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A. R. HINKS, M. A.
FROM THE SMITHSONIAN REPORT FOR 1905, PAGES 101–118.
(No. 1deo.)
WASHIN(#TON:
GOVERNMENT PRINTING OFFICE.
19 () 7. -


Astronsmical
Observ, fory
oger ºvaroRY L. BRARY 9 P.
NEW MEASUREMENTs of THE DISTANCE ºf
OF THE SUN. .--
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FROM TH E SM ITI ISON IAN REPORT FOR 1905, PA(; ES 101-118.
(No. 1669.)
WASH IN (;"I'()N:
(+() VII: NMIN'T PRINT1 NC; () FFICE.
1907.

NEW MEASUREMENTS () F THE I) ISTANCE OF THE SUN."
Hy A. R. H IN ks, M. A. -
When I received the honor of an invitation to lecture at the School
of Military Engineering on some astronomical subject, I had little
difficulty in making my choice of a topic. There is just one subject
on which I may speak with some little first-hand knowledge; and
by great good fortune that subject is concerned with a problem which
has both in its nature and its history a connection with the Corps of
Royal Engineers.
The problem of the determination of the distance of the sun is, in
some respects at least, the most fundamental in the whole range of
astronomy, for the number which represents it is involved in almost
any calculation of distances and masses, of sizes and densities, either
of planets or their satellites or of the stars. The distance of the sun
bears somewhat the same relation to other problems of celestial sur-
veying as the size and shape of the earth bear to terrestrial. It may
not always appear on the surface, but it is generally concealed some-
where in the depths of the calculations. And I am compelled to
confess that in one respect the earth measurers have the advantage
over astronomers. The utmost that the astronomer can do is to
show that the distance of the sun is so many times the radius of the
earth. Ibut ask him to put it into miles and he is powerless to do
so until the geodesists have told him how large the earth is; and it
is there that, in the very nature of the case, we are compelled to
depend in the end upon the scientific labors of your corps.
a Lecture delivered at the Royal Engineers' Institute on February 9, 1905.
Reprinted, by permission, from the IRoyal Engineers' Journal, Volume II, No. 1,
July, 1905, Chatham, England, Itoyal Engineers' Institute.
101
l68986
| ()2 NEW MEASUREMENTS () F DISTANOE OF SUN.
1)istance of sun corresponding lo different values of the solar parallaa and
Clarke's figure of 1880.
7T, Miles, Rilometers.
Af
8.760 93,321,000 | 150, 180,000
8.770 214,000 | 150,010, 000
s'780 108,000 | 1.49, 8:10,000
S-700 2,000 670,000
8:800 92,896,000 500,000
8 '81() 701,000 330,000
S 820 (86,000 || 1:19, 160,000
S 8:30 581,000 || 1:18,990, 000
S "S:[() 176,000 820,000
A difference of 0:01" in the parallax is equivalent to 106,000 miles, or 170,000 kilometers.
Let us look at the matter for a moment as a problem in pure Sur-
veying. To measure the distance of the sun we have as a base a
chord somewhat less than the diameter of the earth, since observa-
tions can not be made on a heavenly body when it is actually on the
horizon. Suppose we put our base line at nine-tenths of the diam-
eter. Our problem is to determine the distance of a body so far away
that the whole diameter of the earth subtends at it an angle of only
about 17.6 seconds of arc; and with our somewhat diminished base
this angle is reduced to a little less than 15 seconds. I believe that
the length of your base upon the great lines of Chatham is about
1,730 feet. Imagine that from that base you had to determine with
an accuracy greater than one in a thousand the distance of an inter-
sected point about 4,500 miles away, as far away as Chicago, and you
have a problem which is by comparison simplicity itself. For the
ends of our 7,000-mile base are not visible from each other, being on
opposite sides of the world, and our angles at the base must be
determined by a complicated reference to the zenith, with all the
well-known impossibilities of determining absolute places in the sky
increased by the special difficulties that arise when the object to be
observed is the sun. You will readily grant that to determine the
distance of the sun by direct observation of that body is impossible,
unless you are content with an accuracy of about 1 in 10.
Now, it is a curious fact that there is a way of obtaining the dis-
tance of the sun with an accuracy of 10 per cent with no other instru-
ment than a clock keeping accurate time. You do it by observing
the times of minima of the variable star Algol. Every two days
twenty-one hour's Algol drops more than a magnitude, and does
this with a regularity which would be unfailing were it not for the
fact that at one season of the year we are nearer the star by nearly
the whole diameter of the earth's orbit than we are at the opposite
NEW MEASUREMENTS () F DISTA NOE OF SUN. 103
season; and light takes about sixteen minutes to traverse that dis-
tance. In the middle of November the eclipses of Algol are taking
place eight minutes earlier than the average. In May, could we
observe the star so near the sun, they would be found eight minutes
behind their time; and a practised observer could, on a long series of
observations, determine that inequality, with a total range of sixteen
minutes, well within two minutes—that is to say, with an accuracy
of about 10 per cent. We have then only to combine this quantity
with the known velocity of light and we have a measure of the sun's
distance. A mere curiosity in itself, it will serve to introduce us to
Some indirect ways of determining the distance of the sun which
have, both practically and historically, a peculiar interest and im-
portance.
At the present time we are in the thick of a new determination of
the distance of the sun on a scale of operations greater than has been
Known before. More than fifty observatories of the Northern Iſemi-
sphere are engaged more or less deeply on the work, which has occu-
pied a great many of us closely for the last four years and will give
plenty of trouble to some of us for several years to come. Before
we enter upon the consideration of the new method and the new
opportunities we might well pause to answer the question, which is
by no means superfluous, IIow does it come about that, at the end of
the nineteenth century, which had seen attempts almost innumerable
to measure the distance of the sun, the result was still so much in
doubt that it was worth while to concentrate quite a large proportion
of the total astronomical energy of the world upon a new attempt :
I believe that we shall find some explanation of this fact if we
examine the history of the various values of the solar parallax that
were used in the Nautical Almanac during the nineteenth century.
A determination of the distance of the sun by direct observation of
the sun itself is impracticable; the sun is too difficult an object to
observe with any great accuracy; its distance is too great, and our
base is too small for any method of direct trigonometrical survey to
be possible. But we can in effect diminish its distance by substitut-
ing for it one of the planets, which can be more accurately observed,
for when the distance of any one planet from the earth is known, the
dimensions of other orbits follow by the application of Kepler's third
law. And at the same time we can, as we shall see, secure the ines-
timable advantage that the measures to be made are relative and not
absolute.
Let me digress for a moment-to insist upon the importance of this
distinction. If you wished to find the difference in latitude and lon-
gitude between your Institute and the trigonometrical point at Dar-
land, you might determine the latitude and longitude of each and
take the differences, or you might triangulate from one to the other.
1()4 NEW MEASUREMENTS OF DISTANCE OF SUN.
One is an absolute method, the other a relative, and it is scarcely
necessary to emphasize the difference in accuracy between the two.
We shall see that, various as are the kinds of measurement which
may be made to contribute to a knowledge of the solar parallax, they
are all of them relative measurements. For example, one may ob-
serve the displacement of the planet Mars among the stars, as seen
from a northern and a Southern station—say Greenwich and the
Cape—or one may observe the displacement of the place of Venus in
transit across the Sun from stations suitably chosen. In each case we
are measuring the displacement as viewed from different stations of a
near object with respect to one farther off, the displacement of Mars
among the stars or of Venus against the sun. We have secured the
advantages that the parallactic displacement to be measured is
greater than that of the sun itself; that the objects to be observed,
Mars or Venus, are better adapted for observation, and that the meas-
ures are relative. .
In the middle of the eighteenth century Lacaille made observations
of Mars at the Cape of Good Hope, which were compared with others
made at various observatories in Europe, and he deduced a parallax
of about ten seconds. In the same century there occurred the two
famous transits of Venus of 1761 and 1769, which were very exten-
sively observed, among others by Captain Cook on his celebrated ex-
pedition for that purpose to the South Seas. Many and various were
the results obtained by different discussions of the observations, lying
between eight and one-half and nine and one-half seconds, but decid-
edly less than the parallax found from Mars, and we find that at the
beginning of the nineteenth century the Nautical Almanac adopted
a value in round numbers, nine seconds, as the best that could be
made of them.
Values of the solar parallaa, used in the Nautical Almanac during the nineteenth
century.
. 7:
1801-18% --------------------------------------------------------- 9”
1884–1809 ------------------------------------ gº- 8 .5776”
Encke, from transits of Venus, 1761 and 1769.
1870-1881 ------------------------------------------------------ ___ 8 -95."
Leverrier, from parallactic inequality of moon (1858).
1882–1900 ------------------------- -------------------------------- 8.848”
Newcomb, from general mean of many methods (1867). . -
In 1824 the German astronomer Encke submitted to a very search-
ing examination the collected results of the transit of 1769 and
deduced the result 8-5776 seconds, which, with its imposing train of
decimals intact, was incorporated in our Nautical Almanac for 1834;
survived until 1869, and was responsible for the statement, which
many of us can remember in the schoolbooks, that the distance of
the sun is 95,000,000 miles. - . . .
NEW MEASUREMENTS OF DISTANCE OF SUN. 105
Meanwhile the attack upon the problem had been maintained in
Several different ways, and particularly by an indirect method that
has many points of interest. -
In the lunar theory there occurs, among the short-period perturba-
tions to which the motion of the moon is subject, an inequality in a
period of a month which depends upon the fact that the disturbing
action of the Sun is greater on that half of the moon’s orbit which lies
toward the sun than upon the other half. The result of this is that
the moon is more than two minutes behind at first quarter and two
minutes ahead at last quarter of the place which she would occupy
were there no perturbation. It is clear that the magnitude of the
effect must depend upon the ratio of the distances of the sun and
moon from the earth; and since the effect is large, an oscillation
either way of about one hundred and twenty-five seconds, this should
give a strong determination of the solar parallax, provided that the
moon can be observed with the required accuracy and that the theo-
retical relation between the perturbation and the solar parallax is
firmly established. In 1858 Leverrier found in this way a value of
895 seconds; several other determinations supported this large
value, and practically all the determinations made since 1830, how-
ever much they might disagree among themselves, agreed at any rate
in one thing, that Encke's value was much too small. We find, there-
fore, that in the Nautical Almanac for 1870, published in 1866,
Leverrier's value, 8 95 seconds, is adopted, and the official distance of
the Sun changed at one swoop from 95,000,000 to 91,000,000 miles.
I3ut now preparations were in full swing for the observations of
the transit of Venus of 1874 and 1882, which for many years had been
eagerly awaited in the full expectation and belief that then, with all
the manifold improvements in the arts of observation, in the inven-
tion of the heliometer and the application of photography to celestial
measurement, the question of the solar parallax would be definitely
settled. We can not do more than glance at the most beautiful and
most complicated geometrical problems involved in the consideration
of all the circumstances of a transit of Venus. But these two
diagrams" will show some of the circumstances of the very important
phenomena, the times of internal contact at ingress and egress, the
times when Venus is just completely on the sun and just about to
begin to go off. Great preparations were made for observing these
times of ingress and egress, and the results would undoubtedly have
been successful had it not been for the cruel way in which the
geometrical sharpness of the phenomenon is ruined by the lighting
a Showing the passage of the earth through the cones enveloping the Sun and
Venus. (Not reproduced.—EDR.)
SM 1905 11
106 NEW MEASUREMENTS OF DISTANCE OF SUN.
up of the atmosphere of Venus; there was no instant when tangency
was perceptible, and, to be frank, the transit of Venus as a means of
determining the distance of the sun was a failure. The photographic
and heliometer observations had for various reasons met with no
better success than the observations of contacts; there was no con-
sistency about the results.
But just as the preparations for the transits were beginning in
1867 Prof. Simon Newcomb had published an elaborate discussion
of the solar parallax based upon several different methods. With
Some of these we are already familiar, and I will call attention to one
only, the last, which we have not as yet discussed.
Components of Nellycomb’s value.
*. 7t
Newcomb, “Observation of Mars, 1862 °-____________________ Seconds—- 8 '855
Hall, “Observation of Mars, 1862 "------------------------------ (lo____ 8 ‘842
IHansen, Stone, and Newcomb, from “Parallactic inequality of
moon" -------------------------------------------------- Seconds__ 8 '83S
Newcomb, “I unar equation of the earth "----------------------- dO____ 8 '809
IPOwalky, “Transit of Venus, 1769 °––––––––––––––––––––––––––––– dO_ _ _ _ 8 ‘832
Foucault’s “Velocity of light,” and Struve's “Aberration const.”———do____ 8.860
Weighted mean------------------------ — — — — — — — — — — — — — — — seconds__ 8:848
It is an effect of aberration that every star describes yearly in the
sky an ellipse of which the Semimajor axis is about 20:5 seconds, and
this number is called the constant of aberration. It is the ratio of
the velocity of the earth in its orbit to the velocity of light. When
the constant is known and the velocity of light is known, the velocity
of the earth in its orbit is known; and since the time of describing
that orbit is also known, the size of the orbit and the distance of the
earth from the Sun follow immediately. *
In 1876 it appeared then that there was strong evidence against the
value 8 95 seconds; and without waiting for the results of the tran-
sit of Venus expeditions, the Nautical Almanac adopted for the while
the value 8-848 seconds found by Newcomb from this galaxy of results
which looked so accordant; and that value was first used in the
Almanac for 1882, the year of the second transit.
But meanwhile Sir David Gill, who had observed the transit of
1874 at Mauritius and had made up his mind very definitely that no
good would come out of the transit of 1882, had borrowed Lord
Lindsay’s heliometer and established himself on the island of Ascen-
sion to observe with the heliometer the opposition in 1877 of the
planet Mars. Every night the observing station in Mars Bay was
carried some six or seven thousand miles by the rotation of the earth
and the planet thereby displaced among the stars by some forty Sec-
onds. The heliometer is by far the most refined instrument for the
NEW MEASUREMENTS OF DISTANCE OF SUN. 107
visual measurement of distance from star to star; the observations
extended over months instead of hours; they could be pursued without
any of the disquieting feelings that a temporary breakdown would
ruin everything; and they were brought to a successful end in a paral-
lax of 8-78 seconds. But one doubt was cast upon the result. Was it
possible that the red color of Mars had influenced the measures syste-
matically? It could not be denied that the effect of the dispersion of
the air, which gave the planet a blue fringe above that might be lost
in the blue sky, and a red fringe below that, would be indistinguish-
able from the red planet itself, might have produced some effect; and
Sir David Gill resolved to try again, utilizing this time three minor
planets farther away than Mars, with less parallax therefore but with
disks so small that they were indistinguishable from stars.
In 1888 and 1889 five observatories, the Cape in the Southern
Hemisphere, and Yale, Göttingen, Leipzig, and the Radcliffe Obser-
vatory at Oxford in the Northern Hemisphere, combined to observe
the planets Victoria, Iris, and Sappho with the heliometer. The
labor was immense. The observations proved to be so accurate that
they demanded the use in a great part of the work of eight figure
logarithms. When only a few years ago the whole work was
published in two enormous volumes of Annals of the Cape Obser-
vatory, it might well have been thought that here was the last word
of observation for many years. Yet we are now attacking the
problem with more energy than ever.
About ten years ago the end of the century was in sight, and there
was a general impression abroad that it was time to set one's house
in order and to make a good start on the 1st of January, 1901. The
directors of the four nautical almanacs (the British, French, German,
and American) resolved to meet in Paris in 1896, and with the help
of certain distinguished advisers to agree upon a uniform set of con-
stants to be adopted in all the Almanacs from the year 1901. Among .
these constants was the Solar parallax. We may summarize the infor-
mation which was at the disposal of the conference thus:
Solar parallax from— Seconds.
Gill's heliometer, minor planets --------------------- *— — — — — — — —- — — — — — S - S02
Constant of aberration of light----------------------------------- S. 799
Parallactic inequality of moon ––––––––––––––--------------------- S 74).ſ.
Mass of earth from motion of Inode of Venus alone---------________ S 7(52
Mass of earth from secular variation of four inner planets_________ S - T54)
Gill’s heliometer measures of minor planets gave 8-802 seconds, and
no other direct observational result could be compared with this; the
transits of Venus were discredited even though some of the final
results had not, and have not even now, been published. The most
recent determinations of the constant of the aberration of light gave
8-799 Seconds, the parallactic inequality of the moon, 8 794 seconds.
108 NEW MEASUREMENTS OF DISTANOT OF SUN.
There were thus three powerful methods which converged upon a
value close to 8:80 seconds. But to set against them was a method
which we have not yet noticed. s .
The perturbations in the motions of other planets produced by
the earth depend upon the mass of the earth, and from them that mass
:an be determined. There is further a well-known relation between
the mass of the earth, the value of the gravitation constant, the length
of the year, and the distance of the sun, from which the latter may
therefore be derived when we know the others. Professor Newcomb
had thus determined the parallax in two different ways, and had
found two results agreeing closely among themselves, with mean 8-76
seconds, but differing widely from the others. No explanation of this
divergence could be found. But the evidence was 3 to 1 in favor of
8:80 seconds, and 8:80 seconds was adopted in 1896 as the value to be
used in all the almanacs from the beginning of this century.
It might well have been thought that the question would have been
allowed to rest there for a while. At the end of a century of labor
four principal results had emerged, and there was a majority of 3 to 1
in favor of 8:80 seconds. But there is a phenomenon, known in
politics as the swing of the pendulum or the flowing tide, by whose
operation a majority hardly won begins immediately to melt away.
A like phenomenon appears to affect the solar parallax. We have
seen how its adopted value has swung from 8:57 to 8 95 seconds, and
back again to 8.85 and 8:80 seconds. Scarcely had the resolution of
the Paris Conference been taken than the majority in favor of 8.80
seconds began to melt away. The beginning of the century had been
chosen as an auspicious moment in which to make a change, without
considering that there were at the end of the preceding century many
investigations just then drawing to a close. The value of the aberra-
tion constant corresponding to 8:80 seconds is 20:478 seconds. Al-
most every determination of that constant published since 1896—and
there are many—had come out above 20:50 seconds, many of these a
long way above. I’urther investigation of the parallactic inequality
of the moon had not only altered the observed value of the inequality,
but had modified the theoretical relation by which the parallax is
deduced therefrom. The evidence for 8:80 seconds was giving way
badly; and before the 1901 Almanac came into use we had this revised
table propounded by one of the chief instigators of the adoption of
8 '80 seconds. The majority was now 3 to 1 in favor of a value at
least as low as 8.77 seconds.
- Ičevised table,
Solar parallax from— Seconds,
Gill's heliometer, minor planets ------------------- .* - * * * * * * * * * * * * = 8 : S02
Constant of aberration of light----------------------------------- S. 77
Parallactic inequality of moon, probably-------------------------- S. 77
Mass of earth from secular variations---------------------------- 8 : 750
NEW MEASUREMENTS OF DISTANCE OF SUN. 109
I suppose that there will always be two opinions upon the question:
Is the adopted value of the solar parallax to depend upon direct
observation or are the indirect determinations through the constant
of aberration, the parallactic inequality, and the mass of the earth to
be allowed a weight in some proportion to their numbers? I take it
that those of us who have determined the parallax by direct obser-
vations may not unnaturally look upon these indirect methods as
interesting confirmations of our result if they agree with it, while if
they differ there must be something wrong with them. Put in the
absence of a direct determination of overwhelming weight there
must always be a feeling of uneasiness when one sees three or more
results conspiring to deny the truth of one. And however that may
be, it is certainly true that about the year 1898 there was a very gen-
eral suspicion abroad that the value 8:80 seconds was too large.
At this moment there came a curious stroke of fortune. Doctor
Witt, of the Urania Sternwarte, Berlin, was engaged in a photo-
FIG. 1.-Eros campaign 1900–01. Distribution of Observatories,
graphic Search for a minor planet which had long been lost. IIe
failed, but found instead a minor planet for which one would will-
ingly barter the remaining five hundred odd; a minor planet indeed,
but moving in a most remarkable orbit, lying for the most part
within that of Mars, very eccentric, considerably inclined to the
elliptic, and approaching the earth on favorable occasions within
about 15,000,000 miles. It was immediately recognized that here was
a new opportunity for determining the solar parallax and that the
determination must be made at once or left alone for thirty years,
for a comparatively favorable opposition was due in 1900 and no
more good ones till 1930 and 1937. At the meeting of the permanent
committee which directs the making of the astrographic chart and
'atalogue of the whole sky it was resolved to invite a great coopera-
tion of observatories to make a combined onslaught on the problem.
The suggestion was readily taken up, with an alacrity, indeed, which
might almost have suggested that the observatories concerned had
nothing to do and were glad of a job, an imputation which is immedi-

11() NEW MEASUREMENTS OF DISTANCE OF SUTN.
ately rejected when one finds that some of the most energetic partici-
pants were precisely those observatories that had their hands most full
with the astrographic chart (fig. 1). Dy a cruel stroke of fate Sir
David Gill at the Cape was compelled to remain a spectator of the
work, for the planet came so far north that it was practically unob-
servable in the Southern Hemisphere, while in England we had the
unique spectacle of a planet north of the zenith.
Figure 2, borrowed from Professor Wilson's articles in Popular
Astronomy, shows very clearly the circumstances. Corresponding
DEC, 30
DEC. f6
JAN. 24 Nov.30
JAN, 28 NOV N
N' . N.
FEB, 13 & DEC 30 DEC 16 "Oct. 31
2^ (YJAN. 24 NOV, 30 \ * - - -
FEB, 28 /2 NOV, 15 OCT,16.
/ JAN 28. \
/ oct. 31 oct. I'
FEB 13 w W
\
OCT, 16 \
FEB. 28 \
\
OCT. 1. | . .
UN | vehnal-
S | Eouſnox
|
|
N /
N ſ
N /
/
N /
N /
% N / ... "
/ O “A co / CO
F THE EAW QS / Q
\ WS /
/ Q-
\ zº \ 2^ </
N N 2^
*
*SS OK .** \
- • * \
\s O |T --~~ \ <
S----- R B - ~ * * VNO
S. < x^
Y ~s O R eVV_2~ N
* - - - - - *
FIG. 2.-Relative positions of Iºros and Earth from Oct. 1, 1900, to Feb. 28, 1901.
positions of the earth and the planet are joined, and if we follow out
in imagination the directions that these lines must have, remembering
that the orbit of the planet is inclined 10° to that of the earth, we
see that the planet described a loop at opposition, as all exterior
planets do, but that the loop was of very unusual proportions
(fig. 3). - 4.
To discuss in any detail the circumstances of the apparition and
the way in which they can be utilized for a determination of the
parallax would take too long. ISut we may get a good idea of a






NEW MEASUREMENTS OF DISTANCE OF SUN. 111
fairly typical case by transplanting ourselves in imagination to the
planet Eros on the evening of the 2d of December, 1900, armed with
an imaginary telescope ridiculously out of proportion to the real size
of the planet, which is probably not more than 20 miles in diameter
(fig. 4). The earth is past inferior conjunction with the sun, and
appears as a crescent. The North Pole of the earth is tilted toward
us, and by the aid of this projection of the meridians and parallels of
latitude we can with great ease trace the path of each observatory
as it is carried round by the rotation of the earth and can measure
from the scales the angular distance at any moment of an observatory
from the center, or the distance between two observatories, which
angular distances as seen from the planet are the precise equivalents
of the parallactic diplacements of the planet as seen from the earth.
FIG. 3.-Path of Eros, 1900–01.
In the programme of observations there was one novel and prom-
ising feature—the application of photography. With the exception
of the transit of Venus observations, in which its success was not
striking, photography had not been previously applied in a deter-
mination of the solar parallax, for the very good reason that in
1889, at the time of the opposition of Victoria, there was practically
only one telescope in existence which was capable of taking photo-
graphs for exact measurement, that pioneer photographic equatorial
made by the Brothers Henry at Paris. The fact that there were in
1900 eighteen photographic telescopes engaged in observing Eros
shows how rapidly the equipment of astronomy has grown in the last
few years. We were so fortunate at Cambridge as to have our new

112 NEW MEASUREMENTS OF DISTANCE OF SUN.
photographic equatorial just completed and made to work. (I may
remark parenthetically that it took longer to make the machine
work than to build it, for when one embarks upon a large experiment
and sets up an instrument, the first of its kind, built upon improved
lines, one sets out upon a Sea of troubles.)
The great advantage of the photographic method in such an under-
taking must be sufficiently well known by you. It is, of course, this,
that one is rendered very much more independent of continued fine
weather. A photograph of the planet and the surrounding stars
could be made in two or three minutes of actual exposure. Given an
hour's break in the clouds, one could accumulate far more valuable
SCALE: SECS. OF ARC.
1 O 20 30 40 50
10 O
Li | | | | | | | | | |
FIG. 4.—Meridians and parallels of latitude of the Earth as seen from Eros, Dec. 2, 1900 (negative).
The blackened portion represents the bright crescent of the Earth, the planet being more than a
month past opposition.
material than could be obtained in a whole night's visual observation,
for the photograph once Secured could be measured at leisure, by day
or on cloudy nights. -
Throughout Europe the skies of that winter were far from clear.
I had the pleasure at Cambridge of sitting up from dusk till dawn for
nearly three months on end and during that time had not half a
dozen nights clear right through. Had I been making visual observa-
tions I should have done little; as things turned-out I was able to get
Some five hundred exposures. The programme was to get four ex-
posures per hour throughout the night, making a number of exposures
on each plate, and moving the plate a little between each exposure.

NEW MEASUREMENTS OF DISTANCE OF SUN. 113
The stars are then arranged in columns of fours; the images of the
planet, owing to its rapid motion, are in echelon.
Now each exposure gives very accurately the place of the planet
with reference to the group of stars around it, and for merely parallax
purposes the ideal would be to have pairs of such photographs taken
at the same instant at stations widely separated. Iły a very simple
use of the measures of some ten or twelve stars suitably disposed
about the planet, it would be possible to allow almost automatically
for the differences of refraction, orientation, scale value, etc., which
make the plates not immediately comparable, and to find at once the
parallactic displacement.
We have been speaking of the displacement as very large, and so
it is when compared with the displacements dealt with in previous
determinations. But look at it this way: We saw that the earth as
seen from Eros subtended an angle of 53 seconds. The scale of the
Cambridge plates is such that if we draw a circle having a diameter
of a little over 14 mm. we represent the apparent diameter on our
plate of the earth as seen from Eros; and within that small circle the
whole of the parallactic displacement must necessarily lie. About
a millimeter was the average displacement obtained in a favorable
combination of observations, and when we consider that we are trying
to measure that with a resultant accuracy of 1 in 1,000 it does not
seem so very great after all.
We have put the problem heretofore in its very simplest form. In
actual fact the exposures at different stations were not simultaneous.
Early morning observations made at Cambridge might be combinable
with evening observations at Lick more or less simultaneous, or with
evening observations ten or twelve hours before at (say) Oxford; or
they might have to stand alone. Any general method of utilizing all
the results must secure the possibility of reducing each plate, so to
speak, on its own merits, to allow it to contribute its quota, be it
large parallactic displacement or none at all, to the general collection
of equations of condition. This requires that we shall know the
relative places of all those stars which are to be used as comparison
stars for the planet, right along the whole track of the planet. And
this derivation of a standard star system is by far the most delicate
and difficult part of the whole work. One must start with a founda-
tion of stars observed with the meridian circle, and fill in the fainter
stars from the photographs themselves, taking care to provide at the
same time the places of all those faint comparison stars which have
been used by the visual observers. And all these places of stars must
be tied together, so to speak, by the overlapping of the photographs,
so that the system may run smoothly throughout its length. Abso:
lute errors of zero there no doubt will be, and must be, but it is
114 NEW MEASUREMENTS OF DISTANCE OF SUN.
required that there shall be no sudden jumps in the errors exceeding
one or two hundredths of a second of arc.
Now, when one comes to face a problem like this, one must inquire
very carefully what is the real accuracy of the photograph. There is
no doubt that the ordinary photographic telescope properly worked
will repeat itself very well; it will take two plates of the same region
which agree with one another excellently. But the question is, How
would two plates of the same region taken with different telescopes
agree? We know that individual observers have peculiarities of
their own which they can repeat almost ad infinitum. Does a photo-
graphic telescope do the same, or has it at last conquered that bad
habit of idiosyncrasy which has made so much trouble in all refined
astronomical work of the older kinds? When we started on the
Eros campaign there was practically no information to be obtained
upon this point. Almost all the photographic telescopes at work had
been engaged upon their own Zone of the chart, and almost nothing
was known of how the results from different instruments would com-
bine. But in our parallax problem this question is fundamental, and
must be answered as soon as possible. I therefore ventured to
propose to myself to undertake the reduction of a small section of
the photographic results, for a period of nine days in November,
1900, having before me two objects: Firstly, to discover how far it is
possible to combine photographs taken at different observatories, how
far, in fact, photographic telescopes are giving really accurate results
or merely reproducing their own errors; secondly, to obtain a pro-
visional value of the Solar parallax, with a probable error if possible as
small as that found by Sir David Gill with the heliometer, and to find
out provisionally whether Eros was going to confirm that result or to
join in the secession from the adopted value.
Perhaps I may venture to think that the results of this enterprise
have been in some measure successful. I found that as a general
rule the results from different telescopes do not combine directly as
well as could be hoped and that there are many precautions which
must be taken in using them if we are to avoid serious systematic
crror and a ruination of the parallax determination; but I believe
that it is possible to avoid these difficulties and that the photographs
properly treated will give a determination of the parallax of far
greater accuracy than has hitherto been obtained. I found also that
the 300 exposures in that period of nine days, contributed altogether
by nine different observatories, gave a value of the solar parallax,
8 797 seconds + 0-0047 second, which is in such nice agreement with
Gill’s 8.802 seconds + 0-005 second that one may feel in one's heart
(though of course must never express the feeling so prematurely as
this) some hope that, in adopting 8-80 seconds as the official value
of the solar parallax, the conference of 1896 was not so wrong as
some people have been prepared to believe. • J
NEW MEASUREMENTS OF DISTANCE OF SUN. 115
JFrom heliometer observations of Victoria, I)istance of sun in miles.
Iris, and Sappho. ** =y ºf
92,875,000
7t = 8-802 seconds -- 0:005 second. 92,928,000
Jºrom 295 photographs of Eros.
71 = 8.7 97 seconds == 0-0047 second.
I can not refrain from calling your attention to a by-product of
this work which has for me a singular interest, because it seems to
exhibit in a favorable light the accuracy which we may obtain with
these photographic methods. After Eros had been under observation
for some time it was discovered that its light was varying in a short

FIG. 5.-Light curve of Eros. Whole period 5 h. 16 m.
period, which was at first thought to be 2h. 38m. Afterwards it was
found that the alternate minima of light was unequal, and that the
true period should be reckoned as 5h. 16m., two equal maxima and
two unequal minima being included within that space of time
(fig. 5). The variation appears to be continuous, without sensible
pause, which precludes the idea that the planet is double and that the
minima are due to eclipses of one body by the other. We must find
some other cause. There are two which suggest themselves quite
naturally—irregularity of shape and irregularity of surface bright-
+.650. O
--ó50. O
FIG. 6.-Residuals grouped in eighths of the whole period.
neSS. For our purpose the important point is this—that either of
these causes might produce an apparent oscillation in the place of
the planet. To discover if this were so, I grouped the residuals in
my equations of condition according to their epoch into eight columns,
corresponding to successive eighths of the whole period of 5h. 16m.,
and took the means for each column. If there were a sensible
Oscillation in a period of 5h. 16m., these would lie on a sine curve.
They obviously do not; there is no sensible oscillation in that period
(fig. 6). Iłut notice that if we add together the first and fifth, the
Second and sixth, and so on—-that is to say, if we search for the half
period of 2h. 38m.—we get quite strong evidence of periodicity (fig. 7).
116 NEw MEASUREMENTS OF DISTANCE OF SUN.
Now, the semiamplitude of the oscillation is only 0.03 second, a
quantity so small that one can not but feel doubts as to its reality.
At first I was myself inclined to disbelieve; but when a new distribu-
tion of the residuals, starting from a different zero of time, gave a
similar periodicity, it began to look as if there were something in it.
The more I look at it the more I believe that it is a reality, and that
the photographs have shown themselves accurate enough to detect an
inequality of 0.03 second, corresponding to a shift of 5 miles at a
distance of 25,000,000 miles—by far the smallest inequality in the
motion of a planet ever brought to light by observation. - g
It is this circumstance that encourages one to believe in the accu-
racy of the photographs. There are altogether 10,000 separate expo-
sures of the planet which will within the next few years be meas-
ured and made available for discussion. If 300 give a P. E. of
0-005 second, what will 10,000 give, added to 6,000 or 7,000 sets of
FIG. 7.-Residuals grouped in quarters of the half period. -
visual observations? It would be going too far to apply the simple
rules of probability and say a good deal less than 0-001 second. Dut
I fully believe that if this great array of observations is ever sub-
Imitted to complete discussion the probable error of the result will not
be much above 0-001 second. And supposing that it should support
with its greater weight the value 8:80 seconds which has been
assailed, I believe that we should be justified in saying that the Solar
parallax is 8:80 seconds, and in maintaining the proposition that the
determination of the solar parallax is a problem of geometry and
celestial surveying, and that upon the sponsors of the indirect meth-
ods lies the onus of showing cause for their disagreement. *
This opens up an interesting prospect. Suppose that in course
of time there should come to be a clear and definite agreement among
the values found for the constant of the aberration of light, and that
its value was (let us say) 20:54 seconds, corresponding, as this table
shows, to a parallax of 8 '77 seconds, not 8:80 seconds, on the assump-
tion at least that the velocity of light is exactly determined, as it
Seems to be, and that the simple theory of aberration is correct.
NEw MEASUREMENTS OF DISTANCE OF SUN. 117
Relation between solar parallaº, and constant of aberration.

Aberra-
tion. Tr.
* / //
20 '46 8 '808
'48 '799
•50 '790
‘52 '782
'54 •773
'56 *764
And suppose that by that time we are prepared to say quite defi-
nitely that the geometrical value is not 8-77 seconds but 8:80 seconds.
The most obvious solution of the difficulty would be to conclude that
the simple theory of aberration is not true, and to hand over the
problem to the mathematical physicists, who might in the result find
that a definite geometrical determination of the solar parallax had
provided just the criterion which they required to settle certain vexed
questions in dynamics.
Again, should further investigation confirm the conclusion that
8.76 seconds is the only value of the solar parallax which will
reconcile the existing theory of the motion of the planet with the
observed value of the constant of gravitation, it may be that the con-
tradiction between the direct and the indirect methods will at last
enable the dynamical astronomers to lay a finger upon that flaw
which exists somewhere or other in the theory and makes it impossi-
ble to say at the present time that all the motions of the solar system
can be completely explained.
I have ventured to point out that the determination of the solar
parallax is a problem of wide interest, since it throws upon so many
different people the task of keeping up their particular end against an
attack whose accuracy is gradually becoming more and more deadly.
The dimensions of the earth, as obtained by geodetic operations, are
necessarily beyond the reach of any criticism derived from solar
parallax results.
Equatorial radius of cdrth.
- Miles.
Méchain and Delambre, 1799–-------------------------------------- 3,961 -74
Airy, 1880-------------------------------------------------------- 3, 962 “S2
Everest, 1830----------------------------------------------------- 3, 962-67
Bessel, 1841 ------------------------------------------------------ 3, 962 -76
Clarke, 1858 ------------------------------------- * * * * * = ** * * * * = − = ** = --> 3, 963 -31
Clarke, 1866 ------------------------------------------------------ 3,963 -28
Clarke, 1878------------------------------------------------------ 3, 963 -37
Clarke, 1880 ------------------------------------------------------ 3, 963 “29
Extreme range of these determinations is only 1% in 4,000.
118 NEW MEASUREMENTS OF DISTANCE OF SUN.
But it is interesting to speculate whether astronomers will ever be
in the position to say, “We have now determined the solar parallax
in seconds of arc to a higher degree of accuracy than that of the
measurement of the earth,” and to call upon geodesists for better re-
sults. I can conceive only one direction in which we may be able to
worry the successors in your corps of Everest and Clarke. Is the
form of the equator a circle or an ellipse? I believe that there is
some slight evidence for ellipticity, and that it has been put as high
as one in three thousand. If that is so, it is just barely possible that
we may have to introduce into the computation of the parallax factors
for different observatories a term depending upon the shape of the
equator. But I confess that this prospect is remote, and that for
many years, in all probability, geodesists who achieve accuracies of
one in a hundred thousand and even talk of one in a million will be
able to take a serene view of the labors of astronomers to arrive at
the distance of the sun to one part in ten thousand.