they are disseminated, and that more for the more refrangible rays than
for the less so.
(64.) Until lately this difference of velocity between
the differently refrangible rays had always been considered an insuperable obstacle to the admission of the
undulatory hypothesis. All sounds of whatever pitch (it
was contended) travel equally fas.t in one and the same
elastic medium.  The profounder researches of later
mathematicians, however, have shown that this conclusion is not absolute, and that on certain suppositions
which are not altogether inadmissible in respect of the
vibrations of light, the difference is not contradictory to
strict dynamical laws.
(65.) As we have attempted to form an estimate of the
intensity of the forces required to account for observed
facts on the corpuscular hypothesis, let us now attempt
a parallel estimate on the undulatory.  And here the
way is equally open and obvious.  Starting with the observed facts, that sound travels in air at the rate of o090
feet per second, while light is propagated through the
ether I86,ooo miles in the. same time (that is to say,
90o,ooo times as fast), we are enabled to say how many
fold the elastic force of the air, or its resistance to compression, would require to be increased in proportion to




282                   ON LIGHT.
the inertia of its molecules, to give rise to an equally rapid
transmission of a wave through it. For it results from
the theory of sound that in media of different elasticities
(so understood), but similarly constituted in other respects, these forces are to each other as the squares of
the velocities with which the waves travel: so that the
elastic force of the air would require to be increased in
the proportion of the square of goI,ooo (i.e., 8rI,80I
millions) to i, to produce an equal velocity. Even this
enormous number must be still further increased, since
the velocity of sound is augmented by a peculiarity in
the constitution of air which we should hardly be justified
in attributing to the luminiferous ether, in virtue of
which its elasticity is increased by heat given out in the
act of its compression, and without which the velocity of
sound would be only 9I6 feet per second instead ot
iogo.  Thus the number above arrived at has to be
further increased in the proportion of the square of Io90
to that of 916, which brings it to I,I48,000,000,000.
Let us suppose now that an amount of our etherial
medium equal in quantity of matter to that which is contained in a cubic inch of air (which weighs about onethird of a grain) were enclosed in a cube of an inch in the
side.  The bursting power of air so enclosed we know to
be I5 lbs. on each side of the cube.  That of the imprisoned ether then would be 15 times the above immense
number (or upwards of 17 billions) of pounds.  Do what
we will-adopt what hypotheses we please-there is no
escape, in dealing with the phaenomena of light, from
these gigantic numbers; or from the conception of enor



ON LIGHT.                    283
mous physical force in perpetual exertion at every point,
through all the immensity of space.
(66.) As this is the conclusion we are landed in-(for
the evidence for the truth of the undulatory doctrine, or
something equivalent to it, accumulating, as we shall see,
in all quarters, and in the most unexpected manner receiving confirmation from facts utterly uncontemplated
by its originator, obliges us to look on this result as something more than a scientific rhodomontade)-we shall
cndeavour to present it to the conception of our readers
in a point of view which may enable them to realize it
more distinctly.  All who know the nature of a barometer are aware that the column of mercury 30 inches
in height sustained in its tube, is the equivalent of the
pressure of the aerial ocean which covers us, on its sectional area; and is just sufficient to counterbalance the
pressure, on an equal area, of an atmosphere five miles
in height of air everywhere of the same density as at the
surface of the earth.  This height (five miles) is what is
termed in Barometry, "the height of a homogeneous
atmosphere," and affords a measure of what may be
called the intrinsic elasticity of the air, of an exceedingly
convenient nature; and which is received as a kind of
natural unit, in Meteorology and Pneumatics. Substituting now light for sound, and for air the luminiferous
ether, we should have for the corresponding height of
our homogeneous atmosphere (gravity being supposed
uniform) five and a half billions of miles, or about onethird of the distance. to the nearest fixed star!  The
measure thus afforded of intrinsic elastic power is of the




284                   ON LIGHT.
same kind as that afforded of the intrinsic tensile strength
of a wire or thread of any material by the statement of
how much in length of itself it can bear without breaking. It frees us from the necessity of any mental reference to the' actual weight or specific gravity of the
material, which in this case is the more necessary, as,
though we suppose the ethereal molecules to possess
inertia, we cannot suppose them affected by the force of
gravitation.
(67.) There is yet another theory of light which might
be proposed, in which, still retaining the idea of an
ethereal medium, its constitution should be conceived
as an indefinite number of regularly arranged equidistant
points (mathematical localities) absolutely fixed and immovable in space, upon which, as on central pivots, the
molecules of the ether, supposed polar in their constitution, like little magnets (but each with three pairs of poles,
at the extremities of three axes at right angles to each
other), should be capable of oscillating freely, as a compass-needle on its centre, but in all directions.  Any one
who will be at the trouble of arranging half a dozen
small magnetic bars on pivots in the linear arrangement
of the annexed figure, will at once perceive how any
Fig. 5.
vibratory movement given to one, at any point of the
chain, will run on, wave-fashion, both ways through its
whole length. And he will not fail to notice that the




ON LIGHT.                       285
bodily movement of each  vibrating  element will be
transverse to the direction of the propagcted wave-a condition which, as we shall hereafter see, is essential to be
fulfilled in the luminous undulations.   As this hypothesis, however, has hitherto received no discussion, and
is here suggested only as one not unworthy of consideration, however strange its postulates, we shall not dwell
on it; remarking only that every phenomenon of light
points strongly to the conception of a solid rather than
a fluid constitution of the luminiferous ether, in this
sense,/that none of its elementary molecules are to be szpposed capable of interchanging places, or of bodily transfer
to any measurable distance from their own special and
assigned localities in the universe.  The constitution
above suggested would merely superadd to this abstract
idea of a solid structure, the further conception of polar
forces bearing some general analogy to those which may
possibly subsist among the gross particles of a tesseral
crystal.
(68.) This would go to realize (in however unexpected
a form), the ancient idea of a crystalline orb. And it
deserves notice that under no conception but that of a
solid can an elastic and expansible medium  be self-contained.*  If free to expand in all directions, it would
require a bounding envelope of sufficient strength  to
resist its outward pressure. And to evade this by supposing it infinite in extent, is to solve a difficulty by
words without ideas-to  take refuge from  it in the
* From a liquid the extreme particles would be constantly flying
off in vapour and dissipating themselves in space.




286                    ON LIGHT.
simple negation of that which constitutes the difficulty.
On the other hand, such a " crystalline orb" or "firmamnent" of solid matter conceived as a hollow  shell of
sufficient strength to sustain the internal tension, and
filled with a medium  attractively, and not repulsively
elastic, might realize (without supposing a solid structure in the contained ether) the condition of transverse
vibration; by establishing, ipso facto, lines of tension in
every possible direction, along which undulations might
be conveyed, like waves along a stretched cord, thus
furnishing a fourth hypothesis, which, to those fond of
such speculations may afford matter, sui generis, for consideration.
(69.) Interference of the rays of Zig/ht.  There is hardly
a more beautiful or a more instructive object in nature
than a large well-blown soap-btbble.  Whether we consider the perfect regularity of Its form, illustrating, as it
does, in its exact equilibration the great mechanical
laws to which the sun and planets owe their spherical
figure-demonstrating, by its resistance to disruption by
blasts of wind which distort it, and by its ready and
complete resumption of its normal shape on their cessation, the powerful tensile force which holds it together;
and proving, by the instantaneous collection of its filmy
tissue into water-globules; in the act of bursting, the
immense intrinsic energy of that force as compared with
gravitation-to the mechanician it is fraught with matter
of the highest interest.  To the photologist, on the other
hand, the vivid colours which glitter on its surface afford
at once the simplest and most elegant optical illustra



ON LIGHT.                        287
tion of the "law of interference" of the rays of light: a
law we shall now proceed to explain, taking for our
first exemplification of it this very phenomenon.
(7o.) If a soap-bubble be blown in a clean circular
saucer with  a very smooth, even rim, well moistened
with the soapy liquid,* and care be taken in the blowing
that it be single, quite free from any small adhering
bubbles, and somewhat more than hemispherical; so
that, while it touches and springs from the rim all round,
it shall somewhat overhang the saucer: and if in this
state it be placed under a clear glass hemisphere or
other transparent cover to defend it from  gusts of air
and prevent its drying too quickly;-the colours, which
in the act of blowing wander irregularly over its surface,
will be  observed  to  arrange  themselves into  regular
circles surrounding the highest point or vertex of the
sphere.  If the bubble be a thick one (i.e., not blown to
near the bursting point), only faint, or perhaps no colours
at all will at first appear, but will gradually come on
growing more full and vivid, and that, not by any par* M. Plateau gives the following recipe for such a liquid.  I.
Dissolve one part, by wezigzt, of MAarseilles soap, cut into thin slices
in forty parts of distilled water, and filter. Call the filtered liquid
A   2. Mix two parts, by measure, of pure glycerine with one part
of the solution A, in a temperature of 66~ Fahr., and after shalking
them together long and violently, leave them at rest for some days.
A clear liquid will settle, with a turbid one above. The lower is
to be sucked out from beneath the upper with a siphon, taking the
utmost care not to carry down any of the latter to mix with the
clear fluid.  A bubble blown with this will last several hours even
in the open air. Or, the mixed liquid, after standing twenty-four
hours, may be filtered,




288                    ON LIGHT.
ticular colour assuming a greater richness and depth of
tint, but, by the gradual withdraw7al of the faint tints
from  the vertex, while fresh, and more and more intense hues appear at that point, and open out into circular rings surrounding it; giving place as they enlarge
to others still more brilliant, until at length a very bright
white spot makes its appearance, quickly succeeded by
a perfectly black one.  Soon after the appearance of
this the bubble bursts. During the whole process it has
been growing gradually thinner by the slow descent of
its liquid substance on all sides from the vertex, till at
length the cohesion of the film  at that point gives way
under the general tension of the surface. The annular
arrangement of the colours, and the coincidence of their
common centre with this, the thinnest point of the film,
evidently go to connect their tints with the thicknesses
of that film at their points of manifestation, and to indicate that a certain tint is developed at a certain thickness,
and at no other. This, we shall presently see, is really
the case.
(7 I.) The order of the colours and the sequence of the
tints is in all cases one and the same, provided the series
be complete, i.e., provided time has been given for the
black central spot to form.  Thus the first series, or
order, contained within thefirst ring consists of black,
very pale blue, brilliant white, very pale yellow, orange,
red; the second of dark purple, blue, imperfect yellowgreen, bright yellow, crimson; the third of purple, blue,
grass green, fine yellow, pink, crimson; the fourth of
bluish-green, pale pink inclining  to yellow, red; tghe




ON LIGHT.                     289
fifth pale bluish-green, white, pink.  After these the
colours grow paler and paler, alternately bluish-green
and pink, and can hardly be traced beyond the seventh
order.
(72.) None of these tints are pure prismatic colours.
To see them  to the best advantage the bubble with its
glass shade should be placed out of direct sunshine,
where only dispersed light, such as that of a cloudy sky,
shall fall on it. Or, the illumination of the rings may be
effected by a thin semi-transparent paper, or a groundglass screen interposed between them and the incident
light. And if, instead of illuminating this with the direct
light of the sky, the coloured rays of a spectrum, formed
by passing a sunbeam through a glass prism, be thrown
upon it, the composite nature of their tints will be at
once apparent.  If all the rays but those at the red end
of the spectrum be excluded from the illuminating beam,
the rings will appear wholly red, separated by black
intervals, and much more numerous.  And if, now, the
colour of the illuminating light be changed, so as to pass
in succession through the whole prismatic scale of tints
-orange, yellow, green, &c., from the red to the violet
-the clour of the rings will undergo a corresponding
change, the dividing intervals preserving their blackness,
but their number still continuing greater than in white
light.  But, besides this, a very remarkable phxenomenQn
will be observed.  The rings contract rapidly in Zdiameter
as the colour of the illumination changes, being a maximum for a red and a minimum for a violet illumination;
and if, by a slight movement given to the prism, the
1'




290                   ON LIGHT.
spectrum be made to traverse to and fro on the illuminating screen, the rings will appear to open and close in
an exceedingly beautiful manner, undergoing at the same
time a corresponding change of colour.
(73.) The composite nature of the rings, as seen in
white light, is now abundantly clear. White light is a mixture of all the prismatic rays, and the set of rings seen in
such light is of course a mixture of the several individual
sets (concentric, but differing by a regular gradation of size),
of all the several coloured elements of which white light
consists.  Imagine a painter who could "dip in the
rainbow" and lay on, one after another, on the same
paper and with the same centre, such a series of rings
gradually decreasing in diameter, and each set tinted
with the pure prismatic hue which corresponds to its
size, from the extreme red to the extreme violet, in their
proper degrees of intensity;-he would produce just
such a series. If the diameters for all colours were
alike, the compound rings would evidently be white and
infinite in number, separated by black intervals. If they.
differed only a little-starting from a common originthe first ring would be nearly white, but exhibiting a
bluish border inwards and a reddish outwards, growing
more and more " pronounced," and broken into intermediate tints in those beyond; but if considerable, the
rings of different orders for different colours would soon
mingle with and confuse each other's tints, creating the
sensation of uniform whiteness: thus accounting for the
comparative paucity of the mixed series.




ON LIGHT..291
(74.) In order, then, clearly to understand the nature
of this phenomenon, it must be divested of this source
of complexity, and studied in reference to light of one
single colour or refrangibility-or, as it is called, " homogeneous" light, pure red or yellow, for instance.  But before proceeding further, something more must be said of
the whole class of phenomena referable to this. head.
And first, these colours are not dependent in any way
on any colorific quality of the liquid of which the
bubbles consist. Any sufficiently thin film, of any kind,
suffices to produce them.  They are seen in the oily
scum on the surface of a stagnant pool. They are seen
on the brilliant scales of old glass ih stable windows, or
on the wings of gaudy-coloured insects, or even on
polished steel.  Bubbles may be blown of a variety of
liquids-nay, even of glass.  However highly coloured,
their intrinsic colour disappears when reduced to such
extreme tenuity as is requisite for the purpose in question. But all exhibit the same hues in the same invariable
order.  Nay, more-it requires no medium at all to produce them, but only an interval between two surfaces.
They are seen in the crack of a thick piece of glass
which does not extend quite through its whole substance.
They are seen when a piece of mica is partially split and
one of the lamina lifted up, following as a series of
coloured lines the limit of the commencing fissure.
It may be said that though no solid or liquid miedium is
here present, there is air between the divided surfaces.
But under the exhausted receiver of an air-pump, there




292                    ON LIGHT.
is no diminution of the colours, or alteration of their
forms.  It is to the interval between the surfaces that we
have to look for their origin.
(75.) Here, then, we have LIGHT brought face to face
with SPACE, and no escape!  What happens at or between these surfaces.  How is it that while a single
surface reflects a dispersed beam of light indifferently
over its whole extent, this indifference is destroyed by
placing another reflecting surface behind it; and the
reflexion (at least the efective refexion as regards the
spectator) rendered impossible when the second surface
is at a certain distance, or at certain distances, from the
first; while if placed at intermediate distances, it is
either not at all affected, or only to a certain extent
enfeebled  and that, when there is nothing, or at least
nothing realizable to any of our methods of observation,
between them?  This is the problem before us, reduced
to its simplest terms,-a problem which the corpuscular
theory of light resolves imperfectly and unsatisfactorily,
and the undulatory fully and without reserve.
(76.) When instead of using the prismatic spectrum
(of which it is next to impossible to insulate from the
rest a ray of perfectly definite refrangibility) to illuminate
the film, we employ artificial light (such as that of a
spirit lamp with a salted wick, which may be considered
as almost perfectly homogeneous), the rings are seen
with extraordinary sharpness; their central spot and their
divisions having the blackness of ink, and absolutely innumerable; being traceable with a magnifier when too
close to be otherwise distinguishable, apparently without




ON LIGHT.                     293
limit.  Thus disembarrassed of the complexity of overlapping rings of several colours, the phaenomenon now is
studied to greater advantage, and its explanation on
either theory is more readily intelligible. That afforded
by the corpuscular theory (supplemented by the Newtonian hypothesis of the fits of easy reflexion and transmission) is very simple and obvious.  These "fits" or
phases, it will be remembered, are supposed periodically
recurrent-i.e., succeed one another, or rather are repeated over and over again, in the same order and intensity, at equal intervals of time.  The same phase then
will recur to the corpuscules, at equidistant points of
space in their progress through any uniform medium (in
which the velocity of light is constant).  Where the
thickness of the film is nil, or so very minute as to bear
no comparison to the distance which separates two of
the equidistant points, it is obvious that having passed
one surface they will still be in a state to pass through
another, and will therefore not be reflected, so that in
that case the reflected illumination of the first surface
will receive no augmentation from light reflected at the
second.  The same is true if the thickness of the film be
exactly that of two such equidistant points, or its double,
triple, &c., for in those cases the corpuscule will arrive at
the second surface in the same state and with the same
dispositions as to reflexion or transmission as at the first;
and therefore, having penetrated the first, will also penetrate the second. On the other hand, for thicknesses of
the film exactly intermediate between these, the corpuscule on arrival at the second surface will be exactly




294                    ON LIGHT.
in the opposite state or disposition. Having been transmitted then at the first, it will be reflected at the second,
and, having in its passage back through another equal
thickness reassumed its original state in which it first entered, it will there be transmilted, and so will reinforce by
its light the general reflected illumination of that surface.
Since the per-centage of the total light reflected at any
transparent medium is but trifling, the light so sent back
from the second surface will be nearly equal to that reflected from the first. Thus for these exactly intermediate thicknesses, the joint-reflected illumination is very
nearly doubled, and between these and the former series
of thicknesses will increase and diminish alternately and
gradually.
(77.) Suppose now in the case of our soap-bubble
the thickness of the film to increase uniformly outwards
from  its vertex (where it is nearly nit).  Then it is evident that when exposed to dispersed light it will appear
divided into equivalent circular zones alternately bright,
and comparatively dark, the centre being also dark.  And
here we have a representation of our observed rings, with,
however, this remarkable and most important difference,
viz.: that the central spot and the dark divisions, on this
explanation, ought not to appear absolutely black, but
haf brzght, when compared with the brightest portions
between them.  In point of fact, some exceedingly slight
reflexion is perceivable in the dark centre, but instead
of half, it cannot be estimated at the fiftieth part of the
illumination of the bright ring which immediately adjoins it.




ON LIGHT.                     295
(78.) As the thickness of a soap-bubble cannot be subjected to direct measurement, it is impracticable, in its
case, to verify what must be considered the fundamental
principle of this explanation — viz., the regular increase,
in aritmlieticalprograession, of the thicknesses at which the
several successive black or bright rings appear. But of
this we may satisfy ourselves, by adopting a different
mode of producing and viewing them. When a spectacleglass or any other convex glass lens of long focus is laid
Fig. 6.
down upon a plane glass before an open window (both
being scrupulously clean and well polished), and a slight
pressure applied, the same dark spot, surrounded by the
same series of coloured rings, is seen, their centre being
at the point of contact of the glasses, where of course
their distance is nil. If the focal length of the lens be




296                    ON LIGHT.
not very large, they will require a magnifier to be well
seen, their diameters being in that case very small; but
with a lens of 20 or 30 feet focal length it is considerable, and the rings may be seen, and their diameters
measured, with ease.  Now it is found that these diameters, for the first, second, third, &c., dark rings in order
(reckoned from the centre), are not in the proportion of
the numbers I, 2, 3, &c., but of the numbers I, I'414,
I'732, 2'000, &c., which are their exact square roots,
giving to their system the appearance represented in the
preceding diagram; and this is exactly the progression of
distances from  the point of contact measured on the
surface of the plane glass which  correspond  to the
series of peIsrendicuiar distances between it and the convex
sphtericalsurfatce of the zypper glass in the proportion of the
arithmetical series, as may be seen in Fig. 7.
(79.) So far, then, the Newtonian hypothesis affords a
satisfactory account of the facts; in all, that is, but that
one particular already adverted to. This, however, must
be considered as conclusive against it; while, on a consideration of the whole case, there remains outstanding
this strange fact-that at certain distances between two
partially reflecting surfaces, forming a regular arithmetical
progression from nil upwards, the portion of a beam of
light reflected from  the  second, after passing  back
through the first, so far from augmenting the first reflected
light, annihilates it, and furnishes us with an instance
(which is, as we shall see hereafter, not the only one) of
the combination of lighlts creating darkness /
(80.) The question now arises,-Will the undulatory




ON LIGHT.                    297
theory help us in this difficulty, while at the same time
rendering an equally satisfactory account of the other
facts. To this we are enabled to reply in the affirmative. Two equal sounds we know, under certain circumstances, can produce silence, as when the two strings
which, in a pianoforte, go to produce, when exactly in
unison, a uniform and liquid note; if very slightly out
of tune, produce what are called 3bcas, or a succession
more or less rapid (accordingly as the strings are more
or less discordant) of sound and silence.  The same
tide-wave arriving at the same spots in the sea by two
courses of different lengths, results in producing no rise
and fall of the water at all, if the difference ef path be
such that the high water of one portion shall reach
~5Ill\^~_    i=- LF.l  
Fig. 7.
the place at the same moment with the low water of
the other.  This is the case at a point in the North
Sea, midway between Lowestoft and the coast of Holland, in lat. 520 27' N., long. 3~ I4' E.  Its position was
pointed out by Dr Whewell from  theory, and the fact
verified by Captain Hewett, R.N.
(8I.) This latter exemplification contains the essential
principle of the explanation in question, in nearly its
simplest state. If two waves, or rather two regular series
of equal waves all exactly like one another, and all




298                  ON LIGHT.
having set out inizially from one common ori~gin, reach the
same point by two different channels or lines of cornj
rdf j m   l      trae
munication differing just so much in length that the




ON LIGHT,                     299
crests of the one series shall reach it at the same identical moment with the crests of the other;'the two series of
crests conspiring and being superposed on each other
will produce crests of double the height of either singly:
while, on the other hand, if the difference of channels be
such that the crests of the first series shall reach it simultaneously with the troughs (or lowest depressions) of the
second; the one will destroy the other, and there will be
neither elevation nor depression at their joint point of
arrival. In the former case, supposing the two channels
thenceforward to unite into one (as in the annexed figures,
which require no explanation further than that the series
of cross lines represent the crests of the waves), the two
series when they reunite in a channel c D, as in Fig. 8, the
exact size of the initial one, A B, will form a joint series
exactly similar to that in A B, which will run on in that
channel thenceforward; but in the latter, as in Fig. 9, there
will be produced no waves at all, and the water in c D
will (except just close to the point of junction, where
some kind of eddy will be formed) remain undisturbed.
(82.) Accepting the term "wave" in its most general
sense, in whatever way we suppose it propagated, whether
by alternate up-and-down movements of the successive
particles, as in water-waves-by transverse lateral ones,
as in a stretched cord ewagged horizontally-or by direct
to-and-fro vibration, as in the air-waves, in which sound
consists-or in any more complex manner, the same
considerations evidently apply. If two sets of exactly
equal and similar waves can by any previous arrangement be made to arrive simultaneously at the "entrance"




300                   ON LIGHT,
of one and the same "channel" (using these terms also
in their most general sense) along which each set, separately, might be freely propagated-i.e., so that the foremost crest of the first set shall strike the mouth of the
channel at the same moment with that of the other-they
will combine and run on along the channel as a single
set or series of waves of double the height or intensity.
In this case they are said to arrive "in the samephase"
(a term  borrowed from the phases of the moon which
passes periodically through the states of full and new,
increase and wane).  The same will be the case if the
foremost crest of the series be so timed (by the previous
arrangements) as to reach the mouth of the channel
simultaneously with the second, third, or fourth crest of
the other, in which case the one set is said to be in
arrear or advance of the other (as the case may be) by
one, two, or more entire "z undulations."  On the other
hand, if the foremost crest of the one set be so timed as to
arrive simultaneously with the first, second, third, &c.,
troozh of the other-up to the time of its arrival indeed
the one, two, or three foremost waves which are not contradicted will run forward;but, from the moment when
the others begin to arrive, they will cease to be followed
up by any more. In this case the one set is in advance
or arrear of the other by exactly one, or three, or five,
&c., semi-'undulations, and the series are said to be in
oppositep/hases.  In the intermediate " phases " it is easy
to see that a combined set of waves will be produced, but intermediate in height, intensity, or (as
it is called) "amplitude" between these two extremes




ON LIGHT.                    301
-viz., nil on the one hand, and redzlication on the
other.
(83.) The vibrations by which light and musical sounds
(to which light is analogous) are conveyed are so exceedingly minute, and the sho'ck conveyed by each separately
to our nerves, in consequence, so small, that it requires
a continued series of them to impress our senses. The
first few vibrations therefore which run on " uninterfered
with" produce no sensation, and are as if they existed
not. And thus we see how it may happen, that in the
case of a complete opposition of phase two equal musical
sounds may produce silence, and two equal rays of light
conmplete and continued darkness; that a perfect coincidence of phase has the effect of doubling the sensation;
and the intermediate states, a greater or less intensity as
the case may be, short of that limit.
(84.) Let us now proceed to apply our principle (that
of "su2eriposed and INTERFERING VIBRATIONS ) to the
matter in hand. Suppose a series of equal and equidistant light-waves (such as a ray of homogeneous light is
in this theory always understood to mean) to fall perpendicularly upon a plate of any transparent medium.  A
certain very small per-centage of it will be reflected back
by the first surface-that is to say, a series of similar
undulations, but of much less intensity or "amplitude,"
will be propagated back from the point of incidence.
The remainder of the total movement thus subdivided
will pass on, and, arriving at the second surface, again a
very nearly equal series (the per-centage being the same,
and the total incident light having suffered very little




302                    ON LIGHT.
diminution) will be returned, and, passing back through
the first surface (with only the same trifling per-centage of
loss), will, on emerging, be szperposed on the first reflected
series, with which it will be coincident in direction. If
then the thickness of the plate be such that in passing
to the hinder surface, back again, and out at the first, the
second series shall have lost upon the first precisely one,
three, five, or any odd number of semi-undulations, it
will begin to emerge in the exact opposite "phase" of
its period to that of the undulation of the first reflected
series which starts from the same point at the same instant.  Here, then, we have the case contemplated above
of two series of equal waves entering the same " channel" in opposite phases.  They will therefore destroy
each other, or the intensity of the joint ray will be nil.
The contrary will happen if the thickness be such as to
produce a retardation of two, four, or any even number
of semi-undulations.  In that case the two reflected rays
will conspire and produce a joint one of double intensity: and of intermediate in the various cases of intermediate retardation. 
(85.) Thus we see that the degree of brightness of the
reflected light depends on the thickness of the reflecting
film, and that for a certain series of thicknesses in arithmeticalprogression, the joint reflection is nil; for another
series exactly intermediate, it attains a maximum of intensity; and between these limits, all gradations of illumination will arise according to the intermediate thicknesses
supposed to exist. This is so far in general accordance with
the phenomena described: but before applying it to the




ON LIGHT.                       303
case of our coloured rings, it must be mentioned that in
reckoning the number of undulations or semi-undulations
by which the second reflected ray actually is in arrear of
the first on emergence, we have to consider the different
modes in which the reflexion of a wave is accomplished
at the surface of a medium denser or rarer than that in
which it moves and is reflected.  To present this clearly,
we will take the most familiar illustration-that of the
propagation of motion by the collision of elastic balls.
Imagine a great number of equal ivory balls (supposed
perfectly elastic) in contact, but connected only by an elastic
string passing centrally through each and along the common axis of all; and pinned or fastened to each at its centre
so that the separation of any two shall stretch only that
part of the string between their centres. Suppose now
that a shock is given to the extreme ball at one end in
the direction of the common axis, by another similar and
equal detached ball driven against it. By the received
laws of elastic collision it will give up its whole motion to
that which it first strikes, and be itself reduced to rest.
In like manner the motion so communicated to the first
will be handed on undiminished to the second; itself resting and therefore remaining in contact with the striking
ball, and so on.  Thus what may be termed a "wave of
compression," will run along the series till it reaches the
ball at the other end. This, having none in front to
communicate its motion to, will start off; and, were it
free, would quit the series.  But this it cannot do, by
reason of the elastic thread; which however it will stretch
in its effort to do so, and be ultimately brought back




304                   ON LIGHT,
by its pull. But in so doing the same pull will also be
communicated to the ball behind it, drawing it forward,
and so in succession to those yet behind; and in this
manner, a wave of extension will run back along the
series. If the tension of the string be very violent (suppose equal to the repulsive elasticity of the balls), this
wave will run back with the same velocity as the other.
Here we have then a case of the reflexion of a wave,
where, in the very instant of reflexion, its character is
changed zpso facto from that of a wave of compression
to one of extension-in other words, it starts backwards
in the opposite phase to that of its arrival; or, again in
other words, a semi-undulation is lost or gained (for it
matters not which) in the act of refexion.
(86.) This is the extreme case of reflexion from a
denser medium on a rarer-for here there is absolutely
nothing to carry on the motion beyond the terminal
ball.  Such a case never occurs in nature as regards
light; since even what we call a vacuum  is filled with
the luminiferous ether. To assimilate it to such as do
occur, suppose a second series of smaller balls, similarly
connected with each other, but not zeith the first set, and
brought end to end with it, with just room between for
one intermediate free ball of the smaller size to play
backwards and forwards as a go-between; and let this,
in the first instance, be placed in contact with the last
ball of the first set.  When the movement reaches it, it
will be driven off, and immediately striking the end ball
of the.second set, will propagate along it a wave of compression, coming itself to rest.  In so doing it will carry




ON LIGHT.                     305
off some, but not all of the motion of the terminal ball of
the first set. This will still continue to advance after
the blow, but to a less extent, and with less momentum
than in the former case, and, just as in that case, will
propagate backward a wave, though a feebler one, of
extension.  Starting, then, from  the same place at the
same moment, the two waves-the reflected portion (or
echo) and that which runs forward in the second set of
balls, set out each in its own direction in opposite
lphases.
(87.) The intensity of the reflected wave or echo will
be feebler the nearer the balls of the two sets approach
to equality (or the less the difference of density in the two
media). If they are exactly equal, the go-between ball
will carry off all the motion of the ball which strikes itor there will be no reflected wave, no echo.  And this
agrees with fact.  At the common surface of two transparent media of equal refractive power, however they
may differ in other respects, there is no reflexion.  But
suppose the second set of balls, as also the single intermediate one, larger than the first.  In that case (still
according to the laws of elastic collision) the last ball
of the first set not only will not advance after the shock,
but will be driven back, and the wave which it will propagate backwards will no longer be one of extension,
but of conzpression.  This being also the case with that
propagated onwards in the second series,-in this case
both will start on their respective courses from the point
of reflexion in the same phase.
(88.) In the undulatory theory of light the "denser"
U




306                   ON LIGHT.
medium corresponds to the series of larger balls in this
illustration. This ought to be so, for the velocity is less
in the denser medium as it is in the larger of two balls
after their collision; and because, as already remarked,
the ether in such media must be either denser in proportion to its elastic force, or somehow encumbered by
their material atoms.  And hence we finally conclude
that in the act of the reflexion of light on the surface of
a rarer medium, the phase of the undulation changes,
and a semi-undulation is lost (or gained-it matters not
which):- but not so when the light is reflected from a
denser medium.
(89.) To return now to the case of a thin pellucid
film.   If- its thickness, i.e., the interval separating its
two surfaces, be any number of seri-undulations; double
that number, i.e., an exact number of entire waves, will
have been lost by the wave reflected from the second
surface at its re-emergence from the first, by reason of
its greater length of path; and thus were no part of an
undulation lost or gained in the act of reflexion, it would
start thence in exact harmony with the first reflected ray.
But the second reflexion being made at the surface of a
rarer medium, an additional semi-undulation will have
been lost, so that the two reflected rays will really start
from the first surface in coimplete discordance, and destroy
each other.  The same is the case if the thickness be
nil, or so excessively minute as to be much less than the
length of a wave, as at the vertex of a soap-bubble when
just about to burst.  Here also will the same mutual
destruction of the reflected waves take place.  And thus




ON LIGHT.                      307
we have explained the complete or very nearly complete darkness of the central spot, and of a series of
rings corresponding to thickness of, 2, 3, or more
semi-wave lengths.   At the intermediate thicknesses
(i.e., of I, 3, 5, &c., quarter-wave-lengths) the exact reverse will happen-the reflected rays will start together
in harmony and appear as a ray of double intensity,
thus explaining the intermediate bright rings.
(90.) In the case of the rings produced between two
glasses of the same material, the intermediate film being
air, it is the reflexion from its firstsurface, not its second,
that is effected from a rarer medium; so that it is at this
surface that the additional semi undulation is gained by
the first reflected ray.  In all other respects the reasoning is the same in both  cases, and the explanation
equally complete in both.
(9I.) It will be perceived that we have not been
sparing of words in this explanation.  The epigrammatic style is ill-suited to clearness in the exposition
of a principle which it is essential to seize with perfect
distinctness, and in seizing which considerable difficulty
is commonly experienced.  If any doubt or misgiving,
however, should still linger on the mind as to the applicability of the analogy by which the loss of half an undulation necessitated by the blackness of the central
spot has been explained, a simple but striking experiment will suffice to dissipate it.  Let a set of rings be
formed by interposing, between two glasses of very different refractive densities, a film of liquid intermediate
in that respect-as, for instance, oil of sassafras be



308                   ON LIGHT.
tween a lens of light crown, and a plate of heavy flintglass. In this case the reflexions from the two surfaces
are performed either both from a denser medium upon a
rarer, or both from a rarer on a denser according as one
or the other glass is uppermost. In the former case
two semi-(or one entire) undulation will be gained or
lost between the reflected rays at emergence, in addition
to the entire ones lost betzeen the glasses: in the latter
none. At the central spot, then, the two reflected rays
will start on their backward course in exact harmony,
and the spot will be white, not black; and a similar reversal of character will of course pervade the whole
series of rings. This result, predicted by theory, has
been found confirmed by experiment.
(92.) It was a favourite idea of Newton that the
colours of all natural bodies are in fact the colours of
thin pellucid particles of such sizes and thicknesses
as to reflect those tints which, in the scale of tints of the
coloured rings above described, most nearly correspond
to them.  This idea we know now to be untenable, if
for no other reason than that we are sure the ultimate
particles or indivisible atoms of bodies (if any such there
be), are at all events many hundreds, thousands, or
millions of times smaller than even a single wave-length
of any homogeneous ray of light.  It will, of course, be
asked how we know these wave-lengths.  And this we
must now explain: in doing which we shall have to develop the most astounding facts in the way of numerical
statement which physical science has yet revealed.
(93.) In a series of equal waves running along still




ON LIGHT.                     309
water, the "wave-length," or "length of an entire undulation," is the linear distance between two consecutive
crests or two consecutive troughs.  This is its simplest conception, and it will suffice for our immediate
purpose.  The waves being equal and similar will all run
on with the same velocity, which may be ascertained by
noticing how long any one takes to run over a measured
distance on the surface, or the distance run over in a
determinable time, suppose a second   And if at the
same time we note the number of waves whose crests
pass a fixed point (a float, for instance) in the surface, in
a second of time the interval between two consecutive
crests will of course become known.  And vice versac, if
this interval be known, and the velocity of the waves;
the number of undulations passing the float per second
is easily calculated.  Now  this number is necessarily
identical with that of the periodically reciprocatinfg movemients or vibrations of thefirst mover (whatever it be) by
uwhich the waves are originally excited.  This continuing the same, the same number of waves will pass the
float in the same time, whatever be their velocity of propagation.  Of these three things-the velocity of propagation, the number of alternating movements, waves, or
pulses per second, and the linear interval between two
consecutive ones-any two being given, the third is
easily calculated.  For example, a string sounding a
certain note C in the musical scale makes 256 comp[lete
oscillations to and fro, per second. As each of these
sends forward an air-wave consisting of a semi-wave of
conpression by which the particles of air advance, and




310                   ON LIGHT.
another of expansion by which they return to their places,
these waves, 256 in number, being all comprised in, and
exactly filling the distance (Iogo feet) run over by sound
in that time, each entire wave will occupy 4'254 ft.
And, vice versa, if we knew this aipriori to be the wavelength, we should rightly conclude 256 to be the number of complete vibrations or pulses per second.
(94.) Mechanical processes enable us to grind and
polish. a glass surface into the segment of a sphere of
any required radius-as well as to a plane almost mathematically true.  Suppose such a glass surface worked,
we will say, to a sphere of Ioo feet radius, to be laid
(convexity downwards) on a truly plane glass.  The
coloured rings will be formed, as above described, about
a central dark spot; and if illuminated, instead of
ordinary daylight, by the prismatic rays, in succession,
a series of simply bright and dark rings of the several
colours in their order will be formed, whose diameters in
different series will correspond to their respective tints.
Under these circumstances, the linear measurement of
these diameters may be performed with ease and with
great precision. Now these diameters are the chords of
arcs of a circle on a radius of ioo feet represented in fig.
7, by the horizontal lines, the versed sines of whzose halves
corresponding (represented by the perpendicular lines) are
the distances between the glasses at those points, or the
thicknesses of the interposed film of ai;r and are easily
calculated when the radius and the chords are known.
On executing the measurements it is found that these
distances, reckoning outwards and commencing with the




ON LIGHT.                    311
centre, do actually follow the law of arithmetical progression (as on the above theory they should do), being
in the proportions of the numbers o, I, 2, 3, etc.
(95.) By measuring then the diameter of (say) the
tenth dark ring (for the sake of greater precision), calculating the corresponding interval, or versed sine, and
taking one-tenth of the result, we shall get the interval
corresponding to the first dark ring-for any particular
coloured light-and this, by what has been above shown,
is the half of a wave-length for such light.  Proceeding.thus, Newton found for what he considered the most
luminous yellow rays, one 89,oooth part of an inch for
the interval in question, which gives for the length of an
entire undulation of such rays, one 44,5ooth of an inch.
This comes exceedingly near to the result which later
experimenters have obtained for that purely homogeneous yellow light emitted by a salted spirit-lamp, which is
one 43,I97th of an inch.  For the extreme red and extreme violet rays, (as well as their limits can be fixed,) the
corresponding wave-lengths are respectively one 33,866th,
and one 70,555th of an inch.
(96.) These, it will be observed, are the lengths of
the undulations in air. In water, glass, or other media,
they are smaller, in the inverse proportion of the refractive index of the medium; for in such media the velocity of light, as we have seen, is less in that proportion; and the number of undulations per second remaining the same, while the space occupied by them is
less, their individual extent must of course be less in
the same proportion. This, too, is in accordance with




312                    ON LIGHT.
experiment. If water, oil, or any other liquid be introduced between the glasses, the rings are observed to
shrink in diameter, and the more so (and to the exact
extent required by theory) the greater the refractive
power of the liquid.
(97.) If the sensation of colour be, in analogy to that
of tone or musical pitch, dependent on the frequency of
the vibrational movements conveyed to our- nerves of
sensation, it becomes highly interesting to ascertain their
degree of frequency, in order to establish the relation between the two senses of hearing and seeing in that respect.  The ear, we know, can discriminate tones only
between certain limits, comprising about nine octaves,
the lowest sound audible as a note making about i6,
and the highest about 8200 vibrations per second.
Taking the velocity of light (as above) at I86,ooo miles*
per second, and reckoning 33,866 wave-breadths to the
inch for the extreme red, 43, 97 for the soda-yellow,
and 70,555 for the extreme violet, we find for the impulses on the retina per second which produce these
sensations of colour, respectively, the following enormous
numbers:Extreme red,.   399, 101,000, 000ooo,
Soda-yellow,.               509,069,000,000,000 ooo
Extreme violet,...   83I,479,ooo,ooo,ooo
These extremes are nearly in the proportion of 2 to I,
so that the whole range of visual sensation on this view
of the subject is comprised in about one octave.  If the
* Roughly, Iooo million feet.




ON LIGHT.                    313
ear could appretiate vibrations of this degree of frequency, the sensation corresponding to the middle ray
of the spectrum  would be that of a note about fortytwo octaves above the middle C of a pianoforte.
(98.) In each of these inconceivably minute intervals
of time (compared to which a single second is a sort of
eternity), a process has been gone throug6h by every molecule
of the ether concerned in the propagation of the ray: a process as strictly definite, as exactly regulated, as the
movement of a drop of the ocean in its conveyance of
the tide-wave.  Taking up its motion from  the particle
immediately  behind  it (whose  movement it exactly
imitates), and transmitting it on to that immediately
before, it starts from rest, not suddenly, with a jerk, but
(under the strict control of those elastic forces already
mentioned), increasing gradually in speed to a maximum-then, as gradually, relaxing, coming to a momentary rest, and retreating to its original position by the
same series of measured gradations in reverse order, to
be ready in its place for the reception of the next impulse. Nor does it seem possible to avoid the conclusion, if we trace up the movement to its commencement
-to the source of the light-the material particle in
whose combustion or incandescence it originates-that
such is the actual vibratory movement of that particle
itself. And thus we are brought into the presence of
the working of that mechanism  by which flame and incandescence (" Xo7w7Trov aua  uvo0-the brilliant miracle
of fire," as the Greek poet* not inaptly terms it) are pro* Aschylus.




314                  ON LIGHT.
duced. In the disruption of one chemical combination,
and the constitution of another, a movement of mutual
approach, more or less direct, is communicated to the
uniting molecules, which, under the influence of enormous coercive powers, is converted into a series of
tremulous, vibratory, or circulating movements communicated from them to the luminiferous ether, and so
dispersed through space. Incandescence without combustion (as in a piece of red-hot iron) must be looked
upon, from this point of view, as a result of the continuance of this vibratory movement after the primary
exciting cause has ceased, and of its gradual decay by
communication to the surrounding ether; as a musical
string continues to sound after the blow which set it in
motion, till gradually brought to rest by the surrounding air.
(99.) This may perhaps appear a digression from our
subject.  But it will be recollected that our object in
these lectures is not to produce a treatise on optics,
but to fix attention on the immensity of the forces
in action, and the minuteness and delicacy of the mechanism which they animate in the most ordinary operations of Nature, and which the phenomena of light have
been the means of revealing to us. We have no means,
indeed, of measuring the actzal intensity of the " coercive
forces" so called into action in the excitement of a luminous vibration, but that we are fully justified in applying
to them the epithet " enormous," the following consideration will suffice to show.  Whatever be the extreme
distance of excursion to which a vibrating molecule is




ON LIGHT.                      315.carried from its point of repose, or its medium situation,
in the act of vibration; the acting or coercive force
must suffice to bring it back from  that distance in one
fourth part of that inconceivably minute fraction of a
second by which, as above shown, the period of a complete vibration is expressed. Taking the case, then, of
any particular ray (as for instance that between the
green and blue rays of the spectrum, corresponding
to a wave-length of one 50,oooth of an inch, and.to a
period of one 589 billionth of a second), if we assume
the extent of excursion, we can very readily calculate the
intensity of the force (as compared with that of gravitation) which, acting uniformly during that time, would
urge it through that space. Let us suppose then, that the
nerves of the retina are so constituted as to be sensibly
affected by a vibratory movement of no greater extent
or actmpiitude than one trillionth* part of an inch either
way; and the calculation executed, we shall find that
a force exceeding that of gravity in the proportion of
nearly thirty thousand millions to one must be called
into action to keep up such a movement.  Our choice
lies between two immensities, we had almost said between two infinities.  If we would bring the force within
the limits of human  comprehension, we must in the
same proportion exaggerate the delicacy of our nervous
mechanism, and vice versd.t
* A trillion is a million of billions = Io10, or I,ooo,ooo,ooo.-.000, 000,000.
t The hypothesis of a uniform action of the coercive force in the
text is only assumed for the convenience of such of my readers




316                     ON LIGHT.
(Ioo.) Connected with the colours of thin plates are
several distinct classes of optical phlenomena, in which
colours of the same kind, and explicable on the same
principle, arise in the reflexion and transmission of light
through or between pellucid plates of considerable thickness, or through spherical drops of water, examples of
which are to be observed in the pink and green fringes
which are often seen bordering the interior of a rainbow,
and in those similarly coloured fringes (of exceedingly
rare occurrence) which sometimes run, like a bordering
ribband, just within the contour of a thin white cloud
in the near neighbourhood of the sun.  Upon this class
of phenomena, however, we shall not dwell further than
to observe that they prove the law of the periodical recurrence of similar phases at equal intervals, not to be
confined to very minute  distances in the immediate
neighbourhood of reflecting or refracting surfaces, but to
extend over the whole course of a ray of light-as, on
the undulatory theory, it necessarily must do.  We now,
whose knowledge of dynamics is limited by this very elementary
application.  Properly speaking, we ought to assume the coercive force to vary in the direct ratio of the distance; on which
supposition only will large and small vibrations be executed in
equal times. Calculating on this (the correct) principle, and taking
the extreme excursion (as in the text) at one-t-illionth of an inch,
the ratio of the coercive force to gravity at that distance will be
found as 35.465,oo0,ooo  to I. On the other hand, as a strange
contrast to the immensity of such a force, we shall find the maximum velocity it will have generated on the arrival of the molecule
at the medial point of its vibration not to exceed 1-270th part of an
inch per second!




ON LIGHT.                     317
therefore, proceed to the next branch of our general
subject, that of the Diffraction of Light.
(ioi.) DIFFRACTION.-The optical phrenomena which
refer themselves to this head are many and various.
They are not, for the most part, very obvious, but are
exceedingly curious and interesting in their details, and
some of them, under careful arrangement and with good
optical appliances, very brilliant.  Familiar examples
offer themselves in the twinkling of the stars and the
changes of colour they exhibit during the different
phases of their scintillations:-iin the vivid radiating
streaks of light which seem to stream outwards from any
small and dazzlinZly brilliant point of light (as for instance
the reflection of the sun on a small polished globe, as a
thermometer ball):-~in the colours exhibited when a
bright point is seen reflected on or refracted through a
surface regularly striated or scratched across with fine
equidistant lines, as beautifully exhibited in the so-called
"Barton's buttons " (fiom the name of the ingenious and
skilful amateur mechanist who first executed them);
brass or steel buttons delicately cross-lined by engine
work:-in the lateral images of a candle seen reflected
on polished mother-of pearl: and in the coloured halos
often seen to surround the flame of a candle in certain
states of the eye and their artificial imitations in a mode
presently to be described.  Less obvious to common
observation, and requiring particular arrangement, instrumental or otherwise, to see them distinctly, are the
phbnomena (referable to the head of diffraction) of the
rings and other appendages seen to surround the images




3I8                   ON LIGHT.
of stars when viewed through telescopes of great magnifying power, and with  apertures either of the usual
circular form, or of forms otherwise varied for this express purpose.  And though last in our order of enumeration, by far the most important and instructive as
elucidatory of the principle of explanation, applicable to
all the phenomena of this class;-the coloured fringes
seen to follow the outlines of shadows when thrown by
a light emanating from an extremely small but intensely
luminous point. With these, therefore, we shall begin.
(102.) It was objected to the undulatory theory of
light; by Newton himself, that sound, to which that
theory assimilates it, spreads from  an aperture through
which it is transmitted, or round the edge of an intercepting screen of any kind, equally in all directions; and
thus, were the analogy exact, there could be no shadows.
The objection is founded partly on an imperfect statement of the fact, and partly on omitting to allow for possible differences in the natures of the conveying media,
and in the modes of vibratory motion conveyed.  Every
one is familiar with the sudden outbreak of sound from
a railway train heard at a great distance when it emerges
from a cutting, or turns the corner of a wall or of a hill.
Sound is propagated through water with greater sharpness, velocity, and distinctness, than through air.  But
an obstacle interposed under water, as a projecting pier,
or a rock, cuts off the rays of sound, as appears from
direct experiment, with much greater definiteness than
in air, and casts, so to speak, an evident acoustic shadow.
Nor will it appear at all surprising that an effect of this




ON LIGHT.                    319
kind should, in the case of light, be carried still farther
when we consider that the aerial impulses by which
sound is propagated, take place in the direction of the
sound-ray, so that in passing (for instance) through an
aperture in a screen, a quantity of air is puszed bodily
through it, and issuing on the other side, causes an increase of local density due to the actual introduction'of
additional air at a given. spot, which of course tends to
expand laterally as well as to push forward, and is not restrained from so doing by the lateral pressure of the
rest of the wave, which is suppressed. Light, as we have
already intimated, is propagated  through  an elastic
medium  more in analogy with a solid than  a fluid,
(which Newton's objection implies,) and by vibrational
movements not in the direction of the ray, but transverse to it, so that in its passage through an aperture,
or beside the edge of an obstacle, this cause of lateral
spreading, at least, is absent; whatever other this
peculiar mode of propagation may call into action.
Lastly, however, the phenomena of diffraction with
which we are now concerned rely for their explanation
on this very principle-that shadows are not strictly
definite, and that there really is a certain, and not very
small amount of lateral spreading of the light into the
space occupied by what may be called the geometrical
shadow.
(103.) If a room be darkened and the sun allowed to
shine into it only through a very small aperture, as a
pin-hole, the rays which emanate from  different points
of its apparent disc, passing straight through and cross



320                   ON LIGHT.
ing at the hole, will depict on a white screen held at a
distance of several feet from the hole a circular image or
inverted picture of the sun, which may be considered as
the circular base of a cone of rays having the pin-hole
for its vertex.  In this case, the illumination of the
screen, if placed at a great distance, is feeble, and, if
near, the circular patch of light inconveniently small.
But if instead of a pin-hole, be substituted a convex
glass lens of short focus, the whole of the sun-light received on it will be concentrated in the very small
image of the sun formed in its focus, and, diverging
thence will spread out into a much wider cone of light,
and form a much larger circular and brilliantly illuminated area on the screen, affording every facility for the
examination of the shadows of objects thrown upon it;
with the additional convenience that by a reflector outside of the window, the illuminating sunbeam  may be
thrown horizontally, at whatever time of day the experiment is made.
(Io4.) The condition essential to the distinct exhibition
of all phsenomena of this class-that of a very brilliant
light emanating from  a very small point-being thus
secured, let an opake body of any form  be placed
between the point and the screen, so as to cast a shadow
on it. It would naturally be expected under such circumstances that the termination of the shadow on all
sides should be a clear and sharply-marked outline,
separating a uniformly bright space on the outside from
a uniformly dark one within, and free from that external
gradation from light to darkness which constitutes what




ON LIGHT.                       321
is called the penumbra in ordinary shadows, which arises
from the angular diameter of the sun.* Quite otherwise.
A shadow indeed is formed, but instead of a sharp and
sudden transition from darkness to light, it terminates in
three coloured fringes, following its contour, the inner
being the broadest and more distinctly coloured, the
outer extremely faint and feebly tinted. The order of
the colours, reckoning from  the first dark fringe, is,
generally speaking, analogous to that of the colours of
thin plates proceeding outwards from  the dark centre
rings, only degrading more rapidly, viz., blue within, and
yellow and red without. And that the tints originate in
the same way from the superposition of a series of dark
and bright fringes of the different prismatic colours, of
different breadths, is shown (as in the colours of thin
plates) by throwing on the lens in succession the several
coloured prismatic rays, when the fringes are seen in each
colour much  more numerously  and  sharply  defined,
being broadest in red light and narrowest in violet.
(io5.) If the object casting the shadow be long and
very narrow, as a hair or a strip of card not more than a
30th of an inch broad, the phenomena are still more
curious and complex.   Besides the exterior coloured
fringes already described, others are seen wzithin the
shzadwe, running parallel to its length, similarly disposed
along both its edges, and blending in the middle into a
* The diffracted fringes may be seen very well on the borders of
shadows cast by the light of Venus when at its greatest brightness,
on a white surface, in a room with a single window, and under
favourable circumstances as to twilight.
X




322                   ON LIGHT.
central line devoid of colour. That these fringes originate in the mutual interference of rays which have passed
beside both the edges of the object and entered the
shadow, is proved by intercepting the light on one side
only, leaving that on the other to pass freely. All the
interior fringes and the central streak disappear, leaving
only the exterior ones on the illuminated sidle outstanding.
The shadow (which is now formed under the same circumstances as in the former case) must, it is clear, be
still receiving one-half the total quantity of light which
it did before; and if its edge be narrowly examined, it
will be seen not to terminate in any sharply-defined line
cutting it off from the fringes, but to graduate off insensibly; and hence arises a very singular phenomenon.
If the light be readmitted on both sides, and the breadth
of the shadow, or what under such circumstances must be
accepted as such, be measured, it is found to be much
broader than it ought to be were it limited by straight
lines drawn from the illuminating point through the edges
of the object. And, what is still more remarkable, if its
breadth be measured on a screen, successively placed at
different distances from  the object, its increase of
breadth is found not to be in the simple proportion of
its increased distance  as it would were the aerial shadow
(or the space shaded by the object) bounded by straight
lines; but as if by curves starting from  its edges, and
having their convexities towards the light. And, finally,
if the object and the screen, preserving the same distance
between them, be moved gradually nearer and nearer to
the illuminating point, the fringes, both interior and ex



ON LIGHT.                    323
terior, are observed to dilate in breadth, according to a
certain law which it is not necessary here to state, but
whose agreement with the result of calculation affords a
very satisfactory verification of the theory adopted for
the explanation of the whole series of these phenomena
on the undulatory hypothesis: while, on the other hand,
it is very obvious that no such dilatation could possibly
take place were the fringes produced by any kind of
action on the rays in their passage by or near to the
edges of the object, in the nature of attractive or repulsive forces originating in the material substance of which
it consists, and deflecting them from their rectilinear
paths; inasmuch as such action could neither be increased
nor diminished, or in any way modified, by the greater
or less distance traversed by the rays before their arrival
within its sphere.
(1o6.) The appearances exhibited when the light is
transmit/ed through a narrow rectangular slit, are even
more curious. In this case a bright image of the opening is thrown on the screen, but instead of being an
evenly illuminated narrow band, bounded on either side
by uniform darkness, it is bordered both externally and
internally by parallel fringes.  The external ones are
bright and highly coloured, and vary in breadth, but not
materially in brightness, as the screen is withdrawn from
the slit; but the interior fringes undergo singular changes
as the distance increases.  At near distances they are
narrow and close, and leave a medial space of uniform
light; but as the distance increases they enlarge in
breadth, and close in on the illuminated space, so that




324                   ON LIGHT.
at a certain distance a medial dark line makes its appearance-which, if the distance be still further increased,
changes to a bright one, and so on alternately till after a
certain distance is attained the alternations cease.  If
the screen be stopped at the last position in which the
medial line is dark, and there fixed, and an opake strip,
exactly half the breadth of the slit, be held medially
along its whole length, so as to divide the slit and reduce
it to two parallel ones, each one quarter of the original
breadth (by which, of cowse, the total light traversing the
aperture will be'reduced to half its amount),-instead of
darkening still more the medial dark fringe on the screen,
as would.naturally be expected on throwing a shadow upon it, the very reverse happens: the dark fringe in question disappears altogether, and is replaced by a bright one.
(Io7.) If the shape of the body which casts the shadow
be angular, having salient and re-entering angles; the
fringes where they surround the re-entering angles cross
and pursue their courses up to the shadows of the sides
respectively opposite to them; but those which surround
salient ones curve round them, preserving their continuity.
At an angle of the latter kind too, crested or plumeshaped interior fringes are seen-" Grimaldi's crested
fringes," as they are called, from the name of Father
Grimaldi of Bologna, who first described (in I665) these
curious appearances. If a re-entering angle, however, be
very acute, the external fringes which border its sides on
approaching the angular point curve outwards, cross one
another, and run out both ways into the shadow in elegant curves of a hyperbolic form.  Nothing can be ima



ON LIGHT.                    325
gined more singular and bizarre than the appearance of
shadows cast on a screen in this manner by a variety of
minute objects of different shapes,-needles, feathers,
lace-work, locks of hair, &c.; and as their observation,
as we have shown, is exceedingly simple and easy, we
earnestly recommend  them  to the  attention of our
readers-a bit of looking-glass, or, still better, a polished
metallic reflector, a hole in a window shutter, a lens of
an inch focus, a screen of white paper, and a sunny day,
being all the requisites.
(Io8.) When the image of a small circular aperture (as
a pin hole) is thrown on the screen, it is seen as a small
round disc, highly coloured, the colours varying as the
screen is approached from  a distance to the hole-presenting in regular succession the tints of the reflected
colours of thin plates described in a former part of this
article, beginning with the first white: or, if the illumination be effected by homogenous light, alternate gradations of light from brightness down to total obscurity,
and thence through an alternate succession of light and
darkness.  Around the central spot, too, coloured rings
are formed, the tints of which vary in dependence on
those of the centre.  When the light is transmitted
through two holes side by side, and very near together,
besides the rings belonging to each, a set of intersectional
coloured streaks is formed, straight if the holes be equal,
hyperbolically curved if unequal. With three holes forming an equilateral triangle, or with a still greater number
arranged with perfect regularity (as in machine-stamped
paper in patterns), an endless variety of elegant and




326                   ON LIGHT.
pleasing appearances will be witnessed. To see them to
the greatest advantage, a magnifying glass should be
used, placing the eye ein the place of the screen, and looking
throught the glass at the fringes and images of the holes as if
they were real objects in ilsf; cus.
(109.) When the system of apertures examined consists of a great multitude of exceedingly narrow parallel
slits, precisely equal and equidistant, they constitute
what is called a "diffractive grating," and present very
curious, and in some cases brilliant, phbenomena, which
are best Viewed by placing the eye close behind the grating.  The luminous point (which appears colourless) is
then seen accompanied laterally and on either side by a
succession of highly coloured spectra, arranged in a line
passing through it, and with their lengths directed'along
that line; their colours, unlike those of the fringes
(which are composite) are the pure unmingled hues of
the prismatic spectrum: even more vivid (if the grating
be delicately executed) than the best spectrum which
can be formed by refracting a sunbeam through a prism;
and exceedingly remarkable in another respect, viz., that
the proportional lengths of the coloured spaces in each,
instead of depending, as in the case of the spectrum
formed by a prism, on the nature of the particular
medium of which the prism  consists, is independent of
any such consideration, and determined solely by the
proportion between the wave-lengths corresponding to
the colours of the rays. They are, therefore, what may
be called normal spectra.  So pure and undiluted indeed
are their tints, that by the aid of a magnifying telescope




ON LIGHT.                     327
the "fixed lines," so often above referred to, may be
seen in them, and thus the wave-lengths, corresponding
to the most conspicuous of these lines, ascertained with
great precision. The violet ends of all the spectra are
nearest to the central p.oint, and the more distant spectra
longer than the nearer, so that at length they overlap
and confuse one another by the intermingling of the red
end of one with the violet of that next in order.
(Iio.) If the apertures of which the grating consists
be formed by removing with a graver portions of an
opake varnish covering a glass surface, spectra exactly
similar are seen accompanying the image of the luminous point reflected on the anterior surface of the glass
from  the polished portions laid bare.  The same is
observed, and with far more brilliancy, when a, highly
polished surface of metal is furrowed in equidistant parallel grooves by a graver or diamond point (which destroys the polish of those lines), and if the metal be
hardened steel, the furrows so formed are transferable
by violent pressure to the polished surface of a softer
metal, which then in its turn exhibits similar appearances, and thus are produced the "buttons" above
spoken of.  Mother-of-pearl, too, which consists of exceedingly thin layers of calcareous matter superposed,
and agglutinated or otherwise held together; when
ground and polished, has these layers, which lie very
little oblique to the general surface, torn up at their
edges, where they crop out; which remain rough and unpolished, however brilliantly polished the general surface.
The polished surface, therefore, is lined all over with




328                   ON LIGHT.
almost exactly equidistant, exceedingly minute, nonreflective grooves, and when, if held close to the eye, a
candle is seen in it reflected, its image   accompanied
with two lateral and very vivid spectra of similar origin,
and an impression of the surface taken on black sealing-wax presents the same phlenomenon.
(III.) When, as occasionally happens, the eyes are
suffused with a nebulous film (due to the presence in the
lacrymatory secretion of extremely minute globular particles of equal size), the image of a candle in a dark
room some feet distant is seen surrounded with two or
three broad circular halos of rainbow colours alternately
ruddy and green.  Similar halos are formed round the
candle when viewed through two pieces of clear glass
between which has been placed a little oil mixed with
the delicate powder of the common puff-ball or lycoperdonz, reduced to a thin even film by pressure and gently
rubbing them  together.  In this case they are much
more vivid and beautiful, the tints being those of the
colours of thin plates beginning from the centre, only
more dilute, so that it is difficult to discern more than
a feeble indication of the fourth ring.  Their diameters,
however, unlike those of the coloured rings figured in
Fig. 6, increase in arithmetical progression, or nearly so;
that of the first or smallest reckoned to the minimum
of illumination, being. 21~ 36' or thereabouts.  They owe
their origin to the exceeding minuteness, uniformity of
size and sphericity (or at least circularity) of outline (if
flat discs) of the spores of this fungus.
(I 12.) The explanation of these and of other phaeno



ON LIGHT.                    329
mena referable to the head of diffraction, turns on two
considerations, one of which may be regarded as a
theoretical postulate (founded, however, on the analogy
of sound), viz., that if a portion of a luminous wave be
intercepted, the  non-intercepted  undulation  spreads
laterally into the dark space beyond, diminishing, however, in intensity as the lateral deviation of the ray (or
perpendicular to the wave) from its original rectilinear
course increases:-the other, a natural consequence of
the mode in which a wave is propagated, viz., that every
point in the surface of the non-intercepted portion may be
regarded as the origin of a new wave spreading out spherically in all directions from that point as a centre; only with
this proviso, that all such secondary waves start, each from
its own origin, at the same precise instant of time and
in the sane precise p/ase of its undulation.  And this, be~0 ~\
Fig. to.
cause all belong to one wave surface, and are therefore
necessarily coincident in time and identical in phase.
(II3.) To show how this last consideration affects the
question of diffraction, let us suppose a point P on a




330                    ON LIGHT.
screen illuminated  by light emanating from  a single
bright point o (Fig. io), from which is propagated a series
of equidistant spherical waves corresponding to light of
any one refrangibility, and therefore distant from each
other by one entire undulation of such light (say, to fix
our ideas, a 5o,oooth of an inch).  If o P be joined, intersecting the surface of any one such wave, at a given
distance, o A from o in A; PA will be the shortest line
that can be drawn from  P to that surface.  Suppose,
now, we take on either side of A a series of points B, b;
c, c; D, d, &c., progressively more distant (by pairs)
from  P than A is, by I, 2, 3, &c., hundred-thousandths
of an inch, or semi-undulations of the light under consideration; and let the whole figure be conceived as
turned round on o P as an axis. Then these points will
mark off on the spherical surface of the wave, a central
circular area (call it the area A), and a series of concentric rings or rather zones of the waves (call them in
succession B, C, D, &c.), surrounding it, like those represented in Fig. 7, from every point in each one of which
the light sent to P will reach it in more or less discordance of phase, with that which reaches it from the next
in succession.  Thus if all the vibrations propagated
from the central circle (A) arrive at P in a phase of compression, all these simultaneously reaching it front the
zone (B) will arrive in a phase of expansion, all from
(c) again in one of compression, and so on alternately.
Now if the distance A P of P from the wave be anything
considerable, suppose a few  feet or even inches, it
will be enormously great in proportion to one semi



ON LIGHT.                    331
undulation or ioo,oooth of an inch, the length by which
the distances P A, P B, &c., differ from each other, and
in that case it is very easy to show by geometry, that the
successive areas (A), (B), (c), &c., are almost exactly
equal.  Were these areas rigorously equal, and were
moreover the vibrations (propagated as they are from
them to P more and more obliquely with respect to the
general surface of the wave at their points of emanation)
all of equal intensity, it would follow therefore that the
otality of the movement propagated to P from (A) would
be precisely opposed and destroyed by that from  (B),
that from  (c) by that from (D), and so on; so that an
ethereal molecule at P would in effect be agitated by no
preponderating movement, one way or another, and
there would be no illumination on the screen at P. Inasmuch, however, as the vibrations diminish in intensity
as they are propagated more obliquely, and as the areas
(A), (B), (c), (D), &c., are, though very nearly, yet not
rigorously equal, this mutual destruction in the case of
each consecutive pair is only partial, and the point P
will be agitated by the sum  of all these outstanding
excesses (taken in pairs) from  the centre outwards;
which, though excessively small individually, in virtue of
their immense number make up a finite sum.  And as
the same is true for each point of the screen (if spherical,
and therefore everywhere equidistant from o), the whole
of its surface will be equally illuminated: if plane, very
nearly so, in all the region around P.
(II4.) A very singular consequence follows from this
reasoning, and one admirably calculated to test its




332                    ON LIGHT.
validity, and the soundness of the theory it relies on, by
experiment.   There can  be  no  better presumptive
evidence of the truth of a physical theory than  its
enabling us to predict, antecedent to trial, a result in
direct contradiction to what mankind in general would
consider as the obvious conclusion of common sense
founded on all ordinary experience.  This is the case in
the present instance.  Since the total illumination of one
point P on the screen is only that due to the undulations. which remain outstanding after the mutual destruction of'by far the greater proportion of those propagated
from the zones (A), (c), (E), &c., (the odd zones, reckoning (A) as No. 1), by those emanating from  the even
ones (B), (D), (F), &c., it follows that if all the even zones
could be entirely suppressed or rendered ineffective, the
illumination at P would be prodigiously increased, and
that even the obliteration of a few of them would produce a very material augmentation of brightness at that
point.  In other words, that by stopping out a large pro.
portion of the luminous rays passing through a circular
aperture from a bright illuminating point, the illumination of the central point of the image of such aperture
thrown on a screen at a certain distance behind it, may
be made to exceed by many times what it would be were
the whole aperture 1eft Op5en.  This strangely paradoxical
result is stated by M. Billet* to have been experiment-.
* Billet, Traitg d'optique Physique, 1858, ii. ~ 55, by far the
fullest risumn  of that subject hitherto published; only too little explanatory, and sadly deficient in facility of reference. Jt deserves a
good index.




ON LIGHT.                      333
ally verified by M. Fresnel (to whom  its suggestion is
due), and more recently by M. Billet himself, who by
merely interposing (concentrically) between the luminous
point and the centre of the screen, a small opake annulus exactly corresponding to the calculated dimensions
(for red rays and using red light) of the first even ring (B)
obtained an illumination at P estimated at five times
that when no obstacle was interposed.
(II5.) By way of showing the kind of explanation
these principles afford of some of the simplest and
easiest cases of diffraction (for their calculation is for the
most part very complicated in its details, though simple
enough in its principles); let us suppose first the case of
a screen illuminated by a minute radiant point o through
a small circular aperture, and consider only the illumination of the central point of projection on the screen, or
of P in our figure. Suppose P to approach the screen
from a very great distance-so great that the difference of
its distance from the centre and either edge of the aperture
shall be less than a semi-undulation of the light considered (say Ioo,oooth of an inch).  Then the undulations from every part of the aperture will reach P in
phases more or less accordant with each other, and P
will therefore be more or less illuminated  and, P still
approaching, its illumination will increase till it attains
such a distance that the difference in question exactly
equals a semi-undulation. In this case the portion of
the wave transmitted corresponds precisely to the whole
of. the central circle (A) of our system of wave-zones
above discussed, and we have here the greatest possible




334                   ON LIGHT,
amount of concordant and no discordant rays, and the
illumination will be a maximum.  But if P approach
nearer, the difference in question will be greater than a
semi-undulation, and the portion of an aperture near the
edges will send rays to P more or less in discordance with
those from  the centre, and these will destroy a portion of P's illumination. P approaching this will go on
till the difference  amounts to  an entire undulation
(I-5o,oooth); that is to say, till the aperture extends (as
respects the new situation of P) over the whole of the two
first zones (A) and (B), of which the second (B) destroys
almost the whole of the light from (A) (being equal in
area, and differing very little in obliquity). Here then
the illumination at P will be nil or very small.  P still
approaching, the third zone (c) (which sends vibrations
in unison with (A)) will begin to be included within the
limits of the aperture, and the illumination will again increase to another maximum, viz., when the three, (A),
(B), (C), are just included; thence again it will diminish
to a degree of obscuration not quite so complete as before; and so on.  Thus as the screen approaches the
aperture, its central point, after attaining a maximum of
illumination, will suffer a succession of eclipses or obscurations gradually less and less complete, with intermediate
recoveries, just as we have seen above, is really the case.
When the light is not homogeneous, the different coloured
rays having different wave-lengths, the obscurations of
one colour will not correspond to those of the others,
and thus will arise a succession of colours at the central
point of the screen, agreeing with those there described.




O-N LIGHT.                      335
(iI6.) Take now the case of the exterior fringes, when
the shadow of a broad straight-edged body, as a ruler, is
thrown on a fixed screen at a considerable distance behind it.  Suppose P first placed exactly at the edge of
the geometrical shadow.  In that case, the view of exactly half of each of the concentric wave-zones (A), (B),
(c), &c., will be intercepted, and P will therefore receive
from the remaining halves just half the amount of luminiferous agitation it received when opposed to the whole
wave, viz., half the amount of concordant and half of
discordant undulation.  Its intensity of illumination will
therefore be one-fourth of that when the ruler is altogether
removed.*  Now, suppose the ruler withdrawn gradually,
and lateraZlly, so as to disclose to the view of P successively, ist, the whole of the central zone (A) of the wave
surface; 2dly, the whole of the two first zones (A), (B);
3dly, the three first, (A), (B), (c), and so on. It is very
evident then, on merely casting our eyes on Fig. 6, (p.
295), and imagining a line drawn through the common
centre of all the circles to be removed parallel to itself,
step by step, so as to become in succession a tangent to
the ist, 2d, 3d, &c., circles; that in the first step of its
removal it will disclose to P all the remaining half of the
central area (A), which sends to it undulations concordant
with those by which P is already illuminated, but less
* The effect on the retina is estimated, not by the simple mlometntum or velocity of the impulse communicated by the vibration, but
by the " vis viva," "energy," or "work ldone," which is proportionate to the squzare of Sfe velocity of movement. In this the undulatory
doctrine of light agrees with the theory of sound.




336                  ON LIGHT.
than half of the second (discordant), still less of the third,
&c., so that on the whole there will be a preponderance
of the concordant undulations so introduced, and P will
be more strongly illuminated than before.  When removed one step farther however, since the newly introduced half of (B) the second zone almost exactly counteracts that of (A), the effect of the change will have its
character decided by the proportional magnitudes of the
segments of (c), (D), &c., disclosed, among which the
preponderance is evidently in favour of (c), that is, of
discordant undulation, so that by this removal of the
shading obstacle the illumination of P will be diminished;
and so on alternately.  Now at each stage of these removals of the shading body, the edge of the geometrical
shadow retreats farther and farther from p, or (which is
the same thing) P is successively farther and farther outside of the edge of the shadow, becoming alternately
more and less illuminated than at the actual edge.
Here then we see the origin of the bright and dark external fringes exhibited in homogeneous light; and therefore by the very same reasoning, of the coloured ones
produced by the successive overlapping of those formed
by several coloured rays to each of which corresponds a
different breadth of fringe; that for the red being broadest and for the violet narrowest.
(  17.) The twinkling or scintillation of the stars partakes
so far of the nature of a phenomenon of diffraction, as
that it depends for its origin on the mutual interference
of discordant rays arriving at one instant, but by dfferent
routes, on the same point of the retina of the eye; and




ON LIGHT.                     337
which, therefore, do not interfere with or enfeeble one
another in any part of their previous course. The image
of a star on the retina is formed by the union in a focal
point of the whole bundle or pencil of parallel rays contained within a cylindrical space or column, having the
circular opening of the pupil for a base or section, continued through the whole atmosphere, however far it may
extend. Now the air, though a very feebly refracting
medium, has still a certain amount of refractive power,
and that a variable one, depending on its density, temperature, and  moisture;  and  corresponding  to  the
degree of this power is the velocity with which it is traversed by the luminous undulations. Now; however
the density, temperature, and moisture of the lower and
upper regions of the air may differ; if throughout the
whole extent of this column it were perfectly uniform in
these respects, at every point of each cross section of it
(however it might differ in different sections) all the rays
traversing its length from the star to the eye would have
their undulations equally retarded by the aerial medium:
and therefore all the rays belonging to any one wave
setting out at the same instant of time from the star
would reach the focal point on the retina at the same
moment; such being the condition which determines the
focal point of a lens. But if the air in one side of the
column should for any considerable distance along it be
slightly different in these respects from that in the other,
the undulations transmitted along that side would be
differently retarded from those along the other, and would
not arrive on the retina at the same instant.  The one
Y




338                   ON LIGHT.
portion, then, on its arrival would meet there, not the
other portion of the same wave to which it originally belonged, but one in advance or in arrear of that by either
a whole, a half, or any part of an undulation, or any
number of such, according to the extent of the difference
in the quality of the aerial contents of the column. Suppose, for instance, the light from the two halves of the
column to differ in their time of arrival by I, 3, 5, or any
odd number of semi-undulations of the most luminous
or the yellow rays; these then would interfere and totally
extinguish each other, and the apparent light of the star
would undergo a great obscuration, assuming at the same
time a hue complementary to yellow; i.e., dark purple:
and so for other rays. Now the constitution of the air
is so irregular-such a perpetual mixture of masses of it,
differing in temperature and moisture, is continually going on under the influence of wind-currents, that such
differences as above supposed must be almost constantly in progress, even within the narrow space of a
column no wider than the pupil of the eye, much more
in that corresponding to the aperture of a small telescope.
The scintillations, with their accompanying changes of
colour, are beautifully seen through an  opera-glass
(nzot binocular), especially if somewhat out of focus, in
which case the colours and the darkness are seen, as it
were, to run over the circular disc into which the image
is dilated in a very singular and capricious manner. If
a small circular motion be given to the glass, so as to
make the image of the star (when in focus) describe a
circle, this will be seen as a luminous circle (as when a




ON LIGHT.                      339
burning stick is whirled round, forming a ring of light),
and in the circle so formed spaces highly colouredred, blue, or green, as well as dark and bright-will
be seen, corresponding to the state of the image at the
instant it occupied those spaces, forming an easy, pleasing, and very interesting experiment.
(118.) An effect, the precise parallel to the scintillation
of the stars, might be produced, affecting the ear instead
of the eye, by sounding together two strings, at first exactly in unison, and then very slightly increasing and
diminishing alternately the tension of one of them, thus
producing a succession of beats, not regular as in the
case of two strings permanently differing by a minute
interval of pitch, but capricious in their succession.




LECTURE VII.
ON LIGHT.
PART III.-DOUBLE REFRACTION-POLARIZATION.
N  that most wonderful work, the Optics of
Sir I. Newton, among the queries annexed
at the end, occurs this very singular one:
"Have not the rays of light different sides,
endued with different original properties     The conception intended to be conveyed, as further illustrated
by Newton himself, embodies that abstract notion of
polarity which Dr Whewell in his " Philosophy of Inductive Science," expresses by " opposite qualities in opposite directions, or, as we should prefer to say, for this
purpose, "different qualities in different directions," with
reference (that is) to surrounding space and the objects
therein situated.  The same form of the general conception, as regards light, which Newton employed to designate the very same peculiarity in its habitudes, was
adopted by Malus in his first announcement of the re* "Optics," Book iii., Query 26. 4th Edition.




ON LIGHT.                        341
markable discovery which introduced the term POLARIZATION into optical language.  "We find," says he, "that
light acquires properties which are relative only to the
sides of the ray-which are the same for the north and
south sides of the ray" (i.e., of a vertical ray), " using the
points of the compass for description's sake only, and
which are different when we go from the north and south
to the east and west sides of the ray." The polarization
of light has in fact been an integral part of the science of
optics (wanting only a name to designate it) ever since
this suggestion of Newton, who derived it from the contemplation of one of what Bacon calls "instantime luciferae," zlminiferous instances, exhibiting the property or
"nature searched after" "in an eminent manner," or in
its clearest or most manifest form; and who described
with the utmost clearness and precision the phaenomenon
in which its manifestation consisted in the special case
before him.*  We shall, therefore, approach the subject
from Newton's point of view, choosing for our illustration
the very phaenomenon which led him  to the singular
conclusion embodied in his query.
* The same phaenomenon is described, and with no less clearness and precision, by Huyghens, in his admirable work, "Traite
de la lumiere," published in 69o0, fourteen years before the Optics
of Newton-and from that epoch, or from 1678, when that treatise
was communicated to the French Academy, must date the discovery
of the polarization of light as afact. Huyghens, moreover, correctly
attributed it to a peculiarity impressed on the vibrations of the
ethereal medium. But the picturesque phrase of Newton embodies
the idea in a form easily apprehended, while it seems to have floated
rather vaguely before the mind of his great predecessor, not so much
as a general attribute, but as a specialty limited to the case in
question.




342                   ON LIGHT.
(I20.) As we have already stated when speaking of refraction generally, a ray of light incident on any transparent crystal (certain specified classes of crystals excepted) is subdivided by refraction into two distinct rays,
pursuing different paths within the crystal, and of course
emerging from it at different points, and so, of necessity,
reappearing, not as a single, but as two distinct and
separate rays, each pursuing its subsequent course independent of the other through space.  Of these, when
traced, one is found to have been refracted in the plane
of its incidence on the transmitting surface, and according to the ordinary simple "law of the sines" already
explained.  It is therefore said to be ordinarily refracted,
and it is called the ordinary ray.  The other, except in
special cases, deviates after refraction from the plane of
its incidence, more or less according to the situation of
that plane with respect to the faces of the crystal: and,
moreover, in respect of the amount of its flexure, does
not conform to the simple law of the sines, but to a rule
much more complex in its expression, called the law of
extraordinary refraction; this ray being designated as the
extraordinary ray. Such is the case if the original, incident ray be one directly emitted from the sun, a candle,
or any self-zmnin:us body.  But if in place of such a ray,
we employ either of the two rays so separated as above
described, for transmission through a second crystal of
the same kind, the result will be very different. If it fall
upon such second crystal in the same manner, according
to the same angles and with the same relative situation
as to its plane of incidence with the sides of the crystal,




ON LIGHT.                      343
as in the case of the original incident ray, it will not be
further subdivided, but refracted singly: if an ordinary
ray, ordinarily; and if extraordinary, extraordinarily. Its
refraction will also be single, if the second crystal be
turned round on the ray as an axis exactly through a right
angle; but in this case the second refraction, if an ordinary ray have been used, will be extraordinay, and vice
versca. In every intermediate situation of the second
crystal, it will be subdivided into two, the one ordinarily,
the other extraordinarily refracted, but the two fractions
will be found to difer in relative intensity: generally
speaking, the more according as the conversion of the
second crystal has been through a less angle from  its
first position, and they are equal when the angle of conversion is 45~, 135~, 225, or 315~, i.e., exactly half-way
between the rectangular positions of the crystal.
(12I.) All these particulars are easily and elegantly
exhibited by means of two crystals of the mineral called
Iceland spar (crystallized carbonate of lime), a mineral
of perfect and colourless transparency, which, if fractured, will always separate itself      /\\
along its three "planes of cleav- /    \ 
age" (which in this mineral are 
singularly distinct and palpable)  /
into forms whose type is the obtuse rhomboid (whose six faces,         \/
all equal and similar rhombs of             Fig. II.
IOI~ 32' and 780 28', are united  three and three, by
their obtuse angles, at the opposite extremities of a
line called the axis of the rhomboid, the shortest that




344                   ON LIGHT.
can be drawn across it, and to which it is symmetrical,
as shown in the preceding figure).
(122.) If such a rhomboid be laid down on an inkspot on white paper, or, still better, on a small pinhole
in a plate of metal, and held up to the light, the ink-spot,
or the dot of light, will appear through it doubled: the
two images being separated, in the direc-.  tion of the shorter diagonal of the face
/ ___/    through which they are seen, by an inter-'Fig. 2.   val of about one-ninth part of the thickness seen through.  Thus, if over'the first rhomboid
another of equal thickness be laid conformably (i.e., so
that all the faces of the second shall be parallel to the
corresponding ones of the first), the only effect will be
that the apparent separation of the two images will be
doubled, just as if a single crystal of double thickness
had been used.  But if from  this position the upper
crystal be turned slowly round in its own plane upon
the lower, kept firm; two other images will make their
appearance between the former, at first very faint and
almost close together, but, as the rotation of the upper
crystal continues, gaining strength (while the others grow
fainter) and opening out from each other in a direction
transverse to the line of junction of the first. When the
angle of rotation attains 45~, four images are seen of
equal intensity, after which the two first grow fainter,
and at  o~0 vanish,-the whole of their light having
passed into the other two-and so on alternately. When
the upper rhomboid has made an exact semi-revolution
on the other, the image is single, and contains the whole




ON LIGHT.                    345
of the incident light.  In this case, the ordinary ray has
been refracted ordinarily, and preserves its situation;
the extraordinary extraordinarily, but its displacement
by the second refraction being exactly equal and opposite (in consequence of the now reversed position of the
refracting rhomb) to that by the first, it is brought to
coincidence with the other, and the two united form one
image.
(I23.) The opposite sides of a rhomboid being parallel, both the ordinary and extraordinary rays after
transmission emerge parallel to the incident ray, by a
necessary consequence of that general law of retro-version, in virtue of which a ray of light, whatever path it
may have pursued from one point to another, can always
retrace that path; the opposite faces being symmetrically situated with respect to the axis. And the same
is true for a parallel plate of this or any other crystallized
substance artificially cut and polished, whatever be the
position which such plate may have held in the interior
of the crystal from which it is cut. Now it is found, by
cutting from  rhombs of Iceland spar parallel plates in
various directions, that there is one through which a ray
of ordinary light can be transmitted perpendicularly
without being divided into two.  This is the case when
the faces of the plate are at right angles to the line above
designated as the axis of the rhomboid. And generally
that a ray which within the crystal pursues a path parallel to this axis, will emerge from it single, whatever be
the situation of the surface of emergence.  The axis,
then, is a line of no double refraction, and in the case of




346                    ON LIGHT.
the substance in question (or of any crystallized body
whose primitiive form  is the acute or obtuse rhomboid,
the regular hexagonal prism, and some others, comprising all those primitive forms which can be described as
symmetrical to one line and to one only) it is the only direction endued with this property. And on the other hand,
the amount of the double refraction or the angular separation of the two rays into which the incident ray is
divided, is greatest when they lie in a plane perpendicular to this axis.  On account of these properties, the.
line in question is sometimes called the optic axis of the
crystal.
(124.) If a crystal of Iceland spar, or any similar
body, be cut into the form of a prism, in such a manner
as to have its refracting edge parallel to its optic axis,
neither of the two refracted rays will emerge parallel to
the incident one, or to each other. They will diverge,
including an angle. between them, greater as the refracting angle of the prism is greater, exactly as if the medium
had two different refractive indices.  And in this particular case both refractions follow the ordinary "law of
the sines," and there is no deviation of either ray from
the plane of incidence. And what is extremely relnarkable, not only the refractive indices, but the dispersive
powers of the two refractions differ, in some cases widely,
so as to give two spectra (when a sunbeam is refracted)
of very different lengths.  In the case of Iceland spar,
the respective refractive indices for the ordinary and
extraordinary ray are i'654 and I'483. It is in consequence of this great difference that the two images of a




ON LIGHT.                     347
point, seen through a rhomboid of the mineral, appear
unequally raised above their natural level; that seen by
the ordinarily refracted rays, appearing nearer the eye
than the other.
(I25.) By the employment of such a prism  as here
described, it is easy to insulate either the ordinary or
extraordinary refracted ray, and examine it separately.
Suppose, for instance, the latter to be stopped by a
screen, and the former only allowed to reach the eye.
If before doing so it be made to pass through a second
such prism, whose refracting edge is parallel to that of
the first, it will be refracted singly and ordinarily. if the
edge be held perpendicularly to that of the other, then,
singly but extraordinarily.  In every intermediate position the image will be doubled, more of the light passing
into the extraordinary image, and less into the ordinary,
according as the angle at which the edges cross is increased from  o~ to 90~; and at 45~ of inclination the
light is equally divided between the two.  This, it is
obvious, could not be if the ray were indifferently disposed with respect to surrounding space.  There sub.
sists in it a difference of properties depending on situation-a difference analogous to that between a square
rod and a round one.  It has acquired sides in its passage through the crystal, which it preserves in its subsequent course through space till it meets some body whose
action on it may bring their existence into ocular evidence.  It would seem almost as if light consisted of
particles having polarity, like magnets; and that in its
passage through a doubly refracting substance these




348                  ON LIGHT.
came to be arranged, half with their poles in one direction (as regards the sides of the crystal), and half in a
direction at right angles to the former. And this is the
way in which Newton conceived it, as he himself distinctly states (Opt., Query 2 ); and as it necessarily must
be conceived if the corpuscular theory were to be
adopted.  How it is explained on the undulatory hypothesis, we shall presently see.
(i26.) It was while gazing one evening in i808, through
such a prism of Iceland spar as we have just described,
from his study in the Rue d'Enfer at the windows of the
Luxembourg Palace in Paris, that M. Malus, at that time
engaged in studying the law of extraordinary refraction in
this body, happened to notice that the reflexion of the sun
on a window of the palace disappeared from one of its
images, in a certain position of the prism, and from the
other when held at right angles to that position; while in
the intermediate situations, the glare was visible in both
images, unequally divided, however, between them, except when held in a situation exactly intermediate, or at
45~ from its first position:-in a word, that the light reflected from the window had acquired precisely the peculiarity which would have been impressed on it by previous transmission through a similar prism.  To this
peculiarity he.gave the name of POLARIZATION, and light
so affected has ever since been said to be POLARIZED.
(12.7.) Total and partiaZpolarization of light by reflexion.
-The angle at which a ray of light must be incident on
glass that the reflected ray may acquire this property is
560 45' from the perpendicular, or at an inclination of




ON LIGHT.                       349
33~ 15' to the surface, and in this case the polarization is
covopete, or the whole of the reflected light has acquired
the property in question.*  If at any other obliquity; it
is only partially polarized, or a portion only of the reflected light has acquired it.  How this portion is to be
distinguished and separated from the ulpiolarized portion,
we shall presently explain.   Suffice it here to observe
that this latter portion bears a greater proportion to the
whole reflected beam, as the angle of incidence deviates
more from that above specified (which is called the poarizing canle).  The plane in which reflexion has been
made is called the plane of polarization; and two rays
which have undergone reflection at the polarizing angle
in planes perpendicular to each other, are said to be
oppositely polarized.
(128.) The angle of incidence 560 45' has this l)eculiarity-that if we consider the directions subsequently
pursued by the two portions into which a ray so incident
on glass is divided, the one pursuing its course by reflexion in the air, the other by refraction within the glass,
these two directions include a right angle as in the figure
overleaf, where A C is the incident, c B the reflected,
and-c D the refracted rays, at the surface of a glass P Q.
When the angle A c P or B C Q is 33~ 5' Q c D is 56 45',
and D c B is a right angle. The law of polarization so
announced, as Sir David Brewster has shown, is general,
* In point of fact the differently coloured rays are not all polarized at exactly the same angle, so that this is rigorously exact only
for homogeneous light. But the difference is so trifling that it is
purposely here kept out of view.




350                   ON LIGHT.
and extends to all media, whatever their refractive
powers. Thus, for water, the polarizing angle is 53~ II',
and for diamond 68~ 6'-numbers concluded from this
simple rule (equivalent to the geometrical property above
A                    /
D\
Fig. 13.
stated) that the index of refraction is in all cases the tangent
of the polarizing angle.
(X29.) If a ray of light so polarized by reflexion be
received on such a prism  as is above described, held
with its refracting edge (i.e., the optic axis of the crystal)
at right angles to the plane of reflexion, or parallel to
the reflecting surface, it will entirely pass into the ordinary, or most refracted image; vice verst —if the prism be
turned round go9, so as to have its edge parallel to the
plane of reflexion (i.e., of polarization), wholly into the
extraordinary.   The same interchange will of course
take place if the prism be held immovable, and the reflecting glass turned round, so as to change the plane of
reflexion, and thus we perceive that rays oppositely polarized are distinguished by the characters of passing entirely
into the one and entirely into the other of the two images,
when so refracted.  A beam  of light partially polarized
may be regarded as a mixture of two portions, the one
wholly polarized, the other wholly unpolarized; and a




ON LIGHT.                      351
beam of un polarized light may, conversely, always be regarded as a mixture of two equal rays oppositely polarized, in any two planes at right angles to each other.
(I30.) If a ray reflected from  any medium  at the
polarizing angle (and therefore wholly polarized) be
received on a second surface of the same medium  at
the same angle of incidence, and in a plane cozincident
with that of the first reflexion, it undergoes partial reflexion just as an unpolarized ray would do, and both
the reflected and refracted portions retain their polarization. But if the plane of the second incidence be at
right angles to that of the first, no portion of the light is
reflected, but the whole passes into the refracted ray, retaining its polarization,-just in the same manner as,
had it been incident on our doubly refracting prism held
with its edge at right angles to its plane of polarization,
it would have wholly passed into the extraordinary ray.
Vice versc, if the ray extraordinarily refracted by such
a prism be received on a glass plate at the polarizing
angle of incidence, no reflexion will take place if the
edge of the prism be parallel to the plate. Hence we
are entitled to conclude that it is the very same property
which is impressed on light in both cases, and that a
ray polarized by reflexion differs in no respect from one
which has received this property by passing through a
doubly refracting crystal.
(I3I.) A  ray partially polarized  by reflexion at a
greater or less incidence than that at which it would
have been completely so, may be wholly polarized, or
nearly so, by repeated reflexions at the same angle.




352                   ON LIGHT.
This, which might be concluded  priori by considering
that the unpolarized portion differs in no respect from
ordinary light, and is therefore susceptible of so receiving partial polarization, while the polarized portion retains its polarization unchanged by reflexion, is verified
by experiment.
(132.) If a ray partially polarized in any plane be
received on the doubly refracting prism already mentioned, with its edge perpendicular to the plane of
polarization, the polarized portion will pass wholly into
the ordinary image, while the unpolarized will be equally
divided between the two.  Thus the two images will be
unequally bright. By turning round such a prism, then,
till a position is found at which the contrast between
the two images is most striking, this plane will be discovered, and the difference of their illuminations is the
measure of the quantity of polarized light in the beam.
(133.') Polarization of light by refraction.-When light
is incident on glass or any uncrystallized transparent
body at the polarizing angle, the reflected portion (a
small per-centage, not more than one-twelfth of the whole
light) is wholly polarized in the plane of incidence, as
already stated.  The refracted beam  (by far the larger
portion), when examined in the mode just described, is
found to be partially polarized in a plane at rizlzt angles
to that of incidence, and the amount of polarized light
which it contains to be precisely equal to that in the
reflected beam.  Thus we see that when light falls upon
such a surface, the greater portion passes unchanged,
while the other is divided into two equal portions oppo



ON LIGHT.                    353
sitely polarized, the one being reflected, the other transmitted, and intermingled with the unpolarized part.
(I34.) If a parallel plate of glass be used for this experiment, the same process is repeated at the hinder
surface. An equal per-centage of the unpolarized portion is similarly divided  between the reflected and
transmitted rays, oppositely polarized, and as the transmitted polarized portion is, ipso facto, guaranteed from
subsequent reflection at the polarizing angle, the total
amount of polarized light in each of the two beams is
nearly doubled. If behind this a second parallel glass
plate be applied, the same process is again repeated on
the remaining unpolarized portion, and so, by multiplying the plates, the whole incident beam is ultimately
divided equally into a reflected and a refracted beam
completely polarized in opposite planes. Such at least
would be the case were the plates perfectly transparent
and infinite in number; but as these conditions cannot
be fully realized, the transmitted beam is never completely polarized, though enough so to afford a very
convenient mode of viewing many optical phaenomena.
On the other hand, if the plates be truly plane and their
surfaces exactly parallel, the reflected beam is wholly
polarized, and as its intensity is nearly half that of the
incident light, this affords an excellent mode of procuring a polarized beam available for purposes of experiment.  A frame containing six or eight squares of good
window glass laid one on the other, and backed by a
sheet of black velvet, is one of the most convenient and
useful of optical instruments, and will be frequently
z




354                   ON LIGHT.
referred to in what follows as a "polarizing frame," a
similar series set transparently being termed a " polarizing pile."
(I35.) Other modes ofpolarization.-There are certain
doubly refractive crystals, more or less coloured, which
possess the singular property of absorbing or stifling in
their passage through them, unequally, the two oppositely
polarized rays into which they divide the incident light.
Two bodies especially have been noticed in an eminent
degree endowed with this property-the one a mineral
occurring more or less frequently among the rocks of
igneous origin, called the tourmaline, the other an artificial chemical compound, the iodo-sulphate of quinine.
The former crystallizes for the most part in long prisms of
many sides, terminated by faces, three of which belong
to the primitive form, an obtuse rhomboid, whose axis is
that of the prism  itself.  In consequence, like all crystals of this class, it is doubly refractive, and if artificially cut and polished into a doubly refracting prism,
having its refracting edge parallel to that of the rhomboid, an object viewed  transversely through  it will
appear double; provided the eye be held quite close to
the refracting edge; but if ever so little removed, so as
to look through a greater thickness of the substance, one
of the images will be observed to diminish rapidly in
intensity; and at a certain, usually very moderate, thickness to disappear altogether, as if extinguished by a
deeper colour or a higher degree of opacity in the.
medium, the other remaining undiminished.  The unextinguished ray is, of course, completely polarized, and




ON I1GHT.                    355
that in the plane of the section of the prism  at right
angles to the edge.  If, instead of cutting the crystal
into such a prism, it be formed into a flat plate, with its
faces parallel to the axis of the rhomboid; such plate
will in like manner extinguish one of the pencils into
which a ray incident perpendicularly on it is divided,
allowing the other to pass; and the pencil so transmitted
is completely polarized in a plane perpendicular to the
axis of the plate. This property of a tourmaline plate
renders it invaluable as an optical instrument, affording
the readiest and most convenient means of procuring a
polarized beam of light for the examination of crystals
and other purposes.  Its only drawback is, that this
mineral is most commonly coloured with a strong tint of
blue or green, which affects the colour of the transmitted light.  Some specimens, however, while equally
effective in destroying one of the refracted pencils, are
yet but slightly tinged with colour as respects the other,
which is therefore transmitted fully polarized, but with
only a slight tinge of brownish yellow.  The other
substance, of late much resorted to for the same purpose, the iodo-sulphate of quinine, crystallizes in very
thin scales like mica, of a purplish-brown hue, which in
like manner polarize completely one half the incident
light, which passes freely through them; the other half
being extinguished.  This curious property was discovered by Mr Herapath, who first'formed the compound in question.
(I36.) When two parallel plates of tourmaline cut
from the same crystal in the mode above described, or




356                  ON LIGHT.
two laminse of Mr Herapath's quinine salt, are laid one
on the other conformably (or with their axes parallel),
the light polarized by one passes freely through the other;
but if the one be turned round on its own plane, on the
other, the intensity of the transmittted beam gradually
diminishes, until the axes cross at right angles, in which
position the combination is quite opake.  A similar
gradual diminution of light, up to complete extinction,
takes place when a ray polarized by reflexion from glass,
or in any other manner, is received on such a plate, made
to rotate in its own plane. The effects are just what
might be expected to happen if a flight offattened arrows
were discharged at a grating of parallel wires. Those
only whose planes were parallel to the wires would be
able to pass, and having passed one such grating, would
penetrate any number of others placed conformably behind it, but not if placed transversely.  This is a simile,
not an explanation, but it conveys, though coarsely, to
the mind a conception of the distinction between polarized and unpolarized light, not to be despised as an aid
to the imagination.
(I37.) If a "polarizing frame" of glass plates, such as
above described, be laid down before an open window,
and, the eye being held near it so as to embrace a large
illuminated area or " field of view," a tourmaline plate be
looked through, and turned slowly round, in its own plane
before the eye; a position will be found in which the
appearance of a dark cloud comes over the frame, extending over a very considerable visual angle; the central
portion being completely obscure; and the darkness shad



ON LIGHT.                     357
ing off at the borders by insensible though rapid degrees.
Within this "polarized field," a vast variety of brilliant
and beautiful optical phaenomena., hereafter to be described, are very conveniently and elegantly exhibited.
One effect is very striking.  If instead of a black velvet
backing, the glasses be laid on any bright surface, the
printed page of a book, for instance-this, which, without the interposition of the tourmaline, cannot be discerned for the glare of light reflected from  the glasses,
becomes distinctly visible, and may be read with facility
when that glare is taken off in the manner described.
So, too, by looking through a tourmaline plate held transversely, on the surface of a pond, at the polarizing angle;
the reflected light from the surface being destroyed, the
objects at the bottom, the fishes, &c., are distinctly seen,
though completely invisible to a bystander. So, too, by
polarizing alternately in a vertical and a horizontal plane,
the light of one or more lamps, night signals may be
made, and a message transmitted, visible andinterpretable
as signals, to a distant spectator provided with a tourmaline plate, while a bystander not so provided, though he
see the lamps, will have no suspicion that any such communication is in progress.*
(138.) Polarization of the sky lighzt.The light of a clear
and perfectly cloudless blue sky is partially polarized in a
plane passing through the sun, the eye, and the point of
the sky examined.  At each point in that great circle of
* I mention this to prevent a patent being hereafter taken out
"for secret communication at a distance by means of polarized
light."




358                   ON LIGHT.
the celestial concave, which is 900 remote from the sun's
place, the amount of polarized light which it sends to
the eye bears a very considerable proportion to the total
illumination, amounting to nearly a fourth of the whole.
At every other inclination of the visual ray to the direct
sunbeam, the proportion is less, and in the neighbourhood of the sun, or of the point on the horizon directly
opposed to it very small.  When examined in a mode
hereafter to be described, by the intervention of a tourmaline plate, and a crystallized lamina, this gives rise to
a series of exceedingly beautiful and brilliant phaenomena,
productive of the greatest astonishment to those who
learn for the first time by their exhibition, that totally
different, and even opposite qualities, characterize different portions of an illuminated surface apparently so
perfectly uniform and homogeneous.  This effect is sup.
posed to originate in the reflexion of the solar rays on
the particles of the air itself, an explanation encumbered
with many difficulties, but the best (indeed the only one)
that has yet been offered.
(I39.) Polarization interpreted on the undulatory theory.
-According to any conception we can form of an elastic
medium, its' particles must be conceived free to move
(within certain limits greater or less according to the
coercive forces which may restrain them) in every direction from their positions of rest, or equilibrium. It by
no means follows, however, that the nerves of the retina
are equally susceptible of excitement by vibrations of the
luminiferous ether (in which they may be conceived immersed) in all directions.  In the case of sound, the




ON LIGHT.                   359
tympanum of the ear which receives the impulse of the
aerial medium, would appear to vibrate like the parchment of a drum, by the direct impact of its waves perpendicular to its surface.  It is, therefore, sensible to
such of the movements of the vibrating medium only as
are in the direction of the sound-ray, and not at all to
transverse vibrations.  But if we conceive the nervous
filaments of the retina as minute elastic fibres, standing
forth at right angles to its plane, like the bristles of a
brush (the reader will pardon the apparent coarseness of
the illustration, which is only intended as an illustration
of what may be, and no doubt is, a process of transcendent delicacy), immersed in the ether; it is evident
that movements of the latter parallel to their direction
would not, but that those transverse to it would tend to
throw them into vibration, just as ears of corn would be
little or not at all agitated by a straight and slender
rod moved up and down between the stalks, or to and
fro in the direction of its own length, but violently by
a transverse horizontal motion of the rod.
(I40.) Whatever be, at any instant, the motion of an
ethereal molecule, it may always be resolved into two,
one in the direction of the ray in the act of propagation,
and the other in a direction transverse to it, in the plane
of the wave surface.  If the sensation of light be supposed to be produced by the former resolved portion,
no account can be given of the phenomenon of polarization; such movement being equally related to surrounding space in all directions outward from the ray
as an axis.  The contrary is obviously the case with




360                  ON LIGHT.
the other resolved portion. Suppose one end of a long
horizontal cord fastened to a wall, the other held in the
hand, and tightly strained. If a small vibratory motion
cross-wise to the cord be given to the hand in a horizontal plane, an undulation confiSed to that pfane, will
run along the cord; if in a vertical one, then will the
undulation be wholly performed in a vertical plane.  If
the propagation of a wave along a stretched cord be
assimilated to that of a ray of light, the former of
these cases will convey the idea of a ray polarized in
a horizontal, the latter in a vertical plane.  If the
movement of the hand (always transverse to the cord)
be not confined to any particular plane, but take place
sometimes in one, sometimes in another, at all sorts
of inclinations to the horizon-the undulation which
runs along the cord in this case will convey the idea of
an unpolarized ray. (According to Sir David Brewster,
however, a partially polarized ray would, in this manner
of viewing it, be assimilated to the case when the vibratory movement should neither be strictly confined to one
plane, nor altogether irregular, but confined in its deviations from it to some angular limit less than a right angle.)
(I4I.) There is nothing to lead us to believe that the
vibratory motions of the particles of material bodies,
especially those in the state of gases in the act of combustion, in virtue of which they are luminous, are necessarily confined to any particular plane.  Many thousands, or even millions, of vibrations in one plane may
be succeeded by as many in any other, according to the
direction and frequency of the shocks which give rise to




ON LIG.HT.                  36i
them within an interval of time inappretiably short, and
without prejudice to the continuous perception of the
vibratory movement communicated to the ether as light.
The act of polarization consists then in the subsequent
arrangement, at some definite point in the line of progress
of the ray, of all these vibratory movements, into parallelism with each other, or into a single plane from which
they have afterwards no tendency (per se) to deviate.
As the particles of crystallized bodies must be conceived to be arranged in definite lines and planes, it
is easily conceivable that, whether among them, or in
conjunction with them, the ethereal molecules may
be  confined  in  their vibrations to  two  particular
planes determined by  the  internal constitution  of
the crystal and the incidence of the light; that a
vibratory movement propagated into a body so constituted should ipso facto resolve itself into two such
movements in these two planes (according to the general
mechanical principle of the composition and resolution
of motion); that it should be so propagated during its
progress through the crystal; and that at its emergence
into free space, each vibration should thenceforward subsist separately, there being nothing to change it. Again,
it is no less conceivable that in these vibrations the
molecules of the ether moving in one plane may be
differently impeded by, or stand in a different connexion
with those of the medium, from  those moving in the
other, and that, in consequence, their propagation of
the movement may be effected with a different velocity,
and thus give rise to a difference of refractive power,




362                   ON LIGHT.
which,.as we have seen, depends on the proportion of
velocity of the light in and out of a medium.  In the
case of one set of vibrations, again, the propagation of
the medium  may be equally impeded or influenced in
all directions of the ray-in which case a wave starting
from any point in tht surface would run out spherically
within the crystal, while in that of the other the amount
of obstruction might vary with the direction of the ray,
and thus give rise to a wave running out with different
velocities in different directions from its centre of propagation, and therefore not sphericaZly.
(I42.) To this conclusion, but without passing through
the intermediate considerations which have led us up to
it, Huyghens (who certainly had formed no conception
of transverse vibrations) appears to have jumnped, by one
of the happiest divinations on record in the history of
science, viz., that in the double refraction of Iceland
spar, while the ordinary ray is propagated in a spzerical
that of the extraordinary spreads from its point of origin
at the surface of the crystal in an elliptical wave, the
form  being that of an oblate spheroid of revolution,
having its polar axis parallel to the axis of the rhomboid, and bearing to its equatorial diameter a definite
numerical proportion, viz., that of eight to nine (very
nearly).  Making this assumption, and laying it down
as a principle (capable of demonstration), that the
direction of a ray of light in such a mode of propagation is not that of a perpendicular to the surface of the
wave at any point, but that of a line drawn from  the
centre of the wave to its point of contact with a plane,




ON LIGHT.                   363
touching at the same time all the wave surfaces in progress, at the same time, through the crystal, which have
originated in one and the same plane wave sweeping
over its external surface (just as in the explanation of
ordinary refraction given in our first part, in the case of
spherical waves, in which case the latter line is perpendicular to the wave surface); he was enabled to explain
every particular of the double refraction in Iceland spar,
so far as the direction of the extraordinary ray is concerned, including its deviation from the plane of the
angle of incidence, and its non-conformity with the
ordinary law of the sines except in special cases. The
results of his reasoning have been compared with experiment, with extreme care, by M. Malus, as already mentioned, and found exactly in accordance with fact. We
cannot, of course, in an essay like the present, give any
account of the special conclusions, or of the mathematical reasoning on which they are founded; which
involve more geometry than the generality  of our
readers are likely to possess.  But we can put into a
very few words, and we think make readily intelligible,
the main feature of the reasoning, that which determines
the deviation of the extraordinary ray from perpendicularity to the wave surface, and from the plane of incidence.
(I43.) Let A B c D represent a plane wave descending
perpendicularly upon the upper surface E H (supposed
horizontal) of a crystal of Iceland spar, of which E H M I
is the principal section, or that cutting through both the
obtuse angles of the rhomboid, and in which its axis lies.




364                 ON LIGHT.
The light then which this wave conveys will be incident
perpendicularly on the surface E H, or in the direction of
the lines B F, C G, and these lines continued to K and L,
on the lower surface, would be the course of the rays B F,
C G, supposing them  to undergo the ordinary refraction. Considering now the extraordinary; suppose the
portions E F, G H of the surface screened, and only the
portion F G of the wave allowed to enter. This on striking the surface, will excite at every point over its whole
extent a luminiferous vibration, which will be propagated
A   B                 C   D
/?    \
E  IF,'_______  C. H
I K    N           L    0   M
Fig. T4.
within the crystal in a spheroidal wave, having its shorter
axis parallel to that of the crystal: and all these spheroids
being equal and similar, the plane which touches them all,
and which is, in effect, the extraordinarily refracted plane
wave zeithin the coystal, will advance parallel to the surface E H. Suppose it arrived at the other surface I M,
and let NO be the points of contact of that surface with
the spheroidal elementary waves whose centres are F and
G at that moment.  Then will N o be that portion of the




ON LIGHT.                    365
posterior surface which willfirst be struck by the refracted
wave.  The portions beyond on either side, I N and o M,
will subsequently receive the divergent undulations, which
(as we have already explained) give rise to diffracted
fringes bordering the shadows of the screens E F, G H.
Thus we see that the space between N and o, and not
that between K and L, will receive the full illumination
from the aperture F G, which has therefore been propagated obliquely in the direction of the lines F N, G o, and
not of the perpendiculars F K, G L.*
(I44.) The deviation of the refracted ray from theplane
of incidence, and from that of ordinary refraction, will
be readily understood when it is borne in mind that
whether at a perpendicular or an oblique incidence, a
plane exterior wave is transformed by the extraordinary,
as well as the ordinary refraction, into a plane interior
one, and that the plane of incidence of a ray is perpendicular to both these planes.  It cannot therefore contain the extraordinary refracted ray (which is a radius of
the spheroid) without containing at the same time a
normal to the elliptic surface of propagation at its point
of contact with the interior plane wave, that is to say,
unless it contain also the axis of the spheroid. In other
words, the extraordinary ray will always deviate from the
plane of incidence, unless in the case when that plane
coincides with some one of the meridians of the spheroid
in question.
(145.) Since there is no double refraction in the direction of the axis of the rhomboid, it follows that in that
* This is Huygliens's explanation, and the correct one.




366                   ON LIGHT.
direction the velocities of propagation of the ordinary
and extraordinary rays within the crystal are the same,
and that therefore, supposing the two corresponding undulations propagated from the same point in its surface
to run out internally, the one in the form of a spherical,
the other of a spheroidal shell, these shells will have a
common axis, viz.: —the shorter axis of the spheroid,
which will therefore wholly include the sphere, being in
contact with it at the poles of the spheroid.  Cwteris
paribus, too, it is equally obvious that, when we come to
consider different sorts of crystals possessing the property of double refraction, the intensity of this quality,
or the amount of angular separation of the two refracted
rays at the same.incidence, will be determined by the
greater or less amount of ellipticity of the spheroid in
question. Should this ellipticity be nil, the spheroid will
coincide over its whole extent with the sphere, and there
will be no double refraction. This is the case with all crystallized bodies, whether mineral or artificial salts, whose
primitive form  is the cube.  In some cases (comparatively rare ones), of which quartz or common rock crystal
is an example, the spheroid is of the kind called prolate,
or one formed by the revolution of an ellipse round its
longest diameter, and is therefore wholly contained within
the sphere.  In these, then, the velocity of the extraordinary ray within the crystal is less than that of the ordinary; and the latter ray, which is the more refracted of
the two in Iceland spar, is in such crystals the less so.
On comparing different crystals, however, it is not found
(which perhaps might have been expected) that the el



ON LIGHT.                    367
lipticity of the spheroid in question is determined solely,
or even principally, by the degree of obtuseness of the
rhomboidal form of the crystal. It appears to be regulated far more by the chemical and other physical qualities of the material.
( 46.) Of the interference of polarized rays.-The assimilation of a ray of light to a series of equidistant waves
running along a stretched string, will afford a very clear
conception of the interference of polarized rays.  Suppose a vibratory movement in a horizontal plane to be
communicated to one end of such a string, and to propagate along it such a series of waves, which will therefore
all be confined to the same horizontal plane. If then a
simultaneous movement, exactly equal and similar, and
in t/ze.same plane, were commiunicated to a point in the
string exactly half a wave breadth in advance of the point
where the first series originated; each point in its length
anywhere in advance of both these origins of movement
would be always solicited by two equal and opposite impulses, the one of which would contradict the other, and
in consequence it would remain at rest, and the two
series of waves would destroy one another. If the origin
of the two vibratory movements were distant from each
other by a whole wave breadth, they would conspire to
produce a double extent of vibratory excursion all along
the string. All this is merely recapitulatory of what was
stated, in Lecture VII., when explaining the general
nature of the interference of rays.  But it is evident that
these conclusions only follow if the interfering vibratory
movements are performed in the same plane.  Supposing




368                  ON LIGHT.
them performed in planes at right angles to each other,
no such mutual destruction or reinforcement of movement can take place.  Two movements at right angles
to each other, communicated at the same instant to the
same material molecule, combine, in virtue of the mechanical principle of the composition of motions, to produce a movement intermediate in direction; and can in
no case destroy each other.
(i47.) It follows from this, that if such be really the
nature of the luminous vibrations and such the true explanation of the phaenomenon of polarization-interference can only take place between rays polarized in the
same plane-such complete interference at least as shall
result in the extinction of both, in the manner above described.  This conclusion is, happily, capable of being
brought to the test of experiment, and the result is found
to be in exact accordance with the a p.riori reasoning.
The experiment is simple and direct.  Let two small
holes, or, better, parallel slits very near each other in a
thin opake screen, be placed between the eye and a
very minute and brilliant point of light; and viewed
through a lens, as described in a former paragraph; so
as to see the diffractive fringes. Now over the holes or
slits let two plates of tourmaline of precisely equal thickness and in every respect similar be applied (to secure
which conditions, the two halves of a single plate worked
to exact parallelism and cut across, may be used). Then
if the axes of these plates be parallel, in which case the
light passing through both the apertures will be similarly
polarized, the fringes will continue to be seen. If one




ON LIGIT.                    369
of them be slowly turned round in its own plane till its
axis comes to be situate at right angles to that of the
other, they will gradually decrease in intensity and at
length disappear altogether when this rectangularity is
precisely attained.  In the first case, then, the rays have
interfered-in the last, not: while in the intermediate
states a partial interference takes place, the more complete the nearer the axes are to parallelism. How this
is operated we shall now proceed to explain.
(148.) Circular and elliptic polarization. -If we regard
the vibratory movement of any single particle of an elastic medium in its most general mode of conception, we
shall find that it may always be considered as capable of
resolution into three rectilinear vibrations in three planes
at right angles to each other, each going on as if the
others had no existence: and its place in space at any
instant will be had by estimating its distance on one side
or the other of its neutral or central position (those of
perfect equilibrium and rest), reckoned along each of the
three lines in which these planes intersect (which, after
the manner of geometers, may be considered as three
rectangular axes, or co-ordinate lines), which it would
have attained at that instant in virtue of each separately,
and independent of the others. This is nothing more
than the enunciation of one of the simplest of mechanical
laws, that of the composition and resolution of motions.
But the theory of movements propagated through elastic
media (a theory far too elevated and intricate to admit
of any explanation in these pages, and whose results the
reader must take for granted) further teaches us that a
2A




370                  ON LIGHT.
vibratory movement once set up and steadily maintained,
according to a regular law of periodicity in any one
molecule of such a fluid will, sooner or later (according
to its distance and situation), reach every other, which
from that moment will be agitated by a vibratory movement precisely similar in its phases (though of inferior
extent in its excursions) to the original movement, and
performed in t/e same period of time.  It matters not
whether the medium be or be not equally elastic in all
directions. This will affect the rate of progress of a wave
through it in different directions, and by consequence
the form of the wave, and the length of time that has to
elapse before the molecule in question begins its vibratory movement; but once set up in any molecule, that
movement will be maintained, so long as it is, so to
speak, fed from behind-so long as successive waves
continue to pass through it. In the theory of light, the
eye being insensible to vibratory movements in the direction of the ray, we have only to consider those components of the motion which lie in a plane at right
angles to that direction, and which, for the present, we
will suppose to be that of the paper before us.
(I49.) Let us consider, then, the kind of motion which
an ethereal molecule will assume, under the influence of
two such vibratory movements simultaneously affecting
it, in directions transverse or otherwise inclined to each
other, but both directions lying in one common plane,
that of the paper, or of the wave-surface; each of which
will therefore represent the vibratory movement proper
to a ray polarized in a plane at right angles to our paper,




ON LIGHT.                    371
and intersecting it in its line of direction. And first, for
simplicity, let us suppose the two vibrations of equal intensity (i.e., in both which the molecular excursions on
either side of the point of rest are equal), and that their
directions form a right angle with each other. Let A B
and a b, fig. i5, represent two such lines of vibratory
movement, c, c, their central points, or the positions of
rest of the molecules when undisturbed, and c A, c B;
c a, c b; their extreme excursions to and fro.  The times
of vibration being equal (which is an indispensable
condition for the union into one of two distinct luminous
rays: as a red ray, for instance, cannot interfere with a
violet one), let each be supposed divided into the same
number of equal parts (say 36o).  Then supposing the
molecules to set out at the same instant from  c and c,
they will arrive at A a, respectively in go such units of
time, will have returned again to. c c, in I80; have
reached B, b, in 270, and again returned to c and c, in
360.  In so doing, however, their motions are not uniform, but most rapid when traversing the central points,
and gradually retarded as they recede from these: so
that in equal intervals of time the spaces traversed along
the lines C A, c a, will be unequal. Then let the whole
time (90) of describing c A, be divided into five equal
times of I8 each, and  suppose that at the end of
the ist, 2d, 3d, 4th, and 5th of these, the molecule has
arrived at the points i, 2, 3, 4, 5. It is demonstrable,
then, that the several distances C I, C 2, C 3, C 4, C 5,
of these points from c will be to each other in the proportion of the Sines of 18~, 360, 54~, 72~, and of 9go




372                   ON LIGHT.
or radius; and the same is true of. c, c 2, C 3,  4,
c 5.
(I50.) This premised, we are now in a condition to
trace the movement of a molecule affected at once by
both these causes of displacement. Let it be 0. Then
at the expiration of the first interval of I8 units of time
it will in virture of the vibration parallel to C A, be
carried to a distance equal to C I in a direction O P
parallel to that line, and will be found so fir from the.Al *'',     MB
Fig. x5.
line 0 p parallel to c a.  And in virtue of the other
vibration similarly it will be found at the same time at




ON LIGI-IT.                   373
the distance c i (= C i) from O P, or in the direction 0p
parallel to c a. In virtue of both movements, then, it
will be found at x, the extremity of the diagonal of the
square O x at that moment.  And similarly at the end
of the 2d, 3d, &c., interval, it will be found at the extremities of the diagonals of the squares next in succession, and as these all lie in one line, o E, 45~ inclined
both to O P and O _, it appears that in this case the
resultant vibration will be rectilinear, and will be performed along the diagonal E G of the square E F G H;
and thus it appears that the superposition of two rays of
equal intensity, polarized in opposite (i.e., rectangular)
planes, results in the production of a ray polarized in a
plane 45~ inclined to each of the former.  Moreover,
the square of the diagonal being double that of either
side of a square, and the intensity of a ray being measured by the square of the vibrational excursion of its
ethereal molecules, the intensity of the compound ray
will be double that of the components, or, equal to their
sum.  And, vice versa, any polarized ray may be considered as equivalent to two rays, each of half its intensity, polarized in planes 45~ inclined on one side,
and on the other of its plane of polarization. It need
hardly be observed that if the molecule in starting from
O be moving in the direction C A, in virtue of the one
vibration, and of c b in virtue of the other,-that is, if
it be commencing its first semi-vibration in the one
direction, and its second in the other, or again in other
words, if the vibrations differ in phase by an exact semiundulation; all the same reasoning will apply, with this




374                   ON LIGHT.
only difference: viz., that the resultant rectilinear vibration will be performed along the other diagonal, H F, of
the same square.
(I5I.) It appears, then, that a change of phase in the
vibrations of one of the component rays, of half an undulation, exactly reverses the polarization of the compound ray, and causes its vibration to be performed
along the diagonal H F instead of G E. Let us now
examine by what sort of gradations the one of these
movements passes into the other, when the phase of one
of the vibrations C c is changed gradually.  Suppose,
for instance, the vibration a b (so, for brevity, we will
designate it) to be in advance of the vibration A B by
one-twentieth part of a complete undulation, so that at
the moment when c starts from c in the direction c A,
c shall have already got to I in the direction c a. Then
at that moment our molecule O will not be at O but at y.
After the lapse of one-twentieth more of a period, C will
have got to I in the direction C A, and c to 2 in the
direction c a, and 0, actuated by both movements, will
have arrived at z, having of course described in the interval a line y z, connecting these two extremities of the
diagonal of the rectangle xyz. And exactly in the same
way, at the expiration of the next twentieth of a period,
it will be found in u, the extremity of the diagonal of
the next rectangle-and thus tracing its course step by
step through the whole  twenty, which  constitute  a
period, we shall see that it will have described a narrow
ellipse, having m n for its shorter axis, and E G for Mte
direction of its longer, and touching the four sides of the




ON LIGHT.                    375
square E F G H.  If the initial difference of phase be
two, three, or four twentieths of the period, it will be
seen, by following out the movement in the same way,
that more and more open ellipses will come to be
described as represented in the figure; and that, when
this difference amounts to five twentieths or a quarter
undulation, the movement will be circular in the direction p P q Q, or of the arrow marked thus —.  The
difference of phases still continuing to increase, this
will again degenerate into an ellipse by a continued
elongation in the direction  H  F, and  contraction in
the direction E G, till it passes at length, after another
quarter-undulation of phase-difference, into the straight
line H F.  The circulation in all, however, being in the
same direction, or +.  On the other hand, if instead of
supposing the vibration a b to be initially in advance of
A B by one-twentieth, we suppose it to be so much in
arrear, we shall have the same ellipse n E m described
as in the former case, but in the opposite direction, that
of the arrow marked -, as will be easily seen by going
through the successive steps of our reasoning: and so
for all the rest; so that in the case of a circular revolution, the direction of -the rotation will be one way or the
other, according as the vibration a c is a quarter-undulation in advance or in arrear, in respect of phase, of A c.
(I52.) This, then, is what is meant by circular and
elliptic polarization. It is easy to extend the reasoning
above stated to cases in which the component vibrations
are of unequal intensity (or extent of excursion), and
make other than a right-angle with each other's direc



376                   ON LIGHT.
tions.  We have only to suppose our lines A B, b a, and
their parallels P Q, p q, inclined to each other at the
angle in question, and of unequal length; to divide them
similarly (i.e., in the same proportion) in the points i, 2,
3, 4, 5-and we shall obtain a set of ellipses, none of
which, however, can in either of the cases have its axes
equal, or pass into a circle, for this plain reason-that
no circle can touch internally all the four sides of any
parallelogram except a rhomb.
(I53.) Conversely, a ray circularly polarized may be
considered as compounded of, and may (by suppressing
either of them  and letting the other pass, through a
tourmaline plate) be resolved into two equal rays, each
of half its intensity, polarized at right-angles to each
other, and differing in phase by a quarter-undulation.
If one of them be in advance of the other by that phasedifference, the rotation will be in one direction-if in
arrear, in the other. Elliptic polarization, on the other
hand, when it exists, may be recognized by the possibility of resolving the ray so polarized into two oppositely polarized, and either of unequal intensity, or, if
equal, differing in phase otherwise than by a quarterundulation.
(154.) Finally, a ray polarized in any one plane may
be regarded as equivalent to two equal rays, circularly
polarized in opposite directions of rotation, and having
a common zero-point.
(I55.) A ray of ordinary light may be considered as a
confused assemblage of rays, polarized indifferently in
all sorts of planes.  It is, therefore, a mixed phenome



ON LIGHT.                      377
non; and to study it in its simplicity, we must in idea
break it up into its component elements, and examine
their phaenomena per se.  Now it results, from  a series
of experiments too extensive and refined to be here detailed, and from reasonings upon them which the generality of our readers could hardly be expected to follow,
that when a ray, pplarized in any plane, undergoes reflexion in a different plane, the reflected portion comes
off in all cases more or less elliptically polarized —that
is to say, that it consists of, or can. be resolved into, two
rays, the one polarized in the plane of incidence, the
other in a plane at right angles to it-that both these
portions have undergone a change of phase at the moment of reflexion, but not the same for both, so that
arriving at the surface in the same phase, they quit it in
different, and therefore constitute by their superposition
an elliptically polarized ray. The amount of ellipticity
varies, for each reflecting medium  (according to the
nature of its material) with the angle of incidence at
which the reflexion takes place, and also with the inclination of the plane of incidence to that of the primitive
polarization of the incident ray.   If the reflexion take
place on ordinary transparent media of not very high
refractive power, as glass, or water, and at the polarizing angle, the degree of ellipticity is so slight that the
vibration may be considered as rectilinear, and the reflected ray as completely polarized  in the plane  of
incidence.   As the refractive power of the surface increases, the ellipticity impressed is greater, and in some
substances, of very high refractive power, such as dia



378                     ON LIGHT.
mond, and all those bodies which possess what is called
the adamantive lustre (a consequence of such high refractive power) it is considerable. From such bodies accordingly it is not possible, at any angle of incidence to obtain
a reflected ray completely polarized in one plane.   And
when we come to reflexion from  polished metals,* the
ellipticity becomes very considerable.   In consequence,
only a very imperfect polarization of the reflected light
in the plane of incidence can be obtained by reflexion
from any metalic surface at any angle.
(I56.) In all the above enumerated cases, the degree
of ellipticity increases wit/i the refective power of the
medium  of which the reflecting surface is constituted;
which itself stands in intimate connexion with the magnitude of the refractive index. It might naturally, therefore, be expected to attain its maximum possible amount,
or that the ellipse should become a circle in the case
of total reflexion. This can only take place, however,
when the reflexion is made on the interncz   surface of a
transparent medium.  This accordingly happens in the
case of a beautiful experiment of M. Fresnel, who found
that a parallelopiped of glass,t A B c D, fig. 15, being
cut and polished, having the acute angles at A and D,
* All metals, even the densest, are in some slight degree transparent, and all have enormously large refractive indices.  The
transparency of gold is perceptible in gold leaf, which transmits a
green light. That of silver is perceptible in the thin films deposited
on glass in Liebig's process for silvering mirrors-the transmitted
light being bluish.
+ The glass used was that known in France as "XVrre de St.
Gobain."




ON LIGHT.                    379
each 54~ 37, and a ray P Q, polarized in a plane 45~
inclined to the plane of the section A B c D intromitted
perpendicularly at the face A B, so as to be reflected internally at Q on the side A c, (in which case, the reflexion
being at an angle of incidence 54~ 37' was total); and
A
P  
D
Fig. I6.
again at R, at the same angle, on the opposite side D B,
it emerged from the face D c, along the line R s, circularly polarized. In this case, the plane of reflexion
making an angle of 45~, with that of original polarization, the reflected ray will consist of two equal rays,
oppositely polarized; and of these the one in each act of
reflection has lost, in the other gained, an exact i6th of
an undulation, making an 8th diefferezce at each reflexion,
or a quarter after both; so as to emerge under all the
conditions of circular polarization.  In consequence,
when analysed at its emergence by a tourmaline plate,
it is found to undergo no change of brightness on turning
the plate in its own plane, whereas the original ray, P Q,




380                    ON LIGHT.
would have been wholly extinguished at each quarter
revolution.
(I 5 7.) Another mode of communicating circular polarization to a ray, is to transmit it at a perpendicular incidence through a parallel plate of any perfectly colourless and transparent doubly refracting crystal, of such
thickness, that in the passage through it of the two
waves, parallel to its surfaces, into which the incident
wave (supposed plane) is divided, (the one conveyed by
ordinary refraction, the other by extraordinary, and therefore travelling with different velocities in the crystal,)
the one shall have gained  or lost, after emergence,
exactly a quarter of an undulation on the other. For as
the corresponding rays emerge of equal intensity, and
oppositely polarized, they here also fulfil all the conditions of circular polarization.  If the thickness of the
plate be-such, that the difference of phases is more or
less than an exact quarter (or any number of quarters)
of an undulation, the compound ray will be elliptically
polarized, and the degree of ellipticity will be determined
by the thickness of the plate.
(I58.) It may be asked, in what does a ray so circularly polarized differ from an ordinary unpolarized ray,
seeing that the latter may always be regarded as compounded of two ordinary rays of half the intensity oppositely polarized?  We reply, in this: viz., that if again
transmitted through another such glass parallelopiped,
similarly situated, the difference of phase will be doubled.
The emergent ray then will consist of two equal rays
oppositely polarized (and therefore not interfering), dif



ON LIGHT.                    381
fering in phase by half an undulation, and which therefore (by what we have before shown) compound a single
ray polarized in a plane half-way intermediate, or 45~
inclined to the original plane of polarization; whereas a
ray of ordinary light so transmitted would show no signs
of polarization in any one plane more than in any other.
(I59.) The most remarkable cases of circular polarization, however, are those which occur when a ray is
transmitted along the optic axis of a crystal of quartz,
and some few other crystals, as also through certain
liquids. The phaenomena so exhibited cannot be explained, or even described, however, till we shall have
said something
OF THE COLOURS EXHIBITED BY CRYSTALLIZED PLATES
ON EXPOSURE TO POLARIZED LIGHT.
(I6o.) Uniaxal crystals.-If a plate cut from a crystal
of Iceland spar, so as to have its faces perpendicular to
the axis of the primitive rhomboid, be placed close to
or very near the eye; and before it a tourmaline plate
having its axis vertical, so as to polarize all the light incident upon it in vertical planes passing through the
eye; and if any brightly illuminated white surface, such
as a white cloud, or a sheet of paper laid in the sunshine, be viewed through it: or if, instead of a tourmaline plate, a "polarizing frame" of glass plates, such as
above described, be laid horizontally, and the reflexion
of a clouded sky be in like manner viewed through the
crystal; in the "polarized field" so obtained nothing




382                   ON LIGHT.
especially is seen which would lead to a suspicion that
the crystal were other than an ordinary piece of glass.
But if, in this state of things, between the crystal and
the eye, be placed another tourmaline plate, having its
axis horizontal, a magnificent set of coloured rings will be
seen; the exact counterpart of the reflected rings described
by Newton (only infinitely more vivid and brilliant), il
every respect but these:-First, that they are all divided
into four quadrants of coloured light by a dark cross
passing through their common centre, and having its
arms vertical and horizontal; and, secondly, that the
rings themselves are of unequal brightness in different
parts of their circumference, being most luminous at the
middle points of the quadrants into which the cross
divides them, and fading away very gradually on either
side of these points, till they cease to be traceable and
are lost in the darkness of the cross.  On the other
hand, if the tourmaline plate between the eye and the
crystal (which we shall call the " analyzingplate," or the
" analyzer," for a reason which will presently appear) be
placed with its axis vertical, a series of rings will also be
seen: but they are, now, the complementary seriesthose seen by transmission in the Newtonian experiment; and the cross, instead of black, is now white.
Lastly, if the analyzing plate be placed obliquely, both
sets of rings will be partially, and, as it were, confusedly,
exhibited; the one dislocating the other, in consequence
of the brighter annuli of the one set abutting upon the
obscurer of the other, the reds on the greens, the purples
on the yellows, &c.: the preponderance in light, distinct



ON LIGHT.                    383
ness, and extent, falling to the share of that set which
the position of the analyzer most favours.
(I6I.) It is manifest that these colours originate in
the interference of two series of undulations propagated
with different velocities within the crystal, and which
therefore  must necessarily belong  the one to  the
ordinary, the other to the extraordinary, pencils into
which the incident light is divided, which, as before
shown, travel with different velocities within its substance.  These pencils, however, during their progress
through it, are proceeding in different directions (by
reason of the double refraction of the medium) and are
oppositely polarized-so that, while within the crystal,
they cannot interfere. Their interference, then, must be
accomplished after their emergence, when their directions have been again reduced to parallelism, and they
have been (wholly or partially) brought to a common
plane of polarization by the action of the second tourmaline.  Let us, therefore, examine how this is brought
about.  And first, along the vertical arm  of the black
cross, the whole of the incident light being polarized-in
the plane of a vertical section of the crystal containing
its axis, will pass into the ordinary pencil, and none into
the extraordinary-so that there will be nothing to interfere with it: and emerging wholly polarized in that
plane, will be wholly stopped by the analyzing tourmaline-the result being darkness.  But if this tourmaline
be turned 90~ round in its own plane, it will be wholly
transmitted, and the arm of the cross in question will be
white.  As regards the horizontal arm  of the cross, in




384                   ON LIGHT.
like manner, the visual ray throughout its whole extent
is inclined to the axis in a plane at right angles to that
of the primitive polarization. The light, therefore, incident in this plane through the first tourmaline will
pass wholly into the extraordinary pencil, and will therefore emerge polarized in a plane at riht angles to the
(now) horizontal section of the crystal containing its axis
in which its direction lies, i.e., again, in a vertical plane,
and will be stopped, for the same reason, by the second
tourmaline; so that this arm of the cross also will be
black in the horizontal, and white in the vertical, position of the analyzer.  Let us now consider a ray incident in a plane 45~ inclined to the vertical, or in a plane
intermediate between the arms of the cross (the axis of
the crystal being in all cases supposed held horizontally).
The incident ray then will fall on the crystal in a section through its axis 450 inclined to that of its primitive
polarization, and will therefore be equally divided between the ordinary and extraordinary pencils.  These
portions will emerge parallel, and of equal intensity,
though differing in phase by such a number of undulations, and parts of an undulation, as the latter, by
reason of its greater velocity, has gained on the former.
In this state they are both incident on the second tourmaline, having its axis 45~ inclined to both their planes
of polarization, which therefore will subdivide each of
them into two equal portions oppositely polarized, suppressing or absorbing one, and allowing the other to pass,
and the transmitted portions, being of equal intensity,
similarly polarized (viz., both in the plane of the axis of




ON LIGHT.                    385
the analyzing plate), and differing in phase, will interfere and give rise to the phenomena of coloration in the
manner already sufficiently explained. It remains now
to account for the colours being arranged in regular
succession in rings round the centre of the black cross
(which corresponds to the axis of the crystal). Now the
colour developed, or the order of the tinl, in the series of
the Newtonian rings, increases with the difference of
phase, and this difference increases with the difference of
velocities of the two pencils within the crystal, and with
the length of the path traversed with those velocities.
Both these increase with the inclination of the visual
ray to the axis of the crystal: since along the axis there
is no double refraction, which increases gradually from
that direction outwards up to a right angle. This, then,
explains the progressive increase, of colour or order of
tint in proceeding from  the centre outwards.  The
circular arrangement is a consequence of the symmetry
of the crystalline plate in all directions around its axis;
the amount of double refraction being the same at
equal obliquities to that line in all directions around it,
as also the increase of thickness traversed by rays
equally oblique in all directions to the surfaces of the
plate. It only now remains to explain how it happens
that, in this situation of the analyzing plate (at right
angles to the polarizing one), the tints are those of the
reflected, not of the transmitted series in the Newtonian
rings.  And the reason is very similar to, that by 1vhich,
in the colours of thin plates, the difference of phase is
assumed (justifiably assumed) to commence, not from
2B




386                   ON LIGHT.
zero, but from  half an undulation.  Of the two partial
systems of waves that interfere, in the case considered,
that which belonged to the ordinary pencil in the crystal passes, as an extraordinary one, through the analyzing plate.  Now it is a law, susceptible of demonstration, but which it would lead us too far aside at present
to demonstrate-that in the transition from an ordinary
to an extraordinary refraction, half an undulation is
gained. With the other portion of the interfering pencil,
no such transition takes place. Half an undulation then
has to be reckoned in addition to the phase-difference
due to the simple passage of the two rays through the
crystal-just as is the case in the Newtonian reflected
rings, and with the same result.
(I62.) If we follow out the same chain of reasoning
in the case when the analyzing plate is parallel to the
polarizing one, the conclusions will be identical up to
this last step.  But here the cases differ.  Neither of
the interfering pencils here at its entry into the second
tourmaline undergoes extraordinary refraction, and there
is accordingly no semi-undulation to be added to the
phase-difference.  The rings, therefore, will have the
characters of the transmitted series of Newton's colours.
(163.) In the generality of uniaxal crystals, the tints
of the rings, when the crystal itself is colourless (or as
nearly as its colours will allow), follow a succession identical with that of the Newtonian colours of their plates.
I have elsewhere called attention, however, to several
instances of deviation from this rule, some of which are
of so remarkable a nature as to deserve special mention.




ON LIGHT.                     387
The most remarkable is in the case of one variety of the
mineral called apophyllite which (from the peculiarity in
question) I have proposed to call Leucocyclile, in which
the rings are almost devoid of colour, being merely a
succession of dark and light circles, much more numerous
than the coloured ones usually seen, and the more remote of which, from  the centre,'graduate into -feeble
shades of purplish and yellowish light. The physical interpretation of this phcenomenon is as follows. Since the
colours originate in the superposition of rings about a
common centre, differing in diameter for the several
coloured rays throughout the spectrum, (as already explained in Lecture VII.), it follows that in this case, no
such difference of diameter, or but a very slight one
exists. Now, for crystalline plates so cut, of a given
thickness, the apparent diameters of the rings seen are a
measure of the doubly refractive energy. The more intense this energy the closer and more compact the system of rings;-for this obvious reason, that the same
difference of phases between the ordinary and extraordinary pencils is developed at a less angle of inclination to
the axis; and the difference of phases is a direct result
of difference of velocities in their internal propagation;
and this again, of the doubly refractive energy. Hence
we conclude that in the leucocyclite all the coloured rays
throughout the spectrum  undergo equal, or very nearly
equal separation at a given angle of incidence, by double
refraction; and that therefore in a doubly refracting prism
cut from this substance, the two spectra formed by a sunbeam  would be of precisely equal lengths, though un



388                   ON LIGHT.
equally refracted, or that the highest index of refraction
would be accompanied with the least dispersive power.  I
have not made the experiment, but that such would be
the case there can be no doubt. In the spectra formed
by an Iceland spar prism, the reverse is the case-the
higher refractive index corresponding to a much higher
dispersive power, and the most refracted spectrum being
much longer and much more brilliantly coloured than
the least.
(I64.) Another highly remarkable example of this kind
is found in the mineral called Vesuvian, a uniaxal crystal
of a greenish hue, which to a certain degree interferes
with the vivid development of its coloured rings. It does
not, however, prevent their being well observed-and
they present this very singular anomaly, viz., that the
system of rings formed by the red rays is considerably
smaller than those formed by the violet, and in consequence that the order of tints in the rings formed in
white light is inverted, so that, of the spectra formed by
a prism of this substance, the more refracted ought to be
the shorter, and the least coloured. This kind of anomalous action is, however, carried still further in another
variety of uniaxal apophylite, in a plate of which perpendicular to the axis, rays of a medium refrangibilityforn
no rings at all, so that for such rays the substance is singly
refractive.  Proceeding from this medium  refrangibility
towards either end of the spectrum, rings are formed,
contracting in diameter, as the red or violet end is approached, but most rapidly towards the red. It would
not be too much to expect that if a prism  could be




ON LIGHT.                    389
formed of this mineral (unfortunately very rare), and a
bright point illuminated in succession with all the prismatic rays viewed through it, beginning with the red,
two images would at first be seen, the one formed by
ordinary refraction, fixed, the other gradually approaching it; at a certain stage of the illumination coinciding
with it; then crossing to the other side and separating
more and more from it as the light verged more to the
extreme violet.  The experiment, which would be a very
beautiful one, is recommended to the attention of those
in possession of such crystals which they may not be indisposed to sacrifice.
(165.) Of the colours developeed by circularjpolarization.Quartz, or ordinary rock crystal is uniaxal: and when
a plate of it of moderate thickness, cut from one of the
six-sided prisms in which it usually occurs.at right angles
to its axis, is examined in the mode above described
with a polarizer and analyzing plate, a superb system
of coloured rings and black cross is exhibited-but with
this peculiarity, that the cross does not come up to the
centre, and that the interior rings are blotted out and
obliterated by a round patch of coloured light; whose
tint, when the tourmalines are at right angles, varies with
the thickness of the plate; being white when very thin,
and passing, for plates successively increasing in thickness, through all the series of tints of Newton's transmitted rings. Keeping to one plate, the tint also varies
on turning round the analyzing plate in its own plane,
and with this very extraordinary peculiarity, viz., that
while in some crystals a certain succession of colours is




390                    ON LIGHT.
observed, on turning it from right to left; in plates of
the same thickness cut from other crystals the same succession is seen on turning it from left to right. Yet
more singular, is the fact that this inversion-this rightand-left-handedness in the succession of tints, corresponds
to, and is predictable beforehand from, the appearance
of certain small obliquely posited facets on the crystal
previous to polishing, which lean unsymmetrically in
some crystals to the right, in others to the left hand of
the axis held up straight before the eye. In all other
respects the crystals are identical.*  A similar right-andleft-handedness in the external form of their crystals,
accompanied with the very same optical phaenomena,
has been remarked by M. Pasteur in the salts called paratartrates and their crystallized acid.
(I66.) The account given by the undulatory theory of
these phenomena is this.  Quartz (to adhere to our first,
chosen instance) is uniaxal, but it differs from Iceland
spar and others of that class in a most essential point
first noticed by Mr Airy, yiz.: that the sphere and spheroid representing the simultaneous surfaces of the ordinary and extraordinary waves propagated within them,
though having a common axis, do not touch each other
internally. Hence, in the direction of that axis, though
there is, at a perpendicular incidence, no double refraction,
there is a difference of velocity in the two rays. Now
the theory at present adopted is, that owing to some
peculiarity at present not understood; when a polarized
* Amethyst consists of thin alternate layers of right-handed and
left-handed quartz superposed, parallel to their axes.




ON LIGHT.                    39!
ray (which may always be considered as compounded of
two circularly-polarized ones of opposite characters as
already stated, i.e., in which the particles of the ether circulate in opposite directions) is incident on a quartz
plate, in this manner; the crystal operates an analysis of
the ray and resolves it into two such rays circularly polarized; which it propagates as such, the one as an ordinary, the other as an extraordinary one. On their emergence at the opposite face of the plate they recompound
a plane-polarized ray; but, having gained or lost on one
another, by reason of their difference of velocity in their
passage through it, a number of revolutions or parts of a
revolution proportional to the thickness of the plate, the
two circular rays at the instant of their reunion have no
longer a common zero-point as at their entry: and from this
it may be demonstrated  that the plane of polarization
of the recomposed will not be coincident with that of
the incident ray, but will have been turned round,
in the direction of the rotation of the ray which travels
fastest within the quartz, through an angle also proportional to the thickness of the plate. As the angle of displacement, moreover, differs for the differently coloured
rays of the spectrum; the effect will be that, when passed
through an analyzing tourmaline the different colours
will be differently absorbed, and the result will be the
production of a compound tint in the beam finally delivered into the eye, the colour of which will vary with
the rotation of that plate in its own plane, as observed.
* Our necessary limits forbid us to give the steps of the demonstration, which, however, are very obvious.




392                    ON LIGHT.
(I67.) It is not in crystallized bodies only that this singular effect is produced.  Strange as it may seem that a
colourless, transparent, and perfectly homogeneousf7uid
should deviate the plane of polarization of a ray passing
perpendicularly through it at all; still stranger that it
should do so constantly in one direction for the same
fluid, but in opposite directions for different fluids;
-strangest of all, that even vapours should be found possessing the same property: such is the case. Thus, oil
of turpentine and its vapour turn the plane of polarization to the right hand, solution of sugar to the left, and
so for a variety of other substances.* This property has
been made the basis of an elegant instrument called the
saccharometer, by which the quantity of sugar contained
in a given solution is ascertained by simple inspection
of the tint so produced.
(i68.) Struck by the fact, apparently so singular, of a
"right-and-left-handedness" inherent as it were in the
molecules of material bodies-by the correlative fact of
such a tendency, or so to speak idiosyncrasy, manifesting itself in the forms of crystals-and again, in quite a
different field of scientific research, in the action of an
electrified  cylindrical wire  on  a magnetized needle
placed parallel' to its direction, (which turns the north
end of the needle to the right or to the left according to
the direction of the current along the wire): it early
occurred  to the writer of these  pages that it was
* Mr Jellett, of Trinity College, Dublin, has, I am informed,
recently discovered a liquid which is right-handed for one end of the
spectrum, but left-handed for the other 




ON LIGHT.                    393
scarcely possible such singularities should stand in
no natural connexion.  Between two of the cases adduced the connexion had been proved by himself.  It
remained to enquire whether the third could be brought
into obvious relation to the other two. Accordingly on
the i4th of March 1823, having prepared a long spiral
coil of copper wire enclosed in an earthenware tube,
furnished with a polarizing reflector at one end and an
analyzer at the other; by the kindness of the late Mr
Pepys, he was permitted to bring the coil into connexion
with the great magnetic combination of the London
Institution, consisting of one enormous couple, expressly
arranged for producing the greatest possible magnetic
effect. His expectation was that light would appear in
the dark polarized field on making the contact, and be
maintained during its continuance.  The experiment,
however, proved unsuccessful.  No direct action upon
light could so be made manifest.  At a later period,
however (1845), by introducing into a similar coil a
certain highly refractive glass consisting chiefly or wholly
of borate of lead, as well as a variety of other solids
and liquids (water among others), Professor Faraday
succeeded in communicating, temporarily, and during
the continuance of the passage of the current, the property in question to them.
(I69.) Biaxal Crystals.-By far the greater number
of crystallized substances do not present that single symmetry (symmetry on all sides of a single central line or
axis), which we have spoken of as indicative of a single
axis of double refraction, and of a spherical propagation




394                   ON LIGHT,
of the ordinary, and spheroidal of the extraordinary ray,
within them.  In all or nearly all these, two lines inclined to one another at an angle greater or less according to the nature of the substance can always be found
(either by a careful examination of the crystal in polarized light through the faces of its natural form, or by
cutting and artificially polishing plates of it), which
possess the properties of such axes;-along which, that
is to say, refraction is single for a ray passing either way
out of the crystal; and in which when examined in
polarized light with an analyzing plate between the eye
and the crystal, coloured rings are seen. The simplest
and readiest instance of a crystal of this kind is furnished
by a sheet of ordinary mica, such as may easily be procured in large sheets. If a sheet of this be held before
the eye in a polarized field perpendicularly (an analyzing plate being interposed) and turned round in its own
plane, two portions will be found at right angles to each
other, in which the polarization of the incident light is
not disturbed, and the field remains dark. Of the two
planes perpendicular to the plate in which the plane of
polarization cuts it in these two positions, one is the
4 principal section " of the plate, and contains its " optic
axes."  These may be brought into sight by holding the
eye (armed with the analyzer) quite close to the mica,
and inclining the latter, either forward or backward in
one of these two section-planes so as to make an angle
of about 35~ with the visual ray on either side of the
perpendicular.  In either situation a set of coloured
rings will be seen, not circular, but of an oval form,




ON LIGHT.                    395
about a common centre, and intersected, not by the two
arms of a black cross as in Iceland spar, but by one
vertical dark bar cutting centrally across them. This
dark bar is converted to a white one, and the colours
of all the rings changed to their complementary ones,
by turning the analyzing plate through go" in its plane.
(I70o.) In mica, the angular separation of the optic
axes is too large to allow both these sets of rings to be
seen at once, so as to examine the nature of their
mutual connexion.  In nitre however, in which it is
only about 5~ (within the crystal), this may be very conveniently done, by cutting from the clear transparent
portion of a large hexangular-prismatic crystal (such as
may always be found in searching over a lot of the
ordinary commercial saltpetre) a plate about a quarter
of an inch thick, perpendicular to the axis of the prism,
and polishing its faces. If this be placed between two
crossed tourmalines, and held up against the light, the
normal phenomenon of the biaxal rings will be seen in
its utmost perfection, as in fig. i7, the upright and horizontal lines in which indicate broad brushes as it were of
shadow, cutting across the system of ovals, and breaking
them up into four similar quadrants. If, retaining the
tourmalines in the same position, the nitre plate be
turned round in its own plane, this cross breaks up
into two curved arcs, as represented in fig. I8, corresponding to a movement through a quarter of a right
angle,-then, as in fig. I9, corresponding to 45~ of
change, and so on till after a quarter of a revolution
the original appearance of fig. 17 is restored. If the




396                   ON LIGHT.
tourmalines instead of being crossed, are laid parallel,
the forms of the ovals are the same, but the colours
complementary, and the  cross and curved branches
white.
(I7I.) The forms of these curves are governed by a
Fig.17.           Fig. 18-           Fig. x9.
very simple and elegant general law, common to all
biaxal crystals, and applicable to every angular separation of the axis: and when this separation is small, as
in the case before us, they may be regarded as " lemniscates," of which the property is this, that for every point
in the circumference of each oval the prodzuc (not as in
an ellipse the sum) of two lines drawn to the two centres
or foci, is invariable; and for successive ovals proceeding outwards from  either focus, these products increase
in regular arithmetical progression. When the two foci
coincide, that is to say, when the two axes of the crystal coalesce, and it becomes uniaxal, the ovals pass into




ON LIGHT.                    397
circles, and we fall back upon the circular rings and
cross proper to that class of bodies.
(172.) Neglecting the bending which the rays undergo
at their emergence from the posterior surface of the
crystal, or conceiving the eye as immersed within its
substance, it is evident that when looking in the direction of either of the foci of the ovals, the visual ray will
be directed along one of two axes, or lines of no double
refraction; while if looking towards any point in the
circumference of any one of the ovals, the visual ray will
traverse the crystal in such a direction that an ordinary
and extraordinary ray following that path shall gain or
lose on each other so many semi-undulations, or parts
of one, as shall correspond to the tint developed in that
direction; and that, therefore, in all the directions
marked out by the circumference of each individual
oval, the tints being the same, the phase-difference, and
therefore the difference of velocities of the interfering
rays, and therefore again, the amount of double refraction
in that direction is the same.  The forms of these ovals,
therefore, stand in immediate and intimate connexion
with the law of double refraction in such crystals, and
with the forms of the two wave surfaces belonging to the
ordinary and extraordinary rays. The theory of these
wave-surfaces belongs, however, to a higher department
of geometry than we could hope to make intelligible in
these pages.  Suffice it to say that as delivered by M.
Fresnel and his followers it explains all the facts in the
most complete and satisfactory manner, and has even
led to the prediction, antecedent to observation, of some




398                    ON LIGHT.
phrenomena so apparently paradoxical as to stand in
seeming  contradiction  with  all previous  optical experience; and which any one, antecedent to their verification by trial, would have pronounced impossible.'
(I73.) One highly important conclusion  from  this
theory must, however, be noticed. The directions within
the crystal of the two axes of double refraction or the
" optic axes" stand in no abstract geometrical relation to
those of the angles and edges of its " primitive form," or
to its axes of symmetry. They are resultant lines determined by the law of elasticity of the luminiferous ether
within its substance as related to its crystalline form, and
to the wave-length of the jparticular coloured ray transmitted.
They are' not, therefore, the same for all the coloured
rays. In the generality of biaxal crystals, the difference
of their situations and of the angle between the two, is
but small: but in some, as in the salt called Rochelle salt
(tartrate of soda and potash), it is very great, amounting
to at least Io~, by which the direction within the crystal
of either axis for the extreme red rays differs from that
for the extreme violet. t In this salt the variation in position of the optic axes progresses pretty uniformly in
passing from  a red to a violet illumination.  In Carbonate of lead, on the other hand, it varies slowly in
* This alludes to the phaenomena of what is called conical refraction, pointed out by the late Sir Wm. R. Hamilton, as a necessary consequence of Fresnel's theory, and demonstrated to exist as
a matter of fact, subsequently, by Dr Lloyd.
+ See a paper by the author of these pages in Phil. Trans., 1820,
" On the action of crystallized bodies on homogeneous light," where
the singular phenomena to which this gives rise are fully described.




ON LIGHT.                    399
passing from red to green, but with increasing and finally
with extreme rapidity in the passage thence to violet.
(I74.) It is time, however, to bring this long Lecture to
a conclusion. -To describe the variety of splendid and
singular phaenomena, developed in every department of
physical enquiry by the use of polarized light, not one
of which has hitherto afforded any, the smallest, ground
for doubt as to the applicability of the undulatory theory
to its complete explanation, would require volumes. We
would gladly have said something of the magnificent
phaenomena, exhibited by "macled" crystals,* and by
unannealed, or compressed glass; of the changes produced by change of temperature on the optical relations
of bodies, and of the calorific and chemical rays of the
spectrum; but our limits forbid it. Suffice it to add,
that what the telescope and the microscope effect for us
in the discovery of outward and visible form, the properties of light, and especially of polarized light, effect in
subjecting to our intellectual vision the intimate structure
of material bodies.  Within the compass of the smallest
visible atom they open out a world of wonders-a universe si genzeris, and for each atom of a different material
a different one-all, however, related and bound together
in one vast harmony.
* These may find a place elsewhere. The phenomena alluded
to have not, so far as I am aware, been hitherto described.




LECTURE IX
ON SENSORIAL VISION.*
ROM what I have understood respecting the
objects of this Institution, as one equally
addressing itself to the cultivation of Philosophy and Literature, I am led to believe
that the subject which I propose to bring before it, in
compliance with an invitation which I feel to be both
honourable and gratifying in no common degree, is one
not altogether foreign to them; inasmuch as the history
of vision has both a strictly scientific and a more abstract
and philosophical bearing; the one referring itself to
material, the other to mental science.  The one regards
only the means and adaptations by which we see, and the
other refers to the action of the mind itself in seeibg, that
is, in intepreli'tg the impressions produced on our visual
* This lecture was delivered before the Philosophical and Literary Society of Leeds, on the 30th September 1858, at the request
of that society.




ON SENSORIAL VISION.               40!
organs.  It is to this latter division of the subject that I
shall chiefly address myself, while taking the opportunity
thus kindly afforded me of putting on record certain
visual phenomena which I have from time to time noticed,
belonging to that obscure class of impressions which
may be termed Sensorial Vision-by which I mean visual
sensations or impressions bearing a certain considerable
resemblance to those of natural or retinal vision, but
which differ from these in the very marked particular
of arising when the eyes are closed and in complete
darkness.
(2.) Few persons, I suppose, are ignorant, as a matter
of personal experience, of the sort of appearances known
by the name of Ocular Spectra, which are produced by
the impression of a strong light on the retina of the eye,
and which continue to force themselves on the attention,
sometimes in a very pertinacious and disagreeable way
for some time afterwards, when the eyes are closed. In
one lamentable instance, that of an eminent Belgian
Philosopher, they have caused actual loss of sight; and
in that of Sir Isaac Newton, their obstinate recurrence is
said to have deprived him of sleep for several days and
nights successively, and to have driven him to the verge
of distraction.  These are cases when the stimulus of
light has been pushed to the extreme; but when moderate and regulated, these spectra admit of being studied:
and the laws of their production-the singular and beautiful. phases they pass through-their periodical extinction and renewal (which extend over a very considerable
interval of time from their first production), the orderly
2 C




402             ON SENSORIAL VISION.
recurrence of the colours they assume, which are peculiarly rich and various-the singular effects of gentle pressure on the eye, and partial light admitted through the
eyelids in modifying them or in renewing them when extinct-all these offer a subject of much attraction and
interest.  A very interesting memoir on them has been,
within these few  years, communicated to the Royal
Society, by Dr Scoresby; but the subject is far from
being exhausted, and it is to the habit of attention to
such sensorial impressions, fostered by frequently watching the development of these spectra under a variety of
circumstances in my own case, that I attribute my having
been led to notice that other class of phaenomena of
which I shall presently speak, and which from their inconspicuousness, I suppose, escape the notice of most
people.
(3.) The production of Ocular Spectra refers itself, I
presume, to what I have described as the purely physical
branch of the general subject of vision. Their seat, it
can hardly be doubted, is the retina itself,* and their
production is in all probability, part and parcel of that
photographic process by which light chemically affects
the retinal structure, and of the gradual restoration of
that structure to its normal state of sensitiveness by the
fading out of the picture impressed. Cases are not wanting in artificial photography where an impression made
* In speaking of the retina, I would not be understood to express
any opinion on the disputed question whether the rezina anatomically so called or the choroid coat of the eye be really the seat of
vision.




ON SENSORIAL VISION.                403
on sensitive paper dies out, and can be replaced by
another without the renewed application of any chemical
agent.
(4.) Thus considered, ocular spectra are quite as much
entitled to be considered as things actually seen, as the
retinal pictures of which they are the successors, or rather
remnants. It is quite otherwise with that other class of
visual impressions to which I now refer, and which differ
altogether from ocular spectra, not only in being for the
most part (though not always) much less vivid and much
more dreamy (if I may use the term without casting a
doubt on their reality as facts), but also in having no
reference or resemblance to any objects recently seen, or
even recently thought of. Of course, when I speak of
their reality as facts, I do so on the ground of their
admitting of being watched and studied with the same
sort of wide-awake attention which might be given to
any faint and fugitively-presented real object: though it
is no more possible to describe them  accurately, much
less to draw them, than it would be to do so in the case
of objects dimly seen in the dusk of evening, and capriciously appearing and disappearing. But this does not
preclude their being observed and described, pro tanto,
in general terms.
(5.) I fancy it is no very uncommon thing for persons in
the dark, and with their eyes closed, to see, or seem to
see, faces or landscapes.  I believe I am as little visionary as most people, but the former case very frequently
happens to myself.  The faces present themselves involuntarily, are always shadowy and indistinct in outline




404            ON SENSORIAL VISION.
-for the most part unpleasing, though not hideous; expressive of no violent emotions, and succeeding one
another at short intervals of time, as if melting into each
other.  Sometimes ten or a dozen appear in succession,
and have always, on each separate occasion, something of
a general resemblance of expression or some peculiarity
of feature common to all, though very various in individual
aspect and physiognomy. Landscapes present themselves
much more rarely but more distinctly, and on the few
occasions I remember, have been highly picturesque and
pleasing, with a certain but very limited power of varying them by an effort of the will, which is not the case
with the other sort of impressions.  Of course I now
speak of waking impressions, in health, and under no
kind of excitement.  When the two latter conditions are
absent, numerous instances are on record of both voluntary and involuntary impressions of this kind, and singular
as some of the facts related may appear, I am quite prepared, from my own experience on two several occasions,
to receive such accounts with much indulgence.
(6.) A great many years ago, when recovering from
fever, my chief amusement for two  or three  days
consisted in the exercise of a power of calling up
representations both  of scenes and  persons, which
appeared with almost the distinctness of reality. One
of these scenes I perfectly recollect.  A  crowd was
assembled round a hole in the ice, into which a youth
had fallen. His mother was standing in agony on the
brink, and there were the floating fragments and something of a shadowy form under the blue transparent ice.




ON SENSORIAL VISION.             405
In this case there was, of course, the excitability of nerve
connected with the remains of bodily disorder. On the
other occasion to which I allude, I had been witnessing
the demolition of a structure familiar to me from childhood, and with which many interesting associations were
connected: a demolition not unattended with danger to
the workmen employed, about whom I had felt very uncomfortable.  It happened to me at the approach of
evening, while, however, there was yet pretty good light,
to pass near the place where the day before it had stood;
the path I had to follow leading beside it.  Great was
my amazement to see it as if still standing-projected
against the dull sky. Being perfectly aware that it was a
mere nervous impression, I walked on, keeping my eyes
directed to it, and the perspective of the form and disposition of the parts appeared to change with the change
in the point of view as they would have done if real. I
ought to add, that nothing of the kind had ever occurred
to me before, or has occurred since. On this occasion,
no doubt, the daily habit of seeing the same object from
the same point of view for years would naturally give
great efficacy to the associative principle, and the fact
can only be regarded as an exemplification of a physiological process which I shall presently have occasion to
speak of more particularly.
(7.) But it is not to phenomena of this kind that I am
about specially to direct your attention. The human
features have nothing abstract in their forms, and they
are so intimately connected with our mental impressions
that the associative principle may very easily find, in




406             ON SENSORIAL VISION.
casual and irregular patches of unequal darkness, caused
by slight local pressure on the retina, the physiognomic
exponent of our mental state. Even landscape scenery,
to one habitually moved by the aspects of nature in association with feeling, may be considered as in the same
predicament.  There is nothing definite or structural in
its forms, which are arbitrary to any extent, and composed
of parts having no regular or symmetrical relations. It
is perfectly conceivable that the imagination may interpret forms, in themselves indefinite, as the conventional
expressions of realities not limited to precise rules of
form.  We all know how easy it is to imagine faces in
casual blots, or to see pictures in the fire.
(8.) But no such explanation applies to the class of
phzenomena now in question, which consist in the involuntary production of visual impressions, into which geometrical regularity of form enters as the leading character, and that, under circumstances which altogether preclude any explanation drawn from a possible regularity of
structure in the retina or the optic nerve.
(9.) I was sitting one morning very quietly at my breakfast-table doing nothing, and thinking of nothing, when
I was startled by a singular shadowy appearance at the
outside corner of the field of vision of the left eye.  It
gradually advanced into the field of view, and then appeared to be a pattern in straight-lined-angular forms,
very much in general aspect like the drawing of a fortification, with salient and re-entering angles, bastions, and
ravelins, with some suspicion of faint lines of colour between the dark lines.  The impression was very strong:




ON SENSORIAL VISION.                407
equally so with the eyes open or closed, and it appeared
to advance slowly from out of the corner till it spread all
over the visual area, and passed across to the right side,
where it disappeared.  I cannot say how long it lasted,
but it must have been a minute or two.  I was a little
alarmed, looking on it as the precursor of some disorder of
the eyes, but no ill consequence followed. Several years
afterwards the same thing again occurred, and I recognized, not indeed the same precise form, but the same
general character-the fortification outline, the dark and
bright lines, and the steady progressive advance from left
to right. I have mentioned this to several persons, but
have only met with one to whom it has occurred. This
was a lady of my acquaintance, who assured me that she
had often experienced a similar affection, and that it was
always followed by a violent headache, which was not
the case with me. In this case the regularity of the pattern was not great, but the lines were quite straight and
the angles sharp and well defined.  Had it remained
stationary, it might be assumed that the retina had a
structure corresponding to the figure; and that some
undue pressure might render that structure visible.  But
such an hypothesis is precluded by the gradual transit of
the lines over every part of the visual area.
(Io.) I come now to cases of perfect symmetry, and geometrical regularity. The most ordinary class of patterns
of this sort I find to be formed only in darkness, and if
the darkness be complete, equally with open as with
closed eyes.  The forms are not modified by slight pressure, but their degree of visibility is much and caprici



408            ON SENSORIAI VISION.
ously varied by that cause. They are very frequent. In
the great majority of instances the pattern presented is
that of a lattice work; the larger axes of the rhombs
being vertical. Sometimes, however, the larger axes are
horizontal. The lines are sometimes dark on a lighter
ground, and sometimes the reverse.  Occasionally at
their intersections appears a small, close, and apparently
complex piece of pattern work, but always too indistinctly seen to be well made out. The lattice pattern if
constant, and if always upright, might beexplained by
the habit of looking fixedly at a lattice window, with a
view to noting the order of succession of colours in the
Ocular Spectra, which this mode of viewing them shows
finely. Occasionally, however, the latticed pattern is
replaced by a rectangular one, and within the rectangles
occurs in some cases a filling in of a smaller lattice
pattern, or of a sort of lozenge of fillagree work, of which
it is impossible to seize the precise form, but which is
evidently the same in all the rectangles. Occasionally
too, but much more  rarely, complex  and  coloured
patterns like those of a carpet appear, but not of any
carpet remembered or lately seen, and in the two or
three instances when this has been the case, the pattern
has not remained constant, but has kept changing from
instant to instant, hardly giving time to apprehend its
symmetry and regularity before being replaced by another; that other, however, not being a sudden transition to something totally different, but rather a variation
on the former.
(I I.) Hitherto I have mentioned only rectilinear forms.




ON SENSORIAL VISION.              409
I come now to circular ones. Having had to submit to a
surgical operation, I was put under the blessed influence
of chloroform.  The indication by which I knew when
it had taken effect consisted in a kind of dazzle in the
eyes, immediately followed by the appearance of a very
beautiful and perfectly regular and symmetrical " Turkscap" pattern, formed by the mutual intersection of a
great number of circles outside of, and tangent to, a
central one. It lasted long enough for me steadily to
contemplate it so as to seize the full impression of its
perfect regularity, and to be aware of its consisting of
exceedingly delicate lines; which seemed, however, to be
not single but close assemblages of coloured lines not
unlike the delicate coloured fringes formed along the
shadows of objects by very minute pencils of light. The
whole exhibition lasted, so far as I could judge, hardly
more than a few seconds, and I should observe that I
never lost my consciousness of being awake, and in full
possession of my mind, though quite insensible to what
was going on.  I spoke, but the words I am told I uttered had no relation to what I know I meant to say.
(12.) After a considerable interval of time it became necessary to undergo another operation, which was also performed under chloroform, but this time the dose was less
powerful, or differently administered. Again the " Turkscap" pattern presented itself on the first impression,
which I watched with much curiosity, but it did not
seem quite complete, nor was it identical with the former.
In the intersections of the circles with each other, I
could perceive small lozenge-shaped forms or minute




410             ON SENSORIAL VISION.
patterns, but not clearly enough to make them well out.
On both these occasions the patterns were far more
lively and conspicuous than the dim and shadowy forms
before spoken of, and probably belong to quite a different class of phenomena.
(I3.) Since that time circular forms have presented themselves spontaneously, of the shadowy and obscure class,
on three occasions, one of them quite recently. On the
first of these, circular were combined with straight lines
forming a series of semicircular arches, supported by, or
rather prolonged beneath  into, tall slender vertical
columns, the whole like small wirework; mere lines,
and bright on a dark ground; while another series of
similar arches and uprights darker than the general
ground appeared, intersecting the former so as to have
the dark uprights just intermediate between the bright
ones of the first set. On the second occasion the pattern
consisted of a very slender and delicate circular hoop,
surrounded with a set of other circles of the same size,
exterior tangents to the central circle and to each other.
On the third, the whole visual area was covered with
separate circles, each having within it a four-sided
pattern of concave circular arcs.  All these phaenomena
were, however, much fainter than the chloroform exhibitions, and of the order of the lattice patterns.
(r4.) Now the question at once presents itself-What
are these Geometrical Spectra? and how, and in what
department of the bodily or mental economy do they
originate  They are evidently not dreams. The mind
is not dormant, but active and conscious of the direction




ON SENSORIAL VISION.              411
of its thoughts; while these things obtrude themselves
on notice, and, by calling attention to them, direct the
train of thought into a channel it would not have taken
of itself. Retinal impressions they can hardly be, for
what is to determine the incidence of pressure or the
arrival of vibrations from without upon a geometrically
devised pattern on the retinal surface, rather than on its
general ground. The effect of some cause in the nature
of pressure I on one occasion experienced, and it manifested itself quite differently, viz:-as an Ocular Spectrum, consisting in a round, deep purple, feebly luminous spot, dying gradually away into darkness at the
borders. It was not exactly in the middle of the visual
area, and was caused by no external light: for it was
perceived one morning immediately on waking in the
morning twilight, and with the face shaded from a direct
view of the window.
(I5.) It is quite clear that a regular geometrical pattern
cannot be suggested to the imagination by forms having
no regularity, however presented to it: so that the
explanation which in the other instances adduced might
have a certain plausibility, breaks down in these cases.
It may be said that the activity of the mind, which in
ordinary vision is excited by the stimulus of impressions
transmitted along the optic nerve, may in certain circumstances take the initiative, and propagate along the
nerve a stimulus, which, being conveyed to the retina,
may produce on it an impression analagous to that
which it receives from  light, only feebler, and which,
once produced, propagates by a reflex action the sensa



412             ON SENSORIAL VISION.
tion of visible form to the sensorium. Still, even granting that such reflex action is possible, and the retina is
so impressed, the question remains-Where does the
pattern itself or its prototype in the inzlelec originate 
certainly not in any action consciously exerted by the
mind, for both the particular pattern to be formed and
the time of its appearance are not merely beyond our
will and control, but beyond our knowledge. If it be
true that the conception of a regular geometrical pattern
implies the exercise of thought and intelligence, it would
almost seem that in such cases as those above adduced
we have evidence of a thought, an intelligence, working.
within our own organization distinct from that of our
own personality.  Perhaps it may be suggested that
there is a kaleidoscopic power in the sensorium to form
regular patterns by the symmetrical combination  of
casual elements, and most assuredly wonders may be
worked in this way.  But the question still recurs in
another form:   How is it that we are utterly unconscious of the possession of such a power; utterly unable
voluntarily to exert it; and only aware of its being exerted at times, and in a manner we have absolutely no
part in except as spectators of the exhibition of its
results?"
(16.) But again, it may be urged that the particular
geometrical forms presented are familiar ones, and are
not created or invented pro re nata, but simply old ones
reproduced-their reproduction being an act, not of
invention, but of memory.  But against this view of the
matter there appears to me to exist an insuperable objec



ON SENSORIAL VISION.              413
tion.  Memory does not produce its effect by creating
before the eyes a visible picture of the object remembered. When Hamlet says, " Methinks I see my father,"
we all know that the expression is a purely figurative
one, and have no need to be told, as in his reply to
Horatio's " Where l my lord," (a question perfectly
natural to one who had just seen his ghost and knew
not but that it might still be present), that it is to the
" mind's eye," a merely figurative and metaphorical eye,
and not to that of the body, that the expression applies.
The act of reminiscence is a conscious and a mental act,
and if, under the influence of powerful excitement and
strong associations it ever results in the production of
a visible picture by the sort of reflex action I have
described, it must precede such formation-or any how
not be itself called up by the picture of its own creation.
Of such cases whenever they occur (and I have related
what may be considered a case in point) the same
account is to be given as in that of certain eminent
painters, who are said to have declared that they see
upon the paper or the canvas the forms they are about
to delineate-a quasi-image being formed on the retina by
the sympathy of the nerve with the brain, and its impression delivered back to the sensorium as that of a reality.
(I7.) I ought perhaps to apologize for saying so much
about myself and my personal experiences in this line,
but the nature of the subject is such as to render this
inevitable; and it is one which can only be elucidated
by the individual putting on record his own personal
contrrbution to the stock of facts accumulating. And




414             ON SENSORIAL VISION.
having gone so far in this direction, I may perhaps be
borne with if I add one or two more observations of a
similar personal nature, which, though not bearing on
the subject hitherto spoken of, seem  to me not without
some interest as contributions to that mass of unaccountable.or difficultly explicable facts with which the history
of vision teems so abundantly.
(I8.) The first of these is one of constant occurrence
to myself in railway travelling. When looking out on a
sloping bank, the train going rapidly, if the sight be
directed fixedly out in one direction, all near objectsstones, grass tufts, &c.,-are of course seen as if drawn
out into horizontal lines. Now what I constantly perceive is the appearance of slender obscure lines like
dimly seen dark wires at regular intervals asunder, crossing those linear streaky images nearly at right angles,
and which always seem not to stand vertically up and
down, but as if they reclined backwards on the slope of
the bank.  I find it best to let the eyes take their own
focus without endeavouring to  adjust them  to any
object.
(I9.) It is generally taken for granted that to see any
object whatever, the best way is to look straight at it,
and get its image impressed on the centre of the retina.
This is certainly, however, not the case with a single
bright luminous point, if no brighter than a star of the
third or fourth magnitude, as any body may convince
himself by trying the experiment the first clear night.
When two such stars of equal magnitude, within a
degree or two of each other, are looked at, nothing is




ON SENSORIAL VISION.                415
easier than to make either of them  disappear as if
blotted out from the sky, by looking full and fixedly at
it, while the other remains conspicuously visible. In
this way I find stars of the second magnitude considerably enfeebled, though they cannot be made wholly to
disappear.  Those of the first are but little affected.  I
have found many persons incredulous on their first hearing of this fact, who yet have satisfied themselves by
trial of its reality.  I at one time believed that this
comparative insensibility of the centre of the retina
arose from  the greater wear and tear consequent on
directing the attention continually to it, and habitually
directing it to any more conspicuous object, but I find
that the same thing.happens to very young persons to
quite as great an extent-in whom, of course, this cause
of deterioration cannot have gone so far as in adults.
There is reason to believe moreover, that this comparative insensibility of the middle part of the retina to faint
impressions extends over a pretty considerable area, for I
find that in a room but feebly lighted, and with the back
to the light, it is possible by long looking fixedly inl the
direction of an object of considerable angular diameter,
gradually to lose sight of it, and at length entirely cease
to see it-and then, by an effort of the will, accompanied
with some kind of organic act in the eye itself, which I
know by sensation, but am unable to describe in words,
but which is not the action of adjusting the focus, it is
at once realized to sight, without any alteration of the
direction of the optic axis, or any motion given to the
head or person.  It is an experiment which will not




4I6            ON SENSORIAL VISION.
always succeed, and  requires a peculiar adjustment
of the light, and of the comparative illumination of the
objects and the ground on which it is seen projected,
and perhaps also a peculiar state of nerve; but when it
does succeed, the effect is exceedingly singular and
anomalous.
(20.) It would lead me into too great a length of detail,
and I may also add, into a labyrinth of metaphysical
considerations, out of which I should find some difficulty of getting disentangled, if I were to go into a discussion on those points of connexion between our
mental and our bodily organization which these facts
seem to suggest.  There is a very curious chapter in
Stuart Mill's Treatise on Logic, devoted to the question
whether we are quite sure that every event has a cause.
He decides it, as every reasonable man must do, in
favour of the universality of the proposition, but he is
compelled to admit, as every one who considers it
closely must, I think, equally do, that the phenomena
of the human will stand in a very peculiar relation to
that question; and that granting volition to be a cause
of action, and granting the entire freedom of our will and
its complete indzependenzce to choose when a choice of
lines of action is brought before us, there is still the
question behind-What determines the will? To this
question an answer must be found which will leave man
a moral and responsible agent.  To choose the right
and to avoid the wrong, as such, must be left in his
power, and a freedom and independence of choice as
between these two grand lines of action must be left




ON SENSORIAL VISION.                417
him, if we would not reduce him to a machine.  So far
then, and to this extent, I do not see how it is possible
not to recognize an original causation, or at least one
which it is morally, intellectually, and logically impossible for us to find an antecedent for by any power of
merely human inquiry.  But still there arises this other
and further question-What determines the will in cases
where a variety of modes of action exist; all, so far as
we can see, equally open to choice?   Mr Mill here
refers us to the associative principle; and refers the
moral position of the individual to the education or
early discipline of this associating principle, by which
it may be habituated  to suggest right and virtuous
courses of action among the many possible ones more
readily, more powerfully, and more suggestively (if one
may tautologize so far) than those of a contrary nature.
It is very evident that with the greatest rectitude of intention, if a course of action the most conducive to the
interests of good do not suggest itself, or be not suggested from without, the course actually adopted may
be one less so.  It is then to the suggestive principle,
whatever that be, and however it may act, that we must
look for much that is determinant and decisive of our
volition when carried out into action, even when the
choice has been made between right and wrong in the
abstract; and the "way in which thoughts come into
our minds" is part and parcel of the nature and mode
of action of that principle-if it be not merely another
form of words for the same thing.  Of course this is a
subject so obscure and so mysterious, that it is quite
2 D




418            ON SENSORIAL VISION.
out of the question to pretend to raise any theory-state
any doctrine-or'say anything in the least degree satisfactory, or on which any two opinions would agree,
about it. Still it strikes me as not by any means devoid
of interest, to contemplate cases where, in a matter so
entirely abstract, so completely devoid of any moral or
emotional bearing as the production of a geometrical
figure, we, as it were, seize upon that principle in the
very act, and in the performance of its office.
(21.) I will not, however, pursue this further, lest I get
bewildered myself and bewilder all who listen to me, and
it only remains for me to thank you for your patience
in listening to me so far, and to apologize once more
for dwelling upon my personal impressions.  There is
one thing more I would add-which is to congratulate
this town of Leeds on the existence within it of a society
of such a nature as that here assembled, and numbering among its members so many gentlemen of large and
liberal views, of extensive information and high acquirements, both scientific and literary-equally the ornaments of this their city, and of our common country.




LECTURE X.
THE YARD, THE PENDULUM, AND THE
METRE.
CONSIDERED IN REFERENCE TO THE CHOICE OF A
STANDARD OF LENGTH.*
HE attention of the public has of late been
strongly drawn to the subject of a proposed
alteration of our national system of weights
and measures, by the attempt made during
the last session of Parliament to carry through a bill,
having for its object the abolition of our existing system
in its entirety, and the introduction, in its place, of what
is known as the " French Metrical System."  The bill, it
is true, was withdrawn after passing the second reading
(by which the House, as is usually supposed, "affrmze
* This Lecture or Essay was communicated to the Leeds Astronomical Society, and read at a meeting of that Society on October 27,
1863.




420     THE YARD, PENDULUM, AND METRE.
bhe princzipe of the measure"), and it may therefore be
reasonably presumed that it will be brought forward
again in the next session, in the same or a modified
form.  As the discussion it received in the House
seemed to be in no respect commensurate with the immense importance and sweeping nature of the change
proposed, and with the exception of one or two rather
cursory notices in The Times, excited a marvellously
small amount of public interest pending its progress; it
will not be amiss if, being called upon by the committee
of the Leeds Astronomical Society for an exposition of
some point of general interest in the form of a Lecture
or Essay, to be read at one of their Evening Meetings,
I select this for its subject; and endeavour to place before you the several conditions which any standard or
typical unit of length which shall be assumed as the
basis of a system of measures and weights intended to
be national, and which may justly claim to be universal,
ought to fulfil; and to compare with these conditions,
in order to see how far they are fulfilled in fact, both
our actual standard, the French metre now in use, and
the length of the pendulum, which has been more than
once proposed as a natural unit of length. And this I
will endeavour to do in as elementary and familiar a
way as shall be consistent with perfect correctness.
Those of the present audience who are not already
familiar with the subject will thus be better enabled to
form an opinion as to the desirableness of the change
actually proposed, or of any legislative change in our
existing standard, and  in  our system  of measures,




THE YARD, PENDULUM, AND METRE.             421
weights, and coinage generally. And to such it will not
be amiss to observe in the outset that, the subject being
an exceedingly delicate and refined one, they must not
be surprised at seeing very minute quantities and very
small fractions treated as matters of much greater importance than they may have been accustomed to regard
them.
(2.) The general subject of a national system of weights
and measures, be it observed, divides itself into two very
distinct and separate points of inquiry, viz.: first, What
is intrinsically the best and most available unit of linear
measure to adopt as a basis: and, secondly, what system
of numerical multiplication and aliquot sub-division of
such unit for measures of length, and of its derivative
units of area, of capacity, and of weight (for these all
refer themselves naturally and easily to the unit of linear
measure, or at least ought to do so) is most advantageous-either in a great mercantile community like our
own, or for the great mass of mankind in the ordinary
transactions of life.  And it cannot be too strongly
impressed, and too perseveringly borne in mind, that
these two questions stand in no natural and necessary
relation to each other, but are perfectly independent.
We may resolve, with perfect logical consistency, either
to toss aside our present system  in toto, and adopt the
metrical one in preference; or to retain our fundamental
unit (the Imperial foot or yard), and decimalize our
system  of denominations; or, lastly, by a slight, and,
practically speaking, imperceptible change in our present
standard, to bring it into conformity with our views of




422     THE YARD, PENDULUM, AND METRE.
theoretical perfection (which, I shall show, may be
done).  We may, too, retaining, all the convenience of
our existing denominations (so far as t/ey are convenient)
superadd to them, by permissive legislation, the additional convenience of a decimal system for facility of
calculation: relying on its holding its ground if really
affording such facility, or working its way into general
use, and ultimately driving out the old system, if found
by the mass of the population to be practicably preferable. This last is the course I would myself prefer,
and I think it best to say so in the outset, lest those
who may take a contrary view should imagine a foregone
conclusion to be urged upon them under the semblance
of free inquiry.
(3.) It is unnecessary, of course, to observe that, the
measurement of length being required for almost every
purpose of construction as well as for every intelligible
statement of the sizes of material objects, the lengths
of journeys, the distances of places, &c.-renders indispensable the recognition, in every community, of some
common standard, some well-known and identifiable
unit, by whose repetition great, and by whose aliquot
subdivision small lengths, distances, sizes, &c., may be
expressed in words and numbers. The common sense
of mankind; moreover, would naturally point, in the
selection of such unit, to some object of common occurrence, of moderate linear dimension, and of which
individual exemplars differed but little, or, if possible,
not at all in this respect; so that appeal might at
once be made to such exemplar in case of a question




THE YARD, PENDULUM, AND METRE.            423
arising as to the length of any object stated to contain
a given number of such units or its aliquots. A very
moderate experience would however suffice to convince
anybody that among natural objects of the same kind,
even those most common, perfect identity of length, of
breadth, of thickness, any more than of weight, is never
observed-even a close approach to it rarely-and a
very close one extremely so. Still, with all drawbacks
so arising on the adoption of a natural standard, the first
rude demand for such a standard would be easily enough
satisfied, and that in two ways, viz.: ist, by actually
fixing upon some individual among all the existing objects of the sort selected, to the exclusion of others-or,
2dly, by the very natural, though somewhat more refined-conception of an ideal medium, or mean among a
very great multitude of such objects, such as might be
regarded as neither unusually great nor unusually little
ones of their kind.
(4.) Among objects of common  occurrence, the
human person, or some distinct member of it would be
most likely to claim the attention of mankind as affording a standard of' measure; if only for the very obvious
reason that the relation of the sizes of material objects
to that of man mainly determines his facility of handling, or otherwise applying them to human uses. Accordingly, the height of a full grown person, the length
of his arm, his fore-arm (ulna or ell), his foot, his
hand, his ordinary step, &c., would present, and is well
known to have presented itself among almost all communities of mankind to their choice for this purpose.




424     THE YARD, PENDULUM, AND METRE.
And so, among all nations whose measures have been
handed down to us, we find in speaking of the unit of
length, some members of the human person designated.
Thus, the bed of the gigantic king of Basan is related to
have measured eight cubits in length "after the cubit
(i.e., the fore-arm) of a man." The height of Goliath
the Philistine was " six cubits and a span."  The bow
of Pandarus, described by Homer, was formed of
the horns of an Ibex, which grew out sixteen jailms
(or hand-breadths) from  his head.  The  Romans
reckoned their distances by intervals of iooo paces
(miilia jassuium) whence our name for a mile, though
differing widely in reality. If, however, we may judge
from the great diversity in the actual lengths adopted
under the common name of " a foot" as the standards
of different nations, we shall see reason to believe that
the typical foot selected was usually that of an individual-some Chief, King, or High Priest, who could
claim pre-eminence among them as a man par excellence,
and who would seem to have been generally above the
average stature.  Thus we find the Roman foot equivalent to i r6 of our inches; the English to I2; the
Greek to I2'I; the French to I2,8; and the Egyptian
or "Drusian" to I31 —all of them  (especially the two
last) in excess of the real length of the foot of a wellproportioned man of medium  stature (say 5ft. Ioin.)
which does not exceed io{, or at the most iI inches.
(5.) Another class of objects, which, from the universality of their occurrence in vast numbers, and their
general uniformity of dimension, would naturally occur as




THE YARD, PENDULUM, AND METRE.             425
unit types, available for the measurement of small lengths,
or for the small aliquots of a larger unit, has been found in
the cereal grains of most common use, and of these, the
barley corn, and the rice grain, have found the preference.
Our inch, for instance, has been defined in an old statute
(now repealed) as the length of three grains of barley,
taken from the middle of the ear, and placed end to end.
And in a somewhat similar manner have been derived
from those cereals the smaller sub-divisions of the Hebrews and Hindoos; while the larger have, in these, as in
other nations, originated in parts of the human person.
(6.) It is very evident, however, that types of this kind
admit of no precise and rigorous identification or intercomparison.  The medium stature of a man is very different in different countries. That of an adult French
conscript for instance, is (or at least was in 1817) 5ft.
4in., as concluded from  the measurement of ioo,ooo individuals, while the Belgian type, or mean adult stature,
has been placed at 5ft. 7in. -8, and that of a Lancashire
non-manufacturing labourer, as high as 5ft. Io4in. So
great a discordance as a result of local and secondary
circumstances, is of course fatal to the pretensions of the
human person as a natural type. So again of the cereals.
The difference of soil, climate, and cultivation must produce, and does in fact produce very great variety in the
medium  size of grain grown in different countries, and
in different years: so that, even supposing, them to be
measured by millions, the mean results would be found to
differ too much for the object in view. And the same
kind of objection holds good against having recourse to




426     THE YARD, PENDULUM, AND METRE.
any kind of medium  magnitude, among multitudes of
objects of a like species which occur in nature. Such
must, of necessity, be chosen among organic structures
of the animal or vegetable kingdom  (for among inorganic masses of whatever kind, nature presents no instance of a mean or typical magnitude, as distinct from
the average of a number accidentally assembled, which
may differ to any extent from an average similarly taken
of an equal number elsewhere collected).  And among
the former classes of objects, even were it possible to assemble and measure them in sufficient numbers to afford
a true lypical mean, we should have no security for its
identity in different ages and climates.
(7.) We are driven then, in our choice of a universal
standard to the selection, either of some individual object, (if such there be) natural or artificial, imperishable
in its nature, unsusceptible of variation by lapse of time
or decay, and indestructible by accident-or else, to
some ideal or resultant length or magnitude (if such
there be), susceptible by its definition of being as it
were translated into a material expression, and marked
out as the result of some process which we are sure will,
in all ages and places reproduce the same identical
result.  And besides these qualities of invariability, indestructibility and identical reproducibility it ought to
possess some obvious claim to general acceptation as of
common interest to all mankind, or at least to all the
civilized portion of it: an interest from  which national
partialities and rivalries should be altogether excluded.
(8.) The individual human type is at once excluded




THE YARD, PENDULUM, AND METRE.           427
by these conditions. Supposing the foot of the most remarkable person who ever lived to be marked out on
steel or adamant, it would be at the mercy of fire, earthquake, loss in political convulsions, and a hundred other
forms of destruction or disappearance, without the possibility of reappeal to the original form.  Of human
works, the most permanent, no doubt, and the most imposing as well as generally interesting and respected, are
those mighty monumental structures which have been
erected as if for the purpose of defying the powers of
elementary change. Take the vastest of them-that to
which appeal has been often made for this very purpose
-the great pyramid of Cheops. When built it was 481
ft. in height, and the square area of its base was 764 ft.
in the side. The height is now only 451 ft. and the side
of the base only 746; and the sole means by which we
are now enabled to determine the original height consists
in a block of the exterior marble casing which will in
all probability disappear in the hands of " the curious"
within the next century. Nature presents to us but one
material object which combines all the requisites enumerated, and combines them all in perfection-viz.: the
globe itself that we inhabit. And in that globe we find
only two naturally-defined lengths which unite the requisites of individuality to identify them under every
change of human relations and even of geological revolutions and catastrophes, and of universality, so as to
stand in the same relation to both hemispheres and to
all meridians-viz.: the earth's polar axis, and its
equatorial circumference. For the latter, the equatorial




428     THE YARD, PENDULUM, AND METRE.
diameter might be more advantageously substituted: but
that we have good reason to believe the equator to be
not strictly circular, but in some degree elliptic, the proportion of its greatest and least diameters not being yet
precisely known, though very much nearer to equality
than that of the equatorial and polar diameters. This
however would not prevent its mean equatorial diameter
from being assumed in preference to its circumference,
were not the polar axis, for very obvious reasons, preferable to both.  Of the latter, and indeed of all three
(thanks to the elaborate geodesical surveys which have
been made within the century last elapsed), we possess
a knowledge so precise as to render them perfectly available for our purpose.
(g.) Of lengths which exist not marked by the dimensions of any material object, but which are defined by
the nature of things and by physical relations, and which
are susceptible of exact determination and of being
marked off on a scale, and so of becoming materialized
for practical reference; there have been proposed only
three which can be considered theoretically, and of these
only one practically available. These are, ist, the velocity of light or the space travelled over by light in some
definite time (say the ten-millionth part of a second,
which would give a modulus of about ioo feet); 2dly,
the length of an undulation of a ray of light of some
definite refrangibility-a length so minute as to require
multiplication a million-fold to give a modular unit; and
3dly, the length of a pendulum vibrating seconds under
certain definite and normal circumstances-or rather




THE YARD, PENDULUM, AND METRE.             429
that of an ideal seconds-pendulm supposed to be placed
at the extremity of the earth's polar axis.  To this is
in effect equivalent, and derivable from it, as a mere
arithmetical conclusion, the space fallen through by a
heavy body on the same place by the earth's attraction
in a second of time.  The modulus so obtained is therefore a measure of the earth's total attractive power (independent of centrifugal fcrce arising from its rotation),
as that derived from the length of its diameter is of its
total bulk, and equally unalterable and universal.  As
for the other two which depend on the nature of light,
the difficulty and delicacy of the processes they would
involve render all idea of resorting to either of them
purely visionary.
(io.) The linear dimensions of the earth then, on the
one hand, and the linear measure of its attractive force
embodied in the pendulum on the other, are the two,
and, so far as we can see, the only two available sources
of the invariable and universal standard length which
we seek.  And it is curious to observe that while the
French after considering both of them  threw aside the
pendulum in favour of the metre (or ten millionth of the
meridian quadrant); the English on the other hand, by
the Act of Parliament in I824, which repealed the old
statute already alluded to (and so threw  aside the
principle of resorting to an organic type) did in effect,
at that time, adopt the pendulum as their ultimate resort.
For while that act declares that a certain metallic bar
made by Bird in I760 when at the temperature of 62
Fahr. should, without any further reference to its origin,




430     THE YARD, PENDULUM, AND METRE.
be considered the standard yard of the British empire,
it provided for its recovery and reproduction in case of
the total destruction or loss of it and all its authentic
copies and facsimiles, by a declaration that its length is
36 inches, such that 39'I3929 of them are equal to the
length of a pendulum vibrating seconds in vaczuo and at
the sea-level, in the latitude of London. The report of
the French commissioners also in 1798 which led to the
enactment of the metrical system, is careful to state that
in the event of the total loss or destruction of all
material representatives of the metre its value would be
easily recoverable from a numerically specified relation
between its length and that of the pendulum vibrating
seconds at Paris, which had been determined with great
accuracy by Borda, one of the commissioners.  So that,
practically speaking, in the event of the total destruction,
by political convulsions, of every authentic yard and
metre (supposing any written record of our existing
knowledge to survive them) the metre would have been
recovered, not by the laborious and costly process
of remeasuring the French meridian arc, but by the infinitely more summary one of a precise repetition of
Borda's experiments and the exact re-application of all
his corrections and reductions.
(i.) For the reproduction of the English yard, a similar repetition of those experiments in London which led
to the adoption of the number 3913929 in. as the measure of the pendulum would, in such an event, no doubt
have been, at that epoch, resorted to; though in departure from the wording of the act, which speaks of a




THE YARD, PENDULUM, AND METRE.            431
pendulum vibrating seconds, not at but in the latitude of
London: a very different thing, as General Sabine has
pointed out in his "Account of Experiments to determine
thefigure of the Earth by means of a Pendulum vibrating
Seconds in different latitudes."  For the object would have
been then, as it really was on the occasion of the actual
destruction of the parliamentary standard in I834, not
to produce a theoretically better, but as far as possible to
reproduce the same identical length by the most summary
process; without undertaking circumnavigatory voyages,
or entering on any theoretical discussion. The new act
necessary for legalizing the standard so arising would
probably have sanctioned this procedure, and we should
have thenceforward had a standard of a purely local
character, assuming for the fundamental basis the individual seconds pendulum in London.
(12.) This, however, is not now the case.  On the destruction of the standard of 1760 by the burning of the
Houses of Parliament, the new standard was constructed,
not by any measurement of the length of the pendulum
(for in the ten years elapsed since I826 very grave
doubts had been raised, or rather very serious sources
of error pointed out in the processes used for the purpose on the former occasion)-but, by an assemblage
and most careful comparison of all the scales and standards of any authority which could be got together-resulting in the production of one primary and a great
many secondary standards, in all human probability absolutely identical with that destroyed. The act, moreover, (of 1855) which constituted that one our legal yard,




432      THE YARD, PENDULUM, AND METRE.
and named the others in a certain order as its successors
in the event of its destruction or loss, omitted the clause
identifying its length with any numerical multiple of the
pendulum.  In fact, then, our yard is a purely individual
material object, multiplied and perpetuated by careful
copying; and from which all reference to a natural origin
is studiously excluded, as much as if it had dropped
from the clouds. Apart, then, from the extraordinary
pains taken in its construction, and from the singularly
fortunate but at the same time purely accidental coincidence which I shall presently mention, it has no pretensions whatever to be regarded as a scientific unit.
(13.) Let us now consider the claim which the pendulum, in the abstract, as a measure of the earth's gravitation, can advance for its reception as a fundamental
and universal standard of length (and here, incidentally
it may be remarked that, as a lengzth, it is not more inconvenient than the metre, being within about a quarter of
an inch the same).*  One of the reasons assigned by the
French Savans for their rejection of it in favour of the
metre, and, as  would  appear, the  only one which
weighed with them  (for their other reason ostensibly
advanced is a mere appeal to the political passions of the
time) was the dependence of the length of the pendulum
* The metre has this inconvenience, as compared with the yard
-that while the latter can be readily extemporized by a man ot
ordinary stature (and often is so in practice) by holding the end of a
string or ribband between the finger and thumb of one hand at the
full length of the arm extended horizontally sideways, and marking
the point which can be brought to touch the centre of the lips
(facing full in front); the former is considerably too long to afford
the same facility.




THE YARD, PENDULUM, AND METRE.            433
on the time of its vibration; as if the 86,400th part of a
day which we call a second of time were not as definite
and as invariable a quantity as the Ioo,oooth part which,
in their rage for decimalization, they proposed to call
one; and as if they might not have fixed on a pendulum
vibrating Ioo,ooo times in a day (which would have given
a very near approach to our yard). But their stumblingblock was the introduction of an extraneous element,
time, at all, into the subject: as if the length of the
day were not as much an invariable, universal, and
physical element as the dimensions of the earth or its
gravitation. But in this they seem to have overlooked
the fact that their adoption of the quadrant of a meridian
for the base of their system does really admit this extraneous element, time, into that system, though in a much
more insidious way.  For the total bulk or mean radius
and the total mass or gravitating energy of the earth
remaining the same, the ellipticity of its meridians, and
therefore their absolute length, depends on the period
of its rotation or the length of the day. The same ob.
jection, to besure, if it be one, would equally apply to
the adoption of the polar axis, or the equatorial diameter
of the earth; and the only way to exclude all ideas of
time and force from a metrical system, and render it
pfurely metrical, i.e., dependent on geometrical magnitude
alone, would be to take for a fundamental unit the
radius, diameter, or circumference of a sphere, or the
side of a cube, equal in volume to that of the earth.
And perhaps were a tabula rasa made; were the
ground totally unoccupied and the whole matter to do
2E




434     THE YARD, PENDULUM, AND METRE.
over again, this would be as good a unit as could be
proposed.
(I4.) But the true objection to the choice of the pendulum for a universal unit of measure lies, not in any
metaphysical and abstract considerations of this kind;
but in the uncertainty which prevails, and must necessarily always prevail as to the true length of that normal
or ideal pendulum which shall stand equally related to
the whole globe, and from which the mean length corresponding to any assigned latitude can be calculated:
that is to say, the length of a pendulum which would
swing seconds at the pole of the terrestrial spheroidan uncertainty which, as I shall proceed to show, must
affect the result of every attempt to deduce it with the
precision the subject requires from experiments made on
the surface of our planet: however refined the methods
employed, and however numerous and diversified the
geographical stations at which they may be instituted.
(I5.) In practice, the mean length of the polar or
equatorial pendulum is concluded from an assemblage ot
the observations of the times of oscillation of one and
the same invariable pendulum  at a multitude of geographical stations in all accessible latitudes in both
hemispheres: no two combinations agreeing in giving
the same precise length, by reason of the local deviations
of the intensity of gravity due to the nature of the soil,
and the configuration of the ground immediatety beneath
and around the places of observation..Now, since the
pendulum  cannot be observed at sea, the whole seacovered surface of the globe is of necessity excluded




THE YARD, PENDULUM, AND METRE.             435
from furnishing its quota of observations to the final or
mean conclusion.  And the influence of this, it should
be observed, is not self-compensating as that of local
inequalities of mere density on land would be, but tells
all in one direction. For water being, on the average,
not more than one-third the weight of an equal bulk of
land (such land as the earth's surface consists of) and
only P2- of the mean density of the globe, the force of
gravity at the surface of the sea is less than at the sealevel on land by the attractive force of as much material
taken at twice the specific gravity of water, or at -~ths
that of the globe, as would be required to raise the bottom  to the surface.  Supposing then the difficulty of
observing the pendulum  at sea overcome, and that the
whole surface of the globe were dotted over with stations
of observation equally distributed over sea and land,
from whose intercomparison it were required to derive
the mean co-efficient of terrestrial gravitation, or the mean
length of the polar pendulum; it is evident that the sea
stations would everywhere conspire to give a less result
than the land.  According to Dr Young (Phil. Trans.,
vol. cix., page 93) the attraction of an extensive flat
mass of any thickness on a point in the middle of its
surface is three times that of a sphere of the same materials having that thickness for its diameter. And from
this it is very easy to conclude that, supposing the sea to
have a mean depth of four miles (which seems not improbable) the mean defalcation of gravity at its surface,
due to the deficiency of attracting matter, would be three
times the attraction of a sphere four miles in diameter




436     TfTE YARD, PENDULUM, AND METRE.
and A-lths of the earth's mean density-that is by a
simple calculation — i-, or rather less than one i8ooth
part of the whole attraction of the earth-a fraction far
too large, as well as far too uncertain in its amount
either at any given spot or in general, not to vitiate irremediably any conclusion as to the ultimate result of the
operation.
(I6.) Similarly, if we look to the reductions to the
sea level necessary for stations in the interior of continents, we shall find that they depend, partly on the
diminution of gravity due to the height above the sealevel, or to the increase of distance from  the earth's
centre, which always tells in diminiution of gravity; and
partly on the protuberant matter, be it mountain or
elevated table-land immediately beneath and around the
pendulum, which always tells in favour of increased gravitation.  The former portion is rigorously calculable, and
therefore need not trouble us, but the latter is in an extreme degree uncertain in particular localities, and in a
general estimate falls very short of compensating for the
sea-deficiency.  For the mean height of the European
continent is only 1342 feet; of Asia 2274; of North
America 1496; and of South America, 2302.  The
mean is i840 feet, or rather more than a third of a
mile, wl;ich, on the same principle of reckoning, would
be equivalent to about T-.oth part only of the total
gravity, which has to be reduced to one-third of its
amount, or to I-45oooth, inasmuch as the proportion of
land to water over the whole globe is only that of 5 I to
T46, or about I to 3.  This is the mean effect of the




THE YARD, PENDULUM, AND METRE.            437
elevated matter to increase gravitation.  That of mere
elevation above the sea-level to the height of - of a mile
(similarly reduced) is, however, one 36oooth in the opposite direction, or to diminish it-and the difference or
one i8o,ooo of the whole is effective not to compensate
but to add to the sea-deficiency.
(I7.) To obtain the real length of the normal pendulum then we must go out of our own globe, and ascertain the true co-efficient of gravity from astronomical
facts; and, as the only one available for the purpose,
compute the distance fallen through by the moon in a
second of time towards. the earth from a tangent to her
orbit. This, it is evident, is independent of the influence
of those local inequalities which affect the pendulum
measurements. But, on the other hand, it must be remembered-ist, That our knowledge of the distance in
question depends on our previous knowledge of the
moon's distance, which, in its turn, depends on that of
the earth's diameter, and therefore presupposes the
metre to be accurately known.  For any aliquot error in
the metre will produce an equal aliquot error in the
moon's distance estimated in metres, and therefore also
in the linear deflection per second from the tangent to
the orbit. 2d, That this linear deflection, or approach
of the moon to the earth in one second of time, is the
result of the joint attraction of the earth on the moon
and of the moon on the earth, and is in effect the sum of
the spaces fallen through by the moon towards their com-,mon centre of gravity, in virtue of the earth's attraction,
and by the earth towards that point in virtue of the




438     THE YARD, PENDULUM, AND METRE.
moon's.  Now the mass of the moon is about one 88th
part of that of the earth, so that one 88th part of the force
that draws them together is due to the moon.  By so
much then must the space fallen through be diminished,
to get that due to the earth's alone.  Suppose, now, that
the moon's mass assumed should be in error by a 5oth
part of its whole amount -(and Laplace's estimate of it
differs by as much from that at present received)-and
we shall find ourselves landed, from this cause of uncertainty alone, in an error to the extent of nearly one
4oooth of the quantity sought.
(18.) Lastly, our knowledge of the moon's mass is
mainly derived from its effect in producing the phaenomenon of nutation, which it does through the medium of
the earth's ellipticity, so that not only the dimensions,
but the figure of the earth are thus mixed up in our
attempt to derive the length-of the normal pendulum from
the moon's motion.
(I9.) I cannot but consider then that the uncertainty
of the one mode of obtaining the length of the normal
pendulum, and the non-independence of the other, unfit
it for being received as the ultimate scientific basis of a
universal standard; whatever merit it may possess in an
abstract and metaphysical point of view-and that the
true and only practical use of the pendulum in relation
to such a standard is the ready, cheap, and perfectly unobjectionable means its measurement, at a determinate
spot and under defined circumstances, affords of recovering it when lost, by the recorded statement of its length
in terms of such standard.




THE YARD, PENDULUM, AND METRE.             439
(20.) The causes of uncertainty which tell with such
very appretiable effect on the local determination of
the force of gravity by the pendulum, have little or no
influence on the local curvature of the surface of equilibrium, and absolutely none on the measures of large
arcs of the meridian. Suppose, for example, a sea of
four miles in depth, and of great extent, to cover one
part of the earth's surface.  Its surface water will gravitate less by one i8ooth part of its proper weight, owing
to the deficiency of attracting matter below it; and, the
diminution of gravity growing less and less in descending (being proportional to the height of a particle above
the bottom), the whole weight of the column of water
vertically above a given spot will be diminished by one
36ooth part, so that to maintain the equilibrium, one
36ooth part of four miles, or one gooth of a mile, i.e.,
about six feet of additional water, must be heaped on: a
mere infinitesimal of the radius of curvature of its surface,
which is that of the earth itself.
(2I.) Let us now see how far the French metre, as it
stands, fulfils the requirements of scientific and ideal
perfection.  It professes to be the io,ooo,oooth part of
the quadrant of the meridian passing through France
from Dunkirk to Formentera, and is therefore, scientifically speaking, a local and national, and not a universal
measure.  The earth's equator is not a perfect circle,
but slightly elliptic, and the meridians of'places differing in longitude are therefore not all of the same length.
The difference, however, is so trifling (the ellipticity of
its equator being not more than a thirtieth part of that




440     THE YARD, PENDULUM, AND METRE.
of its meridian) that to raise an objection against the
practical reception of the metre, eitherperse, or as a substitute for the yard, on this score, would savour of hypercriticism.  A more serious objection is the choice made
of the circumference of the meridional or generating
ellipse of the terrestrial spheroid in preference to its
axis of revolution. This is a blemish on the very face
of the system —a sin  against geometrical simplicity.
Still, were the length of the metre as determined by the
French geometers rigorously exact, or correct within
limits which the much more extensive measurements of
meridian arcs since made elsewhere than in France have
proved to be attainable, this would be only a matter of regret, and could hardly, of itself, be drawn into an argument
for its rejection.  But this is far from  being really the
case. The metre, as represented by the material standard adopted as its representative, is too short by a
sensible and measurable quantity, though one which
certainly might be easily corrected.  To show this it
will be necessary to enter into some detail.
(22.) In effect, that standard is declared, in the Annuary of the Bureau des Longitudes, to be equal to
39'37079 British imperial standard inches.  The quadrant of the French meridian then ought, if this be correct,
to be 393,707,900 such inches, or 32,808,992 feet. And
by whatever aliquot part of its whole length the true
quadrant exceeds this, by that same aliquot of its length
is the metre, so stated, erroneous.
(23.) Mr Airy, by a combination of the whole series of
meridian arcs whose measures had been obtained in




THE YARD, PENDULUM, AND METRE.               441
every part of the globe in 1830, was led to conclude for
the value of the minor or polar axis of the terrestrial
spheroid, 4I,707,620 feet; while the late Professor Bessel,
pursuing a course similar in its general principle-that is
to say, using all the measured arcs, great and small, in
combination  one with another, and taking the most
probable mean among the (necessarily) discordant results,
obtained by combining them two and two-arrived at a
value very slightly different, viz., 4I,707,3I4 feet. The
mean of these gives, as the result of this mode of procedure, 4I,707,467.
(24.) Quite recently, M. Schubert in a very elaborate
memoir which appears as part of the ist vol., 7th series,
of the Memoirs of the Petersburg Academy, has pointed
out the inconvenience, and necessarily discordant results
which the combination by pairs of a multitude of small
arcs, each  of itself insufficient to afford  any precise
measure of the ellipticity, affords; and assigned his reasons for restricting the inquiry in the first instance into
the length of the polar axis, as an element unique in
itself, and common to all the meridians: deducing it
separately from each of the most extensive arcs, the Russian, the Indian, and the French, each taken independently;-comparing  the three values so obtained, and
thence concluding the final result. In this manner he
obtains the following three values of the axis, viz.:From the Russian arc (of 25) 20' in extent) 4I,71I,oI9'2 feet.
Indian,, (of I~ 2I',,  ) 41,712,534'2feet.,,   French,, (of I2~ 22',,  ) 4,697,496'4feet.
In concluding for these a mean, or final value, M.




442      THE YARD, PENDULUM, AND METRE.
Schubert however, arbitrarily, and as I think quite indefensibly, rejects altogether the result of the French arc,
and assigns to the Russian double the weight of the
Indian; a mode of precedure in which he will find, I
presume, few to agree with him. A much fairer, indeed
the only fair way to treat them, is obviously to ascribe to
each of the separate results in taking the mean, a
weight proportional to the total extent of the arc, and
this gives for the length of the axis 41,708,70'o0 feet.
Comparing then the final results of the two modes of
procedure we find,
From  the former,.............................  41,707,467 feet.
And from  the latter,........................... 41,708,7I0,,
which differ only by I243 feet, or less than I of a mileso that their mean or 4I,708,088'5 f. is in all probability
within a furlong, or one part in 64,000 of the truth.
(25.) From each of the great arcs of Russia and India,
M. Schubert then obtains a separate value of the equatorial or the larger axis of the elliptic meridian to which
it belongs; and by a similar treatment of the arc of Peru,
which, lying under the equator, is especially favourable
for the purpose, he obtains a third value of the equatorial diameter.  The three diameters of the equatorial
ellipse thus obtained, with the angles they include at the
centre (which are the differences of longitude of the respective meridians, and which are as favourably arranged
for the purpose as the nature of the case seems to admit),
suffice for the determination of the major and minor axis
of the equator, regarded as an ellipse, and the longitudes
in which they lie, viz.:



THE YARD, PENDULUM, AND METRE.                443
Axis major = 41,854,800 feet, in long. 380 44' E. from
Paris (one end falling about half-way between Mount
Kenia and the east coast of Africa, the other in the
middle of the Pacific Ocean).
Axis minor - 4i,850,007 feet, in long. 128~ 44' E. from
Paris (one end falling on Waygiou, one of the Molucca
Islands, and the other at the mouth of the Amazon
River), giving an ellipticity of one 888oth, or about onethirtieth part of that of the meridians as already stated.
(26.) The figure of the equator, and its dimensions
thus obtained, the exact equatorial diameter corresponding to any given longitude is easily calculated. And by
comparing this with the polar axis, the precise ellipticity
of the meridian for that longitude may be computed.
And executing this computation for Paris, M. Schubert
finds 2i-  for the ellipticity of the French meridian.
(27.) With these data, viz., a Polar axis of 41,708,088
feet, and an ellipticity of -.h-  which certainly may lay
claim  to greater precision  than  anything previously
obtained, I shall now proceed to calculate the true length
of the quadrant of the French meridian, for which purpose the following very simple and convenient formula
may be used,* viz.:Q(-=     A (I + 2n + 9gm2 + 38m3)
* For the present purpose it is necessary to carry out the calculation to the cube of the ellipticity-but in cases where the
square of that fraction may be neglected, the following simple rule
for finding the circumference of an ellipse is worth remembering.
On the longer axis of the ellipse describe a circle, and between this
and the ellipse, describe a small circle having its centre in the prolongation of the minor axis, and touching the ellipse externally, and,




444      THE YARD, PENDULUM. AND METRE.
in which Q  represents the length of the quadrant required, A that of the polar axis, -r the circumference of
a circle whose diameter is i, and m, one fourth part
of the fraction  expressing  the ellipticity, or in  this
case -a.
Executing the calculation the result is...32,813,000 feet.
Substract o,000,000ooo metres -  32,808,992
Remain, excess...............    4,008
for the excess of the true quadrant over that assumed
as the basis of the metrical system, that is to say, one
8194 aliquot part of the whole, or one 2o8th of an inch
on the whole metre, which is therefore the quantity by
which the French standard is actually too short.
(28.) It must.not be denied that this is a very wonderful approximation, and in the highest degree creditable
to the science, skill, and devotion of the French astronomers and geometricians who carried on their operations
under every difficulty, and at the hazard of their lives in
the midst of the greatest political convulsion of modern
times.   And adopted as it is over a large portion of
Europe; were the question an open one what standard a
new nation, unprovided with one, unfettered by usages
of any  sort, and in the absence of any knowledge
of the existence of the British yard, should select; there
could be no hesitation as to its adoption (with that very
slight correction above pointed out-which would in no
the circumscribed circle internally. The circumference of this small
circle is the difference between those of the ellipse and of the larger
or circumscribing circle.




THE YARD, PENDULUM, AND METRE.             445
way interfere with its practical use-a correction which
the French themselves might, under such circumstances,
consent to adopt).  But the question now  arising is
quite another thing, viz.: whether we are to throw overboard an existing, established, and, so to speak, ingrained
system-adopt the metre as it stands, for our standard
-adopt moreover its decimal sub-divisions, and carry
out the change into all its train of consequences; to
the rejection of our entire system of weights, measures,
and coins. If we adopt the metre we cannot stop short
of this.  It would be a standing reproach and anomaly
-a change for changing's sake.  The change, if we
make it, must be complete and thorough.  And this in
the face of the fact that England is beyond all question
the nation whose commercial relations, both internal and
external, are the greatest in the world, and that the
British system of measures is received and used, not only
throughout the whole British empire (for the Indian
"Hath" or revenue standard is defined by law to be IS
British imperial inches) but throughout the whole North
American continent, and (so far as the measure of length
is concerned) also throughout the Russian empire; the
standard unit of which, the Sagene, is declared by an
imperial ukase to contain exactly seven British imperial
feet, and the Archine and Vershock precise fractions
of the Sagene.  Taking  comrrerce, population, and
area of soil then into account, there would seemn to be
far better reason for our continental neighbours to
conform to our linear unit could it advance the same,
or a better a priori claim, than for the move to, conme




446      THE YARD, PENDULUM, AND METRE.
from our side.  (I say nothing at present of decimalization).
(29.) Let us see then how this part of the matter stands.
Taking the polar axis of the earth as the best unit of
dimension which  the terrestrial spheroid  affords  (a
better a priori unit* than that of the metrical system) we
have seen that it consists of 41,708,088 imperial feetwhich, reduced to inches, is 500,497,056 imperial inches.
Now  this differs only by 2944 inches, or by 82 yards
from 500,500,000 (five hundred million and five hundred
thousand) such inches-and this would be the whole error
on a length of 8000 miles which would arise from the
adoption of this precise round number of inches for its
length, or from making the inch, so defined, our fundamental unit of length.  Suppose, then, that any length
were proposed  in English measure, and we desire to
know  what decimal fraction such length were of the
earth's axis. We have only to express it in inches and
decimals, and from  the number so stated take off its
thousandth part (a calculation involving only the writing
down the number twice over, removing the figures of the
* A writer in Quesneville's Moniteur Scienltfique, No. I63, v. 736,
argues that itinerary measures ought to be based on the circunference of the globe and not on its axis —by reason that the decimal
principle of sub-division, if carried out, would apply to the decimal
graduation of the quadrant-adding that "the greatest advantage
of the French system is in reality its decimal division"-butforgetting to add that the decimal division of the quadrant was introduced in France, but waus abandoned by common consent even in
France, and can never be reintroduced. In the " Mondes " (Suppl.
38, p. 6i6) the same argument is advanced, and the same answer
applies.




THE YARD, PENDULUM, AND METRE.                447
under line three places to the right and subtracting), and
the thing is done, and vice versas.* Suppose now the
same length  stated in French metres, and we would
ascertain what decimal fraction it is of a quadrant of the
French meridian.  The number of metres assigned must
be divided by 8I94 either by a long division sum or by
the use of a table, before the proper number to be subtracted can be found.  Which then is the shorter process? and which, both scientifically and practically, the
preferable unit?
(30.) If we are to legislate at all on the subject then,
the enactment ought to be to increase our present standard yard (and of course all its multiples and submultiples)
by one precise thousandth part of their present lengths,
and we should then be in possession of a system  of
linear measure the purest and most ideally perfect imaginable.  The change, so far as relates to any practical transaction, commercial, engineering, or architectural,
would be absolutely unfelt, as there is no contract for
work even on the largest scale, and no question  of
ordinary mercantile profit or loss, in which oneper milke
in measure or il coin would create the smallest difficulty.
Neither could it be doubted that our example would be
* Strictly speaking for the conversion and reconversion we should
szutract one 999th and add one Ioooth. But the difference is only
one part in a million which can never be of the slightest importance.
Per contra the conversion of the metre according to the process here
stated leads to a result which, though exact in par s of the Frelnch
meridian, is erroneous in parts of the mnean terrestr.al meridian by
a considerably larger proportional part, and this is whliat we really
want to know.




448     THE YARD, PENDULUM, AND METRE.
very speedily followed both in America and Russia, so
soon as the reason of the thing and the trifling amount
of the change came to be understood.  And even without legislation the relation between the proposed new or
geometrical measure and the imperial ones is so simple
and striking- fixing itself so easily in the memory, and the
conversion from one to the other so ready, that, were
there no other reason, it might almost be questioned
whether it would be worth while to make the change.
(31.) But there is another reason, and I think a decisive
one.  Hitherto I have said nothing about our weights
and measures of capacity. Now, as they stand at present nothing can be more clumsy and awkward than the
numerical connexion between these and our unit of
length. A grain is defined as the weight of distilled
water, so that 252'724 of such grains at the freezing
temperature, or 252-46 at that of 62~ Fahr. which is the
standard temperature of our imperial yard, shall fill a
cubic inch. Of such grains, so defined, the pound contains 7000, the ounce 437, and the gallon of water at
62n, 70,ooo. According to this system, the cubic foot of
water at our standard temperature weighs 997'I45 oz.,
falling short of Iooo oz. by very nearly 3 oz. However
tempting this approximation might appear, still, in the
absence of any more cogent reason, the commissioners
who recommended our system of weights and measures
legalized in 1824 forbore to recommend such a change
in the ounce (about i~ grain) as would have brought it
about; though the rule that a cubic foot of water weighs
Iooo ounces is still handed down as a rough and ready




THE YARD, PENDULUM, AND METRE.    449
way of converting cubic measure into weight.  But were
we to adopt thegeometrical instead of the present imperial
standard-the linear foot being increased by one thousandth, the cubic foot would be increased by three times
that aliquot, or would become'1003 times our present
cubic foot —and so would make up just the deficient
three ounces, or at least so very nearly that a legislative
change in the ounce, increasing it by only one part in
8000, or by one I8th part of a grain, would bring everything into decimal coincidence, by making the ounce and
the cubic foot the links of connexion between weights
and measures instead of the grain and the cubic inch, as
at present.  As regards our measures of capacity, the connexion would be equally consecutive, as a decimal one,
between the cubic foot and the half pint, which for the
purpose in view, ought to have a distinct name (such as
a "tumbler," or a " rummer," or a " beaker ")-and which
would contain exactly one Iooth part of a cubic foot,with whatever liquid or solid matter it might be filled.
And thus the change which would place our system of
linear measure on a perfectly faultless basis, would at the
same time rescue our weights and measures of capacity
from their present utter confusion, and secure that other
advantage, second only in importance to the former, of
connecting them decimally with that system on a regular,
intelligible and easily-remembered principle; and that by
an alteration practically imperceptible in both cases, and
interfering with no one of our usages or denominations,
(32.) On the subject of decimalization, it will be gathered from what I have soid that I would make any de2 F




450      THE YARD, PENDULUM, AND METRE.
cimalized denominations which anybody might agree to
buy, sell, or contract by, permissive.  There seems to be
a doubt whether such is now the case, and if so the law
should I think be altered. But I would leave untouched
all our present idenominzations and their relations to the
standard-and the only new measure I would legalize
would be a "module" (or some other name at present unoccupied) of 50 geometrical inches being the ten millionth
of the polar axis, or its half, the "geometrical cubit" of
25 such inches-leaving its use quite voluntary.
COLLINGWOOD, Seot. 30, I863.
ADDENDUM.
(33.) Since the foregoing remarks were written my
attention has been called by the Astronomer Royal to
a very elaborate memoir by Captain  Clarke, in vol.
xxix. of the Memoirs of the Royal Astronomical Society,
whose conclusions, though differing from those of M.
Schubert in some particulars (as in making the equator
more elliptic) yet, so far as the present subject is concerned, tend in the same direction, and that, as regards
the aliquot error of the metre, even more strongly.
(34.) Captain Clarke assigns for the three axes of the
earth the following values:Polar axis........................41,707, 536 feet.
Or in inches...............500,490,432.
Longer equatorial axis........4I,852,970 feet.
Shorter  do.   do...4.... 4,842,354,,




THE YARD, PENDULUM, AND METRE.               45I
Longitude of the vertex of the longer axis=-3~ 58' 30'
east-or II~ 35' 15" E. of Paris) whence it is easy to
conclude as follows:
Diameter of equator in the longitude of Paris...41,852,695 feet.
Ellipticity of the Paris meridian.......................  say -d(35.) Calculating now the quadrant from this ellipticity, and from Captain Clarke's polar axis, we find it
32,814,1I6 feet, which exceeds ten million metres by
5I24 feet, being in excess of thatabove found (4008)
by IiI6 feet; and corresponding to an aliquot error of
one part in 6404, or on the metre itself to one I63d part
of an inch.   The aliquot error in our "geometrical
yard" is also somewhat increased by the adoption of
this polar axis, viz., to one part in 52,3IO, or to about
one 1453d part of an inch on the yard.
(36.) As this memoir of Captain Clarke contains by far
the most complete and comprehensive discussion which
the subject of the earth's figure has yet received, and
must be held as the ultimatum of what scientific calculation is as yet enabled to exhibit as to its true dimensions and form-this conclusion will of course be considered to supersede that arrived at in the foregoing
pages.
COLLINGWOOD, Oct. II, 1863.
P.S.-Some slight subsequent corrections made by Capt.
Clarke in his calculations, founded on data quite
recently published, make the polar axis approximate
still more nearly to 500,500,000 inches.




ON ATOMS.*
6" I sing of atoms."'-Rejeced Addresses.
DIALOGUE.-Hermogenes et Hermione interloquuntur.
ERMION E.-What strange people those
Greeks were?  I was reading this morning
about Democritus, "who first taught the
doctrine of atoms and a vacuum." I suppose
he must have meant that there is such a thing as utterly
empty space, and that here and there, scattered through
it, are things called atoms, like dust in the air. But then
I thought, "What are these atoms?" for if this be true,
then, these are all the world, and the rest is-nothing!
Hermogenes.-Yes.  That is the natural conclusion:
unless there be something that does not need space
to exist in; or unless there be things that are not mate* From the Fortnightly Review.




ON ATOMS.                   453
rial substances; or unless space itself be a thing: all
which is deep metaphysic, such as I am just now rather
inclined to eschew.  But, dear Hermione, how am I
to answer such a host of questions as you seem  to
have raised-allin a breath.   The Greeks! Yes; they
were a strange people-so ingenious, so excursive, yet so
self-fettered; so vague in their notions of things, yet so
rigidly definite in their forms of expressing them. Extremes met in them.  In their philosophy they grovelled
in the dust of words and phrases, till, suddenly, out of
their utter confusion, a bound launched them into a new
sphere. There is a creature, a very humble and a very
troublesome one, which reminds me of the Greek mind.
You might know it for a good while as only a fidgety,
restless, and rather aggressive companion, when, behold,
hop! and it is away far off, having realized at one
spring a new arena and a new experience.
Hermione.-Don't!  But a truce to the Greek mind
with its narrow pedantry and its boundless excursiveness.
The excursiveness was innate, the pedantry superinduced
-the result of their perpetual rhetorical conflicts and
literary competitions.  I have read the fifth book of
Euclid and something of Aristotle; so you need not talk
to me on that theme. Do tell me something about these
atoms.  I declare it has quite excited me;'specially because it seems to have something to do with the atomic
theory ofDalton.
Hermogeenes. -Higgins, if you please. But the thing,
as you say, is as old as Democritus, or perhaps older;
for Leucippus, Democritus's master, is said to have




454                  ON ATOMS.
taught it to him.  Nay, there is an older authority still,
in the personage (as near to an abstraction as a traditional human being can be) Moschus (not he of the
Idyls).  But the fact is that the notion of THE ATOMthe indivisible, the thing that has place, being, and poweer
-is an absolute necessity of the human thinking mind,
and is of all ages and nations. It underlies all our
notions of being, and starts up, per se, whenever we come
to look closely at the intimate objective nature of things,
as much as space and time do in the subjective. You
have dabbled in German metaphysics, and know the
distinction I refer to.
lermnione.-You don't mean to say that we are nothing
but ATOMS — Place! being! power! Why, that is I, it
is you, it is all of us. Nay, nay. This is going too
fast.
Hermzogenes.-Perhaps it is.-(You have forgot thought,
by-the-by, and will.)-But I am not going to make a
single hop quite so far. We shall divide that into two
or three jumps, and loiter a little in the intermediate
resting-places.  But, to go back to your atoms and a
vacuum. What does a vacuum mean i
Hermione.-Vacuum    Why, emptiness, to be surei
I mean empty space. Space where no th/ing is. I am
not so very sure that I can realize that notion. It is
like the abstract idea of a lord mayor that Pope and
Atterbury talk about; and in getting rid of the man, the
gold chain and the custard are apt to start up and vindicate their claim to a place in the world of ideas. And
yet I do mean something by empty space. I mean dis



ON ATOMS.                     455
tance-I mean direction: that steeple is a mile off, and
not here where we sit; and it lies south-east of' us, and
not north or west.  And if the steeple were away, I
should have just as clear a notion of its p/ace as if I saw
it there.  There now! But then distance and direction
imply twoplaces.  So there are three things anyhow that
belong to a vacuum; and let me tell you, it is not everything that three things positively intelligible can be
" predicated " of (to speak your jargon).
Hermogeses.-Dear me, Hermione! how can you twit
me so? Jargon! Every speciality has its "jargon." Even
the Law, that system of dreams, has its "jargon "-the
more so, to be sure, because it is a system of dreams, or
rather of nightmares (God forgive me for saying so!).
Well, then, you seem  to have tolerably clear notions
about a vacuum-at least, I cannot make them clearer.
Much clearer, an yhow, than Des Cartes had, who maintained that if it were not for the foot-rule between them,
the two ends of it would be in the same place. Still,
there is much to be said about that same Vacuum, especially when contrasted with a Plenum, which means (if it
mean anything) the exact opfposile of a vacuum.  In other
words, a "jam," a " block," a "fix."  But, on the whole,
I lean to a vacuum.  The other idea is oppressive.  It
does not allow one to breathe. There is no elbow-room.
It seems to realize the notion of that great human
squeeze in which we should be landed after a hundred
generations of unrestrained propagation.'  One does not
* For the benefit of those who discuss the subjects of Population,
War, Pestilence, Famine, &c., it may be as well to mention that the




456                     ON ATOMS.
understand how anything could get out of the way of
anything else.
Rermione.-Do come back to our dear atoms.  I love
these atoms: the  delicate little creatures!  There is
something so fanciful, so fairy-like about them..Hermogenes.-Well they have their idiosyncrasies.  I
mean, they obey the laws of their being.  They comport
themselves according to their primary constitution. They
conform to the fixed rule implanted in them in the instant of their creation.  They act and react on each
other according to the rigorously exact, mathematically
determinate relations laid down for them ab initio. They
work out the preconceived scheme of the universe by
their-their    colHeermione.-Their?  Stop, stop! mydearHermogenes.
Where will you land us?  Obey laws!  Do they know
them?  Can they remember them?  How else can they
obey them?  Comport themselves according to their
primary constitution!  Well, that is so far intelligible:
they are as they are, and not as they are not. Conform
to a fixed rule! But then they must be able to apply
the rule as the case arises. Act and react according to
number of human beings living at the end of the hundredth generation, commencing from a single pair, doubling at each generation
(say in thirty years), and allowing for each man, woman, and child
an average space of four feet in height, and one foot square, would
form a vertical column, having for its base the.whole surface of the
earth and sea spread out into a plane, and for its height 3674 times
the sun's distance from the earth! The number of human strata
thas piled one on the other would amount to 460, 79o,oo,ooo,000.




ON ATOMS.                    457
determinate relations! I suppose you mean relations
with each other.  But how are they to know those relations l Here is your atom A, there is your atom B (I
speak as you have taught me to speak), and a long interval between them, and no link of connexion. How
is A to know where B is; or in what relation it stands to
B? Poor dear atoms! I pity them..HerWzoenes.-You may spare your sympathy.  They
are absolutely blind and passive.
Hermione.-Blind and passive! The more the wonder
how they come to perceive those same relations you talk
about, and how they "comport themselves," as you call
it (act, as I should say), on that perception. I have a
better theory of the universe.
Hermlogenes.-Tell it me.
Hermtione.-In the beginning was the nebulous matter,
or Akasch.  Its boundless and tumultuous waves heaved
in chaotic wildness, and all was oxygen, and hydrogen,
and electricity. Such a state of things could not possibly continue; and as it could not possibly be worse,
alteration was here  synonymous with  improvement.
Then camelermnogenes.-Now it is my turn to say, Stop  stop!
Solvuntur risu tabule.  Do let us be serious.  Remember, it was you who began the conversation. Je me suis
seulement laisse entrainer. The fact is, I have only so far
been trying you, and I see you are apt. There lies the
real difficulty about these atoms. These same "relations"
in which they stand to one another are anything but




458                  ON ATOMS.
simple ones.  They involve all the " ologies "and all the
"ometries," and in these days we know something of
what that implies. Their movements, their interchanges,
their "hates and loves," their "attractions and repulsions," their " correlations," their what not, are all determined on the very instant. There is no hesitation, no
blundering, no trial and error. A problem of dynamics
which would drive Lagrange mad, is solved instanter,
Solvitur ambulando."  A differential equation which,
algebraically written out, would belt the earth, is integrated in an eye-twinkle; and all the numerical calculation worked out in a way to frighten Zerah Colburn,
George Bidder, or Jedediah Buxton.  In short, these
atoms are most wonderful little creatures.
Hermione.-Wonderful indeed! Anyhow, they must
have not only good memories, but astonishing presence
of mind, to be always ready to act, and always to act
without mistake, according to " the primary laws of their
being," in every complication that occurs.
Her;mogenes.-Thou hast said it! This is just the point
I knew you must come to.  The presence of MIND is what
solves the whole difficulty; so far, at least, as it brings it
within the sphere of our own consciousness, and into
conformity with our own experience of zwha/at action is.
We know nothing but as it is conceivable to us from our
own mental and bodily experience and consciousness.
When we know we act, we are also conscious of will
and effort; and action without will and effort is to us,
constituted as we are, unrealizable, unknowable, inconceivable.




ON ATOMS.                    459
Hermione.-That will do.  My head begins to turn
round.  But I hardly fancied we had got on such an
interesting train.  We will talk of this again.  More
to-morrow.  Now to the feast of flowers the children are
preparing.
COLLINGWOOD, Aug. I6,  186.




XII,
ON THE ORIGIN OF FORCE.*
Mens agitat molem et magno se corpore miscet."
HAT is it that we ought to understand by
the theory of any natural phenomenon?
This is a question not without its importance
when we are told, as we so frequently are,
that it is useless to inquire into causes: that, in fact,
causes are to us as though they were not; seeing that
all we can ever attain to is the observation and registry
of constant laws of phenomenal sequence:-in other
words, that phenomenon succeeds phaenomenon, event
event, according to certain rules, which are all we have
any business to inquire into.
(2.) It is unfortunate for this doctrine that within the
range of every individual's momentary experience there
occurs the phmnomenon of volition; and that there are
* From the Fortnightly Review.




ON THE ORIGIN OF FORCE.             46r
large classes of phaenomena, and those most important
ones, which, we are. quite sure, take place in virtue of
such volitions, and without which we are equally sure
they would not take place at all. In that peculiar
mentad sensation, clear to the apprehension of every one
who has ever performed a voluntary. act, which is present
at the instant when the determination to do a thing is
carried out into the act of doing it-(a sensation which,
in default of a term more specifically appropriated to it,
we may call that of effort)-we have a consciousness of
immediate and personal causation which cannot be disputed or ignored.'And when we see the same kind of act
performed by another, we never hesitate in assuming for
him that consciousness which we recognize in ourselves:
and in this case we can verify our conclusion by oral
communication. The first step in the way of generalization thus taken, the next is obvious enough. Though a
flight rather than a step, it forces itself on our thoughts with
ever-increasing cogency, the more it is dwelt upon, and
the more utterly abortive all attempt to render any other
account of that deep mystery of nature-mechanical
force-is found to be. Whenever, in the material world,
what we call a phlenomenon or an event takes place, we
either find it resolvable ultimately into some change of
place or of movement in material substance, or we endeavour to trace it up to some such change; and only
when successful in such endeavour we consider that we
have arrived at its theory. In every such change we recognize the action of FORCE. And in the only case in
which we are admitted into any personal knowledge of




462          ON THE ORIGIN OF FORCE.
the origin of force, we find it connected (possibly by intermediate links untraceable by our faculties, but yet
indisputably connected) with volition, and by inevitable
consequence, with motive, with intellect, and with all those
attributes of mind in which-and not in the possession
of arms, legs, brains, and viscera-personality consists.
In limiting thus the domain of physical theory, we keep
on the outside of the apparently interminable discussions
and difficulties as to the origin of the will itself, which
seem to have culminated in some minds in the denial
of volition as a matter of fact, and in the dictum of
Judge Carleton,; that what men term the will, is " sihmply
a passive capacity to receive pleasure from whatever
affects us agreeably at the time."
(3.) It may, however, be said, and indeed there are
not wanting those who appear very much disposed to
say, if not totidem verbis, at least by strong implication,
that the conception of Force itself, as part and parcel of
the system of the material universe, is superfluous and
therefore illogical. They argue thus. All we know of
material phaenomena, it is true, resolves itself into the
transference of motion from  matter to matter.  This,
however, may be effected by mere collision.  Now, when
A strikes B, and motion is thereby communicated from
A to B, why not at once admit this as a sequence?  Why
interpose an unknown agent, or intermedium, Force, as
part of the process?  Having come to regard Heat,
Light, Electricity, and the "imponderables" generally,
* "Proceedings of the American Philosophical Society," ix. p.
136-Report of Meeting of January 2, 1863.




ON THE ORIGIN OF FORCE.              463
some upon more, others on less, cogent evidence, as
"modes of motion," they seem to consider Force itself
as included in the same category, and think there is
"reason to believe that it depends on the diffusion of
highly-attenuated matter through space." * This doctrine
goes to resolve the entire assemblage of natural phaenomena into the mere knocking about of an inconceivable
number of inconceivably minute billiard balls (or cubes,
or tetrahedrons, if that be preferred), which once set in
motion and abandoned to their mutual encounter and
impact, work out the totality of natural phenomena.
With the amount of forethought and intelligence called
for in the initiatory disposal of the place and movement
of every individual of this multitude; to work out for
countless ages the orderly sequence of observed facts,
by theirblind conformity to the laws of collision, those
disposed to adopt such a view of nature would probably
concern themselves little.  Their actual disposal at the
present moment is afait accom5Zli; and from this point
it would be possible, at least in imagination, if we knew
the present position and movement of every particle of
matter in the universe, to work backwards, up to any
epoch which we might choose to assign as that of creation, by a simple reversal of the velocity and direction of
each:-~nay, having thus uncreated the world, the molecules would of themselves work out a pre-existent order
of things into all past eternity: an image of what vmight
have existed in the past (though it did not) seen, as it
were, reflected in the future.
* North British Review, vol. xl. p. 4I.




464          ON THE ORIGIN OF FORCE.
(4.) This simplification (if such it be) of our view of
material action is altogether untenable; nor will it be
difficult, I think (and certainly not superfluous), to show
that such an arrangement must of necessity be rapidly
self-destructive, and must result in the gradual but
speedy dying away of all relative motion, and the reduction of the universe either to a single block of matter
moving uniformly on, for ever, in one direction, without
relative motion of its parts; or else in the dispersion into
space, and absolute final dissociation of its molecules.
(5.) For, be it observed, force (except in the sense of
bodily extrusion) being non-existent, our billiard-balls
must of necessity be supposed inelastic.  Elasticity implies force. If this be disallowed,-if elasticity be not
force, but collision,-each billiard-ball (each  ultimate
atom, that is to say) must be itself a universe in miniature
composed of other more minute ones, moving and colliding, inter se to give them  that resilience which we term
elasticity, but which, in this view of the matter, is nothing
but "clash."  Now what is to prevent these ultimate
atoms of the second order, animated with velocities immense, as compared with their mutual distances, coerced
by no mutual attractions, subject to no control but from
their mutual collisions; from  dispersing themselves out
in all directions into space and abdicating their functions
as a group?  If we waive this objection (which, however, is fatal) nothing is gained.  The original objection
applies in its full force to these sub-atoms, and so on ad
infinitum.
(6.) Now, in the collision of inelastic bodies, vis viva




ON THE ORIGIN OF FORCE.              465
is necessarily and invariably destroyed. The destruction
may be total, or may fall short of totality in any proportion according to the directness of the impact, and the proportion of the moving masses; but whenever contact occurs between such bodies, vis viva disappears, and, once
lost, is gone for ever. Taking such a system in its entirety
(wh7ere force exists hot), there is no possibility of its reproduction. There is therefore a necessary and unceasing drain on the vis viva of such a system. Everything
which constitutes an event, whatever its nature, exhausts
some portion of the original stock. Such a system has
no vitality. It feeds upon itself, and has no restorative
power.  All relative motion in it tends rapidly to decay,
or at all events to a final state, when there will occur no
more collision, i.e., when phxenomena cease altogether;
when the minimum of vis viva consistent with the conservation of momentum is attained; and nothing remains
but either a single caput mortuum, journeying through
space, or a multitude of such, travelling different ways;
having parted company never to meet again.
(7.) It will of course be urged that this reasoning takes
for granted the law just mentioned of the conservation of
momentum estimated in any given direction: since we
cannot assert apriori that two inelastic bodies, after collision, must move on with a common velocity and unchanged joint momentum.  Of course it does so.  But
the object of the hypothesis we are combating is to exhibit collision as a substitute for force; i.e., to give an
account of the acknowledged laws of motion without introducing the conception of force.  We are therefore
2 G




466           ON THE ORIGIN OF FORCE.
justified, when arguing against it, in assuming all the
results of those laws as established truths: they being,
in effect, the very things which the hypothesis is framed
to account for. The law in question, constituted as the
material universe is, is absolute and universal: and no
view of matter and motion can be a true one which is
incompatible with it.
(8.) The inward pressure of an etherial medium surrounding the sun upon the earth and planets, suggested
by Newton as a mode of escape from  the metaphysical
difficulty of attraction at a distance, is either only another
form  of the collision theory above combated, or an
evasion of the difficulty by substituting repulsive for
attractive force.  If the ether press by its elasticity, besides supposing its particles endowed with the necessary amount of repulsion; what, it must be asked, but a
repulsion emanating from the sun (and thereby equilibrating and rendering ineffective its inward pressure) is to
keep it from rushing in on all sides, and destroying that
inequality of density on which its supposed inward pressure depends    If not, its agency must be simply that
of an inert resisting medium, rendering the continued
revolution of the planets round the sun impossible, and
causing them, while it lasts, to rotate on their axes in a
direction contrary to that of their orbital m.:tion, as a direct
consequence of the more rapid abstraction of motion
from their outer than from their inner hemispheres.  The
hypothesis of Le Sage which assumes that every point oj
space is penetrated at every instant of time by material
particles, sui generis, moving in right lines in every possible




ON THE ORIGIN  OF FORCE.              467
direction, and impinging upon the material atoms of
bodies; as a mode of accounting for gravitation, is too
grotesque to need serious consideration; and besides, will
render no account of the phaenomenon of elasticity. Besides this, I am not aware of any other attempt to embody
in a tangible form the notion of a substitute for the conception of dynamical force arising out of the elementary
conceptions of motion and inertia. There is a tendency
indeed, of late apparent, to attribute the elastic pressure
of a gas on its containing envelope, as due to the collisive
shock of its particles conceived as existing in a continual
state of vibration, or of circulation round each other.
But the maintenance of such vibrations or revolutions involves the supposition of inter-molecular coercive forces,
and is not, therefore, to be classed with such attempts.
(9.) If it be true, then, that the conception of FORCE
as the originator of motion in matter without bodily contact, or the intervention of any intermedium, is essential
to a right interpretation of physical phaenomena; and if
it be equally so, on the other hand, that its exertion
makes itself manifest to our personal consciousness by
that peculiar sensation of effort which is not without its
analogue in purely intellectual acts of the mind; it comes,
not unnaturally, to be regarded as affording a point of
contact, a connecting link between these two great departments of being-between mind and matter-the one
as its originator, the other as its recipient. The control
we possess over the external world we are sure must
arise from a capacity somehow inherent in the intellectual part of our nature, to originate or call into action




468          ON THE ORIGIN OF FORCE.
this one and only agent which matter obeys in its changes
of form and situation.  We may hesitate about admitting
into the system of created things around us so vast an
amount of additional or extraneous zvis viva, as the totality of animal exertion since the first introduction of life
upon earth would seem to imply.  But this is not necessary.  The actualforce necessary to be orfiginated to give
rise to the utmost imaginable exertion of animal power
in any case, may be no greater than is required to remove a single material molecule from its place through
a space inconceivably minute-no more in comparison
with the dynamical force disengaged, directly or indirectly,
by the act, than the pull of a hair trigger in comparison
with the force of the mine which it explodes. But without
the power to make some material disposition, to originate
some movement, or to change, at least temporarily, the
amount of dynamical force appropriate to some one or
more material molecules, the mechanical results of
human or animal volition are inconceivable.  It matters
not that we are ignorant of the mode in which this is
performed.  It suffices to bring the origination of dynamical power, to however small an extent, within the
domain of acknowledged personality.
(io.) It will perhaps be objected to this, that the principle so generally cited, and' now so universally recognized as a dominant one in physics-that of the "conservation of force"-stands opposed to any, even the
smallest amount of arbitrary change in the total of
"force " existing in the universe.  This principle, so far
as it rests upon any scientific basis as a legitimate conclu



ON THE ORIGIN OF FORCE.               469
sion from  dynamical laws, is no other than the wellknown dynamical theorem of the conservation of vis viva
(or of " energy," as some prefer to call it) sipplzemented to
save the truth of its verbal enunciation, by the introduction of what is called " potential energy," a phrase which
I cannot help regarding as unfortunate, inasmuch as it
goes to substitute a truism for the announcement of a
great dynamical fact.  No such conservation, in the
sense of an identity of total amount of vis viva at all
times, and in all circumstances, in fact, exists. So far
as a system is maintained by the mutual actions and reactions of its constituent elements at a:distance (i.e., by
force), vis viva may temporarily disappear, and be subsequently reproduced between certain limits. Collision,
indeed, betwfi its ultimate atoms, regarded as absolutely!
rigid, and therefore inelastic (for that which cannot change
itsfigure can have no resilience), cannot take place without
producing a permanent destruction of it, which there
exists no means of repairing.  And here we may remark
that, this being the case, to ascribe to such atoms any
magnitude becomes not only superfluous, but embarrassing.  The system of Boscovich has to be accepted in
its integrity, if absolute permanence is to be one of the
conditions insisted on; and they come to be considered
as mere localizations of inertia and such other attributes,
including the centralization of force-if any other than
this there be-which belong to our notion of material
substance. The conservation of energy, then, is in effect
no conservation at all in any strict sense of the term,
unless so supplemented.  It is a fact dynamically demon



470  ON THE ORIGIN OF FORCE.
stratable that the total amount of vis viva in any moving
system abandoned to the mutual reaction of its particles,
while depending at every instant of time, solely for its
magnitude, on the then relative situation of those particles (or being, in algebraical phrase, a function of their
mutual distances), has a maximum value which it cannot
exceed, and a minimum below which it cannot descend.
Let its state then be what it will, there is sure to be a
certain amount of vis viva by which its actual falls short
of its extreme possible value; and to say that the amount
of this deficiency added to the actual present amount
will make up the maximum, is neither more nor less than
a truism: whether expressed in so many words, or by saying that the potential together with the actual energy of
the system is invariable; or, again, in other words, that
when certain changes have taken place in the relative
situations of the parts of the system, what it has lost in
actual it has gained in potential energy.  When in speaking of a mechanical combination we say that what is lost
in time is gained in power, though equally a translation
in ordinary language of a dynamical equation, the terms
used refer to different modes of viewing the expenditure of force.  But in the case before us they stand in
their nakedness of similar meaning and convey to the
mind no equivalence available for any purpose of reasoning. If, indeed, we could be assured,  priori, that the
system is one of simple or compound periodicity in which
a certain lapse of time will restore every molecule to
identically the same relative situation with respect to all
the rest; we should then be sure that in the nature of




ON THE ORIGIN OF FORCE.              471
things there would take place periodically, so to speak,
a winding up from a lower to a higher state of potential
energy, to be subsequently exchanged for newly-created
zis viva.  But as we can have no such a priori assurance, can only assume such restoration to be possible,
and can see no means of effecting it, if possible, otherwise than by foresight and prearrangement; the one
equally with the other is an unknown function, variable within unknown limits, and susceptible of fluctuations to an unknown extent, nor can we have any,
the smallest, right to assert that what is expended in the
one form is, necessarily, laid up in reserve for further use
in the other. It would be very diffcult, I apprehend, to
show whether in the winding up of a clock, or the building of a pyramid, taking into consideration all the various
modes in which vis viva disappears and reappears in the
expenditure of muscular power, the evolution of animal
heat, the consumption of the materials of our tissues
(laying aside all question as to the evolution of force
from intellectual effort), the propagation of vibratory
motion, and a thousand other modes of transfer; the total
vis viva of this our planet is increased or diminished.
That it should remain absolutely unchanged during the
process is in the last degree inconceivable.  The amount
of vis viva latent in the form  of heat or molecular
motion in the sun and planets in our immediate system
may bear, and probably does bear, a by no means inapprefiable ratio to that more distinctly patent in the form
of bodily motion in the periodical circulation of the
planets round the sun, and the sun and planets round




472          ON THE ORIGIN OF FORCE.
their axes.  The latter amount fluctuates to and fro
according to laws easily calculable; but the former we
have no means whatever of computing, and to what extent, or within what limits, it may be variable, we are
altogether ignorant.
(ii.) In what is here said, it is by no means intended
to call in question the validity or to underrate the importance of those remarkable physical investigations which
have resulted in exhibiting heat as one of the forms in
which vis viva reappears in the apparent destruction of
motion.  That all heat consists in molecular tremor (or
circulation), and is therefore  accompanied with  the
alternate development and disappearance of vis viva
within a limited space and quantity of matter according
to the dynamical laws of such tremulous or rotating movements, may very readily be granted.  But that there are
no forms of internal molecular movement other than
heat, and what we now speak of as its "correlated
forces" in which vis viva may be temporarily stored up,
to make its appearance ultimately in a form cognizable
to our senses, is what can by no means be so readily admitted.  Nor (while accepting with all due admiration
as approximate truths these great revelations as to the
mutual convertibility of these correlatives according to
the measure of vis viva appropriate to each) shall we
advance any nearer to a rational theory of any one of
them, till it shall be shown with much more distinctness than at present appears, in what these molecular
movements themselves consist; by what forces (in the
dynamical acceptation of the term) they are controlled;




ON THE ORIGIN OF FORCE.               473
in what manner, or by what mechanism, they are propagated from one body to another; and how their mutual
interconversion is effected.  In referring them  to the
action of dynamical force upon matter, and in getting
rid of the " imponderables " (other than the luminiferous
ether) we are at length fairly entered on the construction
of a theory of their phzenomena, in what, as above remarked, must be considered the true acceptation of that
term in physics: and once satisfied that dynamical force
itself is a phaenomenon sui generis; that it is not a result
of collision-an educt from  the duality Inertia and
Motion;-one of those correlatives, in short, to which
the epithet " Physical forces" has of late been so generally, and, in my opinion, so very improperly applied, we
have reached the point where theory ends and speculation begins,-where we cease to inquire into the causes
ofphoenomena, and direct our consideration thenceforward to their reasons.
(12.) The universe presents us with an assemblage of
phaenomena, physical, vital, and intellectual-the connecting link between the worlds of intellect and matter
being that of organized vitality, occupying the whole
domain of animal and vegetable life, throughout which
in some way inscrutable to us, movements among the
molecules of matter are originated of such a character as
apparently to bring them under the control of an agency
other than physical,@  superseding the ordinary laws
* Take for instance the formative nisus, which determines the
production of a supernumerary finger in the humnan hand. Here is
tio gradual change from generation to generation, no first develop.




474             ON  TIE ORIGIN OF FORCE.
which regulate the movements of inanimate matter, or,
in other words, giving rise to movements which would not
result from  the action of those laws uninterfered with;
and therefore implying, on the very same principle, the
origination  of force.   The first and  greatest question
which Philosophy has to resolve in its attempts to make
out a Kosmos,-to bring the whole of the phenomena
exhibited in these three domiains of existence under the
contemplation  of the mind as a congruous whole,-is,
ment of a rudimentary joint followed in slow succession after centuries
of hereditary improvement, by tie others, up to the perfect meml)er.
It starts at once into completeness. The change in the workizg-plan
of the whole hand has been carried out at once, by a systematic
engraftment of blood-vessels and nerves into effective connexions
with the centres of nutritive, mechanical, and sensitive action in the
frame, as if by some preconceived arrangement. [Since this was
written I have been informed of two or three instances of superfluous thumbs.  They were imperfectly formed, not movable, and
so far might be considered rudimentary.]
In direct reference to this point I would call the reader's attention to a very striking passage in the Croonian Lecture for I865,
delivered before the Royal Society by Prof. Ieale, where, after
stating that " phtenomena occur in the simplest form of living
matter, which never have been, and which," he believes, "never
can be explained upon any known physical or chemical laws "-he
goes on to say," Living matter is not a machine, nor does it act upon the principles of a machine, nor is force conditioned in it as it is in a machine,
nor have the movements occurring in it been explained by physics,
or the changes which take place in its composition by chemistry.
The phlenomena occurring in living matter are peculiar, differing
firom any other known phenlomena; and therefore, until 1e can explain them, they may well be distinguished by the term viza. Not
the slightest step has yet been made towards the production of
matter possessing the properties which distinguish living matter from
matter in every other known state. "-Proceedings of th/e ZRoyal
Society, xiv. p. 282, No. 72.




ON THE ORIGIN OF FORCE.             475
whether we can derive any light from our internal consciousness of thought, reason, power, will, motive, design
-or not: whether, that is to say, nature is or is not more
interpretable by supposing these things (be they what they
may) to have had, or to have, to do with its arrangements.  Constituted as the human mind is, if nature be
not interpretable through these conceptions, it is not
interpretable at all; and the only reason we can have
for troubling ourselves about it is either the utilitarian
one of bettering our condition by "subduing nature" to
our use through a more complete understanding of its
"laws,' so as to throw ourselves into its grooves, and
thereby reach our ends more readily and effectually; or
the satisfaction of that sort of aimless curiosity which
can find its gratification in scrutinizing everything and
comprehending nothing.  But if these attributes of mind
are not consentaneous, they are useless in the way of explanation.  Will without Motive, Power without Design,
Thought opposed to Reason, would be admirable in
explaining a chaos, but would render little aid in account,
ing for anything else.




ON THE ABSORPTION OF LIGHT BY
COLOURED MEDIA,
VIEWED IN CONNEXION WITH THE UNDULATORY THEORY.*
HE absorption of light by coloured media is
a branch of physical optics which has only
since a comparatively recent epoch been
studied with that degree of attention which
its importance merits. The speculations of Newton on
the colours of natural bodies, however ingenious and
elegant, can hardly, in the present state of our knowledge, be regarded as more than a premature generalization; and they have had the natural effect of such
generalizations, when specious in themselves and supported by a weight of authority admitting for the time
of no appeal, in repressing curiosity, by rendering further
inquiry apparently superfluous, and turning attention
* The substance of this paper was read before, the Section of
Physics of the British Association, at Cambridge, 1833. Some inaccuracies of wording are corrected, but nothing introduced bearing on the views more recently entertained as to the conversion of
motion into heat-vibratiaon.




ON THE ABSORPTION OF LIGHT, ETC.           477
into unproductive channels.  I have shown, I think
satisfactorily, however, in my Article on Light,* that the
applicability of the analogy of the colours of thin plates
to those of natural bodies is limited to a comparatively
narrow range, while the phaenomena of absorption, to
which I consider the great majority of natural colours
to be referrible, have always appeared to me to constitute a branch of photology suii generis to be studied in
itself by the way of inductive inquiry, and by constant
reference to facts as nature offers them.
(2.) The most remarkable feature in this class of
facts consists in the unequal absorbability of the several
prismatic rays, and the total abandonment of anything
like regularity of progress in this respect as we proceed
from one end of the spectrum  to the other.  When we
contemplate the subject in this point of view, all idea of
regular functional gradation is at an end.  We seem to
lose sight of the great law of continuity, and to find ourselves involved among desultory and seemingly capricious relations, quite unlike any which occur in other
branches of optical science.  It is, perhaps, as much
owing to this as to anything, that the phaenomena of
absorption in some recently-published speculations, and
in the view which Mr Whewell has taken in his Report
of the progress and actual condition of this department
of natural philosophy, read to this meeting, have been
characterized as peculiarly difficult to reconcile with the
undulatory theory of light.  In so far as I have above
* This refers to the Article on Light published in the " Encyclopaedia Metropolitana" in I826-7.




478       ON THE ABSORPTION OF LIGHT
described the phenomena in appropriate terms, it will
be evident that a certain difficulty must attach to their
reduction under the dominion of any theory, however
competent, ultimately, to render a true account of them.
Where such evidence of complication and suddenness
of transition subsists on the face of any large assemblage
of facts, we are not to expect that the mere mention of
a few general propositions, like cabalistic words, shall
all at once dissipate the complication, and render the
whole plain and intelligible. If we represent the total
intensity of light, in any point of a partially-absorbed
spectrum, by the ordinate of a curve whose abscissa indicates the place of the ray in order of refrangibility, it
will be evident, from the enormous number of maxima
and minima it admits, and from the sudden starts and
frequent annihilations of its value through considerable
amplitudes of its abscissa, that its equation, if reducible
at all to analytical expression, must be of a singular and
complex nature; and must at all events involve a great
number of arbitrary constants dependent on the relation
of the medium  to light, as well as transcendents of a
high and intricate order.  We must not, therefore, set
it down to the fault of either of the two rival theories if
we do not at once perceive how such phenomena are
to be reconciled to the one or to the other; but rather
endeavour to satisfy ourselves whether there be, in the
first instance, anything in the phaenomena, generally
considered, repugnant either to sound dynamical principles, or to the notions which those theories respectively
involve as fundamental features,




BY COLOURED MEDIA.                479
(3.) Now, as regards only the general fact of the obstruction and ultimate extinction of light in its passage
through gross media, if we compare the corpuscular and
undulatory theories, we shall find that the former appeals
to our ignorance, the latter to our knowledge, for its
explanation of the absorptive phenomena.  In attempting to explain the extinction of light, on the corpusculai
doctrine, we have to account for the light so extinguished
as a material body, which we must not suppose annihilated. It may, however, be transformed; and among
the imponderable agents, heat, electricity, &c., it may
be that we are to search for the light which has become
thus comparatively stagnant. The heating power of the
solar rays gives a prizma facie plausibility to the idea of
a transformation of light into heat by absorption.  But
when we come to examine the matter more nearly, we
find it encumbered on all sides with difficulties. How is
it, for instance, that the most luminous rays are not the
most calorific, but that, on the contrary, the calorific
energy accompanies, in its greatest intensity, rays which
possess comparatively feeble illuminating powers? These
and other questions of similar nature may perhaps admit
of answer in a more advanced stage of our knowledge;
but at present there is none obvious. It is not without
reason, therefore, that the question, "What becomes of
light " which appears to have been agitated among the
photologists of the last century, has been regarded as one
of considerable importance as well as obscurity by the
corpuscular philosophers.
(4.) On the other hand, the answer to this question




480        ON THE ABSORPTION OF LIGHT
afforded by the undulatory theory of light is simple and
distinct.  The question, "What becomes of light?"
merges in the more general one, "What becomes of
motion  "  And the answer, on dynamical principles, is,
that it continues for ever. No motion is, strictly speaking, annihilated; but it may be divided, and the divided
parts made to oppose and, in point of ultimate effect,
counteract each other. A body struck, however perfectly
elastic, vibrates for a time, and then appears to sink into
its original repose. But this apparent rest (even abstracting from the inquiry that part of the motion which may
be conveyed away by the ambient air), is nothing else than
a state of subdivided and mutually-compensating motion,
in which every molecule continues to be agitated by an
indefinite multitude of internally-reflected waves, propagated through it in every possible direction, from every
point in its surface on which they successively impinge.
The superposition of such waves will, it is easily seen, at
length operate their mutual counteraction, which will be
the more complete, the more irregular the figure of the
body and the greater the number of internal reflections.
(5.) In the case of a body perfectly elastic and of a
perfectly regular figure, the internal reflection of a wave
once propagated within it in some particular direction
might go on for ever without producing mutual destruction; and in sonorous bodies of a highly elastic nature
we do in fact perceive it to continue for a very long time.
But the least deviation from perfect eZlasticity resolves our
conception of the vibrating mass into that of a multitude
of inharmonious systems communicating with each other.




BY COLOURED MEDIA.                  481
At every transfer of an undulation from one such system
into that adjacent, a partial echo is produced. The
unity of the propagated wave is thus broken up, and a
portion of it becomes scattered through the interior of
the body in dispersed undulations from each such system,
as from a centre of divergence. In consequence of the
continual repetition of this process, after a greater or less
number of passages to and fro of the original wave across
the body (however perfect we may suppose the reflections from its surface to be), it becomes frittered away
to an insensible amplitude, and resolved into innumerable others; crossing, recrossing, and mutually compensating each other, while each of the secondary waves so
produced is in its turn undergoing the same process of
disruption and degradation.
(6.) In this account of the apparent destruction of
motion, I have purposely supposed the body set in vibration to be insulated from communication with any other.
In the case of a perfectly or highly elastic body struck in
air, it will vibrate so long that a great part of its motion
is actually carried off in sonorous tremors communicated
to the air. But in the case of an inelastic or imperfectly
elastic body, the internal process above described goes
on with such excessive rapidity, as to allow of very few,
and those rapidly degrading, impulses to be communicated from its surface to the air.
(7.) In my Article on Sound,* I have explained, on this
principle of internal reflection and continual subdivision,
* Published like that on Light, above cited, in the EJncyclofedia
Metropolizana, 1829-30.
2 H




482        ON THE ABSORPTION OF LIGHT
in a medium consisting of loosely-aggregated earth intermixed with much air, the hollow sounds which are often
attributed to the reverberation of subterrannean cavities,
and in particular the celebrated instance of this kind of
sound heard at the Solfaterra near Pozzuoli. The dull
and ill-defined sound thus produced from a succession of
partial echoes is there assimilated to the nebulous light
which illuminates a milky medium when a strong beam
is intromitted.  If we suppose, now, such a mass of
materials insulated from communication with the external air by some souznd-tight envelope, these partial echoes,
when they reach the surface in any direction, will be all
sent back again as so many fresh impulses, till at length
it will become impossible to assign a point within the
mass which will not be agitated at one and the same
moment by undulations traversing it in every possible
phase and direction.  Now the state of a molecule, under the influence of an infinite number of contradictory
impulses thus superposed, is undistinguishable from  a
state of rest.
(8.) The only difficulty, then, which remains in the
application of the undulatory theory to the absorptive
phaenomena, is to conceive how a medium (i.e., a combination of ethereal and gross* molecules) can be constituted
so as to be transparent, or freely permeable to one ray
or system of undulations, and opake, or difficultly per* By gross molecules, or gross bodies, I understand the ponlderable
constituents of the material world, whether solid, liquid, or gaseous;
using the term in contradistinction to rethereal, Nwich has reference to the luminiferous oether.




BY COLOURED MEDIA.                483
meable to another, differing but little in frequency. Now
it is sufficient for our present purpose if, without pretending to analyze the actual structure of any optical medium,
we can indicate structures and combinations in which
air, in lieu of the oether, is the undulating medium, and
which shall be either incapable of transmitting a musical
sound of a given pitch, or shall transmit it much less
readily than sounds of any other pitch, even those nearly
adjacent to it. For that which experiment, or theory so
well grounded as to be equally convincing with experiment, shows to be possible in the case of musical sounds,
will hardly be denied to have its analogue or representative among the phenomena of colour, when referred to
the vibrations of an tether.
(9.) An example of an acoustic combination, or compound vibrating system, incapable of transmitting a
c
AD
musical sound of a given pitch, is furnished b  the ipe
musical sound of a given pitch, is furnished by the pipe
A E, which, after proceeding singly a certain length A B,
at B branches off into two equal and symmetrically disposed pipes B C and b c, which reunite again at D d, and
there again constitute a single pipe D E, whose direction




484         ON THE ABSORPTION  OF LIGHT
shall (like A B) bisect the angle between the branches.
The branches, however, are of unequal length, the one
B C D being longer than the other, by a quantity equal
to half the length of the undulation or pulse of the musical note in question. It is evident, then, that if that
note be sounded at A, each pulse will subdivide itself at
B b, and the divided portions will run on along the two
branches with equal intensities till they reunite at D d.
They will arrive there, however, in opposite phases, and
will therefore counteract each other at their point of reunion, and in every point of their subsequent course
along the pipe D E; so that on applying the ear at E
no sound should be heard, or at best a very feeble one,
arising from  some slight inequality in the intensities
wherewith the undulations arrive by the longer and
shorter pipe-a difference which may be made to disappear, by giving the longer a trifle larger area for its
section.*
(io.) Suppose now that the pipes instead of being
cylindrical were square, and that the whole surface of
one side of a chamber were occupied with the orifices
A of such pipes, leaving only such intervals as might be
necessary to give room for their due support, and for
* I ought to observe, that I have not made the experiment described in the text, nor am I aware that it has ever been made; but
it is easy to see that it ought to succeed, and would furnish an apt
enough illustration of the principle of interference. Instead of a
pipe, inclosing air, a canal of water might be used, in which waves
of a certain breadth, excited by some mechanical contrivance at one
end, would not be propagated beyond the point of reunion, D, of
the two canals into which the main channel, A B, was divided.




BY COLOURED MEDIA.                485
their subdivision according to the condition above explained; and suppose, further, that the other ends (E)
of all the reunited pipes opened out, in like manner, into
another chamber, at some considerable distance from the
first, and separated from it by masonry or some material,
filling in all the intervals between the pipes, so as to be
completely impervious to sound.  Things being so disposed, let the whole scale be sounded, or a concert of
music performed in the first chamber, then will every
note, except that one to which the pipes are thus rendered impervious, be transmitted.  The scale, therefore,
so transmitted, will be deficient by that note, which has
been, to use the language of photologists, absorbed in its
passage. If several such chambers were disposed in
succession, communicating by compound pipes, rendered impervious (or untuned, as we may term it) to so
many different notes, all these would be wanting in the
scale on its arrival in the last chamber; thus imitating a
spectrum  in which several rays have been absorbed in
their passage through a coloured medium.
(i i.) In my Article on Light, above referred to, Art. 505,
I have suggested, as a possible origin of the fixed lines
in the solar spectrum, and (pari ratione) of the deficient
or less bright spaces in the spectra of various flames, that
the same indisposition in the molecules of an absorbent body to permit the passage of a particular coloured
ray through them, may constitute an obstacle, in limine, to
the production of that rayfrom them. The following easy
experiment will explain my meaning. Take two tuning
forks of the same pitch, and heating the ends of them,




486        ON THE ABSORPTION OF LIGHT
fasten with sealing-wax, on one of them one, and on the
other two, disks' of card (all equal in size), on the inner
surfaces, having the plane of the card perpendicular to
that of a section of the fork through the axes of both its
branches. -The cards on that fork which has two, should
have their surfaces about a tenth of an inch asunder, and
their centres just opposite; and the other fork should be
brought into unison with it by loading its undisked
branch with additional wax, equal in weight to the disk
and wax on the other.  Now strike the forks, and a remarkable difference will be perceived in the intensity of
their sounds.  The fork with one disk will utter a clear
and loud sound, while that of the other will be dull and
stifled, and hardly audible, unless held close to the ear.
The reason of this difference is that the opposite branches
of the fork are always in opposite states of motion, and
that in consequence the air is agitated by either the two
branches vibrating freely, or by both loaded with equal
disks, with nearly equal and opposite impulses; whereas
in the case of a fork furnished with only one disk, a
greater command of the ambient medium is given to the
branch carrying it, and a much larger portion of uncounteracted motion is propagated into the air. Here, then, we
have a case in which a vibrating system  in full activity
is rendered, by a peculiarity of structutre, incapable of
sending forth its undulations with effect into the surrounding medium; while the very same mass of matter,
vibrating weith the same intensity, but more favourably disposed as to the arrangement of its parts, labours under
no such disability.




BY COLOURED MEDIA.                 487
(12.) The disked tuning fork is a most instructive instrument, and I shall not quit it until I have availed myself of its properties to exemplify the easy propagation of
vibrations, of a definite pitch, through a system comparatively much less disposed to transmit those of any other
pitch.  Take two or more forks in unison, and furnish
each of them with a single disk of the size of a large
wafer, looking outwards.  Having struck one of them,
let its disk be brought near to that of the other,
centre opposite to  centre, and it will immediately
set the other in vibration, as will be evident by the
sound produced by it when
the first fork is stopped, as        A     B      C
well as by its tremors, sensible
to. the hand which holds it. 
The  communication  of the
vibration is much more powerful and  complete  when  a
small loop of fine silver wire
is fixed to one of the forks,  
and brought lightly into con-   l        
tact with the other, with its             
looped or convex side.  Ima- 
gine now  a series  of such
forks and loops arranged as in the annexed figure, and
let the first, A, be maintained in vibration by any exciting cause, as, for instance, by sounding a musical note
opposite to its disk, A, in unison with its pitch.  The
vibrations so excited will, as is evident, run along the
whole line, tnough with diminishing intensity, to the last




488        ON THE ABSORPTION OF LIGHT
fork. Here, then, we have a case analogous to the easy
transmission of a ray of definite colour, accompanied with
its gradual extinction, in traversing a considerable thickness of the absorbing medium.  If we would avoid the
actual contact of the vibrating systems, we may conceive
an arrangement like that here depicted, where, in place
of forks, straight bars, disked at both ends and supported
at their centres, are used to form the vibrating series.
(1.3.) When two disked tuning forks slightly out of
unison are opposed to each other, the vibrations of one
are still communicated to the other, even when they differ
sufficiently to' produce audible and pretty rapid beats.
But the communication in this case is less complete, and
the sound produced feebler, than in that of perfect unison, and the degradation of intensity in the communicated sound is very rapid as the forks recede from
unison.  We have here a fact analogous to the appearance of a bright line in the spectrum situated between
dark spaces, and as it is not difficult to imagine com



BY COLOURED MEDIA.                489
binations of the nature above mentioned, in which several different notes shall be transmitted, while the intermediate one, finding no unisons, or near approaches to
unison in the systems established, shall be extinguished;
so by analogy we may perceive how any number of
bright and dark lines may be produced in a spectrum
unequally absorbed.
(I4.) The case last put is entirely analogous in its
principle to that of a phenomenon which is described in
my Treatise on Sound, and of which, at the time of the
publication of that Treatise, I believed myself to have
been the first and only observer, though I have recently
learned to rectify that impression, and have great pleasure in referring the experiment, which is a remarkably
easy and striking one, to Mr Wheatstone, the author of
so many other ingenious and instructive experiments in
this department of physics. If a tuning fork be held
over the open end of a pipe pitched in unison with it,
the pipe will speak by resonance. (If the fork be disked,
and the aperture of the pipe be nearly covered by the
disk, the tone brought out is one of a clearness and
purity quite remarkable.)  Now both Mr Wheatstone
and myself have observed that -if two forks, purposely
pitched out of unison with each other, so as to yield the
beats of imperfect concords, be at once held over the
orifice, the pipe will, at one and the same moment, yield
both the notes, and will utter loud beats, being actually
out of unison with itself.  In proportion, however, as
the pitch of one or other fork deviates from that to which
the length of the pipe corresponds, and which the pipe




490       ON THE ABSORPTION OF LIGHT
alone would utter, the resonance of its tone is feeble, and
beyond a certain interval becomes inaudible.
(I5.) The dynamical principle on which these and
similar phanomena depend is that of " forced vibrations,"
as it is stated in the Essay on Sound above referred to,
or, more generally, in a more recent publication (Cab.
Cyclop., volume on Astronomy), in terms as follow:
" If one part of any system, connected either by material
ties or by the mutual attractions of its members, be continually maintained by any cause, whether inherent in
the constitution of the system or external to it, in a state
of regular periodic motion, that motion will be propagated throughout the whole system, and will give rise in
every member of it, and in every part of each member,
to periodic movements, executed in equal periods with
that to which they owe their origin, though not necessarily syancronous with them  in their maxima and minima."  The general demonstration of this as a dynamical
theorem is given in the Essay on Sound already referred
to, and its applicability to the transmission of light
through material bodies is indicated in a note thereto
appended.
(16.) The mode, then, in which we may conceive the
transmission of light through gross media to be performed, so as to bring the absorptive phsenomena within
the wording of this principle, is, to regard such media
as consisting of innumerable distinct vibrating parcels
of molecules, each of which parcels, with the portion of
the luminiferous sether included within it (with which it
is connected, perhaps, by some ties of a more intimate




BY COLOURED MEDIA.                49I
nature than mere juxtaposition), constitute a distinct
compound vibrating system, in which parts differently
elastic are intimately united and made to influence each
other's motions. Of such systems in acoustics we have
no want of examples-in membranes stretched on rigid
frames, in cavities stuffed with fibrous or pulverulent
substances, in mixed gases, or in systems of elastic
laminse, such as boards, sheets of glass, reeds, tuning
forks, &c., each having a distinct pitch of its own, and
all connected by some common bond of union.  In all
such systems the whole will be maintained in forced
vibration so long as the exciting cause continues in
action, but the several constituents, regarded separately,
will assume, under that influence, widely different amplitudes of oscillation, those assuming the greatest whose
pitch taken singly is nearest to coincidence with that of
the exciting vibrations.  Everybody is familiar with the
tremor which some particular board in a floor will
assume at the sound of some particular note of an organ;
but when that note is not sounded, it is sufficiently
apparent that the board is no less occupied in performing its dynamical office of transmitting to the soil below,
or dispersing through its own substance and the contiguous bodies, the motion which the oscillation of the
air above is continually imparting to it.
(I7.) As we know nothing of the actual forms and
intimate nature of the gross molecules of material bodies,
it is open to us to assume the existence, in one and the
same medium, of any variety of them which may suit
the explanation of phenomena.  There is no necessity




492        ON THE ABSORPTION OF LIGHT
to suppose the luminiferous molecules of gross bodies
to be identical with their ultimate chemical atoms.  I
should rather incline to consider them as minute groups,
each composed of innumerable such atoms; and it
may be that in what are called uncrystallized media,
the axes or lines of symmetry of these groups may have
no particular direction, or rather all possible directions,
or the groups themselves may be unsymmetrical. Such
a disposition of things would correspond with a uniform
law of absorption, independent of the direction of the
transmitted ray; while in crystallized media a uniformity
of constitution and position of these elementary groups,
or rather of the cells or other combinations which they
may be regarded as forming with the interfused aether,
may be readily supposed to draw with it differences in
their mode of vibration, and even different disposals of
their nodal lines and surfaces, according to the different
directions in which undulations may traverse them: and
which may not impossibly be found to render an account
of the change of tint of such media according to the
direction of the rays in their interior, as well as of the
different tints and intensities of their. oppositely polarized pencils; of which latter class of phlenomena,
however, I shall immediately have occasion to speak
further.
(I8.) But as my present object is merely to throw out,
as a subject for examination, a hint of a possible explanation of the phaenomena of absorption, on the undulatory
theory, I shall not.now pursue its application into any
detail, nor attempt the further development of particular




BY COLOURED MEDIA.                493
laws of structure competent to apply to this or that phaenomenon.  I will, however, mention one or two facts in
acoustics which appear to me strongly illustrative of corresponding phaenomena in the propagation  of light.
The first of these is the impeded propagation of sound in
a mixture of gases differing much in elasticity as compared with their density. The late Sir J. Leslie's experiments on the transmission of sound through mixtures of
hydrogen with atmospheric air sufficiently establish this
remarkable effect. It would be desirable to prosecute
those experiments in larger detail, but hitherto I am not
aware of anybody having ever repeated them. It would
be interesting, for instance, to inquire whether the impediment offered by such a mixture of gases be the
same for all pilches of a musical note, or not; and how
far this phenomenon might be imitated by mixing actual
dust of a uniform size of particle, such as the dust of
Lycoperdon, &c.; or aqueous fog, and how far such mixture would affect unequally sounds of different pitches.
(I9.) The other fact in the science of acoustics which
I would notice as illustrative of a corresponding phienomenon in photology, is one observed by Mr Wheatstone,
which I have his permission to mention.  In attempting
to propagate vibrations along wires, rods, &c., to great
distances, he was led to remark a very great difference
in respect of facility of propagation between vibrations
longitudinal and transverse to the general direction of
propagation.  The former were readily conveyed with
almost undiminished intensity to any distance; the latter
were carried off so rapidly by the air, as to be incap



494     ON THE ABSORPTION OF LIGHT, ETC.
able of being transmitted with any considerable intensity
to even moderate distances.  This strikes me as obviously analogous to the ready transmissibility of a ray
polarized in one certain direction, through a tourmaline
or other absorbing doubly-refracting crystal, while the
oppositely-polarized ray (whose vibrations are rectangular to those of the first) is rapidly absorbed and stifled,
i.e., dispersed, by the agency of the colouring matter
which acts the part of the air in Mr Wheatstone's experiment, and self-neutralized by the opposition of its subdivided portions as above explained.
SLOUGH, October 9, 1633




XI!V
ON  THE  ESTIMATION  OF  SKILL  IN
TARGET-SHOOTING.
gjAPPENING  to be present at an archery
meeting at St Leonard's not long ago, I was
struck, on examining the target, by observing a much less degree of concentration of
"hits," as indicated by the marks left on them about
the centre and within the "gold" (accompanied by a
rapidly-increasing frequency of marks within the immediately-surrounding circles, proceeding thence outwards
from the centre), than could be at all reconciled with my
own preconceived impression of what ought to be the
proportional numbers, according to what I then considered as results afforded by a legitimate application of
the calculus of probabilities to such a question. The
proportional numbers of hits in the several areas distinguished as gold, red, blue, white, black, marked out
by equidistant rings of 4-8 inches each in breadth, surrounding the gold circle of that radius, ought, accord



496            ON THE ESTIMATION  OF
ing to the statement given by myself in my review
of M. Quetelet's work on Probabilities,' to run as follows:-In the gold (out of 500 hits), 107; in the red
annulus, 106; in the blue, ioI; in the black, 97; and
in the white, 89; supposing the target (terminating with
the white) to receive half the entire number (iooo) ot
arrows discharged; which  in the case observed was
not far from  the truth.  Wiitteas by the actual record
of that day's shooting, handed to me afterwards, the
proportional numbers corresponding to a total of 500
hits were:-Gold, 31; red, 89; blue, I21; black, 140;
white, II9.  This discordance with observation, being
far too great to be attributable to ordinary casualty (the
whole number of arrows discharged on the day in question being upwards of 7000), led me, of course, to
re-examine the reasoning on which the first expectation
had been grounded.  And so enlightened, I was at no
loss to discover its fallacy,-affording, as it does, a good
example of the necessity of close attention to the wording of all reasonings on questions of probability.  It
was, in fact, traceable to the wording of a proposition
perfectly true, and, as applied to the case where it was
employed in another inquiry, correctly applicable, viz.,t
"Suppose a ball dropped from  a given height, with the
intention that it shall fall on a given mark.  Fall as it
may, its deviation from the mark is error; and the probability of that error....  decreases in geometrical
* Essays from the Edinburgh and Quarterly Reviews, &c., &c.
Longman, 1857. P. 401.
i Essays, &c., &c. Pp. 398, 399.




SKILL IN TARGET-SHOOTING.                497
progression as the square of the error increases in arithmetical."  Now, it is perfectly true that the deviation
of the point of incidence from the mark is error.  But
it is something more special.  It is error in that one
particular direction in which the point of incidence lies
from the mark aimed at.  In estimating, therefore, the
probability of striking a target at a certain definzite distance from the centre aimed at, we must multiply the probability of striking a determinate point at that distance
from  the centre, by the number of points within the
extent of the target which actually do lie at that distance
from it, without regard to the directions in which they
lie: i.e., we have to multiply the fractional number expressing the abstract probability of committing a given
error out of an indefinite number of equally possible ones,
by a number proportional to the degree of opportunity
which the circumstances of the special case afford for
its commission.  In this case that degree of opportunity
is evidently measured by, and proportional to, the length
of the circumference of the circle about whose centre,
at the distance specified, an arrow may strike, or a ball
drop from a height.
(2.) Reasoning on this (the correct principle in the
case of target-shooting), any one conversant with matheliiatical analysis will find no difficulty in arriving at the
Iollowing singularly neat and simple formula for the pr-obability of missinZ, in any one single shot, a circular area
of given radius (r), at whose centre the shooter aims.*
* The demonstration of this formula is annexed in the form of a
note at the end of this essay.
2 




498           ON THE ESTIMATION OF
Denoting by a the radius of the circular area within which his skill would, on the average  of an immense number of shots, enable him to plant half the
total number discharged; and by M  the fraction expressing the probability in question, certainty being expressed by i, we shall have
72
_    a2
while for H  the probability of hitting the same area
we have
I= — M
(3.) From these expressions, knowing the value'of a,
which is the inverse measure of the skill of the shooter
(being less the greater that skill), it is easy to calculate
his chance of hitting a circle of any given radius in a
single shot.  And, reversing the  question, his skill
(measured by the fraction  -) may be ascertained, by
observing what percentage of shots he can plant, on a
large average, from a given distance, within a circle of
any given radius (r).  For that percentage being the
numerical expression of his probability of hitting the
circle, or the value of HY, or i~M, iM is known, and a
will be given by the formula.
Log. 2          / Log. 2
a= r  -  Log. M.   r -   Log. -H)
Thus, if a marksman  be  observed to plant 9 per
cent. of his arrows within a circle of one foot in
diameter at the distance of one hundred yards, we have




SKILL IN TARGET-SHOOTING.              499
r =  -; H=  -;  M =. _i9, whose logarithm is -oo40g6,
I00       100
/ 30I03
that of 2 being + o30I03: so that a =         ~ 1   4096
f.      f. in.                            f.  in.
I'355= I'4  4; which, doubled, gives 2-8   for
the diameter of a target which he might make an even
bet to hit at the first shot.  And according to the values
of this constant, so determined in the case of each
several competitor, ought their names to be arranged in
a prize-list, the smaller values ranking higher than the
larger.
(4.) If the object of the competition be merely to
arrange the competitors correctly in order of skill at
the moment, without deducing for each any definite and
normal numerical result expressive of his absolute skill,
and comparable with others derived from practice with
targets of other dimensions, and at other distances; it is
evident that the trouble of any such computation as the
above maybe spared, since the same precise order must
necessarily result from merely tabulating the total number of hits of each competitor (practising with an equa3
number of arrows, and at one and the same distances)
Were the number of shots allowed to each immensely
large, the same order of merit and the same set of values
of the constant a would result from a record of the hits
within the total area of each of the several circles marked
out by the outer circumferences of the gold, red, blue,
black, and white colours.  The only use of these rings
is to give opportunity for a variety of prizes, and that
piquancy and interest to the result of a day's shooting




500            ON THE ESTIMATION OF
which arises from the element of luck mixing itself in the
competition. This it does the more, the fewer the shots
allowed to each, nor can it be eliminated, so as to make
skill the sole determining power, but on the average of
very enormous numbers, such as, for instance, ten or
twenty thousand arrows discharged by each marksman.
Every shooter, of course, aims to the best of his ability,
exclusively with a view to hit the centre of the gold;
nor is it conceivable that, having that intention, there
should exist in any individual such specialty of aiming
as should disperse his shots, failing the gold, so as to
strike preferentially (say) the blue, rather than the red
ring on one side of it and the black on the other.
(5.) The following table shows the respective numbers of "hits" per iooo shots, which may be expected
to occur on a calculation from our formulae, within the
several coloured areas of the five equidistant rings (considering the central gold as the first ring) into which an
ordinary target is divided. Considering its diameter as
divided into ten equal parts, the outside diameters of
those rings will be respectively 2, 4, 6, 8, Io; their radii,
i, 2, 3, 4, 5; and the areas of their containing circles,
in the proportion of the squares of these numbers, i,
4, 9, I6, 25,-so that the areas of the several coloured
spaces form the progression i, 3, 5, 7, 9. The usual
rule of valuation, then, which accords to hits in any ot
the rings (from the white inwards), values in the proportion of these numbers; assumes the probability of hitting
to be in the simple proportion of the area struck (as
would be the case were the shooting entirely at random),




SKILL IN TARGET-SHOOTING.                   501
and the merit to increase as the probability, so estimated
diminishes. The range in this table of the quantity a,
or what may be termed the probable error from  the
centre of a single shot, includes what may be taken as
the extremes of good and bad shooting:TABLE I.
Probable hits per thousand in the
J.... B~-   ~           llisses
a    Gold      Red      Blue     Black    White       s
5 to (Z>.
o- I.   I - 2.    2-3.    3- 4.    4  5.
I    500      438       42        20        0         0
2    I59      341       290      I47       50        13
3     74       I91      235      208       146      146
4     42       117      I64      I77       i6i      339
5     27       78       II6      137       142      500
6     19       55        85      io6       118      617
7     14       41        65       82        96      702
8     II       31        51       66        78      763
9      9       25        40       54        65      807
In      7       20        33       45       54       841
(6.) For the purpose of comparing this theory with
practice, I have been favoured with the series of annual reports of the practice  at the Grand  National
Archery Meeting, with their target lists, and awards of
prizes, for fifteen successive years, commencing with
I850; which record the hits made by each competitor
in each of the colours, from  specified distances, and
with specified numbers of arrows. The number of shots
delivered amounts, collectively, to upwards of half a
million; and excluding I69 cases in which it is noted
that the shooter did not deliver all his arrows, and those
comparatively much more rare ones in which the record
of the shots is incompatible with the awarded value
from some other cause than a mere misprint (which can
generally be rectified), to 474,384; of which 168,239
were hits, and 306,I45 misses, on a target of 48 inches in




502           ON THE ESTIMATION OF
diameter, which gives 4 8 in. for the unit of our a.  This
gives as a general average, 644 misses per iooo shots;
and therefore were the distances all alike, or for an
average distance of 80 yards, would correspond to a
value of a in our table, of very nearly 6~, or to a mean
probable deviation of a single shot, of 30'4 in.; the
total number of competitors being 2075 (reckoning the
same individual appearing in several lists as so many
distinct competitors), shooting at 430 targets. As the
causes of linear deviation may be considered as increasing proportionally to the distance, and as in fixing the
average distance as above at 80 yards, (strictly 79',) the
number of arrows discharged at each distance is taken
into account; this may be regarded as a fair estimate of
our national proficiency in archery, and as comparable,
in the terms of its statement, with what may be obtained
at a future period, or in other countries.
(7.) In deducing the results embodied in the following tables, the numbers of hits made by all. the shooters
at each target in  its several colours were summed
separately.  The results so obtained for all the targets
for each class of shooters, and for each distance, in
each year of the series, were then grouped together and
summed, and the fifteen sets of annual sums so obtained, united into general sums, as exhibited below in
Table II., to shorten which it is to be borne in mind
that of the lady competitors, 853 in number, each delivered 96 arrows at 60 yards, and 48 at 50;  and the
* In the year I850 the arrows delivered by each lady were only
72 and 36 at the same distances.




SKILL  IN  TARGET-SHOOTING.                           503
gentlemen, numbering  1222, 144  arrows at ioo yards,
96 at 80, and  48 at 60  yards: the  number of targets
being, for the former, 164, and for the latter 266.
TABLE II.
Dis-  Total       Numbers of hits in the several 
Class of   tance No. ofcolours.
shooters,   in   arrows                    ~;o_ rs   t          Misses.
y de-s                                           Msse
yards. livered.  Gold.  Red.  Blue. Black. White.
Ladies...... 60    81696   I722   4927   7279   8572   8688    50s o8
Do..........  50    40848   1364   3799   5145   5640   5159   19741
Geeentlem           7 9en  i 759 873   535   8239 i062   11605  938257
oo.737 5o,  o 56    839  i      oo29 ~!l t85
Do.......... 80   7312   2516   706i  10137  I2067  I2058   73473
Do.......... 6    58560   2553   6651   8455   8983   7752   24166
Sums total         474384   1 0028  27803  39255  45891  45262  306145
(8.) To compare  these  results with theory, and ascertain  how  far the  distribution  of the hits in  each  series
corresponds with  our formula, the  best way will be  to
deduce, in  each, five separate values of a  the  constant
appropriate to each mi, from-iSt, the hits in the gold; 2d,
the  sum   of those in  the gold  and red; 3d, the  sum  of
those in the gold, red, and blue, and so on. These, it
is manifest, in each series ought to agree inter se, though
different  for different series.   Applying, then, the  expression  given  in ~ (3.) for a to  these entries of "hits"
in'able II. on this principle, we derive corresponding
values of our constant or modulus as in' the annexed
table (Table III.), in the first division of which it is set
down in units and decimals, as in Table I.; while in the
second are entered the same values reduced to inches
and decimals by the multiplier 4'8.




504                   ON THE ESTIMATION OF
TABLE III.
Dis-     Values of a as deduced from the numbers of
tance      hits falling within the circles externally      Mean
Class.      in                      limiting the                      value
yards   i      n       ___________                       of a.
| yards.   Gold.    Red.    Blue.    B:ack.  White.
Ladies......  60       5'704     5'7I5     5'777     5'867    6'003      5'8I3
Do..........  50      4'518     4'530     4'631    4'75I    4'882       4'662
Gentlemen   ioo         8'048     8'125     8'232    8'311     8'476     8'238
Do..........  80      5'654     5'693     5 823     5'925    6'o86      5'836
Do..........  60     3943      4'027     4'70      4275      4425       4'68
in.       in.      in.        in.      in.        in.
Ladies......  60     27 380   27'432   27'730   28163   28'8T2    27'903
Do.........  50     21'685   2T'743    22'231   22'804   23'432    22'379
Gentlemen   ioo        38'631   38 998   39'512   39'893   40'686    39'544
Do..........  80     27'4I   27'388    27'950    28'438   29,210    28'025
Do..........  60     18'928   I9'324  20'012   20'519   21'239    20-004
(9.) Although  the  general agreement of the results in
each  horizontal line  of this  table  is  quite  sufficient to
afford  a  highly  satisfactory  verification   of  the  theory,
it is impossible  not to be struck with the  uniform
and steady increase  (though small) in the value of a
in proceeding from  the gold outwards.  There occurs
not throughout the whole table a single instance in
which this progressive dilatation is not maintained. For
this there must be a reason; and  the only rational
account of it, so far as I can perceive, is this:  Were the
number of shooters infinite, including (indifferently) every
gradation of skill, from absolute random shooting up to
absolute certainty of striking the point aimed at: the
result of their combination would be one from which individual  skill would  be   entirely   eliminated;  and   the
distribution  of the  hits  would  be  regulated  purely  and
simply by the  inztention  of hitting  the  centre.   The skill
in that case (on which the value of a depends) would be
the average  skill of the whole human race; and  the value




SKILL IN TARGET-SHOOTING.              505
of a would conform to that average. But the number of
shooters at each target being limited, never more than
six, and sometimes not more than two or three (owing
to our rejection of those scores where the arrows were not
all delivered), the distribution of the hits on each results
from the summation or superposition of several series of
numbers graduated according to the values of so many
different specified values of a as a modulus; the intermediate values being absent: and it by no means follows
that such a series of sums will follow the law of gradation
of either separately, or accommodate itself rigorously to
an average modulus; any more than it would follow that
a curve whose ordinate is the sum of the ordinates of (say),
two concentric circles should itself be a circle. Suppose,
for instance, we were to ground our calculation of an
average modulus or value of a on a series of hits given
by summing up each separate column of Table I. This
would give the following series:-Gold, 862; Red, I337;
Blue, IT2I; Black, 1042; White, 910, on a total number of io,ooo shots. And from this deducing five several
values of a by the use of the formula of ~ (3), after the
manner of those in Table III., we should obtain the
series,
a= 2'77I, 3'340, 3'93I 4'399, 4'809,
which exhibits (only in a much more exaggerated form)
precisely the sort of dilatation in question. This being
then the tendency, in the case of each particular target,
a similar tendency will of course be exhibited by the
successive values resulting from a combination of any
numlber.




506             ON THE ESTIMATION OF
(Io.) The same principles apply of course equally to
rifle-shooting as to archery, provided the target aimed at
be circular. If rectangular, and especially if an elongated rectangle, the same'formule will not apply; and
the appropriate formulae would be necessarily much more
complex and their results proportionably more difficult
of calculation. This is a strong argument for the use
of circular targets: for, though for the mere decision of
the order of merit in a distribution of prizes almost any
impartial rule, rough and readily applicable, may suffice,
the same cannot be said when the object is to obtain a
true numerical measure of the national skill in the use
of that great weapon' for which purpose it is highly
desirable that the data afforded by our rifle priwe meetings should be preserved, collected, and reduced systematically.
NOTE.
Demonstration of the formula in ~ (2.) and (3.)
The probability of committing the specific error r (all errors presenting equal facility for their commnission) is proportional to
E (-kr2), the characteristic sign E being used to denote the exponential or anti-logarithmnic function; and k being some certain constant to be determined or eliminated. And in the case of aiming at
the central point of a circular target, the degree of facility afforded
for the commission of a lineal error r, no matter in what direction,
is proportional to 27rr, the circumference of a circle of that radius,
or, simply to r: so that the probability of planting a shot somewhere on the circunference of that circle is measured by r. E ( —kr),
and therefore the probability of making a hit anywhere within its
area is proportional tofrdr. E (-kr2) taken between the limits
o and r. Representing certainty therefore by I; this probability
(which we have denoted by H in the foregoing pages) will be ex



SKILL IN  TARGET-SHOOTING.                  507
pressed numerically by such a multiple of this integral, so taken, as
to give I for its value when r is infinite: which gives
H= I - E (-kr2); and therefore M = E (-kr2).
Now, when r- a, the radius of that circle within which just half
the total number of arrows strike; the probabilities of hitting and
missing that circle are equal: so that H  and M  are in that case
each = ~. We have, consequently,
E (-ka2) = -,
and eliminating k, we obtain
Log. M ='   log. (1) 
or,
2
COLLINGWOOD, 2zune 8, I866.
THE END.