7
upons Luthers
;
1
!
1837
ARTES
VERITAS
LIBRARY
SCIENTIA
OF THE
UNIVERSITY OF MICHIGAN
É PLURIBUS UN
!
SI-QUAERIS PENINSULAM AMOENAME
¿CIRCUMSPICE
THE GIFT OF
{
"Q
157
73600
1776
LECTURES
ON
SELECT SUBJECTS.
Published by the fame Author.
1.
A
STRONOMY explained upon Sir ISAAC
NEWTON's Principles, and made easy to tho e
who have not ftudied Mathematics. To which is added,
the Method of finding the Dittances of the Planets from
the Sun, by the TRANSIT of VENUS over the Sun's Diſc
in the Year 1761. Theſe Diſtances deduced from that
Tranfit; and an account of Mr. HORROX's Obfervations
of the Tranfit in the Year 1639: Illuftrated with 18 Cop-
per-plates. A New Edition, Octavo,
2. An Eaſy Introduction to ASTRONOMY, for young
GENTLEMEN and LADIES: Defcribing the Figure,
Motions, and Dimenſions of the Earth; the different Sea-
fons; Gravity and Light; the Solar Syftem; the Tranfit
of Venus, and its Ufe in Aftronomy; the Moon's Motion
and Phaſes; the Eclipfes of the Sun and Moon: the Caufe
of the Ebbing and Flowing of the Sea, &c. Second
Edition, Price 5 s.
3. TABLES and TRACTS relative to feveral Arts and
Sciences. Price 5 s.
55.
4. An Introduction to ELECTRICITY, in fix Sections.
1. Of Electricity in general. 2. A Defcription of the
Electrical Machine. 3. A Defcription of the Apparatus
(belonging to the Machine) for making Electrical Expe-
riments. 4. How to know if the Machine be in good
order for performing the Experiments, and to put it in
order if it be not. 5. How to make the Electrical Expe-
riments, and to preſerve Buildings from Damage by Light-
ning. 6. Medical Electricity. Price 55.
5. Select Mechanical Exercifes, fhewing how to construct
different Clocks, Orreries, and Sun Dials, on plain and eafy
Principles. With feveral Miſcellaneous Articles and Tables.
Illuftrated with Copperplates. To which is prefixed, a ſhort
Account of the Life of the Author. Price
5 s.
6. The Art of Drawing in Perſpective made easy to thoſe
who have no previous Knowledge of the Mathematics,
Illuftrated with Plates. Price 5 s.
t
LECTURES
ON
SELECT SUBJECTS
MECHANICS,
HYDROSTATICS,
HYDRAULICS,
IN
PNEUMATICS,
AND
OPTICS.
WITH
The USE of the GLOBES,
The ART of DIALING,
AND
The Calculation of the Mean Times of New
and FULL MOONS and ECLIPSES.
By JAMES FERGUSON, F. R. S.
THE FIFTH EDITION.
Philofopbia mater omnium bonarum artium ef. CICERO, 1. Tufc.
LONDON:
Printed for W. STRAHAN, J. and F. RIVINGTON, J. HIN-
TON, L. HAWES and Co. S. CROWDER. T. Longman,
B. Law, G. ROBINSON, T. CADELL, and E. JOHNSTON.
MDCCLXXVI.
0187153
ΤΟ ΗΙS
ROYAL HIGHNESS
Prince ED WARD.
SIR,
AS Heaven has infpired
your ROYAL HIGHNESS
with fuch love of ingenious
and uſeful arts, that you not
only ſtudy their theory, but
have often condefcended to
honour the profeſſors of me-
chanical and experimental
philoſophy with your pre-
A 3. fencę
274253
DEDICATION.
fence and particular favour;
I am thereby encouraged to
lay myſelf and the following
work at your ROYAL HIGH-
NESS's feet; and at the fame
time beg leave to expreſs that
veneration with which I am,
SIR,
Your ROYAL HIGHNESS'S
Moft obliged,
And moſt obedient,
Humble Servant,
JAMES FERGUSON.
THE
PREFACE.
E'
VER fince the days of the LORD Chan-
CELLOR BACON, natural philofophy
hath been more and more cultivated in Eng-
land. THAT great genius firft ſet out with
taking a general furvey of all the natural
Sciences, dividing them into diftinct branches,
which he enumerated with great exactness.
He inquired fcrupulously into the degree of
knowledge already attained to in each, and
drew
up a lift of what fill remained to be
difcovered: this was the fcope of his first un-
dertaking. Afterward he carried his views
A 4
much
Viii
PREFACE.
much farther, and fhewed the neceffity of an
experimental philofophy, a thing never before
thought of. As he was a profeſſed enemy to
fyftems, he confidered philofophy, no otherwis
than as that part of knowledge which con-
tributes to make men better and happier: he
feems to limit it to the knowledge of things
ufeful, recommending above all the study of
nature, and ſhewing that no progreſs can be
made therein, but by collecting facts, and
comparing experiments, of which he points
out a great number proper to be made.
But notwithstanding the true path to fcience
was thus exactly marked out, the old notions
of the Schools fo firongly poffeffed people's minds
at that time, as not to be eradicated by any
new opinions, how rationally foever advanced,
until the illuftrious Mr. BoYLE, the first
who pursued LORD BACON's plan, began
to put experiments in practice with an
affiduity equal to his great talents.
Next,
the ROYAL SOCIETY being established, the
true philofophy began to be the reigning taſte
of the
and continues fo to this day.
age,
3
The
PREFACE.
ix
The immortal SIR ISAAC NEWTON in-
fifted even in his early years, that it was
high time to banish vague conjectures and
hypothefes from natural philofophy, and to
bring that Science under an entire fubjection
to experiments and geometry. He frequently
called it the experimental philofophy, So
to exprefs fignificantly the difference between
it and the numberless fyftems which had arifen
merely out of the conceits of inventive brains:
the one fubfifting no longer than the Spirit of
novelty lofts; the other never failing whilst
the nature of things remain unchanged.
The method of teaching and laying the
foundation of phyfics, by public courses of
experiments, was first undertaken in this
kingdom, I believe, by Dr. JOHN KEILL,
and fince improved and enlarged by Mr.
HAUKSBEE, Dr. DESAGULIERS, Mr:
WHISTON, Mr. COTES, Mr. WHITESIDE,
Dr. BRADLEY, our late Regius and Savi-
lian profeffor of Aftronomy, and the Re-
verend Dr. BLISS his fucceffor:
Nor
x
PREFACE.
J
Nor has the fame been neglected by Dr.
JAMES, and Dr. DAVID GREGORY, Sir
ROBERT STEWART, and after him Mr.
MACLAURIN.Dr. HELSHAM in Ire-
land, Meffieurs s'GRAVESANDE and
MUSCHENBROEK, and the Abbé NOLLET
in France, have alfo acquired just applaufe
thereby.
The fubftance of my own attempt in this
way of inftrumental inftruction, the following
Sheets (exclufive of the aftronomical part)
will fhew: the fatisfaction they have gene-
rally given, read as lectures to different
audiences, affords me fome hope that they may
be favourably received in the fame form by
the Public.
I ought to obferve, that though the five laft
lectures connot be properly faid to concern ex-
perimental philofophy, I confidered, however,
that they were not of fo different a claſs, but
that they might, without much impropriety,
be fubjoined to the preceding ones.
My
PREFAC E.
xi
*
My apparatus (part of which is defcribed
here, and the rest in a former work) is
rather fimple than magnificent; which is
owing to a particular point I had in view
at firft fetting out, namely, to avoid all fu-
perfluity, and to render every thing as
plain and intelligible as I thought the ſub-
ject would admit of.
* Aftronomy explained upon SIR ISAAC NEWTON'S
principles, and made eaſy to thoſe who have not ſtudied
mathematics.
DIRECTIONS to the BOOKBINDER.
The plates must open to the left-hand, fronting
the right-hand pages in the following order.
PLATE I
II
fronting page 5
19
III
25
IV
27
V
49
VI
59
VII
69
VIII
83
IX
97
X
ΙΟΙ
XI
115
XII
125
XIII
151
XIV
179
XV
201
XVI
209
XVII
215
XVIII
22I
XIX
237
XX
311
XXI
323
XXII
331
XXIII
353
'
THE
CONTENT S.
LECTURE I.
OF
F matter and its properties.
Page 1
LECTURE II.
Of central forces.
19
LECTURE III.
Of the mechanical powers.
47
LECTURE
IV.
for driving piles.
71
Of mills, cranes, wheel-carriages, and the engine
LECTURE V.
Of hydroftatics, and hydraulic machines in general.
LECTURE VI.
ΙΟΙ
Of pneumatics.
168
LEC-
CONTENT S.
Of optics.
LECTURE VII.
Page 201
LECTURE VIII. and IX.
The defcription and ufe of the globes and armillary
Sphere.
!
247, 296
LECTURE X. and XI.
The principles and art of dialing.
LECTURE
316, 350
XII.
Shewing how to calculate the mean time of any new
or full moon, or eclipfe from the creation of the
world to the year of Chrift 5800.
The SUPPLEMENT.
LE C-
LECTURES
ON
SELECT SUBJECTS.
A
LECT. I.
Of Matter and its Properties.
S the defign of the first part of this
courfe is to explain and demonſtrate thoſe
laws by which the material univerfe is governed,
regulated, and continued; and by which the
various appearances in nature are accounted for;
it is requifite to begin with explaining the pro-
perties of matter.
By the word matter is here meant every thing Matter,
that has length, breadth, and thicknefs, and what.
refifts the touch.
The inherent properties of matter are folidity, Its pro-
inactivity, mobility, and diviſibility.
perties.
The folidity of matter arifes from its having solidity.
length, breadth, thickneſs; and hence it is that
all bodies are comprehended under fome fhape
or other, and that each particular body hinders
all others from occupying the fame part of ſpace
which it poffeffeth. Thus, if a piece of wood
or metal be ſqueezed ever ſo hard between two
plates, they cannot be brought into contract.
And even water or air has this property; for if
a ſmall quantity of it be fixed between any other
bodies,
Of the Properties of Matter.
Inactivity.
bodies, they cannot be brought to touch one
another.
A fecond property of matter is inactivity, or
paffiveness; by which it always endeavours to
continue in the ftate that it is in, whether of reft
or motion. And therefore, if one body contains
twice or thrice as much matter as another body
does, it will have twice or thrice as much inac-
tivity; that is, it will require twice or thrice as
much force to give it an equal degree of motion,
or to ftop it after it hath been put into fuch a
motion.
That matter can never put itfelf into motion is
allowed by all men. For they fee that a ſtone,
lying on the plane furface of the earth, never
removes itſelf from that place, nor does any one
imagine it ever can. But most people are apt
to believe that all matter has a propensity to
fall from a ſtate of motion into a ftate of reft;
becauſe they ſee that if a ftone or a cannon ball
be put into ever ſo violent a motion, it ſoon ſtops;
not confidering that this ftoppage is caufed,
By the gravity or weight of the body, which
finks it to the ground in fpite of the impulfe;
and, 2. By the reſiſtance of the air through which
it moves, and by which its velocity is retarded
every moment till it falls.
A bowl moves but a fhort way upon a bowl-
ing-green; becauſe the roughness and uneven-
neſs of the graffy furface foon creates friction
enough to ſtop it. But if the green were per-
fectly level, and covered with poliſhed glaſs, and
the bowl were perfectly hard, round, and ſmooth,
it would go a great way farther; as it would
have nothing but the air to refift it; if then the
air were taken away, the bowl would go on
without any friction, and confequently without
any
1
Of the Properties of Matter:
3
any diminution of the velocity it had at fetting
out and therefore, if the green were extended
quite around the earth, the bowl would go on,
round and round the earth, for ever.
If the bowl were carried feveral miles above
the earth, and there projected in a horizontal
direction, with fuch a velocity as would make
it move more than a femidiameter of the earth,
in the time it would take to fall to the earth by
gravity; in that cafe, and if there were no re-
fifting medium in the way, the bowl would not
fall to the earth at all; but would continue to
circulate round it, keeping always in the fame
tract, and returning to the fame point from
which it was projected, with the fame velocity
as at first. In this manner the moon goes round
the earth, although fhe be as unactive and dead
as any ſtone upon it.
The third property of matter is mobility; for Mobility.
we find that all matter is capable of being moved,
if a fufficient degree of force be applied to over-
come its inactivity or refiftance.
lity.
The fourth property of matter is divifibility, Divifibi
of which there can be no end. For, fince matter
can never be annihilated by cutting or breaking,
we can never imagine it to be cut into fuch ſmall
particles, but that if one of them be laid on a
table, the uppermoft fide of it will be further
from the table than the undermoft fide. More-
over, it would be abfurd to ſay that the greateſt
mountain on earth has more halves, quarters, or
tenth parts, than the fmalleft particle of matter
has.
We have many furprifing inftances of the
fmallneſs to which matter can be divided by art:
of which the two following are very remarkable.
B
1. If
Of the Properties of Matter.
1
~3
1. If a pound of filver be melted with a fingle
grain of gold, the gold will be equally diffufed
through the whole filver; fo that taking one
grain from any part of the maſs (in which there
can be no more than the 5760th part of a grain
of gold) and diffolving it in aqua fortis, the
gold will fall to the bottom.
2. The gold beaters can extend a grain of gold
into a leaf containing 50 fquare inches; and this
leaf may be divided into 500000 vifible parts.
For an inch in length can be divided into 100
parts, every one of which will be vifible to the
bare eye confequently a fquare inch can be
divided into 10000 parts, and 50 fquare inches
into 500000. And if one of thefe parts be
viewed with a microſcope that magnifies the
diameter of an object only 10 times, it will
magnify the area 100 times; and then the 100th
part of a 500000th part of a grain (that is, the
50 millionth part) will be vifible. Such leaves
are commonly uſed in gilding; and they are fo
very thin, that if 124500 of them were laid upon
one another, and preffed together, they would
not exceed one inch in thickness.
Yet all this is nothing in compariſon of the
lengths that nature goes in the divifion of mat-
ter. For Mr. Leewenboek tells us, that there are
more animals in the milt of a fingle cod-fifh,
than there are men upon the whole earth and
that, by comparing theſe animals in a micro-
fcope with grains of common fand, it appeared
that one fingle grain is bigger than four millions
of them. Now each animal muft have a heart,
arteries, veins, mufcles, and nerves, otherwiſe
they could neither live nor move. How incon-
ceivably ſmall then muſt the particles of their
blood be, to circulate through the ſmalleſt rami-
fications
PLATE I.
E
R
Fig. 3.
C
A
A
I. Ferguson delin
Fig. 1.
B
H
K
L
M
N
O
D
H
F
Fig. 5.
A
Fig. 4.
A
E
A
Fig. 2.
000
S
'D
B
F
008,
D
9000
J.Mynde fc.
Of the Properties of Matter.
fications and joinings of their arteries and veins?
It has been found by calculation, that a particle
of their blood muſt be as much ſmaller than a
globe of the tenth part of an inch in diameter, as
that globe is finaller than the whole earth; and
yet, if thefe particles be compared with the par-
ticles of light, they will be found to exceed
them as much in bulk as mountains do fingle
grains of fand. For, the force of any body
ftriking againſt an obſtacle is directly in pro-
portion to its quantity of matter multiplied into
its velocity and fince the velocity of the par-
ticles of light is demonftrated to be at leaſt a
million times greater than the velocity of a can-
non-ball, it is plain, that if a million of theſe
particles were as big as a fingle grain of fand,
we durft no more open our eyes to the light,
than we durft expoſe them to fand fhot point-
blank from a cannon.
nite divi-
fibility of
That matter is infinitely divifible, in a mathe- Plate I.
matical fenfe, is eafy to be demonftrated. For, Fig. 1.
let AB be the length of a particle to be divided;
and let it be touched at oppofite ends by the pa-
rallel lines CD and EF, which, fuppofe to be
infinitely extended beyond D and F. Set off
the equal divifions BG, GH, HI, &c. on the The infi-
line EF, towards the right hand from B; and
take a point, as at R, any where toward the left matter
hand from A, in the line CD: Then, from this proved.
point, draw the right lines RG, RH, RI, &c.
each of which will cut off a part from the par-
ticle AB. But after any finite number of fuch
lines are drawn, there will ftill remain a part, as
AP, at the top of the particle, which can never
be cut off: becaufe the lines DR and EF being
parallel, no line can ever be drawn from the
point R to any point of the line EF that will
B 2
coincide
Of the Properties of Matter.
Attrac
tio...
Cohefion.
coincide with the line RD.
Therefore the
Therefore the par-
ticle AB contains more than any finite number
of parts.
A fifth property of matter is attraction, which
ſeems rather to be infuſed than inherent. Of
this there are four kinds, viz. cohesion, gravita
tion, magnetiſm, and clectricity.
The attraction of cobefion is that by which the
fmall parts of matter are made to ftick and co-
here together. Of this we have feveral in-
ftances, fome of which follow.
1. If a ſmall glaſs tube, open at both ends, be
dipt in water, the water will rife up in the tube
to a confiderable height above its level in the
bafon: which must be owing to the attraction
of a ring of particles of the glaſs all round in
the tube, immediately above thofe to which the
water at any inftant rifes. And when it has riſen
fo high, that the weight of the column balances
the attraction of the tube, it rifes no higher.
This can be no ways owing to the preffure of the
air upon the water in the bafon; for, as the tube
is open at top, it is full of air above the water,
which will prefs as much upon the water in the
tube as the neighbouring air does upon any
column of an equal diameter in the bafon. Be
fides, if the fame experiment be made in an
exhauſted receiver of the air-pump, there will
be found no difference.
2. A piece of loaf-fugar will draw up a fluid,
and a fpunge will draw in water and on the
fame principle fap afcends in trees.
3. If two drops of quickfilver be placed near
each other, they will run together and become
one large drop.
4. If two pieces of lead be fcraped clean, and
preffed together with a twift, they will attract
each
Of the Properties of Matter.
7
each other fo ftrongly, as to require a force
much greater than their own weight to ſeparate
them. And this cannot be owing to the preffure
of the air, for the fame thing will hold in an
exhauſted receiver.
5. If two polished plates of marble or brafs
be put together, with a little oil between them
to fill up the pores in their furfaces, and prevent
the lodgement of any air; they will cohere fo
ftrongly, even if fufpended in an exhauſted re-
ceiver, that the weight of the lower plate will
not be able to ſeparate it from the upper one. In
putting theſe plates together, the one ſhould be
rubbed upon the other, as a joiner does two
pieces of wood when he glues them.
6. If two pieces of cork, equal in weight, be
put near each other in a baſon of water, they will
move equally faft toward each other with an
accelerated motion, until they meet: and then,
if either of them be moved, it will draw the
other after it. If two corks of unequal weights
be placed near each other, they will approach
with accelerated velocities inverfely proportio-
nate to their weights: that is, the lighter cork
will move as much faſter than the heavier, as the
heavier exceeds the lighter in weight. This
fhews that the attraction of each cork is in direct
proportion to its weight or quantity of matter.
This kind of attraction reaches but to a very
fmall diſtance; for, if two drops of quickfilver
be rolled in duft, they will not run together,
becauſe the particles of duft keep them out of
the ſphere of each other's attraction.
Where the fphere of attraction ends, a repul- Repul-
five force begins; thus, water repels moſt bodies fion.
ill they are wet; and hence it is, that a fmall
B 3
needles.
8
Of the Properties of Matter.
Gravita-
tion.
"}
needle, if dry, fwims upon water; and flies walk
upon it without wetting their feet.
The repelling force of the particles of a fluid
is but fmall; and therefore, if a fluid be divided,
it easily unites again. But if glafs, or any other
hard fubftance, be broke into finall parts, they
cannot be made to flick together again without
being first wetted: the repulfion being too great
to admit of a re-union.
The repelling force between water and oil is
fo great, that we find
that we find it almoft impoffible to mix.
them fo, as not to feparate again. If a ball of
light wood be dipt in oil, and then put into wa-
ter, the water will recede fo as to form a channel
of fome depth all around the ball.
The repulfive force of the particles of air is fo
great, that they can never be brought fo near to-
gather by condenſation as to make them flick or
cohere. Hence it is, that when the weight of
the incumbent atmoſphere is taken off from any
fmall quantity of air, that quantity will diffuſe it-
felf fo as to occupy (in compariſon) an infinitely
greater portion of ſpace than it did before.
Attraction of gravitation is that power by
which diftant bodies tend towards one another.
Of this we have daily inftances in the falling
of bodies to the earth. By this power in the
earth it is, that bodies, on whatever fide, fall in
lines perpendicular to its furface; and confe-
quently, on oppofite fides, they fall in oppoſite
directions; all towards the center, where the
force of gravity is as it were accumulated: and
by this power it is, that bodies on the earth's
furface are kept to it on all fides, fo that they
cannot fall from it. And as it acts upon all bo-
dies in proportion to their reſpective quantities,
of matter, without any regard to their bulks or
figures,
I
Of the Properties of Matter.
୭
figures, it accordingly conftitutes their weight.
Hence,
If two bodies which contain equal quantities
of matter, were placed at ever fo great a distance
from one another, and then left at liberty in free
fpace; if there were no other bodies in the uni-
verſe to affect them, they would fall equally ſwift
towards one another by the power of gravity,
with velocities accelerated as they approached
each other; and would meet in a point which
was half-way between them at firft. Or, if two
bodies, containing unequal quantities of matter,
were placed at any diftance, and left in the fame
manner at liberty, they would fall towards one
another with velocities which would be in an
inverſe proportion to their refpective quantities
of matter; and moving fafter and faſter in their
mutual approach, would at laſt meet in a point
as much nearer to the place from which the
heavier body began to fall, than to the place
from which the lighter body began to fall, as
the quantity of matter in the former exceeded
that in the latter.
All bodies that we know of have gravity or
weight. For, that there is no fuch thing as po-
fitive levity, even in ſmoke, vapours, and fumes,
is demonftrable by experiments on the air-
pump; which fhews, that although the ſmoke
of a candle afcends to the top of a tall receiver
when full of air, yet, upon the air's being ex-
hauſted out of the receiver, the fmoke falls down
to the bottom of it. So, if a piece of wood be
immerfed in a jar of water, the wood will rife to
the top of the water, becauſe it has a lefs degree
of weight than its bulk of water has: but if the
jar be emptied of water, the wood falls to the
bottom.
B 4
Ai
10
Of the Properties of Matter.
Gravity
ſtrated to
As every particle of matter has its proper
demon- gravity, the effect of the whole muſt be in pro
be as the portion to the number of the attracting particles;
quantity that is, as the quantity of matter in the whole
of matter body. This is demonftrable by experiments on
in bodies. pendulums; for, if they are of equal lengths,
It de-
of the
diſtance
whatever their weights be, they vibrate in equal
times. Now it is plain, that if one be double or
triple the weight of another, it muſt require a
double or triple power of gravity to make it
move with the fame celerity: juſt as it would
require a double or triple force to project a bul-
let of twenty or thirty pounds weight with the
fame degree of fwiftnefs that a bullet of ten
pounds would require. Hence it is evident,
that the power or force of gravity is always pro-
portional to the quantity of matter in bodies,
whatever their bulks or figures are,
:
Gravity alfo, like all other virtues or emana-
creafes as tions which proceed or iffue from a center, de-
the fquare creaſes as the distance multiplied by itſelf in-
creaſes that is, a body at twice the diftance of
increaſes. another, attracts with only a fourth part of the
force; at thrice the diftance, with a ninth part;
at four times the diftance, with a fixteenth part;
and fo on. This too is confirmed by comparing
the diſtance which the moon falls in a minute,
from a right line touching her orbit, with the
diſtance through which heavy bodies near the
earth fall in that time. And alſo by comparing
the forces which retain Jupiter's moons in their
orbits, with their refpective diftances from Ju-
piter. Thefe forces will be explained in the
next lecture.
The velocity which bodies near the earth ac-
quire in defcending freely by the force of gravity,
is proportional to the times of their defcent.
For,
Of the Properties of Matter.
IF
For, as the power of gravity does not confift in
a fingle impulfe, but is always operating in a
conftant and uniform manner, it muſt produce
equal effects in equal times; and confequently in
a double or triple time, a double or triple effect.
And fo, by acting uniformly on the body, muft
accelerate its motion proportionably to the time
of its deſcent.
To be a little more particular on this ſubject,
let us ſuppoſe that a body begins to move with
a celerity conſtantly and gradually increaſing, in
fuch a manner, as would carry it through a mile
in a minute; at the end of this fpace it will have
acquired ſuch a degree of celerity, as is fufficient
to carry it two miles the next minute, though it
ſhould then receive no new impulfe from the
cauſe by which its motion had been accelerated:
but if the fame accelerating caufe continues, it
will carry the body a mile farther; on which
account, it will have run through four miles at
the end of two minutes; and then it will have
acquired fuch a degree of celerity as is fufficient
to carry it through a double ſpace in as much
more time, or eight miles in two minutes, even
though the accelerating force fhould act upon it
no more. But this force ſtill continuing to ope-
rate in an uniform manner, will again, in an
equal time, produce an equal effect; and fo, by
carrying it a mile further, cauſe it to move
through five miles the third minute; for, the
celerity already acquired, and the celerity ftill
acquiring, will have each its complete effect.
Hence we learn, that if the body thould move
one mile the first minute, it would move three
miles the fecond, five the third, feven the fourth,
mine the fifth, and fo on in proportion.
And
12
Of the Properties of Matter.
The de-
velocity
will give
a power
afcent.
And thus it appears, that the ſpaces deſcribed
in fucceffive equal parts of time, by an uniformly
accelerated motion, are always as the odd num-
bers 1, 3, 5, 7, 9, &c. and confequently, the
whole ſpaces are as the fquares of the times, or of
the laſt acquired velocities. For, the continued
addition of the odd numbers yields the fquares
of all numbers from unity upwards. Thus, I is
the firft odd number, and the fquare of 1 is 1;
3 is the fecond odd number, and this added to
I makes 4, the fquare of 2; 5 is the third odd
number, which added to 4 makes 9, the fquare
of 3; and fo on for ever. Since, therefore, the
times and velocities proceed evenly and conſtant-
as I, 2, 3, 4, &c. but the ſpaces defcribed in
each equal times are as 1, 3, 5, 7, &c. it is evi-
dent that the ſpace deſcribed
In 1 minute will be
In 2 minutes
In 3 minutes
C
Ifquare of I
1+3=4=fquare of 2
1+3+5=9=fquare of 3
In 4 minutes 1+3+5+7=16=fquare of
4, &c.
N. B. The character + fignifies more, and
equal.
As heavy bodies are uniformly accelerated by
fcending the power of gravity in their defcent, it is plain
that they must be uniformly retarded by the
fame power
in their aſcent. Therefore, the ve-
of equal locity which a body acquires by falling, is fuffi-
cient to carry it up again to the fame height
from whence it fell: allowance being made for
the refiftance of the air, or other medium in
which the body is moved. Thus, the body D
in rolling down the inclined plane AB will
acquire fuch a velocity by the time it arrives at
Fig. 2:
B, as
Of the Properties of Matter.
13
B, as will carry it up the inclined plane BC, al-
moſt to C; and would carry it quite up to C, if
the body and plane were perfectly smooth, and
the air gave no refiftance.-So, if a pendulum
were put into motion, in a ſpace quite free of
air, and all other refiftance, and had no friction
on the point of fufpenfion, it would move for
ever for the velocity it had acquired in falling
through the deſcending part of the arc, would
be ſtill fufficient to carry it equally high in the
afcending part thereof.
The center of gravity is that point of a body The cen-
in which the whole force of its gravity or weight ter of
is united. Therefore, whatever fupports that gravity,
point bears the weight of the whole body: and
whilst it is fupported, the body cannot fall;
becauſe all its parts are in a perfect equilibrium
about that point.
An imaginary line drawn from the center of
gravity of any body towards the center of the
earth, is called the line of direction. In this line and line
all heavy bodies defcend, if not obſtructed.
of direc-
Since the whole weight of a body is united in tion.
its center of gravity, as that center afcends or
defcends, we muſt look upon the whole body to
do ſo too. But as it is contrary to the nature of
heavy bodies to afcend of their own accord, or
not to defcend when they are permitted; we
may be fure that, unless the center of gravity
be ſupported, the whole body wai tumble or
fall. Hence it is, that botes ftand upon their
bafes when the line of direction falls within the
bafe; for in this cafe the body cannot be made
to fall without firft raifing the center of gravity
higher than it was before. Thus, the inclining
body ABCD, whofe center of gravity is E, Fig. 3.
tands firmly on its baſe CDIK, becauſe the line
S
of.
14
Of the Properties of Matter.
1
of direction EF falls within the bafe. But if a
weight, as ABGH, be laid upon the top of the
body, the center of gravity of the whole body
and weight together is raifed up to I; and then,
as the line of direction ID falls without the baſe
at D, the center of gravity I is not fupported;
and the whole body and weight tumble down
together.
Hence appears the abfurdity of people's rifing
haftily in a coach or boat when it is likely to
overfet for, by that means they raife the cen-
ter of gravity fo far as to endanger throwing it
quite out of the bafe; and if they do, they
overftt the vehicle effectually. Whereas, had
they clapt down to the bottom, they would
have brought the line of direction, and confe-
quently the center of gravity, farther within the
baſe, and by that means might have ſaved them-
felves.
The broader the bafe is, and the nearer the
line of direction is to the middle or center of it,
the more firmly does the body ftand. On the
contrary, the narrower the bafe, and the nearer
the line of direction is to the fide of it, the more
eafily may the body be overthrown, a lefs change
of pofition being fufficient to remove the line
of direction out of the bafe in the latter cafe
than in the former. And hence it is, that a
fphere is ſo eaſily rolled upon a horizontal plane;
and that it is fo difficult, if not impoffible, to
make things which are fharp-pointed to ftand
upright on the point.-From what hath been
faid, it plainly appears that if the plane be in-
clined on which the heavy body is placed, the
body will flide down upon the plane whilft the
line of direction falls within the bafe; but it will
tumble or roll down when that line falls without
the
Of the Properties of Matter.
15
the baſe. Thus, the body A will only flide
down the inclined plane C D, whilft the body B
rolls down upon it.
When the line of direction falls within the
baſe of our feet, we ſtand; and moſt firmly when
it is in the middle: but when it is out of that
baſe, we immediately fall. And it is not only
pleaſing, but even furprifing, to reflect upon
the various and unthought-of methods and pof-
tures which we uſe to retain this pofition, or to
recover it when it is loft. For this purpofe we
bend our body forward when we rife from a
chair, or when we go up ftairs: and for this
purpoſe a man leans forward when he carries a
burden on his back, and backward when he car-
ries it on his breaft; and to the right or left fide
as he carries it on the oppofite fide. A thou-
fand more inſtances might be added.
The quantity of matter in all bodies is in ex-
act proportion to their weights, bulk for bulk.
Therefore, heavy bodies are as much more denſe
or compact than light bodies of the fame bulk,
as they exceed them in weight..
Fig. 4.
All bodies are full of pores, or ſpaces void of All bodies
matter and in gold, which is the heaviest of porous.
all known bodies, there is perhaps a greater
quantity of ſpace than of matter. For the par-
ticles of heat and magnetiſm find an eaſy paffage
through the pores of gold; and even water itfelf
has been forced through them. Befides, if we
confider how eaſily the rays of light paſs through
fo folid a body as glafs, in all manner of direc-
tions, we ſhall find. reafon to believe that bodies
are much more porous than is generally ima-
gined.
All bodies are fome way or other affected by The ex-
heat; and all metallic bodies are expanded in pantion of
8
length,
metals..
16
Of the Properties of Matter.
The py-
length, breadth, and thickness thereby.-The
proportion of the expanfion of feveral metals,
according to the beſt experiments I have been
able to make with my pyrometer, is nearly thus:
Iron and ſteel as 3, copper 4 and an half,
braſs 5, tin 6, lead 7. An iron rod
An iron rod 3 feet long
is about one 70th part of an inch longer in
fummer than in winter.
The pyrometer here mentioned being (for
rometer. aught I know) of a new construction, a de-
fcription of it may perhaps be agreeable to the
Fig. 5.
reader.
AA is a flat piece of mahogany, in which are
fixed four braſs ftuds B,C,D,L; and two pins,
one at F and the other at H. On the pin
F turns the crooked index E I, and upon the
pin H the ſtraight index G K, againſt which a
piece of watch-fpring R bears gently, and fo
preffes it towards the beginning of the ſcale MN,
over which the point of that index moves. This
ſcale is divided into inches and tenth parts of an
inch the firft inch is marked 1000, the ſecond
2000, and fo on A bar of metal O is laid into
notches in the top of the ftuds C and D; one
end of the bar bearing againſt the adjufting
fcrew P, and the other end againſt the crooked.
index EI, at a 20th part of its length from its
center of motion F.-Now it is plain, that how-
ever much the bar O lengthens, it will move
that part of the index EI, againſt which it bears,
just as far: but the crooked end of the fame
index, near H, being 20 times as far from the
center of motion F as the point is againſt
which the bar bears, it will move 20 times as
far as the bar lengthens. And as this crooked
end bears against the index G K at only a 20th
part of the whole length GS from its center of
motion
1
!
Of the Properties of Matter.
I
motion H, the point S will move through 20
times the ſpace that the point of bearing near H
does. Hence, as 20 multiplied by 20 produces
400, it is evident that if the bar lengthens but a
400th part of an inch, the point S will move a
whole inch on the fcale; and as every inch is
divided into 10 equal parts, if the bar lengthens
but the 10th part of the 400th part of an inch,
which is only the 4000th part of an inch, the
point S will move the tenth part of an inch,
which is very perceptible.
To find how much a bar lengthens by heat,
first lay it cold into the notches of the ftuds, and
turn the adjuſting fcrew P until the fpring R
brings the point S of the index G K to the begin-
ning of the divifions of the ſcale at M: then,
without altering the fcrew any farther, take off
the bar and rub it with a dry woollen cloth till
it feels warm; and then, laying it on where it
was, obſerve how far it puſhes the point S upon
the ſcale by means of the crooked index E I;
and the point S will fhew exactly how much the
bar has lengthened by the heat of rubbing. As
the bar cools, the fpring R bearing againſt the
index KG, will caufe its point S to move gra-
dually back towards M in the ſcale: and when
the bar is quite cold, the index will reft at M,
where it was before the bar was made warm by
rubbing. The indexes have fmall rollers under
them at I and K; which, by turning round on
the ſmooth wood as the indexes move, make
their motions the eafier, by taking off a great
part of the friction, which would otherwife be
on the pins F and H, and of the points of the
indexes themſelves on the wood.
Beſides the univerfal properties above men- Magne-
tioned, there are bodies which have properties
peculiar
tifm.
18
Of the Properties of Matter.
}
Electri-
city.
peculiar to themfelves: fuch as the loadſtone,
in which the most remarkable are thele: 1. It
attracts iron and ſteel only. 2. It conftantly
turns one of its fides to the north and another
to the fouth, when fufpended by a thread that
does not twist. 3. It communicates all its pro-
perties to a piece of fteel when rubbed upon it,
without lofing any itſelf.
According to Dr. Hellham's experiments, the
attraction of the loadftone decreaſes as the ſquare
of the diſtance increaſes. Thus, if a loadſtone
be fufpended at one end of a balance, and coun-
terpoiſed by weights at the other end, and a
flat piece of iron be placed beneath it, at the
diſtance of four tenths of an inch, the ftone will
immediately defcend and adhere to the iron.
But if the ſtone be again removed to the fame
diſtance, and as many grains be put into the
fcale at the other end as will exactly counterba-
lance the attraction, then, if the iron be brought
twice as near the ftone as before, that is, only
two tenth parts of an inch from it, there muſt
be four times as many grains put into the fcale
as before, in order to be a juft counterbalance
to the attractive force, or to hinder the ſtone
from defcending and adhering to the iron. So,
if four grains will do in the former cafe, there
muſt be fixteen in the latter. But from ſome
later experiments, made with the greateſt ac-
curacy, it is found that the force of magnetifm
decreaſes in a ratio between the reciprocal of the
fquare and the reciprocal of the cube of the di-
ſtance; approaching to the one or the other, as
the magnitudes of the attracting bodies are varied.
Several bodies, particularly amber, glaſs, jet,
fealing-wax, agate, and almoſt all precious
ftones, have a peculiar property of attracting
and
1
LATE II.
!
t
i
Fig. 1.
Fig. 2.
E
1
W
Ferguson delin...
Fig. 5.
{
B
D
A
Fig.4.
G
H
B
1
1
B
C
Da
E
A
M
D
G
S
B
E
Fig. 3.
F
H
M
1
K
>
S
1
F
T
Myndi je.
1
Of central Forces.
19
and repelling light bodies when heated by rub-
bing. This is called electrical attraction, in
which the chief things to be obſerved are, 1. If
a glaſs tube about an inch and a half diameter,
and two or three feet long, be heated by rub-
bing, it will alternately attract and repel all light
bodies when held near them. 2. It does not
attract by being heated without rubbing.
3. Any light body being once repelled by the
tube, will never be attracted again till it has
touched ſome other body. 4. If the tube be
rubbed by a moift hand, or any thing that is
wet, it totally deftroys the electricity. 5. Any
body, except air, being interpofed, ftops the
electricity. 6. The tube attracts ftronger when
rubbed over with bees-wax, and then with a dry
woollen-cloth. 7. When it is well rubbed, if
a finger be brought near it, at about the dif
tance of half an inch, the effluvia will fnap
againſt the finger, and make a little crackling
noife; and if this be performed in a dark place,
there will appear a little flash of light.
WE
LEC T. II.
Of central Forces.
different
to motion
E have already mentioned it as a necef- All bodies
fary confequence arifing from the dead- equally in-
nefs or inactivity of matter, that all bodies
endeavour to continue in the flate they are in, or reft.
whether of reft or motion. If the body A were Plate I.
placed in any part of free fpace, and nothing Fig. 1.
either drew or impelled it any way, it would for
ever remain in that part of fpace, becauſe it
could have no tendency of itſelf to remove any
way from thence. If it receives a fingle im-
C
pulfe
20
Of central Forces.
All mo-
tion na-
turally
reclili-
neal.
pulſe any way, as fuppofe from A towards B, it
will go on in that direction; for, of itſelf, it
could never fwerve from a right line, nor ftop
its courſe.—When it has gone through the ſpace
AB, and met with no refiftance, its velocity
will be the fame at B at it was at A: and this
velocity, in as much more time, will carry it
through as much more ſpace, from B to C; and
fo on for ever. Therefore, when we fee a body
in motion, we conclude that fome other fub-
ftance must have given it that motion; and
when we ſee a body fall from motion to reſt, we
conclude that ſome other body or cauſe ſtopt it.
As all motion is naturally rectilineal, it ap-
pears, that a bullet projected by the hand, or
ſhot from a cannon, would for ever continue to
move in the ſame direction it received at firſt, if
no other power diverted its courfe. Therefore
when we fee a body move in a curve of any kind
whatever, we conclude it must be acted upon by
two powers at leaft; one putting it in motion,
and another drawing it off from the rectilineal
courfe it would otherwife have continued to
move in and whenever that power, which bent
the motion of the body from a ſtraight line into
a curve, ceaſes to act, the body will again move
on in a ſtraight line touching that point of the
curve in which it was when the action of, that
power cealed. For example, a pebble moved
round in a fling ever fo long a time, will fly off
the moment it is fet at liberty, by flipping one
end of the fling cord; and will go on in a line
touching the circle it defcribed before: which
line would actually be a ftraight one, if the
earth's attraction did not affect the pebble, and
bring it down to the ground. This fhews that
the natural tendency of the pebble, when put
into
Of central Forces.
21
into motion, is to continue moving in a ſtraight
line, although by the force that moves the fling
it be made to revolve in a circle.
The change of motion produced is in propor- The ef-
tion to the force impreffèd: for the effects of fects of
natural cauſes are always proportionate to the
force or power of thofe caufes.
combined
forces.
By thefe laws it is eafy to prove that a body
will defcribe the diagonal of a fquare or pa-
rallelogram, by two forces conjoined, in the
fame time that it would defcribe either of the
fides, by one force fingly. Thus, fuppofe the
body A to repreſent a ſhip at ſea; and that it is Fig. 2.
driven by the wind, in the right line AB, with
fuch a force as would carry it uniformly from A
to B in a minute: then fuppoſe a ſtream or cur-
rent of water running in the direction AD, with
ſuch a force as would carry the ſhip through an
equal ſpace from A to D in a minute. By thefe
two forces, acting together at right angles to
each other, the fhip will defcribe the line AEC
in a minute which line (becauſe the forces are
equal and perpendicular to each other) will be
the diagonal of an exact fquare. To confirm
this law by an experiment, let there be a wooden
ſquare ABCD ſo contrived, as to have the part Fig. 3.
BEFC made to draw out or puſh into the ſquare
at pleaſure. To this part let the pully H be
joined, fo as to turn freely on an axis, which
will be at H when the piece is puſhed in, and
at b when it is drawn out. To this part let the
ends of a ſtraight wire k be fixed, fo as to move
along with it, under the pulley; and let the ball
G be made to flide eafily on the wire. A thread
m is fixed to this ball, and goes over the pulley
to I; by this thread the ball may be drawn up
on the wire, parallel to the fide AD, when the
C 2
part
1
22
Of central Forces.
Fig. 4.
part BEFC is puſhed as far as it will go into
the fquare. But, if this part be drawn out, it
will carry the ball along with it, parallel to the
bottom of the fquare DC. By this means, the
ball G may either be drawn perpendicularly up-
ward by pulling the thread m, or moved hori-
zontally along by pulling out the part B E FC,
in equal times, and through equal ſpaces; each
power acting equally and ſeparately upon it.
But if, when the ball is at G, the upper end of
the thread be tied to the pin 1, in the corner A
of the fixed fquare, and the moveable part
BEFG be drawn out, the ball will then be acted
upon by both the powers together: for it will
be drawn up by the thread towards the top of
the fquare, and at the fame time be carried with its
wire k towards the right hand BC, moving all
the while in the diagonal line L; and will be
found at g when the fliding part is drawn out as
far as it was before; which then will have cauſed
the thread to draw up the ball to the top of the
infide of the fquare, juft as high as it was before,
when drawn up fingly by the thread without
moving the fliding part.
If the acting forces are equal, but at oblique
angles to each other, fo will the fides of the
parallelogram be: and the diagonal run through
by the moving body will be longer or fhorter,
according as the obliquity is greater or fmaller.
Thus, if two equal forces act conjointly upon the
body A, one having a tendency to move it
through the ſpace AB in the fame time that the
other has a tendency to move it through an equal
Space AD; it will defcribe the diagonal AGC
in the fame time that either of the fingle forces
would have caufed it to defcribe either of the
fides. If one of the forces be greater than the
2
other,
Of central Forces.
23
other, then one fide of the parallelogram will be
fo much longer than the other. For, if one force
fingly would carry the body through the ſpace
AE, in the fame time that the other would have
carried it through the ſpace AD, the joint action
of both will carry it in the fame time through
the ſpace AHF, which is the diagonal of the
oblique parallelogram ADE F.
If both forces act upon the body in fuch a
manner, as to move it uniformly, the diagonal
defcribed will be a ftraight line; but if one of
the forces acts in fuch a manner as to make the
body move faster and fafter, then the line de-
fcribed will be a curve, And this is the cafe
of all bodies which are projected in rectilineal
directions, and at the fame time acted upon by
the power of gravity; which has a conftant ten-
dency to accelerate their motions in the direction
wherein it acts.
motions.
From the uniform projectile motion of bodies in The laws
ftraight lines, and the univerfal power of gravity of the
or attraction, arifes the curvilineal motion of all planetary
the heavenly bodies. If the body A be projected
along the ſtraight line AFH in open fpace, Fig. 5.
where it meets with no refiftance, and is not
drawn afide by any power, it will go on for
ever with the fame velocity, and in the fame
direction. But if, at the fame moment the
projectile force is given it at A, the body S be-
gins to attract it with a force duly adjuſted*,
and perpendicular to its motion at A, it will then
be drawn from the ſtraight line AFH, and forced
* To make the projectile force a juſt balance to the gra-
vitating power, fo as to keep the planet moving in a circle,
it muſt give fuch a velocity as the planet would acquire by
gravity when it had fallen through half the femidiameter of
that circle.
C 3
to
24
Of central Forces.
1
to revolve about S in the circle ATW; in the
fame manner, and by the fame law, that a peb-
ble is moved round in a fling. And if, when
the body is in any part of its orbit (as ſuppoſe
at K) a ſmaller body as L, within the ſphere of
attraction of the body K, be projected in the
right line L M, with a force duly adjuſted, and
perpendicular to the line of attraction LK; then,
the ſmall body L will revolve about the large
body K in the orbit NO, and accompany it in
its whole courſe round the yet larger body S.
But then, the body K will no longer move in
the circle ATW; for that circle will now be
deſcribed by the common center of gravity be-
tween K and L. Nay, even the great body S
will not keep in the center; for it will be the
common center of gravity between all the three
bodies S, K, and Z, that will remain immove-
able there. So, if we ſuppoſe S and K connected
by a wire P that has no weight, and K and Ľ
connected by a wire q that has no weight, the
common center of gravity of all theſe three
bodies will be a point in the wire P near S.
which point being fupported, the bodies will be
all in equilibrio as they move round it. Though
indeed, ftrictly speaking, the common center of
gravity of all the three bodies will not be in the
wire P but when theſe bodies are all in the right
line. Here, S may repreſent the fun, K the
earth, and L the moon.
In order to form an idea of the curves de-
ſcribed by two bodies revolving about their com-
mon center of gravity, whilst they themſelves
with a third body are in motion round the com-
mon center of gravity of all the three; let
See Plate us firſt fuppofe E to be the fun, and e the
earth going round him without any moon; and
III.
their
t
PLATE III.
15
?
6
A
14
B.
¿
13
R
A
16
N
L
M
!
117
P
1
E
I. Ferguson delin.
W
18
19
K
H
12
23
G
72
20
5
J. Mynde Jo
22
Of central Forces.
25
d
bodies re-
their moving forces regulated as above. In
this cafe, whilft the earth goes round the fun in
the dotted circle RTUW X, &c. the fun will The
go round the circle AB D, whofe center C is curves de-
the common center of gravity between the fun fcribed by
and earth the right line 3 reprefenting the volving
mutual attraction between them, by which they about
are as firmly connected as if they were fixed at
the two ends of an iron bar ftrong enough to
hold them. So, when the earth is at e, the
fun will be at E; when the earth is at T, the fun
will be at F; and when the earth is at g, the fun
will be at G, &c.
Now, let us take in the moon q (at the top of
the figure) and fuppofe the earth to have no pro
greffive motion about the fun; in which cafe,
whilft the moon revolves about the earth in her
orbit ABCD, the earth will revolve in the
circle S 13, whofe center R is the common cen-
ter of gravity of the earth and moon; they be-
ing connected by the mutual attraction between
them in the fame manner as the earth and fun
are.
their
common
center of
gravity.
But the truth is, that whilft the moon revolves
about the earth, the earth is in motion about
the fun and now, the moon will caufe the
earth to deſcribe an irregular curve, and not a
true circle, round the fun; it being the common
center of gravity of the earth and moon that will
then deſcribe the fame circle which the earth
would have moved in, if it had not been at-
tended by a moon. For, fuppofing the moon
to deſcribe a quarter of her progreffive orbit
about the earth in the time that the earth moves
from e to f; it is plain, that when the earth
comes to f, the moon will be found at r; in
which time, their common center of gravity
C 4
will
26
Of central Forces.
:
will have deſcribed the dotted arc R IT, the
earth the curve R 5 f, and the moon the curve
q 14 r. In the time that the moon defcribes
another quarter of her orbit, the center of gra-
vity of the earth and moon will defcribe the dot-
ted arc T2 U, the earth the curve f 6 g, the
moon the curve r 15 s,
5 s, and fo on-And thus,
whilſt the moon goes once round the earth in
her progreffive orbit, their common center of
gravity deſcribes the regular portion of a circle
R 1 T 2 U 3 V 4 W, the earth the irregular curve
R 5 ƒ 6 g 7 b 8 i, and the moon the yet more
irregular curve q 14 r 15 s 16 t 17 u; and then,
the fame kind of tracks over again.
The center of gravity of the earth and moon is
6000 miles from the earth's center towards the
moon; therefore the circle S 13 which the earth
deſcribes round that center of gravity (in every
courfe of the moon round her orbit) is 12000
miles in diameter. Confequently the earth is
12,000 miles nearer the fun at the time of full
moon than at the time of new. [See the earth at
ƒ and at b.]
To avoid confufion in fo fmall a figure, we
have ſuppoſed the moon to go only twice and a
half round the earth, in the time that the earth.
goes once round the fun: it being impoſſible to
take in all the revolutions which the makes in a
year, and to give a true figure of her path, un-
leſs we ſhould make the femidiameter of the
earth's orbit at least 95 inches; and then, the
proportional femidiameter of the moon's orbit.
would be only a quarter of an inch.-For a true
figure of the moon's path, I refer the reader to
my treatiſe of aſtronomy.
If the moon made any complete number of
revolutions about the earth in the time that the
**
earth
PLATE IV.
M
a
b
d
O
E
Fig. 7.
Fig. 2.
B
Fig. 9.
H
I K
I
~
12
H
b
mn
B
Fig.1.
Fig.3.
e
C
h
Fig. 8.
MN
H
h
B
I
'Ρ
K
C
Fig. 10.
H
h
J. Ferguson delin.
K
Fig.1.
A
N
P
T
A
Fig. 4.
B
C
F
A
Fig. 5.
A
d Fig. 6.
B
୯
B
E
Fig.12.
B
J.Nynde je.
jo
Of central Forces.
27
earth makes one revolution about the fun, the
paths of the fun and moon would return into
themſelves at the end of every year; and fo be
the fame over again but they return not into
themſelves in less than 19 years nearly; in which
time, the earth makes nearly 19 revolutions
about the fun, and the moon 235 about the earth.
lances a
If the planet A be attracted towards the fun, Plate II.
with fuch a force as would make it fall from A Fig. 5.
to B, in the time that the projectile impulfe
would have carried it from A to F, it will de-
ſcribe the arc AG by the combined action of theſe A double
forces, in the fame time that the former would projectile
have cauſed it to fall from A to B, or the latter force ba-
have carried it from A to F. But, if the projec- quadruple
tile force had been twice as great, that is, fuch as power of
would have carried the planet from A to H, in gravity.
the fame time that now, by the fuppofition, it
carries it only from A to F; the fun's attraction
muſt then have been four times as ftrong as for-
merly, to have kept the planet in the circle
ATW; that is, it muſt have been fuch as would
have cauſed the planet to fall from A to E,
which is four times the diftance of A from B, in
the time that the projectile force fingly would
have carried it from A to H, which is only twice
the diſtance of A from F*. Thus, a double pro-
jectile force will balance a quadruple power of
gravity in the fame circle; as appears plain by
the figure, and fhall foon be confirmed by an
experiment.
The whirling-table is a machine contrived for Plate IV.
fhewing experiments of this nature, AA is a Fig. 1.
ftrong frame of wood, B a winch or handle
* Here the arcs AG, AI muſt be ſuppoſed to be very
fmall; otherwiſe AE, which is equal to HI, will be more
than quadruple to AB, which is equal to F G.
1
fixed
28
Of central Forces.
The
whirling
table de⚫
fcribed.
fixed on the axis C of the wheel D, round which
is the catgut ſtring F, which alfo goes round the
fmall wheels G and K, croffing between them
and the great wheel D. On the upper end of
the axis of the wheel G, above the frame, is
fixed the round board d, to which the bearer
MSX may be faftened occafionally, and remov-
ed when it is not wanted. On the axis of the
wheel His fixed the bearer NTZ: and it is
eaſy to ſee that when the winch B is turned, the
wheels and bearers are put into a whirling mo-
tion.
Each bearer has two wires, W, X, and Y, Z,
fixed and ſcrewed tight into them at the ends by
nuts on the outfide. And when thefe nuts are
unfcrewed, the wires may be drawn out in or-
der to change the balls U and V, which ſlide
upon the wires by means of brafs loops fixed in-
to the balls, which keep the balls up from touch-
ing the wood below them. A ftrong filk line
goes through each ball, and is fixed to it at any
length from the center of the bearer to its end
as occafion requires, by a nut-fcrew at the top of
the ball; the fhank of the fcrew goes into the
center of the ball, and preffes the line againſt
the under fide of the hole that it goes through,
The line goes from the ball, and under a ſmall
pulley fixt in the middle of the bearer; then up
through a focket in the round plate (fee S and T)
in the middle of each bearer; then through a
flit in the middle of the fquare top (0 and P)
of each tower, and going over a ſmall pulley on
the top, comes down again the fame way, and is
at laft faftened to the upper end of the focket
fixt in the middle of the above-mentioned round
plate. Theſe plates S and T have each four
round holes near their edges for letting them
flide
Of central Forces.
29
flide up and down upon the wires which make
the corners of each tower. The balls and plates
being thus connected, each by its particular
line, it is plain that if the balls be drawn outward,
or towards the ends M and N of their reſpective
bearers, the round plates S and T will be drawn
up to the top of their refpective towers O and P.
There are feveral brafs weights, fome of two
ounces, fome of three, and fome of four, to be
occaſionally put within the towers O and P, upon
the round plates S and T: each weight having
a round hole in the middle of it, for going upon
the fockets or axes of the plates, and is it from
the edge to the hole, for allowing it to be flipt
over the aforefaid line which comes from each
ball to its reſpective plate. (See Fig. 2.)
The experiments to be made by this machine
are as follows:
matter to
1. Take away the bearer MX, and take the Fig. 1.
ivory ball a, to which the line or filk cord b is
faſtened at one end; and having made a loop on
the other end of the cord, put the loop over a
pin fixt in the center of the board d. Then,
turning the winch B to give the board a whirling The pro-
motion, you will fee that the ball does not imme- penfity of
diately begin to move with the board, but, on keep the
account of its inactivity, it endeavours to conti- ftate it is
nue in the ſtate of reft which it was in before.- in.
Continue turning, until the board communicates
an equal degree of motion with its own to the
ball, and then turning on, you will perceive that
the ball will remain upon one part of the board,
keeping the fame velocity with it, and having no
relative motion upon it, as is the caſe with every
thing that lies looſe upon the plane furface of the
earth, which having the motion of the earth
communicated to it, never endeavours to remove
from
3
30
Of central Forces.
Bodies
have a
}
from that place. But ftop the board fuddenly
by hand, and the ball will go on, and con-
tinue to revolve upon the board, until the
friction thereof ftops its motion: which fhews,
that matter being once put into motion would
continue to move for ever, if it met with no
reſiſtance. In like manner, if a perfon ftands
upright in a boat before it begins to move, he
can ſtand firm; but the moment the boat fets
off, he is in danger of falling towards that place
which the boat departs from: becauſe, as mat-
ter, he has no natural propenfity to move.
when he acquires the motion of the boat, let it
be ever ſo ſwift, if it be ſmooth and uniform, he
will ſtand as upright and firm as if he was on
the plain fhore; and if the boat ftrikes againſt
any obſtacle, he will fall towards that obftacle;
on account of the propenſity he has, as matter,
to keep the motion which the boat has put him.
into.
But
2. Take away this ball, and put a longer cord
to it, which may be put down through the hol-
low axis of the bearer MX, and wheel G, and
fix a weight to the end of the cord below the
machine; which weight, if left at liberty, will
draw the ball from the edge of the whirling-
board to its center.
Draw off the ball a little from the center, and
moving in turn the winch; then the ball will go round and
orbits round with the board, and will gradually fly off
tendency farther and farther from the center, and raiſe up
to fly out the weight below the machine: which fhews
of thefe that all bodies revolving in circles have a ten-
dency to fly off from theſe circles, and muſt have
ſome power acting upon them from the center of
motion, to keep them from flying off. Stop the
machine, and the ball will continue to revolve
orbits.
for
Of central Forces.
31
for fome time upon the board; but as the fric-
tion gradually ſtops its motion, the weight acting
upon it will bring it nearer and nearer to the
center in every revolution, until it brings it
quite thither. This fhews, that if the planets
met with any refiftance in going round the fun,
its attractive power would bring them nearer
and nearer to it in every revolution, until they
fell upon it.
fafter in
3. Take hold of the cord below the machine Bodies
with one hand, and with the other throw the ball move
upon the round board as it were at right angles fmall or
to the cord, by which means it will go round bits than
and round upon the board. Then obferving in large
with what velocity it moves, pull the cord be- ones.
low the machine, which will bring the ball nearer
to the center of the board, and you will fee that
the nearer the ball is drawn to the center, the
fafter it will revolve; as thofe planets which are
neareſt the fun revolve fafter than thoſe which
are more remote; and not only go round fooner,
becauſe they deſcribe ſmaller circles, but even
move fafter in every part of their refpective
circles.
centrifu-
4. Take away this ball, and apply the bearer Their
MX, whofe center of motion is in its middle at
gal forces
w, directly over the center of the whirling-board ewn.
d. Then put two balls (V and U) of equal
weights upon their bearing wires, and having
fixed them at equal diftances from their reſpective
centers of motion w and x upon their filk cords,
by the ſcrew nuts, put equal weights in the
towers O and P. Lastly, put the catgut ftrings
E and F upon the grooves G and H of the fmall
wheels, which being of equal diameters, will give
equal velocities to the bearers above, when the
winch B is turned: and the balls U and V will
Ay
32
Of central Forces.
fly off towards M and N; and will raiſe the
weights in the towers at the fame inftant. This
fhews, that when bodies of equal quantities of
matter revolve in equal circles with equal velo-
cities, their centrifugal forces are equal.
5. Take away thefe equal balls, and inſtead
of them, put a ball of fix ounces into the bearer
MX, at a fixth part of the diſtance w z from the
center, and put a ball of one ounce into the op-
pofite bearer, at the whole diſtance x y, which
is equal to w z from the center of the bearer;
and fix the balls at theſe diſtances on their cords,
by the ſcrew nuts at top; and then the ball U,
which is fix times as heavy as the ball V, will be
at only a fixth part of the diſtance from its cen-
ter of motion; and confequently will revolve in
a circle of only a fixth part of the circumference
of the circle in which revolves. Now, let any
equal weights be put into the towers, and the
machine be turned by the winch; which (as the
catgut ftring is on equal wheels below) will
cauſe the balls to revolve in equal times; but V
will move fix times as faft as U, becauſe it re-
volves in a circle of fix times its radius; and
both the weights in the towers will rife at once.
This fhews, that the centrifugal forces of revolv-
ing bodies (or their tendencies to fly off from the
circles they defcribe) are in direct proportion to
their quantities of matter multiplied into their
reſpective velocities; or into their diſtances from
the centers of their refpective circles. For, fup-
pofing U, which weighs fix ounces, to be two
inches from its center of motion w. the weight
multiplied by the diſtance is 12: and fuppofing
V, which weighs only one ounce, to be 12 inches
diftant from the center of motion x, the weight
1 ounce multiplied by the diftance 12 inches
5
is
Of central Forces.
33
is 12. And as they revolve in equal times, their
velocities are as their diftances from the center,
namely, as 1 to 6.
If these two balls be fixed at equal diftances
from their respective centers of motion, they
will move with equal velocities; and if the
tower has 6 times as much weight put into it
as the tower P has, the balls will raife their
weights exactly at the fame moment. This
fhews that the ball U being fix times as heavy as
the ball V, has fix times as much centrifugal
force, in defcribing an equal circle with an equal
velocity.
in the
power of
gravity.
6. If bodies of equal weights revolve in equal A double
circles with unequal velocities, their centrifugal velocity
forces are as the fquares of the velocities. To fame cir-
prove this law by an experiment, let two balls cle, is a
U and V of equal weights be fixed on their cords balance
at equal diſtances from their reſpective centers to a qua-
of motion w and x; and then let the catgut duple
ftring E be put round the wheel K (whofe cir-
cumference is only one half of the circumference
of the wheel H or G) and over the pulley s to
keep it tight; and let four times as much weight
be put into the tower P, as in the tower 0.
Then turn the winch B, and the ball will re-
volve twice as faſt as the ball U in a circle of the
fame diameter, becauſe they are equidiſtant from
the centers of the circles in which they revolve;
and the weight in the towers will both rife at
the fame inftant, which fhews that a double ve-
locity in the fame circle will exactly balance a
quadruple power of attraction in the center of
the circle. For the weights in the towers may
be confidered as the attractive forces in the cen-
ters, acting upon the revolving balls; which,
moving
34
Of central Forces.
Kepler's
moving in equal circles, is the fame thing as if
they both moved in one and the fame circle.
7. If bodies of equal weights revolve in un-
Problem. equal circles, in fuch a manner that the fquares
of the times of their going round are as the
cubes of their diſtances from the centers of the
circles they deſcribe; their centrifugal forces are
inverſely as the fquares of their diſtances from
thoſe centers. For, the catgut ftring remaining
as in the laſt experiment, let the diftance of the
ball from the center x be made equal to two
of the cross divifions on its bearer; and the dif-
tance of the ball U from the center w be three
and a fixth part; the balls themselves being of
equal weights, and making two revolutions
by turning the winch, in the time that U makes
one: fo that if we fuppofe the ball V to revolve
in one fecond, the ball U will revolve in two
feconds, the fquares of which are one and four:
for the fquare of 1 is only 1, and the fquare of
2 is 4; therefore the fquare of the period or
revolution of the ball V, is contained four times
in the ſquare of the period of the ball U. But
the diſtance of Vis 2, the cube of which is 8,
and the diſtance of U is 3%, the cube of which
is 32 very nearly, in which 8 is contained four
times; and therefore, the fquares of the periods
of V and U are to one another as the cubes of
their diſtances from x and w, which are the cen-
ters of their refpective circles. And if the
weight in the tower O be four ounces, equal to
the ſquare of 2, the diftance of V from the cen-
ter x; and the weight in the tower P be 10
ounces, nearly equal to the fquare of 3%, the dif
tance of U from w; it will be found upon turn-
ing the machine by the winch, that the balls U
and will raife their refpective weights at
the
Of central Forces.
35
the fame inftant of time. Which confirms that
famous obfervation of KEPLER, viz. That the
fquares of the times in which the planets go round
the fun are in the fame proportion as the cubes of
their diſtances from him; and that the fun's at-
traction is inverſely as the fquare of the diſtance
from his center: that is, at twice the diftance,
his attraction is four times lefs; and thrice the
diſtance, nine times lefs; at four times the dif
tance, fixteen times lefs; and fo on, to the re-
moteft part of the ſyſtem.
fian vor-
texes
8. Take off the catgut ftring E from the
great wheel D and the fmall wheel H, and let
the ftring F remain upon the wheels D and G.
Take away alfo the bearer MX from the whirl-
ing-board d, and inſtead thereof put the ma-
chine AB upon it, fixing this machine to the
center of the board by the pins c and d, in fuch Fig. 3.
a manner, that the end ef may rife above the
board to an angle of 30 or 40 degrees. In the The ab-
upper fide of this machine are two glafs tubes furdity of
a and b, clofe ftopt at both ends; and each the Carte-
tube is about three quarters full of water. In
the tube a is a little quickfilver, which naturally
falls down to the end a in the water, becauſe
it is heavier than its bulk of water; and in the
tube b is a ſmall cork which floats on the top
of the water at e, becauſe it is lighter; and it
is fmall enough to have liberty to rife or fall
in the tube. While the board b with this ma-
chine upon it continues at reft, the quickſilver
lies at the bottom of the tube a, and the cork
floats on the water near the top of the tube b. But,
upon turning the winch, and putting the ma-
chine in motion, the contents of each tube will
fly off towards the uppermoft ends (which are
farthest from the center of motion) the heaviest
D
with
36
Of central Forces.
If one bo-
round
both of
with the greateſt force. Therefore the quick-
filver in the tube a will fly off quite to the end
f, and occupy its bulk of fpace there, excluding
the water from that place, becauſe it is lighter
than quickfilver; but the water in the tube b
flying off to its higher end e, will exclude the
cork from that place, and cauſe the cork to de-
fcend towards the lowermoft end of the tube,
where it will remain upon the loweſt end of the
water near b; for the heavier body having the
greater centrifugal force, will therefore poffefs
the uppermost part of the tube; and the lighter
body will keep between the heavier and the
lowermoſt part.
This demonftrates the abfurdity of the Carte-
fian doctrine of the planets moving round the
fun in vortexes: for, if the planet be more
denfe or heavy than its bulk of the vortex, it will
fly off therein, farther and farther from the fun;
if lefs denſe, it will come down to the loweſt
part of the vortex, at the fun: and the whole
vortex itſelf muſt be furrounded with fomething
like a great wall, otherwiſe it would fly quite off,
planets and all together. But while gravity ex-
ifts, there is no occaſion for ſuch vortexes; and
when it ceaſes to exiſt, a ſtone thrown upwards
will never return to the earth again.
9. If a body be fo placed on the whirling-
dy moves board of the machine (Fig. 1.) that the center of
gravity of the body be directly over the center
another, of the board, and the board be put into ever fo
them muft rapid a motion by the winch B, the body will
turn round with the board, but will not remove.
round from the middle of it; for, as all parts of the
their com- body are in equilibrio round its center of gravity,
and the center of gravity is at reft in the center
gravity. of motion, the centrifugal force of all parts of
move
mon cen-
ter of
I
the
Of central Forces.
37
the body will be equal at equal diſtances from
its center of motion, and therefore the body will
remain in its place. But if the center of gravity
be placed ever fo little out of the center of mo-
tion, and the machine be turned fwiftly round,
the body will fly off towards that fide of the
board on which its center of gravity lies. Thus, Fig. 4.
if the wire C with its little ball B be taken away
from the demi-globe A, and the flat fide ef of
this demi-globe be laid upon the whirling-board
of the machine, fo that their centers may coin-
cide; if then the board be turned ever fo quick
by the winch, the demi-globe will remain where
it was placed. But if the wire C be ſcrewed into
the demi-globe at d, the whole becomes one
body, whofe center of gravity is now at or near
d. Let the pin c be fixed in the center of the
whirling-board, and the deep groove b cut in the
flat fide of the demi-globe be put upon the pin,
fo as the pin may be in the center of A (See Fig.
5. where this groove is reprefented at b] and let
the whirling-board be turned hy the winch,
which will carry the little ball B (Fig. 4.) with
its wire C, and the demi-globe A, all round the
center-pin ci; and then, the centrifugal force of
the little ball B, which weighs only one ounce,
will be ſo great, as to draw off the demi-globe
A, which weighs two pounds, until the end of
the groove at e ftrikes against the pin c, and
fo prevents the demi-globe A from going any
farther otherwife, the centrifugal force of B
would have been great enough to have carried
A quite off the whirling-board. Which fhews,
that if the fun were placed in the very center of
the orbits of the planets, it could not poffibly
remain there; for the centrifugal forces of the
planets would carry them quite off, and the fun
D 2
with
Fig. 5.
38
Of central Forces.
with them; eſpecially when ſeveral of them hap
pened to be in any one quarter of the heavens.
For the fun and planets are as much connected
by the mutual attraction that fubfifts between
them, as the bodies A and B are by the wire C
which is fixed into them both. And even if
there were but one fingle planet in the whole
heavens to go round ever fo large a fun in the
center of its orbit, its centrifugal force would
foon carry off both itſelf and the fun. For, the
greateſt body placed in any part of free ſpace
might be eaſily moved: becauſe if there were no
other body to attract it, it could have no weight
or gravity of itſelf, and confequently, though it
could have no tendency of itſelf to remove from
that part of space, yet it might be very eaſily
moved by any other fubftance.
10. As the centrifugal force of the light body
B will not allow the heavy body A to remain in
the center of motion, even though it be 24 times
as heavy as B; let us now take the ball A (Fig.
6.) which weighs 6 ounces, and connect it by
the wire C with the ball B, which weighs only
one ounce; and let the fork E be fixed into the
center of the whirling-board: then hang the
balls upon the fork by the wire C in fuch a man-
nor, that they may exactly balance each other;
which will be when the center of gravity between
them, in the wire at d, is fupported by the fork.
And this center of gravity is as much nearer to
the center of the ball A, than to the center of the
ball B, as A is heavier than B, allowing for the
weight of the wire on each fide of the fork.
This done, let the machine be put into motion
by the winch; and the balls A and B will go
round their common center of gravity d, keep-
ing their balance, becaufe either will not allow
the
Of central Forces.
39
the other to fly off with it. For, fuppofing the
ball B to be only one ounce in weight, and the
ball A to be fix ounces; then, if the wire C were
equally heavy on each ſide of the fork, the center
of gravity d would be fix times as far from the
center of the ball B as from that of the ball A,
and confequently B will revolve with a velocity
fix times as great as A does; which will give B
fix times as much centrifugal force as any fingle
ounce of A has: but then, as B is only one
ounce, and A fix ounces, the whole centrifugal
force of A will exactly balance the whole centri-
fugal force of B: and therefore, each body will
detain the other fo as to make it keep in its
circle. This fhews that the fun and planets muft
all move round the common center of gravity
of the whole ſyſtem, in order to preferve that juſt
balance which takes place among them. For,
the planets being as unactive and dead as the
above balls, they could no more have put them-
felves into motion than theſe balls can; nor have
kept in their orbits without being balanced at
first with the greatest degree of exactnefs upon
their common center of gravity, by the Almighty
hand that made them and put them in motion.
Perhaps it may be here afked, that fince the
center of gravity between thefe balls must be
ſupported by the fork E in this experiment,
what prop it is that fupports the center of gra-
vity of the folar fyftem, and confequently bears
the weight of all the bodies in it; and by what
is the prop itſelf ſupported? The anſwer is eaſy
and plain; for the center of gravity of our balls
muſt be ſupported, becauſe they gravitate to
wards the earth, and would therefore fall to it s
but as the fun and planets gravitate only towards
D 3
one
40
Of central Forces.
one another, they have nothing elfe to fall to;
and therefore have no occafion for any thing to
fupport their common center of gravity: and if
they did not move round that center, and confe-
quently acquire a tendency to fly off from it by
their motions, their mutual attractions would
foon bring them together; and fo the whole
would become one nafs in the fun: which would
alfo be the cafe if their velocities round the fun
were not quick enough to create a centrifugal
force equal to the fun's attraction.
But after all this nice adjustment, it appears
evident that the Deity cannot withdraw his re-
gulating hand from his works, and leave them
to be folely governed by the laws which he has
impreft upon them at firft. For if he fhould
once leave them fo, their order would in time
come to an end; becauſe the planets muft ne-
ceffarily disturb one another's motions by their
mutual attractions, when feveral of them are in
the fame quarter of the heavens; as is often the
cafe and then, as they attract the fun more
towards that quarter than when they are in a
manner difperfed equably around him, if he was
not at that time made to defcribe a portion of a
larger circle round the common center of gravity,
the balance would then be immediately de-
ftroyed; and as it could never reſtore itſelf again,
the whole ſyſtem would begin to fall together,
and would in time unite in a mafs at the fun.-
Of this disturbance we have a very remarkable
inftance in the comet which appeared lately; and
which, in going laft up before from the fun, went
fo near to Jupiter, and was fo affected by his
attraction, as to have the figure of its orbit much
changed; and not only fo, but to have its period
ปี
altered,
Of central Forces.
41
altered, and its courſe to be different in the hea-
vens from what it was laſt before.
11. Take away the fork and balls from the Fig. 7.
whirling.board, and place the trough AB there-
on, fixing its center to the center of the whirl-
ing-board by the pin H. In this trough are two
balls D and E, of unequal weights, connected
by a wire f; and made to flide eafily upon the
wire C ftretched from end to end of the trough,
and made faſt by nut-ſcrews on the outſide of the
ends. Let theſe balls be fo placed upon the wire
C, that their common center of gravity g may be
directly over the center of the whirling-board.
Then, turn the machine by the winch, ever ſo
fwiftly,and the troughand balls will go round their
center of gravity, fo as neither of the balls will fly
off; becauſe, on account of the equilibrium, each
ball detains the other with an equal force acting
against it. But if the ball E be drawn a little
more towards the end of the trough at A, it will
remove the center of gravity towards that end
from the center of motion; and then, upon
turning the machine, the little ball E will fly off,
and ſtrike with a confiderable force againſt the
end A, and draw the great ball B into the middle
of the trough. Or, if the great ball D be drawn
towards the end B of the trough, fo that the cen-
ter of gravity may be a little towards that end
from the center of motion, and the machine be
turned by the winch, the great ball D will fly off,
and ſtrike violently againſt the end B of the
trough, and will bring the little ball E into the
middle of it. If the trough be not made very
ſtrong, the ball D will break through it.
12. The reaſon why the tides rife at the fame Of the
abfolute time on oppofite fides of the earth, and tides.
confequently
D 4
42
Of the Tides.
Fig. 8.
Fig. 9.
-
confequently in oppofite directions, is made
abundantly plain by a new experiment on the
whirling-table. The caufe of their rifing on the fide
next the moon every one underſtands to be owing
to the moon's attraction: but why they ſhould
rife on the oppofite fide at the fame time, where
there is no moon to attract them, is perhaps not
fo generally underſtood. For it would feem
that the moon fhould rather draw the waters (as
it were) cloſer to that fide, than raiſe them upon
it, directly contrary to her attractive force. Let
the circle abcd repreſent the earth, with its fide
c turned toward the moon, which will then at-
tra the waters fo, as to raiſe them from c to g.
But the question is, why ſhould they rife as high
at that very time on the oppofite fide, from a to
e? In order to explain this, let there be a plate
AB fixed upon one end of the flat bar DC; with
fuch a circle drawn upon it as abcd (in Fig. 8.)
to repreſent the round figure of the earth and
fea; and fuch an ellipfis as efg b to repreſent the
fwelling of the tide at e and g, occafioned by the
influence of the moon. Over this plate AB let
the three ivory balls e, f, g, be hung by the filk
lines b, i, k, faſtened to the tops of the crooked
wires H, I, K, in fuch a manner, that the ball at
e may hang freely over the fide of the circle e,
which is fartheft from the moon M (at the other
end of the bar); the ball at ƒ may hang freely
over the center, and the ball at g hang over the
fide of the circle g, which is neareſt the moon.
The ball ƒ may reprefent the center of the earth,
the ball g fome water on the fide next the moon,
and the ball e fome water on the oppofite fide,
On the back of the moon M is fixt the fhort bar
N parallel to the horizon, and there are three
holes in it above the little weights p, q, r. A
fill
Of the Tides.
43·
filk thread o is tied to the line k clofe above the
>
ball
g and paffing by one fide of the moon M,
goes through a hole in the bar N, and has the
weight p hung to it. Such another thread n is
tied to the line i, clofe above the ball f, and
paffing through the center of the moon M and
middle of the bar N, has the weight q hung to
it, which is lighter than the weight p. A third
thread m is tied to the line b, clote above the ball
e, and paffing by the other fide of the moon M,
through the bar N, has the weight r hung to it,
which is lighter than the weight 4.
So,
The ufe of theſe three unequal weights is to
repreſent the moon's unequal attraction at diffe-
rent diſtances from her. With whatever force
ſhe attracts the center of the earth, fhe attracts
the fide next her with a greater degree of force,
and the fide farthest from her with a lefs.
if the weights are left at liberty, they will draw
all the three balls towards the moon with diffe-
rent degrees of force, and caufe them to make
the appearance fhewn in Fig. 10; by which Fig. 10.
means they are evidently farther from each other
than they would be if they hung at liberty by the
lines h, i, k; becauſe the lines would then hang
perpendicularly. This fhews, that as the moon
attracts the fide of the earth which is neareſt her
with a greater degree of force than fhe does the
center of the earth, fhe will draw the water on
that fide more than fhe draws the center, and fo
cauſe it to riſe on that ſide: and as ſhe draws the
center more than fhe draws the oppofite fide,
the center will recede farther from the furface of
the water on that oppofite fide, and fo leave it as
high there as the raifed it on the fide next to her.
For, as the center will be in the middle between
the
44
Of the Tides.
1
the tops of the oppofite elevations, they muſt of
courfe be equally high on both fides at the fame
time.
But upon this fuppofition the earth and moon
would foon come together: and to be fure they
would, if they had not a motion round their
common center of gravity, to create a degree of
centrifugal force fufficient to balance their mu-
tual attraction. This motion they have; for as
the moon goes round her orbit every month, at
the diſtance of 240000 miles from the earth's
center, and of 234000 miles from the center of
gravity of the earth and moon, fo does the earth
go round the fame center of gravity every month
at the diſtance of 6000 miles from it; that is,
from it to the center of the earth. Now as the
earth is (in round numbers) 8000 miles in dia-
meter, it is plain that its fide next the moon is
only 2000 miles from the common center of gra-
vity of the earth and moon; its center 6000
miles diftant therefrom; and its farther fide from
the moon 10000. Therefore the centrifugal
forces of theſe parts are as 2000, 6000, and
10000; that is, the centrifugal force of any fide.
of the earth, when it is turned from the moon,
is five times as great as when it is turned towards
the moon. And as the moon's attraction (ex-
preſt by the numbers 6000) at the earth's center
keeps the earth from flying out of this monthly
circle, it muſt be greater than the centrifugal
force of the waters on the fide next her; and
confequently, her greater degree of attraction on
that fide is fufficient to raiſe them; but as her
attraction on the oppofite fide is less than the
centrifugal force of the water there, the excefs
of this force is fufficient to raiſe the water juft as
high
The Earth's Motion demonftrated.
45
14-
high on the oppofite fide.-To prove this expe- Fig. 9.
rimentally, let the bar DC with its furniture be
fixed upon the whirling-board of the machine
(Fig. 1.) by puſhing the pin P into the center
of the board; which pin is in the center of gra-
vity of the whole bar with its three balls e, f, g,
and moon M. Now if the whirling-board and
bar be turned flowly round by the winch, until
the ball ƒ hangs over the center of the circle, as
in Fig. 1. the ball g will be kept towards the
moon by the heaviest weight p, (Fig. 9.) and
the ball e, on account of its greater centrifugal
force, and the leffer weight r, will fly off as far
to the other fide, as in Fig. 11. And fo, whilſt
the machine is kept turning, the balls e and g
will hang over the ends of the ellipfis lf k. So
that the centrifugal force of the ball e will ex-
ceed the moon's attraction just as much as her
attraction exceeds the centrifugal force of the
ball g, whilft her attraction juft balances the cen-
trifugal force of the ball f, and makes it keep
in its circle. And hence it is evident that the
tides muſt riſe to equal heights at the fame time
on oppofite fides of the earth. This experi-
ment, to the beft of my knowledge, is entirely
new.
motion
From the principles thus eftabliſhed, it is The
evident that the earth moves round the fun, and earth's
not the fun round the earth; for the centrifugal demon-
law will never allow a great body to move round ftrated.
a fmall one in any orbit whatever; fpecially
when we find that if a fmall body moves round
a great one, the great one muſt alſo move round
the common center of gravity between them two.
And it is well known that the quantity of matter
in the fun is 227000 times as great as the quan-
tity of matter in the earth. Now, as the fun's
diſtance
!
46
The Earth's Motion demonftrated.
4
diſtance from the earth is at leaft 81,000,000 of
miles, if we divide that diſtance by 227,000, we
ſhall have only 357 for the number of miles that
the center of gravity between the fun and earth
is diſtant from the fun's center. And as the
fun's femidiameter is of a degree, which, at fo
great a diſtance as that of the fun, muft be no
leſs than 381500 miles, if this be divided by
357, the quotient will be 1068, which fhews
that the common center of gravity between the
fun and earth is within the body of the fun;
and is only the 1068 part of his femidiameter
from his center toward his furface.
All globular bodies, whofe parts can yield,
and which do not turn on their axes, muſt be
perfect ſpheres, becauſe all parts of their ſurfaces
are equally attracted toward their centers. But
all fuch globes which do turn on their axes will
be oblate ſpheroids; that is, their furfaces will
be higher, or farther from the center, in the
equatoreal than in the polar regions. For, as
the equatoreal parts move quickest, they muft
have the greateſt centrifugal force; and will
therefore recede farthest from the axis of mo-
tion. Thus, if two circular hoops AB and
Fig. 12. CD, made thin and flexible, and croffing one
another at right angles, be turned round their
axis E F by means of the winch m, the wheel n,
and pinion o, and the axis be looſe in the pole
or interfection e, the middle parts A, B, C, D
will ſwell out fo as to ftrike against the fides of
the frame at F and G, if the pole e, in finking
to the pin E, be not ftopt by it from finking
farther fo that the whole will appear of an oval
figure, the equatoreal diameter being confide-
rably longer than the polar. That our earth is
of this figure, is demonftrable from actual mea-
furement
Of the mechanical Power's.
47
furement of ſome degrees on its furface, which
are found to be longer in the frigid zones than
in the torrid: and the difference is found to be
fuch as proves the earth's equatoreal diameter
to be 36 miles longer than its axis.-Seeing then,
the earth is higher at the equator than at the
poles, the fea, which like all other fluids natu-
rally runs downward (or towards the places
which are neareſt the earth's center) would run
towards the polar regions, and leave the equato-
real parts dry, if the centrifugal force of the
water, which carried it to thoſe parts, and fo
raiſed them, did not detain and keep it from
running back again towards the poles of the
earth.
I
LECT. III.
Of the mechanical Powers.
all me-
chanics.
F we confider bodies in motion, and com- The
pare them together, we may do this either founda-
with reſpect to the quantities of matter they tion of
contain, or the velocities with which they are
moved. The heavier any body is, the greater
is the power required either to move it or to ſtop
its motion and again, the fwifter it moves, the
greater is its force. So that the whole momen-
tum or quantity of force of a moving body is the
reſult of its quantity of matter multiplied by the
velocity with which it is moved. And when the
products ariſing from the multiplication of the
particular quantities of matter in any two bodies.
by their reſpective velocities are equal, the mo-
menta or intire forces are fo too. Thus, fup-
poſe a body, which we fhall call A, to weigh 40
pounds, and to move at the rate of two miles
1
in
48
Of the mechanical Powers:
in a minute; and another body, which we ſhall
call B, to weigh only four pounds, and to move
20 miles in a minute; the entire forces with
which theſe two bodies would ſtrike againſt any
obſtacle would be equal to each other, and there-
fore it would require equal powers to ſtop them.
For 40 multiplied by 2 gives 80, the force of
the body A and 20 multiplied by 4 gives 80,
the force of the body B.
Upon this eaſy principle depends the whole
of mechanics: and it holds univerfally true,
that when two bodies are fufpended on any
machine, ſo as to act contrary to each other; if
the machine be put into motion, and the per-
pendicular aſcent of one body multiplied into
its weight, be equal to the perpendicular defcent
of the other body multiplied into its weight,
thoſe bodies, how unequal foever in their weights,
will balance one another in all fituations: for,
as the whole afcent of one is performed in the
fame time with the whole defcent of the other,
their reſpective velocities muſt be directly as the
ſpaces they move through; and, the exceſs of
weight in one body is compenfated by the exceſs
of velocity in the other.-Upon this principle it
compute is easy to compute the power of any mechanical
the power engine, whether fimple or compound; for it is
but only finding how much fwifter the power
moves than the weight does (i.e. how much far-
ther in the fame time) and juft fo much is the
power increaſed by the help of the engine.
How to
of any
mechani-
cal en-
gine.
In the theory of this fcience, we fuppofe all
planes perfectly even, all bodies perfectly ſmooth,
levers to have no weight, cords to be extremely
pliable, machines to have no friction; and in
fhort, all imperfections muſt be ſet aſide until
the
PLATE V.
A B
Fig. 1.
1 1 1 1 5 6 7 8 9 1
AD
12
W
2
Fig. 2.
A
G
A
E
W
A
S
C
10
บ
12
Fg.5.
H
E
PO
1
3
1
5
B
P
D
C
Fig. 3.
2
E
F
5
3
P
b
A
D
3
E
S
S
K
B
B
I
W
Fig. 6.
и
H
C
B
R
X
Ꮐ.
Fig. 4.
12
E
3
B
B
G
M
F
K
a
D
2
1
1
W
P
P
D
B
P
W
W
d
P
2
W
T
1
5
W
W
4
1
P
7. Myude pulf.
I. Ferguson delin.
Of the mechanical Powers.
49
+
the theory be eſtabliſhed; and then, proper
allowances are to be made.
The fimple machines, ufually called mechanical The me-
powers, are fix in number, viz. the lever, the chanic
wheel and axle, the pulley, the inclined plane, the powers,
wedge, and the ſcrew.-They are called mecha- what.
nical powers, becauſe they help us mechanically
to raiſe weights, move heavy bodies, and over-
come refiftances, which we could not effect with-
out them.
1. A lever is a bar of iron or wood, one part The le-
of which being fupported by a prop, all the ver.
other parts turn upon that prop as their center
of motion: and the velocity of every part or
point is directly as its diftance from the prop.
Therefore, when the weight to be raiſed at one
end is to the power applied at the other to raiſe
it, as the diſtance of the power from the prop
is to the diftance of the weight from the prop,
the power and weight will exactly balance or
counterpoife each other: and as a common lever
has next to no friction on its prop, a very
little additional power will be fufficient to raiſe
the weight.
There are four kinds of levers.
1. The
common fort, where the prop is placed between:
the weight and the power; but much nearer to
the weight than to the power. 2. When the
prop is at one end of the lever, the power at the
other, and the weight between them. 3. When
the prop is at one end, the weight at the other,
and the power applied between them. 4. The
bended lever, which differs only in form from
the firſt fort, but not in property. Thofe of the
firſt and ſecond kind are often ufed in mechani-
cal engines; but there are few inftances in which
the third fort is uſed.
A Com-
Of the mechanical Powers.
2
The ba-
lance.
Plate V.
Fig. 1.
kind of
The first
lever.
A common balance is by fome reckoned a lever
of the first kind; but as both its ends are at
equal diftances from its center of motion, they
move with equal velocities; and therefore, as
it gives no mechanical advantage, it cannot pro-
perly be reckoned among the mechanical powers.
A lever of the firſt kind is reprefented by the
bar ABC, ſupported by the prop D. Its prin-
cipal ufe is to loofen large ftones in the ground,
or raiſe great weights to fmall heights, in order
to have ropes put under them for raising them.
higher by other machines.. The parts AB and
BC, on different fides of the prop D, are called
the arms of the lever: the end A of the ſhorter
arm AB being applied to the weight intended
to be raiſed, or to the reſiſtance to be overcome,
and the power applied to the end C of the longer
arm BC.
In making experiments with this machine, the
fhorter arm AB muſt be as much thicker than
the longer arm BC, as will be fufficient to ba-
lance it on the prop. This fuppofed, let P re-
prefent a power, whofe gravity is equal to 1
ounce, and a weight, whofe gravity is equal
to 12 ounces. Then, if the power be 12 times
as far from the prop as the weight is, they will
exactly counterpoife; and a ſmall addition to
the power P will caufe it to defcend, and raiſe
the weight W; and the velocity with which the
power deſcends will be to the velocity with
which the weight rifes, as 12 to 1: that is,
directly as their diftances from the prop; and
conſequently, as the ſpaces through which they
move. Hence, it is plain that a man, who by
his natural ſtrength, without the help of any
machine, could fupport an hundred weight, will
by the help of this lever be enabled to ſupport
twelve
Of the mechanical Powers.
5I
twelve hundred. If the weight be lefs, or the
power greater, the prop may be placed fo much.
farther from the weight; and then it can be
raiſed to a proportionably greater height. For
univerfally, if the intensity of the weight mul-
tiplied into its diftance from the prop be equal
to the intensity of the power multiplied into its
diſtance from the prop, the power and weight
will exactly balance each other; and a little ad-
dition to the power will raife the weight. Thus,
in the prefent inftance, the weight W is 12
ounces, and its diftance from the prop is 1 inch;
and 12 multiplied by 1 is 12; the power P is
equal to 1 ounce, and its diftance from the prop
is 12 inches, which multiplied by 1 is 12 again;
and therefore there is an equilibrium between
them. So, if a power equal to 2 ounces be ap-
plied at the diſtance of 6 inches from the prop,
it will juſt balance the weight W, for 6 multi-
W;
plied by 2 is 12, as before. And a power equal
to 3 ounces placed at 4 inches diftance from the
prop would be the fame; for 3 times 4 is 12;
and fo on, in proportion.
I
The ftatera or Roman fteelyard is a lever of The ſteel-
this kind, and is uſed for finding the weights of yard.
different bodies by one fingle weight placed at
different diſtances from the prop or center of
motion D. For, if a fcale hangs at A, the ex-
tremity of the ſhorter arm A B, and is of fuch a
weight as will exactly counterpoife the longer
arm BC; if this arm be divided into as many
equal parts as it will contain, each equal to A B,
the fingle weight P (which we may ſuppoſe to
be 1 pound) will ferve for weighing any thing
as heavy as itſelf, or as many times heavier as
there are divifions in the arm B C, or any quan
tity between its own weight and that quantity.
E
As
52
Of the mechanical Powers:
t
The fe-
cond kind
of lever.
Fig. 2.
As for example, if P be 1 pound, and placed
at the first divifion in the arm BC, it will
balance 1 pound in the ſcale at A: if it be re-
moved to the fecond divifion at 2, it will ba-
lance 2 pounds in the fcale: if to the third, 3
pounds; and ſo on to the end of the arm B Č.
If each of thefe integral divifions be fubdivided
into as many equal parts as a pound contains
ounces, and the weight P be placed at any of
theſe ſubdiviſions, fo as to counterpoife what is
in the ſcale, the pounds and odd ounces therein
will by that means be afcertained.
To this kind of lever may be reduced feveral
forts of inftruments, fuch as fciffars, pinchers,
fnuffers; which are made of two levers acting
contrary to one another: their prop or center of
motion being the pin which keeps them toge-
ther.
In common practice, the longer arm of this
lever greatly exceeds the weight of the fhorter:
which gains great advantage, becauſe it adds fo
much to the power.
A lever of the fecond kind has the weight
between the prop and the power. In this, as
well as the former, the advantage gained is as
the diſtance of the power from the prop to the
diſtance of the weight from the prop: for the
reſpective velocities of the power and weight are
in that proportion; and they will balance each
other when the intenſity of the power multi-
plied by its diſtance from the prop is equal to
the intensity of the weight multiplied by its dif-
tance from the prop. Thus, if A B be a lever
on which the weight W of 6 ounces hangs at the
diſtance of 1 inch from the prop G, and a power
P equal to the weight of 1 ounce hangs at the
end B, 6 inches from the prop, by the cord
I
CD
Of the mechanical Powers.
53
CD going over the fixed pulley E, the power
will juſt ſupport the weight: and a ſmall ad-
dition to the power will raiſe the weight, inch
for every 6 inches that the power defcends.
This lever fhews the reafon why two men
carrying a burden upon a ftick between them,
bear unequal fhares of the burden in the in-
verfe proportion of their distances from it. For
it is well known, that the nearer any of them is
to the burden, the greater fhare he bears of it:
and if he goes directly under it, he bears
the whole. So, if one man be at G, and the
other at P, having the pole or ſtick AB reſting
on their ſhoulders; if the burden or weight W
be placed five times as near the man at G, as it
is to the man at P, the former will bear five
times as much weight as the latter. This is
likewiſe applicable to the cafe of two horſes of
unequal ſtrength to be fo yoked, as that each
horſe may draw a part proportionable to his
ftrength, which is done by fo dividing the beam
they pull, that the point of traction may be as
much nearer to the ftronger horſe than to the
weaker, as the ftrength of the former exceeds.
that of the latter.
To this kind of lever may be reduced oars,
rudders of ſhips, doors turning upon hinges,
cutting-knives which are fixed at the point of
the blade, and the like.
kind of
lever.
If in this lever we fuppofe the power and The third
weight to change places, ſo that the power may
be between the weight and the prop, it will be-
come a lever of the third kind: in which, that
there may be a balance between the power and
the weight, the intenſity of the power muſt ex-
ceed the intenſity of the weight, juſt as much
as the diſtance of the weight from the prop ex-
E 2
ceeds
1
54
Of the mechanical Powers.
Fig. 3.
The
fourth
kind of
Jever.
Fig. 4.
ceeds the diſtances of the power from it. Thus,
let E be the prop of the lever AB, and W a
weight of 1 pound, placed 3 times as far from
the prop, as the power P acts at F, by the
cord C going over the fixed pulley D; in this
cafe, the power muſt be equal to three pounds,
in order to fupport the weight.
To this fort of lever are generally referred
the bones of a man's arm: for when we lift a
weight by the hand, the muſcle that exerts its
force to raiſe that weight, is fixed to the bone
about one tenth part as far below the elbow as
the hand is. And the elbow being the center
round which the lower part of the arm turns,
the muſcle must therefore exert a force ten times
as great as the weight that is raiſed.
As this kind of lever is a difadvantage to the
moving power, it is never ufed but in cafes of
neceffity; fuch as that of a ladder, which being
fixed at one end, is by the ftrength of a man's
arms reared againſt a wall. And in clock-work,
where all the wheels may be reckoned levers of
this kind, becauſe the power that moves every
wheel, except the firft, acts upon it near the
center of motion by means of a ſmall pinion,
and the reſiſtance it has to overcome, acts againſt
the teeth round its circumference.
The fourth kind of lever differs nothing from
the firſt, but in being bended for the fake of
convenience. ACB is a lever of this fort, bended
at C, which is its prop, or center of motion.
P is a power acting upon the longer arm AC at
F, by means of the cord DE going over the
pulley G; and W is a weight or refiftance acting
upon the end B of the ſhorter arm B C. If the
power is to the weight, as C B is to CF, they
are in equilibrio. Thus, fuppofe W to be 5
pounds
Of the mechanical Powers.
$5
pounds acting at the diſtance of one foot from
the center of motion C, and P to be I pound
acting at F, five feet from the center C, the
power and weight will just balance each other.
A hammer drawing a nail is a lever of this
fort.
axle.
2. The fecond mechanical power is the wheel The
and axle, in which the power is applied to the wheel and
circumference of the wheel, and the weight is
raiſed by a rope which coils about the axle as the
wheel is turned round. Here it is plain that
the velocity of the power muſt be to the velocity
of the weight, as the circumference of the wheel
is to the circumference of the axle: and confe-
quently, the power and weight will balance each
other, when the intensity of the power is to the
intenſity of the weight, as the cicumference of
the axle is to the circumference of the wheel.
Let A B be a wheel, CD its axle, and ſuppoſe Fig. 5.
the circumference of the wheel to be 8 times as
great as the circumference of the axle; then, a
power P equal to 1 pound hanging by the cord
I, which goes round the wheel, will balance a
weight W of 8 pounds hanging by the rope K,
which goes round the axle. And as the fric-
tion on the pivets or gudgeons of the axle is
but ſmall, a ſmall addition to the power will
cauſe it to deſcend, and raiſe the weight: but
the weight will rife with only an eighth part of
the velocity wherewith the power defcends, and
confequently, through no more than an eighth
part of an equal ſpace, in the fame time. If the
wheel be pulled round by the handles S, S, the
power will be increaſed in proportion to their
length. And by this means, any weight may
be raiſed as high as the operator pleaſes.
E 3
To
56
Of the mechanical Powers.
2
2
To this fort of engine belong all cranes for
railing great weights; and in this cafe, the
wheel may have cogs all round it inſtead of han-
dles, and a ſmall lantern or trundle may be made
to work in the cogs, and be turned by a winch;
which will make the power of the engine to ex-
ceed the power of the man who works it, as
much as the number of revolutions of the winch
exceed thoſe of the axle D, when multiplied
by the excess of the length of the winch above
the length of the femidiameter of the axle,
added to the femidiameter or half thickneſs of
the rope K, by which the weight is drawn up.
Thus, fuppofe the diameter of the rope and
axle taken together, to be 13 inches, and confe-
quently, half their diameters to be 6 inches; ſọ
that the weight W will hang at 6 inches per-
pendicular diſtance from below the center of
the axle. Now, let us ſuppoſe the wheel A B,
which is fixt on the axle, to have 80 cogs, and
to be turned by means of a winch 6 inches
long, fixt on the axis of a trundle of 8 ftaves or
rounds, working in the cogs of the wheel.-
Here it is plain, that the winch and trundle
would make 10 revolutions for one of the wheel
A B, and its axis D, on which the rope K winds
in rafing the weight W; and the winch being
no longer than the fum of the femidiameters of
the great axle and rope, the trundle could have
no more power on the wheel, than a man could
have by pulling it round by the edge, becauſe
the winch would have no greater velocity than
the edge of the wheel has, which we here fup-
pofe to be ten times as great as the velocity of
the rifing weight: fo that, in this cafe, the
power gained would be as 10 to 1. But if the
length of the winch be 13 inches, the power
2
gained
Of the mechanical Powers.
57
gained will be as 20 to 1: if 19 inches (which
is long enough for any man to work by) the
power gained would be as 30 to 1; that is, a
man could raiſe 30 times as much by fuch an
engine, as he could do by his natural ſtrength
without it, becauſe the velocity of the handle of
the winch would be 30 times as great as the ve-
locity of the rifing weight; the abfolute force
of any engine being in proportion of the velocity
of the power to the velocity of the weight raifed
by it. But then, juft as much power or advan-
tage as is gained by the engine, ſo much time is
loft in working it. In this fort of machines it is
requifite to have a ratchet-wheel G on one end
of the axle, with a catch H to fall into its teeth;
which will at any time fupport the weight, and
keep it from defcending, if the perſon who turns
the handle ſhould, through inadvertency or care-
leffneſs, quit his hold whilſt the weight is raifing.
And by this means, the danger is prevented which
might otherwiſe happen by the running down
of the weight when left at liberty.
3. The third mechanical power or engine con- The pul
fifts either of one moveable pully, or a system of ley.
pulleys; fome in a block or cafe which is fixed,
and others in a block which is moveable, and
rifes with the weight. For though a ſingle
pulley that only turns on its axis, and moves not
out of its place, may ferve to change the di-
rection of the power, yet it can give no mecha-
nical advantage thereto; but is only as the beam
of a balance, whofe arms are of equal length and
weight. Thus, if the equal weights Wand P Fig. 6.
hang by the cord B B upon the pulley A, whoſe
frame b is fixed to the beam H 1, they will coun-
terpoife each other, juft in the fame manner as
if the cord were cut in the middle, and its two
E 4
ends
}
58
Of the mechanical Powers.
ends hung upon the hooks fixt in the pulley at
A and A, equally diſtant from its center.
But if a weight W hangs at the lower end of
the moveable block p of the pulley D, and the
cord G F goes under that pulley, it is plain that
the half G of the cord bears one half of the
weight W, and the half F the other; for they
bear the whole between them. Therefore,
whatever holds the upper end of either rope,
fuftains one half of the weight: and if the cord
at F be drawn up fo as to raife the pulley D to C,
the cord will then be extended to its whole
length, all but that part which goes under the
pulley and confequently, the power that draws
the cord will have moved twice as far as the
pulley D with its weight W rifes; on which
account, a power whofe intenſity is equal to one
half of the weight will be able to fupport it,
becauſe if the power moves (by means of a finall
addition) its velocity will be double the velocity
of the weight, as may be feen by putting the
cord over the fixt pulley C (which only changes
the direction of the power, without giving any
advantage to it) and hanging on the weight P,
which is equal only to one half the weight W ;
in which cafe there will be an equilibrium, and a
little addition to P will cauſe it to defcend, and
raiſe W through a ſpace equal to one half of that
through which P defcends.-Hence, the advan-
tage gained will be always equal to twice the
number of pulleys in the moveable or undermoft
block. So that, when the upper or fixt block
и contains two pulleys, which only turn on their
axes, and the lower or moveable block U con-
tains two pulleys, which not only turn upon their
axes, but alſo rife with the block and weight;
the advantage gained by this is as 4 to the
5
working
PLATE VI.
F
E
Fig.1.
C
Fig. 2.
C
Fig. 3.
D
E
C
B
Fig. 12.
Figao.
D d
B
E
d
D
Fig. 14.
197
A
B
a
Fig.9.
F
G
I
Fig. 4.
A
B
F
H
C
D
Fig. 5.
H
Fig. 8.
Fig. 6.
K
E
B
Fig. 13.
F
A
k
I
a
10
---་
48 E
J. Ferguson delin.
F
H
R
B
I
G
M
Fig.7
I
G
B
B
a
A
H
Fig. f.
N
10
W
T
S
J. Mynde fc.
Of the mechanical Powers.
59
working power. Thus, if one end of the rope
KM02 be fixed to a hook at I, and the rope
paffes over the pulleys N and R, and under the
pulleys L and P, and has a weight T, of one
pound, hung to its other end at T, this weight
will balance and fupport a weight W of four
pounds hanging by a hook at the moveable
block U, allowing the faid block as a part of the
weight. And if as much more power be added,
as is fufficient to overcome the friction of the
pulleys, the power will defcend with four times
as much velocity as the weight rifes, and confe-
quently through four times as much ſpace.
The two pulleys in the fixed block X, and
the two in the moveable block 2, are in the
fame cafe with thoſe laſt mentioned; and thofe
in the lower block give the fame advantage to
the power.
As a fyftem of pulleys has no great weight,
and lies in a ſmall compafs, it is eafily carried
about; and can be applied, in a great many
cafes, for raifing weights, where other engines
cannot. But they have a great deal of friction
on three accounts : 1. Becauſe the diameters of
their axes bear a very confiderable proportion to
their own diameters; 2. Becaufe in working
they are apt to rub against one another, or againſt
the fides of the block; 3. Becauſe of the ſtiffneſs
of the rope that goes over and under them.
4. The fourth mechanical power is the in- The in
clined plane and the advantage gained by it is clined
plane.
as great as its length exceeds its perpendicular?
height. Let A B be a plane parallel to the hori- Plat. VI.
zon, and C D a plane inclined to it; and ſuppoſe Fig. 1.
the whole length CD to be three times as great
as the perpendicular height G f F: in this cafe,
the cylinder E will be fupported upon the plane
C D,
60
Of the mechanical Powers.
Fig. 2.
Fig. 3.
Fig. 4.
CD, and kept from rolling down upon it, by
a power equal to a third part of the weight of
the cylinder. Therefore, a weight may be rolled
up this inclined plane with a third part of the
power which would be fufficient to draw it up by
the fide of an upright wall. If the plane was
four times as long as high, a fourth part of the
power would be fufficient; and fo on, in pro-
portion. Or, if a weight was to be raiſed from a
floor to the height G F, by means of the machine
ABCD, (which would then act as a half wedge,
where the reſiſtance gives way only on one fide)
the machine and weight would be in equilibrio when
the power applied at G F was to the weight to
be raiſed, as GF to GB; and if the power be
increaſed, fo as to overcome the friction of the
machine againſt the floor and weight, the machine.
will be driven, and the weight raiſed: and when
the machine has moved its whole length upon
the floor, the weight will be raiſed to the whole
height from G to F.
The force wherewith a rolling body defcends
upon an inclined plane, is to the force of its ab-
folute gravity, by which it would defcend per-
pendicularly in a free fpace, as the height of
the plane is to its length. For, fuppofe the plane
A B to be parallel to the horizon, the cylinder C
will keep at reſt upon any part of the plane
where it is laid. If the plane be fo elevated,
that its perpendicular height D is equal to half
its length A B, the cylinder will roll down upon
the plane with a force equal to half its weight;
for it would require a power (acting in the di-
rection of A B) equal to half its weight, to keep
it from rolling. If the plane AB be elevated,
fo as to be perpendicular to the horizon, the cy-
linder C will defcend with its whole force of
gravity,
وعا
Of the mechanical Powers.
61
gravity, becauſe the plane contributes nothing
to its fupport or hindrance; and therefore, it
would require a power equal to its whole weight
to keep it from deſcending.
Let the cylinder C be made to turn upon Fig. 5.
flender pivots in the frame D, in which there is
a hook e, with a line G tied to it: let this line go
over the fixed pulley H, and have its other end
tied to the hook in the weight I. If the weight
of the body 1, be to the weight of the cylinder
C, added to that of its frame D, as the perpen-
dicular height of the plane L M is to its length
AB, the weight will juſt fupport the cylinder
upon the plane, and a fmall touch of a finger
will either cauſe it to afcend or defcend with
equal eafe: then, if a little addition be made to
the weight I, it will defcend, and draw the cylin-
der up the plane. In the time that the cylinder
moves from A to B, it will rife through the
whole height of the plane ML; and the weight
will defcend from H to K, through a ſpace equal
to the whole length of the plane AB.
If the machine be made to move upon rollers
or friction-wheels, and the cylinder be ſupported
upon the plane CB by a line G parallel to the
plane, a power fomewhat lefs than that which
drew the cylinder up the plane will draw the
plane under the cylinder, provided the pivots of
the axes of the friction wheels be fmall, and the
wheels themſelves be pretty large. For, let the
machine A B C (equal in length and height to
ABM, Fig. 5.) move upon four wheels,
two whereof appear at D and E, and the third
under C, whilt the fourth is hid from fight by
the horizontal board a. Let the cylinder F be
laid upon the lower end of the inclined plane
C B, and the line G be extended from the frame
of the cylinder, about fix feet parallel to the
plane
$
I
Fig. 6.
62
Of the mechanical Powers.
The
avedge.
plane C B; and, in that direction, fixed to a hook
in the wall; which will fupport the cylinder, and
keep it from rolling off the plane. Let one end
of the line H be tied to a hook at C in the ma-
chine, and the other end to a weight K, fome-
what lefs than that which drew the cylinder up
the plane before. If this line be put over the
fixed pulley I, the weight K will draw the ma-
chine along the horizontal plane L, and under
the cylinder F: and when the machine has been
drawn a little more than the whole length CA,
the cylinder will be raiſed to d, equal to the per-
pendicular height A B above the horizontal part
at A. The reaſon why the machine muſt be
drawn further than the whole length C A is, be-
cauſe the weight F rifes perpendicular to C B.
To the inclined plane may be reduced all
hatchets, chiſels, and other edge-tools which
are chamfered only on one fide.
5. The fifth mechanical power or machine is
the wedge, which may be confidered as two
equally inclined planes D E F and C E F, joined
Fig. 8. together at their baſes e E FO: then DC is the
whole thickneſs of the wedge at its back ABCD,
where the power is applied: E F is the depth or
heighth of the wedge: D F the length of one of
its fides, equal to CF the length of the other
fide; and O F is its fharp edge, which is entered
into the wood intended to be fplit by the force
of a hammer or mallet ftriking perpendicularly
on its back. Thus, ABb is a wedge driven
Fig. 9. into the cleft C D E of the wood FG.
When the wood does not cleave at any dif
tance before the wedge, there will be an equi-
librium between the power impelling the wedge
downward, and the refiftance of the wood act-
ing againſt the two fides of the wedge when the
power is to the reſiſtance, as half the thickneſs.
of
Of the mechanical Powers.
63
per-
of the wedge at its back is to the length of either
of its fides; becauſe the refiftance then acts
pendicular to the fides of the wedge. But, when
the reſiſtance on each fide acts parallel to the
back, the power that balances the refiftances on
both fides will be as the length of the whole
back of the wedge is to double its perpendicu-
lar height.
When the wood cleaves at any diſtance before
the wedge (as it generally does) the power im-
pelling the wedge will not be to the refiftance of
the wood, as the length of the back of the wedge
is to the length of both its fides; but as half
the length of the back is to the length of either
fide of the cleft, eſtimated from the top or acting
part of the wedge. For, if we fuppofe the wedge
to be lengthened down from b to the bottom of
the cleft at E, the fame proportion will hold;
namely, that the power will be to the refiftance,
as half the length of the back of the wedge is to
the length of either of its fides: or, which
amounts to the ſame thing, as the whole length
of the back is to the length of both the fides.
In order to prove what is here advanced con-
cerning the wedge, let us fuppofe the wedge to
be divided lengthwife into two equal parts; and
then it will become two equal inclined planes;
one of which, as a be, may be made uſe of as a Fig. 7:
half wedge for feparating the moulding c d from
the wainſcot AB. It is evident, that when this
half wedge has been driven its whole length a c
between the wainſcot and moulding, its fide a c
will be at ed; and the moulding will be fepa-
rated to ƒg from the wainſcot. Now, from what
has been already proved of the inclined plane, it
appears, that to have an equilibrium between the
power impelling the half wedge, and the refift-
ance of the moulding, the former muſt be to the
latter,
64
Of the mechanical Powers:
letter, as a b to a c; that is, as the thickneſs of the
back which receives the ftroke is to the length
of the fide against which the moulding acts.
Therefore, fince the power upon the half wedge
is to the reſiſtance against its fide, as the half
back a b is to the whole fide a c, it is plain, that
the power upon which the whole wedge (where
the whole back is double the half back) muſt be
to the reſiſtance againſt both its fides, as the
thickneſs of the whole back is to the length of
both the fides; fuppofing the wedge at the bot-
tom of the cleft: or as the thicknefs of the whole
back to the length of both fides of the cleft,
when the wood ſplits at any diſtance before the
wedge. For, when the wedge is driven quite
into the wood, and the wood ſplits at ever fo
ſmall a diſtance before its edge, the top of the
wedge then becomes the acting part, becauſe the
wood does not touch it any where elfe. And
fince the bottom of the cleft muſt be confidered
as that part where the whole ftickage or reſiſtance
is accumulated, it is plain, from the nature of
the lever, that the farther the power acts from
the reſiſtance, the greater is the advantage.
Some writers have advanced, that the power
of the wedge is to the refiftance to be overcome,
as the thickneſs of the back of the wedge is to
the length only of one of its fides; which feems
very ftrange: for, if we fuppofe A B to be a
Fig. 10. ftrong inflexible bar of wood or iron fixt into the
ground at C B, and D and E to be two blocks of
marble lying on the ground on oppofite fides of
the bar; it is evident that the block D may be
ſeparated from the bar to the diſtance d, equal to
a b, by driving the inclined plane or half wedge
a bo down between them; and the block E may
be ſeparated to an equal diſtance on the other
fide, in like manner, by the half wedge c d o.
But
Of the mechanical Powers.
65
But the power impelling each half wedge will be
to the refiftance of the block against its fide, as
the thickness of that half wedge is to its perpen-
dicular height, becauſe the block will be driven
off perpendicular to the fide of the bar A B.
Therefore the power to drive both the half
wedges is to both the reſiſtances, as both the
half backs is to the perpendicular height of each
half wedge. And if the bar be taken away, the
blocks put clofe together, and the two half
wedges joined to make one; it will require as
much force to drive it down between the blocks,
as is equal to the fum of the ſeparate powers
acting upon the half wedges when the bar was
between them.
To confirm this by an experiment, let two Fig. 11,
cylinders, as AB and CD, be drawn towards one
another by lines running over fixed pulleys, and
a weight of 40 ounces hanging at the lines be-
longing to each cylinder: and let a wedge of
40 ounces weight, having its back juſt as thick as
either of its fides is long, be put between the
cylinders, which will then act against each fide
with a reſiſtance equal to 40 ounces, whilft its
own weight endeavours to bring it down and
ſeparate them. And here, the power of the
wedge's gravity impelling it downward, will be
to the refiftance of both the cylinders againſt the
wedge, as the thickneſs of the wedge is to double
its perpendicular height; for there will then be
an equilibrium between the weight of the wedge
and the reſiſtance of the cylinders againſt it, and
it will remain at any height between them; re-
quiring just as much power to puſh it upward
as to pull it downward.-If another wedge of
equal weight and depth with this, and only half
as thick, be put between the cylinders, it will
require twice as much weight to be hung at the
ends
66
Of the mechanical Powers.
+
Fig. 11.
ends of the lines which draw them together, tơ
keep the wedge from going down between them.
That is, a wedge of 40 ounces, whofe back is
only equal to half its perpendicular height, will
require 80 ounces to each cylinder, to keep it in
an equilibrium between them: and twice 80 is
160, equal to four times 40. So that the power
will be always to the refiftance, as the thickneſs
of the back of the wedge is to twice its perpen-
dicular height, when the cylinders move off in
a line at right angles to that perpendicular.
The best way, though perhaps not the neatest,
that I know of, for making a wedge with its
appurtenances for fuch experiments, is as fol-
lows. Let KILM and LMNO be two flat
pieces of wood, each about fifteen inches long
and three or four in breadth, joined together by
a hinge at L M; and let P be a graduated arch
of brafs, on which the faid pieces of wood may
be opened to any angle not more than 60 degrees,
and then fixt at the given angle by means of
the two ſcrews a and b. Then, IK NO will
repreſent the back of the wedge, L M its fharp
edge which enters the wood, and the outfides of
the pieces KILM and LMNO the two fides of
the wedge againſt which the wood acts in cleav-
ing. By means of the ſaid arch, the wedge may
be opened fo, as to adjuſt the thickness of its
back in any proportion to the length of either of
its fides, but not to exceed that length: and any
weight as p may be hung to the wedge upon the
hook M, which weight, together with the weight
of the wedge itſelf, may be confidered as the
impelling power; which is all the fame in the ex-
periment, whether it be laid upon the back of
the wedge, to puſh it down, or hung to its edge to
pull it down. Let AB and CD be two wooden
cylinders, each about two inches thick, where
they
Of the mechanical Powers.
67
}
they touch the outfides of the wedge; and let
their ends be made like two round flat plates, to
keep the wedge from flipping off edgewife from
between them. Let a fmall cord with a loop on
one end of it, go over a pivot in the end of each
cylinder, and the cords S and T belonging to the
cylinder AB goover the fixt pulleys W and X, and
be faftened at their other ends to the bar wx, on
which any weight as Z may be hung at pleaſure.
In like manner, let the cords and R belonging
to the cylinder CD go over the fixt pulleys Vand U
to the bar vu, on which a weight equal to Z may
be hung. Theſe weights, by drawing the cylin-
ders towards one another, may be confidered as
the reſiſtance of the wood acting equally againſt
oppoſite fides of the wedge; the cylinders them-
felves being fufpended near, and parallel to each
other, by their pivots in loops on the lines
E,F,G,H; which lines may be fixed to hooks in
the ceiling of the room. The longer thefe lines
are, the better; and they ſhould never be leſs than
four feet each. The farther alfo the pulleys
VU and X,W are from the cylinders, the truer
will the experiments be: and they may turn
upon pins fixed into the wall.
7
In this machine, the weights and Z, and the
weight p, may be varied at pleaſure, ſo as to be
adjuſted in proportion of double the wedge's per-
pendicular height to the thicknefs of its back:
and when they are fo adjufted, the wedge will be
in equilibrio with the refiftance of the cylinders.
The wedge is a very great mechanical power,
fince not only wood but even rocks can be ſplit
by it; which would be impoffible to effect by the
lever, wheel and axle, or pulley for the force
of the blow, or ftroke, ſhakes the cohering parts,
and thereby makes them ſeparate the more eaſily,
6. The
F
68
Of the mechanical Powers.
J
The
Screw.
13.
6. The fixth and laft mechanical power is the
Screw; which cannot properly be called a fimple
machine, becauſe it is never ufed without the
application of a lever or winch to affift in turn-
ing it and then it becomes a compound engine
of a very great force either in preffing the parts
of bodies cloſer together, or in raifing great
weights. It may be conceived to be made by
Fig. 12, cutting a piece of paper ABC (Fig. 12.) into
the form of an inclined plane or half wedge, and
then wrapping it round a cylinder AB (Fig. 13).
And here it is evident, that the winch E
muft turn the cylinder once round before the
weight of reſiſtance D can be moved from one
ſpiral winding to another, as from d to c: there-
fore, as much as the circumference of a circle
deſcribed by the handle of the winch is greater
than the interval or diſtance between the ſpirals, fo
much is the force of the fcrew. Thus, fuppofing
the diſtance between the ſpirals to be half an inch,
and the length of the winch to be twelve inches;
the circle deſcribed by the handle of the winch
where the power acts will be 76 inches nearly, or
about 152 half inches, and confequently 152 times
as great as the distance between the fpirals: and
therefore a power at the handle, whofe intenfity
is equal to no more than a fingle pound, will ba-
lance 152 pounds acting againſt the ſcrew; and
as much additional force, as is fufficient to over-
come the friction, will raiſe the 152 pounds; and
the velocity of the power will be to the velocity
of the weight, as 152 to 1.
Hence it appears,
that the longer the winch is, and the nearer
the fpirals are to one another, fo much the
greater is the force of the fcrew.
A machine for ſhewing the force or power of
the ſcrew may be contrived in the following
manner
PLATE VII.
Fig.3.
a
b
#
LI
K
G
k
Fig. 2.
A
I. Ferguson delin.
B
Fig. 4.
L
M
m
A
Fig.i.
共
​A
DAAGLOMNAJUKA
JMBIUMBAUMITRAR
H
A
A
D
a
E
B
WG
་་་་
K
་་་
W
2400
་་་་་་
ཟ་ ་
ས་
མ་་བབས-
J.Mynde foulp.
Of the mechanical Powers.
69
manner. Let the wheel C have a fcrew a b on Fig. 14.
its axis, working in the teeth of the wheel D,
which ſuppoſe to be 48 in number. It is plain,
that for every time the wheel C and fcrew a b are
turned round by the winch A, the wheel D will
be moved one tooth by the fcrew; and there-
fore, in 48 revolutions of the winch, the wheel
D will be turned once round. Then, if the cir-
cumference of a circle defcribed by the handle of
the winch A be equal to the circumference of a
groove e round the wheel D, the velocity of the
handle will be 48 times as great as the velocity
of any given point in the groove. Confequently,
if a line G (above number 48) goes round the
groove e, and has a weight of 48 pounds hung
to it below the pedeſtal E F, a power equal to
one pound at the handle will balance and fupport
the weight.-To prove this by experiment, let
the circumferences of the grooves of the wheels
C and D be equal to one another; and then if
a weight H of one pound be fufpended by a line.
going round the groove of the wheel C, it will
balance a weight of 48 pounds hanging by the
line G; and a fmall addition to the weight H
will caufe it to defcend, and fo raiſe up the other
weight.
If the line G, inftead of going round the
groove e of the wheel D, goes round its axle I;
the power of the machine will be as much in-
creaſed, as the circumference of the groove e
exceeds the circumference of the axle: which,
fuppofing it to be fix times, then one pound at
H will balance 6 times 48, or 288 pounds hung
to the line on the axle: and hence the power or
advantage of this machine will be as 288 to 1.
That is to fay, a man, who by his natural
ftrength could lift an hundred weight, will be
F 2
able
70
Of the mechanical Powers.
all the
mecha-
nical
able to raiſe 288 hundred, or 142% ton weight
by this engine.
But the following engine is ftill more power-
ful, on account of its having the addition of
four pulleys and in it we may look upon all
the mechanical powers as combined together,
Plate VII, even if we take in the balance. For, as the axis
Fig. 1.
D of the bar AB is in its middle at C, it is plain
that if equal weights are fufpended upon any two
A combi- pins equi-diftant from the axis C, they will coun-
nation of terpoife each other.-It becomes a lever by
hanging a ſmall weight P upon the pin n, and a
weight as much heavier upon either of the pins
b, c, d, e, or f, as is in proportion to the pins be-
ing ſo much nearer the axis. The wheel and
axle FG is evident; fo is the ſcrew E which
takes in the inclined plane, and with it the half
wedge. Part of a cord goes round the axle, the
reft under the lower pulleys K, m, over the upper
pulleys L, n, and then it is tied to a hook at m
in the lower or moveable block, on which the
weight W hangs.
powers.
In this machine, if the wheel F has 30 teeth,
it will be turned once round in thirty revo-
lutions of the bar AB, which is fixt on the
axis D of the ſcrew E: if the length of the bar
is equal to twice the diameter of the wheel, the
pins a and at the ends of the bar will move 60
times as faft as the teeth of the wheel do: and
confequently, one ounce at P will balance 60
ounces hung upon a tooth at q in the horizontal
diameter of the wheel. Then, if the diameter of
the wheel F is ten times as great as the diameter
of the axle G, the wheel will have 10 times the
velocity of the axle; and therefore one ounce P
at the end of the lever AC will balance 10 times
60 or 600 ounces hung to the rope H which goes
round
Of Water-Mills.
71
round the axle. Laftly, if four pulleys be added,
they will make the velocity of the lower block
K, and weight W, four times less than the velo-
city of the axle and this being the laſt power
in the machine, which is four times as great as
that gained by the axle, it makes the whole
power of the machine 4 times 600, or 2400.
So that a man who could lift one hundred weight
in his arms by his natural ftrength, would be
able to raiſe 2400 times as much by this en-
gine. But it is here as in all other mechanical
caſes; for the time loft is always as much as the
power gained, becauſe the velocity with which
the power moves will ever exceed the velocity
with which the weight rifes, as much as the in-
tenfity of the weight exceeds the intenfity of the
power.
The friction of the ſcrew itſelf is very confi-
derable; and there are few compound en-
gines, but what, upon account of the friction of
the parts againſt one another, will require a third
part more of power to work them when loaded,
than what is fufficient to conftitute a balance
between the weight and the power.
LECT. IV.
Of mills, cranes, wheel-carriages, and the engine
for driving piles.
A
S theſe engines are fo univerfally uſeful,
it would be needleſs to make any apo-
logy for defcribing them.
In a common breast mill, where the fall of Plate VII.
water may be about ten feet, AA is the great Fig. 2.
wheel, which is generally about 17 or 18 feet ih
F 3
A com-
diameter, mon mill.
7.2
Of Water-Mills.
diameter, reckoned from the outermoft edge of
any float board at a to that of its oppofite float at
b. To this wheel the water is conveyed through
a channel, and by falling upon the wheel, turns
it round.
On the axis B B of this wheel, and within the
mill houſe, is a wheel D, about 8 or 9 feet dia-
meter, having 61 cogs, which turn a trundle E
containing ten upright ftaves or rounds; and
when theſe are the number of cogs and rounds,
the trundle will make 6% revolutions for one
revolution of the wheel.
The trundle is fixt upon a ftrong iron axis
called the ſpindle, the lower end of which turns in
a brafs foot, fixt at F, in the horizontal beam ST
called the bridge-tree; and the upper part of the
fpindle turns in a wooden bufh fixt into the nether
millſtone which lies upon beams in the floor Fr.
The top part of the fpindle above the bufh is
fquare, and goes into a ſquare hole in a ſtrong iron
crofs a b c d, (fee Fig. 3.) called the rynd; under
which, and cloſe to the buſh, is a round piece of
thick leather upon the fpindle, which it turns
round at the fame time as it does the rynd.
The rynd is let into grooves in the under fur-
face of the running millſtone G (Fig. 2.) and ſo
turns it round in the fame time that the trundle E
is turned round by the cog-wheel D. This mill-
ftone has a large hole quite through its middle,
called the eye of the ftone, through which the
middle part of the rynd and upper end of the
ſpindle may be ſeen; whilft the four ends of the
rynd lie hid below the ftone in their grooves.
The end T of the bridge-tree TS (which fup-
ports the upper millstone G upon the fpindle) is
fixed into a hole in the wall; and the end S is let
into a beam QR called the brayer, whofe end R
remains
+
Of Water-Mills.
79
remains fixt in a mortife: and its other end Q
hangs by a ſtrong iron rod P which goes through
the floor rr, and has a ſcrew-nut on its top at
O; by the turning of which nut, the end of
the brayer is raiſed or depreffed at pleaſure; and
confequently the bridge-tree TS and upper mill-
ftone. By this means, the upper millstone may
be fet as cloſe to the under one, or raiſed as high
from it, as the miller pleafes, The nearer the
millſtones are to one another, the finer they grind
the corn, and the more remote from one another,
the coarfer.
The upper millstone G is incloſed in a round
box H, which does not touch it any where; and
is about an inch diftant from its edge all around.
On the top of this box ftands a frame for hold-
ing the hopper kk, to which is hung the fhoe I
by two lines faſtened to the hind-part of it, fixed
upon hooks in the hopper, and by one end of
the crook-ftring K faftened to the fore-part of it
at i; the other end being twiſted round the pin L.
As the pin is turned one way, the ſtring draws
up the fhoe clofer to the hopper, and fo leffens
the aperture between them; and as the pin is
turned the other way, it lets down the fhoe, and
enlarges the aperture.
If the fhoe be drawn up quite to the hopper,
no corn can fall from the hopper into the mill;
if it be let a little down, fome will fall: and the
quantity will be more or lefs, according as the
fhoe is more or leſs let down. For the hopper is
open at bottom, and there is a hole in the bottom
of the fhoe, not directly under the bottom of the
hopper, but forwarder towards the end i, over
the middle of the eye of the millstone.
There is a fquare hole in the top of the fpindle, Fig. 3.
in which is put the feedere: this feeder (as the
F 4
ſpindle
74
Of Water-Mills.
fpindle turns round) jogs the fhce three times in
each revolution, and fo caufes the corn to run
conftantly down from the hopper through the fhoe,
into the eye of the millftone, where it falls upon
the top of the rynd, and is, by the motion of the
rynd, and the leather under it, thrown below the
upper tone, and ground between it and the
lower one. The violent motion of the ſtone
creates a centrifugal force in the corn going
round with it, by which means it gets farther and
farther from the center, as in a fpiral, in every
revolution, until it be thrown quite out; and,
being then ground, it falls through a ſpout M,
called the mill-eye, into the trough N.
When the mill is fed too faft, the corn bears
up the ſtone, and is ground too coarſe; and be-
fides, it clogs the mill fo as to make it go too
flow. When the mill is too flowly fed, it goes
too faft, and the ftones by their attrition are apt
to ſtrike fire againſt one another. Both which
inconveniences are avoided by turning the pin L
backwards or forwards, which draws up or lets
down the fhoe; and fo regulates the feeding as
the miller fees convenient.
The heavier the running millstone is, and the
greater the quantity of water that falls upon the
wheel, ſo much the fafter will the mill bear to be
fed; and confequently fo much the more it will
grind. And on the contrary, the lighter the
ftone, and the lefs the quantity of water, fo much
flower muſt the feeding be. But when the ſtone
is confiderably wore, and become light, the mill
must be fed flowly at any rate; otherwife the
ftone will be too much born up by the corn
under it, which will make the meal coarſe.
The quantity of power required to turn a
heavy milftone is but very little more than what
IS
Of Water-Mills.
75
is fufficient to turn a light one: for as it is fup-
ported upon the fpindle by the bridge-tree ST,
and the end of the fpindle that turns in the braſs
foot therein being but ſmall, the odds arifing
from the weight is but very inconfiderable in its
action againſt the power or force of the water.
And beſides, a heavy ftone has the fame advan-
tage as a heavy fly; namely, that it regulates
the motion much better than a light one.
In order to cut and grind the corn, both the
upper and under millftones have channels or
furrows cut into them, proceeding obliquely from
the center towards the circumference. And theſe
furrows are cut perpendicularly on one fide and
obliquely on the other into the ftone, which
gives each furrow a fharp edge, and in the two
ftones they come, as it were, against one ano-
ther like the edges of a pair of fciffars and fo
cut the corn, to make it grind the eaſier when it
falls upon the places between the furrows.
Theſe are cut the fame way in both ftones when
they lie upon their backs, which makes them run
croſs ways to each other when the upper ftone is
inverted by turning its furrowed furface towards
that of the lower. For, if the furrows of both
ftones lay the fame way, a great deal of the corn
would be driven onward in the lower furrows,
and fo come out from between the ftones with-
out being either cut or bruifed.
When the furrows become blunt and fhallow
by wearing, the running ftone muſt be taken
up, and both ftones new dreft with a chifel and
hammer. And every time the ftone is taken up,
there muſt be ſome tallow put round the ſpindle
upon the buſh, which will foon be melted by
the heat the fpindle acquires from its turning
and rubbing against the bufh, and fo will get in
betwixt
76
Of Water-Mills.
betwixt them
otherwife the bufh would take
fire in a very little time.
The buſh muſt embrace the ſpindle quite
clofe, to prevent any ſhake in the motion, which
would make fome parts of the ftones grate and
fire against each other; whilft other parts of
them would be too far aſunder, and by that
means fpoil the meal in grinding.
1
Whenever the ſpindle wears the buſh fo as to
begin to ſhake in it, the ſtone muſt be taken up,
and a chiſel drove into ſeveral parts of the buſh;
and when it is taken out, wooden wedges muſt be
driven into the holes; by which means the bush.
will be made to embrace the fpindle clofe all
around it again. In doing this, great care muft
be taken to drive equal wedges into the bush on
oppofite fides of the fpindle; otherwiſe it will
be thrown out of the perpendicular, and fo hin-
der the upper ftone from being fet parallel to the
under one, which is abfolutely neceffary for mak-
ing good work. When any accident of this
kind happens, the perpendicular pofition of the
ſpindle muſt be reſtored by adjuſting the bridge-
tree ST by proper wedges put between it and
the brayer QR.
It often happens, that the rynd is a little.
wrenched in laying down the upper ftone upon
it; or is made to fink a little lower upon one
fide of the ſpindle than on the other; and this
will caufe one edge of the upper ftone to drag
all around upon the other, whilft the oppofite
edge will not touch. But this is eafily fet to
rights, by raiſing the ftone a little with a lever,
and putting bits of paper, cards or thin chips,
between the rynd and the ſtone.
The diameter of the upper ftone is generally
about fix feet, the lower ftone about an inch
more:
Of Water-Mills.
77
2
more: and the upper ftone when new contains
about 22 cubc feet, which weighs fomewhat
more than 19000 pounds. A ſtone of this dia-
meter ought never to go more than 60 times
round in a minute; for if it turns fafter, it will
heat the meal.
The grinding furface of the under ſtone is a
little convex from the edge to the center, and..
that of the upper ftone a little more concave: fo
that they are fartheft from one another in the
middle, and come gradually nearer towards the
edges. By this means, the corn at its firft en-
trance between the ſtones is only bruiſed; but as
it goes farther on towards the circumference or
edge, it is cut ſmaller and ſmaller; and at laſt
finely ground juft before it comes out from be-
tween them.
The water wheel muſt not be too large, for
if it be, its motion will be too flow; nor too
little, for then it will want power. And for a
mill to be in perfection, the floats of the wheel
ought to move with a third part of the velocity
of the water, and the ftone to turn round once in
a fecond of time.
In order to conſtruct a mill in this perfect
manner, obferve the following rules:
1. Meaſure the perpendicular height of the
fall of water, in feet, above that part of the
wheel on which the water begins to act; and
call that, the height of the fall.
2. Multiply this conftant number 64.2882 by
the height of the fall in feet, and the fquare root
of the product fhall be the velocity of the water
at the bottom of the fall, or the number of feet
that the water there moves per fecond.
3. Divide the velocity of the water by 3, and
the quotient fhall be the velocity of the float-
boards of the wheel; or the number of feet they
I
muſt
}
78
Of Water-Mills.
muft each go through in a fecond, when the
water acts upon them fo, as to have the greateſt
power to turn the mill.
4. Divide the circumference of the wheel in
feet by the velocity of its floats in feet per fe-
cond, and the quotient fhall be the number of
feconds in which the wheel turns round.
5. By this laft number of feconds divide 60;
and the quotient fhall be the number of turns
of the wheel in a minute.
6. Divide 60 (the number of revolutions the
millstone ought to have in a minute) by the num-
ber of turns of the wheel in a minute, and the
quotient fhall be the number of turns the mill-
ftone ought to have for one turn of the wheel.
7. Then, as the number of turns of the wheel
in a minute is to the number of turns of the
millſtone in a minute, fo muft the number of
ftaves in the trundle be to the number of cogs
in the wheel, in the neareſt whole numbers that
can be found.
By theſe rules I have calculated the following
table to a water wheel 18 feet diameter, which
I apprehend may be a good fize in general.
To conftruct a mill by this table, find the
height of the fall of water in the firſt column, and
againſt that height, in the fixth column, you have
the number of cogs in the wheel, and ftaves in the
trundle, for caufing the millstone to make about
60 revolutions in a minute, as near as poſſible,
when the wheel goes with a third part of the ve
locity of the water. And it appears by the 7th
column, that the number of cogs in the wheel, and
ftaves in the trundle, are ſo near the truth for the
required purpoſe, that the leaft number of revo-
lutions of the millstone in a minute is between 59
and 60, and the greaeft number never amounts
to 61:
The
Of Water-Mills.
79
The MILL-WRIGHT's TABLE.
Rev. of
Velo-
the
water
cond.
Height of the fall of
water.
100 parts
of a
Feet.
foot.
Feet.
of a foot.
100 parts
Feet.
1
Revolu-
Velo- Revolutions of
Cogs in
the
the
city of city oftions of the
wheel
the
wheel wheel
the mill-
mill-
stoneper
and
min. by
ftone
ſtaves in
thefe
per fe- per fe-
per
for one
the
ſtaves
cond.
minute.
of the
trundle.
and
wheel.
cogs.
Rev.
Rev.
of a Rev.
100 parts
Staves.
Cogs'
Rev.
of a Rev.
100 parts
of a Rev.
100 parts
1
I
8.02 2.67 2.8321.20 127
6
59.92
2 11.34 3.78 4.00 15.00 105 760.00
3 13.89 4.63 4.9112.22 98 8 60.14
4 16.04 5.35 5.67 10.58 95 959.87
5 17.93 5.98 6.34 9.46 85 9 59.84
6 19.64 6.55 6.94 8.64 78 960.10
7 21.21 7.07 7.50 8.00 72 960.00
8 22.68 7.56 8.02 7.48 67 9 59.67
9 24.05 8.02 8.51 7.05 70 10 59.57
10 25.35 8.45 8.97 6.69 67 10 60.09
I I
11 26.59 8.86 9.40 6.38 64 1060.16
12 27.77 9.26 9.82
13 28.91 9.64 10.22
14 30.00 10.00 10.60
15 31.05 10.35 10.99
16 32.07 10.69 11.34
17 33.06 11.02 11.70
18
34.02 11.34 12.02
19 34.95 11.65 12.37
11.65|12.37
6.11 61 10 59.90
5.87 59 10 60.18
5.66 56 10 59.36
5.46 55 10 60.48
5.29 53 10 60.10
5.13 51 10 59.67
4.99 50 10 60.10
4.85 49 10 60.61
20 35.86 11.95 12.68 4.73 47 10 59.59
35.8611.95
I
2
3
4
5
6
7
Such
80
Of Water-Mills.
2
Such a mill as this, with a fall of water about
1 feet, will require about 32 hogfheads every
minute to turn the wheel with a third part of the
velocity with which the water falls; and to
overcome the refiftance arising from the friction
of the geers and attrition of the ftones in grind-
ing the corn.
The greater fall the water has, the lefs quan-
tity of it will ſerve to turn the mill. The water
is kept up in the mill-dam, and let out by a
fluice called the penftock, when the mill is to go.
When the penſtock is drawn up by means of a
lever, it opens a paffage through which the water
flows to the wheel: and when the mill is to be
ftopt, the penſtock is let down, which ftops the
water from falling upon the wheel.
A lefs quantity of water will turn an overfhot-
mill (where the wheel has buckets inftead of
float-boards) than a breaft-mill where the fall of
the water ſeldom exceeds half the height Ab of
the wheel. So that, where there is but a ſmall
quantity of water, and a fall great enough for the
wheel to lie under it, the bucket (or overſhot)
wheel is always ufed. But where there is a large
body of water, with a little fall, the breaſt or float-
board wheel muft take place. Where the water
runs only upon a little declivity, it can act but
flowly upon the under part of the wheel at b; in
which cafe, the motion of the wheel will be very
flow and therefore, the floats ought to be very
long, though not high, that a large body of water
may act upon them; fo that what is wanting in
velocity may be made up in power: and then the
cog-wheel may have a greater number of cogs in
proportion to the rounds in the trundle, in order
to give the millstone a fufficient degree of velocity.
They who have read what is faid in the firft
lecture, concerning the acceleration of bodies
falling
Of Water-Mills.
81
falling freely by the power of gravity acting
conftantly and uniformly upon them, may per-
haps afk, Why fhould the motion of the wheel be-
equable, and not accelerated, ſeeing the water act's
conftantly and uniformly upon it? The plain
anfwer is, That the velocity of the wheel can
never be fo great as the velocity of the water
that turns it; for, if it fhould become fo great,
the power of the water would be quite loft upon
the wheel, and then there would he no proper
force to overcome the friction of the geers and
attrition of the ftones. Therefore, the velocity
with which the wheel begins to move, will in-
creaſe no longer than till its momentum or force
is balanced by the refiftance of the working
parts of the mill; and then the wheel will go
on with an equable motion.
[If the cog-wheel D be made about 18 inches A hand-
diameter, with 30 côgs, the trundle as fmall in mill.
proportion, with 10 ftaves, and the millftones be
each about two feet in diameter, and the whole
work be put into a ſtrong frame of wood, as re-
prefented in the figure, the engine will be a hand-
mill for grinding corn or malt in private fami-
lies. And then, it may be turned by a winch
inſtead of the wheel A A: the millftone making
three revolutions for every one of the winch.
If a heavy fly be put upon the axle B, near the
winch, it will help to regulate the motion.]
If the cogs of the wheel and rounds of the
trundle could be put in as exactly as the teeth
are cut in the wheels and pinions of a clock,
then the trundle might divide the wheel exactly:
that is to fay, the trundle might make a given
number of revolutions for one of the wheel,
without a fraction. But as any exact number is
not neceffary in mill-work, and the cogs and
rounds cannot be fet in fo truly as to make all
the
My!
82
Of Horfe-Mills and Wind-Mills.
Fig. 4.
A Horýc
mill.
A wind-
mill.
the intervals between them equal; a ſkilful
mill-wright will always give the wheel what he
calls a hunting cog; that is, one more than what
will answer to an exact divifion of the wheel by
the trundle. And then, as every cog comes to
the trundle, it will take the next ftaff or round
behind the one which it took in the former re-
volution and by that means, will wear all the
parts of the cogs and rounds which work upon
one another equally, and to equal diſtances from
one another in a little time; and fo make a true
uniform motion throughout the whole work.
Thus, in the above water-mill, the trundle has
10 ftaves, and the wheel 61 cogs.
Sometimes, where there is a fufficient quan-
tity of water, the cog-wheel A A turns a large
trundle B B, on whofe axis C is fixed the hori-
zontal wheel D, with cogs all around its edge,
turning two trundles E and F at the fame time;
whofe axes or ſpindles G and H turn two mill-
ftones I and K, upon the fixed ſtones L and M.
And when there is not work for them both,
either may be made to lie quiet, by taking out
one of the ftaves of its trundle, and turning the
vacant place towards the cog wheel D. And
there may be a wheel fixt on the upper end of
the great upright axle C for turning a couple of
boulting-mills; and other work for drawing
up the facks, fanning and cleaning the corn,
fharpening of tools, &c.
If, inſtead of the cog-wheel AA and trundle
B B, horizontal levers be fixed into the axle C,
below the wheel D; then, horfes may be put to
thefe levers for turning the mill: which is often
done where water cannot be had for that pur-
poſe.
The working parts of a wind-mill differ very
little from thoſe of a water-mill; only the former
is
Of Wind-Mills.
83
is turned by the action of the wind upon four
fails, every one of which ought (as is generally
believed) to make an angle of 543 degrees with
a plane perpendicular to the axis on which the
arms are fixt for carrying them. It being de-
monſtrable, that when the fails are ſet to ſuch an
angle, and the axis turned end-ways toward the
wind, the wind has the greateſt power upon the
fails, But this angle anſwers only to the cafe of
a vane or fail juft beginning to move*: for,
when the vane has a certain degree of motion, it
yields to the wind; and then that angle muſt be
increaſed to give the wind its full effect.
Again, the increaſe of this angle fhould be
different, according to the different velocities
from the axis to the extremity of the vane. At
the axis it ſhould be 543 degrees, and thence
continually decreaſe, giving the vane a twiſt, and
ſo cauſing all the ribs of the vane to lie in dif-
ferent planes.
Laſtly, Thefe ribs ought to decreaſe in length
from the axis to the extremity, giving the vane a
curvilineal form,; fo that no part of the force of
any one rib be ſpent upon the reft, but all move
on independent of each other. All this is re-
quired to give the fails of a wind-mill their true
form and we fee both the twift and the diminu-
tion of the ribs exemplified in the wings of birds.
It is almoſt incredible to think with what
velocity the tips of the fails move when acted
upon by a moderate gale of wind. I have fe-
veral times counted the number of revolutions
made by the fails in ten or fifteen minutes; and
from the length of the arms from tip to tip,
have computed, that if a hoop of that diameter
was to run upon the ground with the fame velo-
* See MACLAURIN'S Fluxions, near the end.
G
city
84
Of Cranes.
A crane.
city that it would move if put upon the fail-arms,
it would go upwards of 30 miles in an hour.
As the ends of the fails neareſt the axis can-
not move with the fame velocity that the tips or
fartheft ends do, although the wind acts equally
ftrong upon them; perhaps a better pofition
than that of ftretching them along the arms
directly from the center of motion, might be to
have them fet perpendicularly across the farther
ends of the arms, and there adjuſted lengthwife
to the proper angle. For, in that cafe, both
ends of the fails would move with the fame ve-
locity; and being farther from the center of mo-
tion, they would have fo much the more power:
and then, there would be no occafion for having
them fo large as they are generally made; which
would render them lighter, and confequently,
there would be fo much the lefs friction on the
thick neck of the axle where it turns in the wall.
Plate VII.
Fig. 1.
*
A crane is an engine by which great weights
are raiſed to certain heights, or let down to cer-
tain depths. It confifts of wheels, axles, pul-
leys, ropes, and a gib or gibbet. When the
rope H is hooked to the weight K, a man turns
the winch A, on the axis whereof is the trundle
B, which turns the wheel C, on whofe axis Dis
the trundle E, which turns the wheel F with its
upright axis G, on which the great rope HH
winds as the wheel turns; and going over a
pulley I at the end of the arm d of the gib cc de,
it draws up the heavy weight K; which, being
raiſed to a proper height, as from a ſhip to the
quay, is then brought over the quay by pulling
the wheel Z round by the handles z, z, which
turns the gib by means of the half wheel b fixt
on the gib poft cc, and the ftrong pinion a fixt
on the axis of the wheel Z. This wheel gives
the man that turns it an abfolute command over
the
3
Of Cranes.
85
the gib, fo as to prevent it from taking any un-
lucky fwing, fuch as often happens when it is
only guided by a rope tied to its arm d; and
people are frequently hurt, fometimes killed,
by fuch accidents.
The great rope goes between two upright
rollers i and k, which turn upon gudgeons in
the fixed beams ƒ and g; and as the gib is turn-
ed towards either fide, the rope bends upon the
roller next that fide. Were it not for theſe
rollers, the gib would be quite unmanageable;
for the moment it were turned ever fo little to-
wards any fide, the weight K would begin to
deſcend, becauſe the rope would be ſhortened
between the pulley I and axis G; and fo the gib
would be pulled violently to that fide, and either
be broke to pieces, or break every thing that
came in its way. Thefe rollers muſt be placed
fo, that the fides of them, round which the rope
bends, may keep the middle of the bended part
directly even with the center of the hole in
which the upper gudgeon of the gib turns in
the beam f. The truer thefe rollers are placed,
the eaſier the gib is managed, and the leſs apt to
fwing either way by the force of the weight K.
A ratchet-wheel 2 is fixt upon the axis D,
near the trundle E; and into this wheel the catch
or click R falls. This hinders the machinery
from runing back by the weight of the burden
K, if the man who raiſes it fhould happen to be
careleſs, and ſo leave off working at the winch
A ſooner than he ought to do.
When the weight K is raiſed to its proper
height from the thip, and brought over the
quay by turning the gib about, it is let down
gently upon the quay, or into a cart ftanding
thereon, in the following manner: A man takes
hold of the rope tt (which goes over the pulley
V, and
G 2
86
Of Cranes.
v, and is tied to a hook at S in the catch R) and
fo difengages the catch from the ratchet-wheel
2; and then, the man at the winch A turns it
backward, and lets down the weight K. But if
the weight pulls too hard againſt this man, ano-
ther lays hold of the ftick V, and by pulling
it downward, draws the gripe U cloſe to the
wheel Y, which, by rubbing hard againſt the
gripe, hinders the too quick defcent of the
weight; and not only fo, but even ſtops it at
any time, if required. By this means, heavy
goods may be either raiſed or let down at plea-
fure without any danger of hurting the men
who work the engine.
When part of the goods are craned up, and
the rope is to be let down for more, the catch R
is first difengaged from the ratchet-wheel 2, by
pulling the cord t; then the handle q is turned
half round backward, which, by the crank n n
in the piece o, pulls down the frame b between
the guides m and m (in which it flides in a
groove) and ſo difengages the trundle B from
the wheel C: and then, the heavy hook ẞ at
the end of the rope H defcends by its own
weight, and turns back the great wheel F with
its trundle E, and the wheel C; and this laſt
wheel acts like a fly againſt the wheel F and
hook ; and fo hinders it from going down too
quick; whilft the weight X keeps up the gripe
U from rubbing againft the wheel Y, by means
of a cord going from the weight, over the pulley
w to the hook W in the gripe; fo that the gripe
never touches the wheel, unleſs it be pulled
down by the handle V.
When the crane is to be fet at work again,
for drawing up another burden, the handle q is
turned half round forwards; which, by the
crank nn, raiſes up the frame b, and caufes the
trundle
8
PLATE VIII.
H
Fig. 1.
P
p
H
IM
L
F
R.
X
D
E
G
Y
D
Fig. 2
I
B
J. Ferguson delin.
E
B
m
70
G
Λ
0
Fig. 4.
H
H
Fig. 5.
a
B
D
,
IRMEN
I
K
a
'D
Fig. 6.6
G
н
B
H
M
a
F
H
B
Fig.3.
J. Mynde fo.
Of Cranes.
87
trundle B to lay hold of the wheel C; and then,
by turning the winch A, the burden of goods
K is drawn up as before.
The crank n n turns pretty ftiff in the mortife
near o, and ſtops against the farther end of it
when it has got juſt a little beyond the perpen-
dicular; fo that it can never come back of it-
felf and therefore, the trundle B can never
come away from the wheel C, until the handle
9 be turned half round, backwards.
The great rope runs upon rollers in the lever
I. M, which keeps it from bending between the
axle at G and the pulley I. This lever turns upon
the axis N by means of the weight O, which is
juft fufficient to keep its end Z up to the rope; fo
that, as the great axle turns, and the rope coils
round it, the lever rifes with the rope, and
vents the coilings from going over one another.
pre-
The power of this crane may be eſtimated thus:
ſuppoſe the trundle B to have 13 ftaves or rounds,
and the wheel C to have 78 fpur cogs; the trundle
E to have 14 ftaves, and the wheel F 56 cogs.
Then, by multiplying the ftaves of the trundles,
13 and 14, into one another, their product will be
182; and by multiplying the cogs of the wheels,
78 and 56, into one another, their product will be
4368, and dividing 4368 by 182, the quotient
will be 24; which fhews that the winch Amakes
24 turns for one turn of the wheel F and its
axle G on which the great rope or chain HI H
winds. So that, if the length or radius of the
winch A were only equal to half the diameter
of the great axle G, added to half the thickness
of the rope H, the power of the crane would be
as 24 to 1: but the radius of the winch being
double the above length, it doubles the faid
power, and fo makes it as 48 to 1 in which
caſe, a man may raife 48 times as much weight
G 3·
:
by
88
Of Cranes.
by this engine as he could do by his natural
ftrength without it, making proper allowance
for the friction of the working parts.-Two
men may work at once, by having another
winch on the oppofite end of the axis of the
trundle under B; and this will make the power
double.
If this power be thought greater than what
may be generally wanted, the wheels may be
made with fewer cogs in proportion to the ſtaves
in the trundles; and fo the power may be of
whatever degree is judged to be requifite. But
if the weight be fo great as will require yet more
power to raiſe it (ſuppoſe a double quantity)
then the rope H may be put under a moveable
pulley, as , and the end of it tied to a hook in
the gib at ; which will give a double power to
the machine, and fo raiſe a double weight
hooked to the block of the moveable pulley.
&
When only fmall burthens are to be raiſed,
this may be quickly done by men pufhing the
axle G round by the long fpokes y, y', y, y ;, hav-
ing firſt difengaged the trundle B from the wheel
C: and then, this wheel will only act as a fly
upon the wheel F; and the catch R will prevent
its running back, if the men fhould inadvert-
ently leave off pufhing before the burthen be
unhooked from B.
Laftly, When very heavy burthens are to be
raiſed, which might endanger the breaking of
the
cogs in the wheel F; their force againſt theſe
cogs may be much abated by men puſhing round
the long ſpokes y, y, y, y, whilst the man at A
turns the winch.
I have only fhewn the working parts of this
crane, without the whole of the beams which
fupport them; knowing that theſe are eaſily
fuppofed,
Of Cranes.
fuppofed, and that if they had been drawn,
they would have hid a great deal of the
working parts from fight, and alſo confufed the
figure.
Another very good crane is made in the fol- Another
lowing manner. AA is a great wheel turned crane.
Fig. 2.
by men walking within it at H. On the part
C, of its axle B C, the great rope D is wound as
the wheel turns; and this rope draws up goods
in the fame way as the rope H H does in the
above-mentioned crane, the gib work here be-
ing fuppofed to be of the fame fort. But thefe
cranes are very dangerous to the men in the
wheel; for, if any of the men ſhould chance to
fall, the burthen will make the wheel run back
and throw them all about within it; which
often breaks their limbs, and fometimes kills.
them. The late ingenious Mr. Padmore of Brif
tol, (whofe contrivance the forementioned crane
is, fo far as I can remember its conftruction,
after feeing it once about twelve years ago *,)
obferving this dangerous conftruction, con-
trived a method for remedying it, by putting
cogs all around the outfide of the wheel, and
applying a trundle E to turn it; which increafes
the power as much as the number of cogs in the
wheel is greater than the number of ftaves in
the trundle and by putting a ratchet-wheel F
on the axis of the trundle, (as in the above-
mentioned crane) with a catch to fall into it, the
great wheel is ftopt from running back by
the force of the weight, even if all the men in
* Since the first edition of this book was printed, I have
feen the fame crane again; and do find, that though the
working parts are much the fame as above defcribed, yet
the method of raifing or lowering the trundle B, and the
catch R, are better contrived than I had deſcribed them,
G4
`it
90
Of Wheel-Carriages.
Wheel-
it ſhould leave off walking. And by one man
working at the winch 1, or two men at the op-
pofite winches when needful, the men in the
wheel are much affifted, and much greater
weights are raifed, than could be by men only
within the wheel. Mr. Padmore put alſo a
gripe wheel G upon the axis of the trundle,
which being pinched in the fame manner as de-
fcribed in the former crane, heavy burthens
may be let down without the leaft danger.
And before this contrivance, the lowering of
goods was always attended with the utmoſt
danger to the men in the wheel; as every one
muſt be ſenſible of, who has feen fuch engines
at work.
And it is furpriſing that the maſters of wharfs
and cranes fhould be fo regardleſs of the limbs,
or even lives of their workmen, that excepting
the late Sir James Creed of Greenwich, and
fome gentlemen at Briſtol, there is ſcarce an in-
ſtance of any who has ufed this fafe contri-
vance.
The ftructure of wheel-carriages is generally
carriages. fo well known, that it would be needlefs to de-
fcribe them. And therefore, we fhall only
point out fome inconveniencies attending the
common method of placing the wheels, and
loading the waggons,
In coaches, and all other four-wheeled car-
riages, the fore-wheels are made of a lefs fize
than the hind ones, both on account of turn-
ing fhort, and to avoid cutting the braces:
otherwife, the carriage would go much eafier if
the fore-wheels were as high as the hind ones,
and the higher the better, becauſe they would
fink to leſs depths in little hollowings in the
roads, and be the more eaſily drawn out of
them.
Of Wheel-Carriages.
91
them. But carriers and coachmen give another
reaſon for making the fore-wheels much lower
than the hind-wheels; namely, that when they
are fo, the hind-wheels help to puſh on the fore
ones which is too unphilofophical and abfurd
to deſerve a refutation, and yet for their fatis-
faction we ſhall fhew by experiment that it has
no exiſtence but in their own imaginations.
It is plain that the fmall wheels muſt turn as
much oftener round than the great ones, as
their circumferences are lefs. And therefore,
when the carriage is loaded equally heavy on
both axles, the fore-axle muft fuftain as much
more friction, and confequently wear out as
much fooner, than the hind-axle, as the fore-
wheels are lefs than the hind-ones. But the
great misfortune is, that all the carriers to a
man do obftinately perfift, againſt the cleareſt
reafon and demonſtration, in putting the heavier
part of the load upon the fore-axle of the wag-
gon; which not only makes the friction greateſt
where it ought to be leaft, but alſo prefleth the
fore-wheels deeper into the ground than the
hind-wheels, notwithstanding the fore-wheels,
being less than the hind ones, are with fo much
the greater difficulty drawn out of a hole or over
an obftacle, even fuppofing the weights on
their axles were equal. For the difficulty, with
equal weights, will be as the depth of the hole Fig. 3.
or height of the obftacle is to the femidiameter
of the wheel. Thus, if we fuppofe the fmall
wheel D of the waggon ABto fall into a hole
of the depth E F, which is equal to the femi-
diameter of the wheel, and the waggon to be
drawn horizontally along; it is evident, that
the point E of the fmall wheel will be drawn
directly againſt the top of the hole; and there-
fore,
92
Of Wheel-Carriages.
++
fore, all the power of horfes and men will not
be able to draw it out, unleſs the ground gives
way before it. Whereas, if the hind-wheel G
falls into fuch a hole, it finks not near fo deep
in proportion to its femidiameter; and there-
fore, the point G of the large wheel will not be
drawn directly, but obliquely, againſt the top
of the hole; and fo will be eafily got out of it.
Add to this, that as a fmall wheel will often
fink to the bottom of a hole, in which a great
wheel will go but a very little way, the fmall
wheels ought in all reaſon to be loaded with lefs
weight than the great ones: and then the heavier
part of the load would be lefs jolted upward and
downward, and the horfes tired fo much the
lefs, as their draught raiſed the load to lefs
heights.
It is true, that when the waggon-road is
much up-hill, there may be danger in loading
the hind part much heavier than the fore part;
for then the weight would overhang the hind-
axle, eſpecially if the load be high, and endan-
ger tilting up the fore-wheels from the ground.
In this cafe, the fafeft way would be to load it
equally heavy on both axles; and then, as much
more of the weight would be thrown upon the
hind-axle than upon the fore one, as the ground
rifes from a level below the carriage. But as this
feldom happens, and when it does, a fmall tem-
porary weight laid upon the pole between the
horfes would overbalance the danger; and this
weight might be thrown into the waggon when
it comes to level ground; it is ftrange that an
advantage fo plain and obvious as would arife
from loading the hind-wheels heavieft, fhould
not be laid hold of, by complying with this
method.
To
Of Wheel-carriages.
93
9.
To confirm thefe reafonings by experiment,
let a ſmall model of a waggon be made, with
its fore-wheels 2 inches in diameter, and its
hind-wheels 4; the whole model weighing
about 20 ounces. Let this little carriage be
loaded any how with weights, and have a ſmall
cord tjed to each of its ends, equally high from
the ground it refts upon; and let it be drawn
along a horizontal board, firſt by a weight in a
ſcale hung to the cord at the fore-part; the cord
going over a pulley at the end of the board
to facilitate the draught, and the weight juft
fufficient to draw it along. Then, turn the
carriage, and hang the ſcale and weight to the
hind cord, and it will be found to move along
with the fame velocity as at firft: which fhews,
that the power required to draw the carriage
is all the fame, whether the great or fmall
wheels are foremoſt; and therefore the great
wheels do not help in the leaſt to puſh on the
fmall wheels in the road.
Hang the fcale to the fore-cord, and place
the fore-wheels (which are the ſmall ones) in
two holes, cut three eight parts of an inch
deep into the board; then put a weight of 32
ounces into the carriage, over the fore-axle,
and an equal weight over the hind one: this
done, put 44 ounces into the fcale, which will
be juft fufficient to draw out the fore-wheels:
but if this weight be taken out of the fcale, and
one of 16 ounces put into its place, if the hind-
wheels are placed in the holes, the 16 ounce
weight will draw them out; which is little more
than a third part of what was neceffary to draw
out the fore-wheels. This fhews, that the lar-
ger the wheels are, the lefs power will draw the
carriage, especially on rough ground.
Put
94
Of Wheel-Carriages?
Put 64 ounces over the axle of the hind-
wheels, and 32 over the axle of the fore-ones,
in the carriage; and place the fore wheels in
the holes: then, put 38 ounces into the fcale,
which will just draw out the fore-wheels; and
when the hind ones come to the hole, they will
find but very little refiſtance, becauſe they fink
but a little way into it.
But ſhift the weights in the carriage, by put-
ting the 32 ounces upon the hind-axle, and the
64 ounces upon the fore one; and place the
fore-wheels in the holes: then, if 76 ounces be
put into the ſcale, it will be found no more than
fufficient to draw out theſe wheels; which is
double the power required to draw them out,
when the lighter part of the load was put upon
them which is a plain demonftration of the ab-
furdity of putting the heaviest part of the load
in the fore-part of the waggon.
Every one knows what an out cry was made
by the generality, if not the whole body, of the
carriers, against the broad-wheel act; and how
hard it was to perſuade them to comply with it,
even though the government allowed them to
draw with more horſes, and carry greater loads,
than ufual. Their principal objection was, that
as a broad wheel muft touch the ground in a great
many more points than a narrow wheel, the fric-
tion muft of courſe be just fo much the greater;
and confequently, there muſt be fo many more
horfes than ufual, to draw the waggon. I believe
that the majority of people were of the fame
opinion, not conſidering, that if the whole weight
of the waggon and load in it bears upon a
great many points, each fuftains a propor-
tionably lefs degree of weight and friction, than
when it bears only upon a few points; fo that
what
Of Wheel-Carriages.
95
what is wanting in one, is made up in the other
and therefore will be juft equal under equal de-
grees of weight, as may be fhewn by the follow-
ing plain and eafy experiment.
Let one end of a piece of packthread be
faftened to a brick, and the other end to a com-
mon icale for holding weights: then, having
laid the brick edgewife on a table, and let the
ſcale hang under the edge of the table, put as
much weight into the fcale as will juſt draw the
brick along the table. Then taking back the
brick to its former place, lay it flat on the table,
and leave it to be acted upon by the fame weight
in the ſcale as before, which will draw it along
with the fame eaſe as when it lay upon its edge.
In the former cafe, the brick may be confidered
as a narrow wheel on the ground; and in the
latter as a broad wheel. And fince the brick is
drawn along with equal eaſe, whether its broad
fide or narrow edge touches the table, it fhews
that a broad wheel might be drawn along the
ground with the fame eaſe as a narrow one (fup-
pofing them equally heavy) even though they
fhould drag, and not roll, as they go along.
As narrow wheels are always finking into the
ground, especially when the heaviest part of the
load lies upon them, they must be confidered as
going conſtantly up hill, even on level ground.
And their fides muit fuftain a great deal of friction
by rubbing againft the ruts made by them. But
both theſe inconveniencies are avoided by broad
wheels; which, inſtead of cutting and plough-
ing up the roads, roll them fmooth, and harden
them; as experience teftifies in places where
they have been uſed, eſpecially either on wettiſh
or fandy ground: though after all it muſt be con-
feffed, that they will not do in ftiff clayey crofs
roads;
96
Of Wheel-Carriages.
roads, becauſe they would foon gather up as
much clay as would be almoft equal to the
weight of an ordinary load.
If the wheels were always to go upon ſmooth
and level ground, the beſt way would be to make
the spokes perpendicular to the naves; that is,
to ftand at right angles to the axles; becaufe
they would then bear the weight of the load
perpendicularly, which is the ftrongest way for
wood. But becauſe the ground is generally un-
even, one wheel often falls into a cavity or rut
when the other does not; and then it bears much
more of the weight than the other does: in
which cafe, concave or difhing wheels are beſt,
becaule when one falls into a rut, and the other
keeps upon high ground, the ſpokes become per-
pendicular in the rut, and therefore have the
greateſt ſtrength when the obliquity of the load
throws moſt of its weight upon them; whilſt
thofe on the high ground have lefs weight to bear,
and therefore need not be at their full ftrength.
So that the ufual way of making the wheels con-
cave is by much the beſt.
The axles of the wheels ought to be perfectly
ftraight, that the rim of the wheels may be
parallel to each other; for then they will move
eaſieſt, becauſe they will be at liberty to go on
ftraight forwards. But in the ufual way of prac-
tice, the axles are bent downward at their ends;
which brings the fides of the wheels next the
ground nearer to one another than their oppofite
or higher fides are: and this not only makes the
wheels to drag fidewife as they go along, and
gives the load as much greater power of crushing
them than when they are parallel to each other,
but alſo endangers the over-turning of the car-
riage when any wheel falls into a hole or rut; or
when
"
LATE IX.
K
***
1
O
Fig. 1.
b
b
a
H
Ο O
C
ດ
L
ว
L
Fig. 2.
H
N
A Section of the great Wheel
Drum and Shaft, si.
Y
3
4
B
JE
Fig.3.
F
Tongs
S
T. Ferguson delin.
J. Mynde fe.
.
1
Of Wheel-Carriages.
97
:
*
See
when the carriage goes in a road which has one
fide lower than the other, as along the fide of a
hill. Thus (in the hind view of a waggon or
cart) let A E and B F be the great wheels paral-
lel to each other, on their ſtraight axle K, and Fig. 4°
HC I the carriage loaded with heavy goods from
C to G. Then, as the carriage goes on in the
oblique road Aa B, the center of gravity of the
whole machine and load will be at C*; and the
line of direction Cd D falling within the wheel page 13.
BF, the carriage will not overfet. But if the
wheels be inclined to each other on the ground, Fig. 5.
as AE and B F are, and the machine be loaded
as before, from C to G, the line of direction
Cd D falls without the wheel B F, and the whole
machine tumbles over. When it is loaded with
heavy goods (fuch as lead or iron) which lie low, Fig. 4.
it may travel fafely upon an oblique road fo long
as the center of gravity is at C, and the line of di-
rection C d falls within the wheels; but if it be
loaded high with lighter goods (ſuch as wool-
packs) from C to L, the center of gravity is raiſed Fig. 6.
from C to K, which throws the line of direction
Kk without the loweft edge of the wheel B F,
and then the load overfets the waggon.
If there be fome advantage from fmall fore-
wheels, on account of the carriage turning more
eaſily and ſhort than it can be made to do when
they are large; there is at leaſt as great a difad-
vantage attending them, which is, that as their
axle is below the level of the horſes breaſts, the
horfes not only have the loaded carriage to
draw along, but alſo part of its weight to bear
which tires them fooner, and makes them
grow much ſtiffer in their hams, than they
would be if they drew on a level with the fore-
axle. And for this reaſon, we find coach horſes
foon
98
Of the Pile-Engine.
Plate IX.
foon become unfit for riding. So that on all ag
counts it is plain, that the fore-wheels of all car-
riages ought to be fo high, as to have their axles
even with the breaft of the horſes; which would
not only give the horſes a fair draught, but like-
wife keep them longer fit for drawing the car-
riage.
We fhall conclude this lecture with a deferip-
Fig. 1, 2. tion of Mr. Vauloue's curious engine, which was
made uſe of for driving the piles of Weſtminſter-
bridge and the reader may caft his eyes upon
the firſt and ſecond figures of the plate, in which
the fame letters of reference are annexed to the
fame parts, in order to explain thoſe in the fe-
cond, which are either partly or wholly hid in
the firft.
The pile-
engine.
A is the great upright fhaft or axle, on which
are the great wheel B and drum C, turned by
horfes joined to the bars S, S. The wheel B turns
the trundle X, on the top of whofe axis is the
fly O, which ferves to regulate the motion, and
alſo to act againſt the horſes, and keep them
from falling when the heavy ram Qis diſcharged
to drive the pile P down into the mud in the
bottom of the river. The drum C is looſe upon
the fhaft A, but is locked to the wheel B by the
bolt Y. On this drum the great rope H H is
wound; one end of the rope being fixed to the
drum, and the other to the follower G, to which
it is conveyed over the pulleys I and K. In the
follower Ġ is contained the tongs F (fee Fig.
3.) that takes hold of the ram by the ſtaple R
for drawing it up. D is a fpiral or fufy fixt to
the drum, on which is wound the ſmall rope T
that goes over the pulley U, under the pulley V,
and is faſtened to the top of the frame at 7. To
the pulley block V is hung the counterpoiſe W,
which
Of the Pile-Engine.
99
which hinders the follower from accelerating as
it goes down to take hold of the ram: for, as
the follower tends to acquire velocity in its de-
fcent, the line T winds downwards upon the
fufy, on a larger and larger radius, by which
means the counterpoife W acts ftronger and
ftronger againſt it; and fo allows it to come
down with only a moderate and uniform velo-
city. The bolt 2 locks the drum to the great
wheel, being puſhed upward by the ſmall lever
2, which goes through a mortife in the fhaft A,
turns upon a pin in the bar 3 fixt to the great
wheel B, and has a weight 4, which always tends
to puſh up the bolt through the wheel into
the drum. L is the great lever turning on the
axis m, and reſting upon the forcing bar 5, 5,
which goes down through a hollow in the fhaft
A, and bears up the little lever 2.
H
By the horſes going round, the great rope
is wound about the drum C, and the ram Q is
drawn up by the tongs F in the follower G, until
the tongs comes between the inclined planes E;
which, by fhutting the tongs at the top, opens it
at the foot, and diſcharges the ram, which falls
down between the guides b b upon the pile P;
and drives it by a few ftrokes as far into the mud
as it can go; after which, the top part is fawed
off cloſe to the mud, by an engine for that pur-
pofe. Immediately after the ram is difcharged,
the piece 6 upon the follower G takes hold of the
ropes a, a, which raiſe the end of the lever L, and
cauſe its end N to defcend and prefs down the
forcing bar 5 upon the little lever 2, which by
pulling down the bolt 2, unlocks the drum C
from the great wheel B; and then, the follower,
being at liberty, comes down by its own weight
to the ram; and the lower ends of the tongs flip
H
over
Mor M
100
Of the Pile-Engine.
over the ſtaple R, and the weight of their heads
caufes them to fall outward, and fhuts upon
it. Then the weight 4 pushes up the bolt 2 in-
to the drum, which locks it to the great wheel,
and fo the ram is drawn up as before.
As the follower comes down, it caufes the
drum to turn backward, and unwinds the rope.
from it, whilst the horſes, great wheel, trundle
and fly, go on with an uninterrupted motion:
and as the drum is turning backward, the coun-
terpoife W is drawn up, and its rope T wound
upon the ſpiral fufy D.
There are feveral holes in the under fide of
the drum, and the bolt 2 always takes the firſt
one that it finds when the drum ftops by the
falling of the follower upon the ram; until which
ftoppage, the bolt has not time to flip into any
of the holes.
This engine was placed upon a barge on the
water, and fo was eafily conveyed to any place
defired. I never had the good fortune to fee it,
but drew this figure from a model which I made
from a print of it; being not quite ſatisfied with
the view which the print gives. I have been
told that the ram was a ton weight, and that the
guides bb, between which it was drawn up and
let fall down, were 30 feet high. I fuppofe the
great wheel may have had 100 cogs, and the
trundle 10 ftaves or rounds; fo that the fly
would make 10 revolutions for one of the great
wheel.
LECT.
PLATE X.
Fig. 1.
C
Fig. 2.
Fig. 3.
H
A
D
F
A
B
B
I. Ferguson delin,
C
Fig. 10.
B
I
E
C
E
B
D
B
Fig. 4
Fig. 5.
H
Hil
A
B
D
E
E
C
C
G
Fig. 6.
A
B
B
C
Fig. 7.
Fig. 9.
Fig. 8.
A
H
M
K
L
I
D
9
D
E
B
H
F
B
N
J. Mynde jo.
Of Hydrostatics.
ΙΟΙ
LECT. V.
Of hydrofiatics, and hydraulic machines.
TH
HE fcience of hydrostatics treats of the
nature, gravity, preffure, and motion of
fluids in general; and of weighing folids in
them.
tion of
a fluid.
A fluid is a body that yields to the leaft pref- Defini-
fure or difference of preffures. Its particles are
fo fmall, that they cannot be difcerned by the
beſt microſcopes; they are hard, fince no fluid,
except air or ſteam, can be preffed into a lefs
ſpace than it naturally poffeffes; and they muft
be round and fmooth, feeming they are fo eafily
moved among one another.
All bodies, both fluid and folid, prefs down-
wards by the force of gravity: but fluids have
this wonderful property, that their preffure up-
wards and fidewife is equal to their preffure
downwards; and this is always in proportion to
their perpendicular height, without any regard
to their quantity; for, as each particle is quite
free to move, it will move towards that part or
fide on which the preſſure is leaſt. And hence,
no particle or quantity of a fluid can be at reft,
till it is every way equally preffed.
Fluids
To fhew by experiment that fluids prefs up- Plate X.
ward as well as downward, let A B be a long Fig. 1.
upright tube filled with water near to its top; preis
and C D a ſmall tube open at both ends, and pas
much up
immerfed into the water in the large one; if the ward as
immerfion be quick, you will fee the water rife down-
in the ſmall tube to the fame height that it ſtands
in the great one, or until the furfaces of the
H 2
water
ward.
102
Of Hydrostatics.
water in both are on the fame level: which fhews
that the water is preffed upward into the fmall
tube by the weight of what is in the great
one; otherwife it could never rife therein, con-
trary to its natural gravity; unleſs the diameter
of the bore were ſo ſmall, that the attraction of
the tube would raiſe the water; which will ne-
ver happen, if the tube be as wide as that in a
common barometer. And, as the water rifes no
higher in the fmall tube than till its furface be
on a level with the furface of the water in the
great one, this fhews that the preffure is not in
proportion to the quantity of water in the great
tube, but in proportion to its perpendicular
height therein for there is much more water
in the great tube all around the fmall one, than
what is raiſed to the fame height in the ſmall one,
as it ftands within the great.
Take out the fmall tube, and let the water
run out of it; then it will be filled with air.
Stop its upper end with the cork C, and it will
be full of air all below the cork: this done,
plunge it again to the bottom of the water in the
great tube, and you will fee the water rife up in
it only to the height D; which fhews that the air
is a body, otherwife it could not hinder the water
from rifing up to the fame height as it did be-
fore, namely, to A; and in fo doing, it drove
the air out at the top; but now the air is con-
fined by the cork C: and it alſo fhews that the
air is a compreffible body, for if it were not ſo,
a drop of water could not enter into the tube.
The preffure of fluids being equal in all di-
rections, it follows that the fides of a veffel are as
much preffed by a fluid in it, all around in any
given ring of points, as the fluid below that ring
is preffed by the weight of all that ſtands above
it.
Of Hydrostatics.
103
1
it. Hence the preffure upon every point in the
fides, immediately above the bottom, is equal to
the preffure upon every point of the bottom. To
fhew this by experiment, let a hole be made at Fig. 2.
e in the fide of the tube A B clofe by the bot-
tom; and another hole of the fame fize in the
bottom at C; then pour water into the tube,
keeping it full as long as you chooſe the holes
ſhould run, and have two baſons ready to receive
the water that runs through the two holes, until
you think there is enough in each bafon; and
you will find by meaſuring the quantities, that
they are equal; which fhews that the water run
with equal ſpeed through both holes: which it
could not have done, if it had not been equally
preffed through them both. For, if a hole of
the fame fize be made in the fide of the tube, as
about f, and if all three are permitted to run
together, you will find that the quantity run
through the hole at ƒ is much less than what has
run in the fame time through either of the holes
C or e.
In the fame figure, let a tube be turned up
from the bottom at C into the fhape D E, and
the hole at C be ſtopt with a cork. Then, pour
water into the tube to any height, as Ag, and it
will ſpout up in a jet E FG, nearly as high as it
is kept in the tube AB, by continuing to pour
in as much there as runs through the hole E;
which will be the cafe whilft the furface Ag keeps
at the fame height. And if a little ball of cork
G be laid upon the top of the jet, it will be fup-
ported thereby, and dance upon it. The reafon
why the jet rifes not quite fo high as the furface
of the water Ag, is owing to the reſiſtance it meets
with in the open air: for, if a tube, either great
or fmall, was fcrewed upon the pipe at E, the
H 3
water
104
Of Hydrostatics.
The by-
dreftatic
water would rife in it until the furface of the
water in both tubes were on the fame level; as
will be fhewn by the next experiment.
Any quantity of a fluid, how fmall foever,
paradox. may be made to balance and fupport any quan-
tity, how great foever. This is deſervedly
termed the hydroftatical paradox, which we fhall
first few by an experiment, and then account for
it upon the principle above mentioned; namely,
that the preffure of fluids is directly as their perpen-
dicular height, without any regard to their quantity.
Fig. 3.
Let a fmall glass tube DCG, open throughout,
and bended at E, be joined to the end of a great
one Al at cd, where the great one is alſo open;
ſo that theſe tubes in their openings may freely
communicate with each other. Then pour wa-
ter through a fmall necked funnel into the fmall
tube at H; this water will run through the join-
ing of the tubes at cd, and rife up into the great
tube; and if you continue pouring until the fur-
face of the water comes to any part, as A, in the
great tube, and then leave off, you will fee that
the furface of the water in the ſmall tube will be
juft as high, at D; fo that the perpendicular
height of the water will be the fame in both
tubes, however ſmall the one be in proportion to
the other. This fhews, that the fmall column
DCG balances and fupports the great column
Acd: which it could not do if their preffures
were not equal againſt one another in the re-
curved bottom at B.-If the fmall tube be made
longer, and inclined in the fituation G E F, the
furface of the water in it will ftand at F, on the
fame level with the furface A in the great tube;
that is, the water will have the fame perpendicular
height in both tubes, although the column in the
fmall tube is longer than that in the great one;
the
Of Hydrostatics.
105
the former being oblique, and the latter per-
pendicular.
Since then the preffure of fluids is directly as
their perpendicular heights, without any regard
to their quantities, it appears that whatever the
figure or fize of veffels be, if they are of equal
heights, and if the areas of their bottoms are
equal, the preffures of equal heights of water are
equal upon the bottoms of thefe veffels; even
though the one ſhould hold a thouſand or ten
thousand times as much water as would fill the
other. To confirm this part of the hydroſtatical Fig, 4, 5.
paradox by an experiment, let two veffels be
prepared of equal heights but very unequal
contents, fuch as AB in Fig. 4. and AB in Fig.
5. Let each veſſel be open at both ends, and
their bottoms Dd, Dd be of equal widths. Let
a brass bottom CC be exactly fitted to each vef-
fel, not to go into it, but for it to ſtand upon;
and let a piece of wet leather be put between
each veffel and its brafs bottom, for the fake of
cloſeneſs. Join each bottom to its veffel by a
hinge D, fo that it may open like the lid of a
box; and let each bottom be kept up to its
veffel by equal weights E and E hung to lines
which go over the pulleys F and F (whofe blocks
are fixed to the fides of the veffels at ƒ) and the
lines tied to hooks at d and d, fixed in the braſs
bottoms oppofite to the hinges D and D. Things
being thus prepared and fitted, hold the veffel
AB (Fig. 5.) upright in your hands over a bafon
on a table, and caufe water to be poured into the
veffel flowly, till the preffure of the water bears
down its bottom at the fide d, and raifes the
weight E; and then part of the water will run
out at d. Mark the height at which the ſurface
H of the water ſtood in the veffel, when the bot-
H 4
tom
106
Of Hydrostatics.
Fig. 4.
tom began to give way at d; and then, holding
up the other veffel A B (Fig. 4.) in the fame
manner, cauſe water to be poured into it at H;
and you will fee that when the water rifes to A
in this veffel, juft as high as it did in the former,
its bottom will alfo give way at d, and it will
lofe part of the water.
The natural reafon of this furpriſing pheno-
menon is, that fince all parts of a fluid at equal
depths below the furface are equally preffed in
all manner of directions, the water immediately
below the fixed part B ƒ (Fig. 4.) will be preffed
as much upward against its lower furface within
the veffel, by the action of the column Ag, as
it would be by a column of the fame height, and
of any diameter whatever; (as was evident by
the experiment with the tube, Fig. 3.) and there-
fore, fince action and reaction are equal and
contrary to each other, the water immediately
below the furface Bf will be preffed as much
downward by it, as if it was immediately touch-
ed and preffed by a column of the height g A,
and of the diameter Bf: and therefore, the
water in the cavity B Ddf will be preffed as
much downward upon its bottom CC, as the
bottom of the other veffel (Fig. 5.) is preffed by
all the water above it.
To illuftrate this a little farther, let a hole be
made at ƒ in the fixed top B f, and let a tube G
be put into it; then, if water be poured into the
tube A, it will (after filling the cavity B d) rife
up into the tube G, until it comes to a level with
that in the tube A, which is manifeftly owing to
the preffure of the water in the tube A, upon
that in the cavity of the veffel below it. Con-
fequently, that part of the top B f, in which the
hole is now made, would, if corked up, be
preffed
1
Of Hydrostatics.
107
preffed upward with a force equal to the weight
of all the water which is fupported in the tube G:
and the fame thing would hold at g, if a hole
were made there. And fo if the whole cover or
top Bf were full of holes, and had tubes as high
as the middle one Ag put into them, the water
in each tube would rife to the fame height as it is
kept into the tube A, by pouring more into it,
to make up the deficiency that it fuftains by fup-
plying the others, until they are all full: and
then the water in the tube A would ſupport
equal heights of water in all the reft of the tubes.
Or, if all the tubes except A, or any other one,
were taken away, and a large tube equal in dia-
meter to the whole top Bf were placed upon it,
and cemented to it, and then if water were
poured into the tube that was left in either of
the holes, it would afcend through all the reft of
the holes, until it filled the large tube to the
fame height that it ſtands in the ſmall one, after
a fufficient quantity had been poured into it:
which fhews, that the top Bf was preffed up-
ward by the water under it, and before any
hole was made in it, with a force equal to that
wherewith it is now preffed downward by thẹ
weight of all the water above it in the great
tube. And therefore, the reaction of the fixed
top Bf muſt be as great, in preffing the water
downward upon the bottom CC, as the whole
preffure of the water in the great tube would
have been, if the top had been taken away, and
the water in that tube left to prefs directly upon
the water in the cavity B D d f.
Perhaps the beſt machine in the world for Fig. 6.
demonftrating the upward preffure of fluids, is The by-
the hydroftatic bellows A; which confifts of two drostatic
thick oval boards, each about 16 inches broad,
and 18 inches long, covered with leather, to
bellorus.
5
open
108
Of Hydrostatics.
open and ſhut like a common bellows, but with-
out valves; only a pipe B, about three feet
high, is fixed into the bellows at e. Let fome
water be poured into the pipe at c, which will
run into the bellows, and feparate the boards a
little. Then lay three weights b, c, d, each weigh-
ing 100 pounds, upon the upper board, and
pour more water into the pipe B, which will run
into the bellows, and raiſe up the board with all
the weights upon it; and if the pipe be kept
full, until the weights are raiſed as high as the
leather which covers the bellows will allow them,
the water will remain in the pipe, and fupport
all the weights, even though it fhould weigh no
more than a quarter of a pound, and they 300
pounds nor will all their force be able to caufe
them to defcend and force the water out at the
top of the pipe.
The reafon of this will be made evident, by
confidering what has been already faid of the
refult of the preffure of fluids of equal heights
without any regard to the quantities. For, if a
hole be made in the upper board, and a tube be
put into it, the water will rife in the tube to the
fame height that it does in the pipe; and would
rife as high (by fupplying the pipe) in as many
tubes as the board could contain holes. Now,
fuppofe only one hole to be made in any part of
the board, of an equal diameter with the bore of
the pipe B; and that the pipe holds just a quar-
ter of a pound of water; if a perfon ciaps his
finger upon the hole, and the pipe be filled with
water, he will find his finger to be preffed up-
ward with a force equal to a quarter of a pound.
And as the fame preffure is equal upon all equal
parts of the board, each part whofe area is equal
to the area of the hole, will be preffed upward with
a force equal to that of a quarter of a pound: the
fum
Of Hydrostatics.
109
fum of all which preffures againſt the under fide.
of an oval board 16 inches broad, and 18 inches
long, will amount to 300 pounds; and therefore
fo much weight will be raiſed up and fupported
by a quarter of a pound of water in the pipe.
Hence, if a man ftands upon the upper board, How a
and blows into the bellows through the pipe P, man may
he will raiſe himſelf upward upon the board: raife him-
felf up-
and the ſmaller the bore of the pipe is, the eaſier
ward by
he will be able to raiſe himſelf. And then, by his
clapping his finger upon the top of the pipe, he breath.
can fupport himſelf as long as he pleafes; pro-
vided the bellows be air-tight fo as not to lofe
what is blown into it.
This figure, I confefs, ought to have, been
much larger than any other upon the plate; but
it was not thought of, until all the reft were
drawn; and it could not fo properly come into
any other plate.
[wim in
water.
Upon this principle of the upward preffure of How folid
fluids, a piece of lead may be made to fwim in lead may
water, by immerfing it to a proper depth, and be made to
keeping the water from getting above it. Let
CD be a glafs tube, open throughout, and
EFG a flat piece of lead, exactly fitted to the Fig. 7.
lower end of the tube, not to go within it, but
for it to ſtand upon; with a wet leather between
the lead and the tube to make cloſe work. Let
this leaden bottom be half an inch thick, and
held cloſe to the tube by pulling the packthread
IHL upward at L with one hand, whilft the
tube is held in the other by the upper end C.
In this fituation, let the tube be immerfed in
water in the glafs veffel AB, to the depth of fix
inches below the furface of the water at K; and
then, the leaden bottom E F G will be plunged
to the depth of fomewhat more than eleven times
its
110
Of Hydrostatics.
be made
to lie at
the bot-
tom of
water.
its own thickness: holding the tube at that
depth, you may let go the thread at Z; and
the lead will not fall from the tube, but will be
kept to it by the upward preffure of the water
below it, occafioned by the height of the water
at K above the level of the lead. For as lead is
11.33 times as heavy as its bulk of water, and is
in this experiment immerſed to a depth fome-
what more than 11.33 times its thickneſs, and
no water getting into the tube between it and
the lead, the column of water E abc G below the
lead is preffed upward againſt it by the water
KDEGL all around the tube; which water
being a little more than 11.33 times as high as
the lead is thick, is fufficient to balance and fup-
port the lead at the depth K E. If a little water
be poured into the tube upon the lead, it will
increaſe the weight upon the column of water
under the lead, and caufe the lead to fall from
the tube to the bottom of the glafs veffel, where
it will lie in the fituation b d. Or, if the tube be
raiſed a little in the water, the lead will fall by its
own weight, which will then be too great for the
preffure of the water around the tube upon the
column of water below it.
How light Let two pieces of wood be plained quite flat, fo
wood may as no water may get in between them when they
are put together: let one of the pieces, as b d,
be cemented to the bottom of the veffel A B
(Fig. 7.) and the other piece be laid flat and cloſe
upon it, and held down to it by a ſtick, whilſt
water is poured into the veffel; then remove
the ſtick, and the upper piece of wood will not
rife from the lower one: for, as the upper one is
preffed down both by its own weight and the
weight of all the water over it, whilſt the con-
trary preffure of the water is kept off by the
wood
Of Hydraulics.
IIE
wood under it, it will lie as ftill as a ſtone would
do in its place. But if it be raiſed ever ſo little
at any edge, ſome water will then get under it;
which being acted upon by the water above, will
immediately preſs it upward; and as it is lighter
than its bulk of water, it will rife, and float upon
the furface of the water.
All fluids weigh juft as much in their own
elements as they do in open air. To prove
this by experiment, let as much ſhot be put into
a phial, as, when corked, will make it fink in
water and being thus charged, let it be
weighed, firſt in air, and then in water, and
the weights in both cafes wrote down. Then,
as the phial hangs fufpended in water, and
counterpoifed, pull out the cork, that water may
run into it, and it will defcend, and pull down
that end of the beam. This done, put as much
weight into the oppofite ſcale as will reſtore the
equipoiſe; which weight will be found to anſwer
exactly to the additional weight of the phial when
it is again weighed in air, with the water in it.
The velocity with which water ſpouts out at a The velo-
hole in the fide or bottom of a veſſel, is as the city of
* fquare root of the depth or diftance of the ſpouting
hole below the furface of the water. For, in water.
order to make double the quantity of a fluid
run through one hole as through another of the
fame fize, it will require four times the preffure
of the other, and therefore must be four times
the depth of the other below the furface of the
water and for the fame reaſon, three times the
quantity running in an equal time through the
* The fquare root of any number is that which being
multiplied by itſelf produces the faid number. Thus, 2 is
the ſquare root of 4, and 3 is the fquare root of 9: for 2
multiplied by 2 produces 4, and 3 multiplied by 3 pro-
duces 9, &c.
fame
112
Of Hydraulics.
*
fame fort of hole, muft run with three times
the velocity, which will require nine times the
preffure; and confequently must be nine times
as deep below the furface of the fluid and fo
on. To prove this by an experiment, let two
Fig. 8. pipes, as C and g, of equal fized bores, be
fixed into the fide of the veffel A B; the pipe
g being four times as deep below the ſurface of
the water at b in the veffel as the pipe C is: and
whilſt theſe pipes run, let water be conftantly
poured into the veffel, to keep the furface ftill
at the fame height. Then, if a cup that holds
a pint be fo placed as to receive the water that
fpouts from the pipe C, and at the fame moment
a cup that holds a quart be fo placed as to receive
the water that ſpouts from the pipe g, both cups
will be filled at the fame time by their refpec-
tive pipes.
The hori
zontal
to which
water will
Spout
• from
pipes.
The horizontal diſtance, to which a fluid will
fpout from a horizontal pipe, in any part of the
distance fide of an upright veffel below the furface of the
fluid, is equal to twice the length of a perpen-
dicular to the fide of the veffel, drawn from the
mouth of the pipe to a femicircle deſcribed upon
the altitude of the fluid: and therefore, the
fluid will ſpout to the greateſt diſtance poffible
from a pipe, whofe mouth is at the center of
the femicircle; becauſe a perpendicular to its
diameter (ſuppoſed parallel to the fide of the
veffel) drawn from that point, is the longeſt that
can poffibly be drawn from any part of the
diameter to the circumference of the femicircle.
Thus, if the veſſel A B be full of water, the
horizontal pipe D be in the middle of its fide,
and the femicircle N d c b be deſcribed upon D
as a center, with the radius or femidiameter
Dg N, or D fb, the perpendicular Dd to the
diameter N D b is the longeſt that can be drawn
Fig. 8.
from
Of Hydraulics.
113
from any part of the diameter to the circumfe-
rence Ndc b. And if the veffel be kept full,
the jet G will ſpout from the pipe D, to the
horizontal diftance N M, which is double the
length of the perpendicular D d. If two other
pipes, as C and E, be fixed into the fide of the
veffel at equal diftances above and below the
pipe D, the perpendiculars Cc and E e, from
theſe pipes to the femicircle, will be equal; and
the jets F and H fpouting from them will each
go to the horizontal diftance NK; which is
double the length of either of the equal perpen-
diculars Cc or E H.
be con-
Fluids by their preffure may be conveyed over How wa-
hills and vallies in bended pipes, to any height ter may
not greater than the level of the fpring from veyed
whence they flow. But when they are defigned over hills
to be raiſed higher than the fprings, forcing en- and val-
gines muſt be uſed; which fhall be defcribed lies.
when we come to treat of pumps.
A Syphon, generally ufed for decanting li-
quors, is a bended pipe, whofe legs are of un-
equal lengths; and the ſhorteſt leg must always
be put into the liquor intended to be decanted,
that the perpendicular altitude of the column of
liquor in the other leg may be longer than the
column in the immerfed leg, eſpecially above
the furface of the water. For, if both columns
were equally high in that refpect, the atmo-
fphere, which preffes as much upward as down-
ward, and therefore acts as much upward
againſt the column in the leg that hangs without
the veffel, as it acts downward upon the fur-
face of the liquor in the veffel, would hinder
the running of the liquor through the fyphon,
even though it were brought over the bended
part by fuction. So that there is nothing left to
3
cauſe
i14
Of Hydraulics?
Fig. 9.
cauſe the motion of the liquor, but the fuperior
weight of the column, in the longer leg, on
account of its having the greater perpendicular
height.
For
Let D be a cup filled with water to C, and
ABC a fyphon, whofe fhorter leg B C F is im-
merſed in the water from C to F. If the end of
the other leg were no lower than the line AC,
which is level with the furface of the water, the
fyphon would not run, even though the air
fhould be drawn out of it at the mouth A.
although the fuction would draw fome water at
firft, yet the water would ftop at the moment
the fuction ceaſed; becauſe the air would act as
much upward againſt the water at A, as it acted
downward for it by preffing on the ſurface at C.
But if the leg A B comes down to G, and the
air be drawn out at G by fuction, the water will
immediately follow, and continue to run, until
the ſurface of the water in the cup comes down
to F; becauſe, till then, the perpendicular
height of the column BAG will be greater than
that of the column CB; and confequently, its
weight will be greater, until the furface comes
down to F; and then the fyphon will ftop,
though the leg C F fhould reach to the bottom
of the cup. For which reafon, the leg that
hangs without the cup is always made long
enough to reach below the level of its bottom;
as from d to E: and then, when the fyphon is
emptied of air by fuction at E, the water im-
mediately follows, and by its continuity brings
away the whole from the cup; juſt as pulling
one end of a thread will make the whole clue
follow.
If the perpendicular height of a fyphon, from
the furface of the water to its bended top at B,
be
PLATE XI.
Fig. 1.
G
H
I. Ferguson delin.
I
F
Fig.3.
DE
B
Fig. 2.
f
1
E
D
Fig. 4.
F
K
G
C
HI
B
K
a
N
M
M
F
J. Mynde fc.
Of Hydraulics.
115
be more than 33 feet, it will draw no water,
even though the other leg were much longer,
and the fyphon quite emptied of air; becauſe
the weight of a column of water 33 feet high
is equal to the weight of as thick a column of
air, reaching from the furface of the earth to
the top of the atmoſphere; fo that there will
then be an equilibrium, and confequently,
though there would be weight enough of air
upon the furface C to make the water afcend in
the leg C B almoſt to the height B, if the fy-
phon were emptied of air, yet that weight would
not be fufficient to force the water over the
bend, and therefore, it could never be brought
over into the leg B AG.
Let a hole be made quite through the bottom Fig. 10.
of the cup A, and the longer leg of the bended Tantalus's
fyphon DEBG be cemented into the hole, fo cup.
that the end D of the fhorter leg DE may al-
moft touch the bottom of the cup within.
Then, if water be poured into this cup, it will
rife in the ſhorter leg by its upward preffure,
driving out the air all the way before it through
the longer leg: and when the cup is filled above
the bend of the fyphon at F, the preffure of
the water in the cup will force it over the bend
of the fyphon; and it will defcend in the longer
leg CBG, and run through the bottom, until
the cup be emptied.
This is generally called Tantalus's cup, and
the legs of the fyphon in it are almoft cloſe to-
gether; and a little hollow ftatue, or figure of
a man, is ſometimes put over the fyphon to con-
ceal it; the bend E being within the neck of
the figure as high as the chin. So that poor
thirſty Tantalus ftands up to the chin in water,
imagining it will rife a little higher, and he
I
may
116
Of Hydraulics.
The foun-
tain at
Fig. 1.
may drink, but inſtead of that, when the water
comes up to his chin, it immediately begins to
deſcend, and ſo, as he cannot ftoop to follow
it, he is left as much pained with thirst as
ever.
The device called the fountain at command
acts upon the ſame principle with the fyphon in
command. the cup. Let two veffels A and B be joined
Plate XI. together by the pipe C which opens into them
both. Let A be open at top, B cloſe both at
top and bottom (fave only a ſmall hole at b to
let the air get out of the veffel B) and A be of
fuch a fize, as to hold about fix times as much
water as B. Let a fyphon D E F be foldered to
the veffel D, ſo that the part DEe may be
within the veffel, and F without it; the end D
almoſt touching the bottom of the veſſel, and
the end F below the level of D: the veſſel B
hanging to A by the pipe C (foldered into both)
and the whole fupported by the pillars G and H
upon the ſtand I. The bore of the pipe muſt
be confiderably lefs than the bore of the fy-
phon.
The whole being thus conftructed, let the
veffel A be filled with water, which will run
through the pipe C, and fill the veffel B. When
B is filled above the top of the fyphon at E, the
water will run through the fyphon, and be dif-
charged at F. But as the bore of the fyphon
is larger than the bore of the pipe, the fyphon
will run faſter than the pipe, and will foon
empty the veſſel B; upon which the water will
ceafe from running through the fyphon at F,
until the pipe C re-fills the veffel B, and then it
will begin to run as before. And thus the fy-
phon will continue to run and ſtop alternately,
until all the water in the veffel A has run
through
Of Hydraulic Engines.
117
through the pipe C.-So that after a few trials,
one may easily gueſs about what time the fy-
phon will ſtop, and when it will begin to run:
and then, to amufe others, he may call cut stop,
or run, accordingly.
Upon this principle, we may eafily account Intermit
for intermitting or reciprocating Springs.
Let ing
AA be part of a hill, within which there is a prings.
cavity B B; and from this cavity a vein or Fig. z.
channel running in the direction BCDE. The
rain that falls upon the fide of the hill will fink
and ftrain through the fmall pores and cranies
G, G, G, G; and fill the cavity with water K.
When the water rifes to the level HHC, the
vein B CD E will be filled to C, and the water
will run through CDF as through a fyphon;
which running will continue until the cavity be
emptied, and then it will ſtop until the cavity
be filled again.
The common pump (improperly called the fuck- The com-
ing pump), with which we draw water out of mon pump.
wells, is an engine both pneumatic and hydraulic.
It confifts of a pipe open at both ends, in which,
is a moveable piſton or bucket, as big as the
bore of the pipe in that part wherein it works ;
and is leathered round, fo as to fit the bore
exactly; and may be moved up and down, with-
out fuffering any air to come between it and the
pipe or pump barrel.
We ſhall explain the conftruction both of
this and the forcing-pump by pictures of glafs
models, in which both the action of the piftons
and motion of the valves are feen.
Hold the model DCBL upright in the veffel
of water K, the water being deep enough to
riſe at leaſt as high as from A to L.
The valve
a on the moveable bucket G, and the valve b
Fig. 3.
I 2
on
118
Of Hydraulic Engines.
on the fixed box H, (which box quite fills the
bore of the pipe or barrel at H) will each lie
clofe, by its own weight, upon the hole in the
bucket and box, until the engine begins to
work. The valves are made of brafs, and
lined underneath with leather for covering the
holes the more clofely: and the bucket G is
raiſed and depreffed alternately by the handle E
and rod Dd, the bucket being fuppofed at B
before the working begins.
Take hold of the handle E, and thereby
draw up the bucket from B to C, which will
make room for the air in the pump all the way
below the bucket to dilate itſelf, by which its
fpring is weakened, and then its force is not
equivalent to the weight or preffure of the out-
ward air upon the water in the veffel K: and
therefore, at the firft ftroke, the outward air
will prefs up the water through the notched
foot A, into the lower pipe, about as far as e:
this will condenfe the rarefied air in the pipe
between e and C to the fame ftate it was in be-
fore; and then, as its fpring within the pipe
is equal to the force or preffure of the outward
air, the water will rife no higher by the firſt
ſtroke; and the valve b, which was raiſed a
little by the dilatation of the air in the pipe, will
fall, and ftop the hole in the box H; and the
furface of the water will ſtand at e. Then,
deprefs the pifton or bucket from C to B, and
as the air in the part B cannot get back again
through the valve b, it will (as the bucket de-
fcends) raife the valve a, and fo make its way
through the upper part of the barrel d into the
open air. But upon raifing the bucket G a fe-
cond time, the air between it and the water in
the lower pipe at a will be again left at liberty to
fill
Of Hydraulic Engines.
119
fill a larger ſpace; and fo its fpring being again
weakened, the preffure of the outward air on
the water in the veffel K will force more water
up
into the lower pipe from e to ƒ; and when
the bucket is at its greateſt height C, the lower
valve b will fall, and ftop the hole in the box
H as before. At the next ftroke of the bucket
or piſton, the water will rife through the box
H towards B, and then the valve b, which was
raiſed by it, will fall when the bucket G is at
its greateſt height. Upon depreffing the bucket
again, the water cannot be pushed back through
the valve b, which keeps clofe upon the hole
whilft the pifton defcends. And upon raifing
the piſton again, the outward preffure of the air
will force the water up through H, where it will
raiſe the valve, and follow the bucket to
C. Upon the next depreffion of the bucket
G, it will go down into the water in the barrel.
B; and as the water cannot be driven back
through the now clofe valve b, it will raife the
valve a as the bucket defcends, and will be
lifted up by the bucket when it is next raiſed.
And now, the whole fpace below the bucket
being full, the water above it cannot fink when
it is next depreffed; but upon its depreffion,
the valve a will rife to let the bucket go down;
and when it is quite down, the valve a will fall
by its weight, and ſtop the hole in the bucket.
When the bucket is next raiſed, all the water
above it will be lifted up, and begin to run off
by the pipe F. And thus, by raifing and
depreffing the bucket alternately, there is ftill
more water raiſed by it; which getting above
the pipe F, into the wide top I, will fupply
the pipe, and make it run with a continued
ftream.
I 3
So,
120
Of Hydraulic Engines.
So, at every time the bucket is raiſed, the
valve b riles, and the valve a falls; and at every
time the bucket is depreffed, the valve b falls,
and a rifes.
As it is the preffure of the air or atmoſphere.
which caufes the water to rife, and follow the
pifton or bucket G as it is drawn up; and fince
a column of water 33 feet high is of equal
weight with as thick a column of the atmo-
fphere, from the earth to the very top of the air;
therefore, the perpendicular height of the piſton
or bucket from the furface of the water in the
well muſt always be lefs than 33 feet; otherwiſe
the water will never get above the bucket.
But, when the height is lefs, the preffure of the
atmoſphere will be greater than the weight of
the water in the pump, and will therefore raiſe
it above the bucket: and when the water has
once got above the bucket, it may be lifted
thereby to any height, if the rod D be made
long enough, and a fufficient degree of ftrength
be employed, to raife it with the weight of the
water above the bucket.
The force required to work a pump, will be
as the height to which the water is raiſed, and
as the fquare of the diameter of the pump-bore,
in that part where the pifton works. So that,
if two pumps be of equal heights, and one of
them be twice as wide in the bore as the other,
the wideft will raife four times as much water
as the narroweft; and will therefore require four
times as much ſtrength to work it.
The wideneſs or narrowness of the pump, in
any other part befides that in which the pifton
works, does not make the pump either more or
lefs difficult to work, except what difference
arife from the friction of the water in the
may
bore;
Of Hydraulic Engines.
121
bore; which is always greater in a narrow bore
than in a wide one, becauſe of the greater
velocity of the water.
The pump-rod is never raiſed directly by fuch
a handle as E at the top, but by means of a
lever, whofe longer arm (at the end of which
the power is applied) generally exceeds the
length of the ſhorter arm five or fix times; and,
by that means, it gives five or fix times as much
advantage to the power. Upon theſe principles,
it will be eaſy to find the dimenſions of a pump
that ſhall work with a given force, and draw
water from any given depth. But, as theſe
calculations have been generally neglected by
pump-makers (either for want of fkill or in-
duſtry) the following table was calculated by the
late ingenious Mr. Booth for their benefit*.
In this calculation, he fuppofed the handle of
the pump to be a lever increaſing the power
five times; and had often found that a man can
work a pump four inches diameter, and 30 feet
high, and diſcharge 27 gallons of water (Eng-
liſh wine meaſure) in a minute. Now, if it be
required to find the diameter of a pump, that
fhall raiſe water with the fame eafe from any
other height above the furface of the well; look
for that height in the firft column, and over-
againſt it in the ſecond you have the diameter or
width of the pump; and in the third, you find
the quantity of water which a man of ordinary
ftrength can diſcharge in a minute.
2
* I have taken the liberty to make a few alterations in
Mr. Booth's numbers in the table, and to lengthen it out
from 80 feet to 100.
Height
1 4
122
Of Hyaraulic Engines.
f
Height of the
pump above
the furface of
the well.
Diameter of the Water difcharged in
bore where the
bucket works.
a minute, English
wine meaſure.
Feet.
100 parts.
Inches.
Gallons..
Pints.
ΙΟ
6 .93
81 6
15
5:
.66
54
4
20
4
.90
40
7
25
4
•38
30
4 .00
32
32
6
27
2
35
3
.70
23
3
40
3
•46
20
3
45
50
55
60
65
70
75
80
85
332 2 2 2 2 2 2
78
50
.27
18
I
3 .10
16
3
.95
14
7
.84
13
5
.72
12
4
.62
I I
5
.53
10
7
•45
10
2
.38
9
5
90
2
.31
9
I
95
2
.25
8
5
2 .19
8
I
Fig. 4.
The
ICO
The forcing pump raifes water through the
box H in the fame manner as the fucking-pump
forcing- does, when the plunger or pifton g is lifted
・·pump.
up by the rod Dd. But this plunger has no
hole through it, to let the water in the barrel
BC
get above it, when it is depreffed to B, and
the valve b (which rofe by the afcent of the
water
Of Hydraulic Engines.
123
water through the box H when the plunger g
was drawn up) falls down and ſtops the hole in
H, the moment that the plunger is raiſed to its
greateft height. Therefore, as the water be-
tween the plunger g and box H can neither get
through the plunger upon its defcent, nor back
again into the lower part of the pump Le, but
has a free paſſage by the cavity around H into
the pipe MM, which opens into the air-veffel
KK at P; the water is forced through the pipe
MM by the defcent of the plunger, and driven
into the air-veffel; and in running up through
the pipe at P, it opens the valve a; which ſhuts
at the moment the plunger begins to be raiſed,
becauſe the action of the water againſt the under
fide of the valve then ceaſes.
The water, being thus forced into the air-
veffel KK by repeated ftrokes of the plunger,
gets above the lower end of the pipe G HI,
and then begins to condenſe the air in the veffel
KK. For, as the pipe G H is fixed air-tight
into the veſſel below F, and the air has no way
to get out of the veſſel but through the mouth
of the pipe at I, and cannot get out when the
mouth is covered with water, and is more
and more condenfed as the water rifes upon
the pipe, the air then begins to act forcibly by
its fpring againſt the furface of the water at H
and this action drives the water up through the
pipe IHG F, from whence it fpouts in a jet S
to a great height; and is fupplied by alternately
raifing and depreffing of the plunger g, which
conftantly forces the water that it raiſes through
the valve H, along the pipe MM, into the air-
yeffel K K.
The higher that the furface of the water H is
raiſed in the air-veffel, the lefs fpace will the
air
124
Of Hydraulic Engines.
*
air be condenfed into, which before filled that
veffel; and therefore the force of its ſpring will
be fo much the stronger upon the water, and
will drive it with the greater force through the
pipe at F: and as the fpring of the air con-
tinues whilſt the plunger g is rifing, the ftream
or jet S will be uniform, as long as the action
of the plunger continues: and when the valve b
opens, to let the water follow the plunger up-
ward, the valve a fhuts, to hinder the water,
which is forced into the air veffel, from running
back by the pipe M M into the barrel of the
pump.
If there was no air-veffel to this engine, the
pipe GHI would be joined to the pipe MMN
at P; and then, the jet S would ftop every
time the plunger is raiſed, and run only when
the plunger is depreſſed.
Mr. Newfham's water-engine, for extinguiſh-
ing fire, conſiſts of two forcing-pumps, which
alternately drive water into a cloſe veffel of air;
and by forcing the water into that veſſel, the
air in it is thereby condenſed, and compreffes
the water ſo ſtrongly, that it rushes out with
great impetuofity and force through a pipe that
comes down into it; and makes a continued
uniform ſtream by the condenſation of the air
upon its furface in the veffel.
By means of forcing-pumps, water may be
raiſed to any height above the level of a river
or fpring; and machines may be contrived
to work theſe pumps, either by a running
ftream, a fall of water, or by horfes. An
inſtance in each fort will be fufficient to fhew
the method.
First,
PLATE XII.
B
80
то
70
60
A
Level
1.Peroufen delin.
70
Ꮧ
R
S
Women
50
10 2030
40 50 60
910
100 S
D
40
Fig. 3.
30
E
20
F
118
F
11
H
A
Which
G
H
Fig. 1.
FARKTAREIT
V
L
M
E
Fig. 2.
D E F
J.Mynde jõulp
Of Hydraulic Engines.
125
go by
water.
Firſt, by a running ftream, or a fall of wa- Plate XII,
ter. Let AA be a wheel, turned by the fall Fig. 1.
of water B B; and have any number of cranks
(ſuppoſe fix) as C, D, E, F, G, H, on its axis,
according to the ſtrength of the fall of water,
and the height to which the water is intended to
be raiſed by the engine. As the wheel turns
round, theſe cranks move the levers c, d, e, f, g, b A pump
up and down, by the iron rods i, k, l, m, n, o; engine to
which alternately raiſe and depreſs the piſtons by
the other iron rods p, q, r, s, t, u, w, x, y, in
twelve pumps; nine whereof, as L, M, N, O, P,
Q, R, S, T, appear in the plate; the other three
being hid behind the work at V. And as pipes
may go from all theſe pumps, to convey the
water (drawn up by them to a ſmall height) into
a cloſe ciſtern, from which the main pipe goes
off, the water will be forced into this ciftern
by the deſcent of the piſtons. And as each
pipe, going from its refpective pump into the
ciftern, has a valve at its end in the ciftern,
thefe valves will hinder the return of the water
by the pipes; and therefore, when the ciftern
is once full, each pifton upon its defcent will
force the water (conveyed into the ciftern by a
former ftroke) up the main pipe, to the
height the engine was intended to raiſe it:
which height depends upon the quantity raiſed,
and the power that turns the wheel. When
the power upon the wheel is leffened by any
defect of the quantity of water turning it, a
proportionable number of the pumps may be
fet afide, by difengaging their rods from the
vibrating levers.
This figure is a reprefentation of the engine
erected at Blenheim for the Duke of Marlborough,
by the late ingenious Mr. Alderfea. The water-
I
wheel
126
Of Hydraulic Engines.
A pump-
Fig. 2.
wheel is 7 feet in diameter, according to Mr,
Switzer's account in his Hydraulics.
When fuch a machine is placed in a ſtream
that runs upon a fmall declivity, the motion of
the levers and action of the pumps will be but
flow; fince the wheel muft go once round for
each ſtroke of the pumps. But, when there is a
large body of flow running water, a cog or fpur-
wheel may be placed upon each fide of the
water-wheel AA, upon its axis, to turn a trundle
upon each fide; the cranks being upon the axis
of the trundle. And by proportioning the cog-
wheels to the trundles, the motion of the pumps
may be made quicker, according to the quantity
and ſtrength of the water upon the firſt wheel;
which may be as great as the workman pleaſes;
according to the length and breadth of the float-
boards or wings of the wheel. In this manner,
the engine for raiſing water at London-Bride is
conſtructed; in which, the water-wheel is 20
feet diameter, and the floats 14 feet long.
Where a ſtream or fall of water cannot be had,
engine to and gentlemen want to have water raiſed, and
go by
brought to their houſes from a rivulet or fpring;
horfes.
this may be effected by a horſe-engine, working
three forcing pumps which ſtand in a refervoir
filled by the ſpring or rivulet: the piſtons being
moved up and down in the pumps by means of a
triple crank ABC, which, as it is turned round
by the trundle G, raifes and depreffes the rods
D,E,F. The trundle may be turned by ſuch a
wheel as Fin Fig. 1. of Plate VIII, having levers
y,y,y,y, on its upright axle, to which horſes may
be joined for working the engine. And if the
wheel has three times as many cogs as the
trundle has ſtaves or rounds, the trundle and
cranks will make three revolutions for every one
of
Of Hydraulic Engines.
[27
of the wheel: and as each crank will fetch a
ſtroke in the time it goes round, the three cranks
will make nine ſtrokes for every turn of the great
wheel.
The cranks fhould be made of cast iron, be
cauſe that will not bend; and they ſhould each
make an angle of 120 with both of the others,
as at a,b,c; which is (as it were) a view of their Plate XII.
radii, in looking endwife at the axis: and then Fig. 2.
there will be always one or other of them going
downward, which will push the water forward
with a continued ftream into the main pipe.
For, when b is almoft at its loweſt pofiion, and
is therefore juſt beginning to lofe its action upon
the pifton which it moves, c is beginning to move
downward, which will by its piſton continue the
propelling force upon the water: and when c is
come down to the pofition of b, a will be in the
poſition of c.
The more perpendicularly the piſton rods
move up and down in the pumps, the freer and
better will their ſtrokes be: but a little devia-
tion from the perpendicular will not be material.
Therefore, when the pump-rods D, E, and F
go down into a deep well, they may be moved
directly by the cranks, as is done in a very good
horfe-engine of this fort at the late Sir James
Creed's at Greenwich, which forces up water about
64 feet from a well under ground, to a refervoir
on the top of his houfe. But when the cranks
are only at a ſmall height above the pumps, the
piſtons must be moved by vibrating levers, as in
the above engine at Blenheim: and the longer
the levers are, the nearer will the ftrokes be to
a perpendicular.
Let us fuppofe, that in fuch an engine as Sir A calcu-
James Creed's, the great wheel is 12 feet diame- lation of
ter, the trundle 4 feet, and the radius or length the quan-
of tity of
128
Of Hydraulic Engines.
water that of each crank 9 inches, working a pifton in its
may be pump. Let ther be three pumps in all, and the
raifed by bore of each pump be four inches diameter.
a horſe-
engine.
;
Then, if the great wheel has three times as many
cogs as the trundle has ftaves, the trundle and
cranks will go three times round for each revo-
lution of the horfes and wheel, and the three
cranks will make nine ftrokes of the pumps in
that time, each ſtroke being 18 inches (or double
the length of the crank) in a four-inch bore. Let
the diameter of the horſe-walk be 18 feet, and
the perpendicular height to which the water is
raiſed above the furface of the well be 64 feet.
If the horſes go at the rate of two miles an
hour (which is very moderate walking) they will
turn the great wheel 187 times round in an
hour.
9
In each turn of the wheel the piſtons make
ſtrokes in the pumps, which amount to 1683 in
an hour.
Each ſtroke raiſes a column of water 18 inches.
long, and four inches thick, in the pump-bar-
rels; which column, upon the defcent of the
pifton, is forced into the main pipe, whofe per-
pendicular altitude above the furface of the well
is 64 feet.
Now, fince a column of water 18 inches long,
and 4 inches thick, contains 226.18 cubic inches,
this number multiplied by 1683 (the ftrokes in
an hour) gives 380661 for the number of cubic
inches of water raiſed in an hour.
A gallon, in wine meaſure, contains 231 cubic
inches, by which divide 380661, and it quotes
1468 in round numbers, for the number of gal-
lons raiſed in an hour; which, divided by 63,
gives 26 hogfheads.-If the horſes go fafter,
the quantity raiſed will be fo much the greater.
In this calculation it is fuppofed that no water
:
is
Of Hydraulic Engines.
129
is wafted by the engine. But as no forcing
engine can be ſuppoſed to loſe leſs than a fifth
part of the calculated quantity of water, between
the pistons and barrels, and by the opening and
fhutting of the valves, the horſes ought to walk
almoſt 2½ miles per hour, to fetch up this loſs.
A column of water 4 inches thick, and 64
feet high, weighs 349 pounds avoirdupoiſe, or
424 pounds troy; and this weight together with
the friction of the engine, is the refiftance that
muſt be overcome by the ſtrength of the horſes.
5
12
9
The horſe-tackle fhould be fo contrived, that
the horſes may rather puſh on than drag the
levers after them. For if they draw, in going
round the walk, the outfide leather ftraps will
rub againſt their fides and hams; which will
hinder them from drawing at right angles to the
levers, and fo make them pull at a difadvantage.
But if they puſh the levers before their breafts,
inſtead of dragging them, they can always walk
at right angles to theſe levers.
It is no ways material what the diameter of
the main or conduct pipe be: for the whole
reſiſtance of the water therein, against the horſes
will be according to the height to which it is
raiſed, and the diameter of that part of the pump
in which the piston works, as we have already
obferved. So that by the fame pump, an equal
quantity of water may be raiſed in (and confe-
quently made to run from) a pipe of a foot dia-
meter, with the fame eaſe as in a pipe of five or
fix inches or rather with more eaſe, becauſe its
velocity in a large pipe will be leſs than in a
fmall one; and therefore its friction againſt the
fides of the pipe will be lefs alſo.
And the force required to raife water depends
not upon the length of the pipe, but upon the
perpendicular height to which it is raifed therein
above
130
Of Hydraulic Engines.
Fig. 3.
✓
above the level of the fpring. So that the fame
force, which would raiſe water to the height AB
in the upright pipe A i k l m n o p q B, will raiſe it
to the fame height or level BIH in the oblique
pipe AEFGH. For the preffure of the water at
the end A of the latter, is no more that its pref
fure againſt the end A of the former.
The weight or preffure of water at the lower
end of the pipe, is always as the fine of the
angle to which the pipe is elevated above the
level parallel to the horizon. For, although the
water in the upright pipe AB would require à
force applied immediately to the lower end A
equal to the weight of all the water in it, to fup-.
port the water, and a little more to drive it up,
and out of the pipe; yet, if that pipe be inclined
from its upright pofition to an angle of 80 de-
grees (as in A 80) the force required to fupport
or to raiſe the fame cylinder of water will then
be as much lefs, as the fine 80 b is lefs than the
radius AB; or as the fine of 80 degrees is lefs
than the fine of 90. And fo, decreaſing as the
fine of the angle of elevation leffens, until it ar-
rives at its level AC or place of reft, where the
force of the water is nothing at either end of the
pipe. For, although the abfolute weight of the
water is the fame in all pofitions, yet its pref
fure at the lower end decreaſes, as the fine of the
angle of elevation decreaſes; as will appear plain-
ly by a farther confideration of the figure.
Let two pipes, A B and AC, of equal lengths
and bores, join each other at A; and let the
pipe AB be divided into 100 equal parts, as
the fcale S is; whofe length is equal to the
length of the pipe.-Upon this length, as a
radius, defcribe the quadrant BCD, and divide
it into co equal parts or degrees.
Let the pipe AC be elevated to 10 degrees
upon
Of Hydraulic Engines.
131
upon the quadrant, and filled with water;
then, part of the water that is in it will rife in
the pipe AB, and if it be kept full of water, it
will raiſe the water in the pipe AB from A to i;
that is, to a level 10 with the mouth of the
pipe at 10: and the upright line a 10, equal to
Ai, will be the fine of 10 degrees elevation;
which being meaſured upon the fcale S, will be
about 17.4 of fuch parts as the pipe contains
100 in length: and therefore, the force or pref-
fure of the water at A, in the pipe A 10, will
be to the force or preffure at A in the pipe
AB, as 17.4 to 100.
Let the fame pipe be elevated to 20 degrees
in the quadrant, and if it be kept full of water,
part of that water will run into the pipe AB,
and rife therein to the height Ak, which is
equal to the length of the upright line b 20, or
to the fine of 20 degrees elevation; which, be-
ing meaſured upon the fcale S, will be 34.2 of
fuch parts as the pipe contains 100 in length.
And therefore, the preffure of the water at A,
in the full pipe A 20, will be to its preffure, if
that pipe were raiſed to the perpendicular fitua-
tion AB, as 34.2 to 100.
Elevate the pipe to the pofition A 30 on the
quadrant, and if it be fupplied with water, the
water will rife from it, into the pipe AB, to
the height Al, or to the fame level with the
mouth of the pipe at 30. The fine of this ele-
vation, or of the angle of 30 degrees, is c 30;
which is juſt equal to half the length of the pipe,
or to 50 of fuch parts of the fcale, as the length
of the pipe contains 100. Therefore, the pref
fure of the water at A, in a pipe elevated 30
degrees above the horizontal level, will be equal
to one half of what it would be, if the fame
pipe ſtood upright in the fituation AB.
K
And
132
Of Hydraulic Engines.
ļ
And thus, by elevating the pipe to 40, 50,
60, 70, and 80 degrees on the quadrant, the
fines of theſe elevations will be d 40, e 50, ƒ 60,
g 70, and b 80; which will be equal to the
heights Am, An, Ao, Ap, and Aq and thefe
Sine of Parts
Sine of
Parts
Sine of
Parts
D.I
17
D.31
515
D.61
875
2
35
3
52
8
456 7∞
70
77
87
104
122
♡♡♡ M M M
32
530
62
883
33
34
34
545
63
891
559
64
899
35
573
65
906
36
588
66
913
37
602
67
920
139
38
616
68
927
9
156
39
629
69
934
10
174
40
643
70
940
I I
191
41
656
71
945
12
208
42
669
72
951
13
225
43
682
73
956
14
15
456 ♪
242
44
695 74 961
259
16
276
292
66
+4
45
707
75
46
719
966
76 970
47 731 77
974
978
17
18 309 48
743
78
19
325
49 755
79
78 G
20
342
50 766
80
982
985
2 I
358
51
777
81
988
22
375
52
788
82
990
2.3
391
53
799
83 992
24
407
54
809
84 994
25
423
55
819 85 996
26 438
56
829
86 997
27
454
57
28
469
58
29
485
59
857
839
848 88 999
89 1000
87 998
30
500
60
866
90
1000
heights
Of Hydraulic Engines.
133
heights meafufed upon the fcale S will be
64.3, 76.6, 86.6, 94.0, and 98.5; which
exprefs the preffures at A in all thefe elevations,
confidering the preffure in the upright pipe A B
as 100.
Becauſe it may be of ufe to have the lengths
of all the fines of a quadrant from o degrees
to 90, we have given the foregoing table, fhew-
ing the length of the fine of every degree in
fuch parts as the whole pipe (equal to the radius
of the quadrant) contains 1000. Then the fines.
will be integral or whole parts in length. But
if you fuppofe the length of the pipe to be di-
vided only into 100 equal parts, the laſt figure.
of each part or fine must be cut off as a decimal;
and then thoſe which remain at the left hand
of this feparation will be integral or whole
parts.
Thus, if the radius of the quadrant (fup-
poſed to be equal to the length of the pipe AC)
be divided into 1000 equal parts, and the ele-
vation be 45 degrees, the fine of that elevation
will be equal to 707 of thefe parts: but if the
radius be divided only into 100 equal parts, the
fame fine will be only 70.7 or 70% of theſe
parts. For, as 1000 is to 707, fo is Ico to
70.7.
As it is of great importance to all engine-
makers, to know what quantity and weight of
water will be contained in an upright round
pipe of a given diameter and height; fo as by
knowing what weight is to be raiſed, they may
proportion their engines to the force which
they can afford to work them; we fhall fubjoin
tables fhewing the number of cubic inches of
water contained in an upright pipe of a round
bore, of any diameter from one inch to fix and
a half;
K 2
134
Of Hydraulic Engines.
a half; and of any height from one foot to two
hundred together with the weight of the faid
number of cubic inches, both in troy and avoir-
dupoiſe ounces. The number of cubic inches
divided by 231, will reduce the water to gal-
lons in wine meaſure; and divided by 282, will
reduce it to the meaſure of ale gallons. Alfo,
the troy ounces divided by 12, will reduce the
weight to troy pounds; and the avoirdupoiſe
ounces divided by 16, will reduce the weight
to avoirdupoiſe pounds.
And here I muft repeat it again, that the
weight or preffure of the water acting againſt
the power that works the engine, must always
be eſtimated according to the perpendicular
height to which it is to be raiſed, without any
regard to the length of the conduct-pipe, when
it has an oblique pofition; and as if the diame-
ter of that pipe were juft equal to the diameter
of that part of the pump in which the piſton
works. Thus, by the following tables, the
preffure of the water, againſt an engine whofe
pump is of a 4½ inch bore, and the perpendi-
cular height of the water in the conduct-pipe is
80 feet, will be equal to 8057.5 troy ounces,
and to 8848.2 avoirdupoife ounces; which
makes 671.4 troy pounds, and 553 avoirdu-
poſe.
2
2
For any bore whofe diameter exceeds 6
inches, multiply the numbers on the following
page, against any height, (belonging to 1 inch
diameter) by the fquare of the diameter of the
given bore, and the products will be the num-
ber of cubic inches, troy ounces, and avoirdu-
poiſe ounces of water, that the given bore will
contain.
I Inch
Hydrostatical Tables.
135
Feet high.
1 Inch diameter.
Quantity Weight In avoir-
in cubic
in troy
dupoife
inches.
ounces.
ounces.
I
9.42
4.97
5.46
2
11.85
9.95
10.92
3
28,27
14.92
16.38
4
37.70
19.89
21.85
ala
47.12
24.87
27.31
56.55
29.8+
32.77
78
65.97
34.82
38.23
75.40
39.79
43.69
9
84.82
44.76
49.16
10
94.25
49 74
54.62
20
188.49
99.48
109.24
30
282.74
149.21
163.86
40
376.99
198.95
218.47
50
471.24
248.69
273.09
60
565.49
298.43
327.71
70
659.73
348.17
382.33
80
753.98
397.90
436.95
90
848.23 447.64
491.57
942.48 497.38
546.19
100
200
1884.96 994.76 1092.38
EXAMPLE, Required the number of cubic inches, and the
weight of the water, in an upright pipe 278 feet high, and
1½ inch diameter ?
Here the neareſt fingle
decimal figure is only
taken into the account:
and the whole being re-
duced by divifion, a-
mounts to 2 wine gal-
ང
Oz.
Cubic Troy Avoird.
Feet inches OZ.
200--42;1.1 -2238.2--2457.8
;0--1484.4-- 783.3-- gốc.2
8-- 169 6-- 895- 98.3
lons in meaſure; to 259 Anf. 278-5895.1--3111.0--3+16.3
pounds troy, and to 2131
pounds avoirdupoife.
K 3
Thefe
136
Hydrostatical Tables,
1 Inch diameter.
Quantity Weight
in cubic in troy
inches.
ounces.
In avoir-
dupoife
ounces.
Feet high.
12345
I
21.21
11.19
12.29
42.4I
22.38
24.58
63.62 33.57
36.87
84.82
44.76
49.16
105.03
55.95
61.45
6
127.23
67.15
73.73
7
147.44
78.34
86.02
8
169.65
89.53
98.31
9
190.85 100.72
110.60
ΙΟ
212.06 111.91
122.89
20
424.12
223.82
245.78
30
636.17
335.73
368.68
40
848:23
447.64
491.57
50
1060.29
559-55
614.46
60
1272.35 671.46
737.35
1
70
1484.40
783.37
860.24
80
1696.46 895.28
983.14
90
1908.52 1007.19
1106.03
100
200
2120.58 1119.10 1228.92
|
4241.15 2238.20 2457.84
Theſe tables were at firſt calculated to fix
decimal places for the fake of exactneſs; but
in tranfcribing them there are no more than
two decimal figures taken into the account, and
fometimes but one; becauſe there is no neceffity
for
Hydroftatical Tables.
137
Feet high. I
inches.
2 Inches diameter.
Quantity Weight
Weight
in cubic
in troy
Qunces.
In avoir-
dupoife
ounces.
I
37.70
19.89
21.85
2
75.40
39.79
43.69
3
113.10
59.68
65.54
4
150,80
79.58
87.39
5
188.50
99.47
109.24
I
8
6 7∞
226.19 119.37
131.08
263.89 139.26
152.93
301.59
159.16
174.78
9
339.29
179.06
196.03
IO
376.99
198.95
218.47
20
753.98 397.90
436.95
30
1130.97 596.85
655.42
40
1507.97
795.80
873.90
50
1884.96 994.75
1092.37
60
2261.95 1193.70
1310.85
70 2638.94
1392.65
1529.32
80 3015.93
1591.60 1747.80
90 3392.92
1790,56 | 1966.27
100
3769.91 1989.51 2184.75
200 7539.82 3979.00
4369.50
for computing to hundredth parts of an inch or
of an ounce in practice. Ant as they never
appeared in print before, it may not be amifs
to give the reader an account of the principles
upon which they were conftructed.
K 4
The
138
Hydroftatical Tables.
Feet high.!
inches.
2 Inches diameter.
Quantity Weight
in cubic in troy
ounces.
In avoir-
dupoife
ounces.
I
58.90
31.08
34.14
2
117.81
62.17
68.27
3
176.71
93.26
102.41
4
235.62 124.34
136.55
5
294.52
155.43
170.68
629
353.43
186.52
204.82
412.33
217.60
238.96
471.24
248.69 273.09
9
530.14
279.77 307.23
10
589.05
310.86 341.37
20
1178.10 621.72
682.73
30 1767.15 932.58
40
1024.10
2356.20 1243.44 1365.47
50 2545.25 1554.30 1706.83
60 3534.29 1865.16 2048.20
1
70 4123.34 2176.02
|
2389.57
80 4712.39
2486.88
2730.94
3072.30
90 5301.44 2797.74
5890.49 3108.60 2413.67
100
}
200 11780.98
11780.98
6217.20 4827.34
|
The folidity of cylinders are found by mul-
tiplying the areas of their bafes by their alti-
tudes. And ARCHIMEDES gives the following
proportion for finding the area of a circle, and
the folidity of a cylinder raiſed upon that circle;
As
Hydroftatical Tables.
139
Feet high.
in cubic
inches.
in troy
ounces.
3 Inches diameter.
Quantity Weight
In avoir-
dupoiſe
ounces.
I
84.8
44.76
49.16
2
169.6
89.53
98.31
3
254.5
134.29
147.47
4
239.3
179.06
196.63
5
424.I
223.82
245.78
6
508.9
268.58
294.94
78
593.7
313.35 344.10
698.6
358.11
393.25
9
763.4 402.87
442.4I
ΙΟ
848.2 447.64
491.57
20
1696.5
895.28
983.14
30
2544.7
1342.92
1474.70
40
3392.9
1790.56
1790.56 | 1966.27
50
4241.1
2238.19
2238.19
2457.84
60
5089.4
2685.83
2685.83 | 2949:41
70
5937.6
3133.47
3133.47
3440.98
80
6785.8
3581.1I
3932.55
90
7634.1
4028.75
4028.75
4424.12
100
8482.3
4476.39
4476.39 | 4915.68
200
16964.6
8952.78
8952.78 | 9831.36
As I is to 0.785399, fo is the fquare of the
diameter to the area of the circle. And as 1 is
to 0.785399, fo is the fquare of the diameter
multiplied by the height to the folidity of the
cylinder. By this analogy the folid inches and
parts
140
Hydrostatical Tables.
3 Inches diameter.
Quantity Weight
in cubic in troy
inches,
ounces.
In avoir-
dupoiſe
ounces.
Feet high.!
I
115.4
60.9
66.9
2345
230.9
121.8
133.8
346.4
182.8
200.7
461.8
243.7
267.6
577.3
304.6
334.5
6
692.7
365.6
401.4
78
808.2
426.5
468.4
923.6
487.4
535.3
9
1039.I
548.4
602.2
ΙΟ
1154.5
609.3
669.1
20 2309.I
1218.6
1338.2
30
3463.6
1827.9
2007.2
40
4618.1
2437.
2676.3
50
5772.7
3046.4
3345.4
60
6927.2
3655.7
4014.5
70
8081.8
4265.0 4683.6
80
9236.3
4874.3
5352.6
90 10390.8 5483.6 6021,7
100
11545.4 6092.9 6690.8
200 23090.7
12185.7
13381.5
parts of an inch in the tables are calculated to a
cylinder 200 feet high, of any diameter from 1
inch to 61, and may be continued at pleaſure.
And as to the weight of a cubic foot of running
water, it has been often found upon trial, by
Dr.
Hydrostatical Tables.
141
4 Inches diameter.
Quantity Weight
in cubic in troy
inches.
ounces.
In avoir-
dupoife
ounces.
Feet high.!
$
1 2 3 4
I
150.8
79.6
87.4
301.6
159.2
174.8
452.4
238.7
262.2
603.2
318.3
349.6
5
754.0
397.9
436.9
6
904.8 477.3
524.3
78
1055.6
557.1
611.7
1206.4 636.6
699.1
9
1357.2
716.2
786.5
10
1508.0
795.8
873.9
20
3115.9 1591.6
1747.8
30
4523.9
2387.4
2621.7
40
6031.9
3183.2
3495.6
50 7539.8
3997.0
4369.5
60 9047.8
4774.8
5243.4
70
10555.8 5570.6
6117.3
80
12063.7 6366.4
6991.2
90
13571.7 7162.2
7865.1
100
15979.7 7958.0 8739.0
200
30159.3
15916.0 | 17478.0
The
Dr. Wyberd and others, to be 76 pounds
troy, which is equal to 62.5 pounds avoirdu-
poife. Therefore, fince there are 1728 cubic weight of
inches in a cubic foot, a troy ounce of water running
contains 1.8949 cubic inch; and an avoirdupoife water.
ounce
142
Hydrostatical Tables.
Feet high.
4 Inches diameter.
4호
​Quantity Weight
in cubic in troy
In avoir-
dupoife
inches.
ounces.
ounces.
I
190.8
100.7
110.6
2
381.7
201.4
221.2
3
572.6
302.2
331.8
4
763.4
402.9
442.4
5
954.3
503.6
553.0
6
1145.I
604.3
663.6
7
1338.0
705.0
774.2
8
1526.8
805.7
884.8
9
1717.7
906.5
995.4
IO
1908.5
1007.2
1106.0
20
3817.0
2014.4
2212.I
30
5725.6
3021.6
3818.1
40
7634.1
4028.7
4424.I
50
9542.6
5035.9
5530.I
60 11451.1
6043.I
6636.2
1
70
13359.6
7050.3
7742.2
80
15268.2 8057.5
8848.2
90 17176.7 9064.7
9954.3
100
200
19085.2 10071.9 11060.3
38170.4 20143.8
22120.6
ounce of water 1.72556 cubic inch. Confe-
quently, if the number of cubic inches con-
tained in any given cylinder, be divided by
1.8949, it will give the weight in troy ounces;
and divided by 1.72556, will give the weight
#
in
Hydroftatical Tables.
143
Feet high.
in cubic
inches.
in troy
ounces.
5
Inches diameter.
Quantity Weight
In avoir-
dupoife
ounces.
2
12
I
235.6
124.3
136.5
471.2
248.7
273.1
3
706.6
373.0
409.6
4
942.5
497.4
546.2
5
1178.1
621.7
682.7
al
1413-7
746.1
819.3
78
1649.3 870.4
955.8
1885.0 994.8
1092.4
9
10
2120.6 1119.1
1228.9
2356.2 1243.4
1365.5
20
4712.4
2486.9
2730.9
30
7068.6
3730.3
4096.4
40
9424.8
4973.8
5461.9
[89
11780.0
6217.2
6827.3
14137.2
7460.6
8192.8
70 16493.4
8704.1
9558.3
80 18849.6
9947.5
10923.7
90
21205.8
11191.0
12289.2
100
23562.0
12434.4 13654.7
24868.8 | 27309.3
200 47124.0
in avoirdupoife ounces. By this method, the
weights fhewn in the tables were calculated;
and are near enough for any common practice.
The fire-engine comes next in order to be ex- The fire-
plained; but as it would be difficult, even by engine.
the
144
Hydrostatical Tables.
5 Inches diameter.
Quantity Weight
in troy
in cubic
inches.
ounces.
In avoir-
dupoiſe
ounces.
Feet high. !
123+
285.1
150.5
164.3
570.2
300.9
328.5
855.3
451.4
492.8
4
I 140.4
601.8
657.I
5
1425:5
752.3
821.3
678
1710.6
902.7
985.6
1995.7 1053.2
1149.9
2280.8
1203.6
1314.2
9
2565.9
J354.I
1478.4
10
2851.0
1504.6
1642.7
20
5702.0
3009. I
3285-4
30
8553.0
4513.7
4928.I
40 11404.0
6018.2
6570.8
50
14255.0
7522.8
8213.5
60 17106.0 9027.4
9856.2
70 19957.0 | 10531.9
10531.9
11498.9
80
22808.0
12036.5
12036.5
13141.6
90 25659.0 13541.I
14784.3
100
28510.0 15045.6
|
16426.9
200
|
57020.0 30091.2 | 32853.9
the beſt plates, to give a particular defcription
of its feveral parts, fo as to make the whole
intelligible, I fhall only explain the principles
upon which it is conftructed.
I. What-
Hydroftatical Tables.
145
6 Inches diameter.
Quantity Weight
in cubic in troy
inches.
ounces.
In avoir-
dupoiſe
ounces.
Feet high.
!
1
I
339.3
179.1
196.6
234 LO
678.6
358.1
393.3
1017.9
537.2
589.9
1357.2 716.2
786.5
5
1696.5
895.3
983.1
6
2035.7 1074.3
1179.8
7
2375.0
1253.4
1376.4
8
2714.3
1432.4
1573.0
9
3053.6
1611.5
1769.6
IO
3392.9 1790.6
1966.3
20
6785.8
3581.1
3932.5
30
10178.8 5371.7
5898.8
40
13571.7
7162.2
7865.1
50 169'64.6 8952.8 9831.4
бо
20357.5 | 10743.3
11797.6
70
23750.5 12533.9 13763.9
80 27143.4 14324.4 15730.2
90
ΤΟΟ
17696.5
30536.3 16115.0
33929.2 17905.6 19662.7
200 67858.4 35811.2 39325.4
1. Whatever weight of water is to be raiſed,
the pump-rod must be loaded with weights fuf-
ficient for that purpoſe, if it be done by a
forcing-pump, as is generally the cafe; and the
5
power
146
Hydroftatical Tables.
Feet high.
64 Inches diameter.
Quantity Weight
in troy
in cubic
inches.
ounces.
In avoir-
dupoife
ounces.
1 2 3 4
I
398.2
210.1
230.7
797.4
420.3
461.4
1195.6
630.4
692.1
1593.8
840.6
922.8
5
1991.9
1050.8
1153.6
6
2390.I
1260.9
1384.3
7
2788.3
1471.I
1615.0
1500
3186.5
1681.2
1845.7
3584.7
1891.3
2076.4
3982.9
2101.5 2307.1
20
7965.8
4202.9 4614.3
3011948.8
6304.4
6921.4
40
15931.7
8405.9
9228.6
50 19914.6
10507.4 11535.7
60 23897.9
23897.9
12608.9
13842.9
1
16150.0
70 27880.5 14710.4
80 31863.4
31863.4 16811.8 18457.2
90 35846.3 18913.3 20764.3
100 39829.3 21014.8 23071.5
200 79658.6 42029.6 | 46143.0
power of the engine muſt be fufficient for the
weight of the rod, in order to bring it up.
2. It is known, that the atmoſphere preffes
upon the ſurface of the earth with a force equal
to 15 pounds upon every ſquare inch.
3. When
Of Hydraulic Engines.
147
3. When water is heated to a certain degree,
the particles thereof repel one another, and con-
ftitute an elaftic fluid, which is generally called
Steamz or vapour.
4. Hot fteam is very elaſtic; and when it is
cooled by any means, particularly by its being
mixed with cold water, its elaſticity is deſtroyed
immediately, and it is reduced to water again.
5. If a veffel be filled with hot fteam, and
then cloſed, ſo as to keep out the external air,
and all other fluids; when that ſteam is by any
means condenfed, cooled, or reduced to water,
that water will fall to the bottom of the veffel;
and the cavity of the veffel will be almoſt a per-
fect vacuum.
6. Whenever a vacuum is made in any veffel,
the air by its weight will endeavour to rush into
the veffel, or to drive in any other body that
will give way to its preffure; as may be eaſily
ften by a common fyringe. For, if you ſtop
the bottom of a fyringe, and then draw up the
piſton, if it be fo tight as to drive out all the
air before it, and leave a vacuum within the
fyringe, the pifton being let go will be driven
down with a great force.
7. The force with which the pifton is driven
down, when there is a vacuum under it, will be
as the fquare of the diameter of the bore in the
fyringe. That is to fay, it will be driven down
with four times as much force in a fyringe of a
two-inch bore, as in a fyringe of one inch for
the areas of circles are always as the fquares of
their diameters.
8. The preffure of the atmoſphere being
equal to 15 pounds upon a fquare inch, it
will be almoft equal to 12 pounds upon a cir-
cular inch. So that if the bore of the fyringe
L
be
148
Of Hydraulic Engines.
be round, and one inch in diameter, the piiton
will be preft down into it by a force nearly equal
to 12 pounds: but if the bore be two inches
diameter, the pifton will be preft down with
four tithes that force.
And hence it is eafy to find with what force
the atmoſphere preffes upon any given number
either of iquare or circular inches.
Thefe being the principles upon which this
engine is conftructed, we fhall next defcribe the
chief working parts of it: which are, 1. A
boiler. 2. A cylinder and pifton. 3. A beam
or lever.
The boiler is a large veffel made of iron or
copper; and commonly fo big as to contain
about 2000 gallons.
The cylinder is about 40 inches diameter,
bored fo fmooth, and its leathered piſton fitting
fo cloſe, that little or no water can get between
the piſton and ſides of the cylinder.
Things being thus prepared, the cylinder is
placed upright, and the fhank of the pifton is
fixed to one end of the beam, which turns on a
center like a common balance.
The boiler is placed under the cylinder, with
a communication between them, which can be
opened and ſhut occaſionally.
The boiler is filled about half full of water,
and a ſtrong fire is placed under it: then, if the
communication between the boiler and the cy-
linder be opened, the cylinder will be filled with
hot fteam; which would drive the piſton quite
out at the top of it. But there is a contrivance
by which the beam, when the piſton is near the
top of the cylinder, fhuts the communication at
the top of the boiler within.
This
Of Hydraulic Engines.
149
This is no fooner fhut, than another is opened
by which a little cold water is thrown upwards
in a jet into the cylinder, which mixing with the
hot ſteam, condenfes it immediately; by which
means a vacuum is made in the cylinder, and
the piſton is preffed down by the weight of the
atmoſphere; and fo lifts up the loaded pump-
rod at the other end of the beam.
If the cylinder be 42 inches in diameter, the
piſton will be preffed down with a force greater
than 20000 pounds, and will confequently lift
up that weight at the oppofite end of the beam:
and as the pump-rod with its plunger is fixed
to that end, if the bore where the plunger works
were 10 inches diameter, the water would be
forced up through a pipe of 180 yards perpen-
dicular height.
But, as the parts of this engine have a good
deal of friction, and must work with a confi-
derable velocity, and there is no fuch thing as
making a perfect vacuum in the cylinder, it is
found that no more than 8 pounds of preffure
muſt be allowed for, on every circular inch of
the piſton in the cylinder, that it may make
about 16 ftrokes in a minute, about 6 feet
each.
Where the boiler is very large, the pifton
will make between 20 and 25 ftrokes in a mi-
nute, and each ſtroke 7 or 8 feet; which, in a
pump of 9 inches bore, will raife upwards of
300 hogfheads of water in an hour.
It is found by experience that a cylinder, 40
inches diameter, will work a pump 10 inches
diameter, and 100 yards long: and hence we
can find the diameter and length of a pump,
that can be worked by any other cylinder.
L 2
For
150
Of Hydraulic Engines.
For the convenience of thoſe who would
make uſe of this engine for railing water, we
fhall fubjoin part of a table calculated by Mr.
Beighton, fhewing how any given quantity of
water may be raiſed in an hour, from 48 to 440
hogfheads; at any given depth, from 15 to
100 yards; the machine working at the rate
of 16 ftrokes per minute, and each ſtroke being
6 feet long.
One example of the uſe of this table will
make the whole plain. Suppofe it were required
to draw 150 hogfheads per hour, at 90 yards.
depth; in the ſecond column from the right
hand, I find the neareſt number, viz. 149 hogf-
heads 40 gallons, againſt which, on the right
hand, I find the diameter of the bore of the pump
muſt be 7 inches; and in the fame collateral line,
under the given depth 90, I find 27 inches, the
diameter of the cvlinder fit for that purpoſe.-
And fo for any other.
A Table
PLATE XII.
་་
B
I. Ferguson detin.
n
J. Mynde fc.
Hydraulic Table.
151
lons, at 282 cubic inches per gallon.
This table, is calculated to the meaſure of ale gal-
A Table hewing the power of the engine for railing water by fire.
The depth to be drawn in yards.
In one hour.
Diam.
of
pump.
100 Hogh. Gal.} inches.
15
20
25 30 35 40
45
50
60
70
80
90
18/2/
21
1
14
132
754 m ~
19/3/
18
Mi+m/t
986
24
enfor
26/28/1/20
28/12/30/20
22 24
26
28
32 21 34 =
29 31
20
22
233
25
27
283
J
17
2/14/16
165 18
154
20
21 22 23
244 25
NW W W
I
372
4
40
440
12
342
37
39 1/2
369
33
1 I
I
33
36
3840
304
48
10
28
302/20
174
19
2014 21
23
24
26
2644
282
2
18/1/19
20
212 23
25
27
12
14
Ι
5
17
183
21
18 19
22
24426
MMN ~
33
35
36 1/1/20
247
7
31
32 / 35
221
15
29 302 32
195
22
0.0000
- ka
28
291 31
182
13
II 13
mit
15
16일
​18
19
20
21
234
101 13
14
I
15
16
162
181 19
20/12/20
22
~ 2
25
27
281
172
30
24
25/2/2 27
28
149
40
7
10
I 2
13
14
15
16
18
19
20
22
23
24를
​24/12 201
128
54
9/11
I 2
13
14
152
16
17
19
20/21/201
22
23
24/2/2
I 10
I
6
10
1 1
1 2
13
14
15
1537
17
19
20
21
22/1/
04
30
5 =
10
II
1 132
13
134
14
1 5 12/20
163
18
19
201
66 61
5
10
1 1 1/2
+-
1 2
14
15
16
17
18!
60
60
4
-IN
9
II
I I
I 2
1 3 1/2/3
14
15
16
48 51
4
Diameter of the cylinder in inches.
L 3
Water
152
Of Hydraulic Engines.
Plate XIII.
fian
wheel.
Water may be raiſed by means of a ſtream
The Per- AB turning a wheel CD E, according to the
order of the letters, with buckeis a, a, a, a, &c.
hung upon the wheel by ftrong pins b, b, b, b,
&c. fixed in the fide of the rim: but the wheel
muſt be made as high as the water is intended
to be raiſed above the level of that part of the
ftream in which the wheel is placed. As the
wheel turns, the buckets on the right-hand go
down into the water, and are filled therewith, and
go up full on the left hand, until they come to
the top at K; where they ſtrike againſt the end
n of the fixed trough M, and are thereby over-
fet, and empty the water into the trough; from
which it may be conveyed in pipes to the place
which it is defigned for: and as each bucket
gets over the trough, it falls into a perpendi-
cular pofition again, and goes down empty,
until it comes to the water at A, where it is
filled as before. On each bucket is a fpring r,
which going over the top or crown of the bar m
(fixed to the trough M) raiſes the bottom of the
bucket above the level of its mouth, and fo
cauſes it to empty all its water into the trough.
Sometimes this wheel is made to raife water
no higher than its axle; and then, inſtead of
buckets hung upon it, its fpokes C, d, e, f, g, h,
are made of a bent form, and hollow within
thefe hollows opening into the holes C, D, E, F,
in the outfide of the wheel, and alfo into thofe
at O in the box N upon the axle. So that, as
the holes C, D, &c. dip into the water, it runs
into them; and as the wheel turns, the water
rifes in the hollow spokes, c, d, &c. and runs
out in a ſtream P from the holes at O, and falls
into the trough 2, from whence it is conveyed
by pipes. And this is a very eafy way of ráifing
water,
Of the Specific Gravities of Bodies.
153
water, becauſe the engine requires no animal
power to turn it.
The art of weighing different bodies in water, O the
and thereby finding their fpecific gravities, or specific
weights, bulk for bulk, was invented by AR- gravities
CHIMEDES; of which we have the following
account:
Hiero king of Syracuſe, having employed a
goldſmith to make a crown, and given him a
maſs of pure gold for that purpoſe, ſuſpected
that the workman had kept back part of the
gold for his own ufe, and made up the weight
by allaying the crown with copper. But the
king not knowing how to find out the truth of
that matter, referred it to Archimedes; who
having ſtudied a long time in vain, found it out
at laft by chance. For, going into a bathing-
tub of water, and obferving that he thereby
raiſed the water higher in the tub than it was
before, he concluded inftantly that he had raiſed
is juſt as high as any thing elſe could have done,
that was exactly of his bulk: and confidering
that any other body of equal weight, and of lefs
bulk than himſelf, could not have raifed the
water fo high as he did; he immediately told
the king, that he had found a method by which
he could diſcover whether there were any cheat
in the crown. For, fince gold is the heavieft
of all known metals, it must be of lefs bulk,
according to its weight, than any other metal.
And therefore he defired that a maſs of pure
gold, equally heavy with the crown when
weighed in air, fhould be weighed againſt
it in water; and if the crown was not allayed,
it would counterpoife the mafs of gold when
they were both immersed in water, as well as it
did when they were weighed in air. But upon
L 4
making
of bodies.
1
154
Of the Specific Gravities of Bodies.
making the trial, he found that the mafs of
gold weighed much heavier in water than the
crown did. And not only fo, but that, when
the maſs and crown were immerfed feparately
in one veflel of water, the crown railed the
water much higher than the mafs did; which
fhewed it to be allayed with fome ligher metal
that increaſed its bulk. And fo, by making
trials with different metals, all equally heavy
with the crown when weighed in air, he found
out the quantity of alloy in the crown.
The ſpecific gravities of bodies are as their
weights, bulk for bulk; thus a body is faid to
have two or three times the ſpecific gravity of
another, when it contains two or three times as
much matter in the fame ſpace.
A body immerfed in a fluid will fink to the
bottom, if it be heavier than its bulk of the
fluid. If it be fufpended therein, it will lofe
as much of what it weighed in air, as its bulk
of the fluid weighs. Hence, all bodies of equal
bulks, which would fink in fluids, lofe equal
weights when ſuſpended therein. And unequal
bodies loſe in proportion to their bulks.
The by-
The hydrostatic balance differs very little
droftatic from a common balance that is nicely made:
balance.
only it has a hook at the bottom of each ſcale,
on which ſmall weights may be hung by horfe-
hairs, or by filk threads. So that a body, fuf-
pended by the hair or thread, may be immerſed
in water without wetting the fcale from which
it hangs.
How to
find the
fpecific
gravity of
any body.
If the body thus fufpended under the fcale,
at one end of the balance, be firſt counterpoiſed
in air by weights in the oppofite fcale, and then
immerſed in water, the equilibrium will be im-
mediately deſtroyed. Then, if as much weight
be
*
Of the Specific Gravities of Bodies.
155
be put into the fcale from which the body hangs,
as will reſtore the equilibrium (without altering
the weights in the oppofite fcale) that weight,
which reſtores the equilibrium, will be equal to
the weight of a quantity of water as big as the
immerfed body. And if the weight of the body
in air be divided by what it lofes in water, the
quotient will fhew how much that body is hea-
vier than its bulk of water. Thus, if a guinea
fufpended in air, be counterbalanced by 129
grains in the oppofite fcale of the balance; and
then, upon its being immerſed in water, it be-
comes fo much lighter, as to require 74 grains
put into the ſcale over it, to reſtore the equili-
brium, it fhews that a quantity of water, of
equal bulk with the guinea, weighs 74 grains,
or 7.25; by which divide 129 (the weight of
the guinea in air) and the quotient will be
17.793; which ſhews that the guinea is 17.793
times as heavy as its bulk of water. And thus,
any piece of gold may be tried, by weighing it
firft in air, and then in water; and if upon
dividing the weight in air by the lofs in water,
the quotient comes out to be 17.793, the gold
is good; if the quotient be 18, or between 18
and 19, the gold is very fine; but if it be lefs
than 17, the gold is too much allayed, by being
mixed with ſome other metal.
If filver be tried in this manner and found
to be 11 times as heavy as water, it is very
fine; if it be 10 times as heavy, it is ftand-
ard; but if it be of any lefs weight compared
with water, it is mixed with fome lighter me-
tal, fuch as tin.
By this method, the ſpecific gravities of all
bodies that will fink in water, may be found.
But as to thoſe which are lighter than water, as
moft
156
Of the Specific Gravities of Bodies.
moft forts of wood are, the following method
may be taken, to fhew how much lighter they
are than their reſpective bulks of water.
Let an upright ftud be fixed into a thick flat.
piece of brafs, and in this ftud let a ſmall lever,
whofe arms are equally long, turn upon a fine
pin as an axis. Let the thread which hangs
from the ſcale of the balance be tied to one end
of the lever, and a thread from the body to be
weighed, tied to the other end. This done,
put the brafs and lever into a veffel; then pour
water into the veffel, and the body will riſe and
float upon it, and draw down the end of the
balance from which it hangs: then, put as much
weight in the oppoſite ſcale as will raife that end
of the balance, fo as to pull the body down into
the water by means of the lever; and this
weight in the ſcale will fhew how much the body
is lighter than its bulk of water.
There are fome things which cannot be
weighed in this manner, fuch as quickfilver,
fragments of diamonds, &c. becauſe they can-
not be fufpended in threads; and must therefore
be put into a glafs bucket, hanging by a thread
from the hook of one fcale, and counterpoifed
by weights put into the oppofite fcale. Thus,
ſuppoſe you want to know the ſpecific gravity
of quickfilver, with reſpect to that of water; let
the empty bucket be firſt counterpoiſed in air,
and then the quick filver put into it and weighed.
Write down the weight of the bucket, and alfo
of the quick filver; which done, empty the
bucket, and let it be immerfed in water as it
hangs by the thread, and counterpoiſed therein
by weights in the oppofite fcale: then, pour
the quickfilver into the bucket in the water,
which will caufe it to preponderate; and put as
much
Of the Specific Gravities of Bodies.
157
much weight into the oppofite fcale as will re-
ftore the balance to an equipoife; and this
weight will be the weight of a quantity of water
equal in bulk to the quickfilver. Laftly, di-
vide the weight of the quicksilver in air, by the
weight of its bulk of water, and the quotient
will fhew how much the quickfilver is heavier
than its bulk of water.
If a piece of brafs, glaſs, lead, or filver, be
immerfed and fufpended in different forts of
fluids, the different loffes of weight therein will
fhew how much it is heavier than its bulk of the
fluid; the fluid being lighteſt in which the im-
merfed body lofes leaft of its aerial weight. A
folid bubble of glafs is generally uſed for finding
the ſpecific gravities of fluids.
Hence we have an eaſy method of finding the
ſpecific gravities both of folids and fluids, with
regard to their specific bulks of common
pump water, which is generally made a ſtand-
ard for comparing all others by.
In conftructing tables of ſpecific gravities with
accuracy, the' gravity of water muſt be repre-
fented by unity or 1.000, where three cyphers
are added, to give room for expreffing the ratios
of other gravities in decimal parts, as in the
following table.
N. B. Although guinea gold has been gene-
rally reckoned 17.798 times as heavy as its
bulk of water, yet, by many repeated trials, I
cannot fay that I have found it to be more than
17.200 (or 17%) as heavy.
A Table
158
Of the Specific Gravities of Bodies.
A Table of the fpecific gravities of feveral folid
and fluid bodies.
A cubic inch of
Troy weight, Avoirdup. | Compa-
rative
Oz. pw. gr. oz. drams. weight.
Very fine gold
10 7 3.83 1 5.80 19.637
Standard gold
Guinea gold
9 19 6.44 10 14.90
18.888
9
7 17.18 10 4.76 17.793
Moidore gold
9
o 19.84 9 14.71
17.140
Quickfilver
7 7 11.61 8 1.45
14.019
Lead
5 19 17.55 6 9.08
11.325
Fine filver
5 16 23.23 6 6.66
11.087
Standard filver
Copper
Plate-brafs
-
5 11 3.36 6
3.36 6
1.54
1.54
10.535
4 13
7.04 5 1.89
8.843
4 4
9.60 4
10.09
8.000
Steel
4
2 20.12
4 8.70
7.852
Iron
4
0 15 20
4 4 6.77
7.645
Block-tin
3 17 5.68 4 3.79
7.321
Speltar
3 14 12.86 4 1.42
7.065
Lead ore
3 11 17.76 3 14.96
6.800
Glaſs of antimony! 2 15 16.89 3 0.89
5.280
German antimony 2 2 4.80 2 5.04
4.000
Copper ore
2 I 11.83 2 4.43
3.775
Diamond
I 15 20.88
I 15.48
3.4.00
Clear glafs
I 13 5.58 I 13.16
3.150
Lapis lazuli -
I 12 5.27 I 12.27
3.054
Welch aſbeſtos
I 10 17.57 I 10.97
2.913
White marble
I 8 13.41 I
9.06
2.707
Black ditto
I 8 12.65 I
9.02
2.704
Rock cryftal
I 8 1.00 I
8.61
2.658
Green glaſs
1
7 15.38 1
8.26
2.620
Cornelian ftone -
Flint
I 7 1.21 I
7.73
2.568
1
6 19.63 I 7.53
2.542
Hard paving ftone
I
5 22.87
I
6.77
2.460
Live fulphur
I
I 2.40
I
2.52
2.000
Nitre
I O 1.08
I 1.59
1.900
Alabafter
о
o 19 18.74
I 1.35
1.875
Dry ivory
Brimftone
0 19 6.09 1 0.89
1.825
0 18 23.76 1 0.66
1.800
Alum
O 17 21.92 o 15.72.
1.714
The
Of the Specific Gravities of Bodies.
159
-
The Table concluded.
A cubic inch of
Ebony
Human blood
Amber
Cow's milk
Sea water
Pump water
Spring water
Diftilled water
Troy waght. Avoircup. Compa-
rative
oz. pw. gr. oz. drams. weight.
0 11 18.82 0 10.34
2.89 o
Ο ΙΙ
0 10 20.79
9.76
I 117
1.054
9.5÷
I 030
0 10 20.79
9 54
1.030
0 10 20.79 О
9.54
1.030
0 10 13.30 О
926
1.000
0 10 12.94
9.25
0 999
0 10 11.42 о
9.20
o 993
Red wine
O 10 11.42
9.20
0.993
Oil of amber
Ο ΙΟ
7.631 0
9.06
0.978
Proof ſpirits
O 9 19.73
8.62
0.931
Dry oak
9 18.00 0 8.56
0.925
Olive oil
О
9 15.17
o
8.45
0.913
Pureí pirits
9 3.27 O
8.02
с 866
Spirit ofturpentine o 9
2.70 0
7.99
0.804
Oil of turpentine O
8
8.53 0
7.33
0.772
Dry crabtree
。
8
1.69 07.08
0.765
<
00
5
2.04
4.46
0.482
Saffafras wood
Cork
2 12.77 0 2.21 0.240
Take away the decimal points from the num-
bers in the right-hand column, or (which is the
fame) multiply them by 1000, and they will
fhew how many avoirdupoife ounces are con-
tained in a cubic foot of each body.
The uſe of the table of fpecific gravities will How to
beſt appear by an example. Suppoſe a body to fiad out
be compounded of gold and filver, and it is re- the quan-
quired to find the quantity of each metal in tity of
the compound.
adultera-
tion in
Firſt find the fpecific gravity of the com- metals.
pound, by weighing it in air and in water, and
dividing its aerial weight by what it lofes there-
of in water, the quotient will fhew its fpecific
gravity,
160
Of the Specific Gravities of Bodies.
How to
tuous li.
gravity, or how many times it is heavier than
its bulk of water. Then, fubtract the fpecific
gravity of filver (found in the table) from that
of the compound, and the ſpecific gravity of the
compound from that of gold; the first remaineder
fhews the bulk of gold, and the latter the bulk
of filver, in the whole compound: and if theſe
remainders be multiplied by the refpective fpe-
cific gravities, the products will fhew the pro-
portion of weights of each metal in the body.
Example.
Suppoſe the ſpecific gravity of the compound-
ed body be 13, that of ſtandard filver, (by the
table) is 10.5, and that of gold 19.63: therefore
10.5 from 13, remains 2.5, the proportional
bulk of the gold; and 13 from 19.63, remains
6.63 the proportional bulk of filver in the com-
pound. Then, the firft remainder 2.5, multi-
plied by 19.63, the ſpecific gravity of gold,
produces 49.075 for the proportional weight of
gold; and the laft remainder 6.63 multiplied
by 10.5, the ſpecific gravity of filver produces
69.615 for the proportional weight of filver in
the whole body. So that for every 49.07 ounces
or pounds of gold, there are 69.6 pounds or
ounces of filver in the body.
Hence it is eaſy to know whether any fufpect-
ed metal be genuine,, or allayed, or counterfeit;
by finding how much it is heavier than its bulk
of water, and comparing the fame with the
table: if they agree, the metal is good; if they
differ, it is allayed or counterfeited.
A cubical inch of good brandy, rum, or other
try fpiri- proof fpirits, weighs 235.7 grains: therefore, if
a true inch cube of any metal weighs 235.7
grains lefs in fpirits than in air, it fhews the
fpirits are proof. If it lofes lefs of its aerial
quors.
weight
3
D
Of the Specific Gravities of Bodies.
161
weight in fpirits, they are above proof; if it lofes
more, they are under. For, the better the
fpirits are, they are the lighter; and the worſe,
the heavier. All bodies expand with heat and
contract with cold, but fome more and fome lefs
than others. And therefore the ſpecific gravities
of bodies are not precifely the fame in fummer
as in winter. It has been found, that a cubic
inch of good brandy is ten grains heavier in win-
ter than in fummer; as much fpirit of nitre, 20
grains; vinegar 6 grains, and fpring-water 3.
Hence it is moſt profitable to buy ſpirits in
winter, and fell them in fummer, fince they are
always bought and fold by meaſure. It has
been found, that 32 gallons of fpirits in winter
will make 33 in fummer.
The expanſion of all fluids is proportionable
to the degree of heat; that is, with a double or
triple heat a fluid will expand two or three times
as much.
Upon theſe principles depends the conftruc- The ther-
tion of the thermometer, in which the globe or mometer.
bulb, and part of the tube, are filled with a
fluid, which, when joined to the barometer, is
ſpirits of wine tinged, that it may be more eaſily
feen in the tube. But when thermometers are
made by themſelves, quickfilver is generally
uſed.
In the thermometer, a fcale is fitted to the
tube, to fhew the expanfion of the quickfilver,
and confequently the degree of heat. And, as
Fahrenheit's fcale is most in eſteem at preſent, I
fhall explain the conftruction and graduation of
thermometers according to that ſcale.
Firſt, Let the globe or bulb, and part of the
tube, be filled with a fluid; then immerfe the
bulb in water juſt freezing, or fnow juſt thaw-
ing;
162
Of the Specific Gravities of Bodies.
ing; and even with that part in the fcale where
the fluid then ſtands in the tube, place the num-
ber 32, to denote the freezing point: then put
the bulb under your arm-pit, when your body is
of a moderate degree of heat, ſo that it may
acquire the fame degree of heat with your ſkin,
and when the fluid has rifen as far as it can by
that heat, there place the number 97: then
divide the ſpace between thefe numbers into 65
equal parts, and continue thofe divifions both
above 97 and below 32, and number them ac-
cordingly.
This may be done in any part of the world;
for it is found that the freezing point is always
the fame in all places, and the heat of the human
body differs but very little; fo that the thermo-
meters made in this manner will agree with one
another; and the heat of feveral bodies will be
fhewn by them, and expreffed by the numbers
upon the ſcale, thus.
Air, in fevere cold weather, in our climate,
from 15 to 25. Air in winter, from 26 to 42.
Air in fpring and autumn, from 43 to 53. Air
at midfummer, from 65 to 68. Extreme heat
of the ſummer fun, from 86 to 100. Butter
juſt melting, 95. Alcohol boils with 174 or
175. Brandy with 190. Water 212. Oil of
turpentine 550. Tin melts with 408, and lead
with 540. Milk freezes about 30, vinegar 38,
and blood 27.
A body specifically lighter than a fluid will
fwim upon its furface, in fuch a manner, that a
quantity of the fluid equal in bulk with the
immerfed part of the body, will be as heavy as
the whole body. Hence, the lighter a fluid is,
the deeper a body will fink in it; upon which
depends
Of the Specific Gravities of Bodies.
163
depends the conftruction of the hydrometer or
water-poife.
may be
From this we can eaſily find the weight of a How the
ſhip, or any other body that floats in water. weight of
For, if we multiply the number of cubic feet a hip
which are under the furface, by 62.5, the number eftimated.
of pounds in one cubic foot of freſh water; or by
64.4, the number of pounds in a cubic foot of
falt water; the product will be the weight of
the ſhip, and all that is in it. For, fince it is
the weight of the ſhip that diſplaces the water,
it muſt continue to fink until it has removed as
much water as is equal to it in weight; and
therefore the part immerfed must be equal in
bulk to fuch a portion of the water as is equal
to the weight of the whole fhip.
To prove this by experiment, let a ball of
fome light wood, fuch as fir or pear-tree, be
put into water contained in a glafs veffel; and
let the veffel be put into a ſcale at one end of a
balance, and counterpoiſed by weights in the
oppofite fcale: then, marking the height of the
water in the veffel, take out the ball; and fill
up the veffel with water to the fame height that
it ſtood at when the ball was in it; and the fame
weight will counterpoife it as before.
From the veffel's being filled up to the fame
height at which the water ſtood when the ball
was in it, it is evident that the quantity poured
in is equal in magnitude to the immerfed part
of the ball; and from the fame weight coun-
terpoiling, it is plain that the water poured in,
is equal in weight to the whole ball.
In troy weight, 24 grains make a penny-
weight, 20 pennyweights make an ounce, and
12 ounces a pound. In avoirdupoiſe weight,
16 drams make an ounce, and 16 ounces a
M
pound.
164
Of the Specific Gravities of Bodies.
pound. The troy pound contains 5760 grains,
and the avoirdupoife pound 7000; and hence,
the avoirdupoife dram weighs 27.34375 grains,
and the avoirdupoife ounce 437.5.
Becauſe it is often of uſe to know how much
any given quantity of goods in troy weight do
make in avoirdupoife weight, and the reverfe;
we fhall here annex two tables for converting
thefe weights into one another. Thofe from
page 135 to page 146 are near enough for com-
mon hydraulic purpoſes; but the two following
are better, where accuracy is required in com-
paring the weights with one another and I
find, by trial, that 175 troy ounces are preciſely
equal to 192 avoirdupoife ounces, and 175 troy
pounds are equal to 144 avoirdupoife. And
although there are ſeveral leffer integral num-
bers, which come very near to agree together,
yet I have found none lefs than the above to
agree exactly. Indeed 41 troy ounces are for
nearly equal to 45 avoirdupcife ounces, that the
latter contains only 7 grains more than the for-
mer: and 45 troy pounds weigh only 7% drams
more than 37 avoirdupoife.
I
2
I have lately made a fcale for comparing thefe
weights with one another, and fhewing the
weight of pump-water, proof fpirits, pure fpi-
rits, and guinea gold, taken in cubic inches,
to any quantity lefs than a pound, both in troy
and avoirdupoife; only by fliding one fide of a
fquare along the icale, and the other fide crof
fing it.
A Table
Troy Weight reduced into Avoirdupoife:
165
A Table for reducing Troy weight into Avoirdupoiſe weight.
Avoirdupoife.
Avoir.
Troy weight.
Troy weight.
Drams.
lb. oz. drams.
Pounds-4000 3291 6-13.68 Penny wt. 19 16.67
3000 2528 9 2.26
2000 1645 11 6.84
1000
822 13 11.42
900 740 9
800 658 4
18 15.79
17 14.92
16
14.04
2.28
15 13.1
13.16
9.14
14
12.29
700 576 0
600 493 11
500 411 6 13.71
0.00
13
11.41
6.85
12
10.53
I I
9.65
400 329
2
4.57
10
8.78
300
246 13 11.42
9
7.90
200
164 9 2.28
8
7.02
100
82 4 9.15
6.14
90
74
0 13.62
6
5.27
80
65 13
4.11
5
4.39
70
57 9 9.60
60
49 5 15.08
50
41 2 4.57
432
3.51
2.63
1.75
40
30
20
10
32 14 10.05
24 10 15.54 Grains
16 7 5.03
8 3 10.52
I
0.88
9
7
6 7.85
~ ~ ~ ~
23
.84
22
.80
21
.77
20
.73
8
6
9
5.21
19
.69
5 12
2.56
18
.66
6
4 14 15.90
17
.62
5
4
I 13.25
16
.58
∞ N
4
3 4 10.60
15
•55
3
2 7 7.95
14
.51
2
I 10 5.30
13
•47
0 13 2.65
12
•44
Ounces
II
12 1.09
II
•40
10
10 15.54
IO
•36
8 26
9 13.99
8 12.43
7 10.88
6 9.32
9
я со
•33
8 .29
.26
.22
.18
4
5 7.77
4 6.22
4
3
3
4.66
3
.II
2 1
2
3.11
2
.07
I
1.55
1
.04
M 2
A Table
166
Avoirdupoiſe Weight reduced into Troy.
A Table for reducing Avoirdupoife weight into
Troy Weight.
Avoirdupoife Troy weight.
Weight. lb. oz. pw. gr.
Pounds 6000 7291 8 O
5000 6076 4 13
4 13 8
4000/4861 1 6 16
3000 3645 10 O
Avoird.
11 16 23.50
Troy Weight.
weight.
lb. qz. pw. gr.
o Ounces 151
I 13 10.50
141
0 15 5
13
12
10 18 18
2000 2430
6
13
8
II
IO
0 12.50
1000 1215 3
3
616
10
9
2 7
900 1093 9
O
O
9
8
4
1.50
800 972 2 13
8
7
5 20
700 850 8
8
6 16
7
6
7 14.50
600 729 2 O O
6
5 9 9
500 607 7 13 8
5
4 11
3.50
400 486
6 16
4
3 12 22
300 36+ 7 70 O
3
2 14 16.50
200 243 0 13
8
2
100
121 6 6
16
I
90 109 4 10 o Drams 15
1 16 11
O 18 5.50
17 2.10
15 22.76
80
97
2 13
8
14
70
85
0 16 16
13
14 19.42
60
72 11 0 O
12
50
60 9 3 8
13 15.08
11
12 12.74
40
48
7 6 16
10
II
9.40
NW
30
36
5 10 O
10
6.06
20
24
3 13
8
9
2.72
10
12 1 16 16
7
8 23.38
9
10 II 5 о
7 20.04
8
9
8 13 8
5
6 16.79
76
8 6 1 16
4
5 13.36
7 3 10 O
3
3 10.02
5
6
O 18
18 8
2
4
4 10 6 16
3
3 7 15
2
2
5 3
8
I
I 2 11 16
4
film wfmplus 1 N
2 6.68
I '3.34
O 20.51
13.67
6.83
The
Avoirdupoife Weight reduced into Troy.
167
The two following examples will be ſufficient
to explain theſe two tables, and fhew their agree
ment.
Ex. I. In 6835 Troy pounds 6 ounces 9 pennyl
weights 6 grains, Qu. How much Avoirdupoife
weight? (See page 165.)
Avoirdupoife.
lb. oz. drams.
4000
3291 6 13.68
2000
1645 11 6.84
Pounds
800
658 4 9.14
troy-
20
16 7 5.03
ΙΟ
8
3 10.52
4
I 13.25
oż. 6
6 9.32
pw. 9
gr. 6
7.90
.22
Anſwer.
| 5624 10 11 90
Ex. II. In 5624 pounds 10 ounces 12 drams
Avoirdupoife, Qu. How much Troy weight?
(See page 166.)
Troy.
lb.
oz. pw. gr.
5000 6076
4 13 8
Pounds
600
729 2
оо
avoird.
20
24 3
13 8
4
4 10
6 16
02. 10
9
2 2 7
dr.
12
13 15.08
Anfwer.
| 6835 6
9
6.08
M 3
LECT.
t
168
Of Pneumatics.
The pro-
air.
TH
LECT. VI.
Of Pneumatics.
HIS fcience treats of the nature, weight,
preffure, and ſpring of the air, and the
effects ariſing therefrom.
The air is that thin tranfparent fluid body in
perties of which we live and breathe. It encompaffes the
whole earth to a confiderable height; and, to-
gether with the clouds and vapours that float in
it, it is called the atmoſphere. The air is juftly
reckoned among the number of fluids, becauſe
it has all the properties by which a fluid is dif
tinguiſhed. For, it yields to the leaſt force
impreffed, its parts are easily moved among one
another, it preffes according to its perpendicu-
lar height, and its preffure is every way equal.
That the air is a fluid, confifting of fuch
particles as have no coheſion betwixt them, but
eaſily glide over one another, and yield to the
ſlighteſt impreſſion, appears from that eaſe and
freedom with which animals breathe in it, and
move through it without any difficulty or fen-
fible refiftance.
But it differs from all other fluids in the four
following particulars. 1. It can be compreffed
into a much lefs fpace than what it naturally
poffeffeth, which no other fluid can. 2. It cannot
be congealed or fixed, as other fluids may. 3. It
is of a different density in every part, upward
from the earth's furface, decreafing in its weight,
bulk for bulk, the higher it riſes; and therefore
muſt alſo decreaſe in denfity. 4. It is of an
elaftic
Of Pneumatics.
169
elaftic or fpringy nature, and the force of its
fpring is equal to its weight.
That air is a body, is evident from its ex-
cluding all other bodies out of the ſpace it pof-
feffes for, if a glafs jar be plunged with its
mouth downward into a veffel of water, there
will but very little water get into the jar, becauſe
the air of which it is full keeps the water out.
:
As air is a body, it muſt needs have gravity
or weight and that it is weighty, is demon-
ftrated by experiment. For, let the air be
taken out of a veffel by means of the air-pump,
then, having weighed the veffel, let in the air
again, and upon weighing it when re-filled with
air, it will be found confiderably heavier. Thus,
a bottle that holds a wine quart, being emptied
of air and weighed, is found to be about 16
grains lighter than when the air is let into it
again; which fhews that a quart of air weighs
16 grains. But a quart of water weighs 14621
grains; this divided by 16, quotes 914 in round
numbers; which fhews, that water is 914 times.
as heavy as air near the furface of the earth.
As the air rifes above the earth's furface, it
grows rarer, and confequently lighter, bulk for
bulk. For, becauſe it is of an elaftic or fpringy
nature, and its lowermoft parts are preffed with
the weight of all that is above them, it is plain
that the air must be more denfe or compact at
the earth's furface, than at any height above it;
and gradually rarer the higher up. For, the
density of the air is always as the force that.
compreffeth it; and therefore, the air towards
the upper parts of the atmoſphere being lefs
preffed than that which is near the earth, it will
expand itſelf, and thereby become thinner than
at the earth's furface.
Կ
M 4
Dr
170
Of Pneumatics.
Dr. Cotes has demonftrated, that if altitudes
in the air be taken in arithmetical proportion,
the rarity of the air will be in geometrical pro-
portion. For inftance,
୮
>?
1 4
21
~ ~ ~ + +
28
35
42
Miles above the furface of the earth, the air is
٢٠
47
16
64
256
times thinner and lighter than at the earth's furface.
The To-
At the altitude of
49
56
63
70
77
84
91
98
105
I 12
119
126
133
[140]
1024
4096
16384
65536
262144
1048576
4194304
16777216
67108864
268435456
1073741824
4294967296
17179869184
68719476736
274877906944
1099511627776)
And hence it is eafy to prove by calculation,
that a cubic inch of fuch air as we breathe,
would be fo much rarefied at the altitude of 500
miles, that it would fill a hollow fphere equal in
diameter to the orbit of Saturn.
The weight or preffure of the air is exactly
determined by the following experiment.
Take a glafs tube about three feet long, and
ricellian open at one end; fill it with quickfilver, and
experi- putting your finger upon the open end, turn
that end downward, and immerfe it into a fmall
ment.
veffel
Of Pneumatics.
171
veffel of quickfilver, without letting in any air:
then take away your finger; and the quickfilver
will remain fufpended in the tube 29 inches
above its furface in the veffel; ſometimes more,
and at other times lefs, as the weight of the
air is varied by winds and other caufes. That
the quickfilver is kept up in the tube by the
preffure of the atmoſphere upon that in the ba-
fon, is evident; for, if the bafon and tube be
put under a glaſs, and the air be then taken out
of the glafs, all the quickfilver in the tube will
fall down into the bafon; and if the air be let in
again, the quickfilver will rife to the fame
height as before. Therefore the air's preffure
on the furface of the earth, is equal to the
weight of 29 inches depth of quickſilver all
over the earth's furface, at a mean rate.
A fquare column of quickfilver, 29 inches
high, and one inch thick, weighs juſt 15
pounds, which is equal to the preffure of air
upon every ſquare inch of the earth's furface;
and 144 times as much, or 2160 pounds, upon
every fquare foot; becauſe a fquare foot con-
tains 144 fquare inches. At this rate, a middle-
fized man, whoſe ſurface may be about 14 ſquare
feet, fuftains a preffure of 30240 pounds,
when the air is of a mean gravity: a preffure
which would be infupportable, and even fatal
to us, were it not equal on every part, and
counterbalanced by the fpring of the air within
us, which is diffufed through the whole body;
and re-acts with an equal force againit the out-
ward preffure.
Now, fince the earth's furface contains (in
round numbers) 200,000,000 fquare miles,
and every ſquare mile 27,878,400 ſquare feet,
there must be 5,575,680,000,000,000 fquare
feet
172
Of Pneumatics.
The baro-
meter.
feet on the earth's furface; which multiplied by
2160 pounds (the preffure on each fquare foot)
gives 12,043,463,800,000,000,000 pounds for
the preffure or weight of the whole atmo-
ſphere.
When the end of a pipe is immerſed in water,
and the air is taken out of the pipe, the water
will rife in it to the height of 33 feet above
the furface of the water in which it is immerfed;
but will go no higher: for it is found, that a
common pump will draw water no higher than
33
feet above the furface of the well: and unleſs
the bucket goes within that diſtance from the
well, the water will never get above it. Now,
as it is the preffure of the atmoſphere, on the
furface of the water in the well, that caufes the
water to afcend in the pump, and follow the
piſton or bucket, when the air above it is lifted
up; it is evident, that a column of water 33
feet high, is equal in weight to a column of
quickfilver of the fame diameter, 29 inches
high; and to as thick a column of air, reach-
ing from the earth's furface to the top of the
atmoſphere.
2
In ferene calm weather, the air has weight
enough to fupport a column of quickfilver 31
inches high; but in tempestuous ftormy wea-
ther, not above 28 inches. The quickfilver,
thus fupported in a glaſs tube, is found to be a
nice counterbalance to the weight or preffure of
the air, and to fhew its alterations at different
times. And being now generally used to de-
note the changes in the weight of the air, and
of the weather confequent upon them, it is
called the barometer, or weather-glafs.
The preffure of the air being equal on all
fades of a body expofed to it, the fofteft bodies
fuſtain
Of Pneumatics.
173
fuftain this preffure without fuffering any change
in their figure; and fo do the moſt brittle bodies
without being broke.
The air is rarefied, or made to fwell with
heat; and of this property, wind is a neceffary The caufe
confequence. For, when any part of the air is of winds.
heated by the fun, or otherwife, it will fwell,
and thereby affect the adjacent air: and fo, by
various degrees of heat in different places, there
will arife various winds.
When the air is much heated, it will afcend
towards the upper part of the atmoſphere, and
the adjacent air will rufh in to fupply its place;
and therefore, there will be a ftream or current
of air from all parts towards the place where
the heat is. And hence we ſee the reaſon why
the air ruſhes with fuch force into a glaſs-houſe,
or towards any place where a great fire is made.
And alſo, why fmoke is carried up a chimney,
and why the air rufhes in at the key-hole of the
door, or any fmall chink, when there is a fire
in the room. So we may take it in general, that
the air will prefs towards that part of the world
where it is moſt heated.
winds.
Upon this principle, we can eafily account for The
the trade-winds, which blow conſtantly from eaſt trade-
to weſt about the equator. For, when the fun
fhines perpendicularly on any part of the earth,
it will heat the air very much in that part, which
air will therefore rife upward, and when the fun
withdraws, the adjacent air will rush in to fill its
place; and confequently will caufe a ſtream or
current of air from all parts towards that which
is moſt heated by the fun. But as the fun, with
reſpect to the earth, moves from east to west,
the common courfe of the air will be that way
too; continually preffing after the fun and
therefore,
1
174
Of Pneumatics.
The mon
forns.
therefore, at the equator, where the fun fhines
ftrongly, there will be a continual wind from
the east; but, on the north fide, it will incline.
a little to the north, and on the fouth-fide, to
the fouth.
This general courfe of the wind about the
equator, is changed in feveral places, and
upon ſeveral accounts; as, 1. By exhalations
that rife out of the earth at certain times, and
from certain places; in earthquakes, and from
volcanos. 2. By the falling of great quanti-
ties of rain, caufing thereby a fudden conden-
ſation or contraction of the air.
3. By burn-
ing fands, that often retain the folar heat to a
degree incredible to thoſe who have not felt it,
cauſing a more than ordinary rarefaction of the
air contiguous to them. 4. By high moun.
tains, which alter the direction of the winds.
in ftriking againſt them. 5. By the declina-
tion of the fun towards the north or fouth,
heating the air on the north or fouth fide of the
equator.
To theſe and fuch like caufes is owing, 1. The
irregularity and uncertainty of winds in climates
diftant from the equator, as in moſt parts of
Europe. 2. Thofe periodical winds, called
monfoons, which in the Indian ſeas blow half a
year one way, and the other half another.
3. Thoſe winds which, on the coaft of Guiney,
and on the weſtern coafts of America, blow al-
ways from west to east. 4. The fea-breezes,
which, in hot countries, blow generally from
fea to land, in the day-time; and the land-
breezes, which blow in the night; and, in fhort,
all thoſe ſtorms, hurricanes, whirlwinds, and
irregularities, which happen at different times.
and places.
All
Of Pneumatics.
175
All common air is impregnated with a cer Theivi
tain kind of vivifying Spirit or quality, which is fying ipi-
neceffary to continue the lives of animals: and rit in a
this, in a gallon of air, is fufficient for one man
during the ſpace of a minute, and not much
longer.
This ſpirit in air is deftroyed by paffing
through the lungs of animals: and hence it is,
that an animal dies foon, after being put under
a veffel which admits no fresh air to come to it.
This ſpirit is alſo in the air which is in water;
for fiſh die when they are excluded from freſh
air, as in a pond that is clofely frozen over.
And the little eggs of infects, ſtopped up in a
glafs, do not produce their young, though
affifted by a kindly warmth. The feeds alfo of
plants mixed with good earth, and inclofed in
a glafs, will not grow.
This enlivening quality in air, is alfo de-
ſtroyed by the air's paffing through fire; parti-
cularly charcoal fire, or the flame of fulphur.
Hence, fmoking chimneys muſt be very un-
wholeſome, eſpecially if the rooms they are in
be fmall and clofe.
Air is alfo vitiated, by remaining cloſely
pent up in any place for a confiderable time;
or perhaps, by being mixed with malignant
ſteams and particles flowing from the neighbour-
ing bodies or laftly, by the corruption of the
vivifying fpirit; as in the holds of fhips, in
oil-cifterns, or wine-cellars, which have been
ſhut for a confiderable time. The air in any of
them is fometimes fo much vitiated, as to be im-
mediate death to any animal that comes into it.
Air that has loft its vivifying fpirit, is called Damps.
damp, not only becaufe it is filled with humid
or moiſt vapours, but becauſe it deadens fire,
extin-
176
Of Pneumatics:
Fermenta-
tions.
The
extinguiſhes flame, and deftroys life.
dreadful effects of damps are fufficiently known
to fuch as work in mines.
If part of the vivifying ſpirit of air in any
country begins to putrefy, the inhabitants of that
country will be ſubject to an epidemical diſeaſe,
which will continue until the putrefaction is
over. And as the putrefying fpirit occafions
the diſeaſe, ſo if the difeafed body contributes
towards the putrefying of the air, then the dif-
eafe will not only be epidemical, but peftilential
and contagious.
The atmoſphere is the common receptacle of
all the effluvia or vapours arifing from different
bodies; of the fteams and ſmoke of things burnt
or melted; the fogs or vapours proceeding from
damp watery places; and of the effluvia from
fulphureous, nitrous, acid, and alkaline bodies.
In fhort, whatever may be called volatile, rifes
in the air to greater or lefs heights, according
to its ſpecific gravity.
When the effluvia, which arife from acid and
alkaline bodies, meet each other in the air,
there will be a strong conflict or fermentation be-
tween them; which will fometimes be fo great,
as to produce a fire; then if the effluvia be
combustible, the fire will run from one part
to another, juſt as the inflammable matter hap-
pens to lie.
Any one may be convinced of this, by mixing
an acid and an alkaline fluid together, as the
ſpirit of nitre and oil of cloves; upon the doing
of which, a fudden ferment, with a fine flame,
will arife; and if the ingredients be very pure
and ſtrong, there will be a fudden exploſion.
Thunder Whoever confiders the effects of fermenta-
and light- tion, cannot be at a lofs to account for the
ning.
dreadful
Of Pneumatics:
177
dreadful effects of thunder and lightning: for the
effluvia of fulphureous and nitrous bodies, and
others that may rife into the atmoſphere, will
ferment with each other, and take fire very often
of themſelves; fometimes by the affiftance of the
fun's heat.
If the inflammable matter be thin and light,
it will riſe to the upper part of the atmoſphere,
where it will flash without doing any harm:
but if it be denfe, it will lie near the fur-
face of the earth, where taking fire, it will ex-
plode with a furprising force; and by its heat
rarefy and drive away the air, kill men and
cattle, ſplit trees, walls, rocks, &c. and be ac-
companied with terrible claps of thunder.
The heat of lightning appears to be quite
different from that of other fires; for it has
been known to run through wood, leather,
cloth, &c. without hurting them, while it has
broken and melted iron, fteel, filver, gold, and
other hard bodies. Thus it has melted or burnt
afunder a ſword, without hurting the fcabbard,
and money in a man's pocket, without hurting
his cloaths the reaſon of this feems to be, that
the particles of that fire are fo fine, as to paſs
through ſoft looſe bodies without diffolving
them; whilst they ſpend their whole force upon
the hard ones.
It is remarkable, that knives and forks which
have been ſtruck with lightning have a very
ftrong magnetical virtue for ſeveral years after;
and I have heard that lightning ftriking upon
the mariner's compafs, will fometimes turn it
round; and often make it ftand the contrary
way; or with the north-pole towards the fouth.
Much of the fame kind with lightning, are Fire-
thofe exploſions, called fulminating or fire-damps, damps.
which
178
Of Pneumatics.
Earth-
quakes,
which fometimes happen in mines; and are
occafioned by fulphureous and nitrous, or ra-
ther oleaginous particles, rifing from the mine,
and mixing with the air, where they will take
fire by the lights which the workmen are obliged
to make uſe of. The fire being kindled will
run from one part of the mine to another, like
a train of gunpowder, as the combuftible matter
happens to lie. And as the elafticity of the air
is increaſed by heat, that in the mine will con-
fequently fwell very much, and fo, for want of
room, will explode with a greater or lefs degree
of force, according to the denfity of the com-
buftible vapours. It is fometimes fo ftrong, as
to blow up the mine; and at other times fo
weak, that when it has taken fire at the flame
of a candle, it is eafily blown out.
Air that will take fire at the flame of a candle
may be produced thus. Having exhaufted a
receiver of the air pump, let the air run into it
through the flame of the oil of turpentine; then
remove the cover of the receiver, and holding a
candle to that air, it will take fire, and burn
quicker or flower, according to the density of
the oleaginous vapour.
When fuch combustible matter, as is above-
mentioned, kindles in the bowels of the earth,
where there is little or no vent, it produces
earthquakes, and violent ftorms or hurricanes of
wind when it breaks forth into the air.
An artificial earthquake may be made thus.
Take 10 or 15 pounds of fulphur, and as much
of the filings of iron, and knead them with
common water into the confiftency of a paſte :
this being buried in the ground, will, in 8 or
10 hours time, buft out in flames, and caufe
1
the
PLATE XIV.
2
Fig. 1.
P
P
1
¶. Ferguſon delin.
Ꮐ
Fig. 2.
Da
G
B
G
D
I
Fig.5.
H
B
K
N
IMIGAMU
B
OTHENB
F
F
I
K
A
Fig.13
Fig. 7.
GRE
FOH
D
B
L
C
Fig.3.
Fig.15.
Fig.14.
C A
Fw.6.
B
A
B
Fig. 11
T
H
H
Fig. 8.
A
C
Fig.10.
F
Fig. 4.
A
E
F
D
Fig.9.
B
B
Fig.12.
E
A
D
B
G
to fenty.
Of the Air-Pump.
179
the earth to tremble all around to a confiderable
diſtance.
From this experiment we have a very natural.
account of the fires of mount Etna, Vefuvius,
and other volcanos, they being probably fet
or fire at first by the mixture of fuch metalline
and fulphureous particles.
The air pump being conftructed the fame way PlateXIV.
as the water-pump, whoever underftands the Fig. 1.
one, will be at no lofs to underſtand the other.
Having put a wet leather on the plate LL The air-
of the air-pump, place the glafs receiver Mpump.
upon the leather, fo that the hole i in the plate
may be within the glafs. Then, turning the
handle F backward and forward, the air will be
pumped out of the receiver; which will then
be held down to the plate by the preffure of the
external air, or atmoſphere. For, as the handle
F(Fig. 2.) is turned backwards, it raiſes the
pifton de in the barrel BK, by means of the
wheel E and rack Dd: and, as the pifton is lea-
thered fo tight as to fit the barrel exactly, no
air can get between the pifton and barrel; and
therefore, all the air above d in the barrel is
lifted up towards B, and a vacuum is made in
the barrel from b to e; upon which, part of the
air in the receiver M (Fig. 1.) by its fpring,
rushes through the hole i, in the brafs plate
LL, along the pipe GCG (which communi-
cates with both barrels by the hollow trunk IHK
(Fig. 2.) and pushing up the valve b, enters
into the vacant place be of the barrel BK. For,
wherever the refiftance or preffure is taken off,
the air will run to that place, if it can find a
paffage. Then, if the handle F be turned
forward, the pifton de will be depreffed in the
barrel; and, as the air which had got into the
barrel
N
180
Of the Air-Pump.
barrel cannot be pushed back through the valve
b, it will afcend through a hole in the pifton,
and escape through a valve at d; and be hin-
dered by that valve from returning into the bar-
rel, when the pifton is again raiſed. At the
next raifing of the pifton, a vacuum is again
made in the fame manner as before, between b
and e; upon which, more of the air that was
left in the receiver M, gets out thence by its
fpring, and runs into the barrel B K, through
the valve B. The fame thing is to be under-
ftood with regard to the other barrel AI; and
as the handle F is turned backwards and for-
wards, it alternately raiſes and depreffes the pif-
tons in their barrels; always raiſing one whilft
it depreffes the other. And, as there is a va-
cuum made in each barrel when its pifton is
raiſed, the particles of air in the receiver M
push out another by their ſpring or elafticity,
through the hole i, and pipe GG into the bar-
rels; until at laſt the air in the receiver comes to
be fo much dilated, and its ſpring fo far weak-
ened, that it can no longer get through the
valves; and then no more can be taken out.
Hence, there is no fuch thing as making a per-
fect vacuum in the receiver; for the quantity of
air taken out at any one ſtroke, will always be as
the denfity thereof in the receiver and there-
fore it is impoffible to take it all out, becauſe,
fuppofing the receiver and barrels of equal ca-
pacity, there will be always as much left as was
taken out at the laſt turn of the handle.
There is a cock k below the pump plate,
which being turned, lets the air into the receiver
again; and then the receiver becomes loofe, and
may be taken off the plate. The barrels are
fixed to the frame Eee by two fcrew.nuts ff,
which
Of the Air-Pump.
181
which prefs down the top piece E upon the bar-
rels and the hollow trunk H (in Fig. 2.) is
covered by a box, as G H in Fig. 1.
:
There is a glaſs tube Immmn open at both
ends, and about 34 inches long; the upper end
communicating with the hole in the pump-plate,
and the lower end immerfed in quickfilver at n
in the veffel N. To this tube is fitted a wooden
ruler mm, called the gage, which is divided into
inches and parts of an inch, from the bottom at
n (where it is even with the furface of the quick-
filver) and continued up to the top, a little
below 7, to 30 or 31 inches.
As the air is pumped out of the receiver M, it is
likewife pumped out of the glafs tube Im n, be-
cauſe that tube opens into the receiver through
the pump plate; and as the tube is gradually
emptied of air, the quck filver in the veffel N is
forced up into the tube by the preffure of the
atmoſphere. And if the receiver could be per-
fectly exhauſted of air, the quickfilver would
ſtand as high in the tube as it does at that time
in the barometer for it is fupported by the
fame power or weight of the atmoſphere in
both.
The quantity of air exhaufted out of the re-
ceiver on each turn of the handle, is always pro-
portionable to the afcent of the quickfilver on
that turn; and the quantity of air remaining in
the receiver, is proportionable to the defect of
the height of the quickfilver in the gage, from
what it is at that time in the barometer.
I ſhall now give an account of the experiments
made with the air-pump in my lectures; fhew-
ing the reſiſtance, weight, and elaſticity of the
air.
N 2
1. To
182
Of the Air-Pump.
Fig. 3.
Fig. 1.
I. To shew the refiftance of the air.
1. There is a little machine, confifting of two
mills, a and b, which are of equal weights, in-
dependent of each other, and turn equally free
on their axes in the frame. Each mill has four
thin arms or fails, fixed into the axis: thofe of
the mill a have their planes at right angles to its
axis, and thofe of b have their planes parallel to
it. Therefore, as the mill a turns round in com-
mon air, it is but little refifted thereby, becauſe
it's fails cut the air with their thin edges: but
the mill b is much refifted, becauſe the broad
fides of it's fails move against the air when it
turns round. In each axle is a pin near the
middle of the frame, which goes quite through
the axle, and ſtands out a little on each fide of it:
upon thefe pins, the flider d may be made to bear,
and fo hinder the mills from going, when the
ſtrong ſpring c is fet on bend againſt the oppofite
ends of the pins.
+
Having fet this machine upon the pump.
plate LL (Fig. 1.) draw up the flider d to the
pins on one fide, and fet the fpring cat bend
upon the oppofite ends of the pins: then push
down the flider d, and the ſpring acting equally
ftrong upon each mill, will fet them both a going
with equal forces and velocities: but the mill a
will run much longer than the mill b, becauſe the
air makes much lefs refiftance againſt the edges
of its fails, than againft the fides of the fails
of b.
Draw up the flider again, and fet the ſpring
upon the pins as before; then cover the ma-
chine with the receiver M upon the pump-
plate, and having exhauſted the receiver of air,
puſh
Of the Air-Pump.
183
puſh down the wire PP (through the coller of
leathers in the neck q) upon the flider; which
will difengage it from the pins, and allow the
mills to turn round by the impulfe of the ſpring:
and as there is no air in the receiver to make any
fenfible reſiſtance againſt them, they will both
move a confiderable time longer than they did
in the open air; and the moment that one ftops,
the other will do fo too. This fhews that air
refifts bodies in motion, and that equal bodies
meet with different degrees of reſiſtance, accord-
ing as they prefent greater or lefs furfaces to the
air, in the planes of their motions.
2. Take off the receiver M, and the mills; Fig. 4
and having put the guinea a and feather & upon
the brass flap c, turn up the flap, and fhut it into
the notch d. Then, putting a wet leather over
the top of the tall receiver AB(it being open both
at top and battom) cover it with the plate C,
from which the guinea and feather tongs ed will
then hang within the receiver. This done, pump
the air out of the receiver; and then draw up
the wire ƒ a little, which by a fquare piece on its
lower end will open the tongs ed; and the flap
falling down as at c, the guinea and feather will
defcend with equal velocities in the receiver;
and both will fall upon the pump-plate at the
ſame inſtant. N. B. In this experiment, the
obſervers ought not to look at the top, but at the
bottom of the receiver; in order to fee the gui-
nea and feather fall upon the plate: otherwife,
on account of the quicknefs of their motion, they
will efcape the fight of the beholders.
N 3
II. To
1
184
Of the Air-Pump.
1
11. To fhew the weight of the air.
1. Having fitted a brafs cap, with a valve
tied over it, to the mouth of a thin bottle or
Florence flask, whofe contents are exactly known,
fcrew the neck of this cap into the hole i of the
pump-plate: then, having exhauſted the air out
of the flafk, and taken it off from the pump, let
it be fufpended at one end of a balance, and nicely
counterpoiſed by weights in the fcale at the other
end: this done, raiſe up the valve with a pin, and
the air will rush into the flafk with an audible
noife during which time, the flafk will defcend,
and pull down that end of the beam. When the
noiſe is over, put as many grains into the ſcale at
the other end as will reftore the equilibrium;
and they will fhew exactly the weight of the
quantity of air which has got into the flaſk, and
filled it. If the flaſk holds an exact quart, it
will be found, that 16 grains will reftore the
equipoife of the balance, when the quickfilver
ftands at 29 inches in the barometer: which
fhews, that when the air is at a mean rate of den-
fity, a quart of it weighs 16 grains it weighs
more when the quickfilver ftands higher; and
lefs when it ftands lower.
2. Place the ſmall receiver O (Fig. 1.) over the
hole i in the pump-plate, and upon exhaufting
the air, the receiver will be fixed down to the
plate by the preffure of the air on its outfide,
which is left to act alone, without any air in the
receiver to act againſt it: and this preffure will
be equal to as many times 15 pounds, as there
are fquare inches in that part of the plate which
the receiver covers; which will hold down the
receiver ſo faſt, that it cannot be got off, until
5
the
Of the Air-Pump.
185
the air be let into it by turning the cock k; and
then it becomes looſe.
3. Set the little glafs A B (which is open at Fig. 5.
both ends) over the hole i upon the pump-plate
LL, and put your hand cloſe upon the top of it
at B: then, upon exhauſting the air out of the
glafs, you will find your hand preffed down with
a great weight upon it: fo that you can hardly
releaſe it, until the air be re-admitted into the
glaſs by turning the cock k; which air, by act-
ing as ftrongly upward againſt the hand as the
external air acted in preffing it downward, will
releaſe the hand from its confinement.
4. Having tied a piece of wet bladder b over Fig. 6.
the open top of the glaſs A (which is alfo open at
bottom) fet it to dry, and then the bladder will
be tight like a drum. Then place the open end
A upon the pump-plate, over the hole i, and
begin to exhauft the air out of the glafs. As
the air is exhauſting, its fpring in the glass will
be weakened, and give way to the preffure of the
outward air on the bladder, which, as it is pref-
fed down, will put on a ſpherical concave figure,
which will grow deeper and deeper, until the
ftrength of the bladder be overcome by the
weight of the air; and then it will break with a
report as loud as that of a gun.-If a flat piece
of glaſs be laid upon the open top of this re-
ceiver, and joined to it by a flat ring of wet
leather between them; upon pumping the air
out of the receiver, the preffure of the outward
air upon the flat glaſs will break it all to
pieces.
5. Immerſe the neck c d of the hollow glafs Fig. 7:
ball eb in water, contained in the phial aa; then
fet it upon the pump-plate, and cover it and the
hole with the clofe receiver A; and then begin
N 4
to
186
Of the Air-Pump.
Fig. 8.
to pump out the air. As the air goes out of the
receiver by its fpring, it will alfo by the fame
means go out of the hollow ball eb, through the
neck dc, and rife up in bubbles to the furface of
the water in the phial; from whence it will make
its way, with the reft of the air in the receiver,
through the air-pipe GG and valves a and b, into
the open air. When it has done bubbling in
the phial, the ball is fufficiently exhaufted; and
then, upon turning the cock k, the air will get
into the receiver, and prefs fo upon the furface
of the water in the phial, as to force the water
up into the ball in a jet, through the neck cd;
and will fill the ball almoft full of water.
reaſon why the ball is not quite filled, is becauſe
all the air could not be taken out of it; and the
fmall quantity that was left in, and had expanded
itfelf fo as to fill the whole ball, is now condenfed
into the fame ftate as the outward air, and re-
mains in a fmall bubble at the top of the ball;
and fo keeps the water from filling that part of
the ball.
The
6. Pour fome quickfilver into the jar D, and
fet it on the pump-plate near the hole i; then
fet on the tall open receiver AB, fo as to be over
the jar and hole; and cover the receiver with the
brals plate C. Screw the open glaſs tube fg
(which has a braſs top on it at b) into the fyringe
H, and putting the tube through a hole in the
middle of the plate, fo as to immerse the lower
end of the tube e in the quickfilver at D, fcrew
the end of the fyringe into the plate. This
done, draw up the pifton in the fyringe by the
ring I, which will make a vacuum in the fyringe,
below the piſton; and as the upper end of the
tube opens into the fyringe, the air will be di-
lated in the tube, becauſe part of it, by its ſpring,
gets
Of the Air-Pump.
187
gets up into the fyringe; and the ſpring of the
un-dilated air in the receiver acting upon the
furface of the quickfilver in the jar, will force
part of it up into the tube: for the quickfilver
will follow the pifton in the fyringe, in the fame
way, and for the fame reaſon, that water follows
the piſton of a common pump when it is raiſed
in the pump-barrel; and this, according to fome,
is done by fuction. But to refute that erroneous
notion, let the air be pumped out of the receiver
AB, and then all the quickfilver in the tube will
fall down by its own weight into the jar; and can-
not be again raiſed one hair's breadth in the tube
by working the fyringe: which fhews that fuc-
tion had no hand in raifing the quickfilver; and,
to prove that it is done by preffure, let the air
into the receiver by the cock k (Fig. 1.) and its
action upon the furface of the quickfilver in the
jar will raiſe it up into the tube, although the
pifton of the fyringe continues motionleis.-If
the tube be about 32 or 33 inches high, the
quickfilver will rife in it very near as high as it
ftands at that time in the barometer. And, if
the fyringe has a ſmall hole, as m, near the top
of it, and the piſton be drawn up above that hole,
the air will ruſh through the hole into the fy-
ringe and tube, and the quickfilver will imme-
diately fall down into the jar. If this part of the
apparatus be air-tight, the quickfilver may be
pumped up into the tube to the fame height that
it ftands in the barometer; but it will go no
higher, becauſe then the weight of the column in
the tube is the fame as the weight of a column of
air of the fame thickneſs with the quickfilver,
and reaching from the earth to the top of the
atmoſphere.
7. Having
183
Of the Air-Pump.
Fig. 9.
7. Having placed the jar A, with fome quick-
filver in it, on the pump-plate, as in the laſt
experiment, cover it with the receiver B; then
push the open end of the glass tube de through
the collar of leathers in the braſs neck C (which
it fits fo as to be air-tight) almoft down to the
quickfilver in the jar. Then exhauſt the air
out of the receiver, and it will alfo come out of
the tube, becauſe the tube is cloſe at top. When
the gauge mm fhews that the receiver is well
exhauſted, push down the tube, fo as to immerfe
its lower end into the quickfilver in the jar.
Now, although the tube be exhaufted of air,
none of the quickfilver will rife into it, becauſe
there is no air left in the receiver to preſs upon
its ſurface in the jar. But let the air into the
receiver by the cock k, and the quickfilver will
immediately riſe in the tube; and ſtand as high
in it, as it was pumped up in the laft experi-
ment.
Both theſe experiments fhew, that the quick-
filver is fupported in the barometer by the pref
fure of the air on its ſurface in the box, in which
the open end of the tube is placed. And that
the more denfe and heavy the air is, the higher
does the quickfilver rife; and, on the contrary,
the thinner and lighter the air is, the more will
the quicksilver fall. For if the handle F be
turned ever fo little, it takes fome air out of the
receiver, by raiſing one or other of the piſtons in
its barrel; and confequently, that which remains
in the receiver is fo much the rarer, and has fo
much the lefs fpring and weight; and thereupon,
the quickfilver falls a little in the tube: but
upon turning the cock, and re-admitting the air
into the receiver, it becomes as weighty as be-
fore, and the quickfilver rifes again to the fame
height.
|
Of the Air-Pump.
189
height. Thns we fee the reafon why the quick-
filver in the barometer falls before rain or fnow,
and rifes before fair weather; for, in the former
cafe, the air is too thin and light to bear up the
vapours, and in the latter, too denſe and heavy
to ler them fall.
N. B. In all mercurial experiments with the
air-pump, a ſhort pipe muſt be fcrewed into the
hole i, fo as to rife about an inch above the plate,
to prevent the quickfilver from getting into the
air-pipe and barrels, in cafe any of it fhould be
accidentally ſpilt over the jar: for if it once gets
into the pipes or barrels, it fpoils them, by
loofening the folder, and corroding the braſs.
8. Take the tube out of the receiver, and put
one end of a bit of dry hazel branch, about an
inch long, tight into the hole, and the other end
tight into a hole quite through the bottom of a
fmall wooden cup: then pour fome quickſilver
into the cup, and exhauſt the receiver of air, and
the preffure of the outward air, on the furface
of the quickfilver, will force it through the pores
of the hazel, from whence it will defcend in a
beautiful ſhower into a glafs cup placed under
the receiver to catch it.
9. Put a wire through the collar of leathers in
the top of the receiver, and fix a bit of dry wood
on the end of the wire within the receiver; then
exhauſt the air, and push the wire down, fo as to
immerfe the wood into a jar of quickfilver on the
pump-plate; this done, let in the air, and upon
taking the wood out of the jar, and ſplitting it,
its pores will be found full of quickſilver, which
the force of the air, upon being let into the re-
ceiver, drove into the wood.
10. Join the two braſs hemifpherical cups and Fig. 10.
B together, with a wet leather between them, hav-
1
ing
190
Of the Air-Pump.
ing a hole in the middle of it; then fcrew the
end D of the pipe C D into the plate of the
pump at i, and turn the cock E, ſo as the pipe
may be open all the way into the cavity of the
hemifpheres then exhauft the air out of them,
and turn the cock a quarter round, which will
ſhut the pipe C D, and keep out the air. This
done, unfcrew the pipe at D from the pump;
and fcrew the piece Fb upon it at D; and let
two ſtrong men try to pull the hemiſpheres aſun-
der by the rings g and b, which they will find
hard to do for if the diameter of the hemi-
ſpheres be four inches, they will be preffed to-
gether by the external air with a force equal to
190 pounds. And to fhew that it is the preffure
of the air that keeps them together, hang them
by either of the rings upon the hook P of the
wire in the receiver M (Fig. 1.) and upon ex-
haufting the air out of the receiver, they will fall
afunder of themſelves.
It. Place a fmall receiver O (Fig. 1.) near the
hole i on the pump-plate, and cover both it and
the hole with the receiver M; and turn the
wire fo by the top P, that its hook may take
hold of the little receiver by a ring at its top,
allowing that receiver to ftand with its own
weight on the plate. Then, upon working the
pump, the air will come out of both receivers ;
but the large one M will be forcibly held down
to the pump by the preffure of the external air;
whilft the fmall one O, having no air to prefs up-
on it, will continue looſe, and may be drawn up
and let down at pleafure, by the wire P P. But,
upon letting it quite down to the plate, and ad-
mitting the air into the receiver M, by the cock
k, the air will prefs fo ftrongly upon the fmall
receiver O, as to fix it down to the plate; and at
4
the
Of the Air-Pump.
191
the fame time, by counterbalancing the outward
preffure on the large receiver M, it will become
looſe. This experiment evidently fhews, that
the receivers are held down by preffure, and
not by fuction, for the internal receiver conti-
nued looſe whilft the operator was pumping, and
the external one was held down; but the former
became faft immediately by letting in the air
upon it.
12. Screw the end A of the braſs pipe AB F
into the hole of the pump-plate, and turn the
cock e until the pipe be open; then put a wet
leather upon the plate cd, which is fixed on the
pipe, and cover it with the tall receiver G H,
which is cloſe at top: then exhauſt the air out
of the receiver, and turn the cock e to keep it
out; which done, unſcrew the pipe from the
pump, and ſet its end A into a bafon of water,
and turn the cock e to open the pipe; on which,
as there is no air in the receiver, the preſſure of
the atmoſphere on the water in the baſon will
drive the water forcibly through the pipe, and
make it play up in a jet to the top of the re-
ceiver.
13. Set the fquare phial A (Fig. 14.) upon the
pump-plate, and having covered it with the wire
cage B, put a cloſe receiver over it, and exhauſt
the air out of the receiver; in doing of which,
the air will alſo make its way out of the phial
through a ſmall hole in its neck under the valve
b. When the air is exhaufted, turn the cock
below the plate, to re-admit the air into the
receiver; and as it cannot get into the phial
again, becauſe of the valve, the phial will be
broke into ſome thouſands of pieces by the pref-
fure of the air upon it. Had the phial been
of a round form, it would have fuftained this
preffure
Fig. 11.
igz
Of the Air-Pump.
Fig. 7.
Fig. 11.
preffure like an arch, without breaking; but as
its fides are flat, it cannot.
To fhew the elasticity or Spring of the air.
14. Tie up a very fmall quantity of air in a
bladder, and put it under a receiver; then exhauſt
the air out of the receiver; and the fmall quan-
tity which is confined in the bladder (having no-
thing to act againſt it) will expand itſelf fo by
the force of its fpring, as to fill the bladder as
full as it could be blown of common air. But
upon letting the air into the receiver again, it
will overpower the air in the bladder, and prefs
its fides almoft clofe together.
15. If the bladder fo tied up be put into a
wooden box, and have 20 or 30 pound weight
of lead put upon it in the box, and the box be
covered with a clofe receiver; upon exhaufting
the air out of the receiver, that air which is con-
fined in the bladder will expand itſelf ſo, as to raiſe
up all the lead by the force of its fpring.
16. Take the glaſs ball mentioned in the fifth
experiment, which was left full of water all but
a fmall bubble of air at top, and having fet it
with its neck downward into the empty phial aas
and covered it with a clofe receiver, exhauft the
air out of the receiver, and the ſmall bubble of
air in the top of the ball will expand itfelf, ſo as
to force all the water out of the ball into the
phial.
17. Screw the pipe A B into the pump-plate,
place the tall receiver G H upon the plate cd, as
in the twelfth experiment, and exhauft the air
out of the receiver; then, turn the cock e to
keep out the air, unfcrew the pipe from the
pump, and ſcrew it into the mouth of the copper
veffel
Of the Air-Pump.
193
veffel CC (Fig. 15.) the veffel having firſt been
about half filled with water. Then open the
cock e (Fig. 11.) and the ſpring of the air which
is confined in the copper veffel will force the
water up through the pipe A B in a jet into the
exhauſted receiver, as ftrongly as it did by its
preffure on the furface of the water in a bafon, in
the twelfth experiment.
18. If a fowl, a cat, rat, moufe, or bird, be
put under a receiver, and the air be exhauſted,
the animal will be at firft oppreffed as with a
great weight, then grow convulfed, and at laft
expire in all the agonies of a moſt bitter and
cruel death. But as this experiment is too
ſhocking to every fpectator who has the leaft de-
gree of humanity, we ſubſtitute a machine called
the lungs-glass in place of the animal.
19. If a butterfly be fufpended in a receiver,
by a fine thread tied to one of its horns, it will fly
about in the receiver, as long as the receiver
continues full of air; but if the air be exhaufted,
though the animal will not die, and will continue
to flutter its wings, it cannot remove itſelf from
the place where it hangs in the middle of the re-
ceiver, until the air be let in again, and then the
animal will fly about as before.
20. Pour fome quickfilver into the fmall bottle
A, and ſcrew the brass collar c of the tube BC
into the brass neck b of the bottle, and the lower
end of the tube will be immerſed into the quick-
filver, fo that the air above the quicksilver in the
bottle will be confined there, becauſe it cannot
get out about the joinings, nor can it be drawn
out through the quickfilver into the tube. This
tube is alſo open at top, and is to be covered with
the receiver G, and large tube E F, which tube is
fixed by brass collars to the receiver, and is cloſe
Fig. 12.
:
at
194
Of the Air-Pump:
Fig. 13.
at the top. This preparation being made, ex-
hauft the air both out of the receiver and its
tube; and the air will by the fame means
be exhaufted out of the inner tube BC, through
its open top at C; and as the receiver and tubes
are exhaufting, the air that is confined in the glas
bottle A will prefs fo by its ſpring upon the
furface of the quickfilver, as to force it up in the
inner tube as high as it was raiſed in the ninth
experiment by the preffure of the atmoſphere:
which demonftrates that the fpring of the air is
equivalent to its weight.
21. Screw the end C of the pipe C D into the
hole of the pump-plate, and turn all the three
cocks d, G, and H, fo as to open the communi-
cations between all the three pipes E, F, DC,
and the hollow trunk A B. Then, cover the
plates g and b with wet leathers, which have
holes in their middle where the pipes open into
the plates; and place the clofe receiver I upon
the plate g: this done, fhut the pipe F by turn-
ing the cock H, and exhauft the air out of the
receiver I. Then, turn the cock d to fhut out
the air, unfcrew the machine from the pump,
and having fcrewed it to the wooden foot L, put
the receiver K upon the plate h; this receiver
will continue loofe on the plate as long as it
keeps full of air; which it will do until the cock
H be turned to open the communication between
the pipes F and E, through the trunk AB; and
then the air in the receiver K, having nothing to
act againſt its ſpring, will run from K into I, un-
til it be fo divided between theſe receivers, as to
be of equal denfity in both; and then they will
be held down with equal forces to their plates by
the preffure of the atmoſphere; though each
receiver will then be kept down but with one
half
Of the Air-Pump.
195
half of preffure upon it, that the receiver I had,
when it was exhauſted of air; becauſe it has now
one half of the common air in it which filled
the receiver K when it was fet upon the plate;
and therefore, a force equal to half the force of
the fpring of common air, will act within the
receivers againſt the whole preffure of the com-
mon air upon their outfides. This is called
transferring the air out of one veffel into ano-
ther.
22. Put a cork into the fquare phial A, and Fig. 14,
fix it in with wax or cement; put the phial upon
the pump-plate with the wire cage B over it,
and cover the cage with a clofe receiver. Then,
exhauſt the air out of the receiver, and the air
that was corked up in the phial will break the
phial outwards by the force of its ſpring, becauſe
there is no air left on the outſide of the phial to
act againſt the air within it.
23. Put a fhrivelled apple under a cloſe re-
ceiver, and exhauſt the air; then the fpring of
the air within the apple will plump it out, fo as
to cauſe all the wrinkles difappear; but upon
letting the air into the receiver again, to preſs
upon the apple, it will inftantly return to its
former decayed and fhrivelled ftate.
24. Take a freſh egg, and cut off a little of
the ſhell and film from its fmalleft end, then put
the
egg under a receiver, and pump out the air;
upon which, all the contents in the egg will be
forced out into the receiver, by the expanfion of
a ſmall bubble of air contained in the great end,
between the ſhell and film.
25. Put fome warm beer into a glaſs, and hav-
ing fet it on the pump, cover it with a cloſe re-
ceiver, and then exhauſt the air. Whilft this is
doing, and thereby the preffure more and more
taken
1
196
Of the Air-Pump.
taken off from the beer in the glafs, the air there
in will expand itſelf, and rife up in innumerable
bubbles to the furface of the beer; and from
thence it will be taken away with the other air in
the receiver. When the receiver is nearly ex-
hauſted, the air in the beer, which could not
diſentangle itſelf quick enough to get off with
the reft, will now expand itſelf ſo, as to cauſe
the beer to have all the appearance of boiling;
and the greateſt part of it will go over the
glafs.
26. Put fome warm water into a glaſs, and put
a bit of dry wainſcot or other wood into the
water. Then, cover the glass with a clofe re-
ceiver, and exhauft the air; upon which, the air
in the wood having liberty to expand itfelf, will
come out plentifully, and make all the water to
bubble about the wood, efpecially about the
ends, becauſe the pores lie lengthwife. A cubic
inch of dry wainſcot has fo much air in it, that
it will continue bubbling for near half an hour
together.
Mifcellaneous Experiments.
27. Screw the fyringe H (Fig. 8.) to a piece
of lead that weighs one pound at leaft; and,
holding the lead in one hand, pull up the pifton
in the fyringe with the other; then, quitting
hold of the lead, the air will push it upward,
and drive back the fyringe upon the piſton.
The reafon of this is, that the drawing up of the
pifton makes a vacuum in the fyringe, and the
air, which preffes every way equally, having
nothing to refift its preffure upward, the lead is
thereby preffed upward, contrary to its natural
tendency by gravity. If the fyringe, ſo loaded,
be
Of the Air-Pump.
197
be hung in a receiver, and the air be exhaufted,
the fyringe and lead will defcend upon the piſton-
rod by their natural gravity; and, upon admit-
ting the air into the receiver, they will be drove
upward again, until the pifton be at the very
bottom of the fyringe.
28. Let a large piece of cork be fufpended
by a thread at one end of a balance, and coun-
terpoiſed by a leaden weight, fufpended in the
fame manner, at the other. Let this balance be
hung to the infide of the top of a large receiver;
which being fet on the pump, and the air ex-
haufted, the cork will preponderate, and fhew
itſelf to be heavier than the lead; but upon
letting in the air again, the equilibrium will be
reftored. The reafon of this is, that fince the
air is a fluid, and all bodies lofe as much of their
abfolute weight in it, as is equal to the weight
of their bulk of the fluid, the cork being the
larger body, lofes more of its real weight than
the lead does; and therefore muft in fact be
heavier, to balance it under the difadvantage of
lofing fome of its weight: which diſadvantage
being taken off by removing the air, the bodies
then gravitate according to their real quantities.
of matter, and the cork, which balanced the
lead in air, fhews itſelf to be heavier when in
vacuo.
29. Set a lighted candle upon the pump, and
cover it with a tall receiver. If the receiver
holds a gallon, the candle will burn a minute;
and then, after having gradually decayed from
the firſt inſtant, it will go out: which fhews, that
a conſtant ſupply of freſh air is neceffary to feed
flame; and fo it alfo is for animal life. For a
bird kept under a cloſe receiver will foon die,
although no air be pumped out; and it is
Q 2
found
198
Of the Air-Pump.
會
​found that, in the diving-bell, a gallon of air
is fufficient only for one minute for a man to
breathe in.
The moment when the candle goes out, the
fmoke will be feen to afcend to the top of the
receiver, and there it will form a fort of cloud:
but upon exhaufting the air, the fmoke will fall
down to the bottom of the receiver, and leave it
as clear at the top as it was before it was fet upon
the pump. This fhews, that ſmoke does not
afcend on account of its being positively light,
but becauſe it is lighter than air; and its falling
to the bottom when the air is taken away,
fhews, that it is not deftitute of weight.
moft forts of wood afcend or fwim in water; and
yet there are none who doubt of the wood's
having gravity or weight.
So
30. Set a receiver, which is open at top, upon
the air-pump, and cover it with a brafs plate,
and wet leather; and having exhaufted it of air,
let the air in again at top through an iron pipe,
making it pass through a charcoal flame at the
end of the pipe; and when the receiver is full
of that air, lift up the cover, and let down a
mouſe or bird into the receiver, and the burnt
air will immediately kill it. If a candle be let
down into that air, it will go out directly; but,
by letting it down gently, it will purify the air fo
far as it goes; and fo, by letting it down more.
and more, the flame will drive out the bad air,
and good air will get in.
31. Set a bell upon a cufhion on the pump-
plate, and cover it with a receiver; then ſhake
the pump to make the clapper ſtrike againſt the
bell, and the found will be very well heard: but,
exhauſt the receiver of air, and then, if the
clapper be made to ftrike ever fo hard againſt
the
Of the Air-Pump.
199
the bell, it will make no found at all; which
fhews, that air is abfolutely neceffary for the
propagation of found.
32. Let a candle be placed on one fide of a
receiver, and viewed through the receiver at
ſome diſtance; then, as foon as the air begins to
be exhaufted, the receiver will be filled with va-
pours which rife from the wet leather, by the
ſpring of the air in it; and the light of the
candle being refracted through that medium of
vapours, will have the appearance of circles of
various colours, of a faint refemblance to thoſe
in the rain-bow.
The air-pump was invented by Otho Guerick
of Magdeburg, but was much improved by Mr.
Boyle, to whom we are indebted for our greateſt
part of the knowledge of the wonderful proper-
ties of the air, demonftrated in the above expe-
riments.
The elaſtic air which is contained in many
bodies, and is kept in them by the weight of the
atmoſphere, may be got out of them either by
boiling, or by the air-pump, as fhewn in the
25th experiment: but the fixed air, which is by
much the greater quantity, cannot be got out
but by diftillation, fermentation, or putrefac-
tion.
If fixed air did not come out of bodies with
difficulty, and ſpend fome time in extricating
itſelf from them, it would tear them to pieces.
Trees would be rent by the change of air from
a fixt, to an elaſtic ftate, and animals would be
burit in pieces by the explosion of air in their
food.
Dr. Hales found by experiment, that the air
in apples is fo much condenfed, that if it were
let out into the common air, it would fill a ſpace
0 3
48.
200
Of the Air-Pump.
48 times as great as the bulk of the apples them-
felves; fo that its preffure outwards was equal
to 11776 lb. and, in a cubic inch of oak, to
19860 lb. againft its fides. So that if the air
was let loofe at once in theſe ſubſtances, they
would tear every thing to pieces about them
with a force fuperior to that of gunpowder,
Hence, in eating apples, it is well that they part
with the air by degrees, as they are chewed, and
ferment in the ftomach, otherwiſe an apple
would be immediate death to him who eats it.
The mixing of fome fubftances with others,
will releaſe the air from them, all of a fudden,
which may be attended with very great danger.
Of this we have a remarkable inftance in an ex-
periment made by Dr. Slare; who having put
half a dram of oil of carraway-feeds into one glaſs,
and a dram of compound fpirit of nitre in ano-
ther, covered them both on the air-pump with a
receiver fix inches wide, and eight inches deep,
and then exhauſted the air, and continued pump-
ing until all that could poffibly be got both out
of the receiver, and out of the two fluids, was
extricated then, by a particular contrivance
from the top of the receiver, he mixed the
fluids together; upon which they produced
fuch a prodigious quantity of air, as inſtantly
blew up the receiver, although it was preffed
down by the atmoſphere with upwards of 400
pound weight.
N. B. In the 28th Experiment, the cork muft
be covered all over with a piece of thin wet
bladder glued to it, and not uſed until it be
thoroughly dry.
LECT.
..
PLATE XV.
a
Fig. 1
A
B
P
D
Fig. 4.
A
F
Marguson delin.
K
Fig. 2.
D
D
E
A
E
B
:
b
K
a
G
Fig.3.
k
C
C
B
C
D
E
F
G
H
A
E
I-
Fig. 6.
B
D
G
T
H
M
B
L
}
H
K
Fig. 8.
Fig 5
A
17760
VAIB
WETER
| "797} .
C
F
Ꭰ
H
F
D
A.
E
Fig. 9.
TIHERK
U
K
Fig. 7.
B
SELLSO:FIN
J Myudo je.
Of Optics.
201
L
LECT. VIII.
Of Optics.
IGHT confifts of an inconceivably great
number of particles flowing from a lumi-
nous body in all manner of directions; and theſe
particles are ſo ſmall, as to furpaſs all human
comprehenfion.
That the number of particles of light is in-
conceivably great, appears from the light of a
candle; which, if there be no obftacle in the
way to obftruct the paffage of its rays, will fill
all the fpace within two miles of the candle every
way, with luminous particles, before it has loft
the leaft fenfible part of its fubftance.
A ray of light is a continued ftream of thefe
particles, flowing from any visible body in a
traight line and that the particles themſelves.
are incomprehenfibly ſmall, is manifeft from the
following experiment. Make a fmall pin-hole
in a piece of black paper, and hold the paper
upright on a table facing a row of candles ftand-
ing by one another; then place a sheet of pafte-
board at a little diſtance behind the paper, and
fome of the rays which flow from all the candles
through the hole in the paper, will form as many
ſpecks of light on the paſteboard, as there are
candles on the table before the plate: each fpeck The ama-
being as diftinct and clear, as if there was only zing
one fpeck from one fingle candle: which fhews of the
that the particles of light are exceedingly fmall, particles
otherwife they could not pafs through the hole of light.
from fo many different candles without confu-
fion.-Dr. Niewentyt has computed, that there
flows more than 6,000,000,000,000 times as
fmallneſs
04
many
202
Of Optics.
many particles of light from a candle in one
fecond of time, as there are grains of fand in the
whole earth, fuppofing each cubic inch of it to
contain 1,000,000.
Theſe particles, by falling directly upon our
eyes, excite in our minds the idea of light.
And when they fall upon bodies, and are thereby
reflected to our eyes, they excite in us the ideas
of theſe bodies. And as every point of a viſible
body reflects the rays of light in all manner of
directions, every point will be vifible in every
part to which the light is reflected from it.
Plate XV.. Thus the object AC B is viſible to an eye in any
Fig. 1.
part where the rays Aa, Ab, Ac, Ad, Ae, B a,
Bb, B c, Bd, Be, and Ca, Cb, Cc, C d, C e,
come. Here we have fhewn the rays as if they
were only reflected from the ends A and B, and
from the middle point C of the object; every
other point being fuppofed to reflect rays in the
Reflected fame manner. So that wherever a fpectator is
light. placed with regard to the body, every point of
that part of the furface which is towards him will
be visible, when no intervening object ſtops the
paffage of the light.
As no object can be feen through the bore
of a bended pipe, it is evident that the rays of
light move in ſtraight lines, whilft there is no-
thing to refract or turn them out of their recti-
lineal courſe.
*
While the rays of light continue in any me-
dium of an uniform denfity, they are ſtraight;
but when they pafs obliquely out of one medium
into another, which is either more denſe or more
*Any thing through which the rays of light can paſs, is
called a medium; as air, water, glaſs, diamond, or even
a vacuum.
rare,
Of Optics.
203
rare, they are refracted towards the denfer me-
dium and this refraction is more or lefs, as the
rays fall more or leſs obliquely on the refracting
furface which divides the mediums.
To prove this by experiment, fet the empty Fig. 2.
veſſel ABCD into any place where the fun fhines
obliquely, and obferve the part where the
fhadow of the edge BC falls on the bottom of
the veffel at E; then fill the veffel with water,
and the fhadow will reach no farther than e;
which fhews, that the ray a B E, which came
ftraight in the open air, juſt over the edge of the
veffel at B to its bottom at E, is refracted by
falling obliquely on the furface of the water at Refracted
B; and inſtead of going on in the rectilineal di- light.
rection a B E, it is bent downward in the water
from B to e; the whole bend being at the furface
of the water and fo of all the other rays
a b c.
If a ſtick be laid over the veffel, and the fun's
rays be reflected from a glaſs perpendicularly
into the veffel, the fhadow of the ftick will fall
upon the fame part of the bottom, whether the
veffel be empty or full, which fhews, that the
rays of light are not refracted when they fall
perpendicularly on the ſurface of any medium.
The rays of light are as much refracted by
paffing out of water into air, as by paffing out of
air into water. Thus, if a ray of light flows
from the point e, under water, in the direction
e B; when it comes to the furface of the water at
B, it will not go on thence in the rectilineal
courfe B d, but will be refracted into the line Ba.
Therefore,
To an eye ate looking through a plane glafs
in the bottom of the empty veffel, the point a
cannot be feen, becaufe the fide Bc of the veffel
inter-
204
Of Optics.
The days
are made
longer by
interpofes; and the point d will juſt be ſeen over
the edge of the veffel at B. But if the veffel be
filled with water, the point a will be feen from e;
and will appear as at d, elevated in the direction
of the ray e B*.
The time of fun-rifing or fetting, fuppofing
its rays fuffered no refraction, is eaſily found by
calculation, But obfervation proves that the
fun riſes ſooner, and ſets later every day than the
calculated time; the reaſon of which is plain,
fun's rays. from what was faid immediately above. For,
the re-
fraction
of the
Fig. 3.
though the fun's rays do not come part of the
way to us through water, yet they do through the
air or atmoſphere, which being a groffer medium
than the free ſpace between the fun and the top
of the atmoſphere, the rays, by entering ob-
liquely into the atmoſphere, are there refracted,
and thence bent down to the earth. And al-
though there are many places of the earth to
which the fun is vertical at noon, and confe-
quently his rays can fuffer no refraction at that
time, becauſe they come perpendicularly through
the atmoſphere: yet there is no place to which
the fun's rays do not fall obliquely on the top of
the atmoſphere, at his rifing and fetting; and
confequently, no clear day in which the fun will
not be vifible before he rifes in the horizon, and
after he fets in it: and the longer or fhorter, as
the atmoſphere is more or lefs replete with va-
pours. For, let ABC be part of the earth's
furface, D E F the atmoſphere that covers it,
* Hence a piece of money lying at e, in the bottom of an
empty veffel, cannot be ſeen by an eye at a, becauſe the edge
of the veffel intervenes; but let the veffel be filled with
water, and the ray e a being then refracted at B, will ftrike
the eye at a, and fo render the money viſible, which will
appear as if it were raiſed up to ƒ in the line a Bf.
6
and
Gf Optics.
295
and EBGH the fenfible horizon of an obſerver
at B. As every point of the fun's ſurface ſends
out rays of light in all manner of directions,
fome of his rays will conftantly fall upon, and
enlighten, fome half of the atmoſphere; and
therefore, when the fun is at I, below the hori-
zon H, thofe rays which go on in the free ſpace
Ik K preſerve a rectilineal courfe until they fall
upon the top of the atmoſphere; and thofe
which fall fo about K, are refracted at their
entrance into the atmoſphere, and bent down
in the line K m B, to the obferver's place at B:
and therefore, to him, the fun will appear at L,
in the direction of the ray Bm K, above the hori-
zon B G H, when he is really below it at I.
The angle contained between a ray of light,
and a perpendicular to the refracting furface, is
called the angle of incidence; and the angle con- Angle of
tained between the fame perpendicular, and the incidence.
ſame ray after refraction, is called the angle of
refraction. Thus, let L B M be the refracting Fig. 4.
furface of a medium (fuppofe water) and ABC Angle of
a perpendicular to that furface; let D B be a refraction.
ray of light, going out of air into water at B,
and therein refracted in the line B H; the angle
ABD, is the angle of incidence, of which D F
is the fine; and the angle K B H is the angle of
refraction, whofe fine is K I.
When the refracting medium is water, the
fine of the angle of incidence is to the fine of
the angle of refraction, as 4 to 3; which is con-
firmed by the following experiment, taken from
Doctor SMITH's Optics.
Defcribe the circle D AEC on a plane fquare
board, and croſs it at right angles with the
traight lines A B C, and L B M; then, from
the interfection, A, with any opening of the com-
paffes
206
Of Optics.
paffes, fet off the equal arcs AD and A E, and
draw the right line DFE: then, taking Fa
which is three quarters of the length F E, from
the point a, draw a I parallel to AB K, and
join K I, parallel to B M: fo K I will be equal
to three quarters of FE or of DF. This done,
fix the board upright upon the leaden pedeſtal
O, and ſtick three pins perpendicularly into the
board, at the points D, B, and I: then fet the
board upright into the veffel V UT, and fill up
the veffel with water to the line L B M. When
the water has fettled, look along the line D B,
fo as you may ſee the head of the pin B over the
head of the pin D; and the pin I will appear in
the fame right line produced to G, for its head
will be feen juft over the head of the pin at B:
which fhews that the ray I B, coming from the
pin at I, is fo refracted at B, as to proceed from
thence in the line B D to the eye of the obſerver;
the fame as it would do from any point G in the
right line D BG, if there were no water in the
veffel and alfo fhews that K I, the fine of re-
fraction in water, is to D F, the fine of inci-
dence in air, as 3 to 4 *
:
Hence, if DB H were a crooked ſtick put
obliquely into the water, it would appear a
ftraight one, as D B G. Therefore, as the line
BH appears at BG, fo the line B G will appear
at B g; and confequently, a ſtraight ftick DBG
put obliquely into water, will feem bent at the
furface of the water in B, and crooked, as
DB g.
When a ray of light paffes out of air into
glafs, the fine of incidence is to the fine of re-
*This is ftrictly true of the red rays only, for the other
coloured rays are differently refracted; but the difference is
fo ſmall, that it need not be confidered in this place.
fraction,
Of Optics.
207
fraction, as 3 to 2; and when out of air into a
diamond, as 5 to 2.
Glaſs may be ground into eight different Fig. 5.
fhapes at leaſt, for optical purpoſes, viz.
1. A plane glass, which is flat on both fides,
and of equal thickneſs in all its parts, as A.
2. A plano convex, which is flat on one fide, Lenfes.
and convex on the other, as B.
3. A double convex, which is convex on both
fides, as C.
4. A plano-concave which is flat on one fide,
and concave on the other, as D.
5. A double-concave, which is concave on both
fides, as E.
6. A meniscus, which is concave on one fide,
and convex on the other, as F.
7. A flat plano-convex, whofe convex fide is
ground into feveral little flat furfaces, as G.
8. A prifm, which has three flat fides, and
when viewed end wife, appears like an equilateral
triangle, as H.
Glaffes ground into any of the ſhapes B, C, D,
E, F, are generally called lenfes.
A right line LIK, going perpendicularly
through the middle of a lens, is called the axis
of the lens.
A ray of light G b, falling perpendicularly on
a plane glaſs E F, will pafs through the glaſs Fig. 6.
in the fame direction b i, and go out of it into
the air in the fame right courſe i H.
A ray of light AB, falling obliquely on a
plane glafs, will go out of the glaſs in the fame
direction, but not in the fame right line; for in
touching the glafs, it will be refracted in the
line BC, and in leaving the glafs, it will be re-
fracted in the line C D.
3
A ray
463
Of Optics.
Fig. 6.
perties of
lenfes.
Α A ray of light C D, falling obliquely on the
middle of a convex glafs, will go forward in the
fame direction D E, as if it had fallen with the
fame degree of obliquity on a plane glafs; and
will go out of the glaſs in the fame direction
with which it entered: for it will be equally re-
fracted at the points D and E, as if it had paffed
through a plane furface. But the rays CG and
C I will be fo refracted, as to meet again at the
point F. Therefore, all the rays which flow
from the point C, fo as to go through the glafs,
will meet again at F; and if they go farther
onward, as to L, they crofs at F, and go for-
ward on the oppofite fides of the middle ray
CDE F, to what they were in approaching it in
the directions H F and K F.
Fig. 8. When parallel rays, as A B C, fall directly
The pro- upon a plano-convex glafs DE, and paſs through
different it, they will be fo refracted, as to unite in a
point f behind it: and this point is called the
principal focus: the diftance of which, from the
middle of the glafs, is called the focal distance;
which is equal to twice the radius of the ſphere
of the glass's convexity. And,
Fig. 9.
When parallel rays, as AB C, fall directly
upon a glaſs D E, which is equally convex on
both fides, and paſs through it; they will be fo
refracted, as to meet in a point or principal focus
f, whoſe diſtance is equal to the radius or femi-
diameter of the fphere of the glass's convexity.
But if a glaſs be more convex on one fide than
on the other, the rule for finding the focal
diſtance is this; as the fum of the femidiameters
of both convexities is to the femidiameter of
either, fo is double the femidiameter of the
other to the diſtance of the focus. Or, divide
the
PLATE XVI.
L
Fig.1.
Ъ
H
D
L
H
D
E
I. Ferguson delin.
m
E
Fig. 3.
F
1
A
H-
G
Fig. 2.
1-
F
B
K-
k
Fig. 4.
10
Y
to
B
D
E
L
C
*
**
17:
"
B
J. Mynde fc.
Of Optics.
209
the double product of the radii by their fum,
and the quotient will be the diſtance fought.
Since all thoſe rays of the fun which pas
through a convex glafs are collected together
in its focus, the force of all their heat is col-
lected into that part; and is in proportion to
the common heat of the fun, as the area of the
glafs is to the area of the focus. Hence we fee
the reaſon why a convex glaſs cauſes the fun's
rays to burn after paffing through it.
All theſe rays croſs the middle ray in the fo-
cus f, and then diverge from it, to the contrary
fides, in the fame manner Ff G, as they con-
verged in the ſpace D ƒ E in coming to it.
If another glaſs F G, of the ſame convexity
as DE, be placed in the rays at the fame dif-
tance from the focus, it will refract them ſo,
as that after going out of it, they will be all
parallel, as a b c; and go on in the lame man-
ner as they came to the firft glafs D E, through
the ſpace A B C; but on the contrary fides of
the middle ray Bfb: for the ray ADƒ will go
on from ƒ in the direction f G a, and the ray
CEƒ in the direction f F c; and fo of the reft.
The rays diverge from any radiant point, as
from a principal focus: therefore, if a candle
be placed at f, in the focus of the convex glaſs
FG, the diverging rays in the ſpace Ff G will
be fo refracted by the glafs, as, that after going
out of it, they will become parallel, as fhewn
in the space c ba.
If the candle be placed nearer the glass than
its focal diſtance, the rays will diverge after
paffing through the glafs, more or lefs, as the
candle is more or lefs diftant from the focus.
If the candle be placed farther from the glaſs
than its focal diftance, the rays will converge
after
210
Of Optics.
PlateXVI.
Fig. 1.
after paffing through the glafs, and meet in a
point which will be more or lefs diftant from the
glafs, as the candle is nearer to, or farther from
its focus; and where the rays meet, they will
form an inverted image of the flame of the
candle; which may be feen on a paper placed
in the meeting of the rays.
Hence, if any object A B C be placed beyond
the focus F of the convex glafs de f, fome of
the rays which flow from every point of the
object, on the fide next the glaſs, will fall upon
it, and after paffing through it, they will be
converged into as many points on the oppofite
fide of the glaſs, where the image of every point
will be formed and confequently, the image
of the whole object, which will be inverted.
Thus, the rays Ad, A e, Aƒ, flowing from the
point A, will converge in the ſpace d af, and by
meeting at a, will there form the image of the
point A. The rays B d, Be, Bf, flowing from
the point B, will be united at b by the refrac-
tion of the glafs, and will there form the image
of the point B. And the rays Cd, Ce, Cf,
flowing from the point C, will be united at c,
where they will form the image of the point C.
And fo of all the other intermediate points be-
tween A and C. The rays which flow from
every particular point of the object, and are
united again by the glafs, are called pencils of
rays.
If the object A B C be brought nearer to the
glafs, the picture abc will be removed to a
greater diftance. For then, more rays flowing
from every fingle point, will fall more diverging
upon the glass; and therefore cannot be fo foon
collected into the corresponding points behind
it. Confequently, if the diſtance of the object
A B C
Of Optics.
211
ABC be equal to the diftance e B of the focus PlateXVI.
Fig. 2.
of the glafs, the rays of each pencil will be fo
refracted by paffing through the glaſs, that they
will go out of it parallel to each other; as d I,
e H, fh, from the point C; d G, e K, ƒ D,
from the point B; and d K, e E, f L, from the
point A and therefore, there will be no pic-
ture formed behind the glass.
If the focal diftance of the glafs, and the
diſtance of the object from the glafs, be known,
the diſtance of the picture from the glaſs may
be found by this rule, viz. multiply the diſtance
of the focus by the diſtance of the object, and
divide the product by their difference; the
quotient will be the diſtance of the picture.
The picture will be as much bigger or leſs Fig. 1.
than the object, as its diſtance from the glaſs is
greater or less than the diftance of the object.
For, as Be is to eb, fo is AC to c a. So that
if ABC be the object, cb a will be the picture;
or, if cba be the object, A B C will be the
picture.
fion.
Having defcribed how the rays of light, The man-
flowing from objects and paffing through con- ner of vi-
vex glaffes, are collected into points, and form
the images of the objects; it will be eafy to un-
derſtand how the rays are affected by paffing
through the humours of the eye, and are there-
by collected into innumerable points on the bot-
tom of the eye, and thereon form the images of
the objects which they flow from. For, the
different humours of the eye, and particularly
the chryſtalline humour, are to be confidered
as a convex glafs; and the rays in paffing
through them to be affected in the fame manner
as in paffing through a convex glaſs.
P
The
"
212
Of Optics.
PlateXVI.
Fig. 3.
The eye is nearly globular. It conſiſts of
three coats and three humours.
The part
DHHG of the outer coat, is called the fele-
rotica, the reft DEFG the cornea. Next with-
in this coat is that called the choroides, which
ferves as it were for a lining to the other, and
joins with the iris mn, m n.
The iris is com-
pofed of two fets of mufcular fibres; the one of
a circular form, which contracts the hole in the
middle called the pupil, when the light would
The eye otherwife be too ftrong for the eye; and the
defcribed. other of radial fibres, tending every where from
the circumference of the iris towards the middle
of the pupil; which fibres, by their contraction,
dilate and enlarge the pupil when the light is
weak, in order to let in the more of its rays.
The third coat is only a fine expansion of the
optic nerve L, which fpreads like net-work all
over the infide of the choroides, and is therefore
called the retina; upon which are painted (as it
were) the images of all viſible objects, by the
rays of light which either flow or are reflected
from them.
Under the cornea is a fine tranſparent fluid
like water, which is therefore called the aqueous
humour. It gives a protuberant figure to the
cornea, fills the two cavities mm and n n, which
communicate by the pupil P, and has the fame
limpidity, ſpecific gravity, and refractive power
as water. At the back of this lies the chrystalline
bumour I I, which is fhaped like a double con-
vex glafs; and is a little more convex on the
back than the fore-part. It converges the rays,
which paſs through it from every visible object
to its focus at the bottom of the eye. This
humour is tranfparent like chryftal, is much of
the confiftence of hard jelly, and exceeds the
ſpecific
Of Optics.
213
II
Specific gravity of water in the proportion of
11 to 10. It is incloſed in a fine tranfparent
membrane, from which proceed radial fibres
o o, called the ligamentum ciliare, all around its
edge; and join to the circumference of the iris.
Theſe fibres have a power of contracting and
dilating occaſionally, by which means they alter
the ſhape or convexity of the chrystalline hu-
mour, and alfo fhift it a little backward or for-
ward in the eye, fo as to adapt its focal diſtance
at the bottom of the eye to the different diſtances
of objects; without which provifion, we could
only fee thoſe objects diftinctly, that were all at
one diſtance from the eye.
At the back of the chryftalline, lies the vitre-
eus humour K K, which is tranfparent like glafs,
and is largeſt of all in quantity, filling the whole
orb of the eye, and giving it a globular fhape.
It is much of a confiftence with the white of an
egg, and very little exceeds the ſpecific gravity
and refractive power of water.
As every point of an object A B C fends out
rays in all directions, fome rays, from every
point on the fide next the eye, will fall upon
the cornea between E and F, and by paſſing on
through the humours and pupil of the eye,
they will be converged to as many points on
the retina or bottom of the eye, and will thereon
form a diſtinct inverted picture e b a of the ob-
ject. Thus, the pencil of rays qrs that flows
from the point of the object, will be con-
verged to the point a on the retina; thofe from
the point B will be converged to the point b;
thoſe from the point C will be converged to the
point c; and fo of all the intermediate points: by
which means the whole image a b c is formed,
and the object made vifible; although it muft
1
P 2
be
214
Of Optics.
be owned, that the method by which this fenfa-
tion is carried from the eye by the optic nerve to
the common fenfory in the brain, and there
difcerned, is above the reach of our compre-
henfion.
But that vifion is effected in this manner,
may be demonſtrated experimentally. Take a
bullock's eye whilft it is freſh, and having cut
off the three coats from the back part, quite
to the vitreous humour, put a piece of white
paper over that part, and hold the eye towards
any bright object, and you will fee an inverted
picture of the object upon the paper.
*
Seeing the image is inverted, many have
wondered why the object appears upright. But
we are to confider, 1. That inverted is only a
relative term and 2. That there is a very great
difference between the real object and the means
or image by which we perceive it. When all
the parts of a diftant profpect are painted upon
the retina, they are all right with refpect to one
another, as well as the parts of the proſpect
itfelf; and we can only judge of an object's
being inverted, when it is turned reverſe to its
natural poſition, with reſpect to other objects
which we fee and compare it with.-If we lay
hold of an upright ſtick in the dark, we can tell
which is the upper or lower part of it, by mov-
ing our hand upward or downward; and know
very well that we cannot feel the upper end by
moving our hand downward. Juft fo we find
by experience, that upon directing our eyes
towards a tall object, we cannot fee its top by
turning our eyes downward, nor its foot by
turning our eyes upward; but muft trace the
object the fame way by the eye to fee it from
head to foot, as we do by the hand to feel it;
6
and
PLATE XVII.
N
D
ལ
Fig.2.
A
OB
9
U-
a
C
na
1
Fig. 1.
Fig. 5.
a
a
19
Fig. 6.
Fig. 4.
C
E
h
I. Ferguson delin.
B
h
B
A
a
C
A
d
772
E
до
Fig.3.
A
S
t
B
Fig.7
D
J. Mynds fo
Of Optics.
215
and as the judgment is informed by the motion
of the hand in one cafe, ſo it is alfo by the mo-
tion of the eye in the other.
In Fig. 4. is exhibited the manner of ſeeing Fig. 4.
the fame object A B C, by both the eyes D and
E at once.
When any part of the image cb a falls upon
the optic nerve L, the correfponding part of
the object becomes invifible. On which ac-
count nature has wifely placed the optic nerve
of each eye, not in the middle of the bottom of
the eye, but towards the fide next the nofe; ſo
that whatever part of the image falls upon the
optic nerve of one eye, may not fall upon the
optic nerve of the other. Thus the point a of
the image cb a falls upon the optic nerve of the
eye D, but not of the eye E; and the point e
falls upon the optic nerve of the eye E, but not
of the eye D and therefore to both eyes taken
together, the whole object A B C is vifible.
The nearer that any object is to the
eye, the Plate
larger is the angle under which it it feen, and XVII.
the magnitude under which it appears. Thus Fig. 1.
to the eye D, the object A B C is feen under the
angle APC; and its image cba is very large
upon the retina: but to the eye E, at a double
diſtance, the fame object is feen under the angle
Ap C, which is equal only to half the angle
A P C, as is evident by the figure. The image
cba is likewife twice as large in the eye D, as
the other image c ba is in the eye E. In both
theſe repreſentations, a part of the image falls
on the optic nerve, and the object in the corre-
ſponding part is invifible.
'
As the fenfe of feeing is allowed to be occa-
fioned by the impulfe of the rays from the vifible
object upon the retina of the eye, and forming
P 3
the
216
Of Optics.
Fig. 2.
the image of the object thereon, and that the
retina is only the expanſion of the optic nerve all
over the choroides; it fhould feem furprifing
that the part of the image which falls on the
optic nerve fhould render the like part of the
object invisible; efpecially as that nerve is al-
lowed to be the inftrument by which the impulse
and image are conveyed to the common fenfory
in the brain. But this difficulty vanishes, when
we confider that there is an artery within the
trunk of the optic nerve, which entirely ob-
fcures the image in that part, and conveys no
fenfation to the brain.
That the part of the image which falls upon
the middle of the optic nerve is loft, and confe-
quently the correſponding part of the object is
rendered invifible, is plain by experiment. For, if
a perfon fixes three patches, A, B, C, horizontally,
upon a white wall, at the height of the eye, and
the diſtance of about a foot from each other, and
places himſelf before them, fhutting the right
eye, and directing the left towards the patch C,
he will fee the patches A and C, but the middle
patch B will difappear. Or, if he ſhuts his left
eye, and directs the right towards A, he will fee
both A and C, but B will diſappear; and if he
directs his eye towards B, he will fee both B and
A, but not C. For whatever patch is directly
oppoſite to the optic nerve N, vanishes. This
requires a little practice, after which he will find
it eaſy to direct his eye, fo as to loſe the fight
of whichever patch he pleafes.
We are not commonly fenfible of this difap-
pearance, becaufe the motions of the eye are
fo quick and inftantaneous, that we no fooner
lofe the fight of any part of an object, than we
recover it again; much the fame as in the
twinkling of our eyes, for at each twinkling we
are
Of Optics.
217
are blinded; but it is fo foon over, that we are
fcarce ever fenfible of it.
fome eyes
require
Some eyes require the affiſtance of convex Fig. 4.
glaffes to make them fee objects diſtinctly, and Why
others of concave. If either the cornea a b c or
chryſtalline humour e, or both of them, be too fpectacles.
flat, as in the eye A, their focus will not be on
the retina, as at d, where it ought to be, in or-
der to render vifion diſtinct; but beyond the
eye, as at f. Confequently thofe rays which
flow from the object C, and pafs through the
humours of the eye, are not converged enough
to unite at d; and therefore the obferver can
have but a very indiftinct view of the object.
This is remedied by placing a convex glaſs g b
before the eye, which makes the rays converge
fooner, and imprints the image duly on the
retina at d.
If either the cornea, or chryftalline humour,
or both of them, be too convex, as in the eye
f, the rays that enter in from the object C, will
be converged to a focus in the vitreous humour,
as at f; and by diverging from thence to the
retina, will form a very confuſed image thereon:
and fo, of courſe, the obſerver will have as con-
fuſed a view of the object, as if his eye had been
too flat. This inconvenience is remedied by
placing a concave glafs g h before the eye; which
glafs, by caufing the rays to diverge between it
and the eye, lengthens the focal diſtance fo,
that if the glafs be properly chofen, the rays
will unite at the retina, and form a diftinct pic-
ture of the object upon it.
Such eyes as have their humours of a due
convexity, cannot fee any object diftinctly at a
leſs diſtance than fix inches; and there are
numberless objects too fmall to be feen at that
P 4
diſtance,
218
Of Optics.
Fig. 5.
The fingle
microscope.
Fig. 6.
The
double mi
croſcope.
•
diftance, becaufe they cannot appear under any
fenfible angle. The method of viewing fuch
minute objects is by a microſcope, of which there
are three forts, viz. the fingle, the double, and
the folar.
The Single microscope, is only a finall convex
glafs, as cd, having the object a b placed in its
focus, and the eye at the fame diſtance on the
other fide; fo that the rays of each pencil, flow -
ing from every point of the object on the fide
next the glafs, may go on parallel in the ſpace
between the eye and the glafs; and then, by
entering the eye at C, they will be converged
to as many different points on the retina, and
form a large inverted picture A B upon it, as
in the figure.
To find how much this glafs magnifies, di-
vide the leaft diftance (which is about fix inches)
at which an object can be feen diftinctly with
the bare eye, by the focal diftance of the glafs;
and the quotient will fhew how much the glafs
magnifies the diameter of the object.
The double or compound microscope, confifts of
an object-glaſs c d, and an eye glafs e f. The
fmall object a b is placed at a little greater dif-
tance from the glafs c d than its principal focus,
fo that the pencils of rays flowing from the dif-
ferent points of the object, and paffing through
the glafs, may be made to converge and unite
in as many points between g and b, where the
image of the object will be formed: which
image is viewed by the eye through the eye-
glafs e f. For the eye-glafs being fo placed,
that the image gb may be in its focus, and the
eye much about the fame diftance on the other
fide, the rays of each pencil will be parallel,
after going out of the eye-glafs, as at e and f,
till
i
Of Optics.
219
till they come to the eye at k, where they will
begin to converge by the refractive power of
the humours; and after having croffed each
other in the pupil, and paffed through the chryf-
talline and vitreous humours they will be col-
lected into points on the retina, and form the
large inverted image A B thereon.
The magnifying power of this microſcope is
as follows. Suppofe the image gb to be fix
times the diſtance of the object a b from the
object glass c d; then will the image be fix times.
the length of the object: but fince the image
could not be feen diftinctly by the bare eye at
a leſs diſtance than fix inches, if it be viewed
by an eye-glais ef, of one inch focus, it will
thereby be brought fix times nearer the eye;
and confequently viewed under an angle fix times
as large as before; fo that it will be again mag-
nified fix times; that is, fix times by the object-
glafs, and fix times by the eye-glafs, which mul-
tiplied into one another, makes 36 times; and
fo much is the object magnified in diameter more
than what it appears to the bare eye; and confe-
quently 36 times 36, or 1296 times in furface.
But becauſe the extent or field of view is
very ſmall in this microſcope, there are gene-
rally two eye-glaffes placed fometimes clofe
together, and fometimes an inch afunder; by
which means, although the object appears leſs
magnified, yet the vifible area is much enlarged
by the interpofition of a fecond eye-glaſs; and
confequently a much pleafanter view is ob-
$ained.
The folar microſcope, invented by Dr. Lie- Fig. 7.
berkhun, is conſtructed in the following manner. The folar
Having procured a very dark room, let a round microſcope.
hole be made in the window-fhutter, about three
inches
i
Of Optics.
inches diameter, through which the fun may caft
a cylinder of rays A A into the room. In this
hole, place the end of a tube, containing two
convex glaffes and an object, viz. 1. A convex
glafs a a, of about two inches diameter, and
three inches focal diftance, is to be placed in
that end of the tube which is put into the hole.
2. The object b b, being put between two glaffes
(which must be concave to hold it at liberty) is
placed about two inches and a half from the glafs
& a. 3. A little more than a quarter of an inch
from the object is placed the ſmall convex glaſs
cc, whofe focal diſtance is a quarter of an inch.
The tube may be fo placed, when the fun is
low, that his rays A A may enter directly into
it but when he is high, his rays B B muft be
reflected into the tube by the plane mirrour or
looking-glafs C C.
Things being thus prepared, the rays that
enter the tube will be conveyed by the glaſs a a
towards the object b b, by which means it will
be ſtrongly illuminated; and the rays d which
flow from it, through the magnifying glaſs c c,
will make a large inverted picture of the object
at DD, which, being received on a white paper,
will reprefent the object magnified in length, in
proportion of the diftance of the picture from
the glaſs cc, to the diſtance of the object from
the fame glafs. Thus, fuppofe the diftance of the
object from the glafs to be parts of an inch,
3
To
and the diſtance of the diftinct picture to be 12
feet or 144 inches, in which there are 1440 tenths
of an inch; and this number divided by 3 tenths,
gives 480; which is the number of times the
picture is longer or broader than the object; and
the length multiplied by the breadth, fhews how
much the whole furface is magnified.
Before
PLATE XVIII.
:
Fig. 1.
•
q
B
d-
B
7BL
欢
​72
Fig. 4.
m
E
Fig. 5.
m
E
T
Fig. 7.
F
Fig. 2.
Fig. 3.
m
F
Fig. 6.
C
B
E
k
-
-
T
B
B
B
B
C
A
Z
U
I
R
P.......
K
V
H
M
B
E
T
T
S. Ferguson delin.
J.Mynd J.
Of Optics.
221
Before we enter upon the deſcription of tele- Telescopes.
ſcopes, it will be proper to fhew how the rays
of light are affected by paffing through concave
glaffes, and alfo by falling upon concave mir-
rours.
When parallel rays, as a b c d e f g h, paſs Plate.
directly through a glaſs A B, which is equally XVIII.
concave on both fides, they will diverge after Fig. 1.
paffing through the glafs, as if they had come
from a radiant point C, in the center of the
glafs's concavity; which point is called the ne-
gative or virtual focus of the glafs. Thus the
ray a, after paffing through the glafs A B, will
go on in the direction k l, as if it had proceeded
from the point C, and no glaſs been in the way,
The ray b will go on in the direction m n
mn; the
ray in the direction op, &c.-The ray C,
that falls directly upon the middle of the glaſs,
fuffers no refraction in paffing through it; but
goes on in the fame rectilineal direction, as if
no glaſs had been in its way.
If the glafs had been concave only on one
fide, and the other fide quite plane, the rays
would have diverged, after paffing through it,
as if they had come from a radiant point at
double the diſtance of C from the glaſs; that is,
as if the radiant had been at the diſtance of a
whole diameter of the glafs's concavity.
If rays come more converging to fuch a glafs,
than parallel rays diverge after paffing through
it, they will continue to converge after paffing
through it; but will not meet fo foon as if no
glafs had been in the way; and will incline
towards the fame fide to which they would have
diverged, if they had come parallel to the glafs.
Thus the rays f and b, going in a converging
tate towards the edge of the glaſs at B, and
con-
222
Of Optics.
Fig. 2.
converging more in their way to it than the pa-
rallel rays diverge after paffing through it, they
will go on converging after they pafs through
it, though in a lefs degree than they did before,
and will meet at I: but if no glafs had been in
their way, they would have met at i.
When the parallel rays, as d f a, Cm b, el c,
fall upon a concave mirror A B (which is not
tranſparent, but has only the furface Ab B of
a clear poliſh) they will be reflected back from
that mirror, and meet in a point m, at half the
diſtance of the furface of the mirror from C,
the center of its concavity: for they will be
reflected at as great an angle from the perpendi-
cular to the furface of the mirror, as they fell
upon it, with regard to that perpendicular; but
on the other fide thereof. Thus, let C be the
center of concavity of the mirror Ab B, and
let the parallel rays d f a, Cm b, and el c, fall
upon it at the points a b, and c. Draw the
lines Cia, Cm b, and C h c, from the center C
to theſe points; and all thefe lines will be per-
pendicular to the furface of the mirror, becaufe
they proceed thereto like fo many radii or ípokes
from its center. Make the angle C a b equal
to the angle da C, and draw the line a m b,
which will be the direction of the ray dƒ a, after
it is reflected from the point a of the mirror :
fo that the angle of incidence d a C, is equal to
the angle of reflection Cab; the rays making
equal angles with the perpendicular Ci a on its
oppofite fides.
df
Draw alfo the perpendicular C b c to the point.
c, where the ray ele touches the mirror; and,
having made the angle C c i, equal to the angle
Cce, draw the line cmi, which will be the
courfe
Of Optics.
223
courſe of the ray el c, after it is reflected from
the mirror.
L
The ray Cmb paffes through the center of
concavity of the mirror, and falls upon it at
b, the perpendicular to it; and is therefore re-
flected back from it in the fame line bm C.
All theſe reflected rays meet in the point m;
and in that point the image of the body which
emits the parallel rays d a, C b, and e c, will be
formed which point is diftant from the mir-
ror equal to half the radius bm C of its con-
cavity.
The rays which proceed from any celeſtial
object may be eſteemed parallel at the earth,
and therefore, the images of that object will be
formed at m, when the reflecting furface of the
concave mirror is turned directly towards the
object. Hence, the focus m of parallel rays
is not in the center of the mirror's concavity,
but half way between the mirror and that
center.
The rays which proceed from any remote
terreſtrial object, are nearly parallel at the mir-
ror; not strictly fo, but come diverging to it,
in ſeparate pencils, or, as it were, bundles of
rays, from each point of the fide of the object
next the mirror: and therefore they will not
be converged to a point, at the diſtance of half
the radius of the mirror's concavity from its
reflecting ſurface; but into ſeparate points at a
little greater diftance from the mirror. And
the nearer the object is to the mirror, the far-
ther theſe points will be from it; and an in-
verted image of the object will be formed in
them, which will feem to hang pendent in the
air; and will be ſeen by an eye placed beyond
it (with regard to the mirror) in all reſpects
like
224
Of Optics
Fig. 3.
like the object, and as diftinct as the object
itſelf.
Let Ac B be the reflecting furface of a mir-
ror, whofe center of concavity is at C; and
let the upright object D E be placed beyond the
center C, and fend out a conical pencil of di-
verging rays from its upper extremity D, to
every point of the concave furface of the mir-
ror Ac B. But to avoid confufion, we only
draw three rays of that pencil, as DA, Dc,
D B.
From the center of concavity C, draw the
three right lines CA, Cc, CB, touching the
mirror in the fame points where the forefaid
rays touch it; and all thefe lines will be per-
pendicular to the furface of the mirror. Make
the angle C Ad equal to the angle D AC, and
draw the right line Ad for the courfe of the
reflected ray D A: make the angle C 6 d equal
to the angle Dc C, and draw the right line cd
for the courſe of the reflected ray D d make
alſo the angle C B d equal to the angle D B C,
and draw the right line B d for the courfe of the
reflected ray D B. All theſe reflected rays will
meet in the point d, where they will form the
extremity d of the inverted image e d, fimilar to
the extremity D of the upright object D E.
If the pencils of rays E f, Eg, Eb be alfo
continued to the mirror, and their angles of re-
flection from it be made equal to their angles of
incidence upon it, as in the former pencil from
D, they will all meet at the point e by reflection,
and form the extremity e of the image e d, fimi-
lar to the extremity E of the object D E.
And as each intermediate point af the object,
between D and E, fends out a pencil of rays in
like manner to every part of the mirror, the
rays
Of Optics.
225
rays of each pencil will be reflected back from
it, and meet in all the intermediate points be-
tween the extremities e and d of the image; and
fo the whole image will be formed, not at i,
half the diſtance of the mirror from its center
of concavity C; but at a greater diftance, be-
tween i and the object DE; and the image will
be inverted with refpect to the object.
This being well understood, the reader will
eafily fee how the image is formed by the large
concave mirror of the reflecting teleſcope,
when he comes to the defcription of that in-
ftrument.
When the object is more remote from the
mirror than its center of concavity C, the
image will be less than the object, and between
the object and mirror: when the object is nearer
than the center of concavity, the image will be
more remote and bigger than the object: thus,
if D E be the object, e d will be its image; for,
as the object recedes from the mirror, the
image approaches nearer to it; and as the ob-
ject approaches nearer to the mirror, the image
recedes farther from it; on account of the leffer
or greater divergency of the pencils of rays
which proceed from the object; for, the lefs
they diverge, the fooner they are converged to
points by reflection; and the more they di-
verge, the farther they must be reflected before
they meet.
If the radius of the mirror's concavity and
the diſtance of the object from it be known, the
diſtance of the image from the mirror is found
by this rule divide the product of the dif-
tance and radius by double the diftance made
lefs by the radius, and the quotient is the dif
tance required.
i
If
224
Of Optics.
If the object be in the center of the mirror's
concavity, the image and object will be coinci-
dent, and equal in bulk.
If a man places himſelf directly before a large
concave mirror, but farther from it than its
center of concavity, he will fee an inverted
image of himſelf in the air, between him and
the mirror, of a lefs fize than himſelf. And
if he holds out his hand towards the mirror,
the hand of the image will come out towards
his hand, and coincide with it, of an equal
bulk, when his hand is in the center of conca-
vity; and he will imagine he may fhake hands
with his image. If he reaches his hand farther,
the hand of the image will pafs by his hand, and
come between his hand and his body and if he
moves his hand towards either fide, the hand of
the image will move towards the other; fo that
whatever way the object moves, the image will
move the contrary 'way.
All the while a by-ſtander will fee nothing of
the image, becauſe none of the reflected rays
that form it enter his eyes.
If a fire be made in a large room, and a
fmooth mahogany table be placed at a good
diftance near the wall, before a large concave
mirror, fo placed, that the light of the fire
may be reflected from the mirror to its focus
upon the table; if a perfon ftands by the table,
he will fee nothing upon it but a longiſh beam
of light but if he ftands at a diſtance towards
the fire, not directly between the fire and mir-
ror, he will fee an image of the fire upon the
table, large and erect. And if another per-
fon, who knows nothing of this matter before-
hand, fhould chance to come into the room,
and ſhould look from the fire towards the table,
he
Of Optics.
227
he would be ſtartled at the appearance; for the Plate
table would ſeem to be on fire, and by being XVIII.
near the wainſcot, to endanger the whole houſe.
In this experiment, there fhould be no light
in the room but what proceeds from the fire;
and the mirror ought to be at least fifteen
inches in diameter.
If the fire be darkened by a fcreen, and a
large candle be placed at the back of the fcreen;
a perſon ſtanding by the candle will fee the
appearance of a fine large ftar, or rather planet,
upon the table, as bright as Venus or Jupiter.
And if a ſmall wax taper (whofe flame is much
leſs than the flame of the candle) be placed near
the candle, a fatellite to the planet will appear
on the table and if the taper be moved round
the candle, the fatellite will go round the planet.
For theſe two pleafing experiments, I am in-
debted to the late reverend Dr. LONG, Lowndes's
profeffor of aftronomy at Cambridge, who fa-
voured me with the fight of them, and many
more of his curious inventions.
In a refracting teleſcope, the glafs which is The re-
neareſt the object in viewing it, is called the fracting
object-glaſs; and that which is neareſt the eye,
teleſco, es
is called the eye-glass. The object-glafs muft
be convex, but the eye-glafs may be either
convex or concave: and generally, in looking
through a teleſcope, the eye is in the focus of
the eye-glaſs; though that is not very material:
for the diſtance of the eye, as to diftinct vifion,
is indifferent, provided the rays of the pencils
fall upon it parallel: only, the nearer the eye
is to the end of the teleſcope, the larger is the
ſcope or area of the field of view.
Let c d be a convex-glafs fixed in a long tube,
and have its focus at E. Then, a pencil of rays
Q
gb in
Fig. 4
228
Of Optics.
gbi, flowing from the upper extremity A of the
remote object A B, will be ſo refracted by paffing
through the glafs, as to converge and meet in
the point f; whilſt the pencil of rays k l m flow-
ing from the lower extremity B, of the fame ob-
ject A B, and paffing through the glafs, will con-
verge and meet in the point e: and the images
of the points A and B, will be formed in the
points ƒ and e.
And as all the intermediate
points of the object, between A and B, ſend out
pencils of rays in the fame manner, a fufficient
number of theſe pencils will paſs through the
object glaſs c d, and converge to as many inter-
mediate points between e and ƒ; and fo will form
the whole inverted image e E f, of the diſtinct
object. But becauſe this image is fmall, a con-
cave glaſs no is fo placed in the end of the tube
next the eye, that its virtual focus may be at F.
And as the rays of the pencils paſs converging
through the concave glafs, but converge lefs after
paffing through it than before, they go on fur-
ther, as to b and a, before they meet; and the
pencils themſelves being made to diverge by
paffing through the concave glafs, they enter the
eye, and form the large picture ab upon the
retina, whereon it is magnified under the angle
b Fa.
But this teleſcope has one inconveniency which
renders it unfit for moft purpoſes, which is, that
the pencils of rays being made to diverge by
paffing through the concave glafs n o, very few
of them can enter the pupil of the eye; and
therefore the field of view is but very fmall, as
is evident by the figure. For none of the pen-
cils which flow either from the top or bottom of
the object A B can enter the pupil of the eye at
C, but are all ftopt by falling upon the iris
above
Of Optics.
229
above and below the pupil: and therefore, only
the middle part of the object can be feen when
the teleſcope lies directly towards it, by means
of thofe rays which proceed from the middle of
the object. So that to fee the whole of it, the
teleſcope muſt be moved upwards and down-
wards, unless the object be very remote; and
then it is never ſeen diftinctly.
This inconvenience is remedied by fubftitut- Fig. 5.
ing a convex eye-glafs, as gb, in place of the
concave one; and fixing it fo in the tube, that
its focus may be coincident with the focus of the
object-glafs cd, as at E. For then, the rays
of the pencils flowing from the object A B, and
paffing through the object-glaſs c d, will meet in
its focus, and form the inverted image m Ep:
and as the image is formed in the focus of the
eye-glaſs g b, the rays of each pencil will be pa-
rallel, after paffing through that glafs; but the
pencils themſelves will croſs in its focus, on the
other fide, as at e: and the pupil of the eye
being in this focus, the image will be viewed
through the glaſs, under the angle ge h; and
being at E, it will appear magnified, ſo as to fill
the whole ſpace C m e p D.
E
But, as this teleſcope inverts the image with
reſpect to the object, it gives an unpleaſant view.
of terreftrial objects; and is only fit for viewing.
the heavenly bodies, in which we regard not their
pofition, becauſe their being inverted does not
appear, on account of their being round. But
whatever way the object feems to move, this tele-
ſcope muſt be moved the contrary way, in order
to keep fight of it; for, fince the object is in-
verted, its motion will be fo too.
The magnifying power of this teleſcope is,
as the focal diftance of the object-glais to the
Q 2
focal
230
Of Optics.
$
Y
focal diſtance of the eye-glafs. Therefore, if the
former be divided by the latter, the quotient
will exprefs the magnifying power.
When we ſpeak of magnifying by a tele-
ſcope or microſcope, it is only meant with regard
to the diameter, not to the area or folidity of the
object. But as the inftrument magnifies the ver-
tical diameter, as much as it does the horizontal,
it is eafy to find how much the whole viſible area
or furface is magnified: for, if the diameters be
multiplied into one another, the product will
exprefs the magnification of the whole vifible
area. Thus, fuppofe the focal diftance of the
object-glass be ten times as great as the focal
diſtance of the eye-glafs; then, the object will
be magnified ten times, both in length and
breadth and 10 multiplied by 10, produces
100; which fhews, that the area of the object
will appear 100 times as big when feen through
fuch a teleſcope, as it does to the bare eye.
Hence it appears, that if the focal diſtance of
the eye-glafs, were equal to the focal diftance of
the object-glafs, the magnifying power of the
teleſcope would be nothing.
This teleſcope may be made to magnify in any
given degree, provided it be of a fufficient
length. For, the greater the focal diſtance of
the object-glaſs, the lefs may be the focal dif-
tance of the eye-glafs; though not directly in
proportion. Thus, an object-glafs, of 10 feet
focal diſtance, will admit of an eye glafs whoſe
focal dittance is little more than 2 inches ;
which will magnify near 48 times but an ob-
ject-glaſs, of 100 feet focus, will require an eye-
glafs fomewhat more than 6 inches; and will
therefore magnify almoſt 200 times.
A teleſcope for viewing terreftrial objects,fhould
be fo conftructed, as to fhew them in their natural
poſture.
Of Optics.
231
pofture. And this is done by one object glafs Fig. 6.
cd, and three eye-glaffes e f, g h, i k, ſo placed,
that the diſtance between any two, which are
neareſt to each other, may be equal to the fum
of their focal diftances; as in the figure, where
the focus of the glaffes c d and e f meet at F,
thofe of the glaffes e ƒ and g b, meet at l, and of
g
b and i k, at m; the eye being at n, in or near
the focus of the eye-glaſs i k, on the other fide.
Then, it is plain, that theſe pencils of rays, which
flow from the object A B, and pafs through
the object-glafs c d, will meet and form an in-
verted image C F D in the focus of that glaſs;
and the image being alfo in the focus of the glafs
ef, the rays of the pencils will become parallel,
after paffing through that glafs, and croſs at 7,
in the focus of the glafs ef; from whence they
paſs on to the next glass g b, and by going
through it they are converged to points in its
other focus, where they form an erect image
Em F, of the object A B : and as this image is
alfo in the focus of the eye glass i k, and the eye
on the oppoſite ſide of the ſame glaſs; the image
is viewed through the eye-glats in this teleſcope,
in the fame manner as through the eye-glafs in
the former one; only in a contrary pofition,
that is, in the fame pofition with the object.
The three glaffes next the eye, have all their
focal diftances equal: and the magnifying power
of this teleſcope is found the fame way as that
of the laſt above; viz. by dividing the focal
diſtance of the object-glafs cd, by the focal
diſtance of the eye-glaſs i k, or g h, or ef, fince
all theſe three are equal.
When the rays of light are feparated by re-
fraction, they become coloured, and if they be
united again, they will be a perfect white. But
Q3
thoſe
232
Of Optics.
Why the thofe rays which pafs through a convex glafs,
object ap- near its edges are more unequally refracted than
pears co- thofe which are nearer the middle of the glass.
when feen And when the rays of any pencil are unequally
through a refracted by the glafs, they do not all meet
teleſcope. again in one and the fame point, but in feparate
loured
The re
flecting
teleſcope.
Fig. 7.
points; which makes the image indiftinct, and
coloured, about its edges. The remedy is, to
have a plate with a fmall round hole in its mid-
dle, fixed in the tube at m, parallel to the glaffes.
For, the wandering rays about the edges of the
glaffes will be ſtopt, by the plate, from coming
to the eye and none admitted but thofe which
come through the middle of the glaſs, or at leaſt
at a good diſtance from its edges, and paſs
through the hole in the middle of the plate. But
this circumfcribes the image, and leffens the
field of view, which would be much larger if
the plate could be difpenfed with.
:
The great inconvenience attending the ma-
nagement of long teleſcopes of this kind, has
brought them much into difufe ever fince the
reflecting teleſcope was invented. For one of this
fort, fix feet in length, magnifies as much as one.
of the other an hundred. It was invented by
Sir Ifaac Newton, but has received confiderable
improvements fince his time; and is now gene-
rally conſtructed in the following manner, which
was first propoſed by Dr. Gregory.
At the bottom of the great tube TT TT is
placed the large concave mirror DUVF, whofe
principal focus is at m; and in its middle is a
round hole P, oppofite to which is placed the
finall mirror L, concave toward the great
one; and fo fixed to a ftrong wire M, that it
may be moved farther from the great mirror,
or nearer to it, by means of a long ſcrew on the
7
out-
Of Optics.
233
outſide of the tube, keeping its axis ftill in the
fame line P m n with that of the great one.-
Now, fince in viewing a very remote object, we
can ſcarce fee a point of it but what is at leaft as
broad as the great mirror, we may confider the
rays of each pencil, which flow from every point
of the object, to be parallel to each other, and
to cover the whole reflecting furface DUV F.
But to avoid confufion in the figure, we fhall
only draw two rays of a pencil flowing from each
extremity of the object into the great tube, and
trace their progrefs, through all their reflections
and refractions, to the eye f, at the end of the
fmall tube tt, which is joined to the great one.
Let us then fuppofe the object A B to be at
fuch a diſtance, that the rays C may flow from
its lower extremity B, and the rays E from its
upper extremity A. Then the rays C falling
parallel upon the great mirror at D, will be
thence reflected, converging in the direction
DG; and by croffing at I in the principal focus.
of the mirror, they will form the upper extre-
mity I of the inverted image I K, fimilar to the
lower extremity B of the object A B: and paf-
fing on to the concave mirror L (whofe focus
is at n) they will fall upon it at g, and be thence
reflected converging, in the direction g N, becauſe
gm is longer than g n; and paffing through the
hole P in the large mirror, they would meet
fomewhere about r, and form the lower extremity
d of the erect image a d, fimilar to the lower ex-
tremity B of the object A B. But by paffing
through the plano-convex-glafs R in their way,
they form that extremity of the image at b.
In like manner, the rays E, which come from the
top of the object A B, and fall parallel upon the
great mirror at F, are thence reflected converg-
Q4
ing
234
Of Optics.
ing to its focus, where they form the lower ex-
tremity K of the inverted image I K, fimilar to
the upper extremity A of the object A B; and
thence paffing on to the fmall mirror L, and
falling upon it at b, they are thence reflected in
the converging ſtate b 0; and going on through
the hole P of the great mirror, they will meet
fomewhere about q, and form there the upper
extremity a of the erect image a d, fimilar to the
upper extremity A of the object A B: but by
paffing through the convex glaſs R in their way,
they meet and croſs ſooner, as at a, where that
point of the erect image is formed.-The like
being underſtood of all thoſe rays which flow
from the intermediate points of the object, be-
tween A and B, and enter the tube TT; all the
intermediate points of the image between a and
b will be formed and the rays paffing on from
the image through the eye-glafs S, and through
a fmall hole e in the end of the leffer tube t t.
t,
they enter the eye f, which fees the image a d
(by means of the eye-glafs) under the large
angle c e d, and magnified in length, under that
angle from c to d.
:
In the beſt reflecting teleſcopes, the focus of
the ſmall mirror is never coincident with the
focus m of the great one, where the firſt image
IK is formed, but a little beyond it (with refpect
to the eye) as at n: the confequence of which is,
that the rays of the pencils will not be parallel
after reflection from the fmall mirror, but con-
verge ſo as to meet in points about q, e, r; where
they will form a larger upright image than a dy
if the glaſs R was not in their way and this
image might be viewed by means of a fingle
eye-glaſs properly placed between the image
and the eye but then the field of view would be
lefs,
Of Optics.
235
lefs, and confequently not fo pleafant; for which
reaſon, the glaſs R is ftill retained, to enlarge
the ſcope or area of the field.
To find the magnifying power of this tele-
ſcope, multiply the focal diftance of the great
mirror by the diſtance of the fmall mirror from
the image next the eye, and multiply the focal
diſtance of the fmall mirror by the focal dif-
tance of the eye-glafs: then, divide the pro-
duct of the former multiplication by the pro-
duct of the latter, and the quotient will exprefs
the magnifying power.
I fhall here fet down the dimenfions of one of
Mr. Short's reflecting teleſcopes, as deſcribed in
Dr. Smith's Optics.
The focal diſtance of the great mirror 9.6
inches, its breadth 2.3; the focal diſtance of the
fmall mirror 1.5, its breadth 0.6: the breadth
of the hole in the great mirror 0.5; the diſtance
between the ſmall mirror and the next eye-glafs
14.2; the diſtance between the two eye-glaffes
2.4; the focal diſtance of the eye-glafs next the
metals 3.8; and the focal diſtance of the eye-
glafs next the eye 1.1.
One great advantage of the reflecting tele-
fcope is, that it will admit of an eye-glafs of a
much fhorter focal diftance than a refracting
teleſcope will; and, confequently, it will mag-
nify fo much the more for the rays are not
coloured by reflection from a concave mirror,
if it be ground to a true figure, as they are by
paffing through a convex-glafs, let it be ground
ever ſo true.
The adjuſting ſcrew on the outſide of the
great tube fits this teleſcope to all forts of eyes,
by bringing the fmall mirror either nearer to
the eye, or removing it farther by which
means,
236
Of Optics.
means, the rays are made to diverge a little for
fhort-fighted eyes, or to converge for thofe of a
long fight.
The nearer an object is to the teleſcope, the
more its pencils of rays will diverge before they
fall upon the great mirror, and therefore they
will be the longer of meeting in points after re-
flection; ſo that the firft image 1 K will be
formed at a greater diftance from the large mir-
ror, when the object is near the teleſcope, than
when it is very remote. But as this image muft
be formed farther from the ſmall mirror than
its principal focus 2, this mirror muſt be always
fet at a greater diſtance from the large one, in
viewing near objects, than in viewing remote
ones. And this is done by turning the ſcrew on
the outfide of the tube, until the fmall mirror
be fo adjuſted, that the object (or rather its
image) appears, perfect.
In looking through any teleſcope towards an
object, we never fee the object itſelf, but only
that image of it which is formed next the eye in
the teleſcope. For, if a man holds his finger or a
ftick between his bare eye and an object, it will
hide part (if not the whole) of the object from
his view. But if he ties a ſtick acroſs the mouth
of a teleſcope, before the object-glafs, it will hide.
no part of the imaginary object he faw through
the teleſcope before, unleſs it covers the whole
mouth of the tube: for, all the effect will be, to
make the object appear dimmer, becauſe it in-
tercepts part of the rays. Whereas, if he puts
only a piece of wire acroſs the infide of the tube,
between the eye-glafs and his eye, it will hide
part of the object which he thinks he fees: which
proves that he fees not the real object, but its
image. This is alfo confirmed by means of the
fmall
LATE XIX.
n
E
Fig. 1.h
Αν
g it
D
m
•Red
B
B
range
B
C
Violet
Fig. 2.
a
恳
​9
K
E
Fig. 6.
B
08
60
40
60
D
Fig.7.
I. Fergulm delin.
Indigo
k-
m
n
B
80
40T
60 B
60 G
k
48 Y
n
45 R
་ ས།
D
H
F
Fig.3.
E
D
Fig. 4.
C
E
D
F
p
Fig. 5.
R
Y
G
B
I
V
Fig. 8.
S
J.Mynde fo.
Of Optics.
237
fmall mirror L, in the reflecting teleſcope, which
is made of opake metal, and ſtands directly be-
tween the eye and the object towards which the
teleſcope is turned; and will hide the whole ob-
ject from the eye at e, if the two glaffes R and
S are taken out of the tube.
The multiplying glafs is made by grinding PlateXIX.
down the round fide bi k of a convex glafs A B Fig. 1.
into ſeveral flat ſurfaces, as h b, bld, dk. An ob- The mul
ject C will not appear magnified, when feen tiplying
through this glaſs, by the eye at H, but it will glas.
appear multiplied into as many different objects
as the glaſs contains plane furfaces. For, fince
rays will flow from the object C to all parts of ·
the glaſs, and each plane furface will refract theſe
rays to the eye, the fame object will appear to
the eye, in the direction of the rays which enter
it through each furface. Thus, a ray g i H,
falling perpendicularly on the middle furface
will go through the glaſs to the eye without fuf-
fering any refraction; and will therefore fhew
the object in its true place at C: whilſt a ray a b
flowing from the fame object, and falling ob-
liquely on the plane furface bb, will be refracted
in the direction be, by paffing through the glaſs;
and upon leaving it, will go on to the eye in the
direction e H; which will caufe the fame object
C to appear alfo at E, in the direction of the ray
He, produced in the right line Hen. And the
ray cd, flowing from the object C, and falling
obliquely on the plane furface d k, will be refract-
ed (by paffing through the glafs and leaving it
at f) to the eye at H; which will caufe the fame
object to appear at D, in the direction Hf m.-
If the glaſs be turned round the line gl H, as
an axis, the object C will keep its place, becauſe
the furface bld is not removed; but all the
other
238
Of Optics.
Fig. 2.
The ca-
mera ob.
fcura.
other objects will feem to go round C, becauſe
the oblique planes, on which the rays a b, c d
fall, will go round by the turning of the glass.
The camera obfcura is made by a convex glass
CD, placed in a hole of a window-fhutter.
Then, if the room be darkened fo as no light
can enter but what comes through the glafs, the
pictures of all the objects (as fields, trees, build-
ings, men, cattle, &c.) on the outfide, will be
fhewn in an inverted order, on a white paper
placed at G H in the focus of the glaſs; and
will afford a moft beautiful and perfect piece of
perſpective or landſcape of whatever is before
the glass; eſpecially if the fun fhines upon the
objects.
If the convex glafs CD be placed in a tube in
the fide of a fquare box, within which is the
plane mirror EF, reclining backwards in an
angle of 45 degrees from the perpendicular k
q,
the pencils of rays flowing from the outward ob-
jects, and paffing through the convex glaſs to
the plane mirror, will be reflected upwards from
it, and meet in points, as I and K (at the fame
diſtance that they would have meet at H and
G, if the mirror had not been in the way) and
will form the aforefaid images on an oiled paper
ſtretched horizontally in the direction I K; on
which paper, the out-lines of the images may
be eaſily drawn with a black lead pencil; and
then copied on a clean fheet, and coloured by
art, as the objects themſelves are by nature.-
In this machine, it is ufual to place a plane glaſs,
unpolished, in the horizontal fituation I K, which
glaſs receives the images of the outward objects;
and their outlines may be traced upon it by a
black-lead pencil.
3
N. B.
Of Optics.
239
N. B. The tube in which the convex glafs
CD is fixed, muſt be made to draw out, or puſh
in, ſo as to adjuſt the diſtance of that glaſs from
the plane mirror, in proportion to the diſtance
of the outward objects; which the operator does,
until he fees their images diftinctly painted on
the horizontal glaſs at I K.
The forming a horizontal image, as IK, of an
upright object AB, depends upon the angles of
incidence of the rays upon the plane mirror E F,
being equal to their angles of reflection from
it. For, if a perpendicular .be ſuppoſed to be
drawn to the furface of the plane mirror at e,
where the ray A a Ce falls upon it, that ray will
be reflected upwards in an equal angle with the
other fide of the perpendicular, in the line e d I.
Again, if a perpendicular be drawn to the mir-
ror from the point f, where the ray Abf falls
upon it, that ray will be reflected in an equal
angle from the other fide of the perpendicular, in
the line fb I. And if a perpendicular be drawn
from the point g, where the ray Acg falls upon
the mirror, that ray will be reflected in an equal
angle from the other fide of the perpendicular,
in the line gil. So that all the rays of the pencil
a be, flowing from the upper extremity of the
object AB, and paffing through the convex glafs
CD, to the plane mirror E F, will be reflected
from the mirror and meet at I, where they will
form the extremity I of the image I K, fimilar
to the extremity A of the object A B.
like is to be underſtood of the pencil q r s, flow-
ing from the lower extremity of the object A B,
and meeting at K (after reflection from the plane
mirror) the rays form the extremity K of the
image, fimilar to the extremity B of the object :
and fo of all the pencils that flow from the in-
termediate
The
240
Of Optics.
The
opera-
glass.
mon lock-
ing glass.
Fig. 3.
termediate points of the object to the mirror;
through the convex glaſs.
If a convex glaſs, of a fhort focal diſtance, be
placed near the plane mirror, in the end of a
fhort tube, and a convex glafs be placed in a
hole in the fide of the tube, fo as the image may
be formed between the laft-mentioned convex
glafs, and the plane mirror, the image being
viewed through this glafs will appear magnified.
-In this manner the opera-glaffes are conftruct-
ed; with which a gentleman may look at any
lady at a diſtance in the company, and the lady
know nothing of it.
{
The image of any object that is placed before
The com- a plane mirror, appears as big to the eye as the
object itſelf; and is erect, diſtinct, and feeming-
ly as far behind the mirror, as the object is be-
fore it and that part of the mirror, which
reflects the image of the object to the eye (the
eye being fuppofed equally diftant from the glaſs
with the object) is juft half as long and half as
broad as the object itſelf. Let A B be an ob-
ject placed before the reflecting furface g h i of
the plane mirror CD; and let the eye be at o.
Let A b be a ray of light flowing from the top
A of the object, and falling upon the mirror at
b: and h m be a perpendicular to the furface of
the mirror at b, the ray A b will be reflected
from the mirror to the eye at o, making an
angle m bo equal to the angle Abm: then will
the top of the image E appear to the eye in the
direction of the reflected ray o b produced to E,
where the right line Ap E, from the top of the
object, cuts the right line o b E, at E. Let Bi
be a ray of light proceeding from the foot of the
object at B to the mirror at i, and ni a per-
pendicular to the mirror from the point i,
where
of Optics.
241
費
​where the ray B i falls upon it: this ray will be
reflected in the line i o, making an angle n io,
equal to the angle Bin, with that perpendi-
cular, and entering the eye at o: then will the
foot F of the image appear in the direction of
the reflected ray o i, produced to F, where the
right line B F cuts the reflected ray produced to
F. All the other rays that flow from the inter-
mediate points of the object AB, and fall upon
the mirror between h and i, will be reflected to
the eye at ; and all the intermediate points of
the image E F will appear to the eye in the di-
rection-line of theſe reflected rays produced.
But all the rays that flow from the object, and
fall upon the mirror above h, will be reflected
back above the eye at o; and all the rays that
flow from the object, and fall upon the mirror
below i, will be reflected back below the eye at
o: fo that none of the rays that fall above b, or
below i, can be reflected to the eye at o; and
the diſtance between h and i is equal to half the
length of the obje& A B.
in a plane.
Hence it appears, that if a man fee his whole A man
image in a plane looking-glafs, the part of the will fee
glafs that reflects his image must be juſt half as his image
long and half as broad as himſelf, let him ftand looking-
at any diſtance from it whatever; and that his glaſs, that
image muſt appear juſt as far behind the glafs as is but
he is before it. Thus, the man A B viewing half his
himſelf in the plane mirror C D, which is juft Fig. 4.
height.
half as long as himfelf, fees his whole image as.
at E F, behind the glaſs, exactly equal to his
own fize. For, a ray AC proceeding from his
eye at A, and falling perpendicularly upon the
furface of the glafs at C, is reflected back to his
eye in the fame line CA; and the eye of his
image will appear at E, in the fame line pro-
duced
242
Of Optics.
duced to E, beyond the glaſs. And a ray B Dig
D,
flowing from his foot, and falling' obliquely on
the glass at D, will be reflected as obliquely on
the other fide of the perpendicular a b D, in the
direction D A; and the foot of his image will
appear at F, in the direction of the reflected ray
AD, produced to F, where it is cut by the right
line BG F, drawn parallel to the right line AC E.
Juft the fame as if the glafs were taken away,
and a real man ftood at F, equal in fize to the
man ſtanding at B: for to his eye at A, the eye
of the other man at E would be feen in the di-
rection of the line ACE; and the foot of the
man at F would be feen by the eye A, in the
direction of the line AD F.
If the glaſs be brought nearer the man AB,
as ſuppoſe to cb, he will fee his image as at
CDG: for the reflected ray C A (being perpen-
dicular to the glafs) will fhew the eye of the
image as at C; and the incident ray B b, being
reflected in the line b A, will ſhew the foot of his
image as at G; the angle of reflection a b A being
always equal to the angle of incidence B b a:
and fo of all the intermediate rays from A to B.
Hence, if the man AB advances towards the
glafs CD, his image will approach towards it;
and if he recedes from the glaſs, his image will
alfo recede from it.
Having already fhewn, that the rays of light
are refracted when they pafs obliquely through
different mediums, we come now to prove that
fome rays are more refrangible than others; and
that, as they are differently refracted, they ex-
cite in our minds the ideas of different colours.
This will account for the colours feen about the
edges of the images of thofe objects which are
viewed through fome teleſcopes.
Let
Of Optics.
243
Let the fun fhine into a dark room through a Fig. 5.
fmall hole, as at e e, in a window-fhutter; and
place a triangular prifm BC in the beam of rays
A, in fuch a manner, that the beam may fall ob-
liquely on one of the fides a b C of the prifm.
The rays will fuffer different refractions by paf- The
fing through the prifm, ſo that inſtead of going prism.
all out of it on the fide dc C, in one direction,
they will go on from it in the different directions
repreſented by the lines f, g, h, i, k, l, m, n; and
falling upon the oppofite fide of the room, or
on white paper placed as at p q to receive them,
they will paint upon it a ſeries of moſt beautiful
lively colours not to be equalled by art) in this The co-
order, viz. thoſe rays which are least refracted by
lours of
the priſm, and will therefore go on between the
the light,
lines n and m, will be of a very bright intenſe
red at n, degenerating from thence gradually
into an orange colour, as they are nearer the line
m: the next will be of a fine orange colour at
m, and from thence degenerate into a yellow co-
lour towards /: at / they will be of a fine yellow,
which will incline towards a green, more and
more, as they are nearer and nearer k: at k they
will be a pure green, but from thence towards i
they will incline gradually to a blue: at i they
will be a perfect blue, inclining to an indigo co-
lour from thence towards h: at b they will be
quite the colour of indigo, which will gradually
change towards a violet, the nearer they are to
g and at g they will be of a fine violet colour,
which will incline gradually to a red as they
come nearer to f, where the coloured image
ends.
There is not an equal quantity of rays in each
of theſe colours; for, if the oblong image p q
be divided into 360 equal parts, the red ſpace
R will
R
244
Of Optics.
Fig. 6.
R will take up 45 of thefe parts: the orange O,
27; the yellow Y, 48; the green G, 60; the
blue B, 60; the indigo I, 40; and the violet V,
80; all which ſpaces are as nearly proportioned in
the figure as the ſmall ſpace q pwould admit of.
If all theſe colours be blended together again,
they will make a pure white; as is proved thus.
Take away the paper on which the colours p q
fell, and place a large convex glaſs D in the rays
f, g, h, &c. which will refract them ſo, as to make
them unite and crofs each other at W: where, if a
white paper be placed to receive them, they will
excite the idea of a ſtrong lively white. But if
the paper be placed farther from the glaſs, as at
rs, the different colours will appear again upon
it, in an inverted order, occafioned by the rays
croffing at W.
As white is a compofition of all colours, fo
black is a privation of them all, and, therefore,
properly no colour.
C 40
E 60;
Let two concentric circles be drawn on a
fmooth round board ABCDEFG, and the
outermoft of them divided into 360 equal parts
or degrees: then, draw ſeven right lines, as O A,
→ B, &c. from the center to the outermoft circle;
making the lines A and B include 80 de-
grees of that circle; the lines o B and
degrees; C and D 60; O D and
OE and O F 48; O F and 0 G 27 ; © G and ☺ A
45. Then, between theſe two circles, paint the
fpace AG red, inclining to orange near G; GF
orange, inclining to yellow near F; FE yellow,
inclining to green near E; ED green, inclining
to blue near D; DC blue, inclining to indigo
near C; CB indigo, inclining to violet near B;
and B A violet, inclining to a foft red near A.
This done, paint all that part of the board black
which
6
Of Optics.
245
blended
which lies within the inner circle; and putting All the
an axis through the center of the board, let it prifmatic
be turned very ſwiftly round that axis, fo as the colours
rays, proceeding from the above.colours, may be together,
all blended and mixed together in coming to make
the eye; and then, the whole coloured part will white.
appear like a white ring, a little greyish; not
perfectly white, becauſe no colours prepared by
art are perfect.
Any of theſe colours, except red and violet,
may be made by mixing together the two con-
tiguous prifmatic colours. Thus, yellow is made
by mixing together a due proportion of orange
and
green; and green may be made by a mix-
ture of yellow and blue.
All bodies appear of that colour, whofe rays
they reflect moft; as a body appears red when
it reflects most of the red-making rays, and ab-
forbs the reſt.
come
Any two or more colours that are quite tranf- Tranfpa.
parent by themſelves, become opake when put rent co-
together. Thus, if water or fpirits of wine be lours be-
tinged red, and put in a phial, every object feen
opake if
through it will appear red; becauſe it lets only put to-
the red rays paſs through it, and ftops all the gether.
reft. If water or fpirits be tinged blue, and put
in a phial, all objects feen through it will appear
blue, becauſe it tranfmits only the blue rays, and
ſtops all the reſt. But if these two phials are
held cloſe together, fo as both of them may be
between the eye and object, the object will no
more be ſeen through them than through a plate
of metal; for whatever rays are tranfmitted
through the fluid in the phial next the object,
are ſtopped by that in the phial next the eye.
In this experiment, the phials ought not to be
round, but fquare; because nothing but the
R 2
light
246
Of Optics.
Fig. 7.
light itſelf can be feen through a round tranf-
parent body, at any diſtance.
As the rays of light fuffer different degrees
of refraction by paffing obliquely through a
priſm, or through a convex glaſs, and are thereby
ſeparated into all the feven original or primary
colours; ſo they alſo ſuffer different degrees of
refraction by paffing through drops of falling
rain; and then, being reflected towards the eye,
from the fides of theſe drops which are fartheſt
from the eye, and again refracted by paffing out
of theſe drops into the air, in which refracted
directions they come to the eye; they make all
the colours to appear in the form of a fine arch
in the heavens, which is called the rain-bow.
There are always two rain-bows feen together,
the interior of which is formed by the rays a b,
which falling upon the upper part b, of the drop
bcd, are refracted into the line b c as they enter
the drop, and are reflected from the back of it at
c, in the line c d, and then, by paffing out of the
drop into air,they are again refracted at d; and
from thence they paſs on to the eye at e: fo that
to form the interior bow, the rays fuffer two re-
fractions, as at b and d'; and one reflection, as
at c.
The exterior bow is formed by rays which
fuffer two reflections, and two refractions;
which is the occafion of its being lefs vivid than
the interior, and alfo of its colours being invert-
ed with respect to thofe of the interior. For,
when a ray a b falls upon the lower part of the
Fig. 8. drop bcde, it is refracted into the direction b c
by entering the drop; and paffing on to the
back of the drop at c, it is thence reflected in the
line cd, in which direction it is impoffible for it
to enter the eye at f: but by being again re-
flected
Of the Terrestrial Globe.
247
flected from the point d of the drop, it goes on in
the drop to e, where it paffes out of the drop into
the air, and is there refracted downward to the
eye, in the direction ef.
LECT. VIII. AND IX.
The defcription and ufe of the globes, and armil-
lary Sphere.
Fa map
IF
of the world be accurately delineated The ter-
on a ſpherical ball, the furface thereof will reſtrial
reprefent the furface of the earth: for the higheft globe.
hills are fo inconfiderable with respect to the bulk
of the earth, that they take off no more from its
roundneſs, than grains of fand do from the
roundneſs of a common globe; for the diameter
of the earth is 8000 miles in round numbers,
and no known hill upon it is three miles in per-
pendicular height.
being
That the earth is ſpherical, or round like a Proof of
globe, appears, 1. From its cafting a round the earth's
ſhadow upon the moon, whatever fide be turned globular.
towards her when he is eclipfed. 2. From its
having been failed round by feveral perfons.
3. From our feeing the farther, the higher we
ſtand. 4.
4. From our feeing the mafts of a fhip,
whilſt the hull is hid by the convexity of the
water.
And that
The attractive power of the earth draws all it may be
terreftrial bodies towards its center; as is evi- peopled
dent from the defcent of bodies in lines per- without
on all fides
pendicular to the earth's furface, at the places any one's
whereon they fall; even when they are thrown being in
off from the earth on oppofite fides, and con- danger of
fequently, in oppofite directions. So that the
R 3
falling a
way from
earth it.
248
Of the Heavens and the Earth.
Up and
down,
what,
All ob-
jects In
the hea-
earth may be compared to a great magnet rolled
in filings of ſteel, which attracts and keeps them
equally faft to its furface on all fides. Hence,
as all terreftrial bodies are attracted toward the
earth's center, they can be in no danger of fall-
ing from any fide of the earth, more than from
any other.
The heaven or fky furrounds the whole earth:
and when we ſpeak of up or down, we mean
only with regard to ourfelves; for no point,
either in the heaven, or on the furface of the
earth, is above or below, but only with refpect
to ourſelves. And let us be upon what part of
the earth we will, we ftand with our feet to-
wards its center, and our heads towards the fky:
and ſo we ſay, it is up towards the fky, and down
toward the center of the earth.
To an obſerver placed any where in the in-
definite ſpace, where there is nothing to limit
his view, all remote objects appear equally
diftant from him; and feem to be placed in a
ven ap-
valt concave ſphere, of which his eye is the
pear e-
qually center. Every aftronomer can demonftrate,
diſtant, that the moon is much nearer to us than the fun
is; that fome of the planets are fometimes
nearer to us, and fometimes farther from us,
than the fun; that others of them never come fo
near us as the fun always is; that the remoteſt
planet in our fyftem, is beyond compariſon
nearer to us than any of the fixed flars are; and
that it is highly probable fome ftars are, in a
manner, infinitely more diftant from us than
others; and yet all thefe celeftial objects ap-
The face pear equally diftant from us. Therefore, if we
imagine a large hollow fphere of glaſs to have
as many bright ftuds fixed to its infide, as
and earth there are ftars vifible in the heaven, and thefe
of the
heaven
ftuds
Of the Heavens and the Earth.
249
machine.
ſtuds to be of different magnitudes, and placed reprefent-
at the fame angular diftances from each other ed in a
as the ſtars are; the fphere will be a true re-
prefentation of the ſtarry heaven, to an eye fup-
poſed to be in its center, and viewing it all
around. And if a ſmall globe, with a map of
the earth upon it, be placed on an axis in the
center of this ſtarry ſphere, and the ſphere be
made to turn round on this axis, it will repre-
fent the apparent motion of the heavens round
the earth.
If a great circle be ſo drawn upon this ſphere,
as to divide it into two equal parts, or hemi-
ſpheres, and the plane of the circle be perpen-
dicular to the axis of the ſphere, this circle will
repreſent the equino&ial, which divides the hea- The equi-
ven into two equal parts, called the northern and noctial.
the fouthern hemispheres; and every point of that
circle will be equally diftant from the poles, or The poles.
ends of the axis in the fphere. That pole which
is in the middle of the northern hemifphere,
will be called the north pole of the sphere, and
that which is in the middle of the fouthern hemi-
ſphere, the ſouth pole.
If another great circle be drawn upon the
ſphere, in fuch a manner as to cut the equinoc-
tial at an angle of 231 degrees in two oppofite
points, it will repreſent the ecliptic, or circle of The eclip.
the fun's apparent annual motion: one half of tic.
which is on the north fide of the equinoctial,
and the other half on the fouth.
If a large ftud be made to move eastward in
this ecliptic, in fuch a manner as to go quite
round it, in the time that the fphere is turned
round weftward 366 times upon its axis; this
ſtud will repreſent the fun, changing his place The fun.
every day a 365th part of the ecliptic; and
R 4
going
250
Of the Heavens and the Earth.
The earth.
The ap-
motion of
the hea-
parent
vens,
going round weftward, the fame way as the
ftars do; but with a motion fo much flower than
the motion of the ftars, that they will make 366
revolutions about the axis of the fphere, in the
time that the fun makes only 365. During one
half of theſe revolutions, the fun will be on the
north fide of the equinoctial; during the other
half, on the fouth and at the end of each half,
in the equinoctial.
If we fuppofe the terreftrial globe in this ma-
chine to be about one inch in diameter, and the
diameter of the ftarry fphere to be about five
or fix feet, a ſmall infect on the globe would fee
only a very little portion of its furface; but it
would fee one half of the ſtarry ſphere; the con-
vexity of the globe hiding the other half from its
view. If the fphere be turned weftward round
the globe, and the infect could judge of the ap-
pearances which arife from that motion, it would
fee ſome ſtars rifing to its view in the eaftern
fide of the ſphere, whilft others were fetting on
the weſtern: but as all the ftars are fixed to the
ſphere, the ſame ſtars would always rife in the
fame points of view on the caft fide, and ſet in
the fame points of view on the weft fide. With
the fun it would be otherwife, becauſe the fun
is not fixed to any point of the ſphere, but
moves flowly along an oblique circle in it. And
if the infect ſhould look towards the fouth, and
call that point of the globe, where the equi-
noctial in the ſphere feems to cut it on the left
fide, the east point; and where it cuts the globe
on the right fide, the west point; the little ani-
mal would ſee the fun riſe north of the eaſt, and
fet north of the weft, for 182 revolutions;
after which, for as many more, the fun would
rife fouth of the eaſt, and fet fouth of the
weft,
Of the Heavens and the Earth.
251
i
weft. And in the whole 365 revolutions, the
fun would rife only twice in the eaſt point, and
fet twice in the weft. All theſe appearances
would be the fame, if the ftarry fphere ftood
ftill (the fun only moving in the ecliptic) and
the earthly globe were turned round the axis of
the ſphere eaſtward. For, as the infect would
be carried round with the globe, he would be
quite infenfible of its motion; and the fun and
ftars would appear to move weftward.
We are but very ſmall beings when compared
with our earthly glove, and the globe itself is but
a dimenfionleſs point compared with the mag-
nitude of the ftarry heavens. Whether the
earth be at reft, and the heaven turns round it,
or the heaven be at reft, and the earth turns
round, the appearance to us will be exactly the
fame. And becauſe the heaven is ſo immenſely
large, in compariſon of the earth, we fee one
half of the heaven as well from the earth's fur-
face, as we could do from its center, if the
limits of our view are not intercepted by
hills.
We may imagine as many circles defcribed Circles of
upon the earth as we pleafe; and we may the sphere.
imagine the plane of any circle defcribed upon
the earth to be continued, until it marks a circle
in the concave ſphere of the heavens.
The horizon is either fenfible or rational. The The bori-
fenfible horizon is that circle, which a man ftand-zon.
ing upon a large plane, obferves to terminate
his view all around, where the heaven and earth
ſeem to meet. The plane of our fenfible hori-
zon continued to the heaven, divides it into two
hemifperes; one vifible to us, the other hid by
the convexity of the earth.
The
252
Of the Heavens and the Earth.
Poles.
Equator.
Meridian.
The plane of the rational horizon, is fuppofed
parallel to the plane of the fenfible; to pafs
through the center of the earth, and to be
continued to the heavens. And although the
plane of the fenfible horizon touches the earth
in the place of the obferver, yet this plane,
and that of the rational horizon, will feem to
coincide in the heaven, becaufe the whole earth
is but a point compared to the fphere of the
heaven.
The earth being a ſpherical body, the hori
zon, or limit of our view, muft change as we
change our place.
The poles of the earth, are thofe two points on
its ſurface in which its axis terminates. The
one is called the north pole, and the other the
fouth pale.
The poles of the heaven, are thoſe two points.
in which the earth's axis produced terminates in
the heaven fo that the north pole of the heaven
is directly over the north pole of the earth; and
the South pole of the heaven is directly over the
fouth pole of the earth.
The equator is a great circle upon the earth,
every part of which is equally diftant from
either of the poles. It divides the earth into
two equal parts, called the northern and Southern
bemifpheres. If we fuppofe the plane of this
circle to be extended to the heaven, it will
mark the equinoctial therein, and will divide the
heaven into two equal parts, called the northern
and fouthern hemifpheres of the heaven.
The meridian of any place is a great circle
paffing through that place and the poles of the
earth. We may imagine as many fuch meri-
dians as we pleaſe, becauſe any place that is
ever
Of the Heavens and the Earth.
253
ever fo little to the east or weft of any other
place, has a different meridian from that place;
for no one circle can paſs through any two fuch
places and the poles of the earth.
The meridian of any place is divided by the
poles, into two femicircles: that which paffes
through the place is called the geographical, or
upper meridian; and that which paffes through
the oppofite place, is called the lower meridian.
When the rotation of the earth brings the Noon and
plane of the geographical meridian to the fun, mid-night.
it is noon or mid day to that place; and when
our lower meridian comes to the fun, it is mid-
night.
All places lying under the fame geographical
meridian, have their noon at the fame time, and
confequently all the other hours. All thofe
places are faid to have the fame longitude, becauſe
no one of them lies either eastward or weftward
from any of the reft.
cles.
If we imagine 24 femicircles, one of which Hour cin-
is the geographical meridian of a given place,
to meet at the poles, and to divide the equator
into 24 equal parts; each of theſe meridians
will come round to the fun in 24 hours, by the
earth's equable motion round its axis in that
time. And, as the equator contains 360 de-
grees, there will be 15 degrees contained be-
tween any two of theſe meridians which are
neareſt to one another: for 24 times 15 is 360.
And as the earth's motion is eaſtward, the fun's
apparent motion will be weftward, at the rate
of 15 degrees each hour. Therefore,
They whofe geographical meridian is 15 de- Longitude.
grees eastward from us, have noon, and every
other hour, an hour fooner than we have. They
whofe meridian is fifteen degrees weftward from
us,
25
Of the Heavens and the Earth.
us, have noon, and every other hour, an hour
later than we have: and fo on in proportion,
reckoning one hour for every fifteen degrees.
As the earth turns round its axis once in 24
hours, and fhews itſelf all round to the fun in
that time; ſo it goes round the fun once a year,
Ecliptic. in a great circle called the ecliptic, which croffes
the equinoctial in two oppofine points, making
an angle of 23 degrees with the equinoctial on
each fide. So that one half of the ecliptic is in
the northern hemifphere, and the other in the
fouthern. It contains 360 equal parts, called
degrees (as all other circles do, whether great
or fmall) and as the earth goes once round it
every year, the fun will appear to do the fame,
changing his place almoſt a degree, at a mean
rate, every 24 hours. So that whatever place,
or degree of the ecliptic, the earth is in at any
time, the fun will then appear in the oppoſite.
And as one half of the ecliptic is on the north
fide of the equinoctial, and the other half on the
fouth; the fun, as feen from the earth, will be
half a year on the fouth fide of the equinoctial,
and half a year on the north and twice a year
in the equinoctial itſelf.
Signs and
degrees.
3
The ecliptic is divided by aftronomers into
12 equal parts, called figns, each fign into 30
degrees, and each degree into 60 minutes: but
in ufing the globes, we ſeldom want the fun's
place nearer than half a degree of the truth.
The names and characters of the 12 figns are
as follow; beginning at that point of the eclip-
tic where it croffes the equinoctial to the north-
ward, and reckoning eastward round to the
fame point again. And the days of the months
on which the fun now enters the ſigns, are ſet
down below them.
Aries,
Of the Heavens and the Earth.
255
Cancer,
Aries
Taurus, Gemini,
Y
8
II
ந
March
April
May
June
20
20
21
2 I
Leo,
Virgo,
Libra,
Scorpio,
R
m
M
July
23
23
Auguft September October
23
Sagittarius, Capricornus, Aquarius, Pifces,
↑
W
PAR
*
November December January February
23
22
21
20
18
By remembering on what day the fun enters
any particular fign, we may eafily find his
place any day afterward, whilft he is in that
fign, by reckoning a degree for each day;
which will occafion no error of confequence in
uſing the globes.
When the fun is at the beginning of Aries,
he is in the equinoctial; and from that time he
declines northward every day, until he comes
to the beginning of Cancer, which is 23 de-
grees from the equinoctial: from thence he re-
cedes fouthward every day, for half a year; in
the middle of which half, he croffes the equi-
noctial at the beginning of Libra, and at the
end of that half year, he is at his greateſt fouth
declination, in the beginning of Capricorn, which
is alfo 23 degrees from the equinoctial. Then,
he returns northward from Capricorn every day,
for half a year; in the middle of which half, he
croffes the equinoctial at the beginning of Aries;
and at the end of it he arrives at Cancer.
The
256
Of the Heavens and the Earth.
Tropics.
Polar cir-
cles.
The fun's motion in the ecliptic is not per-
fectly equable, for he continues eight days
longer in the northern half of the ecliptic, than
in the fouthern: fo that the fummer half year,
in the northern hemifphere, is eight days longer
than the winter half year; and the contrary in
the fouthern hemifphere.
The tropics are leffer circles in the heaven,
parallel to the equinoctial; one on each ſide of
it, touching the ecliptic in the points of its
greateſt declination; ſo that each tropic is 231
degrees from the equinoctial, one on the north
fide of it, and the other on the fouth. The
northern tropic touches the ecliptic at the be-
ginning of Cancer, the fouthern at the beginning
of Capricorn; for which reafon the former is
called the tropic of Cancer, and the latter the
tropic of Capricorn.
The polar circles in the heaven, are each
231 degrees from the poles, all around. That
which goes round the north pole, is called the
artic circle, from gul, which fignifies a bear;
there being a collection or groupe of ſtars near
the north pole, which goes by that name. The
fouth polar circle, is called the antartic circle,
from its being oppofite to the arctic.
The ecliptic, tropics, and polar circles, are
drawn upon the terreftrial globe, as well as
upon the celeftial. But the ecliptic, being a
great fixed circle in the heavens, cannot pro-
perly be faid to belong to the terreſtrial globe;
and is laid down upon it only for the conveniency
of folving fome problems. So that, if this
circle on the terreftrial globe was properly di-
vided into the months and days of the year, it
would not only fuit the globe better, but would
alfo make the problems thereon much eaſier.
$
In
Of the Heavens and the Earth.
257
In order to form a true idea of the earth's
motion round its axis every 24 hours, which is
the cauſe of day and night; and of its motion
in the ecliptic round the fun every year, which
is the cauſe of the different lengths of days and
nights, and of the viciffitude of feafons; take
the following method, which will be both eaſy
and pleaſant.
Let a fmall terreftrial globe, of about three An idea
inches diameter, be fufpended by a long thread of the
of twisted filk, fixt to its north pole: then hav- feafons.
ing placed a lighted candle on a table, to repre-
fent the fun, in the center of a hoop of a large
caſk, which may repreſent the ecliptic, the hoop
making an angle of 231 degrees with the plane
of the table; hang the globe within the hoop
near to it; and if the table be level, the equa-
tor of the globe will be parallel to the table,
and the plane of the hoop will cut the equator
at an angle of 23 degrees; ſo that one half of
the equator will be above the hoop, and the
other half below it: and the candle will en-
lighten one half of the globe, as the fun
enlightens one half of the earth, whilft the
other half is in the dark.
Things being thus prepared, twift the thread
towards the left hand, that it may turn the
globe the fame way by untwifting; that is, from
weft, by fouth, to eaft. As the globe turns
round its axis or thread, the different places of
its furface will go regularly through the light
and dark; and have; as it were, an alternate
return of day and night in each rotation. As
the globe continues to turn round, and to fhew
itfelf all around to the candle, carry it flowly
round the hoop by the thread, from weft, by
fouth, to eaſt, which is the way that the earth
moves
258
Of the Heavens and the Earth.
moves round the fun, once a year, in the
ecliptic and you will fee, that whilft the globe
continues in the lower part of the hoop, the can-
dle (being then north of the equator) will con-
ſtantly ſhine round the north pole; and all the
northern places which go through any part of
the dark, will go through a leſs portion of it than
they do of the light; and the more fo, the far-
ther they are from the equator: confequently,
their days are then longer than their nights.
When the globe comes to a point in the hoop,
mid-way between the higheft and loweſt points,
the candle will be directly over the equator, and
will enlighten the globe juſt from pole to pole;
and then every place on the globe will go
through equal portions of light and darkneſs,
as it runs round its axis; and confequently, the
day and night will be of equal length at all
places upan it. As the globe advances thence-
forward, towards the higheſt part of the hoop,
the candle will be on the fouth fide of the equa-
tor, fhining farther and farther round the fouth
pole, as the globe rifes higher and higher in the
hoop; leaving the north pole as much in dark-
nefs, as the fouth pole is then in the light, and
making long days and ſhort nights on the ſouth
fide of the equator, and the contrary on the
north fide, whilft the globe continues in the
nothern or higher fide of the hoop: and when
it comes to the higheſt point, the days will be at
the longeſt, and the nights at the ſhorteſt, in the
fouthern hemifphere; and the reverfe in the
northern. As the globe advances and deſcends
in the hoop, the light will gradually recede from
the fouth pole, and approach towards the north
pole, which will caufe the northern days to
lengthen, and the fouthern days to fhorten in
the
3.
Of the Heavens and the Earth.
259
the fame proportion. When the globe comes to
the middle point, between the higheſt and loweſt
points of the hoop, the candle will be over the
equator, enlightening the globe juſt from pole
to pole, when every place of the earth (except
the poles) will go through equal portions of
light and darkness; and confequently, the day
and night will be then equal, all over the globe.
And thus, at a very fmall expence, one may
have a delightful and demonftrative view of
the cauſe of days and nights, with their gradual
increaſe and decreaſe in length, through the
whole year together, with the viciffitudes of
fpring, fummer, autumn, and winter, in each
annual courſe of the earth round the fun,
If the hoop be divided into 12 equal parts,
and the figns be marked in order upon it, be-
ginning with Cancer at the higheſt point of the
hoop, and reckoning eastward (or contrary to
the apparent motion of the fun) you will fee
how the fun appears to change his place every
day in the ecliptic, as the globe advances eaſt-
ward along the hoop, and turns round its own
axis: and that when the earth is in a low fign,
as at Capricorn, the fun muſt appear in a high
fign, as at Cancer, oppofite to the earth's real
place and that whilft the earth is in the
fouthern half of the ecliptic, the fun appears in
the northern half, and vice verſå: that the far-
ther any place is from the equator, between it
and the polar circle, the greater is the difference
between the longest and fhortest day at that
place; and that the poles have but one day and
one night in the whole year.
Theſe things premifed, we fhall proceed to
the deſcription and ufe of the terreſtrial globe,
S
and
2
1
260
The Terrestrial Globe defcribed.
The ter-
reſtrial
fcribed.
and explain the geographical terms as they occur
in the problems.
This globe has the boundaries of land and
water laid down upon it, the countries and
globe de- kingdoms divided by dots, and coloured to
diſtinguiſh them, the islands properly fituated,
the rivers and principal towns inferted, as they
have been ascertained upon the earth by mea-
furement and obfervation.
2
I
2
The equator, ecliptic, tropics, polar circles,
and meridians, are laid down upon the globe in
the manner already deſcribed. The ecliptic is
divided into 12 figns, and each fign into 30
degrees, which are generally fubdivided into
halves, and into quarters if the globe is large.
Each tropic is 23 degrees from the equator,
and each polar circle 23 degrees from its
reſpective pole. Circles are drawn parallel to
the equator, at every ten degrees diftance from
it on each fide to the poles: thefe circles are
called parallels of latitude. On large globes
there are circles drawn perpendicularly through
every tenth degree of the equator, interſecting
each other at the poles: but on globes of or
under a foot diameter, they are only drawn
through every fifteenth degree of the equator:
thefe circles are generally called meridians, fome-
times circles of longitude, and at other times hour-
circles.
The globe is hung in a brafs ring, called the
braſen meridian; and turns upon a wire in each
pole funk half its thickness into one fide of the
meridian ring; by which means, that fide of
the ring divides the globe into two equal parts,
called the eaſtern and western hemispheres; as the
equator divides it into two equal parts, called the
vorthern and Southern hemispheres. This ring is
divided
4
The Terreftrial Globe defcribed.
261
divided into 360 equal parts or degrees, on the
fide wherein the axis of the globe turns. One
half of theſe degrees are numbered, and reck-
oned, from the equator to the poles, where they
end at 90: their ufe is to fhew the latitudes of
places. The degrees on the other half of the
meridian ring, are numbered from the poles to
the equator, where they end at 90: their ufe is
to fhew how to elevate either the north or fouth
pole above the horizon, according to the lati-
tude of any given place, as it is north or fouth
of the equator.
The brafen meridian is let into two notches
made in a broad flat ring, called the wooden
horizon, the upper furface of which divides the
globe into two equal parts, called the upper and
lower hemifpheres. One notch is in the north
point of the horizon, and the other in the ſouth.
On this horizon are feveral concentric circles,
which contain the months and days of the year,
the figns and degrees anfwering to the fun's
place for each month and day, and the 32 points.
of the compafs.-The graduated fide of the
braſs meridian lies towards the eaft fide of the
horizon, and ſhould be generally kept toward
the perſon who works problems by the globes.
There is a ſmall borary circle, fo fixed to the
north part of the brafen meridian, that the wire
in the north pole of the globe is in the center
of that circle; and on the wire is an index,
which goes over all the 24 hours of the circle,
as the globe is turned round its axis. Some-
times there are two horary circles, one between
each pole of the globe and the braſen meridian;
which is the contrivance of the late ingenious Mr.
Jofeph Harris, mafter of the affay-office in the
Tower of London; and makes it very conve-
nient
S 2
262
The Terrestrial Globe defcribed.
Directions
for choof
ing of
globes.
nient for putting the poles of the globe through
the horizon, and for elevating the pole to finall
latitudes, and declinations of the fun; which can-
not be done where there is only one horary cir
cle fixed to the outer edge of the brafen me-
ridian.
There is a thin flip of brafs, called the qua-
drant of altitude, which is divided into 90 equal
parts or degrees, anfwering exactly to fo many
degrees of the equator. It is occafionally fixed
to the uppermoft point of the brafen meridian
by a nut and ſcrew. The divifions end at the
nut, and the quadrant is turned round upon it.
As the globe has been ſeen by moſt people,
and upon the figure of which, in a plate, nei-
ther the circles nor countries can be properly
expreffed, we judge it would fignify very little
to refer to a figure of it; and fhall therefore
only give fome directions how to chooſe a globe,
and then deſcribe its uſe.
1. See that the papers be well and neatly
pafted on the globes, which you may know, if
the lines and circles thereon meet exactly, and
continue all the way even and whole; the cir-
cles not breaking into feveral arches, nor the
papers either coming fhort, or lapping over one.
another.
2. See that the colours be tranfparent, and
not laid too thick upon the globe to hide the
names of places.
3. See that the globe hang evenly between.
the brafen meridian and the wooden horizon;
not inclining either to one fide or to the
other.
4. See that the globe be as cloſe to the hori-
zon and meridian as it conveniently may; other-
wife, you will be too much puzzled to find
againſt
Directions for choofing Globes.
263
againſt what part of the globe any degree of the
meridian or horizon is.
5. See that the equinoctial line be even with
the horizon all around, with the north or fouth
pole is elevated 90 degrees above the horizon.
6. See that the equinoctial line cuts the hori-
zon in the eaſt and weft points, in all elevations
of the pole from o to go degrees.
7. See that the degree of the brafen meridian
marked with o, be exactly over the equinoctial
line of the globe.
8. See that there be exactly half of the braſen
meridian above the horizon; which you may
know, if you bring any of the decimal divifions
on the meridian to the north point of the hori-
zon, and find their complement to go in the
fouth point.
9. See that when the quadrant of altitude is
placed as far from the equator, on the brafen
meridian, as the pole is elevated above the hori-
zon, the beginning of the degrees of the qua-
drant reaches juft to the plane furface of the
horizon.
10. See that whilft the index of the hour-
circle (by the motion of the globe) paffes from
one hour to another, 15 degrees of the equator
pafs under the graduated edge of the brafen
meridian.
11. See that the wooden horizon be made
ſubſtantial and ſtrong: it being generally ob-
ferved, that in moft globes, the horizon is the
first part that fails, on account of its having
been made too flight.
In ufing the globes, keep the eaft fide of the Directions
horizon towards you (unleſs your problem re. for ufing
quires the turning of it) which fide you may them.
know by the word Eaft upon the horizon; for
S 3
then
264
The Ufe of the Terreftrial Globe.
1
then you have the graduated fide of the meri-
dian towards you, the quadrant of altitude before
you, and the globle divided exactly into two
equal parts, by the graduated fide of the me-
ridian.
In working fome problems, it will be necef-
fary to turn the whole globe and horizon about,
that you may look on the weft fide thereof;
which turning will be apt to jog the ball ſo, as
to ſhift away that degree of the globe which
was before fet to the horizon or meridian: to
avoid which inconvenience, you may thrust in
the feather-end of a quill between the ball of
the globe and the brafen meridian; which, with-
out hurting the ball, will keep it from turning
in the meridian, whilft you turn the weft fide of
the horizon towards you.
PROBLEM I
To find the * latitude and † longitude of any given
place upon the globe.
Turn the globe on its axis, until the given
place comes exactly under that graduated fide of
the brafen meridian, on which the degrees are
numbered
*The latitude of a place is its diftance from the equator,
and is north or fouth, as the place is north or fouth of the
equator. Thoſe who live at the equator have no latitude,
becauſe it is there that the latitude begins.
+ The longitude of a place is the number of degrees
(reckoned upon the equator) that the meridian of the faid
place is diftant from the meridian of any other place from
which we reckon, either eastward or weftward, for 180 de-
grees, or half round the globe. The Britiſh reckon the
Jongitude from the méridian of London, and the French
now reckon it from the meridian of Paris. The meridian
of that place, from which the longitude is reckoned, is
called
The Ufe of the Terrestrial Globe.
26
numbered from the equator; and obferve what
degree of the meridian the place then lies under ;
which is its latitude, north or fouth, as the place
is north or fouth of the equator.
The globe remaining in this pofition, the de-
gree of the equator, which is under the brafen
meridian, is the longitude of the place, (from
the meridian of London on the English globes)
which is eaſt or weft, as the place lies on the
eaſt or weft fide of the firft meridian of the
globe. All the Atlantic Ocean, and America,
is on the weft fide of the meridian of London;
and the greateſt part of Europe, and of Africa,
together with all Afia, is on the eaſt fide of the
meridian of London, which is reckoned the first
meridian of the globe by the Britiſh geographers
and aſtronomers.
PROBLEM
II.
The longitude and latitude of a place being given, to
find that place on the globe.
Look for the given longitude in the equator
(counting it eastward or weftward from the first
meridian, as it is mentioned to be eaſt or weft ;)
and bring the point of longtude in the equator
to the brafen meridian, on that fide which is
above the fouth point of the horizon then
count from the equator, on the brafen meridian,
to the degree of the given latitude, towards the
north or fouth pole, according as the latitude is
north or fouth; and under that degree of lati-
tude on the meridian, you will have the place
required.
called the first meridian. The places upon this meridian
have no longitude, becauſe it is there that the longitude
begins.
S 4
PROB-
+
266
The Ufe of the Terrestrial Globe.
i
PROBLEM III.
To find the difference of longitude, or difference of
latitude, between any two given places.
Bring each of theſe places to the brafen me-
ridian, and fee what its latitude is the leffer
latitude fubtracted from the greater, if both
places are on the fame fide of the equator, or
both latitudes added together, if they are on
different fides of it, is the difference of latitude
required. And the number of degrees contained
between theſe plaçes, reckoned on the equator,
when they are brought feparately under the
brafen meridian, is their difference of longitude;
if it be leſs than 180: but if more, let it be ſub-
tracted from 360, and the remainder is the dif
ference of longitude required. Or,
Having brought one of the places to the
brafen meridian, and fet the hour-index to XII,
turn the globe until the other place comes to the
brafen meridian, and the number of hours and
parts of an hour, paſt over by the index, will
give the longitude in time; which may be eaſily
reduced to degrees, by allowing 15 degrees for
every hour, and one degree for every four mi-
nutes.
N. B. When we fpeak of bringing any place
to the brafen meridian, it is the graduated fide
of the meridian that is meant.
請
​PROB-
The Ufe of the Terreftrial Globe.
267
PROBLEM
IV.
Any place being given, to find all thofe places that
have the fame longitude or latitude with it.
Bring the given place to the brafen meridian,
then all thoſe places which lie under that ſide of
the meridian, from pole to pole, have the fame
longitude with the given place. Turn the globe
round its axis, and all thofe places which paſs
under the fame degree of the meridian that the
given place does, have the fame latitude with
that place.
Since all latitudes are reckoned from the
equator, and all longitudes are reckoned from
the firſt meridian, it is evident, that the point of
the equator which is cut by the firſt meridian, has
neither latitude nor longitude.-The greateſt
latitude is 90 degrees, becauſe no place is more
than 90 degrees from the equator. And the
greatest longitude is 180 degrees, becauſe no
place is more than 180 degrees from the firſt
meridian.
*
PROBLEM V.
To find the antoci, ‡ periceci, and ‡ antipodes,
of any given place.
Bring the given place to the brafen meridian,
and having found its latitude, keep the globe in
that fituation, and count the fame number of
degrees
The antoci are thofe people who live on the fame me-
ridian, and in equal latitudes, on different fides of the equa-
tor. Being on the fame meridian, they have the fame hours;
that is, when it is noon to the one, it is alſo noon to the
other; and when it is mid-night to the one, it is alfo mid-
night to the other, &c. Being on different fides of the equa-
tor
268
The Ufe of the Terrestrial Globe.
degrees of latitude from the equator towards the
contrary pole, and where the reckoning ends,
you have the antaci of the given place upon the
globe. Thoſe who live at the equator have no
antaci.
The globe remaining in the fame pofition, fet
the hour-index to the upper XII. on the horary
circle, and turn the globe until the index comes
to the lower XII; then, the place which lies.
under the meridian, in the fame latitude with
the given place, is the periæci required. Thoſe
who live at the poles have no periæci.
As the globe now ftands (with the index at
the lower XII.) the antipodes of the given place
will be under the fame point of the braſen me-
ridian where its antæci ftood before. Every
place upon the globe has its antipodes.
tor, they have different or oppofite feaſons at the fame time;
the length of any day to the one is equal to the length of the
night of that day to the other; and they have equal eleva-
tions of the different poles.
+ The periaci are thoſe people who live on the fame pa-
rallel of latitude, but on oppofite meridians: fo that though
their latitude be the fame, their longitude differs 180 de-
grees. By being in the fame latitude, they have equal ele-
vations of the fame pole (for the elevation of the pole is
always equal to the latitude of the place) the fame length of
days or nights, and the lame feafons. But being on oppo-
fite meridians, when it is noon to the one, it is mid-night
to the other.
I The antipodes are thoſe who live diametrically oppo-
fite to one another upon the globe, ftanding with feet
towards feet, on oppofite meridians and parallels. Being on
oppofite fides of the equator, they have oppofite fealons,
winter to one, when it is fummer to the other; being equally.
distant from the equator, they have their contrary poles equally
elevated above the horizon; being on oppofite meridians,
when it is noon to the one, it must be mid-night to the other;
and as the fun recedes from the one when he approaches to
the other, the length of the day to one must be equal to the
length of the night at the fame time to the other.
PROB
t
The Ufe of the Terreftrial Globe.
269
ļ
PROBLEM VI.
To find the distance between any two places on the
globe.
Lay the graduated edge of the quadrant of
altitude over both the places, and count the
number of degrees intercepted between them on
the quadrant; then multiply theſe degrees by
60, and the product will give the diftance in
geographical miles: but to find the diſtance in
Engliſh miles, multiply the degrees by 69, and
the product will by the number of miles required.
Or, take the diftance betwixt any two places
with a pair of compaffes, and apply that extent
to the equator; the number of degrees, inter-
cepted between the points of the compaffes, is
the diſtance in degrees of a great circle; which
may be reduced either to geographical miles, or
to Engliſh miles, as above.
* Any circle that divides the globe into two equal parts, Great
is called a great circle, as the equator or meridian. Any circle.
circle that divides the globe into two unequal parts (which
every parallel of latitude does) is called a leffer circle. Now, Leffer
as every circle, whether great or ſmall, contains 360 degrees, circle,
and a degree upon the equator or meridian contains 60 geo-
graphical miles, it is evident, that a degree of longitude upon
the equator, is longer than a degree of longitude upon any
parallel of latitude, and must therefore contain a greater
number of miles. So that, although all the degrees of lati-
tude are equally long upon an artificial globe (though not
preciſely fo upon the earth itfelf) yet the degrees of longi-
tude decreaſe in length, as the latitude increaſes, but not in
the fame proportion. The following table fhews the length
of a degree of longitude, in geographical miles, and hun-
dredth parts of a mile, for every degree of latitude, from
the equator to the poles: a degree on the equator being 60
geographical miles.
PROB-
270
The Ufe of the Terrestrial Globe.
PROBLEM VII.
A place on the globe being given, and its diftance
from any other place, to find all the other places
upon the globe which are at the fame distance from
the given place.
Bring the given place to the brafen meridian,
and ſcrew the quadrant of altitude to the meri-
dian, directly over that place; then keeping the
globe in that pofition, turn the quadrant quite
round upon it, and the degree of the quadrant
that touches the fecond place, will pafs over all
the other places which are equally diſtant with it
from the given place.
This is the fame as if one foot of a pair of
compaffes was fet in the given place, and the
other foot extended to the ſecond place, whoſe
diſtance is known; for if the compaffes be then
turned round the first place as a center, the
moving foot will go over all thofe places which
are at the fame diſtance with the fecond from
it.
A TABLE
The Ufe of the Terreftrial Globe.
271
ATABLEЛhewing the number of miles in a de-
gree of longitude, in any given degree of latitude.
Parts.
Miles.
Deg.
Miles.
Parts.
Deg.
Miles.
Parts.
Deg.
I
2
3
pod a♡ + 56 N∞
59.99 31 51.43
61
29.09
59.96 32 50.88
62
28.17
59.92 33 50.32
63
63
27.24
59.85
34
49.74
64 26.30
59.77 35 49.15
59.67 36 48.54
65
25.36
66
24.4I
7
59.56 37 47.92
67
23.44
8
59.42 38 47.28
68
22.48
9
59.26 39
46.63 69
21.50
ΙΟ
59.09 40 45.97 70
20.52
II
58.89 41
45.28 71
19.53
12
58.69 42 44.59 72
18.54
13 58.46 43 43.88 73
17.54
14
58.22 44 43.16 74
74
16.53
15
18
16 73
20
21
56.38
56.02
22
2 2 2 2 2 2
23
24
25
16
17
57.95 45 42.43
57.67 46 41.68
57.38
47 40.92
57.06 48 40.15
19 56.73 49
39.36
50.38.57
51
37.76
36.94
55.6352
55.23 53 36.11
54.81 54 35.27
54.38 55
34.41
26
53.93 56 33.55
~ ~ ~ ~ ~∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞
75 15.52
76
14.51
77
13.50
78
12.48
79
11.45
80
10.42
81
9.38
82
8.35
83
7.32
84
6.28
85
5.24
86
4.20
27
53.46 57
32.68
87
3.15
28
52.96 58 31.79 88
2.10
29 52.47 59
30.90 89
1.05
30
51.99 60 30.00 90
0.00
PROB-
272
The Ufe of the Terreftrial Globe.
PROBLEM VIII.
The hour of the day at any place being given, to find
all thofe places where it is noon at that time.
Bring the given place to the braſen meridian,
and fet the index to the given hour; this done,
turn the globe until the index points to the upper
XII, and then, all the places that lie under the
brafen meridian have noon at that time.
N. B. The upper XII always ſtands for noon;
and when the bringing of any place to the brafen
meridian is mentioned, the fide of that meridian
on which the degrees are reckoned from the
equator is meant, unleſs the contrary fide be
mentioned.
PROBLEM IX.
The hour of the day at any place being given to find
what o'clock it then is at any other place.
Bring the given place to the braſen meridian,
and ſet the index to the given hour; then turn
the globe, until the place where the hour is re-
quired comes to the brafen meridian, and the in-
dex will point out the hour at that place.
PROBLEM X.
To find the fun's place in the ecliptic, and his* de-
clination, for any given day of the year.
Look on the horizon for the given day, and
right againſt it you have the degree of the fign
in which the fun is (or his place) on that day
* The fun's declination is his diſtance from the equinoctial
in degrees, and is north or fouth, as the fun is between the
equinoctial and the north or fouth pole.
at
The Use of the Terrestrial Globe.
273
at noon. Find the fame degree of that fign in
the ecliptic line upon the globe, and having
brought it to the brafen meridian, obferve what
degree of the meridian ſtands over it; for that
is the fun's declination, reckoned from the
equator.
PROBLEM XI.
The day of the month being given, to find all thofe
places of the earth over which the fun will pafs
vertically on that day.
Find the fun's place in the ecliptic for the
given day, and having brought it to the brafen
meridian, obferve what point of the meridian is
over it; then turning the globe round its axis;
all thoſe places which paſs under that point of
the meridian are the places required; for as
their latitude is equal, in degrees and parts of a
degree, to the fun's declination, the fun muſt be
directly over head to each of them at its refpec-
tive noon.
PROBLEM XII.
*
A place being given in the torrid zone, to find thofe
two days of the year, on which the fun fhall be
vertical to that place.
Bring the given place to the brafen meridian,
and mark the degree of latitude that is exactly
over
* The globe is divided into five zones; one torrid, two
temperate, and two frigid. The torrid zone lies between the two
tropics, and is 47 degrees in breadth, or 23 on each fide of
the equator: the temperate zones lie between the tropics and
polar circles, or from 23 degrees of latitude, to 66, on
each
274
The Ufe of the Terrestrial Globe.
F
over it on the meridian; then turn the globe.
round its axis, and obferve the two degrees of
the ecliptic which pafs exactly under that degree
of latitude: Laftly, find on the wooden horizon
the two days of the year on which the fun is in
thoſe degrees of the ecliptic, and they are the
days required: for on them, and none elſe, the
fun's declination is equal to the latitude of the
given place; and confequently, he will then be
vertical to it at noon.
PROBLEM XIII.
To find all thofe places of the north frigid zone,
where the fun begins to Shine conftantly without
fetting, on any given day, from the 20th of March,
to the 23d of September.
On theſe two days, the fun is in the equinoc-
tial, and enlightens the globe exactly from pole
to pole: therefore, as the earth turns round its
axis, which terminates in the poles, every place
upon it will go equally through the light and the
dark, and fo make the day and night equal to all
places of the earth. But as the fun declines
from the equator, towards either pole, he will
fhine juſt as many degrees round that pole, as
are equal to his declination from the equator;
fo that no place within that diſtance of the pole
will then go through any part of the dark, and
confequently the fun will not fet to it. Now, as
2
each fide of the equator; and are each 43 degrees in breadth:
the frigid zones are the fpaces included within the polar
circles, which being each 23 degrees from their reſpective
poles, the breadth of each of thefe zones is 47 degrees. As
the fun never goes without the tropics, he muſt every mo-
ment be vertical to fome place or other in the torrid zone.
6
the
The Use of the Terreftrial Globe.
275
the fun's declination is northward, from the 21ft
of March to the 23d of September, he muſt con-
ſtantly ſhine round the north pole all that time;
and on the day that he is in the northern tropic,
he fhines upon the whole north frigid zone; fo
that no place within the north polar circle goes
through any part of the dark on that day.
Therefore,
Having brought the fun's place for the given
day to the braſen meridian, and found his de-
clination (by Prob. IX.) count as many degrees
on the meridian, from the north pole, as are
equal to the fun's declination from the equator,
and mark that degree from the pole where the
reckoning ends: then, turning the globe round
its axis, obferve what places in the north frigid
zone pafs directly under that mark; for they
are the places required.
The like may be done for the fouth frigid
zone, from the 23d of September to the 21ft of
March, during which time the fun fhines con-
ſtantly on the fouth pole.
PROBLEM XIV.
To find the place over which the fun is vertical, at
any hour of a given day.
Having found the fun's declination for the
given day (by Prob. IX.) mark it with a chalk
on the brafen meridian: then bring the place
where you are (fuppofe London) to the brafer
meridian, and fet the index to the given hour;
which done, turn the globe on its axis, until the
index points to XII at noon; and the place on
the globe, which is then directly under the point
T
of
278
The Ufe of the Terrestrial Globe.
of the fun's declination marked upon the meri-
dian, has the fun that moment in the zenith, or
directly overhead.
PROBLEM XV.
The day and hour at any place being given, to find
all thofe places where the fun is then rifing, or
fetting, or on the meridian: confequently, all thofe
places which are enlightened at that time, and
thofe which are in the dark.
This problem cannot be ſolved by any globe
fitted up in the common way, with the hour
circle fixed upon the brafs meridian; unlefs the
fun be on or near fome of the tropics on the
given day. But by a globe fitted up according
to Mr. Jofeph Harris's invention (already men-
tioned) where the hour-circle lies on the furface
of the globe, below the meridian, it may be ſolved
for, any day in the year, according to his me-
thod; which is as follows.
Having found the place to which the ſun is
vertical at the given hour, if the place be in the
northern hemisphere, elevate the north pole as
many degrees above the horizon, as are equal to
the latitude of that place; if the place be in the
fouthern hemifphere, elevate the fouth pole ac-
cordingly; and bring the faid place to the brafen
meridian. Then, all thofe places which are in
the weſtern femicircle of the horizon, have the
fun rifing to them at that time; and thofe in the
eaſtern femicircle have it fetting: to thofe under
the upper femicircle of the brafs meridian, it is
noon; and to thofe under the lower femicircle,
it is midnight. All thofe places which are
above the horizon, are enlightened by the fun,
and
#
The Ufe of the Terrestrial Globe.
277
and have the fun juft as many degrees high to
them, as they themſelves are above the horizon :
and this height may be known, by fixing the
quadrant of altitude on the brafen meridian over
the place to which the fun is vertical; and then,
laying it over any other place, obferve what
number of degrees on the quadrant are inter-
cepted between the faid place and the horizon.
In all thofe places that are 18 degrees below the
weſtern femicircle of the horizon, the morning
twilight is juſt beginning; in all thofe places that
are 18 degrees below the eaſtern femicircle of
the horizon, the evening twilight is ending; and
all thofe places that are lower than 18 degrees,
have dark night.
If any place be brought to the upper femi-
circle of the brafen meridian, and the hour index
be fet to the upper XII or noon, and then the
globe be turned round eaftward on its axis;
when the place comes to the western femicircle
of the horizon, the index will fhew the time of
fun-rifing at that place; and when the fame
place comes to the eaſtern femicircle of the hori-
zon, the index will fhew the time of fun-fet.
To thofe places which do not go under the
horizon, the fun fets not on that day: and to
thoſe which do not come above it, the fun does
not riſe.
PROBLEM XVI.
The day and bour of a lunar eclipse being given; to
find all thofe places of the earth to which it will
be vifible.
The moon is never eclipfed but when ſhe is
full, and ſo directly oppofite to the fun, that the
earth's
T 2
1
278
The Use of the Terreftrial Globe.
earth's fhadow falls upon her. Therefore, what-
ever place of the earth the fun is vertical to at
that time, the moon muſt be vertical to the anti-
podes of that place : fo that the fun will be then
viſible to one half of the earth, and the moon
to the other.
Find the place to which the fun is vertical at
the given hour (by Prob. XIV.) elevate the pole
to the latitude of that place, and bring the place
to the upper part of the brafen meridian, as in
the former problem: then, as the fun will be
viſible to all thofe parts of the globe which are
above the horizon, the moon will be viſible to all
thofe parts of the globe which are below it, at
the time of her greateſt obfcuration.
But with regard to an eclipfe of the fun, there
is no fuch thing as fhewing to what places it
will be viſible, with any degree of certainty, by
a common globe; becauſe the moon's fhadow
covers but a ſmall portion of the earth's furface;
and her latitude, or declination from the eclip-
tic, throws her fhadow fo variouſly upon the
earth, that to determine the places on which it
falls, recourſe muſt be had to long calculations.
PROBLEM XVII.
To rectify the globe for the latitude, the zenith,
and the fun's place.
Find the latitude of the place (by Prob. I.)and if
the place be in the northern hemifphere, raiſe the
north pole above the north point of the horizon,
* The zenith, in this fenfe, is the higheſt point of the bra-
fen meridian above the horizon; but in the proper ſenſe
it is that point of the heaven which is directly vertical to
any given place, at any given inftant of time.
as
The Ufe of the Terrestrial Globe.
279
as many degrees (counted from the pole upon
the brafen meridian) as are equal to the latitude
of the place. If the place be in the ſouthern
hemiſphere, raiſe the fouth pole above the fouth
point of the horizon, as many degrees as are equal
to the latitude. Then, turn the globe till the
place comes under its latitude on the braſen
meridian, and faſten the quadrant of altitude ſo,
that the chamfered edge of its nut (which is
even with the graduated edge) may be joined
to the zenith, or point of latitude. This done,
bring the fun's place in the ecliptic for the given
day, (found by Prob. X.) to the graduated fide
of the brafen meridian, and fet the hour-index to
XII. at noon, which is the uppermoft XII on the
hour-circle; and the globe will be rectified.
The latitude of any place is equal to the ele- Remark.
vation of the neareſt pole of the heaven above
the horizon of that place; and the poles of
the heaven are directly over the poles of the
earth, each 90 degrees from the equinoc-
tial line. Let us be upon what place of the
earth we will, if the limits of our view be not
intercepted by hills, we fhall fee one half of the
heaven, or 90 degrees every way round, from
that point which is over our heads. Therefore,
if we were upon the equator, the poles of the
heaven would lie in our horizon, or limit of our
view: if we go from the equator, towards either
pole of the earth, we fhall fee the corresponding
pole of the heaven rifing gradually above our
horizon, juft as many degrees as we have gone
from the equator: and if we were at either of
the earth's poles, the correſponding pole of the
heaven would be directly over our head. Con-
ſequently, the elevation or height of the pole in
degrees
I 3
280
The Ufe of the Terreftrial Globe.
1
degrees above the horizon, is equal to the
number of degrees that the place is from the
equator.
PROBLEM XVIII.
The latitude of any place, not exceeding *661 de-
grees, and the day of the month, being given; to
find the time of fun-rifing and ſetting, and confe-
quently the length of the day and night.
Having rectified the globe for the latitude,
and for the fun's place on the given day (as di-
rected in the preceding problem) bring the fun's
place in the ecliptic to the eaſtern fide of the ho-
rizon, and the hour-index will fhew the time of
fun-rifing; then turn the globe on its axis, until
the fun's place comes to the weſtern fide of the
horizon, and the index will fhew the time of fun-
fetting.
The hour of fun-fetting doubled, gives the
length of the day; and the hour of fun-rifing
doubled gives the length of the night.
PROBLEM XIX.
The latitude of any place, and the day of the month,
being given; to find when the morning twilight
bigins, and the evening twilight ends, at that
place.
This ploblem is often limited; for, when the
fun does not go. 18 degrees below the horizon,
the twilight continues the whole night; and for
2
*All places whofe latitude is more than 66 degrees, are
in the frigid zones: and to thofe places the fun does not
fet in fummer, for a certain number of diurnal revolutions,
which occafions this limitation of latitude.
feveral
The Ufe of the Terreftrial Globe.
281
feveral nights together in fummer, between 49
and 66 degrees of latitude: and the nearer
to 66, the greater is the number of theſe nights.
But when it does begin and end, the follow-
ing method will fhew the time for any given
day.
Rectify the globe, and bring the fun's place in
the ecliptic to the eaſtern fide of the horizon;
then mark that point of the ecliptic with a chalk
which is in the weſtern fide of the horizon, it be-
ing the point oppofite to the fun's place: this
done, lay the quadrant of altitude over the faid
point, and turn the globe eastward, keeping the
quadrant at the chalk-mark, until it is juſt 18
degrees high on the quadrant; and the index
will point out the time when the morning twi-
light begins for the fun's place will then be 18
degrees below the eaſtern fide of the horizon.
To find the time when the evening twilight
ends, bring the fun's place to the weſtern fidè
of the horizon, and the point oppofite to it,
which was marked with the chalk, will be rifing
in the eaſt then, bring the quadrant over that
point, and keeping it thereon, turn the globe
weftward, until the faid point be 18 degrees
above the horizon on the quadrant, and the in-
dex will fhew the time when the evening twi-
light ends; the fun's place being then 18 degrees
below the weſtern fide of the horizon.
PRO-
T 4
¥
282
The Ufe of the Terrestrial Globe.
PROBLEM XX.
To find on what day of the year the fun begins to
Shine conftantly without fetting, on any given
place in the north frigid zone; and how long be
continues to do so.
Rectify the globe to the latitude of the place,
and turn it about until fome point of the eclip-
tic, between Aries and Cancer, coincides with
the north point of the horizon where the brafen
meridian cuts it: then find, on the wooden
horizon, what day of the year the fun is in that
point of the ecliptic; for that is the day on
which the fun begins to fhine conftantly on the
given place, without fetting. This done, turn
the globe until fome point of the ecliptic, be-
tween Cancer and Libra, coincides with the
north point of the horizon, where the brafen
meridian cuts it; and find, on the wooden
horizon, on what day the fun is in that point of
the ecliptic; which is the day that the fun leaves.
off conſtantly ſhining on the ſaid place, and riſes
and fets to it as to other places on the globe.
The number of natural days, or complete re-
volutions of the fun about the earth, between
the two days above found, is the time that the
fun keeps conftantly above the horizon without
fetting for all the portion of the ecliptic, that
lies between the two points which interfect the
horizon in the very north, never fets below it:
and there is juſt as much of the oppofite part of
the ecliptic that never rifes; therefore, the fun
will keep as long conſtantly below the horizon
in winter, as above it in fummer.
Whoever
A
The Ufe of the Terreftrial Globe.
283
Whoever confiders the globe, will find, that
all places of the earth do equally enjoy the bene-
fit of the fun, in refpect of time, and are equally
deprived of it. For, the days and nights are
always equally long at the equator: and in all
places that have latitude, the days at one time
of the year are exactly equal to the nights at the
oppoſite ſeaſon.
PROBLEM XXI.
To find in what latitude the fun shines conftantly
without fetting, for any length of time leſs than
* 182% of our days and nights.
Find a point in the ecliptic half as many de-
grees from the beginning of Cancer (either to-
wards Aries or Libra) as there are + natural days
in the time given; and bring that point to the
north fide of the brafen meridian, on which the
degrees are numbered from the pole towards
the equator; then, keep the globe from turning
on its axis, and flide the meridian up or down,
until the forefaid point of the ecliptic comes
to the north point of the horizon, and then, the
elevation of the pole will be equal to the latitude
required.
1
* The reafon of this limitation is, that 182 of our days
and nights make half a year, which is the longeſt time that
the fun fhines without fetting, even at the poles of the
earth.
+ A natural day contains the whole 24 hours: an arti-
ficial day, the time that the fun is above the horizon,
PRO-
284
The Ufe of the Terrestrial Globe.
PROBLEM XXII.
The latitude of a place, not exceeding 66 degrees,
and the day, of the month being given; to find
the fun's amplitude, or point of the compass on
which be riſes or fets on that day.
Rectify the globe, and bring the fun's place
to the eaſtern fide of the horizon; then obferve
what point of the compafs on the horizon ftands,
right against the fun's place, for that is his
amplitude at rifing. This done, turn the globe
weftward, until the fun's place comes to the
weſtern ſide of the horizon, and it will cut the
point of his amplitude at fetting. Or, you may
count the rifing amplitude in degrees, from the
eaft point of the horizon, to that point where
the fun's place cuts it; and the fetting ampli-
tude, from the weft point of the horizon, to the
fun's place at fetting.
PROBLEM XXIII.
The latitude, the fun's place, and his* altitude,
being given; to find the hour of the day, and the
fun's azimuth, or number of degrees that he is
diftant from the meridian.
L
Rectify the globe, and bring the fun's place
to the given height upon the quadrant of alti-
tude; on the eaſtern fide of the horizon, if the
time be in the forenoon; or the weſtern fide, if
* The fun's altitude, at any time, is his height in degrees
above the horizon at that time.
it
The Ufe of the Terreftrial Globe.
285
it be in the afternoon: then, the index will
fhew the hour; and the number of degrees in
the horizon intercepted between the quadrant of
altitude and the fouth point, will be the fun's
true azimuth at that time.
N. B. Always when the quadrant of altitude
is mentioned in working any problem, the gra-
duated edge of it is meant.
If this be done at fea, and compared with the
fun's azimuth, as fhewn by the compaſs, if they
agree, the compaſs has no variation in that place :
but if they differ, the compafs does vary; and
the variation is equal to this difference.
PROBLEM XXIV.
The latitude, bour of the day, and the fun's place,
being given; to find the fun's altitude and
azimuth.
Rectify the globe, and turn it until the in-
dex points to the given hour; then lay the qua-
drant of altitude over the fun's place in the
ecliptic, and the degree of the quadrant cut by
the fun's place is his altitude at that time above
the horizon; and the degree of the horizon cut
by the quadrant is the fun's azimuth, reckoned
from the fouth.
1
PRO-
286
The Ufe of the Terrestrial Globe.
PROBLEM XXV.
The latitude, the fun's altitude, and his azimuth
being given; to find his place in the ecliptic, the
day of the month, and hour of the day, though
they had all been loft.
Rectify the globe for the latitude and * zenith,
and fet the quadrant of altitude to the given
azimuth in the horizon; keeping it there, turn
the globe on its axis until the ecliptic cuts the
quadrant in the given altitude: that point of
the ecliptic which cuts the quadrant there, will
be the fun's place; and the day of the month
anſwering thereto, will be found over the like
place of the fun on the wooden horizon. Keep
the quadrant of altitude in that pofition, and
having brought the fun's place to the brafen
meridian, and the hour index to XII at noon,
turn back the globe, until the fun's place cuts
the quadrant of altitude again, and the index
will fhew the hour.
Any two points of the ecliptic which are
equidistant from the beginning of Cancer or of
Capricorn, will have the fame altitude and azi-
muth at the fame hour, though the months be
different; and therefore it requires fome care in
this problem, not to miſtake both the month,
and the day of the month; to avoid which ob-
ſerve, that from the 20th of March to the 21st
of June, that part of the ecliptic which is be-
*By rectifying the globe for the zenith, is meant fcrew-
ing the quadrant of altitude to the given latitude on the
brafs meridian,
tween
The Ufe of the Terrestrial Globe.
287
1
tween the beginning of Aries and beginning of
Cancer is to be uſed: from the 21st of June to
the 23d of September, between the beginning
of Cancer and beginning of Libra: from the
23d of September to the 21st of December,
between the beginning of Libra and the begin-
ning of Capricorn; and from the 21ft of Decem-
ber to the 20th of March, between the begin-
nining of Capricorn and beginning of Aries. And
as one can never be at a lofs to know in what
quarter of the year he takes the fun's altitude
and azimuth, the above caution with regard to
the quarters of the ecliptic, will keep him right
as to the month and day thereof.
PROBLEM XXVI.
To find the length of the longest day at any given
place.
But if
If the place be on the north fide of the equa-
tor, find its latitude (by Prob. 1.) and elevate
the north pole to that latitude; then, bring the
beginning of Cancer to the brafen meridian,
and fet the hour-index to XII at noon.
the given place be on the fouth fide of the
equator, elevate the fouth pole to its latitude,
and bring the beginning of Capricorn to the
brafs meridian, and the hour-index to XII.
This done, turn the globe weftward, until the
beginning of Cancer or Capricorn (as the latitude
is north or fouth) comes to the horizon; and
the index will then point out the time of fun-
fetting, for it will have gone over all the after-
noon hours, between mid-day and fun-fet;
which
288
The Use of the Terreftrial Globe.
which length of time being doubled, will give
the whole length of the day, from fun-rifing to
fun-fetting. For, in all latitudes, the fun riſes
as long before mid-day, as he fets after it.
PROBLEM XXVII.
To find in what latitude the longest day is of any
given length less than 24 hours.
If the latitude be north, bring the beginning
of Cancer to the brafen meridian, and elevate
the north pole to about 66 degrees; but if
the latitude be fouth, bring the beginning of
Capricorn to the meridian, and elevate the fouth
pole to about 66 degrees; becauſe the longeſt
day in north latitude, is when the fun is in the
first point of Cancer; and in fouth latitude,
when he is in the first point of Capricorn. Then
fet the hour-index to XII at noon, and turn the
globe weftward, until the index points at half
the number of hours given: which done, keep
the globe from turning on its axis, and ſlide the
meridian down in the notches, until the afore-
ſaid point of the ecliptic (viz. Cancer or Capri-
corn) comes to the horizon; then, the elevation
of the pole will be equal to the latitude re-
quired.
6
PRO-
The Use of the Terrestrial Globe.
289
PROBLEM XXVIII.
*
The latitude of any place, not exceeding 66% de-
grees being given; to find in what climate the
plate is.
Find the length of the longeſt day at the
given place by Prob. XXVI. and whatever be
the number of hours whereby it exceedeth
twelve, double that number, and the fum will
anſwer to the climate in which the place is.
PROBLEM XXIX.
The latitude, and the day of the month, being given;
to find the hour of the day when the ſun ſhines.
Set the wooden horizon truly level, and the
braſen meridian due north and fouth by a ma-
riner's compaſs: then, having rectified the
globe, ſtick a fmall fewing-needle into the fun's
place in the ecliptic, perpendicular to that part
of the furface of the globe: this done, turn the
globe on its axis, until the needle comes to the
braſen meridian, and fet the hour-index to XII
* A climate, from the equator to either of the polar cir-
cles, is a tract of the earth's furface, included between two
fuch parallels of latitude, that the length of the longest day
in the one exceeds that in the other by half an hour; but
from the polar circles to the poles, where the fun keeps long
above the horizon without fetting, each climate differs a
whole month from the one next to it. There are twenty-
four climates between the equator and each of the polar cir.
cles; and fix from each polar circle to its reſpective pole.
at
290
The Ufe of the Terreftrial Globe.
at noon; then, turn the globe on its axis, until
the needle points exactly towards the fun (which
it will do when it cafts no fhadow on the globe)
and the index will fhew the hour of the day.
PROBLEM XXX.
A pleasant way of fhewing all thofe places of the
earth which are enlightened by the fun, and alfo
the time of the day when the fun fhines.
Take the terreſtrial ball out of the wooden
horizon, and alſo out of the braſen meridian ;
then fet it upon a pedeſtal in fun-fhine, in fuch
a manner, that its north pole may point directly
towards the north pole of the heaven, and the
meridian of the place where you are be directly
towards the fouth. Then, the fun will ſhine
upon all the like places of the globe, that he
does on the real earth, rifing to fome when he
is fetting to others; as you may perceive by that
part where the enlightened half of the globe is
divided from the half in the fhade, by the
boundary of the light and darknefs all thoſe
places, on which the fun fhines, at any time,
having day; and all thofe, on which he does
not fhine, having night.
If a narrow flip of paper be put round the
equator, and divided into 24 equal parts, be-
ginning at the meridian of your place, and the
hours be fet to thofe divifions in fuch a manner,
that one of the VI's may be upon your meri-
dian; the fun being upon that meridian at noon,
will then ſhine exactly to the two XII's; and at
one o'clock to the two I's, &c. So that the
place,
Obfervations concerning it.
291
place, where the enlightened half of the globe
is parted from the fhaded half, in this circle of
hours, will fhew the time of the day.
The principles of dialing fhall be explained
farther on, by the terrestrial globe. At prefent
we ſhall only add the following obfervations
upon it; and then proceed to the ufe of the ce-
leftial globe.
1. The latitude of any place is equal to the ele-
vation of the pole above the horizon of that place,
and the elevation of the equator is equal to the com-
plement of the latitude, that is, to what the latitude
wants of 90 degrees.
2. Thofe places which lie on the equator, have no
latitude, it being there that the latitude begins; and
thofe places which lie on the first meridian have
no longitude, it being there that the longitude be-
gins. Confequently, that particular place of the earth.
where the first meridian interfects the equator, bas
neither longitude nor latitude.
3. At all places of the earth, except the poles,
all the points of the compafs may be diftinguished in
the horizon: but from the north pole, every place
is fouth; and from the South pole, every place
is north. Therefore, as the fun is conftantly above
the horizon of each pole for half a year in its turn,
he cannot be faid to depart from the meridian of
either pole for half a year together. Confequently,
at the north pole it may be faid to be noon every
moment for half a year; and let the winds blow
from what part they will, they must always blow
from the fouth; and at the fouth pole, from the
north.
4. Because one half of the ecliptic is above the
borizon of the pole, and the fun, moon, and planets
move in (or nearly in) the ecliptic; they will all
U
rife
292
Obfervations concerning the
rife and fet to the poles. But, because the fars
never change their declinations from the equator (at
leaſt not ſenſibly in one age) those which are once
above the horizon of either pole, never fet below it;
and thoſe which are once below it, never riſe.
5. All places of the earth do equally enjoy the be-
refit of the fun, in respect of time, and are equally
deprived of it.
6. All places upon the equator have their days
and nights equally long, that is, 12 hours each, at
all times of the year. For although the fun declines
alternately, from the equator towards the north and
towards the fouth, yet, as the horizon of the equa-
tor cuts all the parallels of latitude and declination
in halves, the fun must always continue above the
horizon for one half a diurnal revolution about the
earth, and for the other half below it.
7. When the fun's declination is greater than the
latitude of any place, upon either fide of the equator,
the fun will come twice to the fame azimuth or point
of the compass in the forenoon, at that place, and
twice to a like azimuth in the afternoon; that is,
be will
80
twice back every day, whilft his declina-
tion continues to be greater than the latitude. Thus,
Suppose the globe rectified to the latitude of Barba-
does, which is 13 degrees north; and the fun to be
any where in the ecliptic, between the middle of
Taurus and middle of Leo; if the quadrant of al-
titude be fet to about * 18 degrees north of the caft
in the horizon, the fun's place be marked with a
chalk upon the ecliptic, aud the globe be then turned
westward on its axis, the faid mark will riſe in the
horizon a little to the north of the quadrant, and
thence afcending, it will cross the quadrant towards
* From the middle of Gemini to the middle of Cancer,
the quadrant may be fet zo degrees.
the
}
Terrestrial Globe.
293
the fouth; but before it arrives at the meridian, it
will croſs the quadrant again, and paſs over the
meridian northward of Barbadoes. And if the
quadrant be fet about 18 degrees north of the west,
the fun's place will cross it twice, as it defcends from
the meridian towards the horizon, in the after-
noon.
8. In all places of the earth between the equator
and poles, the days and nights are equally long, viz.
12 hours each, when the fun is in the equinoctial:
for, in all elevations of the pole, fhort of 90 de-
grees (which is the greatest) one half of the equator
or equinoctial will be above the horizon, and the
other half below it.
9. The days and nights are never of an equal
length at any place between the equator and polar
circles, but when the fun enters the figns Aries
and Libra. For in every other part of the
ecliptic, the circle of the fun's daily motion is divided
into two unequal parts by the horizon.
10. The nearer that any place is to the equator,
the less is the difference between the length of the days
and nights in that place; and the more remote,
the contrary. The circles which the fun defcribes
in the heaven every 24 hours, being cut more nearly
equal in the former cafe, and more unequally in the
latter.
11. In all places lying upon any given parallel
of latitude, however long or short the day or night
be at any one of theſe places, at any time of the
year,
it is then of the fame length at all the reſt;
for in turning the globe round its axis (when recti
fied according to the fun's declination) all theſe
places will keep equally long above or below the
borizon.
12. The fun is vertical twice a year to every
place between the tropics; to thofe under the tropics,
U 2
once
294
Obfervations concerning the
once a year, but never any where else. For, there
can be no place between the tropics, but that there
will be two points in the ecliptic, whofe declination
from the equator is equal to the latitude of that
place; and but one point of the ecliptic which has a
declination equal to the latitude of places on the
tropic which that point of the ecliptic touches; and
as the fun never goes without the tropics, he can
never be vertical to any place that lies without
them.
*
13. To all places in the torrid zone, the dura-
tion of the twilight is leaft, becauſe the fun's daily
motion is the most perpendicular to the horizon. In
the frigid + zones, greatest; because the fun's daily
motion is nearly parallel to the horizon; and there-
fore he is the longer of getting 18 degrees below it
(till which time the twilight always continues.)
And in the temperate zones it is at a medium be-
tween the two, because the obliquity of the fun's
daily motion is fo.
14. In all places lying exactly under the polar
circles, the fun, when he is in the nearest tropic,
continues 24 hours above the horizon without fet-
ting; because no part of that tropic is below their
horizon. And when the fun is in the farthest
tropic, he is for the fame length of time without
rifing; becauſe no part of that tropic is above their
horizon. But, at all other times of the year, he
rifes and fets there, as in other places; becauſe all
the circles that can be drawn parallel to the equator,
between the tropics, are more or less cut by the
horizon, as they are farther from, or nearer to,
that tropic which is all above the horizon: and
*Between the tropics.
+ Between the polar circles and poles.
Between the tropics and polar circles.
when
Terrestrial Globe.
295
when the fun is not in either of the tropics, his
diurnal course must be in one or other of these
circles.
15. To all places in the northern hemisphere,
from the equator to the polar circle, the longest day
and fhortest night is when the fun is in the northern
tropic; and the ſhorteſt day and longeſt night is
when the fun is in the fouthern tropic; becauſe no
circle of the fun's daily motion is fo much above the
horizon, and fo little below it, as the northern tro-
pic; and none fo little above it, and fo much below
it, as the fouthern. In the fouthern hemisphere,
the contrary.
16. In all places between the polar circles and
poles, the fun appears for fome number of days (or
rather diurnal revolutions) without fetting; and at
the oppofite time of the year without rifing; because
Some part of the ecliptic never fets in the former
cafe, and as much of the oppofite part never rifes in
the latter. And the nearer unto, or the more re-
mote from the pole, theſe places are, the longer or
Shorter is the fun's continuing prefence or abfence.
17. If a ſhip ſets out from any port, and fails
round the earth eastward to the fame port again,
let her take what time he will to do it in, the
people in that ſhip, in reckoning their time, will
gain one complete day at their return, or count one
day more than thoſe who refide at the ſame port;
becauſe, by going contrary to the fun's diurnal motion,
and being forwarder every evening than they were
in the morning, their horizon will get ſo much the
fooner above the setting fun, than if they had kept
for a whole day at any particular place. And thus,
by cutting off a part proportionable to their own
motion, from the length of every day, they will
gain a complete day of that fort at their return;
without gaining one moment of abfolute time more
U 3
than
296
The Ufe of the Celestial Globe.
than is elapfed during their course, to the people
at the port. If they fail westward, they will rec-
kon one day less than the people do who refide at
the faid port, because by gradually following the
apparent diurnal motion of the fun, they will keep
bim cach particular day fo much longer above their
horizon, as answers to that day's courfe; and by
that means, they cut off a whole day in reckoning,
at their return, without lofing one moment of ab-
folute time.
Hence, if two ships ſhould ſet out at the fame
time from any port, and fail round the globe, one
eastward and the other weftward, fo as to meet at
the fame port on any day whatever; they will differ
two days in reckoning their time, at their return.
If they fail twice round the earth, they will differ
four days; if thrice, then fix, &c.
LECT. IX.
The ufe of the celeftial globe, and armillary
ཝཱམཙུཤཆ
Sphere.
The celef AVING done for the prefent with the
tial globe. terreftrial globe, we fhall proceed to the
H
ufe of the celeftial; firft premifing, that as the
equator, ecliptic, tropics, polar circles, hori-
zon, and brafen meridian, are exactly alike on
both globes, all the former problems concern-
ing the fun are folved the fame way by both
globes. The method alfo of rectifying the
celeftial globe is the fame as rectifying the ter-
reftrial, viz. Elevate the pole according to the
latitude of your place, then fcrew the quadrant
of altitude to the zenith, on the brafs meridian,
bring the fun's place in the ecliptic to the
graduated edge of the brafs meridian, on the
To reci-
fy it.
fide
The Ufe of the Celestial Globe.
297
fide which is above the fouth point of the
wooden horizon, and fet the hour-index to the
uppermoft XII, which ftands for noon.
N. B. The fun's place for any day of the
year ſtands directly over that day on the hori-
zon of the celestial globe, as it does on that of
the terreftrial.
The latitude and longitude of the ftars, and of Latitude
all other celeftial phenomena, are reckoned in a and longi-
very different manner from the latitude and tude of the
ftars.
longitude of places on the earth for all terref
trial latitudes are reckoned from the equator;
and longitudes from the meridian of fome re-
markable place, as of London by the British,
and of Paris by the French; though moft of
the French maps begin their longitude at the
meridian of the island Ferro.But the aftro-
nomers of all nations agree in reckoning the
latitudes of the moon, ftars, planets, and comets,
from the ecliptic; and their longitudes from the
* equinoctial colure, in that femicircle of it which
cuts the ecliptic at the beginning of Aries ;
and thence eastward, quite round, to the fame
femicircle again. Confequenlty thoſe ſtars which
lie between the equinoctial and the northern
half of the ecliptic, have north declination and
fouth latitude; thofe which lie between the
equinoctial and the fouthern half of the ecliptic,
have fouth declination and north latitude; and
* The great circle that paffes through the equinoctial points
at the beginning of and, and through the poles of
the world (which are two oppofite points, each 90 degrees
from the equinoctial) is called the equinoctial colure: and the
great circle that paffes through the beginning of and,
and also through the poles of the ecliptic, and poles of the
world, is called the folftitial colure.
U 4
all
Colures.
298
The Ufe of the Celestial Globe.
Confiella-
tions.
all thoſe which lie between the tropics and poles,
have their declinations and latitudes of the fame
denomination.
There are fix great circles on the celestial
globe, which cut the ecliptic perpendicularly,
and meet in two oppofite points in the polar
circles; which points are each ninety degrees
from the ecliptic, and are called its poles.
Theſe polar points divide thofe circles into 12
femicircles; which cut the ecliptic at the begin-
nings of the 12 figns. They refemble fo many
meridians on the terreftrial globe; and as all
places which lie under any particular meridian
femicircle on that globe; have the fame longi-
tude, fo all thoſe points of the heaven, through
which any one of the above femicircles are
drawn, have the fame longitude.-And as the
greateſt latitudes on the earth are at the north
and fouth poles of the earth, fo the greateſt lati-
tudes in the heaven, are at the north and fouth.
poles of the ecliptic.
In order to diſtinguiſh the ftars, with regard
to their fituations and pofitions in the heaven,
the ancients divided the whole vifible firmament
of ſtars into particular fyftems, which they called
conftellations; and digeſted them into the forms
of fuch animals as are delineated upon the celef
tial globe. And thoſe ſtars which lie between
the figures of thoſe imaginary animals, and
could not be brought within the compafs of any
of them, were called unformed stars.
Becauſe the moon and all the planets were
obferved to move in circles or orbits which cross
the ecliptic (or line of the fun's path) at ſmall
angles, and to be on the north fide of the eclip-
tic for one half of their courfe round the hea-
ven of ſtars, and on the fouth fide of it for the
other
The Ufe of the Celestial Globe.
299
other half, but never to go quite 8 degrees from
it on either fide, the ancients diftinguiſhed that
ſpace by two leffer circles, parallel to the ecliptic
(one on each fide) at 8 degrees diftance from it.
And the ſpace included between the circles,
they called the zodiac, becauſe moſt of the 12
conftellations placed therein reſemble fome living
creature.-Thefe conftellations are, 1. Aries r,
the ram; 2. Taurus 8, the bull; 3. Gemini ¤,
the twins; 4. Cancer, the crab; 5. Leo &,
the lion; 6. Virgo mp, the virgin: 7. Libra,
the balance; 8 Scorpio m, the fcorpion; 9. Sa-
gittarius, the archer; 10. Capricornus vs, the
goat; 11. Aquarius, the water bearer; and
12. Piſces x, the fifhes.
It is to be obſerved, that in the infancy of Remark.
aſtronomy, theſe twelve conftellations ſtood at
or near the places of the ecliptic, where the
above characteriſtics are marked upon the globe:
but now, each conftellation has got a whole fign
forwarder, on account of the receffion of the
equinoctial points from their former places. So
that the conftellation of Aries, is now in the
former place of Taurus; that of Taurus, in the
former place of Gemini; and fo on.
The ftars appear of different magnitudes to
the eye; probably becauſe they are at different
diſtances from us. Thoſe which appear bright-
eft and largeſt, are called stars of the first mag-
nitude; the next to them in fize and luftre, are
called ftars of the fecond magnitude; and fo on
to the fixth, which are the fmalleft that can be
difcerned by the bare eye.
Some of the moſt remarkable ſtars have names
given them, as Caftor and Pollux in the heads of
the Twins, Sirius in the mouth of the Great
Dog, Procyon in the fide of the Little Dog, Rigel
in
300
The Ufe of the Celestial Globe.
in the left foot of Orion, Ar&turus near the right
thigh of Bootes, &c.
Theſe things being premifed, which I think
are all that the young Tyro need be acquainted
with, before he begins to work any problem by
this globe, we fhall now proceed to the moft
uſeful of thoſe problems; omitting ſeveral which
are of little or no confequence.
*
PROBLEM I.
To find the right afcenfion and
the fun, or any fixed ftar.
declination of
Bring the fun's place in the ecliptic to the
brafen meridian, then that degree in the equi-
noctial which is cut by the'meridian, is the fun's
right afcenfion; and that degree of the meridian
which is over the fun's place, is his declination.
Bring any fixed ftar to the meridian, and its
right afcenfion will be cut by the meridian in the
equinoctial; and the degree of the meridian that
ſtands over it, is its declination.
So that right afcenfion and declination, on the
celeftial globe, are found in the fame manner
as longitude and latitude on the terreſtrial.
* The degree of the equinoctial, reckoned from the be-
ginning of Aries, that comes to the meridian with the fun or
itar, is its right afcenfion.
+ The distance of the fun or ftar in degrees from the equi-
noctial, towards either of the poles, north or fouth, is its
declination, which is north or fouth accordingly.
PROg
The Ufe of the Celestial Globe.
301
PROBLEM II.
To find the latitude and longitude of any ftar.
If the given ftar be on the north fide of the
ecliptic, place the 90th degree of the quadrant
of altitude on the north pole of the ecliptic,
where the twelve femicircles meet; which di-
vide the ecliptic into the 12 figns: but if the
ftar be on the fouth fide of the ecliptic, place
the 90th degree of the quadrant on the fouth
pole of the ecliptic: keeping the 90th degree of
the quadrant on the proper pole, turn the qua-
drant about, until its graduated edge cuts the
ſtar: then, the number of degrees in the qua-
drant, between the ecliptic and the ftar, is its
latitude; and the degree of the ecliptic cut by
the quadrant is the ftar's longitude, reckoned
according to the fign in which the quadrant
then is.
PROBLEM III.
To reprefent the face of the starry firmament, as
Seen from any given place of the earth, at any
bour of the night.
Rectify the celeſtial globe for the given lati-
tude, the zenith, and fun's place, in every re-
ſpect, as taught by the 17th problem, for the
terreftrial; and turn it about, until the index
points to the given hour: then, the upper he-
mifphere of the globe will repreſent the vifible
half of the heaven for that time: all the ſtars
upon
302
The Ufe of the Celestial Globe.
upon the globe being then in fuch fituations, as
exactly correſpond to thoſe in the heaven. And
if the globe be placed duly north and ſouth, by
means of a ſmall ſea-compaſs, every ſtar on the
globe will point toward the like ſtar in the hea-
ven by which means, the conftellations and
All
remarkable ſtars may be eaſily known.
thoſe ſtars which are in the eaſtern ſide of the
horizon, are then rifing in the eaſtern fide of
the heaven; all in the western, are ſetting in
the weſtern fide; and all thofe under the upper
part of the braſen meridian, between the fouth
point of the horizon and the north pole, are at
their greateſt altitude, if the latitude of the
place be north: but if the latitude be fouth,
thofe ſtars which lie under the upper part of the
meridian, between the north point of the hori-
zon and the fouth pole, are at their greateſt
altitude.
PROBLEM IV.
The latitude of the place, and day of the month,
being given; to find the time when any known
Star will rife, or be on the meridian, or ſet.
Having rectified the globe, turn it about un-
til the given ſtar comes to the eaſtern fide of the
horizon, and the index will fhew the time of
the ſtar's rifing; then turn the globe weftward,
and when the ſtar comes to the brafen meridian,
the index will fhew the time of the ftar's coming
to the meridian of your place; laftly, turn on,
until the ftar comes to the weſtern fide of the
horizon, and the index will fhew the time of the
ftar's fetting.
N. B.
The Use of the Celestial Globe.
303
N. B. In northern latitudes, thoſe ſtars which
are leſs diſtant from the north pole, than the
quantity of its elevation above the north point
of the horizon, never fet; and thofe which are
leſs diſtant from the fouth pole, than the num-
ber of degrees by which it is depreffed below
the horizon, never rife: and vice verfâ in fouth-
ern latitudes.
PROBLEM V.
To find at what time of the year a given ſtar will
be upon the meridian, at a given hour of the
night.
Bring the given ftar to the upper femicircle
of the braſs meridian, and fet the index to
the given hour; then turn the globe, until the
index points to XII at noon, and the upper fe-
micircle of the meridian will then cut the fun's
place, anfwering to the day of the year fought;
which day may be eafily found againſt the like
place of the fun among the figns on the wooden
horizon.
PROBLEM VI.
The latitude, day of the month, and* azimuth of
any known ftar being given; to find the hour of
the night.
Having rectified the globe for the latitude,
zenith, and fun's place; lay the quadrant of
• The number of degrees that the fun, moon, or any ſtar,
is from the meridian, either to the eaſt or weſt, is called its
azimuth.
altitude
304
The Ufe of the Celestial Globe.
altitude to the given degree of azimuth in the ho
rizon: then turn the globe on its axis, until the
ftar comes to the graduated edge of the qua-
drant; and when it does, the index will point
out the hour of the night.
PROBLEM VII.
The latitude of the place, the day of the month,
and altitude * of any known ſtar, being given;
to find the bour of the night.
Rectify the globe as in the former problem,
guess at the hour of the night, and turn the
globe until the index points at the ſuppoſed
hour; then lay the graduated edge of the qua-
drant of altitude over the known ftar, and if the
degree of the ſtar's height in the quadrant upon
the globe, anſwers exactly to the degree of the
ftar's obferved altitude in the heaven, you have
gueffed exactly: but if the ſtar on the globe is
higher or lower than it was obferved to be in the
heaven, turn the globe backwards or forwards,
keeping the edge of the quadrant upon the ſtar,
until its center comes to the obſerved altitude in
the quadrant; and then, the index will fhew the
true time of the night.
* The number of degrees that the ftar is above the hori-
zon, as obſerved by means of a common quadrant, is called
its altitude.
PRO.
The Ufe of the Celestial Globe.
305
PROBLEM VIII.
An eafy method for finding the hour of the night by
any two known ſtars, without knowing either
their altitude or azimuth; and then, of finding
both their altitude and azimuth, and thereby the
true meridian.
Tie one end of a thread to a common muſket
bullet; and, having rectified the globe as above,
hold the other end of the thread in your hand,
and carry it flowly round betwixt your eye and
the ſtarry heaven, until you find it cuts any two
known ſtars at once. Then, gueffing at the
hour of the night, turn the globe until the index
points to the time in the hour-circle; which
done, lay the graduated edge of the quadrant
over any one of theſe two ftars on the globe,
which the thread cut in the heaven. If the ſaid
edge of the quadrant cuts the other ftar alfo, you
have gueffed the time exactly; but if it does
not, turn the globe flowly backwards or for-
wards, until the quadrant (kept upon either ftar)
cuts them both through their centers: and then,
the index will point out the exact time of the
night; the degree of the horizon, cut by the
quadrant, will be the true azimuth of both theſe
ftars from the fouth; and the ftars themſelves
will cut their true altitudes in the quadrant. At
which moment, if a common azimuth compaſs
be ſo ſet upon a floor or level pavement, that
theſe ſtars in the heaven may have the fame
bearing upon it (allowing for the variation of
the needle) as the quadrant of altitude has in the
wooden horizon of the globe, a thread extended
over the north and fouth points of that compafs
6
will
306
The Ufe of the Celestial Globe.
will be directly in the plane of the meridian:
and if a line be drawn upon the floor or pave-
ment, along the courſe of the thread, and an up-
right wire be placed in the fouthmoſt end of the
line, the fhadow of the wire will fall upon that
line, when the fun is on the meridian, and fhines
upon the pavement.
PROBLEM IX.
To find the place of the moon, or of any planet; and
thereby to fhew the time of its rifing, fouthing,
and fetting.
Seek in Parker's or White's Ephemeris the
* geocentric place of the moon or planet in the
ecliptic, for the given day of the month, and,
according to its longitude and latitude, as fhewn
by the Ephemeris, mark the fame with a chalk
upon the globe. Then, having rectified the
globe, turn it round its axis weftward; and as
the faid mark comes to the eaſtern fide of the
horizon, to the brafen meridian, and to the
weſtern ſide of the horizon, the index will fhew
at what time the planet rifes, comes to the meri-
dian, and fets, in the fame manner as it would
do for a fixed ſtar.
PROBLEM X.
To explain the phenomena of the harvest moon.
In order to do this, we muft premife the fol-
lowing things. 1. That as the fun goes only
The place of the moon or planet, as feen from the
earth, is called its geocentric place.
3
once
The Use of the Celestial Globe.
307
1
6
2
once a year round the ecliptic, he can be but
once a year in any particular point of it: and
that his motion is almoft a degree every 24
hours, at a mean rate. 2. That as the moon
goes round the ecliptic once in 27 days and 8
hours, the advances 13 degrees in it, every
day at a mean rate. 3. That as the fun goes
through part of the ecliptic in the time the
moon goes round it, the moon cannot at any time
be either in conjunction with the fun, or oppoſite
to him, in that part of the ecliptic where the was
fo the laſt time before; but muft travel as
much forwarder, as the fun has advanced in the
faid time which being 29 days, makes almoft
a whole fign. Therefore, 4. The moon can be
but once a year oppofite to the fun, in any
particular part of the ecliptic. 5. That the
moon is never full but when fhe is oppofite to
the fun, becauſe at no other time can we fee all
that half of her, which the fun enlightens. 6. That
when any point of the ecliptic rifes, the oppofite
point fets. Therefore, when the moon is oppo-
fite to the fun, fhe muft riſe at* fun fet. 7: That
the different figns of the ecliptic rife at very dif-
ferent angles or degrees of obliquity with the
horizon, eſpecially in confiderable latitudes; and
that the fmaller this angle is, the greater is the
portion of the ecliptic that rifes in any ſmall part.
of time; and vice versa. 8. That, in northern
latitudes, no part of the ecliptic rifes at fo fmall
an angle with the horizon, as Pifces and Aries do;
therefore, a greater portion of the ecliptic rifes in
*This is not always ftrictly true, becaufe the moon does
not keep in the ecliptic, but croffes it twice every month.
However, the difference need not be regarded in a general
explanation of the cauſe of the harveſt moon,
X
one
3
J
308
The Use of the Celeſtial Globe.
one hour, about thefe figns, than about any of
the reft. 9. That the moon can never be full
in Pifces and Aries but in our autumnal months,
for at no other time of the year is the fun in the
oppoſite ſigns Virgo and Libra.
Theſe things premiſed, take 134 degrees of
the ecliptic in your compaffes, and beginning at
Pifces, carry that extent all round the ecliptic,
marking the places with a chalk, where the
points of the compaffes fucceffively fall. So
you will have the moon's daily motion marked
out for one complete revolution in the ecliptic
(according to § 2 of the laft paragraph.)
Rectify the globe for any confiderable northern
latitude, (as fuppofe that of London) and then,
turning the globe round its axis, obferve how
much of the hour circle the index has gone over,
at the rifing of each particular mark on the
ecliptic; and you will find that feven of the
marks (which take in as much of the ecliptic as
the moon goes through in a week) will all rife
fucceffively about Pifces and Aries in the time
that the index goes over two hours. Therefore,
whilft the moon is in Pifces and Aries, fhe will not
differ in general above two hours in her rifing
for a whole week. But if you take notice of
the marks on the oppofite figns, Virgo and Libra,
you will find that feven of them take nine hours.
to rife; which fhews, that when the moon is in
theſe two figns, fhe differs nine hours in her
rifing within the compafs of a week. And fo
much later as every mark is of rifing than the
one that roſe next before it, fo much later will
the moon be of rifing on any day than fhe was on
the day before, in the correfponding part of the
heaven. The marks about Cancer and Capricorn
rife
The Ufe of the Celestial Globe.
309
rife at a mean difference of time between those
about Aries and Libra.
Now, although the moon is in Pifces and Aries
every month, and therefore muft rife in thoſe
figns within the ſpace of two hours later for a
whole week, or only about 17 minutes later
every day then ſhe did on the former; yet fhe
is never full in thefe figns, but in our autumnal
months, August and September, when the fun is in
Virgo and Libra. Therefore, no full moon in
the year will continue to rife fo near the time of
fun fet for a week or fo, as thefe two full moons
do, which fall in the time of harveſt.
In the winter months, the moon is in Pifces
and Aries about her first quarter; and as theſe
figns rife about noon in winter, the moon's rif-
ing in them paffes unobſerved. In the fpring
months, the moon changes in thefe figns, and
confequently rifes at the fame time with the fun;
fo that it is impoffible to fee her at that time.
In the fummer months fhe is in thefe figns about
her third quarter, and rifes not until mid-night,
when her rifing is but very little taken notice
of; efpecially as fhe is on the decreafe. But in
the harveft months fhe is at the full, when in
theſe figns, and being oppofite to the fun, fhe
rifes when the fun fets (or foon after) and fhines
all the night.
In fouthern latitudes, Virgo and Libra rife at as
fmall angles with the horizon, as Pifces and Aries
do in the northern; and as our fpring is at the
time of their harveſt, it is plain their harveſt full
moons must be in Virgo and Libra; and will
therefore rife with as little difference of time, as
ours do in Piſces and Aries.
X 2
For
310
The Ufe of the Terreftrial Globe.
For a fuller account of this matter, I muft
refer the reader to my Aftronomy, in which it is
defcribed at large.
PROBLEM XI.
To explain the equation of time, or difference of time
between well regulated clocks and true fun-dials.
The earth's motion on its axis being perfectly
equable, and thereby caufing an apparent
equable motion of the ftarry heaven round the
fame axis, produced to the poles of the heaven;
it is plain that equal portions of the celeftia
equator paſs over the meridian in equal parts of
time, becauſe the axis of the world is perpendi-
cular to the plane of the equator. And there-
fore, if the fun kept his annual courfe in the
celeſtial equator, he would always revolve from
the meridian to the meridian again in 24 hours
exactly, as fhewn by a well-regulated clock.
But as the fun moves in the ecliptic, which is
oblique both to the plane of the equator and axis
of the world, he cannot always revolve from the
meridian to the meridian again in 24 equal
hours; but fometimes a little fooner, and at
other times a little latter, becaufe equal portions
of the ecliptic pafs over the meridian in unequal
parts of time on account of its obliquity. And
this difference is the fame in all latitudes.
To fhew this by a globe, make chalk-marks
all round the equator and ecliptic, at equal
diſtances from one another (fuppofe 10 degrees)
beginning at Aries or at Libra, where thefe two
circles interfect each other. Then turn the
globe
PLATE XX.
Fig. 1.
H
B
T
U
South
A ALAM?
W
Ferguſon delin.
M
L
N
G
C
C
M
Q
P
0
N
L
Z
NE
North
B
H
R
D
Equator
a
Fig. 2.
VI
Q
Lat./514
IX
C
Aris
XII Equator
P
F
Fig. 3.
P
Lat/51
L
Axis
B
E
B
J.Mynde jiulp.
The Ufe of the Terreftrial Globe.
311
globe round its axis, and you will ſee that all
the marks in the firſt quadrant of the ecliptic, or
from the beginning of Aries to the beginning of
Cancer, come fooner to the braſen meridian than
their correfponding marks do on the equator:
thoſe in the ſecond quadrant, or from the be-
ginning of Cancer to the beginning of Libra,
come later thofe in the third quadrant, from
Libra to Capricorn, fooner; and thofe in the
fourth, from Capricorn to Aries, later. But thoſe
at the beginning of each quadrant come to the
meridian at the ſame time with their correfpond-
ing marks on the equator.
Therefore, whilft the fun is in the firſt and
third quadrants of the ecliptic, he comes fooner
to the meridian every day than he would do if
he kept in the equator; and confequently he is
fafter than a well regulated clock, which always
keeps equable or equatorial time: and whilft he
is in the fecond and fourth quadrants, he comes
latter to the meridian every day than he would
do if he kept in the equator; and is therefore
flower than the clock. But at the beginning of
each quadrant, the fun and clock are equal.
And thus, if the fun moved equably in the
ecliptic, he would be equal with the clock on
four days of the year, which would have equal
intervals of time between them. But as he
moves fafter at fome times than at others (being
eight days longer in the northern half of the
ecliptic than in the fouthern) this will caufe a
fecond inequality; which combined with the
former, arifing from the obliquity of the ecliptic
to the equator, makes up that difference, which
is fhewn by the common equation tables to be
between good clocks and true fun-dials.
X 3
The
312
Of the Armillary Sphere.
Plate XX.
Fig. 1.
The ar-
miliary
Sphere.
The defcription and ufe of the armillary Sphere.
Whoever has feen a common armillary Sphere,
and underſtands how to uſe it, muft be fenfible
that the machine here referred to, is of a very
different, and much more advantageous con-
ſtruction. And thoſe who have ſeen the curious
glafs fphere invented by Dr. LONG, or the figure
of it in his Aftronomy, muſt know that the fur-
niture of the terreftrial globe in this machine,
the form of the pedeftal, and the manner of
turning either the earthly globe or the circles,
which furround it, are all copied from the
Doctor's glafs fphere; and that the only diffe-
rence is, a parcel of rings inſtead of a glafs celef
tial globe, and all the additions are a moon
within the fphere, and a femicircle upon the
pedeſtal.
The exterior parts of this machine are a com-
pages of braſs rings, which repreſent the princi-
pal circles of the heaven, viz. 1. The equinoctial
A A, which is divided into 360 degrees, (begin-
ning at its interfection with the ecliptic in Aries)
for fhewing the fun's right afcenfion in degrees;
and alſo into 24 hours, for fhewing his right
afcenfion in time. 2. The ecliptic B B, which is
divided into 12 figns, and each fign into 30 de-
grees, and alfo into the months and days of the
year; in fuch a manner, that the degree or point
of the ecliptic in which the fun is, on any given
day, ſtands over that day in the circle of months,
3. The tropic of Cancer C C, touching the eclip-
tic at the beginning of Cancer in e, and the
tropic of Capricorn DD, touching the ecliptic at
the beginning of Capricorn in f; each 23 degrees
from
Of the Armillary Sphere.
313
from the equinoctial circle. 4. The arctic circle
E, and the antarctic circle F, each 23 degrees
from its refpective pole at N and S.
5. The
equinoctial colure G G, paffing through the
north and ſouth poles of the heaven at N and S,
and through the equinoctial points Aries, and
Libra in the ecliptic. 6. The folftitial colure
HH, paffing through the poles of the heaven, and
through the folftitial points Cancer and Capricorn,
in the ecliptic. Each quarter of the former of
theſe colures is divided into go degrees, from the
equinoctial to the poles of the world, for fhew-
ing the declination of the fun, moon, and ſtars;
and each quarter of the latter, from the ecliptic
at e and f, to its poles b and d, for fhewing the
latitude of the ſtars.
In the north pole of the ecliptic is a nut b, to
which is fixed one end of a quadrantal wire, and
to the other end a ſmall ſun Y, which is carried
round the ecliptic B B, by turning the nut and
in the fouth-pole of the ecliptic is a pin at d, on
which is another quadrantal wire, with a ſmall
moon Z upon it, which may be moved round by
hand: but there is a particular contrivance for
caufing the moon to move in an orbit which
croffes the ecliptic at an angle of 5 degrees, in
two oppoſite points called the moon's nodes; and
alfo for fhifting theſe points backward in the
ecliptic, as the moon's nodes ſhift in the heaven.
Within theſe circular rings is a ſmall terref-
trial globe I, fixt on an axis K K, which extends
from the north and fouth poles of the globe at ʼn
and s, to thoſe of the celeftial ſphere at N and S.
On this axis is fixt the flat celeftial meridian L L,
which may be fet directly over the meridian of
any place on the globe, and then turned round
with the globe, so as to keep over the fame
meridian
X 4
314
Of the Armillary Sphere.
meridian upon it. This flat meridian is gra-
duated the fame way as the brafs meridian of
a common globe, and its uſe is much the fame.
To this globe is fitted the moveable horizon
M M, ſo as to turn upon two ftrong wires pro-
ceeding from its east and weft points to the
globe, and entering the globe at oppofite points
of its equator, which is a moveable brass ring let
into the globe in a groove all around its equator.
The globe may be turned by hand within this
ring, fo as to place any given meridian upon it,
directly under the celeftial meridian L L. The
horizon is divided into 360 degrees all around
its outermoft edge, within which are the points
of the compafs, for fhewing the amplitude of
the fun and moon, both in degrees and points.
The celeftial meridian L L paffes through two
notches in the north and fouth points of the
horizon, as in a common globe: but here, if
the globe be turned round, the horizon and
meridian turn with it. At the fouth pole of the
ſphere is a circle of 24 hours, fixt to the rings,
and on the axis is an index which goes round
that circle, if the globe be turned round its
axis.
The whole fabric is fupported on a pedeſtal
N, and may be elevated or depreffed upon the
joint O, to any number of degrees from o to 90,
by means of the arc P, which is fixed in the
ſtrong brass arm 2, and flides in the upright
piece R, in which is a fcrew at r, to fix it at any
proper elevation.
In the box T are two wheels (as in Dr. Long's
ſphere) and two pinions, whofe axes come out
at V and U; either of which may be turned by
the ſmall winch W. When the winch is put
the axis V, and turned backward, the ter-
reſtrial
upon
Of the Armillary Sphere.
315
reftrial globe, with its horizon and celeſtial me-
ridian, keep at reft; and the whole ſphere of
circles turns round from eaft, by fouth, to weft,
carrying the fun Y, and moon Z, round the fame
way, and cauſing them to rife above and ſet be-
low the horizon. But when the winch is put
upon the axis U, and turned forward, the ſphere
with the fun and moon keep at reft; and the
earth, with its horizon and meridian, turn round
from weft, by fouth, to eaſt; and bring the ſame
points of the horizon to the fun and moon, to
which theſe bodies came when the earth kept at
reft, and they were carried round it; fhewing
that they rife and fet in the fame points of the
horizon, and at the fame time in the hour-circle,
whether the motion be in the earth or in the
heaven. If the earthly globe be turned, the
hour-index goes round its hour-circle; but if
the ſphere be turned, the hour-circle goes round
below the index.
And fo, by this conſtruction, the machine is
equally fitted to fhew either the real motion of
the earth, or the apparent motion of the hea-
ven.
To rectify the ſphere for uſe, firſt ſlacken the
ſcrew r in the upright ftem R, and taking hold
of the arm 2, move it up or down until the
given degree of latitude for any place be at the
fide of the ftem R; and then the axis of the
ſphere will be properly elevated, ſo as to ftand
parallel to the axis of the world, if the machine
be fet north and fouth by a ſmall compafs: this
done, count the latitude from the north-pole,
upon the celeftial meridian L L, down towards
the north notch of the horizon, and fet the hori-
zon to that latitude; then, turn the nut b until
the fun r comes to the given day of the year in
the
316
Of Dialing.
Prelimi-
naries.
the ecliptic, and the fun will be at its proper
place for that day: find the place of the moon's
afcending node, and alfo the place of the moon,
by an Ephemeris, and fet them right accord.
ingly; laſtly, turn the winch W, until either the
fun comes to the meridian L L, or until the me-
ridian comes to the fun (according as you want
the ſphere or earth to move) and fet the hour-
index to the XII, marked noon, and the whole
machine will be rectified.Then turn the
winch, and obferve when the fun or moon rife
and fet in the horizon, and the hour-index will
fhew the times thereof for the given day.
As thoſe who underſtand the uſe of the globes
will be at no lofs to work many other problems
by this fphere, it is needlefs to enlarge any
farther upon it.
A
LECT. X.
The principles and art of dialing.
Dial is a plane, upon which lines are de-
ſcribed in ſuch a manner, that the ſhadow
of a wire, or of the upper edge of a plate ftile,
erected perpendicularly on the plane of the dial,
may ſhew the true time of the day.
The edge of the plate by which the time of
the day is found, is called the ftile of the dial,
which muſt be parallel to the earth's axis; and
the line on which the faid plate is erected, is
called the fubftile.
The angle included between the fubftile and
ftile, is called the elevation, or height of the
ftile.
Thoſe dials whofe planes are parallel to the
plane of the horizon, are called horizontal dials;
4
and
Of Dialing.
317
and thoſe dials whofe planes are perpendicular
to the plane of the horizon, are called vertical,
or erect dials.
Thoſe erect dials, whoſe planes directly front
the north or fouth, are called direct north or
fouth dials; and all other erect dials are called
decliners, becauſe their planes are turned away
from the north or fouth.
Thoſe dials whofe planes are neither parallel
nor perpendicular to the plane of the horizon,
are called inclining, or reclining dials, accord-
ing as their planes make acute or obtufe angles
with the horizon; and if their planes are alfo
turned aſide from facing the fouth or north,
they are called declining-inclining, or declining
reclining dials.
The interfection of the plane of the dial, with
that of the meridian, paffing through the ſtile,
is called the meridian of the dial, or the hour-
line of XII.
Thofe meridians, whofe planes pass through
the ſtile, and make angles of 15, 30, 45, 60,
75, and 90 degrees with the meridian of the
place (which marks the hour-line of XII) are
called hour-circles; and their interfections with
the plane of the dial, are called hour-lines.
In all declining dials, the fubftile makes an
angle with the hour-line of XII; and this angle
is called the diftance of the fubftile from the
meridian.
The declining plane's difference of longitude,
is the angle formed at the interſection of the
ftile and plane of the dial, by two meridians;
one of which paſſes through the hour-line of XII,
and the other through the fubftile.
This
318
Of Dialing.
on which
dialing
depends.
This much being premifed concerning dials in ge-
neral, we shall now proceed to explain the different
methods of their conftruction.
If the whole earth a Pcp were transparent,
Plate XX. and hollow, like a ſphere of glaſs, and had its
Fig. 2.
equator divided into 24 equal parts by ſo many
The uni- meridian femicircles, a, b, c, d, e, f, g, &c. one
verfal of which is the geographical meridian of any
principle given place, as London (which is fuppofed to
be at the point a;) and if the hours of XII
were marked at the equator, both upon that
meridian and the oppofite one, and all the reſt
of the hours in order on the rest of the meri-
dians, thoſe meridians would be the hour-circles
of London then, if the fphere had an opake
axis, as PE p, terminating in the poles P and
P, the fhadow of the axis would fall upon every
particular meridian and hour, when the fun
came to the plane of the oppoſite meridian, and
would confequently fhew the time at London,
and at all other places on the meridian of
London.
Horizon.
If this ſphere was cut through the middle by
tal dial. a folid plane ABCD, in the rational horizon of
London, one half of the axis EP would be
above the plane, and the other half below it;
and if ſtraight lines were drawn from the center
of the plane, to thoſe points where its circum-
ference is cut by the hour-circles of the ſphere,
thoſe lines would be the hour-lines of a hori-
zontal dial for London: for the fhadow of the
axis would fall upon each particular hour-line
of the dial, when it fell upon the like hour-circle
of the ſphere.
Fig. 3.
If the plane which cuts the ſphere be upright,
as AFCG, touching the given place (London)
at F, and directly facing the meridian of Lon-
don,
Of Dialing.
319
don, it will then become the plane of an erect
direct fouth dial: and if right lines be drawn Vertical
from its center E, to thofe points of its circum- dial.
ference where the hour-circles of the ſphere cut
it, theſe will be the hour lines of a vertical or
direct fouth dial for London, to which the hours
are to be fet as in the figure (contrary to thoſe
on a horizontal dial) and the lower half Ep of
the axis will caft a fhadow on the hour of the
day in this dial, at the fame time that it would
fall upon the like hour-circle of the fphere, if
the dial-plane was not in the way.
dials.
If the plane (ftill facing the meridian) be Inclining
made to incline, or recline, by any given number and re
of degrees, the hour-circles of the fphere willclining
ſtill cut the edge of the plane in thoſe points to
which the hour-lines must be drawn ftraight
from the center; and the axis of the fphere will
caft a fhadow on thefe lines at the refpective
hours. The like will ftill hold, if the plane be Declining
made to decline by any given number of degrees dials.
from the meridian, towards the eaft or weft:
provided the declination be less than 90 degrees,
or the reclination be lefs than the co-latitude
of the place and the axis of the fphere will be
a gnomon, or ftile, for the dial. But it cannot
be a gnomon, when the declination is quite go
degrees, nor when the reclination is equal to
the co-latitude; becauſe in theſe two cafes,
the axis has no elevation above the plane of the
dial.
And thus it appears, that the plane of every
dial repreſents the plane of fome great circle
upon the earth; and the gnomon the earth's
axis, whether it be a ſmall wire, as in the above
figures, or the edge of a thin plate, as in the
common horizontal dials.
The
320
Of Dialing.
Fig. 2, 3.
Dialing
by the
common
terrestial
globe.
The whole earth, as to its bulk, is but a
point, if compared to its diftance from the fun :
and therefore, if a ſmall ſphere of glaſs be placed
upon any part of the earth's furface, fo that
its axis be parallel to the axis of the earth, and
the ſphere have fuch lines upon it, and fuck
planes within it, as above deſcribed; it will
Thew the hours of the day as truly as if it were
placed at the earth's center, and the fhell of the
earth were as tranfparent as glaſs.
But becauſe it is impoffible to have a hollow
ſphere of glaſs perfectly true, blown round a
folid plane; or if it was, we could not get at
the plane within the glaſs to ſet it in any given
pofition; we make uſe of a wire-fphere to ex-
plain the principles of dialing, by joining 24
femicircles together at the poles, and putting a
thin flat plate of brafs within it.
A common globe, of 12 inches diameter, has
generally 24 meridian femicircles drawn upon
it. If fuch a globe be elevated to the latitude of
any given place, and turned about until any one
of theſe meridians cuts the horizon in the north
point, where the hour of XII is fuppofed to
be marked, the reft of the meridians will cut
the horizon at the reſpective diſtances of all the
other hours from XII. Then, if theſe points of
diſtance be marked on the horizon, and the
globe be taken out of the horizon, and a flat
board or plate be put into its place, even with
the furface of the horizon; and if ſtraight lines.
be drawn from the center of the board, to thoſe
points of diſtance on the horizon which were
cut by the 24 meridian femicircles, thefe lines
will be the hour-lines of a horizontal dial for
that latitude, the edge of whofe gnomon muſt
be in the very fame fituation that the axis of the
globe
Of Dialing.
321
globe was, before it was taken out of the hori-
zon: that is, the gnomon muft make an angle
with the plane of the dial, equal to the latitude
of the place for which the dial is made.
If the pole of the globe be elevated to the
*co-latitude of the given place, and any meri-
dian be brought to the north point of the hori
zon, the rest of the meridians will cut the horizon
in the refpective distances of all the hours from
XII, for a direct ſouth dial, whofe gnomon muſt
make an angle with the plane of the dial, equal
to the co-latitude of the place; and the hours
muſt be fet the contrary way on this dial, to
what they are on the horizontal.
But if your globe have more than 24 meri-
dian femicircles upon it, you muſt take the
following method for making horizontal and
fouth dials by it.
dial.
Elevate the pole to the latitude of your place, To con-
and turn the globe until any particular meridian fruct a
(fuppofe the firft) comes to the north point of horizontal
the horizon and the oppoſite meridian will cut
the horizon in the fouth. Then, fet the hour-
index to the uppermoft XII on its circle; which
done, turn the globe weftward until 15 degrees
of the equator paſs under the brafen meridian,
and then the hour-index will be at I, (for the fun
moves 15 degrees every hour) and the firſt meri-
dian will cut the horizon in the number of de-
grees from the north point, that I is diftant from
XII. Turn on, until other 15 degrees of the
equator pafs under the brafen meridian, and the
hour-index will then be at II, and the firſt me-
* If the latitude be fubtracted from 90 degrees, the re-
mainder is called the co-latitude, or complement of the
latitude.
ridian
322
Of Dialing!
ridian will cut the horizon in the number of
degrees that II is diſtant from XII: and fo, by
making 15 degrees of the equator paſs under
the brafen meridian for every hour, the firft me-
ridian of the globe will cut the horizon in the
diſtances of all the hours from XII to VI, which
is juft 90 degrees; and then you need go no
farther, for the diſtances of XI, X, IX, VIII,
VII, and VI, in the forenoon, are the fame
from XII, as the diſtances of I, II, III, IV, V,
and VI, in the afternoon: and thefe hour-lines.
continued through the center, will give the
oppofite hour-lines on the other half of the dial:
but no more of thefe lines need be drawn, than
what anſwer to the fun's continuance above the
horizon of your place on the longeſt day, which
may be eaſily found by the 26th problem of the
foregoing lecture.
Thus, to make a horizontal dial for the lati-
tude of London, which is 51 degrees north,
elevate the north pole of the globe 51 degrees
above the north point of the horizon, and then
turn the globe, until the firft meridian (which
is that of London on the English terreftrial
globe) cuts the north point of the horizon, and
fet the hour-index to XII at noon.
Then, turning the globe weftward until the
index points fucceffively to I, II, III, IV, V,
and VI, in the afternoon; or until 15, 30, 45,
60, 75, and 90 degrees of the equator pafs under
the brafen meridian, you will find that the firſt
meridian of the globe cuts the horizon in the
following numbers of degrees from the north
towards the eaſt, viz. 11 24, 38 531,
711's, and 90; which are the refpective diſtances
of the above hours from XII upon the plane of
the horizon.
1 2
To
ATE XXI.
Fig.1.
08
IX IX
#
Id
1
op
9.3.
XI
XI
X
rauson delin.
j
IA
VII
V
II VII
II
I
δο
IX
ав
X
VII
VIII
VIL
IX
TA
Fig. 2.
IA'S
Go
20
40 150 100
Line of Chords.
II
cd
IX
YT
m
II
I
Fig. 4.
F
E
M
T
Scale of Latitudes
V Soale of Hours.
VI
VII
· VIII
· 10
20 30 40 636.
TIX
J. Mynde fi
Of Dialing.
323
To transfer theſe, and the rest of the hours, PlateXXI.
to a horizontal plane, draw the parallel right Fig. 1.
lines ac and bd upon that plane, as far from
each other as is equal to the intended thickness
of the gnomon or ftile of the dial, and the ſpace
included between them will be the meridian
or twelve o'clock line on the dial. Crofs this
meridian at right angles with the fix o'clock line
gh, and fetting one foot of your compaffes in the
interfection a, as a center, defcribe the quadrant
ge with any convenient radius or opening of the
compaffes: then, fetting one foot in the inter-
fection b, as a center, with the fame radius de-
ſcribe the quadrant fb, and divide each qua-
drant into 90 equal parts or degrees, as in the
figure.
Becauſe the hour-lines are lefs diftant from
each other about noon, than in any other part of
the dial, it is beft to have the centers of thefe
quadrants at a little diftance from the center of
the dial-plane, on the fide oppofite to XII, in
order to enlarge the hour-diftances thereabout
under the fame angles on the plane. Thus, the
center of the plane is at C, but the centers of the
quadrants at a and b.
I
Lay a ruler over the point b (and keeping it
there for the center of all the afternoon hours in
the quadrant fh) draw the hour-line of I,
through 11 degrees in the quadrant; the hour-
line of II, through 24 degrees; of III, through
38 degrees; IIII, through 531, and V through
71 and becauſe the fun rifes about four in
the morning, on the longest days at London,
continue the hour-lines of 1III and V, in the
afternoon, through the center b to the oppofite
fide of the dial.—This done, lay the ruler to the
center a, of the quadrant e g, and through the
I 5
Y
like
324
Of Dialing.
like divifions or degrees of that quadrant, viz.
113, 241, 381x, 531, and 717, draw the fore-
noon hour-lines of XI, X, IX, VIII, and VII;
and becauſe the fun fets not before eight in the
evening on the longest days, continue the hour-
lines of VII and VIII in the forenoon, through the
center a, to VII and VIII in the afternoon; and
all the hour-lines will be finiſhed on this dial;
to which the hours may be fet, as in the figure.
Laftly, through 51 degrees of either quad-
rant, and from its center, draw the right line ag
for the hypothenufe or axis of the gnomon agi;
and from g, let fall the perpendicular g i, upon
the meridian line ai, and there will be a triangle
made, whoſe fides are a g, g i, and i a. If a
plate fimilar to this triangle be made as thick as
the diſtance between the lines ac and b d, and fet
upright between them, touching at a and b, its
hypothenufe ag will be parallel to the axis of the
world, when the dial is truly fet; and will caſt a
fhadow on the hour of the day.
N. B. The trouble of dividing the two quad-
rants may be faved, if you have a fcale with a
line of chords upon it, fuch as that on the right
hand of the plate: for if you extend the com-
paffes from o to 60 degrees of the line of chords,
and with that extent, as a radius, deſcribe the
two quadrants upon their reſpective centers, the
above diſtances may be taken with the com-
paffes upon the line, and fet off upon the quad-
rants.
Fig. 2.
To make an erect direct fouth dial. Elevate the
To con- pole to the co-latitude of your place, and pro-
ftruct an, ceed in all refpects as above taught for the hori-
erect ſouth
zontal dial, from VI in the morning to VI in
the afternoon, only the hours muſt be reverfed,
as in the figure; and the hypothenufe ag, of the
dial.
gnomon
Of Dialing.
325
gnomon agf, muft make an angle with the dial-
plane equal to the co-latitude of the place. As
the fun can fhine no longer on this dial, than
from fix in the morning until fix in the evening,
there is no occafion for having any more than
twelve hours upon it.
clining
To make an erect dial, declining from the fouth To con-
towards the eaſt or west. Elevate the pole to the trust an
latitude of your place, and fcrew the quadrant of erea de-
altitude to the zenith. Then, if your dial de- dial.
clines towards the eaft (which we ſhall fuppofe
it to do at prefent) count in the horizon the
degrees of declination, from the eaſt point to-
wards the north, and bring the lower end of the
quadrant to that degree of declination at which
the reckoning ends. This done, bring any par-
ticular meridian of your globe (as ſuppoſe the
firſt meridian) directly under the graduated edge
of the upper part of the brafen meridian, and
fet the hour-index to XII at noon. Then, keep-
ing the quadrant of altitude at the degree of
declination in the horizon, turn the globe eaſt-
ward on its axis, and obferve the degrees cut by
the firſt meridian in the quadrant of altitude
(counted from the zenith) as the hour-index
comes to XI, X, IX, &c. in the forenoon, or as
15, 30, 45, &c, degrees of the equator pafs under
the brafen meridian at theſe hours refpectively;
and the degrees then cut in the qnadrant by the
firft meridian, are the refpective diftances of the
forenoon hours from XII on the plane of the
dial. Then, for the afternoon hours, turn the
quadrant of altitude round the zenith until it
comes to the degree in the horizon oppofite to
that where it was placed before; namely, as far
from the weft point of the horizon towards the
fouth, as it was fet at firft from the eaſt point to-
Y 2
wards
326
Of Dialing.
wards the north; and turn the globe weftward
on its axis, until the firſt meridian comes to the
brafen meridian again, and the hour-index to
XII: then, continue to turn the globe weſt-
ward, and as the index points to the afternoon
hours I, II, III, &c. or as 15, 30, 45, &c. de-
grees of the equator paſs under the brafen meri-
dian, the firſt meridian will cut the quadrant of
altitude in the refpective number of degrees
from the zenith, that each of thefe hours is from
XII on the dial.-And note, that when the firſt
meridian goes off the quadrant at the horizon, in
the forenoon, the hour-index fhews the time
when the fun will come upon this dial: and
when it goes off the quadrant in the afternoon,
the index will point to the time when the fun
goes off the dial.
Having thus found all the hour-diftances from
XII, lay them down upon your dial-plate, either
by dividing a femicircle into two quadrants of
90 degrees each (beginning at the hour-line of
XII) or by the line of chords, as above directed.
In all declining dials, the line on which the
file or gnomon ftands (commonly called the
fubftile-line) makes an angle with the twelve
o'clock line, and falls among the forenoon hour-
lines, if the dial declines towards the eaft; and
among the afternoon hour-lines, when the dial de-
clines towards the weft; that is, to the left hand
from the twelve o'clock line in the former cafe,
and to the right hand from it in the latter.
To find the diſtance of the fubftile from the
twelve o'clock line; if your dial declines from
the fouth towards the eaft, count the degrees
of that declination in the horizon from the eaft
point toward the north, and bring the lower end
of the quadrant of altitude to that degree of
declination
Of Dialing.
327
declination where the reckoning ends: then,
turn the globe until the firſt meridian cuts the
horizon in the like number of degrees, counted
from the fouth point toward the east; and the
quadrant and firft meridian will then crofs one
another at right angles, and the number of de-
grees of the quadrant, which are intercepted
between the firft meridian and the zenith, is
equal to the diſtance of the ſubftile line from the
twelve o'clock line; and the number of degrees
of the first meridian, which are intercepted be-
tween the quadrant and the north pole, is equal
to the elevation of the ftile above the plane of
the dial.
If the dial declines weftward from the fouth,
count that declination from the eaſt point of the
horizon towards the fouth, and bring the quad-
rant of altitude to the degree in the horizon at
which the reckoning ends; both for finding the
forenoon hours, and the diftance of the fubftile
from the meridian: and for the afternoon hours,
bring the quadrant to the oppofite degree in the
horizon, namely, as far from the west towards
the north, and then proceed in all refpects as
above.
Thus, we have finifhed our declining dial;
and in fo doing, we made four dials, viz.
1. A north dial, declining eastward by the
fame number of degrees. 2. A north dial, de-
clining the fame number weſt.
3. A fouth
dial, declining eaſt. And, 4. a fouth dial de-
clining weft. Only, placing the proper number
of hours, and the ftile or gnomon refpectively,
upon each plane. For (as above-mentioned)
in the fouth weſt plane, the fubftilar-line falls
among the afternoon hours; and in the fouth-
eaft, of the fame declination among the forenoon.
hours,
A
¥ 3
328
Of Dialing.
An eafy
method
hours, at equal diſtances from XII. And fo,
all the morning hours on the weft decliner will
be like the afternoon hours on the eaft decliner:
the fouth-east decliner will produce the north-
weft decliner; and the fouth-weft decliner, the
north-east decliner, by only extending the hour-
Jinės, ftile and fubftile, quite through the center:
the axis of the ftile (or edge that cafts the fhadow
on the hour of the day) being in all dials what-
ever parallel to the axis of the world, and confe-
quently pointing towards the north pole of the
heaven in north latitudes, and towards the fouth
pole, in fouth latitudes. See more of this in the
following lecture.
But becauſe every one who would like to make
a dial, may perhaps not be provided with a globe
for con- to affift him, and may probably not underſtand
ftruating the method of doing it by logarithmic calcula-
of dials.
X
tion; we hall fhew how to perform it by the
plain dialing lines, or fcale of latitudes and
hours; fuch as thofe on the right hand of Fig.
4. in Plate XXI, or at the top of Plate XXII,
and which may be had on fcales commonly fold
by the mathematical inftrument makers.
This is the eafieft of all mechanical methods,
and by much the best, when the lines are truly
divided not only the half hours and quarters
may be laid down by all of them, but every fifth
minute by moſt, and every ſingle minute by
thofe where the line of hours is a foot in length.
Having drawn your double meridian line ab,
Fig. 3. cd, on the plane intended for a horizontal dial,
and croffed it at right angles by the fix o'clock line
fe (as in Fig. 1.) take the latitude of your place
with the compaffes, in the fcale of latitudes, and
fet that extent from c to e, and from a to f, on
the fix o'clock line: then, taking the whole fix
hours
Of Dialing.
329
A
hours between the points of the compaffes in the
fcale of hours, with that extent fet one foot in the
point e, and let the other foot fall where it will
upon the meridian line cd, as at d. Do the fame
from f to b, and draw the right lines e d and fb,
each of which will be equal in length to the whole
fcale of hours. This done, fetting one foot of
the compaffes in the beginning of the fcale at XII,
and extending the other to each hour on the
fcale, lay off thefe extents from d to e for the
afternoon hours, and from b to ƒ for thoſe of the
forenoon this will divide the lines de and b f
in the fame manner as the hour-ſcale is divided,
at 1, 2, 3, 4, 5 and 6; on which the quarters
may alſo be laid down, if required. Then, lay-
ing a ruler on the point c, draw the firft five
hours in the afternoon, from that point, through
the dots at the numeral figures 1, 2, 3, 4, 5, on
the line de; and continue the lines of IIII and V
through the center to the other fide of the dial,
for the like hours of the morning; which done,
lay the ruler on the, point a, and draw the laft
five hours in the forenoon through the dots
5, 4, 3, 2, 1, on the line fb; continuing the
hour-lines of VII and VIII through the center a
to the other fide uf the dial, for the like hours
of the evening; and fet the hours to their re-
fpective lines as in the figure. Lastly, make the
gnomon the fame way as taught above for the
horizontal dial, and the whole will be finiſhed.
To make an erect fouth dial, take the co-la-
titude of your place from the fcale of latitudes,
and then proceed in all refpects for the hour-
lines, as in the horizontal dial; only reverfing
the hours, as in Fig. 2; and making the angle
of the ftile's height equal to the co-latitude.
Y 4
I have
330
Of Dialing.
Fig. 4.
Horizon-
I have drawn out a fet of dialing lines upon
the top of the 22d Plate, large enough for mak-
ing a dial of nine inches diameter, or more
inches if required; and have drawn them tole-
rably exact for common practice, to every quarter
of an hour. This fcale may be cut off from the
plate, and paſted on wood, or upon the infide of
one of the boards of this book; and then it will
be fomewhat more exact than it is on the plate,
for being rightly divided upon the copper-plate,
and printed off on wet paper, it ſhrinks as the
paper dries but when it is wetted again, it
itretches to the fame fize as when newly printed;
and if pafted on while wet, it will remain of that
fize afterwards.
But left the young dialiſt ſhould have neither
globe nor wooden fcale, and fhould tear or
otherwife fpoil the paper one in pafting, we ſhall
now fhew him how he may make a dial without
any of thefe helps. Only, if he has not a line
of chords, he muſt divide a quadrant into 90
equal parts or degrees for taking the proper angle
of the ftile's elevation, which is eaſily done.
With any opening of the compaſſes, as Z·L,
defcribe the two femicircles LFk and L2Qk,
upon the centers Z and z, where the fix o'clock
line croffes the double meridian line, and divide
tal dial. each femicircle into 12 equal parts, beginning at
L (though, ftrictly speaking, only the quadrants
from L to the fix o'clock line need be divided):
then connect the divifions which are equidiftant
from L, by the parallel lines KM, IN, HO, GP,
and F2, Draw V Z for the hypothenufe of the
ftile, making the angle VZ E equal to the lati-
titude of your place; and continue the line V Z to
R. Draw the line Rr parallel to the fix o'clock
line, and ſet off the diſtance a K from Z to Y,
the
PLATE XXII.
10
XII
20
30
40
50
610 70 80 90
The Line of Chords.
10
20
30
40
5060
70890
wat
I
III
V
The Line of Latitudes.
The Line of Hours.
JQ
F
F
P
R
H
1
K
A
y
M
N
Fig. 3.
G
D
Fig. 4.
A
k E
H
I
v E n x
Shadow Line
Decem
2.
a
đ
Gnomen
Lat. 51ź
Fig. 2.
80
Nov. Oct.
Jan. Feb.
20
10
Sep. Ang. Jul
Mar.
Apr.
Dec. NorDec.
10 20
May.
Jun's Declination
*atru
XIK
Forenoon (Hours
M X IX VI VIL
VI
V III
50
60
n
22
C
40
m
1 V
Afternoon Hours
VI VIL VILL
开
​HX
30
20
10
D
k
I. Ferguson delin.
102
50
50
40
30
E
Sines
F
Fig. 5.
20
ha
D
G
B
Fig. 1. 3.
Latitudes/
OT
80
70
B
5
3
4
XI
I
I
TIL
V
Hours
50
40
30
20
70
бо
Fact
50
!
Chords
10
10
40
VI
J. Mynde je.
Of Dialing.
331
g
Y
the distance b I from Z to X, c H from Z to W,
de from Z to T, and e F from Z to S. Then
draw the lines S s, Tt, W w, Xx, and ry, each
parallel to Rr. Set off the distance y from a
to 11, and from f to 1; the diſtance x X from b
to 10, and from g to 2; w W from c to 9, and
from b to 3; t T from d to 8, and from i to
4; s S frome to 7, and from 1 to 5. Then lay-
ing a ruler to the center Z, draw the forenoon
hour lines through the points 11, 10, 9, 8, 7;
and laying it to the center z, draw the afternoon
lines through the points 1, 2, 3, 4, 5; continu-
ing the forenoon lines of VII and VIII through
the center Z, to the oppofite fide of the dial, for
the like afternoon hours; and the afternoon lines.
IIII and V through the center z, to the oppofite
fide, for the like morning hours. Set the hours
to theſe lines as in the figure, and then erect
the file or gnomon, and the horizontal dial will
be finished.
To conſtruct a fouth dial, draw the line V Z, South
making an angle with the meridian Z L equal dial.
to the co-latitude of your place; and proceed in
all refpects as in the above horizontal dial for the
fame latitude, reverfing the hours as in Fig. 2.
and making the elevation of the gnomon equal
to the co-latitude,
Perhaps it may not be unacceptable to explain
the method of conſtructing the dialing lines, and
fome others; which is as follows.
With any opening of the compaffes, as E A, Plate
according to the intended length of the ſcale, XXII.
deſcribe the circle ADCB, and crofs it at right
angles by the diameters CE A and DE B. Fig. 1.
Divide the quadrant A B firſt into 9 equal parts, Dialing
and then each part into 10; fo fhall the quadrant lines, how
be divided into 90 equal parts or degrees. Draw contruct-
ed.
i.
the
332
Of Dialing
;
the right line AFB for the chord of this quad-
rant, and fetting one foot of the compaffes in
the point A, extend the other to the ſeveral divi-
fions of the quadrant, and transfer thefe divifions
to the line AFB by the arcs 10 10, 20 20, &c.
and this will be a line of chords, divided into go
unequal parts; which, if transferred from the
line back again to the quadrant, will divide it
equally. It is plain by the figure, that the dif-
tance from A to 60 in the line of chords, is juft
equal to A E, the radius of the circle from which
that line is made; for if the arc 60 60 be con-
tinued, of which A is the center, it goes exactly
through the center E of the arc A B.
And therefore, in laying down any number of
degrees on a circle, by the line of chords, you
muſt firſt open the compaffes fo, as to take in
just 60 degrees upon that line, as from A to 60:
and then, with that extent, as a radius, defcribe
a circle which will be exactly of the fame fize
with that from which the line was divided :
which done, fet one foot of the compaffes in the
beginning of the chord line, as at A, and extend
the other to the number of degrees you want
upon the line, which extent, applied to the circle,
will include the like number of degrees upon
it.
Divide the quadrant CD into 90 equal parts,
and from each point of diviſion draw right lines
as i, k, l, &c. to the line C E; all perpendicular
to that line, and parallel to D E, which will di-
vide EC into a line of fines; and although thefe
are ſeldom put among the dialing lines on a fcale,
yet they aſſiſt in drawing the line of latitudes.
For, if a ruler be laid upon the point D, and
over each divifion in the line of fines, it will
divide the quadrant C B into 90 unequal parts,
as
Of Dialing.
333
as Ba, ab, &c. fhewn by the right lines 10 a,
20 b, 30c, &c. drawn along the edge of the ruler.
If the right line BC be drawn, fubtending this
quadrant, and the neareft diftances B a, Bb, Bc,
&c. be taken in the compaffes from B, and fet
upon this line in the fame manner as directed for
the line of chords, it will make a line of latitudes
BC, equal in length to the line of chords A B,
and of an equal number of divifions, but very
unequal as to their lengths.
Draw the right line D G A, fubtending the
quadrant DA; and parallel to it, draw the right
liners, touching the quadrant DA at the nume-
ral figure 3. Divide this quadrant into fix equal
parts, as 1, 2, 3, &c. and through thefe points of
divifion draw right lines from the center E to
the liners, which will divide it at the points
where the fix hours are to be placed, as in the
figure. If every fixth part of the quadrant be
fubdivided into four equal parts, right lines.
drawn from the center through theſe points of
divifion, and continued to the line rs, will divide
each hour upon it into quarters.
1
In Fig. 2. we have the reprefentation of a dial or
portable dial, which may be eaſily drawn on a a card.
card, and carried in a pocket-book. The lines.
ad, ab and be of the gnomon must be cut quite
through the card; and as the end ab of the gno-
mon is raiſed occafionally above the plane of the
dial, it turns upon the uncut line c d as on a
hinge. The line dotted AB must be fit quite
through the card, and the thread must be put
through the flit, and have a knot tied behind, to
keep it from being eafily drawn out. On the
other end of this thread is a ſmall plummet D,
and on the middle of it a ſmall bead for fhewing
the time of the day.
To
334
Of Dialing.
To rectify this dial, fet the thread in the flit
right againſt the day of the month, and ſtretch
the thread from the day of the month over the
angular point where the curve lines meet at XII;
then ſhift the bead to that point on the thread,
and the dial will be rectified.
To find the hour of the day, raiſe the gnomon
(no matter how much or how little) and hold
the edge of the dial next the gnomon towards
the fun, fo as the uppermoft edge of the fhadow
of the gnomon may juft cover the fhadow-line;
and the bead then playing freely on the face of
the dial, by the weight of the plummet, will
fhew the time of the day among the hour-lines,
as it is forenoon or afternoon.
To find the time of fun-rifing and fetting,
move the thread among the hour-lines, until it
either covers fome one of them, or lies parallel
betwixt any two; and then it will cut the time
of fun-rifing among the forenoon hours, and of
fun-fetting among the afternoon hours, on that
day of the year for which the thread is fet in the
fcale of months.
To find the fun's declination, ftretch the thread
from the day of the month over the angular
point at XII, and it will cut the fun's declina-
tion, as it is north or fouth, for that day, in the
arched ſcale of north and fouth declination.
To find on what days the fun enters the
figns: when the bead, as above rectified, moves
along any of the curve lines which have the figns
of the zodiac marked upon them, the fun enters
thofe figns on the days pointed out by the thread
in the fcale of months.
The conſtruction of this dial is very eaſy,
efpecially if the reader compares it all along
with
Of Dialing.
335
with Fig. 3. as he reads the following explana-
tion of that figure.
Draw the occult line AB parallel to the top of Fig. 3.
the card, and crofs it at right angles with the fix
o'clock line E CD; then upon C, as a center,
with the radius CA, defcribe the femicircle AEL,
and divide it into 12 equal parts (beginning at
A) as Ar, As, &c. and from theſe points of
divifion, draw the hour-lines r, s, t, u, v, E, w,
and x, all parallel to the fix o'clock line E C.
If each part of the femicircle be fubdivided into
four equal parts, they will give the half-hour
lines and quarters, as in Fig. 2. Draw the right
line AS Do, making the angle SAB equal to the
latitude of your place. Upon the center A de-
fcribe the arch RST, and fet off upon it the arcs
SR and ST, each equal to 23 degrees, for the
fun's greateſt declination; and divide them into
23 equal parts, as in Fig. 2. Through the
interfection D of the lines ECD and AD 0,
draw the right line FDG at right angles to
A Do. Lay a ruler to the points A and R, and
draw the line ARF through 231 degrees of
fouth declination in the arc SR; and then lay-
ing the ruler to the points A and T, draw the line
ATG through 23 degrees of north declination
in the arc ST: fo fhall the lines ARF and
ATG cut the line F D G in the proper length
for the fcale of months. Upon the center D,
with the radius DF, defcribe the femicircle
Fo G; and divide it into fix equal parts, Fm,
mn, no, &c. and from thefe points of divifion
draw the right lines m h, ni, pk, and ql, each
parallel to o D. Then fetting one foot of the
compaffes in the point F, extend the other to A,
and deſcribe the arc AzH for the tropic of :
with the fame extent, fetting one foot in G, de-
fcribe
336
Of Dialing.
Fig. 4.
PAN
fcribe the arc AEO for the tropic of . Next
fetting one foot in the point , and extending
the other to A, defcribe the arc ACI for the
beginnings of the figns and ; and with the
fame extent, ſetting one foot in the point l. de-
ſcribe the arc A N for the beginnings of the
figns and . Set one foot in the point i, and
having extended the other to A, defcribe the arc
AK for the beginnings of the figns x and m;
and with the fame extent, fet one foot in k, and
deſcribe the arc AM for the beginnings of the
ſigns 8 and ". Then, fetting one foot in the
point D, and extending the other to A, deſcribe
the curve AL for the beginnings of
and the ſigns will be finiſhed. This done, lay a
ruler from the point A over the fun's declination
in the arch RST (found by the following table)
for every fifth day of the year; and where the
ruler cuts the line FDG, make marks; and
place the days of the months right againſt theſe
marks, in the manner fhewn by Fig. 2. Laftly,
draw the ſhadow line P Q parallel to the occult
line AB; make the gnomon, and fet the hours
to their reſpective lines, as in Fig. 2. and the dial
will be finiſhed.
and~;
There are ſeveral kinds of dials, which are
called univerfal, becauſe they ferve for all lati-
tudes. Of thefe, the beſt one that I know, is
Mr. Pardie's, which confifts of three principal
parts; the firft whereof is called the horizontal
An uni- plane (A), becauſe in the practice it muſt be pa-
rallel to the horizon. In this plane is fixt an
upright pin, which enters into the edge of the
fecond part B D, called the meridional plane;
which is made of two pieces, the loweft whereof
(B) is called the quadrant, becaufe it contains a
quarter of a circle, divided into 90 degrees; and
verfal
dial.
it
Of Dialing.
337
it is only into this part, near B, that the pin enters.
The other piece is a femicircle (D) adjuſted to the
quadrant, and turning in it by a groove, for raiſing
or depreffing the diameter (EF) of the femicircle,
which diameter is called the axis of the inftru-
ment. The third piece is a circle (G), divided
on both fides into 24 equal parts, which are the
hours. This circle is put upon the meridional
plane fo, that the axis (EF) may be perpendicu-
lar to the circle; and the point C be the com-
mon center of the circle, femicircle, and quad-
rant. The ſtraight edge of the femicircle is
chamfered on both fides to a fharp edge, which
paffes through the center of the circle. On one
fide of the chamfered part, the firſt fix months
of the year are laid down, according to the fun's
declination for their respective days, and on the
other fide the laft fix months. And againſt the
days on which the fun enters the figns, there are
ftraight lines drawn upon the femicircle, with the
characters of the figns marked upon them.
There is a black line drawn along the middle of
the upright edge of the quadrant, over which
hangs a thread (H), with its plummet (I), for
levelling the inftrument. N. B. From the 23d
of September to the 20th of March, the upper
furface of the circle muft touch both the center
C of the femicircle, and the line of y and;
and from the 20th of March to the 23d of Sep-
tember, the lower furface of the circle muſt
touch that center and line.
To find the time of the day by this dial. Hav-
ing fet it on a level place in fun-fhine, and ad-
juſted it by the leveling fcrews k and 1, until the
plumb line hangs over the black line upon the
edge of the quadrant, and parallel to the ſaid
edge; move the femicircle in the quadrant, until
1
的
​6
the
338.
Of Dialing.
Fig. 5.
r
the line of and (where the circle touches)
comes to the latitude of your place in the qua-
drant: then, turn the whole meridional plane
BD, with its circle G, upon the horizontal plane
A, until the edge of the fhadow of the circle
falls precifely on the day of the month in the
femicircle; and then, the meridional plane will
be due north and fouth, the axis E F will be
parallel to the axis of the world, and will caft a
fhadow upon the true time of the day, among
the hours on the circle.
N. B. As, when the inftrument is thus reci-
fied, the quadrant and femicircle are in the plane
of the meridian, fo the circle is then in the plane
of the equinoctial. Therefore, as the fun is above
the equinoctial in fummer (in nothern latitudes)
and below it in winter; the axis of the femi-
circle will caſt a fhadow on the hour of the day,
on the upper ſurface of the circle, from the 20th
of March to the 23d of September and from
the 23d of September, to the 20th of March,
the hour of the day will be determined by the
ſhadow of the femicircle, upon the lower ſurface
of the circle. In the former cafe, the fhadow of
the circle falls upon the day of the month, on
the lower part of the diameter of the femicircle;
and in the latter cafe, on the upper part.
The method of laying down the months and
figns upon the femicircle, is as follows. Draw
the right line AC B, equal the diameter of the
femicircle A D B, and crofs it in the middle at
right angles with the line ECD, equal in length
to ADB; then EC will be the radius of the
circle FCG, which is the fame as that of the
femicircle. Upon E, as a center, defcribe the
circle FCG, on which fet off the arcs Chand
Ci, each equal to 23 degrees, and divide them
accordingly into that number, for the fun's de-
3
I
2
clination.
Of Dialing.
339
clination. Then, laying the edge of a ruler
over the center E, and alfo over the fun's decli-
nation for every* fifth day of each month (as in
the card dial) mark the points on the diameter
AB of the femicircle from a to g, which are cut
by the ruler; and there place the days of the
months accordingly, anfwering the fun's declina-
tion. This done, fetting one foot of the com-
paffes in C, and extending the other to a or g,
deſcribe the femicircle abcdefg; which divide
into fix equal parts, and through the points of
divifion draw right lines, parallel to CD, for the
beginning of the fines (of which one half are on
one fide of the femicircle, and the other half on
the other fide) and fet the characters of the figns
to their proper lines, as in the figure.
The following table fhews the fun's place and
declination, in degrees and minutes, at the noon
of every day of the ſecond year after leap-year;
which is a mean between thofe of leap-year it-
felf, and the first and third years after. It is
uſeful for infcribing the months and their days
on fun-dials; and alfo for finding the latitudes.
of places, according to the methods preſcribed
after the table.
*The intermediate days may be drawn in by hand, if
the ſpaces be large enough to contain them.
N
A Table
340
Tables of the Sun's Place and Declination.
Days.
A Table ſhewing the fun's place and declination.
January.
Son's Pl. Sun's Dec.
D. M. D. M.
Days.
February.
Sun's Pl. Sun's Dec
D. M.
D. M.
III
5
523 S
SI
212
6 22 55
I 12 m 38
213 39
MY
17S 2
16 45
313
822
49
314
40
16
16 27
414
9 22
43
415
41
16 10
alos
515
10 22
37
616
1 I
22
29
717
12 22
22
818
13 22
14
6/6700
5 16
41
15 51
6,17
42
15
15
33
718
43
15
14
8,19
43
14
14
55
919
14 22
5
9,20
44 14
36
10/20
16
21
56
10:21
45 14 17
IJ 21 17
2 I
47
II 22
45 13 57
I 222
18
21 37
12:23
46
46 13
13
37
1323 19
21
27
1324
46 13
13
17
1424 20
21
17
1425
47
12 57
1525
21 21 6
15/26 47
12
36
1626 22 20 54
1627 48
12
15
17 27 24 20
43
1728 48
I I
54
18 28 25 20
30
1829 48
11
I
33.
21
28 19
52
22
2 29 19
38
23 3 30
19
24
24 4
31
19
10
55
1929 26 20 18
190X49 II 12
20 027 20 5 20 I 49 ΙΟ 50
29
50 10
3 50 10 7
20 + 46
2I
22
23
4
50
9 45
24 5
51
9
23
2 2
བ་
ww
345
26
6
33
27
7
34
18
24
27
28
8
35
18
9
29 9
35 17
17
53
3010
3111 I
37 17 19
25 5 32 18
18 40 26 7 51 8
36 17 36
8 51
289
SI 7 53
In theſe Tables N fig-
nifies north declina-
tion, and S fouth.
A Table
25
6
51
9 O
38
8 16
Tables of the Sun's Place and Declination.
34I
D. M.
7530
[Days.
A Table fhewing the fun's place and declination.
March.
Sun's Pl. Sun's Dec.
D. M.
110X52
Days.
April.
Sun's Pl. Sun's Dec.
D. M. D. M.
11138
4N 36
2 II
52
7
7
2/12 37
4. 59
3/12
52
6
44
313
36
5
22
413 52
6
2 I
414 35
5
45
514
52
5
58
515
34
6
४
615
52
5 35
616
33
6
31
716 51
5
12
717
31
6
817 51
9/18
4 48
818
30
7
351
36
53
16
51
4 25
919
29
7
38
10 19
51
4
2
10 20
28
8
IJ 20
51
3 38
1121
12/21
50
3
14
1222
13/22
50 2
51
1323
22.2
27
25
24
1423 50 2 27
1424
23
1524
49 2 4
1525 21
754 er medl
∞ ∞
8
22
8
44
9
6
9
28
9
49
16/25
17/26
49
I 40
16/26
ΙΟ
20
II
48
I
16
1727 18
IO
32
1827
18 27 48
о
53
1828
17
ΙΟ
53
19/28
48
O 29
19/29
15
II 14
2029
47
O
5
2008 14
I I
34
21
Or 47
ON 19
21 I 12
1 I
55
22
I 46
о
42
22 2
1 1
12
15
23
2 45
I
6
23 3
9
12
35
10 40 40
24 3 45
I
29
24 4
7
12 5.5
25 4 44
I
53
25
5
6
13 14
2 2
56 7∞
70.
26
27
28
5 43
29 8
42
2 2
17
26
6 4 13 34
40
277
2
13 53
42
3 3
28 8
O
14 12
41
3
27
298
59
14 30
309 9 40
3
50 309 9
57
14
49
3110 39
4 13
Z 2
A Table
342
Tables of the Sun's Place and Declination.
Days.
A Table fhewing the fun's place and declination.
May.
Sun's Pl. Sun's Dec.
D. M.
1108 55
D. M.
15 N 7
2 II 53 15 25
Days.
June.
Sun's Pl.(Sun's Dec.
D. M. D. M.
110
716 43 16 51
3
I 2
413
51 15 43
49 16
18
514 47 16
615 45 16 35
817 41 17
8
817
918
39
17
24
9
18
23
44 22 N
5
2 II
41 22 13
3+4/07co
I 2
39
22
21
413 36 22
28
514 34 22
35
15
31 22
4I
16 28 22 47
261 22
22
53
58
10 19 36
17
40
1019
20 23 3
w ∞w -
1120 34 17
12/21 32 18
13/22 30 18
1423 28 18
55
[1/20
18 23
7
10
12/21
15 23
11
25
13
22
12
12 23
15
40
1423
9 23
18
15/24 25 18
54
15/24
71 23
20
16 25 23 19
2029
1726
18 27 19 19 35
16 19
19/28
21 19 22
∞ 2
8 1625
4 23
22
17
26 123
24
18 26
58 23
26
48
19 27
14 20
21
ΟΠΙΙ
20
13 21 29
22 I 9
20
25 22
1 20 28 53 23 28
28
50 23
047 23 28
56
23
27
23 2 7 20
37 23
I
24 3
4 20
48 24
A W
451 23
28
2 42 23 27
25 4 2
20
59 25 3
39 23
26
26 4 59 21 10 20 4
36 23 24
27
5 57 21
20 27
5
5
33
33 23
21
28 6
54 21
30 28 6
6 31
31 23 19
29
297
7
52
21
39
29
7
28
23
16
30
8
49
21
49
30
8
31 9 47 21
57
25 23
A Table
12
Tables of the Sun's Place and Declination.
343
Days.|
A Table fhewing the fun's place and declination.
July.
Sun's Pl. Sun's Dec.
D. M. D. M.
|Days
Auguſt.
Sun's Pl Sun's Dec.
D. M. D. M.
922 23 N 8
I
858 18N 2
210
19
23
4
2
9
55
17 47
311
16
16
23
310
53 17
32
4
| 2
14
22
55
4II
50 17
16
513
I I
22
49
614
8
22
43
oler
512
48
17
613
45
16 43
715
5
22 37
714 43
16 26
816 O 22 30
917 2 22 23
1017 57 22 16
815 41 16 9
916 38 15
52
1017
36
15
25
{
1118 54 22
8
I! 18
33 15
17
1219 51 22
12/19 31
14 59
13/20
49 21 52
13/20
29
14 41
14/21
46 21
43
14/21
26
14 23
5/22
43
2 I
33
1522
24
14 4
1623
40
21 22
1623
22 13 45
17 24
38
21
21
14
1724 20 13
26
1825 35
2 I
3
1825
17 13
7
19 26
32
32
20
52
19/26
15 I 2
47
22/29
23
2027 29 20
2128 27 20
24 20 18
021 20 6
4!
20/27
13
12
27
30
2 1/2 8
I I
12
7
2229
9
I I
47
23 0mp 7
1 I
27
24
I 19
19
54
24 I
I [
6
25
2
16
19
4 I
25 2 3
IO
46
26 3
3 13
19
28 26
27 4
4
11 19 14
285
29/6
8
19 1
2 2
27
28
78
coco +
3
I
10
25
3
59
10 4
4 57
9
43
6 18 46
29 5 55
9 21
30 7
3 18 32
30 6 53
9
31 8
18
17
31 7
51
8
38
Z 3
A Table
344
Tables of the Sun's Place and Declination.
Days.
A Table fhewing the fun's place and declination.
September.
Sun's Pl. Sun's D-c
D. M.
M.
Days
October.
Sun's Pl. Sun's Dec.
D. M. D. M.
3 S 14
D. M.
I
8 m 49
8 N 16
I
88
2 9 47
7 55
2 9
7
3 37
310
46
7 33
3/10
7
4
411
44
7
10
4II
6
4
24
512
42
6 48
512
5
4
47
613 40 6
26
613
4
IO
714
39
6
3
714 4
5
33
15
37
5
41
815
3
5
56
9/16
35 5
18
9/16
3
6
19
1017
34
4
55
1017
2
6
42
1118
1 / 18
32
4
32
1118
I
7
5
12 19
31
4
9
12 1 19
I
7
27
13/20
29
3 46
13/20
7
50
14 21
28
3.23
14 21
1522
26
3
1522
∞ ∞
8
I2
8
35
1623 25
2 37
1623
о
8
57
1724
241
2 14
17 23
59
9
19
1825
22
I
50
18/24
59
9
41
19/26
21
I 27
19 25
58
10 3
2027 20
I
4
20/26
58
10 24
2 2 2 2
2128
19
O
40.
21 27
58
10
46
212
25
aia A W
22/29
23
24
0±16
I 15
17
17
22 28
58
I I
7
OS 6
23/29 58
I I
28
O 30
24 om58
I I
49.
2 14
0 53 25
I
58
12
IO
~ 22-
26 3
27
28
13
I
17
26
2 58
12
31
4
12
I
40
27 3 58
12
51
5
I
2
4
28 4 58
13
12
29
6 10
2
27
29 5
58
13
32
30 7
9
2
50
30 6
58
58
13
13
51
31 7
58
14
I I
A Table
Tables of the Sun's Place and Declination.
345
29
Days.
A Table fhewing the fun's place and declination.
November.
Sun's Pl. Sun's Dec.
D. M. D. M
18m58 14 S 30
58 14 50
Days.]
December.
Sun's Pl. Sun's Dec.
D. M. D. M.
I
9816
21 S 52
2/10
17
22
310 59 15 8
311
II
18
22
10
411
59 15 27
412
19
22
18
512
59 15 45
513
20 22
26
613 59 16
715
16
21
31
611
14
715
2 2
21 22
33
22 22
40
816 o 16 39
816
23 22
46
917
o 16 56
917
24
22
52
10 18
I
17 13
1018
18
25 22
58
1119
I
17 30
1119
26 23
12 20
2
17
46
12 20 27
23
8
1321
2
18
2
14/22
3
18
18 18
13 21 28
14/22
23
12
30 2
29 23
15
1523 4
16/24 4 18
18
34
15 23
30
23
18
49
16 24
31
23 2I
17 25 5 19
4
17 25
33
33 23 24
1826
5 19
18
18/26
34 23 26
1927
35
22
21 29
06 8
23
I 9 20
25
24
2
1 I
29
7
30 8
25 3
I I 2 I
12 21
261 4
27 5
28 6 13
14
8 15
21 23
2I
21
20
49
1927 6 19 32
20 28 7 19 46
2 2 2
7 19 59
35 23 27
20 28 36 23
37
20 12 22 0138
10 20 37
2 2
33
222
28
2129
23
28
23
28
2 2
23
I 40
23
28
24
2 41
23
27
25
3 42 23 25
-
26
4
43 23
23
12
27 5 44 23
21
28 6
46 23
18
3329
7
47
23
15
43
30
8
48
48
23
I I
31
9 49
23
6
Z 4
To
346
Rules for finding the Latitude.
To find the latitude of any place by obfervation.
The latitude of any place is equal to the
elevation of the pole above the horizon of that
place. Therefore it is plain, that if a ftar was
fixt in the pole, there would be nothing re-
quired to find the latitude, but to take the al-
titude of that flar with a good inftrument. But
although there is no ftar in the pole, yet the
latitude may be found by taking the greatest
and leaſt altitude of any ftar that never fets: for
if half the difference between theſe altitudes be
added to the leaft altitude, or fubtracted from
the greateſt, the fum or remainder will be equal
to the altitude of the pole at the place of ob-
fervation.
But becauſe the length of the night muſt be
more than 12 hours, in order to have two fuch
obfervations; the fun's meridian altitude and
declination are generally made ufe of for finding
the latitude, by means of its complement, which
is equal to the elevation of the equinoctial above
the horizon; and if this complement be fub-
tracted from 90 degrees, the remainder will be
the latitude: concerning which, I think, the fol-
lowing rules take in all the various cafes.
1. If the fun has north declination, and is on
the meridian, and to the fouth of your place,
fubtract the declination from the meridian alti-
tude (taken by a good quadrant) and the re-
mainder will be the height of the equinoctial or
complement of the latitude north.
EXAM-
Rules for finding the Latitude.
347
Suppofe
EXAMPLE.
The fun's meridian altitude 42° 20′ South
And his declination, fubt. 10 15 North
Rem. the complement of the lat. 32 5
Which fubtract from
90
And the remainder is the latitude 57 55 North
2. If the fun has fouth declination, and is
fouthward of your place at noon, add the de-
clination to the meridian altitude; the fum, if
lefs than 90 degrees, is the complement of the
latitude north: but if the fum exceeds 90 de-
grees, the latitude is fouth; and if go be taken
90
from that fum, the remainder will be the la-
titude.
EXAMPLES.
The fun's meridian altitude
The fun's declination, add
Complement of the latitude
Subtract from
Remains the latitude
The fun's meridian altitude
The fun's declination, add
:
The fum is
From which fubtract
65° 10′ South
15 30 South
80
40
90
9 20 North
80° 40′ South
20 10 South
100
50
Remains the latitude
90
10 50 South.
J
3. If
348
Rules for finding the Latitude.
3. If the fun has north declination, and is on
the meridian north of your place, add the decli-
nation to the north meridian altitude; the fum,
if less than 90 degrees, is the complement of
the latitude fouth: but if the fum is more than
90 degrees, fubtract 90 from it, and the re-
mainder is the latitude north.
EXAMPLES.
Sun's meridian altitude
Sun's declination, add
Complement of the latitude.
Subtract from
Remains the latitude
Sun's meridian altitude
Sun's declination, add
The fum is
From which fubtract
Remains the latitude
60°
30 North
20 10 North
- 80
40
90
9
20 South
70° 20′ North
23
20 North
93 40
90
3 40 North.
4. If the fun has fouth declination, and is north
of your place at noon, fubtract the declination
from the north meridian altitude, and the re-
mainder is the complement of the latitude
fouth.
EXAM-
Rules for finding the Latitude.
349
EXAMPLE.
Sun's meridian altitude
Sun's declination, fubtract
Complement of the latitude
Subtract this from
•
50° 30′ North
20
10 South
32 20
90
And the remainder is the latitude 57 40 South
5. If the fun has no declination, and is fouth
of your place at noon, the meridian altitude is
the complement of the latitude north: but if
the fun be then north of your place, his meri-
dian altitude is the complement of the latitude
fouth.
EXAMPLES.
Sun's meridian altitude
Subtract from
Remains the latitude
Sun's meridian altitude
Subtract from
Remains the latitude
38° 30′ South
90 O
51 30 North
38° 30′ North
90 O
51 30 South.
6. If you obferve the fun beneath the pole,
fubtract his declination from 90 degrees, and
add the remainder to his altitude; and the fum
is the latitude.
}
X
EXAM-
350
Rules for finding the Latitude:
1
EXAMPLE.
Sun's declination
Subtract from
Remains
20° 30
90
69 30 add
20
}
Sun's altitude below the pole - 10
The fum is the latitude
79 50.
Which is north or fouth, according as the fun's
declination is north or fouth for when the fun
has fouth declination, he is never feen below
the north pole; nor is he ever ſeen below the
fouth pole, when his declination is north.
7. If the fun be in the zenith at noon, and
at the fame time has no declination, you are
then under the equinoctial, and fo have no
latitude.
8. If the fun be in the zenith at noon, and
has declination, the declination is equal to the
latitude, north or fouth. Theſe two cafes are
fo plain, that they require no examples.
H
LECT. XI.
Of Dialing.
AVING fhewn in the preceding Lec-
ture how to make fun-dials by the affift-
ance of a good globe, or of a dialing fcale, we
fhall now proceed to the method of conſtructing
dials arithmetically; which will be more agree-
able to thoſe who have learnt the elements of
trigo-
Of Dialing.
351
trigonometry, becauſe globes and fcales can
never be ſo accurate as the logarithms, in find-
ing the angular diftances of the hours. Yet, as
a globe may be found exact enough for fome
other requifites in dialing, we fhall take it in
occafionally.
The conſtruction of fun-dials on all planes
whatever, may be included in one general rule:
intelligible, if that of a horizontal dial for any
given latitude be well underſtood. For there is
no plane, however obliquely fituated with re-
ſpect to any given place, but what is parallel
to the horizon of fome other place; and there-
fore, if we can find that other place by a pro-
blem on the terreſtrial globe, or by a trigonome-
trical calculation, and conſtruct a horizontal dial
for it; that dial, applied to the plane where it is
to ſerve, will be a true dial for that place. Thus,
an erect direct fouth dial in 51 degrees north
latitude, would be a horizontal dial on the fame
meridian, 90 degrees fouthward of 514 degrees
north latitude; which falls in with 384 degrees
of fouth latitude. but if the upright plane de-
clines from facing the fouth at the given place,
it would ſtill be a horizontal plane 90 degrees
from that place; but for a different longitude:
which would alter the reckoning of the hours
accordingly.
CASE I.
1. Let us fuppofe that an upright plane at
London declines 36 degrees weftward from
facing the fouth; and that it is required to find
a place on the globe, to whofe horizon the faid
plane is parallel; and alfo the difference of longi-
tude between London and that place.
Rectify
352
Of Dialing.
Rectify the globe to the latitude of London,
and bring London to the zenith under the brafs
meridian, then that point of the globe which lies
in the horizon at the given degree of declination
(counted weftward from the fouth point of the
horizon) is the place at which the above-men-
tioned plane would be horizontal.-Now, to
find the latitude and longitude of that place,
keep your eye upon the place, and turn the
globe eastward, until it comes under the gradu-
ated edge of the braſs meridian; then, the de-
gree of the braſs meridian that ſtands directly
over the place, is its latitude; and the number
of degrees in the equator, which are intercepted
between the meridian of London and the brafs
meridian, is the place's difference of longitude.
Thus, as the latitude of London is 51 de-
grees north, and the declination of the place is
36 degrees weft; I elevate the north pole 511
degrees above the horizon, and turn the globe
until London comes to the zenith, or under the
graduated edge of the meridian; then, I count
36 degrees on the horizon weftward from the
ſouth point, and make a mark on that place of
the globe over which the reckoning ends, and
bringing the mark under the graduated edge
of the brafs meridian, I find it to be under 30
degrees in fouth latitude: keeping it there, I count
in the equator the number of degrees between
the meridian of London and the brafen meridian
(which now becomes the meridian of the required
place) and find it to be 42. Therefore an
upright plane at London, declining 36 degrees
weftward from the fouth, would be a horizontal
plane at that place, whofe latitude is 30 degrees
fouth of the equator, and longitude 423 degrees
weft of the meridian of London.
4.
Which
PLATE XXIII.
Fig.1.
Fig. 2.
C
Fig. 3.
W
P
H
D
h
E
S
Fig. 4.
C
E
H
12
M
XIII
J. Ferguson del.
K
L
R
P
R..
H
850.
N
I
I
Æ
I
I
·H
H
P
&c.
H
R
h
169
P
Q
E
Ⅲ
Fig. 5.
V
S
υ
E
R
Q
Flynde fc.
Of Dialing.
353
Which difference of longitude being con-
verted into time, is 2 hours 51 minutes.
4
The vertical dial declining weftward 36 de-
grees at London, is therefore to be drawn in all
reſpects as a horizontal dial for fouth latitude
30 degrees; fave only, that the reckoning of
the hours is to anticipate the reckoning on the
horizontal dial, by 2 hours 51 minutes: for fo
much fooner will the fun come to the meridian
of London, than to the meridian of any place
whofe longitude is 424 degrees weft from Lon-
don.
2. But to be more exact than the globe will
fhew us, we ſhall uſe a little trigonometry.
› Plate
Let NESW be the horizon of London,
whoſe zenith is 2, and P the north pole of the XXIII.
ſphere; and let Zb be the poſition of a vertical Fig. 1.
plane at Z, declining weftward from S (the
fouth) by an angle of 36 degrees; on which
plane an erect dial for London at Z is to be
defcribed. Make the femidiameter Z D perpen-
dicular to Z h, and it will cut the horizon in D,
36 degrees weft of the fouth S. Then, a plane
in the tangent H D, touching the ſphere in D,
will be parallel to the plane Zb; and the axis of
the ſphere will be equally inclined to both theſe
planes.
Let WQE be the equinoctial, whofe eleva-
tion above the horizon of Z (London) is 38 1/
degrees; and PRD be the meridian of the
place D, cutting the equinoctial in R. Then,
it is evident, that the arc RD is the latitude of
the place D (where the plane Zb would be hori-
zontal) and the arc R 2 is the difference of
longitude of the planes Zb and D H.
In the ſpherical triangle WDR, the arc WD
is given, for it is the complement of the plane's
6
decli-
1
354
Of Dialing.
2
declination from S the fouth; which comple
ment is 54° (viz. 90°-36° :) the angle at R,
in which the meridian of the place D cuts the
equator, is a right angle; and the angle RWD
meaſures the elevation of the equinoctial above
the horizon of Z, namely, 38 degrees. Say
therefore, as radius is to the co-fine of the
plane's declination from the fouth, fo is the co-
fine of the latitude of Z to the fine of RD the
latitude of D: which is of a different denomi-
nation from the latitude of Z, becauſe Z and D
are on different fides of the equator.
10.00000
As radius
To co-fine
36° 0′ = RQ
9.90796
So co-fine
51° 30′ =QZ
9.79415
(9.70211)=
To fine 30º 14=DR
the latitude of D, whofe horizon is parallel to
the vertical plane Zb at Z.
N. B. When radius is made the firft term, it
may be omitted, and then, by fubtracting it
mentally from the fum of the other two, the
operation will be fhortened. Thus, in the pre-
fent cafe,
To the logarithmic fine of WR=* 54° 0′ 9.90796
Add the logarithmic fine of R D=+ 38° 30′ 9.79415
9.70211
Their fum-radius
gives the fame folution as above. And we fhall
keep to this method in the following part of the
work.
*The co-fine of 36°
+ The co-fine of 51º
o, or of R 2.
30', or of QZ.
Q.
2
To
Of Dialing.
355
To find the difference of longitude of the
places D and Z, fay, as radius is to the co-fine
of 38 degrees, the height of the equinoctial at
Z, fo is the co-tangent of 36 degrees, the plane's
declination, to the co-tangent of the difference
of longitudes. Thus,
To the logarithmic fine of * 51° 30′ 9.89354
Add the logarithmic tang. of† 54° 0' 10.13874
Their fum-radius
10.03228
WR; which
is the neareſt tangent of 47° 8'
is the co-tangent of 42° 52′ = R Q, the dif-
ference of longitude fought. Which difference,
being reduced to time, is 2 hours 51 minutes.
3. And thus having found the exact latitude
and longitude of the place D, to whofe horizon
the vertical plane at Z is parallel, we ſhall pro-
ceed to the conftruction of a horizontal dial for
the place D, whoſe latitude is 30° 14′ fouth;
but anticipating the time at D by 2 hours 51
minutes (neglecting the minute in practice)
44
becauſe D is ſo far weftward in longitude from
the meridian of London; and this will be a
true vertical dial at London, declining weftward
36 degrees.
Affume any right line C S L for the fubftile Fig, z.
of the dial, and make the angle K C P equal to
the latitude of the place (viz. 30° 14′) to whoſe
horizon the plane of the dial is parallel; then
CRP will be the axis of the ftile, or edge that
caſts the fhadow on the hours of the day, in the
dial. This done, draw the contingent line EQ,
cutting the fubftilar line at right angles in K;
* The co-fine of 38° 30′, or of IV D R.
The co-tangent of 36°, or of D_W.
A a
and
356
Of Dialing.
Q
and from K make K R perpendicular to the axis.
CR P. Then K G (=K R) being made radius,
that is, equal to the chord of 60' or tangent of
45° on a good ſector, take 42° 52′ (the differ-
ence of longitude of the places Z and D) from
the tangents, and having fet it from K to M,
draw C M for the hour-line of XII. Take KN
equal to the tangent of an angle lefs by 15
degrees than KM; that is, the tangent 27° 52′;
and through the point N draw CN for the hour-
line of I. The tangent of 12° 52′ (which is
15° less than 27° 52') fet off the fame way, will
give a point between K and N, through which
the hour-line of II is to be drawn. The tan-
gent of 2° 8' (the difference between 45° and
42° 52') placed on the other fide of C L, will
determine the point through which the hour-line
of III is to be drawn: to which 2° 8', if the
tangent of 15° be added, it will make 17° 8';
and this fet off from K towards Q on the line
E 2, will give the point for the hour-line of
IV: and fo of the reft.-The forenoon hour-
lines are drawn the fame way, by the continual
addition of the tangents 15º, 30°, 45°, &c. to
42° 52′ (the tangent of K M) for the hours
of XI, X, IX, &c. as far as neceffary; that is,
until there be five hours on each fide of the
fubftile. The fixth hour, accounted from that
hour or part of the hour on which the fubftile
falls, will be always in a line perpendicular to
the fubftile, and drawn through the center C.
4. In all erect dials, C M, the hour-line of
XII, is perpendicular to the horizon of the
place for which the dial is to ferve: for that
Îine is the interfection of a vertical plane with
the plane of the meridian of the place, both
which are perpendicular to the plane of the
horizon:
Of Dialing.
357
a
horizon and any line HO, or ho, perpendi-
cular to C M, will be a horizontal line on the
plane of the dial, along which line the hours
may be numbered: and C M being fet perpen-
dicular to the horizon, the dial will have its true
pofition.
5. If the plane of the dial had declined by an
equal angle toward the eaſt, its defcription would
have differed only in this, that the hour-line of
XII would have fallen on the other fide of the
fubftile C L, and the line HO would have a
fubcontrary poſition to what it has in this
figure.
6. And thefe two dials, with the upper points
of their ſtiles turned toward the north pole, will
ſerve for the other two planes parallel to them;
the one declining from the north toward the
eaft, and the other from the north toward the
weft, by the fame quantity of angle. The like
holds true of all dials in general, whatever be
their declination and obliquity of their planes to
the horizon.
CASE II.
7. If the plane of the dial not only declines, Fig. 3.
but alſo reclines, or inclines. Suppofe its declina-
tion from fronting the fouth S be equal to the arc
SD on the horizon; and its reclination be
equal to the arc Dd of the vertical circle D Z:
then it is plain, that if the quadrant of altitude
Z d D, on the globe, cuts the point D in the
horizon, and the reclination is counted upon the
quadrant from D to d; the interfection of the
hour-circle P Rd, with the equinoctial IQE,
will determine Rd, the latitude of the place d,
whofe
A a 2
358
Of Dialing.
Fig. 4.
whoſe horizon is parallel to the given plane Zb at
Z; and R2 will be the difference in longitude
of the planes at d and Z.
Trigonometrically thus: let a great circle
paſs through the three points W, d, E; and in
the triangle WD d, right-angled at D, the fides
IV D and D d are given; and thence the angle
DWd is found, and fo is the hypothenufe W d.
Again, the difference, or the fum, of DW d
and DW R, the elevation of the equinoctial
above the horizon of Z, gives the angle d WR;
and the hypothenuſe of the triangle WR d was
juſt now found; whence the fides Rd and WR
are found, the former being the latitude of the
place d, and the latter the complement of R 2,
the difference of longitude fought.
Thus, if the latitude of the place Z be 52° 10′
north; the declination S D of the plane Z b
(which would be horizontal at d) be 36º, and
the reclination be 15°, or equal to the arc Dd;
the fouth latitude of the place d, that is, the
arc R d, will be 15° 9'; and R 2, the diffe-
rence of the longitude, 36° 2'. From thefe
data, therefore, let the dial (Fig. 4.) be de-
fcribed, as in the former example.
8. Only it is to be obſerved, that in the re-
clining or inclining dials, the horizontal line
will not ftand at right angles to the hour-line of
XII, as in erect dials; but its pofition may be
found as follows.
To the common fubftilar line CK L, on
which the dial for the place d was defcribed,
draw the dial C rpm 12 for the place D, whofe
declination is the fame as that of d (viz. the arc
SD; and HO, perpendicular to C m, the hour-
line of XII on this dial, will be a horizontal line
on the dial CPRM XII. For the declination
of
Of Dialing.
359
of both dials being the fame, the horizontal line
remains parallel to itſelf, while the erect pofition
of one dial is reclined or inclined with reſpect to
the poſition of the other.
Or, the pofition of the dial may be found by
applying it to its plane, fo as to mark the true
hour of the day by the fun, as fhewn by another
dial; or by a clock, regulated by a true meri-
dian line and equation table.
9. There are feveral other things requifite in
the practice of dialing; the chief of which I
fhall give in the form of arithmetical rules,
fimple and eaſy to thofe who have learnt the ele-
ments of trigonometry. For in practical arts of
this kind, arithmetic fhould be uſed as far as
it can go; and ſcales never truſted to, except in
the final conftruction, where they are abfolutely
neceffary in laying down the calculated hour-
diſtances on the plane of the dial. And al-
though the inimitable artiſts of this metropolis
have no occafion for fuch inftructions, yet they
may be of ſome ufe to ftudents, and to private
gentlemen who amufe themſelves this way.
RULE I.
To find the angles which the bour-lines on any dial
make with the fubftile.
To the longarithmic fine of the given latitude,
or of the ſtile's elevation above the plane of the
dial, add the logarithmic tangent of the hour
* diftance from the meridian, or from the
* That is, of 15, 30, 45, 60, 75°, for the hours of I,
JI, HI, IV, V in the afternoon: and XI, X, ix, vin,
VII in the forenoon.
A a 3
fub-
360
Of Dialing."
+fubftile; and the fum minus radius will be the
logarithmic tangent of the angle fought.
For, in Fig. 2. K C is to K M in the ratio
compounded of the ratio of KC to KG (KR)
and of KG to KM; which, making C K the
radius, 10,000000, or 10,0000, or 10, or 1,
are the ratio of 10,000000, or of 10,0000, or
of 10, or of 1, to KG x K M.
O
Thus, in a horizontal dial, for latitude 51
30', to find the angular diftance of XI in the
forenoon, or I. in the afternoon, from XII.
To the logarithmic fine of 51 30° 9.89354‡
Add the logarithmic tang. of 15° o 9.42805
9.32159—
The fum-radius is
the logarithmic tangent of 11° 50', or of the
angle which the hour-line of XI or I makes
with the hour of XII.
And by computing in this manner, with the
fine of the latitude, and the tangents of 30,
45, 60, and 75°, for the hours of II, III, IV,
and V in the afternoon; or of X, IX, VIII,
and VII in the forenoon; you will find their
angular diftances from XII to be 24° 18′, 38° 3′,
53° 35', and 71° 6'; which are all that there
is occafion to compute for.--And theſe dif-
tances may be fet off from XII by a line of
chords; or rather, by taking 1000 from a fcale
of equal parts, and fetting that extent as a ra
dius from C to XII; and then, taking 209 of
In all horizontal dials, and erect north or fouth dials,
the ſubſtile and meridian are the fame: but in all declining
dials, the fubftile line makes an angle with the meridian.
In which cafe, the radius & Kis fuppofed to be divided
into 1000000 equal parts.
5
the
Of Dialing.
361
the fame parts (which, in the tables, are the
natural tangent of 11° 50) and fetting them
from XII to XI and to I, on the line bo, which Fig. 2.
is perpendicular to C XII: and fo for the rest
of the hour-lines, which in the table of natural
tangents, againſt the above diſtances, are 451,
782, 1355, and 2920, of fuch equal parts from
XII, as the radius C XII contains 1000. And
laftly, ſet off 1257 (the natural tangent of 51°
30′) for the angle of the ftile's height, which is
equal to the latitude of the place.
The reaſon why I prefer the uſe of the tabu-
lar numbers, and of a fcale decimally divided,
to that of the line of chords, is becaufe there is
the leaſt chance of miſtake and error in this way;
and likewife, becauſe in fome cafes it gives us
the advantage of a nonius' divifion.
In the univerſal ring-dial, for inftance, the
divifions on the axis are the tangents of the
angles, of the fun's declination placed on either
fide of the center. But instead of laying them
down from a line of tangents, I would make a
ſcale of equal parts, whereof 1000 fhould an-
ſwer exactly to the length of the ſemi-axis, from
the center to the infide of the equinoctial ring;
and then lay down 434 of theſe parts toward
each end from the center, which would limit all
the divifions on the axis, becaufe 434 are the
natural tangent of 23° 29′. And thus by a
nonius affixed to the fliding piece, and taking
the fun's declination from an' Ephemeris, and
the tangent of that declination from the table of
natural tangents, the flider might be always fet
true to within two minutes of a degree.
And this ſcale of 434 equal parts might be
placed right against the 23 degrees of the fun's
declination, on the axis, inſtead of the fun's
place,
A a 4
A
362
Of Dialing.
Fig. 3.
place, which is there of very little ufe. For
then, the flider might be fet in the ufual way,
to the day of the month, for common ufe; but
to the natural tangent of the declination, when
great accuracy is required.
The like may be done wherever a ſcale of
fines or tangents is required on any inftrument.
RULE II.
The latitude of the place, the fun's declination, and
bis hour distance from the meridian, being given;
to find (1.) his altitude; (2.) his azimuth.
1. Let d be the fun's place, d R, his decli-
nation; and in the triangle P Zd, P d the fum,
or the difference, of d R, and the quadrant P R
being given by the fuppofition, as alfo the com-
plement of the latitude P Z, and the angle
d P Z, which meaſures the horary diſtance of d
from the meridian; we fhall (by Cafe 4. of
Keill's Oblique fpheric Trigonometry) find the
baſe Z d, which is the fun's diftance from the
zenith, or the complement of his altitude.
And (2.) As fine Zd: fine Pd:: fine d P Z:
dZ P, or of its fupplement D Z S, the azimuthal
diſtance from the fouth.
Or, the practical rule may be as follows.
Write A for the fine of the fun's altitude, L
and I for the fine and co-fine of the latitude, D
and d for the fine and co-fine of the fun's de-
clination, and H for the fine of the horary dif
tance from VI.
Then the relation of H to A will have three
varieties.
1. When
Of Dialing.
363
1. When the declination is toward the ele.
vated pole, and the hour of the day is between
XII and VI; it is ALD + Hld, and
A-LD.
H=
I d
2. When the hour is after VI, it is ALD
-Hld. and H-LD+A
I d
3. When the declination is toward the de-
preffed pole, we have A Hld-L D, and
H=
A+LD
I d
Which theorems will be found uſeful, and
expeditious enough for folving thoſe problems.
in geography and dialing, which depend on the
relation of the fun's altitude to the hour of the
day.
EXAMPLE. I.
Suppoſe the latitude of the place to be 51
degrees north; the time five hours diftant from
XII, that is, an hour after VI in the morning,
or before VI in the evening; and the fun's de-
clination 20° north. Required the fun's altitude?
Then, to log. L= log. fin. 51° 30′ 1.89354
add log. D= log. fin. 20° o 1.53405
Their fum
1.42759
gives L D logarithm of 0.267664, in the
natural fines.
=
* Here we confider the radius as unity, and not 10,00000,
by which, inflead of the index 9 we have-1, as above:
which is of no farther uſe, than making the work a little
cafier.
And,
364
Of Dialing.
And, to log. H= log. fin.
† 15° 0′
1.41300
‡
38° 0'
I 70° 0'
1.79414
1.97300
1,18015
log. = log. fin.
add { log. d = log. fin.
Their fum
gives Hld
natural fines.
logarithm of o. 151408, in the
And theſe two numbers of (0.267664 and
0.151408) make 0.419072 A; which, in
the table, is the neareſt natural fine of 24° 47',
the fun's altitude fought.
The fame hour-diftance being affumed on the
other fide of VI, then L D-Hld is 0.116256,
the fine of 6° 40′; which is the fun's altitude
at V in the morning, or VII in the evening,
when his north declination is 20°.
But when the declination is 20° fouth (or to-
wards the depreffed pole) the difference Hld-
LD becomes negative, and thereby fhew that,
an hour before VI in the morning, or paſt VI in
the evening, the fun's center is 6° 40 below
the horizon.
EXAMPLE. II.
In the fame latitude and north declination,
from the given altitude to find the hour.
Let the altitude be 48°; and becauſe, in this
cafe, H —4—LD, and A (the natural fine of
I d
A—LD
48°).743145, and LD=.267664, A-LD
+ The distance of one hour from VI.
The co-latitude of the place.
The co-declination of the fun.
will
Of Dialing.
365
will be 0.475481, whofe logarithmic
fine is
from which taking the logarithmic
fine of
+d=
1.6771331
1.7671354
1.9099977
Remains
the logarithmic fine of the hour-diftance fought,
viz. of 54° 22′; which, reduced to time, is
3 hours 37 min. that is, IX h. 37½ min. in
the forenoon, or II h. 224 min. in the after-
noon.
:
·
Put the altitude 189, whofe natural fine
is .3090170; and thence A-LD will be
=.0491953; which divided by 1 + d, gives
.0717179, the fine of 4° 6', in time 16 mi-
nutes nearly, before VI in the morning, or
after VI in the evening, when the fun's altitude
is 18°.
And, if the declination 20° had been towards
the fouth pole, the fun would have been de-
preffed 18° below the horizon at 16 minutes.
after VI in the evening; at which time, the
twilight would end; which happens about the
22d of November, and 19th of January, in the
latitude of 51° north. The fame way may the
end of twilight, or beginning of dawn, be found
for any time of the year.
NOTE 1. If in theorem 2 and 3 (page 363)
A is puto, and the value of H is computed,
we have the hour of fun-rifing and fetting for
any latitude, and time of the year. And if we
put Ho, and compute A, we have the fun's
altitude or depreffion at the hour of VI. And
laftly, if H, A, and D are given, the latitude
may be found by the refolution of a quadratic
equation; for l=VT-I³,
NOTE
366
Of Dialing.
NOTE 2. When A is equal o, H is equal
LD =TLXT D, the tangent of the latitude
l d
multiplied by the tangent of the declination.
As, if it was required, what is the greatest
length of day in latitude 51° 30′´?
To the log. tangent of 51° 30′ 0.0993948
Add the log. tangent of 23° 29′ 1.6379563
Their fum
2
1.7373511 is
the log. fine of the hour-diftance 33° 7′; in
time 2 h. 12 m. The longeſt day therefore
is 12 h. 4 h. 25 m. = 16 h. 25 m.
And
the ſhorteſt day is 12 h. 4 h. 25 m. 7 h.
35 m.
And if the longeſt day is given, the latitude
H
of the place is found; being equal to T L.
TD
Thus, if the longeſt day is 13½ hours = 2 × 6
h. + 45 m. and 45 minutes in time being equal
to 114 degrees.
From the log. fine of 11° 15' 1.2902357
Take the log. tang. of 23° 29' 1.6379562
Remains
1.6522795
the logarithmic tangent of lat. 24° 11.
And the fame way, the latitudes, where the
feveral geographical climates and parallels begin,
may be found; and the latitudes of places, that
are affigned in authors from the length of their
days, may be examined and corrected.
NOTE 3. The fame rule for finding the
longeſt day in a given latitude, diftinguiſhes the
hour-lines that are neceffary to be drawn on any
dial from thofe which would be fuperfluous.
In lat. 52° 10' the longest day is 16 h. 32 m.
and the hour-lines are to be marked from 44 m.
7
after
Of Dialing.
367
after III in the morning, to 16 m. after VIII in
the evening.
In the fame latitude, let the dial of Art. 7.
Fig. 4. be propoſed; and the elevation of its
ftile (or the latitude of the place d, whoſe hori-
zon is parallel to the plane of the dial) being
15° 9'; the longeſt day at d, that is, the longeſt
time that the fun can illuminate the plane of the
dial, will (by the rule H TLXT D) be
twice 6 hours 27 minutes 12 h. 54 m. The
difference of longitude of the planes d and Z
was found in the fame example to be 36° 2′;
in time, 2 hours 24 minutes; and the declina-
tion of the plane was from the fouth towards the
weft. Adding therefore 2 h. 24 min. to 5 h.
33 m. the earlieſt fun-rifing on a horizontal dial
at d, the fum 7 h. 57 m. fhews that the morn-
ing hours, or the parallel dial at Z, ought to
begin at 3 men. before VIII. And to the lateſt
fun-fetting at d, which is 6 h. 27 m. adding the
fame two h. 24 m. the fum 8 h. 51 m. exceeding
6 h. 16 m. the lateft fun-fetting at Z, by 35 m.
ſhews that none of the afternoon hour-lines are
fuperfluous. And the 4 h. 13 m. from III h.
44 m. the fun rifing at Z to VII h: 57 m. the
fun-rifing at d, belong to the other face of the
dial; that is, to a dial declining 36º from north
to eaſt, and inclining 15º.
EXAMPLE III.
From the fame data to find the fun's azimuth.
If H, L, and D are given, then (by Art, 2.
of Rule II.) from H having found the altitude
and its complement Zd; and the arc PD (the
diſtance
368
Of Dialing.
diſtance from the pole) being given; fay, As
the co-fine of the altitude is to the fine of the
diſtance from the pole, fo is the fine of the hour-
diſtance from the meridian to the fine of the
azimuth diſtance from the meridian.
Let the latitude be 51° 30' north, the decli-
nation 15° 9' ſouth, and the time II h. 24 m.
in the afternoon, when the fun begins to illumi-
nate a vertical wall, and it is required to find
the poſition of the wall.
Then, by the foregoing theorems, the com-
plement of the altitude will be 81° 32%, and
Pd the diſtance from the pole being 109° 5'%
and the horary diftance from the meridian, or
the angle d P Z, 36°.
To log. fin. 74° 51'
1.98464
Add log. fin. 36° o'
1.76922
And from the fum
1.75386
Remains
1.75861 log.
Take the log. fin. 81° 32 1.99525
2
fin. 35°, the azimuth diſtance fouth.
When the altitude is given, find from thence
the hour, and proceed as above.
This praxis is of fingular ufe on many oc-
cafions; in finding the declination of vertical
planes more exactly than in the common way,
eſpecially if the tranfit of the fun's center is ob-
ferved by applying a ruler with fights, either
plain or teleſcopical, to the wall or plane, whoſe
declination is required.-In drawing a meridian-
line, and finding the magnetic variation.-In
finding the bearings of places in terreftrial fur-
veys; the tranfits of the fun over any place, or
his horizontal diſtance from it being obferved,
together with the altitude and hour.-And
thence
Of Dialing.
369
thence determining fmall differences of longi.
tude. In obferving the variation at fea, &c.
The learned Mr. Andrew Reid invented an
inftrument feveral years ago, for finding the
latitude at fea from two altitudes of the fun, ob-
ſerved on the fame day, and the interval of the
obfervations, meaſured by a common watch.
And this inftrument, whofe only fault was that
of its being fomewhat expenſive, was made by
Mr. Jackson. Tables have been lately computed
for that purpoſe.
But we may often, from the foregoing rules,
refolve the ſame problem without much trouble;
eſpecially if we ſuppoſe the maſter of the ſhip to
know within 2 or 3 degrees what his latitude is.
Thus.
Aſſume the two neareſt probable limits of the
A+LD, com-
latitude, and by the theorem H-4+LD
ld
pute the hours of obfervation for both ſuppo-
fitions. If one interval of thofe computed
hours coincides with the interval obferved, the
queſtion is folved. If not, the two diſtances of
the intervals computed, from the true interval,
will give a proportional part to be added to, or
fubtracted from, one of the latitudes affumed.
And if more exactneſs is required, the operation
may be repeated with the latitude already
found.
But whichever way the queſtion is folved, a
proper allowance is to be made for the difference
of latitude ariſing from the fhip's courſe in the
time between the two obfervations.
Of
370
Of Dialing.
Fig. 3.
Of the double horizontal dial; and the Babylonian
and Italian dials.
To the gnomonic projection, there is fometimes.
added a stereographic projection of the hour-
circles, and the parallels of the fun's declination,
on the fame horizontal plane; the upright fide
of the gnomon being floped into an edge, ſtand-
ing perpendicularly over the center of the pro-
jection: fo that the dial, being in its due pofition,
the fhadow of that perpendicular edge is a verti-
cal circle paffing through the fun, in the ftereo-
graphic projection.
The months being duly marked on the dial,
the fun's declination, and the length of the day at
any time, are had by infpection (as alfo his alti-
tude, by means of a ſcale of tangents). But its
chief property is, that it may be placed true,
whenever the fun fhines, without the help of any
other inftrument.
Let d be the fun's place in the ftereographic
projection, x dyz the parallel of the fun's decli-
nation, Z d a vertical circle through the fun's
center, Pd the hour-circle; and it is evident,
that the diameter NS of this projection being
placed duly north and fouth, theſe three circles
will pass through the point d. And therefore,
to give the dial its due pofition, we have only
to turn its gnomon toward the fun, on a hori-
zontal plane, until the hour on the common
gnomonic projection coincides with that marked
by the hour-circle P d, which paffes through the
interfection of the ſhadow Zd with the circle of
the fun's prefent declination.
The Babylonian and Italian dials reckon the
hours, not from the meridian, as with us, but
from
Of Dialing.
371
from the fun's rifing and fetting.
Thus, in Plate
Italy, an hour before fun-fet is reckoned the 23d XXIII.
hour; two hours before fun-fet, the 22d hour;
and fo of the reft.
And the fhadow that marks
them on the hour-lines, is that of the point of a
ftile. This occafions a perpetual variation be-
tween their dials and clocks, which they mult
correct from time to time, before it arifes to any
fenfible quantity, by fetting their clocks ſo much
fafter or flower. And in Italy, they begin their
day, and regulate their clocks, not from fun-fet,
but from about mid-twilight, when the Ave Maria
is faid; which corrects the difference that would
otherwiſe be between the clock and the dial.
The improvements which have been made in
all forts of inftruments and machines for meafur
ing time, have rendered fuch dials of little
account. Yet, as the theory of them is inge-
nious, and they are really, in fome refpects, the
beſt contrived of any for vulgar ufe, a general idea
of their deſcription may not be unacceptable.
Let Fig. 5. repreſent an erect direct fouth
wall, on which a Babylonian dial is to be drawn,
fhewing the hours from fun rifing; the latitude
of the place, whofe horizon is parallel to the
wall, being equal to the angle KC R. Make,
as for a common dial K G=KR (which is per-
pendicular to CR) the radius of the equinoctial
E 2, and draw RS perpendicular to C K for
the ſtile of the dial; the fhadow of whofe point
R is to mark the hours, when SR is fet upright
on the plane of the dial.
Then it is evident, that in the contingent line
Æ 2, the spaces K 1, K 2, K 3, &c. being
taken equal to the tangents of the hour diftances
from the meridian, to the radius KG, one, two,
three, &c. hours after fun rifing, on the equi-
noctial day; the fhadow of the point R will be
B b
found,
372
Of Dialing.
*
found, at thefe times, refpectively in the points.
1, 2, 3, &c.
Draw, for the like hours after fun-rifing, when
the fun is in the tropic of Capricorn v, the
like common lines C D, CE, CF, &c. and at
thefe hours the fhadow of the point R will be
found in thofe lines refpectively. Find the fun's
altitudes above the plane of the dial at theſe
hours, and with their co tangents Sd, Se, Sf,
&c. to radius S R, defcribe arcs interfecting the
hour-lines in the points d, e, f, &c. fo fhall the
right lines id, 2 e, 3 f, &c. be the lines of I, II,
III, &c. hours after fun-rifing.
The conftruction is the fame in every other
cafe, due regard being had to the difference of
longitude of the place at which the dial would
be horizontal, and the place for which it is to
ferve. And likewife, taking care to draw no lines
but what are neceffary; which may be done
partly by the rules already given for determin-
ing the time that the fun fhines on any plane;
and partly from this, that on the tropical days,
the hyperbola defcribed by the fhadow of the
point R, limits the extent of all the hour-lines.
The moſt uſeful however, as well as the
fimpleft of fuch dials, is that which is defcribed
on the two fides of a meridian plane.
That the Babylonian and Italic hours are truly
enough marked by right lines, is eafily fhewn.
Mark the three points on a globe, where the
horizon cuts the equinoctial, and the two tropics,
toward the eaſt or weft; and turn the globe on
its axis 15°, or hour; and it is plain, that the
three points which were in a great circle (viz.
the horizon) will be in a great circle ftill; which
will be projected geometrically into a ftraight
line. But thefe three points are univerſally the
2
1
fun's
Of Dialing.
373
fun's places, one hour after fun-fet (or one hour
before fun-rife) on the equinoctial and folftitial
days. The like is true of all other circles of
declination, befides the tropics; and therefore,
the hours on fuch dials are truly marked by
ftraight lines limited by the projections of the
tropics; and which are rightly drawn, as in the
foregoing example.
Note 1. The fame dials may be delineated
without the hour-lines C D, CE, C F, &c. by
fetting off the fun's azimuths on the plane of the
dial, from the center S, on either fide of the fub-
file CSK, and the corresponding co-tangents of
altitude from the fame center S, for I, II, III,
&c. hours before or after the fun is in the horizon
of the place for which the dial is to ferve, on the
equinoctial and folftitial days.
2. One of thefe dials has its name from the
hours being reckoned from fun-rifing, the be.
ginning of the Babylonian day. But we are not
thence to imagine that the equal hours, which it
fhews, were thofe in which the aftronomers of
that country marked their obfervations. Thefe,
we know with certainty, were unequal, like the
Jewish, as being twelfth parts of the natural day:
and an hour of the night was, in like manner, a
twelfth part of the night; longer or fhorter,
according to the feafon of the year. So that an
hour of the day, and an hour of the night, at the
fame place, would always make of 24, or 2
equinoctial hours. In Falestine, among the
Romans, and in ſeveral other countries, 3 of theſe
unequal nocturnal hours were a vigilia or watch:
And the reduction of equal and unequal hours
into one another, is extremely eafy. If, for in-
ftance, it is found, by a foregoing rule, that in a
certain latitude, at a given time of the year, the
Bb 2
t
I
ΤΣ
length
374
Of Dialing.
1 4
/%/ 7
T2
length of a day is 14 equinoctial hours, the
unequal hour is then or of an hour, that
is, 70 minutes; and the nocturnal hour is 50
minutes. The first watch begins at VII (fun-
fet); the ſecond at three times 50 minutes after,
viz. IX h. 30 m. the third always at midnight;
the morning watch at hour paſt II.
I
रं
2
T29 TZ,
If it were required to draw a dial for fhewing
theſe unequal hours, or 12th parts of the day,
we must take as many declinations of the fun as
are thought neceffary, from the equator towards
each tropic and having computed the fun's
altitude and azimuth for th parts, &c.
of each of the diurnal arcs belonging to the de-
clinations affumed: by thefe, the feveral points.
in the circles of declination, where the fhadow
of the file's point falls, are determined: and
curve lines drawn through the points of an
homologous divifion will be the hour-lines re-
quired.
Of the right placing of dials, and having a true
meridian line for the regulating of clocks and
watches.
The plane on which the dial is to reſt, being
duly prepared, and every thing neceffary for
fixing it, you may find the hour tolerably exact
by a large equinoctial ring-dial, and ſet your
watch to it. And then the dial may be fixed by
the watch at your leiſure.
If you would be more exact, take the fun's
altitude by a good quadrant, noting the precife
time of obfervation by a clock or watch. Then,
compute the time for the altitude obſerved, (by
the rule, page 364) and ſet the watch to agree
with that time, according to the fun. A Hadley's
quadrant
How to make a Meridian Line.
375
quadrant is very convenient for this purpoſe;
for, by it you may take the angle between the
fun and his image, reflected from a bafon of
water: the half of which angle, fubtracting the
refraction, is the altitude required. This is
beſt done in fummer, and the nearer the fun is
to the prime vertical (the eaft or weft azimuth)
when the obſervation is made, fo much the
better.
Or, in fummer, take two equal altitudes of the
fun in the fame day; one any time between 7 and
10 o'clock in the morning, the other between 2
and 5 in the afternoon; noting the moments of
theſe two obfervations by a clock or watch: and
if the watch fhews the obfervations to be at
equal diftances from noon, it agrees exactly
with the fun; if not, the watch muſt be cor-
rected by half the difference of the forenoon and
afternoon intervals; and then the dial may be
fet true by the watch.
Thus, for example, fuppofe you have taken
the fun's altitude when it was 20 minutes paft
VIII in the morning by the watch; and found,
by obſerving in the afternoon, that the fun had
the fame altitude 10 minutes before IIII; then
it is plain, that the watch was 5 minutes too
faſt for the fun: for 5 minutes after XII is the
middle time between VIII h. 20 m. in the
morning, and III h. 50 m. in the afternoon; and
therefore, to make the watch agree with the fun,
it muſt be ſet back five minutes.
A good meridian line, for regulating clocks A meri-
or watches, may be had by the following dian re,
method,
Make a round hole, almoſt a quarter of an
inch diameter, in a thin plate of metal; and fix
the plate in the top of a fouth window, in fuch a
Bb 3
manner,
376
How to make a Meridian Line.
manner, that it may recline from the zenith at
an angle equal to the co-latitude of your place, as
nearly as you can guefs; for then, the plate will
face the fun directly at noon on the equinoctial
days. Let the fun fhine freely through the hole
into the room; and hang a plumb-line to the
ceiling of the room; at leaft five or fix feet from
the window, in fuch a place as that the fun's
rays, tranfmitted through the hole, may fall
upon the line when it is noon by the clock;
and having marked the faid place on the ceiling,
take away the line.
Having adjuſted a ſliding bar to a dove-tail
groove, in a piece of wood about 18 inches long,
and fixed a hook into the middle of the bar, nail
the wood to the above-mentioned place on the
cieling, parallel to the fide of the room in which
the window is the groove and bar being to-
wards the floor. Then, hang the plumb-line
upon the hook in the bar, the weight or plum-
met reaching almoft to the floor; and the whole
will be prepared for farther and proper adjuſt-
ment.
This done, find the true folar time by either
of the two laft methods, and thereby regulate
your clock.
clock. Then, at the moment of next noon
by the clock, when the fun fhines, move the
liding bar in the groove until the fhadow of the
plumb-line bifects the image of the fun (made
by his rays tranfmitted through the hole) on the
floor, wall, or on a white ſcreen placed on the
north fide of the line; the plummet or weight
at the end of the line banging freely in a pail of
water placed below it on the floor.-But becauſe
this may not be quite correct for the first time,
on account that the plummet will not fettle im-
mediately, even in water; it may be farther cor-
rected
The Calculation of mean New and Full Moons.
377
rected on the following days, by the above
method, with the fun and clock; and fo brought
to a very great exactneſs.
N.B. The rays tranfmitted through the hole,
will caft but a faint image of the fun, even on a
white fcreen, unless the room be fo darkened
that no fun fhine, may be allowed to enter, but
what comes through the ſmall hole in the plate.
And always, for fome time before the obferva-
tion is made, the plummet ought to be immerſed
in a jar of water, where it may hang freely; by
which means the line will foon become fteady,
which otherwife would be apt to continue
fwinging.
As this meridian line will not only be fuffi-
cient for regulating of clocks and watches to the
true time by equation tables, but alfo for moft
aftronomical pu: poles, I fhall fay nothing of the
magnificent, and expenfive meridian lines at
Bologna and Rome, nor of the better methods by
which aftronomers obferve precifely the tranfits
of the heavenly bodies on the meridian.
LECT. XII.
Shewing how to calculate the mean time of any New
or Full Mocn, or Eclipfe, from the creation of the
world to the year of CHRIST 5800.
N the following tables, the mean lunation is
about a 20th part of a ſecond of time longer
than its meaſure as now printed in the third
edition of my Aftronomy; which makes a dif-
ference of an hour and 30 minutes in 8000
years. But this is not material, when only the
mean times are required.
B b 4
PRE-
378
The Calculation of mean New and Full Moons.
PRECEPT S.
To find the mean time of any New or Full Moon in
any given year and month after the Chriftian
Æra.
1. If the given year be found in the third
column of the Table of the moon's mean motion from
the fun, under the title Years before and after
CHRIST; write out that year, with the mean
motions belonging to it, and thereto join the
given month with its mean motions. But, if
the given year be not in the table, take out the
next leffer one to it that you find, in the fame
column; and thereto add as many compleat years,
as will make up the given year: then, join the
given month, and all the refpective mean mo-
tions.
2. Collect theſe mean motions into one fum of
figns, degrees, minutes, and feconds; remem-
bering, that 60 feconds (") make a minute, 60
minutes () a degree, 30 degrees (°) a fign, and
12 figns (*) a circle. When the figns exceed
12, or 24, or 36 (which are whole circles) reject
them, and fet down only the remainder; which,
together with the odd degrees, minutes, and
feconds already fet down, muſt be reckoned the
whole fum of the collection.
3. Subtract the reſult, or fum of this collec-
tion, rom 12 figns; and write down the remain-
der. Then, look in the table, under Days, for
the next lefs mean motions to this remainder,
and
The Calculation of mean New and Full Moons.
379
and ſubtract them from it, writing down their
remainder.
This done, look in the table under hours
(marked H.) for the next lefs mean motions to
this laſt remainder, and ſubtract them from it,
writing down their remainder.
Then, look in the table under minutes
(marked M.) for the next lefs mean motions to
this remainder, and fubtract them from it, writ-
ing down their remainder.
Laſtly, look in the table under ſeconds (mark-
ed S.) for the next lefs mean motions to this
remainder, either greater or lefs; and againſt it
you have the feconds anfwering thereto.
4. And theſe times collected, will give the
mean time of the required new moon; which will
be right in common years, and alſo in January
and February in leap-years; but always one day
too late in leap-years after February.
EXAMPLE
380
The Calculation of mean New and Full Moons.
EXAMPLE
I
Required the time of new moon in September, 1764?
(a year not inſerted in the table)
Moon from fun.
୨
9 24 56
O 10 14 20
To the year after Christ's
birth
1753
10
Add compleat years
I I
(fum 1764)
And join September
The fum of theſe mean motions is
which, being fub. from a circle,
or
Leaves remaining
Next lefs mean mot. for 26 days,
fub.
And there remains
Next leſs mean mot. for 2 hours,
fub.
And the remainder will be -
Next lefs mean mot. for 2 min.
fub.
Remains the mean mot. of 12 fec.
2 22 21 8
I 12
0 24
1200 о
10 17 59 36
10 16 57 34
I 2 2
I O 57
I 5
I I
4
Thefe times, being collected, would fhew
the mean time of the required new moon in
September 1764, to be on the 26th day, at 2
hours 2 min. 12 fec. paft noon. But, as it is in
a leap-year, and after February, the time is one
day too late. So, the true mean time is Sep-
tember the 25th, at 2 m. 12 fec. paft II in the
afternoon.
N. B.
The Calculation of mean New and Full Moons.
381
N. B. The tables always begin the day at
noon, and reckon thenceforward, to the noon
of the day following.
To find the mean time of full moon in any given year
and month after the Chriftian Era.
Having collected the moon's mean motion
from the fun for the beginning of the given
year and month, and fubtracted their fum from
12 figns (as in the former example) add 6 figns
to the remainder, and then proceed in all re-
ſpects as above.
EXAMPLE II.
Required the mean time of full moon in September
To the year after Chrift's
birth
Add compleat years
1764 ?
Moon from fun.
1753
IO
9 24 56
I I
O 10 14 20
(fum 1764)
And join September
2 22 21 8
The fum of theſe mean motions
is
Which, being fubt. from a cir-
cle, or
Leaves remaining
To which remainder add
And the fum will be
I 12 0 24
12 000
10 17 59 36
бооо
4 17 59 36
Brought
382
The Calculation of mean New and Full Moons.
Moon from fun.
4 17 59 36
4 14 5 54
Brought over
Next leſs mean mot. for II
days, fubt.
And there remains
Next lefs mean mot. for 7
hours, fubt.
And the remainder will be
Next lefs mean mot. for 40
min. fubt.
Remains the mean mot. for 8
fec.
3 53 42
3 33 20
20 22
20 19
3
So, the mean time, according to the tables,
is the 11th of September, at 7 hours 40 minutes
8 feconds paſt noon. One day too late, being
after February in a leap-year.
And thus may the mean time of any new or
full moon be found, in any year after the Chrif
tian Æra.
To find the mean time of new or full moon in any
given year and month before the Chriftian Era.
If the given year before the year of CHRIST
I be found in the third column of the table,
under the title Years before and after CHRIST,
write it out, together with the given month,
and join the mean motions. But, if the given
year be not in the table, take out the next
greater one to it that you find, which being
ftill farther back than the given year, add as
many compleat years to it as will bring the
time forward to the given year; then join the
month, and proceed in all reſpects as above.
EXAM-
The Calculation of mean New and Full Moons.
383
EXAMPLE III.
Required the mean time of new moon in May, the
year before Chrift 585?
The next greater year in the table is 600;
which being 15 years before the given year,
add the mean motions for 15 years to thofe of
600, together with thofe for the beginning of
May.
To the year before Chrift 600
Add compleat years motion 15
And the mean motions for May
The whole fum is
Which, being fubt, from a cir-
cle, or
Leaves remaining
Moon from fun.
5 11 6 16
6 0 55 24
0 22 53 23
• 4 55 3
12 O O O
II 25 4 57
Next lefs mean mot. for 29
days, fubt.
11 23 31 54
And there remains
I 33 3
Next lefs mean mot. for 3 hours
fubt.
I 31 26
fubt.
And the remainder will be
Next lefs mean mot. for 2 min.
Rem. the mean mot. of
I 37
3
I 31
14
fe.
conds
6
།
So,
384
The Calculation of Eclipfes.
Ofecliffes.
So, the mean time by the tables, was the
29th of May, at 3 hours 3 min. 14 fec. paſt
noon. A day later than the truth, on account
of its being in a leap-year. For as the year of
CHRIST I was the firft after a leap-year,
the year 585 before the year I was a leap-year
of course.
If the given year be after the Chriftian ra,
divide its date by 4, and if nothing remains, it
is a leap-year in the old ftile. But if the given
year was before the Chriftian Era (or Year of
CHRIST 1) fubtract one from its date, and
divide the remainder by 4; then, if nothing
remains, it was a leap-year; otherwiſe not.
To find whether the fun is eclipfed at the time of any
given change, or the moon at any given full.
From the Table of the fun's mean motion (or
diſtance) from the moon's afcending node, collect
the mean motions anſwering to the given time;
and if the refult fhews the fun to be within 18
degrees of either of the nodes at the time of
new moon, the fun will be eclipfed at that time.
Or, if the refult fhews the fun to be within 12
degrees of either of the nodes at the time of full
moon, the moon will be eclipfed at that time, in
or near the contrary node; otherwife not.
EXAM
The Calculation of Eclipfes.
385
EXAMPLE IV.
The moon changed on the 26th of September 1764,
at 2 b. 2 m. (neglecting the feconds) after noon
(See Example I.) Qu. Whether the fun was
eclipfed at that time?
To the year after Chriſt's
birth
Add compleat years
Sun from node.
S
I 28
1753
0 19
I I
7 2 3 56
(fum 1764)
September
26 days
And
2 hours
2 minutes
Sun's diſtance from the afcend-
ing node
8 12 22 49
27 0 13
5 12
5
6 9 32 34
Now, as the defcending node is juft oppofite
to the aſcending, (viz. 6 figns diftant from it) and
the tables fhew only how far the fun has gone
from the afcending node, which, by this exam-
ple, appears to be 6 figns 9 degrees 32 minutes
34 feconds, it is plain that he must have then
been eclipſed; as he was then only 9° 32′ 34″
fhort of the defcending node.
EXAM-
386
The Calculation of Eclipfes.
EXAMPLE V.
The moon was full on the 11th of September,
1764, at 7 h. 40 min. paſt noon. (See Exam-
ple II.) Qu. Whether he was eclipsed at
that time?
Sun from node.
To the year after Chrift's
birth
1753
Q
I 28
0 19
Add compleat years
II
7 2 3 56
(fum 1764)
September
11 days
And
7 hours
8 12 22 49
II 25 29
18 II
40 minutes
Sun's diſtance from the afcend-
ing node
I 44
5 24 12 28
Which being fubtracted from 6 figns, leaves
only 5° 47′ 32" remaining; and this being all
the ſpace that the fun was ſhort of the defcend-
ing node, it is plain that the moon must then
have been eclipfed, becauſe fhe was juft as near
the contrary node.
EXAM-
The Calculation of Eclipfes.
387
EXAMPLE VI,
2. Whether the fun was eclipfed in May, the year
before CHRIST 585? (See Example III.)
To the year before Christ 600
Add the mean motion of 15
complete years
May
Sun from node.
S
9 9 23 51
9 19 27 49
4 4 37 57
And
29 days
I
0
7 10
3 hours
7 48
3 minutes (neglecting
the ſeconds)
8
ing node
0.3 44 43
Sun's diſtance from the aſcend-
Which being less than 18 degrees, fhews that
the fun was eclipſed at that time.
This eclipfe was foretold by Thales, and is Thales's
thought to be the eclipfe which put an end to eclipſe.
the war between the Medes and Lydians.
The times of the fun's conjunction with the When
nodes, and confequently the eclipfe months of any eclipses
given year, are eafily found by the Table of the must hap.
fun's mean motion from the moon's afcending node; pon.
and much in the fame way as the mean con-
junctions of the fun and moon are found by the
table of the moon's mean motion from the fun.
For, collect the fun's mean motion from the
node (which is the fame as his diſtance gone
from it) for the beginning of any given year,
and fubtract it from 12 figns; then, from the
remainder,
Сс
388
To find when there must be Eclipfes.
F
✔
remainder, fubtract the next lefs mean motions
belonging to whatever month you find them in
the table; and from their remainder fubtract the
next lefs mean motion for days, and fo on for
··bours and minutes: the refult of all which will
fhew the time of the fun's mean conjunction
with the afcending node of the moon's orbit.
EXAMPLE VII.
Required the time of the fun's conjunction with the
afcending node in the year 1764?
To the year after Christ's
birth
Add compleat years
Sun from node.
"/
1753
I 28 0 19
II
7
2
3 56
Mean dift at beg. of A.D. 1764
Subtract this diftance from a
circle, or
And there remains
Next lefs mean motion for
March, fubtract
And the remainder will be
Next lefs mean motion for 27
days, fubtract
And there remains
Next lefs mean motion for 14
hours, fubtracted
Remains (nearly) the mean mo-
tion of 5 minutes
'
9 0 4 15
12 O O O
2 29 55 45
2 1 16 39
0 28 39 6
0 28 2 32
36 34
36 21
13
Hence
The Period and Return of Eclipfes.
389
Hence it appears, that the fun will paſs by
the moon's afcending node on the 27th of March,
at 14 hours 5 minutes paft noon; viz. on the
28th day, at 5 minutes paft II in the morning,
according to the tables: but this being in a
leap-year, and after February, the time is one
day too late. Confequently, the true time is at
5 min. paft II in the morning on the 27th day;
at which time, the defcending node will be di-
rectly oppofite to the fun.
If 6 figns be added to the remainder arifing
from the first fubtraction, (viz from 12 figns)
and then the work carried on as in the laft
example, the refult will give the mean time of
the fun's conjunction with the defcending node.
Thus, in
EXAMPLE VIII.
To find when the fun will be in conjunction with the
defcending node in the year 1764?
To the year after Chrift's
birth
Add compleat years
Sun from node.
"
1753
I 28
7 2
0.19
3 56
9
9 0 4 15
M. d. fr. afc. n. at beg. of 1764
Subtract this diftance from a cir-
cle, or
And the remainder will be
To which add half a circle, or
12 O O O
2 29 55 45
And the fum will be
Cc 2
8 29 55 45
Brought
390
The Period and Return of Eclipfes.
The li-
mits of
eclipfes:
'Their pe
riod and
reftitu-
tion.
Brought over
Sun fr. node.
8 29 55 45
Next lefs mean mot. for Sept. fubt. 8 12 22 49
And there remains
Next lefs mean mot. for 16 days,
fubt.
And the remainder will be
Next lefs mean mot. for 21 hours,
fubtracted
O 17 32 56
-
o 16 37 4
55 52
54 32
Rem. (nearly) the mean mot. of
31 min.
I 20
So that, according to the tables, the fun will
be in conjunction with the defcending node on the
16th of September, at 21 hours 31 minutes paſt.
one day later than the truth, on account
noon:
of the leap-year.
When the moon changes within 18 days be-
fore or after the fun's conjunction with either of
the nodes, the fun will be eclipfed at that
change and when the moon is full within 12
days before or after the time of the fun's con-
junction with either of the nodes, fhe will be
eclipfed at that fall: otherwife not.
If to the mean time of any eclipfe, either of the
fun or moon, we add 557 Julian years 21 days
18 hours 11 minutes and 51 feconds (in which
there are exactly 6890 niean lunations) we ſhall
have the mean time of another eclipfe. For at
the end of that time, the moon will be either
new or full, according as we add it to the time
of new or full moon; and the fun will be only
45" farther from the fame node, at the end of
6
the
The Period and Return of Eclipfes.
391
the faid time, than he was at the beginning of
it; as appears by the following example*,
The period.
Compleat
Years
days
hours
{
Moon fr. fun.
S O
Sun fr. node.
S O
8
500-3 5 32 47-10 14 45
40-8 26 50 37-23 58.49
17-3 2 21 39-10 28 40 55
21-8 16
18- 9
minutes II
feconds 51-
Mean motions-o
021-
8 35-
5 35-
26—
( о O
21 48 38
46 44
29
2
Ο 0 0 45
And this period is to very near, that in 6000
years it will vary no more from the truth, as to
the reftitution of eclipfes, than 8 minutes of a
degree, which may be reckoned next to nothing.
It is the ſhorteſt in which, after many trials, I
can find fo near a conjunction of the fun, moon,
and the fame node.
* Dr. HALLEY's period of eclipfes contains only 18 years
11 days 7 hours 43 minutes 20 feconds; in which time, ac-
cording to his tables, there are juft 223 mean lunations: but,
as in that time, the fun's mean motion from the node is no
more than 113 29° 31′ 49″, which wants 28′ 11″ of being
as nearly in conjunction with the fame node at the end
of the period as it was at the beginning; this period can-
not be of conftant duration for finding eclipfes, becauſe it
will in time fall quite without their limits. The following
tables make this period 31 feconds shorter, as appears by the
following calculation,
The period.
Moon fr. Sun.
S O
7
Sun fr. node.
S O
17 46 18
Compleat years
18-7 11 59 4-11
days
11-4 14 5 54-
hours
༡= 3 33 20
min.
42-
21 20
11 25 29
18 11
I 49
fec.
44
22-
2
Mean motions
99 0-11 29 31 49
Cc 3
This
392
A Table of Mean Lunations.
h
This table is made by the continual addition
of a mean lunation, viz. 29° 12' 44™ 3′ 6th 21¹▼
vi ovii
14 24
Lun.
Days. H. M. S. I'n
29 12 44 3
1 28 6
2
59
3
88 14 12
4
118
5
6
689 au sWN
Contain
9
2 56 12
In 100000 mean luna
tions, there are 8085 Julian
6 years 12 days 21 hours 36
13 minutes 30 ſeconds
19 2953059 days 3 hours 36
25 minutes 30 feconds.
147 15 40 15 32
177 4 24 18 38
Proof of the Table.
Moon from lun.
206 17 8 21 44
In
S O
10
20
30
40
50
236 5 52 24 51
265 18.36 27 57
295 7 20 31
590 14 41 2 7
885 22
1181 5 22 4 14
1476 12 42 35 18
3
Jul. years.
4000
I 14 22 12
4000
I 14 22 12
80
1 33 11
Days 12
Hours 21
Min. 56
5 23 41 15
10 O 18 28
4 26 17 20
10 40 I
18 17
IOC
200
300
400
500
1000
200
3000
4000
2953
1 25 10 35 Sec.
5906 2 50 21 |1
20
O O
IS
Q O
Having by the former
57 precepts computed the
54 mean time of new moon in
48 January, for any given year,
42 it is eaſy, by this Table, to
36 find the mean time of new
30 moon in January for any
Oumber of years afterward:]
8859 4 15 31 46 M tr fun.
11812 5 40 42 22
14756 7 5 52
29530 14 11 45
59061 4 23 31
88;91 18 35 17
118122 8 47 3
5000 147652 22 58 49
10000 295305 21 57 39
20000 590611 9 55 18
30000 885917 17 52 57
40000 812 3 15 50 36
5000 14-6529 13 48 15
100000 2953059 3 36 39
In 11 lunations there are
In 12 lunations
In 14 lunations
and by means of a ſmall
ctable of lunations for 12 or
013 months, to make a ge-
oneral table for finding the
ofmean time of new or full
moon in any given year and
month whatever.
D. H. M. S. Th.
324 20 4 34 10.
354 8 48 37 16.
383 21 32 40 23.
But then it would be beft to begin the year with March, to
avoid the inconvenience of lofing a day by mistake in leap-
year,
3
Years
A Table of the Moon's mean Motion from the Sun.
393
5014 4308
5114 4408
5214 4508
* day | Before the year of CHRIST I.
900 10 19 46 36
800
700
7
600 5 11
5 11
500
400
300
O
20010
100
8 16 39
1
6
IOI
5
201
3
Years
of the
Years Years before)
of the and after
Moon from fun.
Com-
pleat
Moon from fun.
period.
years.
"
0
Julian World. CHRIST.
O
706
8
714
1714 1008
2714 2008
3714 3008
38 43108
3914 3208
4-143308
41143408
42143508
43143608
4414 3708
45143808
46143908
4714 4008
4814/4108
4914 4208
4008 5 28 1 17
4000
30c0
I
O 10 14 20
5 9 23 24
12
5
2 3 11
11 20 28 57
13
9 11 40 35
2000
6
1 34 30
14
1 21.18
1000
O 12 40
3
15
6 0 55 24
1510 22 44 15
8 26 53 9
17 3 221 39
7 3 59 43
18
6 16
19/1
7 11 59 4
11 21 36 27
3 18 12 49
20
I 25 19 23
40
4 13 25 19
8 26 50 37
2 25 56
60
1 10 15 56
932 29
80
5 23 41 15
3
100 10 7
6 33
23 45 36
200
•
8 14 13 7
052 9
300
6 21 19 40
7 58 43
400
4 28 26 13
301
1 15 5
5 16
500
3 5 32 47
401 11 22 11 49
1000
6 11 5 33
501 9 29 18 23
2000
O 22 II, 6
5714 5008
1001 I
4 51
9
3000
7 3 16 39
6414 5708
6466 5760
65145808
CHRIST I, was the 4007th year
The 4008th year before the year of
is ſuppoſed to have been the year
before the year of his birth
of the creation.
have 365 days, and the
Julian years, 3 of which
4th 366.
; and
Compleat
1701 0 24 37 2
1753 10 9 24 56
6.5 26
1801
Moon from fun.
4000
1 14 22 12
Moon from fuo.
15
Months.
//
O
Jan.
O о О
"
years.
Feb.
I
2
4. 9 37 24
8 19 14 48
Mar.
O 17 54 48
11 29 15 16
April
0 17 10 3
3
0.28 52 13 Mav
0 22 53 23
510
45.20 41 4
0 18 28
June
1 10 48 11
July
1 16 31 32
6
2
2
9 55 52
Aug.
4 26 20
6 19 33 17
Sept.
2 22 21 8
811
11 22 7
Of.
z 28 429
9 3
20 59 32
Nov.
10
8 0 36 55 Dec. 3 21 42 7
This table agrees with the old file until the year
1753; and after that, with the new.
Cc 4
Days.
3 15 59 17
2
'
394
//
H..
M.
A Table of the Moon's mean Motion from the Sun.
Days. I
Moon from fun. Moon from fun.
S
Moon from iun.
"/
// }}/ 11:1
M.
う​。
I
4
2 3 & NO NO
O 12 11 27
0 24 22 53
S.
///
////
"
////
Th.
V
3 1
6 34 20
I
I
18 45 47
5
2 0 57 13
6
2 13 8 40
7
2 25 20 7
8
3 7 31 34
93 19 43 O
2 3 4 100 1.00
I 31 25
2 I 54
5
232 23
0 3 29
I @ 57
3115 44 47
32 16 15 16
3316 45 44
34 17 16 13
3517 46 42
6
3 2 52
36 18 17 10
IO
4
I 54 27
8
4 3 49
II 4 14 5 54
9
4 34 18
3 33 20
37 18 47 39
3819 18
39 19 48 36
$2
4 26 17 20
10
5
4 46
40 20 19
765
13 5
8 28 47
ΙΙ
5
35 15
41
20 49 33
14
5 20 40 14
12
6
5 43
42 21 20 2
15
6 2 51 40
3 6
36 12
43 21 50 31
16
6 15 3 7
4
7 6 41
44 22 20 59
17
6 27 14 34
15 7 37 9
45 22 51 28
18 7 9 26
O
1687 38
46 23 21 56
19 7 21 37 27
20 8 3 48 5
17
18
78
5+
8 38 6
9 8 35
4725 52 25
4824 22 54
21 8 16 0 21
4924 53 22
22
8 28 11 47
23 9 10 23 14
249 22 34 4
25:10 4.46 7
26/10 16 57 34
27110 29 9 I
28 11 11 20 27
29 11 23 31 54
.30 0 5.43 21
0 17 54 47
I 0 6 15
31
32
19 9 39 4
2010 9 32
2110 40
2211 10 30
2311 40 58
24 12 II 27
25 12 41 55
26 13 12 24
27 13 42 53
28 14 13 21
2914 43 50
3015 14 18
I Lunation 29" 12" 44 39 6: 211
5025 23 51
51 25 54 19
52 26 24 48
53 26 55 17
54 27 25 45
55 27 56 14
56 28 26 43
57 28 57 11
58 29 27 40
59 29 58 8
60 30 28 37
14V 24V Ovil
In leap years, after February, a day and its motion muſt
be added to the time for which the moon's mean diſtance
from the fun is given. But, when the mean time of any
new or full moon is required in leap-year after February,
a day muſt be fubtracted from the mean time thereof, as
found by the tables. In common years they give the day
right.
Years
A Table of the Sun's mean Motion from the Moon's
395
Afcending Node,
1008
1714
2714 2008
3714 3008
38143108
3914 3208
40143308
4114 3408
42143508
4314 3608
4414/3708
45743803
4614 3908
4714 4008
Before the year of CHRIST 1.
Years
of the
period.
706 O
7'1
8
of the
Julian World. CHRIST.
Years Years before Sun from node.
and 'áfter
Com-
pleat
Sun from node.
"
years.
S
0
$
4008 7
4000
6 17
6 17
9
II
0 11 4 55
12
3000 9 10 35 11
2000
1000
6 10 5 28
3 9 35 44
900 7 24 32 46
0 9 29 48
800
700 4 24 26 49
6001 9 9 23 51
IS 9 19 27 49
16/10 9 35 31
1710 28 40 55
1811 17 46 18
0 6 51 43
13
7 2 3 56
7 22 11 39
8 11 17 2
149 0 22 25
19
500
1 24 20 53
20
0 26 59 24
400
6
9 17 54
40
1 23 58 49
300 10
24 14 56
60
2 20 58 13
200
3
9 11 58
80
3 17 56 37
100
7 24 8 59
ICO
I
0 9 6 1
200
48144108
101
4 24
3 3
300
1 14 51
19144208
201
99 O
400
4 14 57 2
8 29 54 3
5
5 29 48 7
50144308
301
123 57
6
500 10 14 45 8
51100
51144408
68
401
54
1000
8
8 29 30 17
5214 4508
501 10 23 51
9
2000
5 29 0 33
5714 5008
1001 9 8 36
18
3000
6414 5708
6466 5760
6514
5808
1701 4 23 15 30
1753 1 28
O 19
1801 8 25 44 44
2 28 30 50
4000 11 28 1 6
Months. Sun from node.
SO
CHRIST 1, was the 4007th year
before the year of his birth; and
is fuppoſed to have been the year
The 4008th year before the year off
of the creation.
have 365 days, and the
Julian years, 3 of which
4th 366.
Compleat Sun from node.
Jan.
O о O
Years.
S
Feb.
I 2 11 48
I
0 19
Mar.
5 23
2
1 16 39
2
1 8 1Q 47
April 3
3 28 27
3
I 27 16 10
May 4 4 37 57
4
2 17 23 53
June
6 49 45
5
3
6 29 16
16
~6 78
2 25 34 40
7 4 14 40 3
5 4 47 46||
95 23 53 9
6 12 58 33
10
July 7 59 14
Aug. 7 9 11
8 12 22 49
Oă. 9 13 32 18
Sept.
Nov. 10 15 44 5
Dec. 11 16 53 34
This table agrees with the old ftile until the
year 1753; and after that, with the new.
Days.
396
{
O
4
7
16 13
5
81
8 18 32
9 20 51
7
A Table of the Sun's mean Motion from the Moon's
Days. I
I
23
56 7¤ a
Sun from node
S o
O
O
8
910
I
2
2 19
4 38
3 6 57
4 9 16
5 11 36
6 13 54
Afcending Node.
Sun from node
Sun from node,
H
M.
1
I
23
"
оо
"
M.
Th
1
፡፡
in
V
2 36 31
I 20 31
I 25 43
I 28
1 28 9
1 31 55
5 12
7 48
32
I 23 7
33
0 10 23
34
0 12 59
35
0 15 35
36
36
I
1 33 31
0 18 11
37
I 36 6
IO 0 10 23 10
8
0 20 47
38
I 38 42
II
0 11 25 29
9
023 23
39
I 41 18
12 0 12 27 4810
0 25 58
40
13
0 13 30 7
0 28 33
41
I 43 54
I 46 36
14 0.14 32 20 12
0 31 9
42
I 49 5
15 0 15 34 15130 33 45
43
1 51 41
16
17
18
19
16 7∞ a
ọ 16 37 4 14
0 36 21
44
I 54 17
0 17 39 2315
0 38 57
45
1 56 53
0 18 41
41. 16
0 41 32
46
I 59 29
0 19 44
20
0 20 46
017
191 18
0 44
8
47
2
2 5
0 46 44
48
2
4 41
21
0 21 48 3819
22 0 22 50 57||20
230 23 53 16|21
24 0 24 55 35|22
25 0 25 57 5423
26
0 27 0 1324
O 49 20
49
2
7 17
0 51 56
50
2
9 53
0 54 32
8
51
2 12 29
0 57
9 59 43
52
53
23
215 5
2 17 41
I
2 IY
54
2 20 17
27
0 28
2 32 25
I
4 55
55
2 22 53
0 29 4 51
4 51 26
I
730
28 0 29
29 1 0 7 10 27
301 I 9 29 28
3 I' 2 11 48 29
32 1 3 14
In leap years, after February, add one day and one
day's motion to the time at which the fun's mean dif-
ance from the afcending node is required.
7 31
56
2 25 29
I 10 7
57
2 28 4
1 12 43
58 2 30 40
I 15 9
59 2 33 16
I 17 55
60 2 35 52
}
INDEX.
INDE X.
A
A Air, its properties
Dulteration of metals, to detect
page 159
168
Air-pu mp
179
experiments upon it.
182-200
Alderfea (Mr.) his engine for raiſing water
Angle, of incidence
125
205
of reflection
of refraction
Antaci
240
205
267
250
Apparent motion of the heavens
Archimedes, his propofition for finding the area of a
circle, and the folidity of a cylinder raiſed upon that
circle
for finding the deceit in king Hiero's crown
Armillary ſphere
Atmoſphere, its whole weight upon the earth.
Attraction, of coheſion
139
153
312
170
6
8
of gravitation
of magnetifm
of electricity
Azimuth
B
Balance
Barometer
from their orbits
Bodies moving in orbits have a tendency to
17
18
303
50
172
fly off
30
Bodies move fafter in fmall orbits than in large ones 31
their centrifugal forces
Burning-glaffes, the force of their heat
Camera obfcura
Cartefian vortexes, abfurd
Center of gravity
C
ib.
208
238
35
13
the curves deſcribed by bodies moving round
it
Central forces
Circles of the ſphere
Climate
25
19-41
251
289
Coloured
?
}
INDE X.
Coloured bodies, which are tranfparent, become opake
if put together
Colures
Combined forces, their effect
245
297
20
Common pump
Conftellations
Cranes
Damps
D
117
298
84-89
175
Danger of people's rifing haftily in a coach or boat
when it is likely to be overfet
14
Days lengthened by the refraction of the fun's rays 204
Declination of the fun and ftars
300
Deſcending velocity, gives a power of equal afcent 12
Dialing
316-377
Double projectile force, a balance to a quadruple
power of gravity
E
Earth, its motion demonftrated
-proof of its being globular
27
45
247
178
Earthquakes
Eclipfes
Ecliptic
Electricity
384
249
18
Engine (any mechanical) how to compute its power 48
for working pumps by water
for raifing water by the ftrength of horfes
Equation of time
Equinoctial
Eye, defcribed
125
128
310
249
212
F
Face of the heaven and earth, how reprefented in a
machine
Fermentations
Fire damps
Fluids, their preffure
Fire engine
Forces, central
-combined
Forcing pump
Foundation principle of all mechanics.
Fountain at command
Frigid zones
248
176
177
101
143
19-41
21
122
47
116
274
Gold,
INDE X.
G
155
Gold, how much heavier than its bulk of water
Gold-beaters, to what a prodigious extent they can
hammer out gold
4
Glafs, the fhapes into which it is generally ground for
optical uſes
Globes, their uſe
Gravity
207
247
8
-decreaſes as the fquare of the diftance increaſes 10
Hand-mill
H
81
Harvest moon
Heavens, their apparent motion
Horizon, fenfible and rational
Horfe-mill
pump
306
250
251
82
126
Hour-circles
Hydraulic engines
Hydroftatics
253
112-134
101-110
Hydroſtatic balance
154
-paradox
104
bellows
107
tables
135-146
I
Inactivity of matter
2
Inclined plane
59
Infinite divifibility of matter
Intermitting fprings
5
117
K
Kepler's problem concerning the fquares of the periods
and cubes of the diftances of the planets
Latitude, how found
L
Laws of the planets motions
Lead, how it may be made to fwim in water
34
346
23
109
Lewenhoek, his account of the number and fize of the
fmall animals in the milt of a cod-fiſh
Lenfes, their properties
Light, the amazing fmallneſs of its particles
Lever, its uſe
reflected
refracted
Line of direction
Loadftone, its properties
4
207
49
201
202
203
13
17
Long
INDE X.
Long (Rev. Dr.) his curious experiment with a con-
cave mirrour
his glaſs ſphere
Looking glafs
227
312
240
need be only half the length and half the
breadth of a man, to fhew him his whole image 241
Magnetiẩm
M
17
Man, how he may raise himſelf up by his breath 109
of a middle ſize, how much he is preffed by the
atmoſphere
171
Matter, its properties
1-19
Mechanical powers
49
all combined in one engine
10
Metals, expand by heat
15
their ſpecific gravities
158
Microſcope, fingle
218
double
ib.
folar
Mills for grinding corn
Mirrours, how they reflect the light
Monfoons
Moon, the law of her motion
Motion (all) naturally rectilineal
Multiplying glafs
219
71-80
221
174
3, 24, 25
20
237
124
Newham's engine for extinguiſhing fire
O
Objects, how their images are formed by means of
glaffes
210
why they appear erect, notwithstanding their
images are inverted in the eye
214
why they appear coloured when feen through
fome telescopes
Opera-glafs
232
240
Optic nerve, why that part of the image which falls
upon it is loft
P
Padmore (Mr.) his improvement of cranes
215
89
Pericci
268
Perfun wheel
152
Pile engine.
98
Planetary motions (the laws thereof)
23
Pales
INDEX
Poles of the earth and heavens
Polar circles
Porofity of bodies.
249-252
256
15
Precepts for calculating the mean times of new and
full moons and eclipfes
377
Prifmatic colours
243
make a white when blended together 245
Pulley
57
Pump, common
117
forcing
122
engine to work by water
125
Pyrometer
by horfes
Q
126
16
Quantity of matter in bodies, is in exact proportion
to their weight
10
Quickfilver its weight
R
Rain-bow
Rays of light
Repulfion
Right afcenfion
Running water, its weight
S
171
246
201
Sails of a wind-mill, their proper form and angle.
their incredible velocity
Screw, its power
fhewn by a machine
7
300
141
82
83, 84
68
ib.
Seaſons, how they may be fhewn by a ſmall globe 257
Signs of the zodiac.
255
Silver, how much heavier than its bulk of water
155
Slare (Dr.) his dangerous experiment
200
Solidity of matter
I
Specific gravities of bodies
153
217
Spectacles, why fome eyes require them
Spirituous liquors, to know whether they are genuine
or not
Spouting fluids
Steam (or fire) engine
Steelyard
160
III
143
51
Sun, appears above the horizon when he is really be-
low it
Syphon
204
113
Tantalus's
INDE X.
}
T
Tantalus's cup
Table for mill-wrights
80
of the quantity of water that may be raiſed to
any given height by a common pump
122
of fines for the elevation of water-pipes 132
of the quantity and weight of water in a pipe
of a given length, and diameter of bore 135-146
of the power of the fteam-engine
of ſpecific gravities
of troy weight reduced to avoirdupoife
-of avoirdupoife weight reduced to troy
of the rarity and expanſion of air
151
158, 159
165
166
170
of the miles in a degree of longitude in all
latitudes
271
-of the fun's place and declination 340-345
Tables for calculating new and full moons and eclipfes 384
Teleſcopes, refracting and reflecting
227-232
Temperate zones
274
Thermometer
161
Thunder and lightning
176
Toricellian experiment
170
Torrid zone
274
Trade winds
173
Tropics
256
U V
Up and down, only relative terms
248
Velocity of fpouting fluids
III
Vifion, how caufed
211
Vivifying ſpirit in air
175
W
Water, how conveyed over hills and valleys
113
Water-mills
Wedge
Wheel and axle
Wheel-carriages
Whirling table
Winds, the cauſe of
Wind-mill
71
62
55
90
28
173
82
Wood, though light, may be made to lie at the bottom
of water
110
World, has a tendency of itſelf to come to an end 42, 43
Ꮓ
Zodiac
Zones
299
274
A SUP-
A
SUPPLEMENT
TO THE PRECEDING
LECTURE S.
D d
A
SUPPLEMENT
TO THE PRECEDING
{
LECTURES.
MECHANICS.
The Defcription of a new and fafe Crane, which
has four different Powers, adapted to different
Weights.
T
HE common crane confifts only of a
large wheel and axle; and the rope, by
which goods are drawn up from ſhips,
or let down from the quay to them, winds or
coils round by the axle, as the axle is turned by
men walking in the wheel. But, as theſe
engines have nothing to ftop the weight from
running down, if any of the men happen to trip
or fall in the wheel, the weight defcends, and
turns the wheel rapidly backward, and toffes the
men violently about within it; which has pro-
duced melancholy inftances, not only of limbs
Dd 2
broke,
--
1
MECHANICS.
broke, but even of lives loft, by this ill-judged
conſtruction of cranes. And befides, they have
but one power for all forts of weights; fo that
they generally ſpend as much time in raiſing a
fmall weight as in raifing a great one.
Theſe imperfections and dangers induced me
to think of a method of remedying them. And
for that purpoſe, I contrived a crane with a
proper stop to prevent the danger, and with
different powers ſuited to different weights; fo
that there might be as little lofs of time as pof-
fible and alfo, that when heavy goods are let
down into fhips, the defcent may be regular and
deliberate.
This crane has four different powers: and, I
believe, it might be built in a room eight feet in
width the gib being on the outfide of the
room.
Three trundles, with different numbers of
ſtaves, are applied to the cogs of a horizontal
wheel with an upright axle; and the rope, that
draws up the weight, coils round the axle. The
wheel has 96 cogs, the largeſt trundle 24 ftaves,
the next largeſt has 12, and the fmalleft has 6.
So that the largeſt trundle makes 4 revolutions.
for one revolution of the wheel; the next makes
8, and the fmalleft makes 16. A winch is
occafionally put upon the axis of either of theſe
trundles, for turning it; the trundle being then
uſed that gives a power beft fuited to the weight:
and the handle of the winch deſcribes a circle in
every revolution equal to twice the circumfe-
rence of the axle of the wheel. So that the
7
length
MECHANICS.
5
&
length of the winch doubles the power gained
by each trundle.
As the power gained by any machine, or
engine whatever, is in direct proportion as the
velocity of the power is to the velocity of the
weight; the powers of this crane are eaſily efti-
mated, and they are as follows.
If the winch be put upon the axle of the
largeſt trundle, and turned four times round,
the wheel and axle will be turned once round:
and the circle defcribed by the power that turns
the winch, being, in each revolution, double the
circumference of the axle, when the thickneſs
of the rope is added thereto; the power goes
through eight times as much ſpace as the weight
rifes through and therefore (making fome
allowance for friction) a man will raife eight
times as much weight by the crane as he would
by his natural ſtrength without it: the power,
in this cafe, being as eight to one.
If the winch be put upon the axis of the next
trundle, the power will be as fixteen to one, becauſe
it moves 16 times as faſt as the weight moves.
If the winch be put upon the axis of the
ſmalleſt trundle, and turned round; the power
will be as 32 to one.
But, if the weight ſhould be too great, even
for this power to raiſe, the power may be
doubled by drawing up the weight by one of
the parts of a double rope, going under a pulley
in the moveable block, which is hooked to the
weight below the arm of the gib, and then the
Dd 3
power
6
MECHANICS,
power will be as 64 to one.
That is, a man
could then raife 64 times as much weight by
the crane as he could raiſe by his natural
ftrength without it; becaufe, for every inch
that the weight rifes, the working power will
move through 64 inches.
By hanging a block with two pullies to the
arm of the gib, and having two pullies in the
moveable block that rifes with the weight, the
rope being doubled over and under theſe pullies,
the power of the crane will be as 128 to one.
And fo, by increafing the number of pullies, the
power may be increaſed as much as you pleaſe:
always remembering, that the larger the pullies
are, the lefs is their friction.
Whilft the weight is drawing up, the ratch-
teeth of a wheel flip round below a catch or click
that falls fucceffively into them, and fo hinders
the crane from turning backward, and detains
the weight in any part of its afcent, if the man
who works at the winch fhould accidentally
happen to quit his hold, or chooſe to reft him-
felf before the weight be quite drawn up.
In order to let down the weight, a man pulls
down one end of a lever of the fecond kind,
which lifts the catch of the ratchet-wheel, and
gives the weight liberty to defcend. But, if the
deſcent be too quick, he pulls the lever a little
farther down, fo as to make it rub againſt the
outer edge of a round wheel; by which means
he lets down the weight as flowly as he pleaſes:
and, by pulling a little harder, he may ftop the
weight, if needful, in any part of its deſcent.
If
MECHANICS.
If he accidentally quits hold of the lever, the
catch immediately falls, and ftops both the
weight and the whole machine.
This crane is reprefented in PLATE I
where A is the great wheel, and B its axle on
which the rope C winds. This rope goes over
a pulley D in the end of the arm of the gib E,
and draws up the weight F, as the winch G is
turned round. H is the largest trundle, I the
next, and K is the axis of the fmalleft trundle,
which is fuppofed to be hid from view by the
upright fupporter L. A trundle M is turned
by the great wheel, and on the axis of this
trundle is fixed the ratchet-wheel N, into the
teeth of which the catch O falls. P is the lever,
from which goes a rope 22, over a pulley R
to the catch; one end of the rope being fixed
to the lever, and the other end to the catch.
is an elaſtic bar of wood, one end of which is
fcrewed to the floor: and, from the other end
goes a rope (out of fight in the figure) to the
further end of the lever, beyond the pin or axis
on which it turns in the upright fupporter T.
The uſe of this bar is to keep up the lever from
rubbing againſt the edge of the wheel U, and to
let the catch keep in the teeth of the ratchet-
wheel: But a weight hung to the farther end of
the lever would do full as well as the elaſtic bar
and rope.
S
When the lever is pulled down, it lifts the
catch out of the ratchet-wheel, by means of the
rope 22, and gives the weight F liberty to
defcend: but if the lever P be pulled a little
farther down than what is fufficient to lift the
catch O out of the ratchet-wheel N, it will rub
againſt
Dd 4
3
MECHANICS.
againſt the edge of the wheel U, and thereby
hinder the too quick defcent of the weight; and
will quite ſtop the weight if pulled hard. And
if the man who pulls the lever, ſhould happen
inadvertently to let it go; the elastic bar will
fuddenly pull it up, and the catch will fall down
and ſtop the machine.
WW are two upright rollers above the axis.
or upper gudgeon of the gib E: their ufe is to
let the rope C bend upon them, as the gib is
turned to either fide, in order to bring the weight
over the place where it is intended to be let
down.
N. B. The rollers ought to be fo placed, that
if the rope C be ftretched cloſe by their utmoſt
fides, the half thickneſs of the rope may be
perpendicularly over the center of the upper
gudgeon of the gib. For then, and in no other
pofition of the rollers, the length of the rope
between the pulley in the gib and the axle of
the great wheel will be always the fame, in all
pofitions of the gib: and the gib will remain in
any pofition to which it is turned.
When either of the trundles is not turned by
the winch in working the crane, it may be drawn
off from the wheel, after the pin near the axis of
the trundle is drawn out, and the thick piece of
wood is raiſed a little behind the outward fup-
porter of the axis of the trundle. But this is
not material: for, as the trundle has no friction
on its axis but what is occafioned by its weight,
it will be turned by the wheel without any fen-
fible reſiſtance in working the crane.
A Pyro-
MECHANICS.
A Pyrometer, that makes the Expansion of Metals
by Heat vifible to the five and forty thousandth
Part of an Inch.
The upper furface of this machine is repre-
fented by Fig. 1. of Plate II. Its frame ABCD
is made of mahogany wood, on which is a circle
divided into 360 equal parts; and within that
circle is another, divided into 8 equal parts. If
the ſhort bar E be pushed one inch forward (or
toward the center of the circle) the index e will
be turned 125 times round the circle of 360 parts
or degrees. As 125 times 360 is 45,000, 'tis evi-
dent, that if the bar E be moved only the 45,000dth
part of an inch, the index will move one degree
of the circle. But as in my pyrometer, the circle
is 9 inches in diameter, the motion of the index
is viſible to half a degree, which anſwers to the
ninety thouſandth part of an inch in the motion
or puſhing of the fhort bar E.
One end of a long bar of metal F is laid into
a hollow place in a piece of iron G, which is
fixed to the frame of the machine; and the
other end of this bar is laid againſt the end of
the ſhort bar E, over the fupporting croſs bar
HI: and, as the end ƒ of the long bar is placed
cloſe againſt the end of the ſhort bar, 'tis plain,
that if F expands, it will puſh E forward, and
turn the index e.
The machine ftands on four ſhort pillars,
high enough from a table, to let a fpirit-lamp
be put on the table under the bar F; and when
that is done, the heat of the flame of the lamp
expands the bar, and turns the index.
There
10
MECHANICS.
There are bars of different metals, as filver,
brafs, and iron; all of the fame length as the
bar F, for trying experiments on the different
expanſions of different metals, by equal degrees
of heat applied to them for equal lengths of
time; which may be meaſured by a pendulum,
that ſwings feconds. Thus,
Put on the brass bar F, and fet the index to
the 360th degree: then put the lighted lamp
under the bar, and count the number of ſeconds
in which the index goes round the plate, from
360 to 360 again; and then blow out the lamp,
and take away the bar.
This done, put on an iron bar F where the
braſs one was before, and then fet the index to
the 360th degree again. Light the lamp, and
put it under the iron bar, and let it remain juſt
as many feconds as it did under the brafs one;
and then blow it out, and you will fee how
many degrees the index has moved in the circle:
and by that means you will know in what pro-
portion the expanfion of iron is to the expanfion
of brafs; which I find to be as 210 is to 360, or
as 7 is to 12.By this method, the relative
expanſions of different metals may be found.
The bars ought to be exactly of equal fize;
and to have them fo, they ſhould be drawn, like
wire, through a hole.
When the lamp is blown out, you will ſee the
index turn backward; which fhews that the
metal-contracts as it cools.
The infide of this pyrometer is conſtructed as
follows.
In
MECHANICS.
II
In Fig. 2. Aa is the fhort bar, which moves.
between rollers; and, on the fide a it has 15
teeth in an inch, which take into the leaves of a
pinion B (12 in number) on whofe axis is the
wheel C of 100 teeth, which take into the 10
leaves of the pinion D, on whofe axis is the
wheel E of 100 teeth, which take into the 10
leaves of the pinion F, on the top of whofe axis
is the index above mentioned.
Now, as the wheels C and E have 100 teeth
each, and the pinions D and F have ten leaves
each; 'tis plain, that if the wheel C turn once
round, the pinion F and the index on its axis
will turn 100 times round. But, as the firſt
pinion B has only 12 leaves, and the bar A a
that turns it has 15 teeth in an inch, which is
12 and a fourth part more; one inch motion of
the bar will caufe the laft pinion F to turn an
hundred times round, and a fourth part of an
hundred over and above, which is 25. So that,
if A a be puſhed one inch, F will be turned 125
times round.
A filk thread b is tied to the axis of the pinion
D, and wound ſeveral times round it; and the
other end of the thread is tied to a piece of
flender watch-fpring G which is fixed into the
ftud H. So that, as the bar f expands, and
puſhes the bar A a forward, the thread winds
round the axle, and draws out the ſpring; and
as the bar contracts, the fpring pulls back the
thread, and turns the work the contrary way,
which pushes back the ſhort bar A a againſt the
long bar f. This fpring always keeps the teeth
of the wheels in contact with the leaves of
the
12
MECHANICS.
the pinions, and fo prevents any ſhake in the
teeth.
In Fig. 1. the eight divifions of the inner
circle are ſo many thoufandth parts of an inch
in the expanfion or contraction of the bars;
which is just one thoufandth part of an inch for
each divifion moved over by the index.
A Water-Mill, invented by Dr. Barker, that has
neither Wheel nor Trundle.
This machine is reprefented by Fig. 1. of
Plate III. in which, A is a pipe or channel that
brings water to the upright tube B. The water
runs down the tube, and thence into the hori-
zontal trunk C, and runs out through holes at
d and e near the ends of the trunk on the con-
trary fides thereof.
The upright fpindle D is fixt in the bottom
of the trunk, and fcrewed to it below by the
nut g; and is fixt into the trunk by two croſs
bars at f: ſo that, if the tube B and trunk C
be turned round, the fpindle D will be turned
alſo.
The top of the fpindle goes fquare into the
rynd of the upper mill-ftone H, as in common
mills; and, as the trunk, tube, and ſpindle turn
round, the mill-ftone is turned round there-
by. The lower, or quiefcent mill-ftone is re-
preſented by I; and K is the floor on which it
reſts, and wherein is the hole L for letting the
meal
MECHANICS.
13
meal run through, and fall down into a trough
which may be about M. The hoop or cafe
that goes round the mill-ftone refts on the floor
K, and ſupports the hopper, in the common
way. The lower end of the ſpindle turns in a
hole in the bridge-tree GF, which fupports the
mill-ftone, tube, fpindle, and trunk. This
tree is moveable on a pin at b, and its other end
is fupported by an iron rod N fixt into it, the
top of the rod going through the fixt bracket
O, and having a fcrew-nut o upon it, above the
bracket. By turning this nut forward or back-
ward, the mill-ftone is raiſed or lowered at
pleaſure.
Whilft the tube B is kept full of water from
the pipe A, and the water continues to run out
from the ends of the trunk; the upper mill-
ftone H, together with the trunk, tube, and
ſpindle turns round. But, if the holes in the
trunk were ſtopt, no motion would enfue; even
though the tube and trunk were full of water.
For,
If there were no hole in the trunk, the pref-
fure of the water would be equal againſt all
parts of its fides within. But, when the water
has free egrefs through the holes, its preffure
there is entirely removed: and the preffure
againſt the parts of the fides which are oppofite
to the holes, turns the machine.
[ 14 ]
HYDROSTATICS.
A Machine for demonftrating that, on equal Bot-
toms, the Preffure of Fluids is in Proportion to
their perpendicular Heights, without any regard
to their Quantities.
T
HIS is termed The Hydrostatical Paradox:
and the machine for fhewing it is repre-
fented in Fig. 2. of Plate III. In which is a
box that holds about a pound of water, a b c de
a glaſs-tube fixt in the top of the box, having a
fmall wire within it; one end of the wire being
hooked to the end F of the beam of a balance,
and the other end of the wire fixt to a moveable
bottom, on which the water lies, within the
box; the bottom and wire being of equal
weight with an empty ſcale (out of fight in the
figure) hanging at the other end of the balance.
If this fcale be pulled down, the bottom will be
drawn up within the box, and that motion will
cauſe the water to rife in the glaſs-tube.
Put one pound weight into the ſcale, which
will move the bottom a little, and caufe the
water to appear juft in the lower end of the
tube at a; which fhews that the water preffes
with the force of one pound on the bottom: put
another pound into the fcale, and the water will
rife from a to b in the tube, juſt twice as high
above the bottom as it was when at a; and then,
as its preffure on the bottom fupports two pound
weight in the fcale, 'tis plain that the preffure
on the bottom is then equal to two pounds.
Put a third pound weight in the fcale, and the
3
water
HYDROSTATICS.
15
water will be raiſed from b to'c in the tube,
three times as high above the bottom as when
it began to appear in the tube at a; which
fhews, that the fame quantity of water that
preffed, but with the force of one pound on
the bottom, when raiſed no higher than 4,
preffes with the force of three pounds on the
bottom when raiſed three times as high to in
the tube. Put a fourth pound weight into the
fcale, and it will caufe the water to rife in the
tube from c to d, four times as high as it was
when it was all contained in the box, which
fhews that its preffure then upon the bottom is
four times as great as when it lay all within the
box. Put a fifth pound weight into the ſcale,
and the water will rife in the tube from d to e,
five times as high as it was above the bottom
before it rofe in the tube; which fhews that its
preffure on the bottom is then equal to five
pounds, feeing that it fupports fo much weight
in the fcale. And fo on, if the tube was ftill
longer; for it would ftill require an additional
pound put into the ſcale, to raiſe the water in
the tube to an additional height equal to the
ſpace de; even if the bore of the tube was fo
fmall as only to let the wire move freely within
it, and leave room for any water to get round
the wire.
Hence we infer, that if a long narrow pipe
or tube was fixed in the top of a cafk full of
liquor, and if as much liquor was poured into
the tube as would fill it, even though it were
fo fmall as not to hold an ounce weight of li-
quor; the preffure arifing from the liquor in
the tube would be as great upon the bottom,
and
16
HYDROSTATICS.
and be in as much danger of burſting it out, as
if the caſk was continued up, in its full fize, to
the height of the tube, and filled with liquor.
In order to account for this furpriſing affair,
we muſt conſider that fluids prefs equally in all
manner of directions; and confequently that
they preſs juſt as ftrongly upward as they do
downward. For, if another tube, as f, be pút
into a hole made into the top of the box, and
the box be filled with water; and then, if water
be poured in at the top of the tube a b c d e, it
will rife in the tube f to the fame height as it does
in the other tube: and if you leave off pouring,
when the water is at c, or any other place in the
tube a b c d e, you will find it juſt as high in the
tube f: and if you pour in water to fill the firft
tube, the ſecond will be filled alfo.
Now it is evident that the water riſes in the
tube f, from the downward preffure of the wa-
ter in the tube a b c d e, on the furface of the
water, contiguous to the infide of the top of the
box; and as it will ftand at equal heights in
both tubes, the upward preffure in the tube fis
equal to the downward preffure in the other tube.
But, if the tube ƒ were put in any other part of
the top of the box, the rifing of the water in it
would ſtill be the fame : or, if the top was full
of holes, and a tube put into each of them, the
water would riſe as high in each tube as it was
poured into the tube abcde; and then the
moveable bottom would have the weight of the
water in all the tubes to bear, befides the weight
of all the water in the box.
And
HYDROSTATICS.
17
And ſeeing that the water is preffed upward
into each tube, 'tis evident that, if they be all
taken away, excepting the tube a b c d e, and
the holes in which they stood be ftopt up; each
part, thus ftopt, will be preffed as much up-
ward as was equal to the weight of water in each
tube. So that, the upward preffure againſt the
infide of the top of the box, on every part equal
in breadth to the width of the tube a b c de, will
be preffed upward with a force equal to the
whole weight of water in the tube. And confe-
quently, the whole upward preffure againſt the
top of the box, arifing from the weight or
downward preffure of the water in the tube, will
be equal to the weight of a column of water of
the fame height with that in the tube, and of the
fame thickneſs as the width of the infide of the
box and this upward preffure against the top
will re-act downward against the bottom, and
be as great thereon, as would be equal to the
weight of a column of water as thick as the
moveable bottom is broad, and as high as the
water ſtands in the tube. And thus, the para-
dox is folved.
The moveable bottom has no friction againſt
the infide of the box, nor can any water get
between it and the box. The method of mak-
ing it fo, is as follows:
In Fig. 3. ABCD repreſents a fection of the
box, and a b c d is the lid or top thereof, which
goes on tight, like the lid of a common paper
fnuff-box. E is the moveable bottom, with a
groove around its edge, and it is put into a
bladder fg, which is tied cloſe around it in thé
E e
groove
18
HYDROSTATIC S.
groove by a ſtrong waxed thread; the bladder
coming up like a purfe within the box, and put
over the top of it at a and d all round, and
then the lid preffed on. So that, if water be
poured in through the hole II of the lid, it will
lie upon the bottom E, and be contained in the
ſpace ƒ E g h within the bladder; and the bot-
tom may be raiſed by pulling the wire i, which
is fixed to it at E: and by thus pulling the
wire, the water will be lifted up in the tube k,
and as the bottom does not touch against the
infide of the box, it moves without friction.
Now, ſuppoſe the diameter of this round bot-
tom to be three inches (in which cafe, the area
thereof will be 9 circular inches) and the diame-
ter of the bore of the tube to be a quarter of an
inch; the whole area of the bottom will be 144
times as great as the area of the top of a pin
that would fill the tube like a cork.
And hence it is plain, that if the moveable
bottom be raiſed only the 144th part of an inch,
the water will thereby be raiſed a whole inch in
the tube; and confequently, that if the bottom
be raiſed one inch, it would raiſe the water to
the top of a tube 144 inches, or 12 feet, in
height.
N. B. The box must be open below the
moveable bottom, to let in the air. Other-
wife, the preffure of the atmoſphere would be
fo great upon the moveable bottom, if it be
three inches in diameter, as to require 108
pounds in the ſcale, to balance that preffure,
before the bottom could begin to move.
A Machine,
HYDROSTATIC S.
19
A Machine, to be fubftituted in Place of the com-
mon Hydroftatical Bellows.
In Fig. 1. of PLATE IV. ABCD is an
oblong ſquare box, in one end of which is a
round groove, as at a, from top to bottom, for
receiving the upright glafs tube I, which is bent
to a right angle at the lower end (as at i in Fig. 2.)
and to that part is tied the neck of a large blad-
der K, (Fig. 2.) which lies in the bottom of the
box. Over this bladder is laid the moveable
board L (Fig. 1, and 3.) in which is fixt an up-
right wire M; and leaden weights, N N, to
the amount of 16 pounds, with holes in their
middle, which are put upon the wire, over the
board, and preſs upon it with all their force.
・
The cross bar p is then put on, to ſecure the
tube from falling, and keep it in an upright pofi-
tion: And then the piece EFG is to be put on,
the part Gliding tight into the dove-tail'd
groove H, to keep the weights N N horizontal,
and the wire M upright; there being a round
hole e in the part E F for receiving the wire.
There are four upright pins in the four cor-
ners of the box within, each almoft an inch long,
for the board L to rest upon; to keep it from
preffing the fides of the bladder below it cloſe
together at firft.
•
The whole machine being thus put together,
pour water into the tube at top; and the
water will run down the tube into the bladder
below the board; and after the bladder has been
E e 2
filled
L
20
HYDROSTATIC S.
filled up to the board, continue pouring water
into the tube, and the upward preffure which it
will excite in the bladder, will raife the board
with all the weight upon it, even though the
bore of the tube fhould be fo fmall, that lefs
than an ounce of water would fill it.
This machine acts upon the fame principle,
as the one laſt deſcribed, concerning the Hydro-
Statical paradox. For, the upward preffure
againſt every part of the board (which the
bladder touches) equal in area to the area of the
bore of the tube, will be preffed upward with a
force equal to the weight of the water in the
tube; and the fum of all theſe preffures, againſt
fo many areas of the board, will be fufficient to
raiſe it with all the weights upon it.
In my opinion, nothing can exceed this fim-
ple machine, in making the upward preſſure of
fluids evident to fight.
The Caufe of reciprocating Springs, and of ebbing
and flowing Wells, explained.
In Fig. 1. of PLATE V. Let a b c d be a hill,
within which is a large cavern AA near the
top, filled or fed by rains and melted fnow on
the top a, making their way through chinks
and crannies into the faid cavern, from which
proceeds a ſmall ftream CC within the body of
the hill, and iffues out in a ſpring at G on the
fide of the hill, which will run conftantly whilſt
the cavern is fed with water.
From the ſame cavern A A, let there be a
fmall channel D, to carry water into the cavern
B;
HYDROSTATIC S.
21
B; and from that cavern let there be a bended
channel E e F, larger than D, joining with the
former channel CC, as at ƒ before it comes to the
fide of the hill: and let the joining at ƒ be
below the level of the bottom of both theſe
caverns.
As the water rifes in the cavern B, it will rife
as high in the channel E e F: and when it rifes
to the top of that channel at e, it will run down
the part e F G, and make a ſwell in the ſpring
G, which will continue till all the water is drawn
off from the cavern B, by the natural fyphon
Ee F, (which carries off the water fafter from B,
than the channel D brings water to it) and then
the fwell will ſtop, and only the fmall channel
CC will carry water to the fpring G, till the
cavern B is filled to B again by the rill D; and
then the water being at the top e of the channel
Ee F, that channel will act again as a fyphon,
and carry off all the water from B to the fpring
G, and fo make a fwelling flow of water at G as
before.
To illuftrate this by a machine (Fig. 2.) let A
be a large wooden box, filled with water; and
let a ſmall pipe C C (the upper end of which is
fixed into the bottom of the box) carry water
from the box to G, where it will run off con-
ſtantly, like a ſmall ſpring. Let another ſmall
pipe D carry water from the fame box to the
box or well B, from which let a fyphon Ee F
proceed, and join with the pipe CC at f: the
bore of the fyphon being larger than the bore of
the feeding-pipe D. As the water from this
pipe rifes in the well B, it will alſo rife as high
in the fyphon Ee F; and when the fyphon is
Ee 3
full
22
HYDRAULICS.
full to the top e, the water will run over the
bend e, down the part e F, and go off at the
mouth G; which will make a great ftream at
G: and that ſtream will continue, till the fyphon
has carried off all the water from the well B;
the fyphon carrying off the water faſter from B
than the pipe D brings water to it and then
the fwell at G will ceafe, and only the water
from the ſmall pipe C C will run off at G, till
the pipe D fills the well B again; and then
the fyphon will run, and make a fwell at G as
before.
And thus, we have an artificial repreſentation
of an ebbing and flowing well, and of a reci-
procating fpring, in a very natural and fimple
manner.
HYDRAULICS.
An Account of the Principles by which Mr. Blakey
propofes to raiſe Water from Mines, or from
Rivers, to fupply Towns and Gentlemen's Seats,
by his new invented Fire-Engine, for which be
bas received His MAJESTY's Patent.
A
LTHOUGH I am not at liberty to de-
fcribe the whole of this fimple engine, yet
I have the patentee's leave to defcribe fuch a
one as will fhew the principles by which it acts.
In Fig. 4. of PLATE IV. let A be a large,
ftrong, clofe veffel; immerfed in water up to
the cock b, and having a hole in the bottom,
with a valve a upon it, opening upward within
the veffel. A pipe B C rifes from the bottom
of
HYDRAULICS.
23
of this veffel, and has a cock in it near the
top, which is ſmall there, for playing a very
high jet d. E is the little boiler (not ſo big as
a common tea-kettle) which is connected with
the veſſel A by the fteam-pipe F; and G is a
funnel, through which a little water must be
occafionally poured into the boiler, to yield a
proper quantity of ſteam. And a ſmall quantity
of water will do for that purpoſe, becauſe ſteam
poffeffeth upwards of 14,000 times as much
ſpace or bulk as the water does from which it
proceeds.
The veffel A being immerfed in water up to
the cock b, open that cock, and the water will
ruſh in, through the bottom of the veffel at a,
and fill it as high up as the water ftands on its
outfide; and the water, coming into the veffel,
will drive the air out of it (as high as the water
rifes within it) through the cock b. When the
water has done rufhing into the veffel, fhut the
cock b, and the valve a will fall down, and hin-
der the water from being pushed out that way,
by any force that preffeth on its furface. All
the part of the veffel above b, will be full of
common air, when the water riſes to b.
Shut the cock c, and open the cocks d and e;
then pour as much water into the boiler E
(through the funnel G) as will about half fill
the boiler; and then fhut the cock d, and leave
the cock e open.
This done, make a fire under the boiler E,
and the heat thereof will raiſe a fteam from the
water in the boiler; and the fteam will make
its way thence, through the pipe F, into the
veffel
Ee 4
7
24
HYDRAULICS.
veffel A; and the fteam will comprefs the air
(above b) with a very great force upon the fur-
face of the water in A.
When the top of the veffel A feels very hot
by the ſteam under it, open the cock in the
pipe C; and the air being ſtrongly compreffed
in A, between the fteam and the water therein,
will drive all the water out of the veffel A, up
the pipe B C, from which it will fly up in a jet
to a very great height. In my fountain,
which is made in this manner after Mr. Blakey's,
three tea-cup-fulls of water in the boiler will
afford fteam enough to play a jet 30 feet high.
When all the water is out of the veffel A, and
the compreffed air begins to follow the jet,
open the cocks b and d to let the ſteam out of
the boiler E and veffel A, and fhut the cock e
to prevent any more fteam from getting into A;
and the air will rush into the veffel A through
the cock b, and the water through the valve a;
and fo the veffel will be filled up with water to
the cock b as before. Then fhut the cock b
and the cocks c and d, and open the cock
and then, the next fteam that riſes in the boiler
will make its way into the veffel A again; and
the operation will go on, as above.
;
When all the water in the boiler E is evapo-
rated, and gone off into ſteam, pour a little
more into the boiler, through the funnel G.
In order to make this engine raiſe water to
any gentleman's houfe; if the houſe be on the
bank of a river, the pipe BC may be continued
up
HYDRAULICS.
25
up to the intended height, in the direction H I.
Or, if the houſe be on the fide or top of a hill,
at a diſtance from the river, the pipe, through
which the water is forced up, may be laid along
on the hill, from the river or fpring to the houſe.
The boiler may be fed by a finall pipe K,
from the water that rifes in the main pipe
BCHI; the pipe K being of a very ſmall bore,
fo as to fill the funnel G with water in the time
that the boiler E will require a freſh ſupply.
And then, by turning the cock d, the water will
fall from the funnel into the boiler. The fun-
nel fhould hold as much water as will about half
fill the boiler.
When either of theſe methods of raifing water,
perpendicularly or obliquely, is uſed, there will
be no occafion for having the cock in the
main pipe BCHI: for fuch a cock is requifite
only, when the engine is uſed as a fountain.
A contrivance may be very eafily made, from
a lever to the cocks b, d, and e; fo that, by pul-
ling the lever, the cocks b and d may be opened
when the cock e muſt be fhut; and the cock e
be opened when b and d muſt be ſhut.
The boiler E ſhould be inclofed in a brick wall,
at a little diftance from it, all around; to give li-
berty for the flames of the fire under the boiler to
afcend round about it. By which means, (the
wall not covering the funnel G) the force of the
fteam will be prodigiously increaſed by the heat
round the boiler; and the funnel and water in
it will be heated from the boiler; fo that, the
boiler
26
HYDRAULICS.
boiler will not be chilled by letting cold water
into it; and the rifing of the fteam will be fo
much the quicker.
Mr. Blakey is the only perfon who ever thought
of making uſe of air as an intermediate body
between ſteam and water: by which means, the
fteam is always kept from touching the water,
and confequently from being condenfed by it.
And, on this new principle, he has obtained a
patent: ſo that no one (vary the engine how he
will) can make uſe of air between fteam and
water, without infringing on the patent, and
being fubject to the penalties of the law.
This engine may be built for a trifling ex-
pence, in compariſon of the common fire engine
now in ufe it will feldom need repairs, and
will not confume half ſo much fuel. And as it
has no pumps with piftons, it is clear of all their
friction and the effect is equal to the whole
ftrength or compreffive force of the ſteam:
which the effect of the common fire engine never
is, on account of the great friction of the piſtons
in their pumps.
ARCHIMEDES's Screw-Engine for raifing
Water,
In Fig. 1. of PLATE VI. ABCD is a
wheel, which is turned round, according to the
order of the letters, by the fall of water E F,
which need not be more than three feet. The
axle G of the wheel is elevated fo, as to make
an angle of about 44 degrees with the horizon;
and on the top of that axle is a wheel H, which
turns fuch another wheel I of the fame number
of
HYDRAULICS.
27
of teeth the axle K of this laft wheel being
parallel to the axle G of the two former wheels.
The axle G is cut into a double-threaded
fcrew (as in Fig. 2.) exactly reſembling the fcrew
on the axis of the fly of a common jack, which
muſt be (what is called) à right-handed fcrew,
like the wood-fcrews, if the firft wheel turns in
the direction ABCD; but muſt be a left-handed
fcrew, if the ſtream turns the wheel the contrary
way. And, which-ever way the fcrew on the
axle G be cut, the fcrew on the axle K muſt be
cut the contrary way; becauſe theſe axles turn
in contrary directions.
The ſcrews being thus cut, they muſt be
covered cloſe over with boards, like thofe of a
cylindrical caſk; and then they will be ſpiral
tubes. Or, they may be made of tubes of ftiff
leather, and wrapt round the axles in ſhallow
grooves cut therein; as in Fig. 3.
The lower end of the axle G turns conftantly
in the ftream that turns the wheel, and the lower
ends of the ſpiral tubes are open into the water.
So that, as the wheel and axle are turned round,
the water rifes in the fpiral tubes, and runs out
at L, through the holes M, N, as they come
about below the axle. Theſe holes (of which
there may be any number, as four or fix) are in
a broad cloſe ring on the top of the axle, into
which ring, the water is delivered from the
upper open ends of the fcrew-tubes, and falls
into the open box N.
The lower end of the axle K turns on a
gudgeon, in the water in N; and the fpiral
tubes
28
HYDRAULICS.
tubes in that axle take up the water from N,
and deliver it into fuch another box under the
top of K; on which there may be fuch another
wheel as I, to turn a third axle by fuch a wheel
upon it. And in this manner, water may be
raiſed to any given height, when there is a
ftream fufficient for that purpoſe to act on the
broad float boards of the firft wheel.
A quadruple Pump-Mill for raiſing Water.
This engine is reprefented in PLATE VII.
In which ABCD is a wheel, turned by water
according to the order of the letters. On the
horizontal axis are four ſmall wheels, toothed
almoſt half round: and the parts of their edges
on which there are no teeth are cut down fo, as
to be even with the bottoms of the teeth where
they ſtand.
The teeth of theſe four wheels take alternately
into the teeth of four racks, which hang by two
chains over the pullies 2 and L; and to the
lower ends of theſe racks there are four iron
rods fixed, which go down into the four forcing
pumps, S, R, M and N. And, as the wheels
turn, the racks and pump-rods are alternately
moved up and down.
Thus, fuppofe the wheel G has pulled down
the rack I, and drawn up the rack K by the
chain as the laft tooth of G juſt leaves the
uppermost tooth of I, the firſt tooth of H is
ready to take into the lowermoft tooth of the
rack K and pull it down as far as the teeth go;
and
HYDRAULICS.
29
and then the rack I is pulled upward through
the whole ſpace of its teeth, and the wheel G is
ready to take hold of it, and pull it down again,
and fo draw up the other. In the fame
manner, the wheels E and F work the racks O
and P.
Theſe four wheels are fixed on the axle of the
great wheel in fuch a manner, with respect to
the pofitions of their teeth; that, whilft they
continue turning round, there is never one
inftant of time in which one or other of the
pump-rods is not going down, and forcing the
water. So that, in this engine, there is no
occaſion for having a general air-veffel to all the
pumps, to procure a conftant ftream of water
flowing from the upper end of the main pipe.
The piſtons of theſe pumps are folid plungers,
the fame as defcribed in the fifth Lecture of my
book, to which this is a Supplement. See
PLATE XI. Fig. 4. of that book, with the
defcription of the figure.
From each of theſe pumps, near the loweſt
end, in the water, there goes off a pipe; with a
valve on its farthest end from the pump; and
theſe ends of the pipes all enter one cloſe box,
into which they deliver the water: and into this
box, the lower end of the main conduct pipe is
fixed. So that, as the water is forced or puſhed
into this box, it is alſo puſhed up the main pipe
to the height that it is intended to be raiſed.
1
There is an engine of this fort, deſcribed in
Ramelli's work: but I can truly fay, that I
2
never
-
30
DIALLING.
never ſaw it till ſome time after I had made this
model.
The faid model is not above twice as big as
the figure of it, here defcribed. I turn it by a
winch fixed on the gudgeon of the axle behind
the water wheel; and, when it was newly made,
and the piſtons and valves in good order, I put
tin pipes 15 feet high upon it, when they were
joined together, to fee what it could do. And
I found, that in turning it moderately by the
winch, it would raiſe a hogfhead of water in an
hour, to the height of 15 feet.
IN
DIALLING.
The univerfal Dialling Cylinder.
N Fig. 1. of PLATE VIII. A B C D re-
prefents a cylindrical glafs tube, cloſed at
both ends with braſs plates, and having a wire or
axis E F G fixt in the centers of the brafs plates
at top and bottom. This tube is fixed to a ho-
rizontal board H, and its axis makes an angle
with the board equal to the angle of the earth's
axis with the horizon of any given place, for
which the cylinder is to ferve as a dial. And it
muſt be ſet with its axis parallel to the axis of
the world in that place; the end E pointing to
the elevated pole. Or, it may be made to move
upon a joint; and then it may be elevated for
any particular latitude.
There are 24 ftraight lines, drawn with a dia-
mond, on the outfide of the glafs, equidiftant
from each other, and all of them parallel to the
axis. Thefe are the hour-lines; and the hours
are
DIALLING.
31
are fet to them as in the figure: the XII next B
ſtands for midnight, and the oppoſite XII, next
the board H, ſtands for mid-day or noon.
The axis being elevated to the latitude of the
place, and the foot-board ſet truly level, with the
black line along its middle in the plane of the
meridian, and the end N toward the north; the
axis EFG will ferve as a ftile or gnomon, and
caft a fhadow on the hour of the day, among the
parallel hour lines when the fun fhines on the
machine. For, as the fun's apparent diurnal
motion is equable in the heavens, the fhadow of
the axis will move equably in the tube; and will
always fall upon that hour-line which is oppofite
to the fun, at any given time.
The braſs plate AD, at the top, is parallel to
the equator, and the axis EFG is perpendicular
to it. If right lines be drawn from the center of
this plate, to the upper ends of the equidiftant
parallel lines on the outſide of the tube; theſe
right lines will be the hour-lines on the equi-
noctial dial AD, at 15 degrees diſtance from
each other and the hour-letters may be fet to
them as in the figure. Then, as the fhadow of
the axis within the tube comes on the hour-lines
of the tube, it will cover the like hour-lines on
the equinoctial plate A D.
If a thin horizontal plate ef be put within the
tube, ſo as its edge may touch the tube all
around; and right lines be drawn from the center
of that plate to thofe points of its edge which are
cut by the parallel hour-lines on the tube; theſe
right lines will be the hour-lines of a horizontal
dial, for the latitude to which the tube is ele-
6
vated.
32
DIALLING.
vated. For, as the fhadow of the axis comes
fucceffively to the hour-lines of the tube, and
covers them, it will then cover the like hour-
lines on the horizontal plate ef, to which the
hours may be fet; as in the figure.
If a thin vertical plate g C, be put within the
tube, ſo as to front the meridian or 12 o'clock
line thereof, and the edge of this plate touch
the tube all around; and then, if right lines be
drawn from the center of the plate to thoſe points
of its edge which are cut by the parallel hour-
lines on the tube; thefe right lines will be the
hour-lines of a vertical fouth-dial: and the fhadow
of the axis will cover them at the fame times when
it covers thoſe of the tube.
If a thin plate be put within the tube fo, as to
decline, or incline, or recline, by any given num-
ber of degrees; and right lines be drawn from
its center to the hour-lines of the tube; theſe right
lines will be the hour-lines of a declining, inclin-
ing, or reclining dial, anfwering to the like
number of degrees, for the latitude to which the
tube is elevated.
And thus, by this fimple machine, all the
principles of dialling are made very plain, and
evident to the fight. And the axis of the tubet
(which is parallel to the axis of the world in
every latitude to which it is elevated) is the ftile
or gnomon for all the different kinds of fun-dials.
And lastly, if the axis of the tube be drawn
out, with the plates AD, ef, and g C upon it;
and ſet it up in fun-fhine, in the fame pofition as
they were in the tube; you will have an equi-
noctial
DIALLING.
32
noctial dial A D, a horizontal dial e f, and a ver-
tical fouth dial g C; on all which, the time of
the day will be fhewn by the fhadow of the axis
or gnomon E F G.
Let us now ſuppoſe that, instead of a glaſs
tube, A B C D is a cylinder of wood; on which
the 24 parallel hour-lines are drawn all around,
at equal diſtances from each other; and that,
from the points at top, where thefe lines end,
right lines are drawn toward the center, on the
flat ſurface AD: Theſe right lines will be the
hour-lines on an equinoctial dial, for the latitude
of the place to which the cylinder is elevated
above the horizontal foot or pedeſtal H; and
they are equidiftant from each other, as in Fig. 2.
which is a full view of the flat furface or top
AD of the cylinder, feen obliquely in Fig. 1.
And the axis of the cylinder (which is a ftraight
wire EFG all down its middle) is the ftile or
gnomon; which is perpendicular to the plane
of the equinoctial dial, as the earth's axis is per-
pendicular to the plane of the equator.
To make a horizontal dial, by the cylinder,
for any latitude to which its axis is elevated;
draw out the axis and cut the cylinder quite
through, as at e bfg, parallel to the horizontal
board H, and take off the top part e A Dƒ e; and
the fection e bf g e will be of an elliptical form,
as in Fig. 3. Then, from the points of this
fection (on the remaining part e B Cf) where
the parallel lines on the outfide of the cylinder
meet it, draw right lines to the center of the
fection; and they will be the true hour-lines for
a horizontal dial, as a b c da in Fig. 3. which may
be included in a circle drawn on that fection.
1
Ff
Then
34
DIALLING.
Then put the wire into its place again, and it
will be a ftile for cafting a fhadow on the time
of the day, on that dial. So, E (Fig. 3.) is the
ftile of the horizontal dial, parallel to the axis
of the cylinder..
To make a vertical fouth dial by the cylin-
der, draw out the axis, and cut the cylinder
perpendicularly to the horizontal board Ĥ, as at
giCkg, beginning at the hour line (B ge A) of
XII. and making the fection at right angles to
the line S HN on the horizontal board. Then,
take off the upper part g A D C, and the face of
the ſection thereon will be elliptical, as fhewn in
Fig. 4. From the points in the edge of this fec-
tion, where the parallel hour-lines on the round
furface of the cylinder meet it, draw right lines
to the center of the fection; and they will be
the true hour-lines on a vertical direct fouth dial,
for the latitude to which the cylinder was ele-
vated and will appear as in Fig. 4. on which
the vertical dial may be made of a circular fhape,
or of a ſquare fhape as reprefented in the figure.
And F will be its ftile parallel to the axis of the
cylinder.
And thus, by cutting the cylinder any way,
fo as its fection may either incline, or decline, or
recline, by any given number of degrees; and
from thofe points in the edge of the fection
where the outfide parallel hour-lines meet it,
draw right lines to the center of the fection; and
they will be the true hour-lines, for the like de-
clining, reclining, or inclining dial: And the
axis of the cylinder will always be the gnomon
or ftile of the dial. For, which-ever way the
plane of the dial lies, its ftile (or the edge thereof
that
DIALLIN G.
35
that cafts the ſhadow on the hours of the day)
muſt be parallel to the earth's axis, and point
toward the elevated pole of the heavens.
To delineate a Sun-Dial on Paper; which, when
pafted round a Cylinder of Wood, ſhall ſhew the
Time of the Day, the Sun's Place in the Ecliptic,
and his Altitude, at any Time of Obfervation.
See PLATE IX.
Draw the right line a A B, parallel to the top
of the paper; and, with any convenient opening
of the compaffes, fet one foot in the end of the
line at a, as a center, and with the other foot de-
ſcribe the quadrantal arc A E, and divide it into
90 equal parts or degrees. Draw the right line.
AC, at right angles to a A B, and touching the
quadrant AE at the point A. Then, from the
center a, draw right lines through as many de-
grees of the quadrant, as are equal to the fun's
altitude at noon, on the longest day of the year,
at the place for which the dial is to ferve;
which altitude, at London, is 62 degrees: and
continue theſe right lines till they meet the tan-
gent line AC; and, from thefe points of meet-
ing, draw ftraight lines across the paper, paral-
lel to the firſt right line AB, and they will be
the parallels of the fun's altitude, in whole de-
grees, from fun-riſe till fun-fet, on all the days
of the year. Theſe parallels of altitude muft
be drawn out to the right line B D, which muſt
be parallel to A C, and as far from it as is equal
to the intended circumference of the cylinder on
which the paper is to be pafted, when the dial is
drawn upon it.
Divide the ſpace between the right lines AC
and BD (at top and bottom) into twelve equal
Ff 2
parts
36
DIALLING.
i
parts, for the twelve figns of the ecliptic; and,
from mark to mark of thefe divifions at top
and bottom, draw right lines parallel to AC and
BD; and place the characters of the 12 figns in
theſe twelve ſpaces, at the bottom, as in the figure:
beginning with or Capricorn, and ending
with or Pifces. The ſpaces including the
figns fhould be divided by parallel lines into
halves; and if the breadth will admit of it
without confufion, into quarters alſo.
At the top of the dial, make a fcale of the
months and days of the year, fo as the days may
ſtand over the fun's place for each of them in
the figns of the ecliptic. The fun's place, for
every day of the year, may be found by any
common ephemeris: and here it will be beft to
make uſe of an ephemeries for the fecond year
after leap year; as the neareſt mean for the fun's
place on the days of the leap-year, and on thoſe
of the firft, fecond, and third year after.
Compute the fun's altitude for every hour (in
the latitude of your place) when he is in the
beginning, middle, and end of each fign of the
ecliptic; his altitude at the end of each fign
being the fame as at the beginning of the next.
And, in the upright parallel lines, at the begin-
ning and middle of each fign, make marks for
theſe computed altitudes among the norizontal
parallels of altitude, reckoning them downward,
according to the order of the numeral figures fet
to them at the right hand, anfwering to the like
divifions of the quadrant at the left. And,
through theſe marks, draw the curve hour-lines,
and fet the hours to them, as in the figure,
reckoning the forenoon hours downward, and
the
DIALLING.
37
the afternoon hours upward.-The fun's alti-
tude ſhould alſo be computed for the half hours;
and the quarter lines may be drawn, very nearly
in their proper places, by eſtimation and accu-
racy of the eye. Then, cut off the paper at the
left hand, on which the quadrant was drawn,
cloſe by the right line AC, and all the paper at
the right hand clofe by the right line BD; and
cut it alſo cloſe by the top and bottom horizon-
tal lines; and it will be fit for paſting round the
cylinder.
This cylinder is reprefented in miniature by
Fig. 1. PLATE X. It fhould be hollow, to
hold the ſtile D E when it is not uſed. The
crooked end of the ftile is put into a hole in the
top AD of the cylinder; and the top goes on
tightiſh, but must be made to turn round on the
cylinder, like the lid of a paper fnuff-box. The
ftile muft ftand ſtraight out, perpendicular to the
fide of the cylinder, juft over the right line AB
in PLATE IX, where the parallels of the fun's
altitude begin: and the length of the ftile, or
diſtance of its point e from the cylinder, muſt be
equal to the radius a A of the quadrant A E in
PLATE IX.
The method of using this dial is as follows.
Flace the horizontal foot B C of the cylinder
on a level table where the fun fhines, and turn the
top AD till the ftile ftands juft over the day of
the then preſent month. Then turn the cylin-
der about on the table, till the fhadow of the
ftile falls upon it, parallel to thefe upright lines
which divide the figns; that is, till the fhadow
be parallel to a fuppofed axis in the middle of
the cylinder: and then, the point, or lowest end
Ff3
of
38
DIALLING.
1
of the fhadow, will fall upon the time of the
day, as it is before or after noon, among the
curve hour-lines; and will fhew the fun's alti-
tude at that time, amongſt the croſs parallels of his
altitude, which go round the cylinder: and, at
the fame time, it will fhew in what fign of the
ecliptic the fun then is, and you may very nearly
gueſs at the degree of the fign, by eftimation of
the eye.
The ninth plate, on which this dial is drawn,
may be cut out of the book, and paſted round a
cylinder whofe length is 6 inches and 6 tenths
of an inch below the moveable top; and its
diameter 2 inches and 24 hundred parts of an
inch-Or, I fuppofe the copper-plate prints
of it may be had at Mr. Cadell's, bookfeller in
the Strand, London. But it will only do for
London, and other places of the fame latitude.
When a level table cannot be had, the dial may
be hung by the ring Fat the top. And when it
is not uſed, the wire that ferves for a ftile may
be drawn out, and put up within the cylinder;
and the machine carried in the pocket.
To make three Sun-dials upon three different Planes,
So as they may all shew the Time of the Day by
one Gnomon.
On the flat board AB C, deſcribe a horizontal
dial, according to any of the rules laid down in
the Lecture on Dialling; and to it fix its gnomon
FG H, the edge of the fhadow from the fide
FG being that which fhews the time of the day,
To this horizontal or flat board, join the
upright board EDC, touching the edge G H of
the gnomon. Then, making the top of the
gnomon
DIALLING.
39
gnomon at G the center of the vertical fouth
dial, deſcribe á ſouth dial on the board E D C.
Laftly, on a circular plate IK deſcribe an
equinoctial dial, all the hours of which dial are
equidiftant from each other; and making a flit
cd in that dial, from its edge to its center, in the
XII o'clock line; put the faid dial perpendicu-
larly on the gnomon FG, as far as the flit will
admit of; and the triple dial will be finiſhed; the
fame gnomon ferving all the three, and fhewing
the fame time of the day on each of them.
An univerfal Dial on a plain Cross:
This dial is repreſented by Fig. 1 of PLATE
XI, and is moveable on a joint C, for elevating
it to any given latitude, on the quadrant C o 90,
as it ftands upon the horizontal board. The
arms of the croſs ftand at right angles to the
middle part; and the top of it from a to n, is
of equal length with either of the arms ne or m k.
Having fet the middle line tu to the latitude
of your place, on the quadrant, the board A
level, and the point N northward by the needle;
the plane of the crofs will be parallel to the
plane of the equator; and the machine will be
rectified.
Then, from III o'clock in the morning, till
VI, the upper edge k l of the arm i o will caft a
fhadow on the time of the day on the fide of the
arm cm: from VI till IX the lower edge i of ·
the arm io will caft a fhadow on the hours on
the fide o q. From IX in the morning to XII at
noon, the edge ab of the top part en will caft a
ſhadow on the hours on the arm neƒ: from XII
to III in the afternoon, the edge cd of the top
F f 4
part
40
DIALLING.
:
part will caft a fhadow on the hours on the
arm k l m from III to VI in the evening, the
edge gb will caft a fhadow on the hours on
the part ps; and from VI till IX, the fhadow
of the edge ef will fhew the time on the top
part a n.
The breadth of each part, a b, ef, &c. muſt
be fo great as never to let the fhadow fall quite
without the part or arm on which the hours are
marked, when the fun is at his greateſt declina-
tion from the equator.
To determine the breadth of the fides of the
arms which contain the hours, fo as to be in juft
proportion to their length; make an angle
ABC (Fig. 2.) of 23 degrees, which is equal
to the fun's greatest declination: and fuppofe
the length of each arm, from the fide of the long
middle part, and alfo the length of the top part
above the arms, to be equal to B d.
2
2
Then, as the edges of the fhadow from each of
the arms, will be parallelto Be, making an angle
of 23 degrees with the fide B d of the arm when
the fun's declination is 23 degrees; 'tis plain,
that if the length of the arm be B d, the leaſt
breadth that it can have, to keep the edge Be of
the fhadow Beg d from going off the ſide of the
arm de before it comes to the end e d thereof,
muſt be equal to ed or d B. But in order to
keep the ſhadow within the quarter divifions of
the hours, when it comes near the end of the
arm, the breadth thereof ſhould be ſtill greater,
fo as to be almoſt doubled, on account of the
diſtance between the tips of the arms,
Τα
DIALLING.
41
To place the hours right on the arms, take the
following method.
Lay down the croſs a cbd (Fig. 3.) on a ſheet
of paper; and with a black lead pencil, held
clofe to it, draw its fhape and fize on the paper.
Then taking the length ae in your compaffes,
and ſetting one foot in the corner a, with the
other foot defcribe the quadrantal arc e f.
Divide this arc into fix equal parts, and through
the divifion marks draw right lines a g, a h, &c.
continuing three of them to the arm ce, which
are all that can fall upon it; and they will meet
the arm in theſe points through which the lines
that divide the hours from each other (as in
Fig. 1.) are to be drawn right acroſs it.
Divide each arm, for the three hours it con-
tains, in the ſame manner; and fet the hours to
their proper places (on the fides of the arms) as
they are marked in Fig. 3. Each of the hour
ſpaces ſhould be divided into four equal parts,
for the half hours and quarters, in the quadrant
ef and right lines fhould be drawn through
theſe divifion marks in the quadrant, to the
arms of the crofs in order to determine the
places thereon where the fub-divifions of the
hours muſt be marked.
This is a very fimple kind of univerfal dial;
it is very eaſily made, and will have a pretty un-
common appearance in a garden. I have feen
a dial of this fort, but never faw one of the kind
that follows.
An
42
DIALLING.
An univerfal Dial, fhewing the Hours of the Day by
a terreftrial Globe, and by the Shadows of feveral
Gnomons, at the fame Time: together with all
the Places of the Earth which are then enlightened
by the Sun; and those to which the Sun is then
rifing, or on the Meridian, or Setting.
This dial (See PLATE XII.) is made of a
thick fquare piece of wood, or hollow metal.
The fides are cut into femicircular hollows, in
which the hours are placed; the flile of each
hollow coming out from the bottom thereof,
as far as the ends of the hollows project. The
corners are cut out into angles, in the infides of
which, the hours are alfo marked; and the edge
of the end of each fide of the angle ſerves as a
ftile for cafting a fhadow on the hours marked
on the other fide.
In the middle of the uppermoft fide or plane,
there is an equinoctial dial; in the center where-
of, an upright wire is fixt, for cafting a ſhadow
on the hours of that dial, and fupporting a fmall
terreſtrial globe on its top.
The whole dial ftands on a pillar, in the
middle of a round horizontal board, in which
there is a compafs and magnetic needle, for
placing the meridian ftile toward the fouth. The
pillar has a joint with a quadrant upon it, divided
into 90 degrees (fuppofed to be hid from fight
under the dial in the figure) for fetting it to the
latitude of any given place; the fame way as
already deſcribed in the dial on the croſs.
The equator of the globe is divided into 24
equal parts, and the hours are laid down upon it
at
DIALLIN G.
43
at theſe parts. The time of the day may be
known by theſe hours, when the fun fhines upon
the globe,
To rectify and uſe this dial, fet it on a level
table, or fole of a window, where the fun fhines,
placing the meridian ftile due fouth, by means
of the needle; which will be, when the needle
points as far from the north fleur-de-lis toward
the weft, as it declines weftward, at your place.
Then bend the pillar in the joint, till the black
line on the pillar comes to the latitude of your
place in the quadrant.
The machine being thus rectified, the plane of
its dial-part will be parallel to the equator, the
wire or axis that fupports the globe will be pa-
rallel to the earth's axis, and the north pole of
the globe will point toward the north pole of
the heavens.
The fame hour will then be fhewn in feveral
of the hollows, by the ends of the fhadows of
their respective ftiles: The axis of the globe.
will caſt a ſhadow on the fame hour of the day,
in the equinoctial dial, in the center of which it
is placed, from the 20th of March to the 23d of
September; and, if the meridian of your place
on the globe be fet even with the meridian ftile,
all the parts of the globe that the fun hines.
upon, will anſwer to thofe places of the real
earth which are then enlightened by the fun.
The places where the fhade is juft coming upon
the globe, anſwer to all thofe places of the earth
to which the fun is then fetting; as the places
where it is going off, and the light coming on,
anſwer to all the places of the earth where the fun
is then rifing. And lastly, if the hour of VI
be
44
DIALLING.
be marked on the equator in the meridian of
your place (as it is marked on the meridian of
London in the figure) the divifion of the light
and fhade on the globe will fhew the time of the
day.
The northern ftile of the dial (oppoſite to the
fouthern or meridian one) is hid from fight in
the figure, by the axis of the globe. The hours
in the hollow to which that ftile belongs, are
alſo ſuppoſed to be hid by the oblique view of
the figure: but they are the fame as the hours
in the front-hollow. Thoſe alſo in the right
and left hand femicircular hollows are moſtly
hid from fight; and fo alfo are all thoſe on the
fides next the eye of the four acute angles.
The construction of this dial is as follows.
See PLATE XIII.
On a thick ſquare piece of wood, or metal,
draw the lines a c and b d, as far from each other
as you intend for the thickneſs of the ftile a b c d
and in the fame manner, draw the like thick-
neſs of the other three ftiles, e f g h i k l m, and
nopq, all ſtanding outright as from the cen-
ter.
With any convenient opening of the com-
paffes, as a A (fo as to leave proper ftrength
of ſtuff when KI is equal to a 4) fet one foot
in a, as a center, and with the other foot de-
fcribe the quadrantal arc A c. Then without
altering the compaffes, fet one foot in b as a
center, and with the other foot deſcribe the qua-
drant d B.. All the other quadrants in the figure
muſt be deſcribed in the fame manner, and with
the
DIALLING.
the fame opening of the compaſſes, on their
centers e, f; i, k; and n, o: and each quadrant
divided into 6 equal parts, for fo many hours,
as in the figure; each of which parts muſt be
fub-divided into 4, for the half hours and quar-
ters.
At equal diſtances from each corner, draw the
right lines Ip, and Kp, L q, and Mq, Nr, and
Or, Ps, and 2s; to form the four angular
hollows IpK, Lq M, Nr O, and Ps Q; mak-
ing the diſtances between the tips of thefe hol-
lows, as IK, LM, NO, and P 2, each equal
to the radius of the quadrants; and leaving fuffi-
cient room within the angular points, p, q, r,
and s, for the equinoctial circle in the middle.
To divide the infides of theſe angles properly
for the hour-ſpaces thereon, take the following
method.
Set one foot of the compaffes in the point I,
as a center; and open the other to K, and with
that opening, deſcribe the arc Kt: then, with-
out altering the compaffes, fet one foot in K,
and with the other foot defcribe the arc It.
Divide each of theſe arcs, from I and K to their
interfection at t, into four equal parts; and
from their centers I and K, through the points
of divifion, draw the right lines I 3, 14, 15,
16, 17; and K 2, K1, K 12, K11, and they
will meet the fides Kp and Ip of the angle Ip K
where the hours thereon must be placed. And
theſe hour-ſpaces in the arcs muſt be fubdivided
into four equal parts, for the half hours and
quarters.Do the like for the other three
angles, and draw the dotted lines, and fet the
hours
45
46
DIALL IN G.
hours in the infides where thofe lines meet them,
as in the figure and the like hour-lines will be
parallel to each other in all the quadrants and in
all the angles.
Mark points for all theſe hours, on the upper
fide and cut out all the angular hollows, and
the quadrantal ones quite through the places
where their four gnomons muft ftand; and lay
down the hours on their infides, as in PLATE
XII, and then fet in their four gnomons, which
muſt be as broad as the dial is thick; and this
breadth and thickneſs muſt be large enough to
keep the fhadows of the gnomons from ever
falling quite out at the fides of the hollows, even
when the fun's declination is at the greateft.
Laftly, draw the equinoctial dial in the mid-
dle, all the hours of which are equidiſtant from
each other; and the dial will be finiſhed.
As the fun goes round, the broad end of
the fhadow of the ftile a b c d will fhew the hours
in the quadrant Ac, from fun rife till VI in the
morning; the fhadow from the end M will fhew
the hours on the fide Lq from V to IX in the
morning; the fhadow of the ſtile e f g h in the
quadrant Dg (in the long days) will fhew the
hours from fun-rife till VI in the morning; and
the fhadow of the end N will fhew the morning
hours, on the fide Or, from III to VII.
Juft as the fhadow of the northern ſtile a b c d
goes off the quadrant Ac, the fhadow of the
ſouthern ftile i k l m begins to fall within the
quadrant Fl, at VI in the morning; and fhews
the time, in that quadrant, from VI till XII at
4
noon;
DIALLING.
47
4
noon; and from noon till VI in the evening in
the quadrant m E. And the fhadow of the end
O fhews the time from XI in the forenoon till
III in the afternoon, on the fide r N; as the
fhadow of the end P fhews the time from IX in
the morning till I o'clock in the afternoon, on
the fide 2s.
At noon, when the fhadow of the eaſtern ſtile
ef g h goes off the quadrant b C (in which it
fhewed the time from VI in the morning till
noon, as it did in the quadrant g D from fun-
rife till VI in the morning) the fhadow of the
weſtern ftile n o p q begins to enter the quadrant
Hp; and fhews the hours thereon from XII at
noon till VI in the evening; and after that till
fun-fet, in the quadrant qG: and the end 2
caſts a ſhadow on the fide P s from V in the
evening till IX at night, if the fun be not fet
before that time.
The fhadow of the end I fhews the time on
the fide Kp from III till VII in the afternoon;
and the fhadow of the ftile a b c d fhews the time
from VI in the evening till the fun fets.
The fhadow of the upright central wire, that
fupports the globe at top, fhews the time of the
day, in the middle or equinoctial dial, all the
fummer half year, when the fun is on the north
fide of the equator.
In this fupplement to my book of Lectures,
all the machines that I have added to my appa-
ratus, fince that book was printed, are de-
fcribed, excepting two; one of which is a model
of
48
DIALLING.
1
of a mill for fawing timber, and the other is a
model of the great engine at London-bridge,
for raifing water. And my reafons for leaving
them out are as follow.
First, I found it impoffible to make ſuch a
drawing of the faw-mill as could be understood;
becauſe, in whatever view it be taken, a great
many parts of it hid others from fight. And,
in order to fhew it in my Lectures, I am obliged
to turn it into all manner of poſitions.
Secondly, Becauſe any perſon who looks on
Fig. 1. of PLATE XII in the book, and reads
the account of it in the fifth Lecture therein,
will be able to form a very good idea of the
London-bridge engine, which has only two
wheels and two trundles more than there are in
Mr. Alderfea's engine, from which the faid figure
was taken.
Y
FINI S.
UNIV. OF WICHIGAN,
FEB 11 1915
PLATE I.
D
F
E
R
iL
B
!
G
T.Ferguson delin.
J. Mynde fc.
PLATE II.
A
•
G
F
H
D
I
Ferguson delin.
1
f
I
GI
Fig.1.
B
300
310,320
330 340
260
270
250
28/0
230 240
290
19.
མ བ་་རྒ་
༡༤ ་ན་ ལས་ འ
110
140
130
140 150
100 170
Z
180
4
200
210
220
f
A
D
་ཚོགས་
D
ཁ ་ པ ས ཀ- ཟཏམ་
CO
350
100
2
40 50 60 70 80 90 100
E
D
B
H
G
OF Fig.2.
J.Mynde fc.
LATE III.
Fig.1.
A
().
N
G
Ferguson delin.
!
K
B
C
F
IM
1
!
OF
1
រ
Fig. 2.
Fig.3.
..
A
A
D
B
C
JMynde fo
PLATE IV.
I
Fig. 2.
d
G
E
I. Ferguson delin,
F
Fig.4.
K
H
K
i
С
L
I
M Fig.3.
Ι
F
Fig.1.
C
E oc
H
A
B
B
D
C
K. Mynde fc.
a
V
Fig. 1.
nyuson delin.
B
E
DA
Fig. 2.
E
F
G
G
JMynde fc.
PLATE VI.
ww
|
Fig.3.
Ferguson delin.
B
筏
​E
#.
D
བབ་
華​華
​net
Fig.1.
G
WHAT
64 + R S T U
4.
作
​N
1053
4,
*» * ས
༧
-...
N
中
​itt, ubens
K
Slov
い
​#6
H
422*) MODEL
抜きま
​4.0
شیدگر
Fig./2.
J. Hynde fc.
B
C
D
wwwn
P
A
E
G
Ferguson delin.
R
M
K
N
JHunde fo
1
E VIII.
5
VI
8
III
a
E
C
IX IX
Fig. 3.
10
4
3
2
11
12
[.
A TA
VI VII
VII VII
Fig. 2.
E
IATA A
B
uton delin.
N XI
II II II
W
་་་
瓜
​LIA JA TA
i
6
E
VII VIII Z
XII
Ꭰ
Fig.4.
JA
IA
7
Fig.1.
X
I A
H
N
III
N I
I HIX IX
12
2
J. Mynde je.
PLATE IX.
January february March April May
June July
70 20 31 10 20 30 10 20 31 10 20 30
11010 16 to 10, 31
.3/ 10
20
10
THE
VII
T
ME
DIE
Auguft September October
10 20 31 10 10
30
10.20
57
X
IL
T
Latitude 51° 30′
XI
C
19'
It
I.Ferguson delin.
November December
10 20 30
2
TO
XU
m'
m
0 B
10
20
30
40
50!
Suns Altitude
60
D
J.Mynde fo
PLATE X.
A
F
D
E
B
!
A
I. Ferguson delin.
20
Fig.1.
30
40
50
60
C
I
B
Y VI
VI VI VI
e
ITA
ΠΛ
K
E
HA
Fig. 2.
IA
D
C
L.Munde fo
PLATE XI.
a
Fig.3.
5
6
2
12
10
7
8
I. Ferguson delin.
3
d
III
Fig.1.
IA
鄉​区
​с
VIL
IX
d
d
B
h
il
Ad
9
h
A
2.
Fig. 2
J.Mynde fc.
LA
!
1
XI
I. Ferguson delin.
AMERICA
HIA
OFF
AFRIC
W m II I IIK X
專車​班
​མ་༦ ྃ་སྒྲ་
NW
M/S
A
OF VIL VIC
NIE
E
}
6
J. Mynde fo.
مجھو۔
PLATE XIII.
SH
12
K
{
1.2
་
**
a
TO
N
P
F
I. Ferguson delin.
10
B
ང
་་་་
་་་་
Ί
про
moshow me to acto que push to the PES + PROTON IS WHAT WE WERE THE
12
1
2
་་་
M
1
3
1
E
J. Mynde Jo.