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.LECTUR’ES
ON

SELECT SUBJECTS.

Publijbed éy the fame Author.

I.._/ A s T R o N o M Y explained upon Sir ISAAC

NEWTON’S Principles, and made eafy to thofe
who have not fiudied Mat/yemm‘icr. T 0 which is added,
the Method of finding the Dif’cances of the Planets from
the Sun, by the TRANSIT of VENUS over the Sun’s Difc
in the Year 1761. Thefe Dif’tances deduced from that-
Tranfit; and an account of Mr. HORROX’S Obfervations
of the Tranfit in the Year 1639: Illufirated with 18 Cop-
per-plates. A New Edition, ' Oé‘tavo. '

2. An Eafy Introdufiion to ASTRONOMY, for young
GENTLEMEN and LADIES: Defcribing the Figure,
Motions, and Dimenfions of the Earth; the different Sea- '
fons; Gravity and Light; the Solar Syfiem ; the Tranfit
of Venus, and its Ufe in Aflronomy; the Moon’s Motion
and Phafes; the Eclipfes of the Sun, and Moon ; the Caufe
_ of the Ebbing and flowing of the Sea, &c. Second -
Edition, Price 55. i -

3. TABLES and TR ACTS relative‘to feveral Arts and

Sciences. Price 5 s..

4. An Introdué‘tion to ELECTRICITY, in fix Sections. ‘
1. Of Eleflricity in general. 2. A' Defcrip‘tiOn of the
Elearical Machine. 3. ADefcription of the Apparatus
(belonging to the Machine) for makinghEleétrical Expe-
riments. 4,. How to know ’if the Machine be in ‘good
. order for performing the Experiments, and to PM it in
order if it be not. 5. How to make the Elefitrical Expe-
riments, and to preferve Buildings from Damage by
Lightning. 6. Medical Eleétricity. Price 5s. ,

L E-C'T U R E 3
SELECT SNUBJ‘ECTS

MECHANICS 'IHPNEUMATICS,
HYDROSTATICS, AND OPTICS.

. W I T H
The USE of the GLOBES,
The ART of DIALINXG,

AND

The Calculation of the Mean} Times of NEW
and FULL MOONs and ECLIPSES.

With )t—he SUPPLEMENT.

By JAMES FERGUSON, F. R. s.

7 THE FOURTH EDITION.

 

Pbilofapbiamater omnium bonarum artium (fl. C1 C EEO. I. Tnfc.

L O N D O N:

Printed for W. STRAHAN, J. and F. RIVING'TON,
J. HINTON, L. HAWES and Co. W. JOHNSTON,
S. CROWDER, T. LONGMAN, B. LAW, G. ROBINSON,

‘ andT. CADELL. MDCCLXXII.

: 7‘1' .
' . '1; ‘ 5.4 ,
a”? )fi‘MévW ‘ vf'jflrvii‘afwww.

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.

$94.,“ 7... %

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' To HIS .'

g oYAL HIGHNESS

iP‘rjince E D W A R D, *

SIR,

  A S heaven has mfpired'

your ROYAL HIGHNESS

with fuch love of 1ngenious

V and ufeFUI arts, that you not .,

only {tudy their theory, but '_

have often condefcended t0”;:

i honour the profeHors of me- 3' . ‘

Chanical and experimental - * ‘ .1
philofophy with your pre-‘s T

- -~ ~ A 3 fence

. 1, r ,i . u~2

DEDICATION.

. fence and particular favour ,
I am thereby encouraged to
lay myfelf and the following »
, work at your ROYAL HIGH- ',
NEss’s feet; and at the fame
time beg leave to exprelis that
(veneration with which I am,

SIR

YOur RoYAL HIGHNEss’S

MQH: obliged
\ And Inofl; obedient,

‘ 1, Humble Servant, a

JAMES. FERGUSON.

 

 

 

 

    
   

 

 
 
 

  
 
 

 
 

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THE
P R E F A C. E.

E V E R fince the days of the LORD CHgN-
CELLOR BACON, natural phzlgfophy " ‘
hath been more and more cultivated inEng-
land. THAT great genius fiijl fet out with
taking a general furvey of all the natural
' » fciences, dividing them into- unmet branches,
which he enumerated with great mam/s.
He enquired fcrupulaujly into the degree of ‘
‘ ~knowledge already attained to in each, and
drew up a [i]? of what flill remained to be
> difl:0<vered : thic wax the fcope qf‘hicfirfl an-” ’
dcrta/eiiig. Afterward he carried his views a,
A 4 . , . much

,viii ' .

y

PREFACE

, -. " mucbfartlaer, ana’fiewea’ 222‘ meg/27y of an .,
' I. . experzmental 107227412972], a t72222g never Ibejore ,,
( 2732:2322 of A: be was a profefli‘a' e22e222y to ‘- - - -‘
-' .‘ fflemy,’ 72e eon/It'a’erea’ploilofpb], no 027927222}:

t72a22 a2 tl'2a2‘ part of knowledge 222/222:7.) 2022—"

; '. '2226I22tes to 22222 222e22 better and happier: 726,-" I .
2" I. , :' flew: to 7222222‘ 27 to '5‘72e 7e22ow7ee7ge of t72222gs‘: -‘ ' ~'

szalI, recommendmg above all 27.26- fad-7’ of

22atu2'e, and/Bewmg 2‘72at no progreff can be: .

‘ 22726146 t72'e22e222, but 72] e077ee'7222g fafie, 222227 .'
7. comparmg expeezmenty, of 20722272 72e pomtfi
Ionzit a great 22222225e2 proper to ée 222222722, j ;

B227 nothtlflaaa‘mg 2‘72e t222e1222t72 to j2‘2e222‘e'”;I .

I ' ~ ."I I was tbmj exae‘tly marked out, t72e ola’ notzom ‘1

oftbefe/ooolsfoflronglypofl'fledpeople J‘ 222222272

7';"“'.‘-I}at"-t}2 ‘2‘; tzme, a: not to be 27222222222222 I72] any I

V ' :22e‘w «91222220222, bow ratzonallyfoe‘uer advanced,

3725-2222227 2722 zllzyzmm Mr. BOYLE, the fig;

.' I 222720 22222222 LORD BACON’ .2 plan, began

‘ --._-"2a 2222 experiments in prafiie’e Wit-721“ a2;

4/ 27222231 22722227 to 7222 great 2a7e222‘2. Next, ,I .
~272.2: ROYAL SOCIETY bemg 4222mm 7/36?

I I. , A. 5tru‘e pbzlo/oplay 223272 to 5e 2‘72e rezg22222g 722/722. ;‘
V - I. qf 2‘72e Iage, and contmszo Ito 2‘7225 272222.. ' '

. g .2 :
. III I

"",f , _.:' . . I l . ‘ ~' \‘, r 2 ~ ‘7
. I . . ‘ .. II -. I . . Y . I. . . ,

H -. .- I._. '..'- I I I I v II _,I -. 'f” I I

, ~. - ‘ . , . ~ --I w
. I 7 i ' '. v -. .
l r . ‘ ‘l ‘ - ‘ ~‘
2 .2 , I

u ..

 

PREFACE.

’ T122 22222220r2‘221 SIR ISAAC NEWTON 222-3
fzfled 222222 222 1.22: early years, 212222‘ 22 was '
high 2.22222 to 1222222 2252222 Conjefiuree 22222! .
"bypm‘befle from 222222222221 1012214022132, 02221 to -'
br222g 2‘12222‘ fizence under 2222 entirefibjefiwq‘
20 experzmem‘s 222222 geometry He frequenZ‘Iy
7. 22211222 22‘ the experimental philofophy, f2: 22: 2
, 2‘0 exprefe/gnficantly 2122 (12272222222 between
- 22‘ 2222212122 2222222ber1fiffle2223 222102210 12222122r2 e22
merely 0222‘ #2132 202222222 0f 2222222222222 brains:
2102 0222 f22bf flmg no longer 21.22222 flue/1222222 0f

1 22022212}! 12%: , 2‘132 02102r 222222rf222122zg. whilfi ‘ I
2122 2222222222 0f 212mg: remain fine/ganged. '

T122 222221200’ 0f 2222221222232 22222! 105222252“ 21.22 .
f0222221222‘2022 of prc:, by public 202223/25 of '_ 7
experiments, 20222 jiM undertaken 222 21322
2222302222, I believe, by Dr. JOHN KEILL,
222221 fflce: imprawed 222221 enlarged by Mr. I
‘ HAUKSBEE, Dr. DESAGULIERS,. Mr._
WHISTON, Mr. COTEs, I W.HITE-'
"SIDE, Dr BRADLEY, our [WA/2: Regiue and

I’Safvilz‘a‘n profflbr 0f Aflr0220222y, 222221 the
Reverend Dr. BLISS b2: fiecflhm

7 N02? . I

PREFACE.“
Nor has the :flzme heen neglec‘ted by Dr.
JAMES, and Di? DAVID GREGORY, Szr
ROBERT STEWART, and (yea him Mr.
MACLAURIN. Dr. ELSHAM 2n Ire—
land, Meflt‘ear: s’GRAVESANDE, ‘. and
MUSCHENBROEK, and the Ahhe NOLLET

en France, have a fo aegazrea’ jnfl applaa/h
'therehy. '

 

‘1'" hefgiahftanee of my own attempt in thie
_'way of z'n/trumental z'n/trne‘tion, the fillowing.
floeete (meta/eve of the tyz’ronomz’eal part):
wiiljhmv : the fatigfizé’t’z‘on they have gene-.
rally given, read a: letturee to dz'ferent
audiences, Writ: me fitme hope that they may
‘ he favourably recervea’ 2n the fame form hy
the pahhe. '

[ought to ohferve, that though the five Icy}
Iee‘taree cannot he properly/find to concern exa '
perimentalphtlofophy, I cotfla’ered, however,
that they were not offo a’ferent a eta/fr, hat
that they might, without much zmpropriety,
he fahjome‘a’ to the preoedzng one:.

2 y . ‘My

PREFACE.

Mfy apparatus (part of whic/a ii a’efcri’bed
’ bare, and the rat m a * former work] 23;
V rat/oer fimplg than magnificent , wlazcla z:
awing to a particular point I had 212 mew
atfitfl fitting oat, namely, ta avoid all fit...
petfflaity, and to render awry ' thing as
plaza and mtallz'gzbla a: I thought the/ub-
jet? wquld aa’mzt g".

* Aflronomy explained upon SIR ISAAC NEW-
TON’ 5 principles, and made eafy to thofe who have
not f’cuaied mathematics.

DL

DIRECTIONS to the BOOKBINDER

The plates muft open to the left-hand, fronting.
the right-hand pages in the following order.

 

BLATEI ’- , . i. . ~fronting page 5 .
H ________ 19
{1V ,. +~ - —- . '-'---» '27
'31 I___ __ , _, 7—... 49 j
, "'"' ,""" 'M ' 59
- VI’IJ ‘ -.- -.. ..... = " 69 *
"IX ~--, -- -— _ —— 97
. X "" _ *‘ "" '-.--- IQ!
gr ....... _ -——........ 11.15 -
' "---- ‘ --—- , ----- 125.
XIV ~— ~ -- ‘—-— 1.79
XV '1 ,-—-—. ~— “ ha...- 201
£37,111 - T“   -—-.-—.’ 209'
_ , --. e -- . ---- . 215
XVIII -¥- —-- -- f22'rf
C i ““ ..._... 5‘ 323,»
.XXII _ -—_ —.... -....- 33;
XXIII . -— —.. ....‘. ' 353 ,

 

THE, N
no N T EN Ts.“

‘LECTUREIU

, . _’ OF matter 1an its properties.- . page I_ I.
L E C T U R E IL

0f centralferees. I

LECTUREJE
Of Ike meebmzieal powers. "

LECTUREIV

,9

Of mills, mmes, wheel-carriages, and the" my”; _ .- , s

for drivingpi/es. . ' . , , 71 .‘ "
,,LECTUREV _, ._:_
Of bydrq/faties, and bydmulie maebmes, in general. I i‘ ‘ U L
" 101 7 "

. LECTUREVI_,_IL

'C OIWTTE Nfr§.
LECTUREVH ¥
qumw: ,1 25:

LECTURE VIII. andIX

flu: dqfcrz'ption' and u/Ie of the gloées and armillary'
" jjibgrg. ' ,. 247, 296

1 ' ”L Ef- CT U R E ‘ X. and XL
gl’be péz'ncz'plefand art of digging. . . 3 1‘ 6, 3 5‘0
‘ LECTUREXE _
‘ Sbewing bow to talmlate‘tbe mean time of any new“

or full moon, or eclipfl’ from tbs? creaiz'm of tbe’
world to fine year of C/arg'fl 5800. 377

XLEC:

 

 

 

LECTURES!
‘ O N ' ..

SELECT SU E‘JEC‘T S

LECT.L'

'Of Matter and its .'Properties.

S the defign of the firf’t part of i this
courfe is to eXplain an d demonfir’ate thofe
laWs by which the material uzninerfe is governed, .
regulated, and continued; and by which the
various appearances in nature at e accounted for;
it is requifite to begin with explaining the pro- ’
perties of matter. ‘ a r .
By the word matter is here meant every thing Matter,
- that has length, breadth, and thicknefs, andWhat. ' ‘
refills the touch. _ ’
The inherent properties of m atter are folidity, Its pro-’ ‘
inactivity, mObility, and divifilaility. Fewes-
The folidz'ty of matter arifesv from its having
length, breadth, thicknefs; an 'd hence it is that
all bodies are comprehended i inder fome fhape
or other, and that each particular body hinders
all others from occupying the f tme part of fpace
which it pofieffeth. Thus, iffa piece of wood
or metal be ‘fqueezed ever f0 hard between two
plates, they cannot be brou; ght into contact.
And even water or air has this pmperty -, for if
a fmall quantity of it be fixed'l ‘yretween any Other
7 bodies,

Solidity.

a , I J ' , Of tbs- Propem'e: qui Matter;

-, ,bodicsgth'ey cannot- be brought to touch one

,. . antithetig .» ' vi
,Inaé‘tiyity,g I'A-‘fe'C'Ond property of matter is imfiz'vity, or
‘, , gatflivezzéfi; bijhi‘ch it always endeavours to.
continue. in the flats»? thatjt is, in, whether of ref’c
l or motion.“ And ,th.$refdre,‘tif one bedy..c0ntains
‘ Mice-or thrice as mtjch matter as another body
does; it; will have twice or thrice as much inac-
‘tivity g" that-gig,- it will; require twice or thrice as
a .' tnUch'force to give it an equal degree of motion, ‘ ,
1 ~ Or to flop it after it hath been putuintolfucha

1

'tnotion...a ”,2; _ .. , r _ , ,
. '. That matter can hevet put itfelf into‘motion is?

‘ 1 allowed by all men; , F of they fee that af’fione,‘
-; lying On” the plane'lifurface'of theieatth,‘ never
' , removes 'itfelf from that place; nor does any one
-. imagine it ever can. But mol’t people are
'Lap't to believe that allmatter has a propenfity to
:‘fall froma {late of motion into a {late of’ refi;

 

betcauiethey fee thatgif af’tone' or a cannonball i i ,

' _ be putinto ever it) violent a motion, itfoon (tops;
not Confidering thatfllthis fiop‘page is caufed,
. I. By the gravny or weight of the body, [which ‘
finks‘, it to the gifound in fpite ofthe impulfeq ’
- ' and, 2-. By the retfif’tance of the airthroUgh which ' ,
'it moves, and by which its VelOCity is retarded, ‘
, every. moment tillit falls. ‘. l t ‘ ‘
' ' ‘ A bowl moves: buthfhort way: upon a bowl-g
. ingegi‘een ;~ beCaffife the roughnefs and un'eVenL
, n‘efs of'the gratify furface {ooh creatcsfricliml’
- 7 ew‘fl'enough to flop it". '. But; if the greeti'werepera“
fienétl‘yilCV61‘5’3nd Coveted with‘polifhed glafs, and a
”the bowl were‘pei‘feé’cly hard,_round, and finooth,‘ ;
_ _\ -’ r , , itjx’v’otild,'go 'a'gfreat way farther; as it Would , :
~ f havenothingubutythe aif‘tosrefil’tit; if'thetlnth’ej ‘
i ' " ,_.:-ait were taken ,zivvaygwthe .b'owl=Would 7 goon I_
1 if Without any] friéliidn,‘ and confcquently withbut .-. ’

V .

Of Me Properties of Matter. 3
any diminution of the velocity it had at fettind‘ ’
out: and therefore, if the green were extended
quite around the earth, the bowl would go 011,
round and round the earth, for ever.

If the bowl were carried feveral milesabove
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-
fifiing medium in the Way, the bowl would not
fall to the earth at all, but would continue
to circulate tonndit, keeping always in-the fame
tract, and returning to the fame point from
which it was projected, with the fame velocity
as at firf’r. In this manner the moon goes round
the earth, although lhe be as unac‘tive and dead
as any {tone upon it“ 1

The third preperty of matter is moéilz'ly , for Mobihty’.
we find that all matter is capable of being moved, '
if a fufiicient degree of force be applied to over-
come its inaétivity or refif’tance.

The fourth pmperty of matter is divi/éilz'iy,D ivifibL
of which there can be no end. For, fince matter 5' 1f)"
can never be annihilated by cutting or breaking
we can never imagine it to be cut into fuch finall
particles, but that if one of them be laid on a
table, the uppermof’t fide of it will be further
from the table than the undermol’t fide. More-
over, it would be abfurd to fay that the grated
mountain 6n earth has more halves quaiters, or ~
tenth parts, than the fmallei’t particle of matter
has. ~ .1

We have many furprifing inflances of the
fmallnefs to which matter can be divided by art ,3 ‘
of which the two following are very remarkable 1

 

B}. 4 1115

Of we. Properties cf Matter;

Ii. If a pound of filverabe melted with a fingle
Vgrain'of gold, the gold will be equally diffufed
through the whole filver; f0 that taking one
grain from any part of the mafs (in which there
can be no more than the 5760th part of a grain
of gold) 1‘ and difi'olving it in aqua fortir, the
gold will fall to the bottom. i
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:'confe’quently 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 'microfcope that magnifies the,
diameter of an object only 10 times, it will
nagnify the area 100 times; and then the tooth
part of a 500000th part of a grain (that is, the
50 millionth part) will be vifible. Such leaves
are commonly ufed in gilding ; .and they are fo
veg thin, that if 124500 of them were laid upon
one another, and prefl'ed. together, they” would
net exceed one inch in thicknefs. 7
Yet all this is nothing in comparifon of the
lengths that natureggoes in the divifion of mat-
ter. For Mr. Leewmboek tel-ls us, that there are
more animals in the ‘milt of a finglé‘ cod~fifh,
than there are men upon the whole earth: and.
.‘that, by comparing thefe animals ignya .micro-
{cupe with grains of" common fand, it appeared-
that one fingle grain is bigger than four millions
~ of them. Now each animal mui’t have a heart, '
arteries, veins, mufclesf and nerVes, otheriivife
they couldneither‘live nor move. How incon}
ceivably finall then mull the particles OFi-thei’tgg.
blood be, to circulate through the {mallef’t ramie”
7, . , hearings;

" _-~ 1'
-, . e

; w; ti

 

 

s

PLATE I.

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s‘ (Immwk

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ea-

u.

Of 2126 Properties of Matter. _ , ,5.
beations and joinings-oftheir arteries and v'ein's ?. ’
It has been found by calculation, that a particle
of their blood mnft be as much {mallet than a
globe of the tenth part of an inch 1n diameter, as
that globe 1s fmaller than the whole earth, and
yet, if theft: particles be compared with the par— 1
ticles of light, they will be found to exceed
them as much in bulk as mountains do fingle
grains of fand. For, the f01ce of any body?
firiking againf’t an obf’tacle is directly in pro-‘
portion too its quantity of matter multiplied into
its velocity. and fince the velocity of the par-
ticles of light 13 demonitrated to be at leal’t a
111.1 illion times greater than the velocity of a can-
non- ball, it is tDplain, that if a million of thefe
particles were as big as a fingle grain of find,
we durf’t no more open our eyes to the lioht,
than we duri’c expofe them to {and [hot point-
blank from a cannon.

That matter is infinitely divilible, in a mathe- Plate 1,,
atical fenfe, is eaiy to be demonl‘trated. For, Fig. 1.
let AB be the length of a particle to be divided; '
and let it be touched at op'pofite ends by the pa—
rall e1 lines CD and E E, which, fuppofe to be
- infinitely extended beyond D and F. Set of?
the equal divifions BG, CH, HI, &c. on the The infi-
line E F‘mwards the right hand from B; and Pill“ div‘} .
take a 991m, as it R, any where toward the left $211,212, 0 _
hand from A, in the line C D: Then, from this Proved,
point, draw the rioht lines R”, R H, R I, Sic.
each of which will cut off as; from the par.
ticle AB. But after any finite mimber of Itich , _~
lines are dtaWn, there will fiill‘iemain a part, as 1-11» ,
A P, at the top ofthe ‘Zticle, which can never "
be cut (in3 becaufe the l111es D R and EF being
parallel, no line can ever be drawn from the
point R to any point of the line EF that will
2 coincide

  

 

Attrac—
lion.

. Cohefion .

Of the Properties of Matter.

coincide with the line R D. I Therefore the par.
ticle A B contains more than any finite number
of parts.

A fifth property ofmatter is attmttzion, which
feems rather to be infufed than inherent. Of
this there are‘four kinds, viz. cobcfion, gravita-
tion, magnetifm, and clet‘trz'rz'ty. i ‘

The attrafiion of cobeflon is that by which the
fmall parts of matter are made to flick and co—
here together. Of this we have feveral in-

.fiances, fome of which follow.

1. If a fmall glafs 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
baton: which mui’t be owing to the attraction
of a ring of particles of the glafs all around in

A the tube, immediately above thofe to which the

water at any inf’tant rifes. And when it has rifen
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 prefl'ure 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.
exhaufied 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. ‘ g V

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 feraped clean, and
pretred together with a twil’t, they will attract
~ each

Ofvjlte Prapertirr of .Mm‘ter.

each other {0. firongly, as to require a force
much greater‘than their own weight to feparate
them. And this cannot be owing to the preflhre
of the air, for the fame thing will hold in an
exhauf’ted receiver.

5. If two polilhed plates of marble or bral's
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 f0
flrongly, even if ful‘pended in an exhaui‘ted re-
ceiver, that the weight of the lower plate will
not be able to feparate it from the upper one. In
putting thefe plates together, the one fhould be

robbed 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 bafon of water, they will
move equally fall 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-
nateto their weights: that is, the lighter cork
will move as much falter than the heavier, as the
heavier exceeds the lighter in weight. This
fl‘lCWS that the attraction of each cork is in direél‘."
prOportion to its weight or quantity of matter.

This kind of attraétion teaches but to a very
‘fmarlbdiflance ; for, if two drops of quickfilver
be rolled in dull, they will not run together,
becaufe the particles of dull: keep them out of
the fphere of each other’s attraction. , .

Where the fphere of attraction ends, a repul RepuI-f
fiveforce begins ; thus, water repels mol’t bodies 13°“-
till they are wet; and hence it is, that a fmall

AB 3 y needle,

Of the Properties of Matter. ‘

needle, if dry, fwims upon water; and flies walk
upon it without wetting their feet. '

The repeiling force of the particles of a fluid
is but {malls and therefore; ‘ifa fluid “be divided,‘
it eafily unites again. But if glafs’,‘ or any other
hard fubf’tance, ibe‘b'roke into fmall *‘parts, they
cannot be made to fiiclg together again without ‘
being firfi‘wett‘ed: the repul‘fion being too great
to admit of a reunion. . i

i The repelling force betWeen Water and oil is
{0 great, that we find it almoi’c impofiible to mix
titém f0," as not to feparate again"; If a ball of

'light‘WQOd be dipt in oil, and then put into wa-i

ter, the" Water will recede f0, as to-for’m a channel
of fome depth all around the ball. ‘
The-repulfiv‘e force of the particles. of air. is {0,
great, that they can never be brought’fo-‘n'ea‘r to-
gether by "con‘denfa’tion as to'imake them flicker.
cohere. “Hence it is, tha't'when the 'we-ight'of
the incumbent atmofphere is taken on? fromjahy
finall‘qhantit‘y of air, that quantity v’Will‘difith
itfidf {o as to occupy (in cOmparifon)*an infie-

‘ ni‘te‘ly greater portion of {pace than it did before.

V Gravita-
tion.

flitfzzfiim‘ef gravitation“ is that“ power by
which ’di‘ltjant Bodies tend towards one*~aho-
ther‘. Of‘ this We have daily inf’ta‘ncesfi’n‘ the fall:
ing of bodies to’ the earth; " 'By this power in the
earth 'it is, *‘that bodies,- ‘ o’n ‘xvhatever"fid’e,-' jfall in
ligiries'oxfierpéhdicular ’to‘its 'furface'; ‘ and confe-
qtiéhtiy,'30h oppofi‘te’ fides; they fall-infopfidite
directions"; all “towards" the center, where the
force “of‘fgravity is as it'were accumulated: and
by this pen/er "it is, that bodies ongthe earth’s
furface'are kept to it On ‘all rides, {a that they
cannot fall from it. ’And as it aé’csfupon all boy?
dies in proportion to their refpeé‘tivefiuant‘ities

of matter, without any regard to their bulks on

figurea

l

Of the rPropmm. of Whiter;
figures, it accordingly-confiitmes their weight.
Hence,’ 5: - m 7‘

g If two, bodies which. icon'tain equal quantities,
of matter, were placed ateyer {0 great a ditlance
from one another, and. then left at liberty in free
fpace; if there were no ‘oth‘er’bodies in the uni-
_.verfe to afieé‘t them, they Would fall equally fwift
towards/ope another «byn'the power of gravity,

—» with velocities accelerated as . they approached

-; each other ;‘~ and would; meet in a point which

2 was,vhalfiwaylxbet‘ween(them at firft. Or, iftwo

«bodies,,geontainingr unequal quantities of matter,

:1 were placedat any diflance,‘ and left in the fame

,manrner at-liberty, the‘yrlwould fall towards one

[another with velocities.:\t\éhich~ would be in an

-inver-fe, proportion to their. refpeétive quantities

of matter; and moving falter and falter in their -
mutual approach, would at lafi: meet in a point
as-muchhearer .to the place from-"which the
heavier body began 'to fall, than to the place
fromiwh-ieh the ,lightergbody began to fall, as
the quantity: of matter in. “the former exceeded
that, in the latter. _, ' ' p -

All bodies that we know of have gravity or
weight.~ ., 'For, that there is no fuch thing as po-
fitive levity, even in fmoke, vapours, and‘fumes,
is demonllréxble ‘ by experiments on the air—
pump; which «fliews, that although the/{moke
of a—eandle iafcendsrtothe top of a tall receiver»
when-full of air, yet, uponthe air’s being ex-
haul’ted {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, becaufe it-has a lefs degree

. hWeightthan its bulk of Water has ‘2. but, if the
jar, be emptied of. water, the wood falls to the

’ battome -
B 4- AS

mi ‘ 'Qffl-stb‘e Properties of Matter.

Gravity. As every particle of matter has- its "proper
' demon? « gravity, the effect of the whole mul’t be in pro-
ggaéfihteo portion to the nomber of the attracting particles ;
quantity that is, as the quantity of matter-m the whole,
ofmarter body. This 18 demonftrable byeixperiments on
in bediES-pendulums; for, if they are oF-eq-ua-l lengths,
"whatever their weights. be, they vibrate inequal
times. Now it is plain, that if one be double or
triple the weight of another, it muPt require a
double or triple power ”of gravity to' make it
move with the fame celerity: qut as it would
require a double or triple force toiproj‘eét‘ar‘bul-
let of twenty or thirty pound Weight withthe
fame degree of fwiftnels that a bullet of ten
pounds would require. Hence it is evident,
that the power or force of gravity is always pro-
portional to tthe qtiantity of matter in bodies,
whatever their bulks or figures are. a _‘ '

Itile. Gravity alfo, like all‘other virtues or emana-
cregies astions, which proceed or iflite from a center, de-
thefquarecreai‘es as the difiance multiplied-by itfelf in-
dififice . creates: thatis, a bodyat twice the dii’tance of
incrgak$ another, attrafts with only a fourth part of- the
‘ force; at thrice the'diflance, with a- ninth part;
at fourtimes the difiance, with a fixteenth part;
and f0 on. . This too is confirmed by comparing
the difi‘ance which the moon falls in a minister,
from sarightnline touching her orbit, with the
fidifiance through which heavy bodies near the
earth fall «in. that time. . And alto by [comparing
_ the forces which retain Jupiter’s moons-in their
orbits, withtheir relpeétive dif’tances from Ju-
.piterg, Thefe‘forces will be explained in' the

_ next leétu're.~~ «. s -» -' - ~-

. Thevelocity which bodies near theiearth ac-
quire in defcend-ing freely by the lforce of gravity,
is proportional to the times of their defcent.’

:19 I For:

 

"FOf ’ the Propertie} 0f *Matter'.‘
For, as the power- OF'grja‘Vi‘ty title’s fiOt confif’t in
a fingle’impitlfefibuf i's<»al*way»s*- operating in a
'conf’tant and’uniform manner; 'it’ mutt produce

equal effects:- in ethal time's -,"_="an<¥‘confequeht‘l'y~ in '

a double "ontriple , omega ’clou’ble or; triple ‘efi'eét.
And fo, jby ”aé‘ting uniformly" on the body; mufi:
accelerate its motion- gproportionably to the time
ofzits defcent; ~ i’.‘ <9" i ‘V - '
To bea little more partictilat’on’this fiihjeél',
"let us fuppofe‘thatra body begins tomove With
a-e‘elerity confiantly‘fiand gradually increafifig, in
a‘l’uch‘a manner, asiifiould carry'it‘through’a mile
"in a minute ~, 'at‘th'e end'of this fpace it will have
'acquired fuch. aldegreeof c‘e‘lerity', as"iS'quicient
to carry it twoniile's'the'hCXt mi‘n‘nte, though it
{hou'ld {then receive no ‘fneW’ impulf'e' ‘fl‘dm‘ "the
caufe by‘which its motion had-been accelerated:
but if the fame accelerating caufe continues, it
will ca‘rr'y. the Body ‘a‘ mile-fartherifonwhich
«account; it Willih‘ave’ run i-thmugh' four miles a:
the‘end of two minutes; "arid then'it' will have
.vauiredlfuchr‘a degree ofi'CEIerlty as is-fuflicient
to carry it through a double fpace in‘as much
é'mérec‘tit-fi'e, ion-eight miles" in two minntes,even
though the accelerating force fhouldehét upon it
nomore.I Butthisforce {till continuing to ope-
rate [in an (inform? hfi’aiih'ei‘} Will 'é'gai'n, in an
equal time», p‘rodiice do‘edlual ”some and to; by

‘Carrying'fiit' (‘a mile? flirth‘e’r, --"csu’l‘e% Pit ‘ to move ,

throUgh fiVE‘filiiféS the- thircl'minute‘rfor, the
“ejelerityva'lready acquired;- and3 the eelefit'y l’cill
:acquiringf, will *liavel’ea'cll its“ c‘ompleat effect.
"Henceiwe learn; th‘étt‘if the b‘oay fh‘ould move
one mile the firf’t minute; it would .r’hOve’three
miles the fecon‘d,‘ five the third; {Even the fourth,
inine‘the fifth, andfo‘bn in prop‘O‘r't’iofi.”

And

xi

:32 Of [be Properties of Matter.

f Andthus. it ap‘pears,.thatthefpaces defcribed
in fucceflive equal parts othime2 by an uniformly
accelerated motion, are alwaflysiasthe ogl‘cl- 1mm}.
ilqers t, 3, .5, 7, 9, &c.jand confequently, the
‘whole {paces are: as the {quares of the times, or of
the laf’t acquired velocities. _ For, the continued
addition of the Odd: numbeiisiyields the fquares.
of all numbers-from tiriity“tipwards.,_ Thus, :1 is
the'firfi oddnzumber, and; the if‘qpare of {is I -,
:3 isthe {econd odd numbertand this added: to
:1 makes 4., the, {quare of "3?? 1.5 is the third odd
number, which :added to 4 mgkes 9, .the l‘qppne
of 3 ; land {glorifor ever- €3.39???» thereforet eh}:
:times andfiéslocisiss. prqsecglsvsnlxand wattage-
:ly ~38, 1, 213,4, 8.4?- btltjthsifaases dcfc-nibed in
reach equal times age‘as 4.1, 3,,5U7, &c.1it isle“-

 

:dcmt thait‘hbg {Pilcf' defcrib€di 1%!" :17 i <1; mitt: s
L? .’ "1 .‘4."".“ HT!) L: '1‘ $17.1. .. 3 ‘. J
:13}. minute- Will be 1' -;.4.- .igfsiugarelofx 1m;-
gln 2 misuts5.,:~w~ 1+3: ,;4r—L:fquarwf;ze-
J.“ 3 slimmer: zwsfiszi 9:.fquar: M233.»
j1n 4rmipugtcsx 1+3 +5+73-16.;fquareofsmyfizs.
H. ‘5 ., , ,rs.é vimzi’rj‘
- {Net 13. The . shéiaétex :+. iii-games more, mad 1
.ji zf; egu‘d-Z'lsf'cfil ‘ ”(C i,i;'i‘:'i*x.r’irtg V 7 midi!
1‘ V's-l 11",‘S'Jil‘ :6.“ xx: in:
The de- * A3,hca-V¥ bsdiesarsuaiformlyzacceleratedby
feending the POW? sfigwsx; in.» thsi::d.e,fce§ats-zdt :is:p.1.ain
WWW the? they smilibs {1,1133%}?an seemed-"bx: the
xiii? 'lfm? Pwse-iimheirusicmge aril‘ghsrsfiqe. filam-
pl equal JOCNY wblghfixali hgdya aFQWF‘v’SJbeallmg, .15 {@352
sfcent- _cient to spamming" algae-.49 thefgmeheéghc
from whence fig fell; .,allpwance , being madefor ‘
the refifiancelof, the .airuor ntherxmedjumjn
’vwhich (kg body is moved, silThus,‘ the.- shady D
' in rolling “down the] iodine-d1 plane AIB- will
acquire Rich ,2; Velocity by the timeéitaarrives at

A

 
 

Of the Prapertz'es of Marian,

B, as will carry it upthe inclined plane B C, al-
mol’t to C ', and would carry it quite up to C, if

i3

the body and plane were perfectly fmooth, and,
7 the air gave no refiftance.—~So, if a pendulum '

_ wereput into motion in a fpace quite free of
, air, and, all other refiitance, and had no friétion
on the point of fufpenfion, it would move for

ever: for the velocity it had acquired in- falling,

through the defcending. part of the arc, would

be {till qufli’cients try—(carry it equally high in the

at‘cending part thereof.
aThe center of gravity is that pointof a body
in which'the whole forceof its gravity or weight,

is uhited. iTherefdreywhatever fupports that.

point bears-the weight of the whole body : and
whilft it. is {up-ported; the body cannot fall;
becaufe alliits parts are in a perfeél: equilibrium
about that "point. ' ' ,
An imaginary line drawn from thencenter of
gravity of any body towards the center of the
earth, is calledthe Zine of direfiz'qn. ‘ In this line
.all ,heaVy bodies defcend, if not obl’trué’ted.
Since the whole weight of a body is united in
its Center of gravity, as that-I center afcends or
defcends, we muf’t look uponthe whole body to
do {0 too. But'asrit is contrary to the nature of
heavy bodies to afcend of their own accord, or
not to defcend when they arepermitted -,, we
, maybe fure that, ”unlefs the center of gravity
he fupported, the whole body will tumble or,

‘ , fall. Hence it is, that bodies {tand :upon their

bafe’s when the line of direé‘tion falls within the
bafe; for in this cafe the body‘azannot be made
to fall without firfl: railing“ the center of gravity
higher than it was before. Thus, the inclining
body ABC D, whofe center of gravity .is E,

finds firrnly. on its bafe C-D 1K, be‘caufe the line

/

The C6114
ter of
grayity,

and line
of direc-
tion.

Fifi‘ 3?

0f.

y :-

‘14

‘_ f3 .
3&5

Of the Properties of Matter.

of direftion E F falls within the bafe; But if a
weight, as AB G H, be laid upon the top ofthe
body, the center of gravity of the whole body
and weight together is rai‘fed up to I 5 and then,
as the line of direction ID falls without the bafe
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
haiiily in a coach or boat when it is likely to
overfet : for, by that means they raife the cen—
ter of gravity fo farias to endanger throwing it
quite out of the bafe; and if they do, they
overfet the vehicle efleé‘tually. 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 hate, and by that means might have faved
themfelve‘s;

The brOader the bafe is, and the nearer the
line of direction is to the middle ‘or center of it,
themo're firmly does the body, Rand. On the.
Contrary, the’narrower the bafe, and the nearer
the line of direction is to the fide bf it, the more
eafily may theibody be overthrown. a lefs change
of pofition being fuflicient to remove the line
of direction out of the "hate in the latter cafe,
than in- the former.’ And hence it is, that a.
fphere is f0 eafily rolled upon a horizontal plane;
and that itiis f0 difficult, if not imp'oflible, to

make things which are {harp-pointed to fiand

upright on the point—From what hath been,
laid, it plainly appears that if the plane be in-
clined on which the heavy body, is placed,ithe
body Will Hide down upon the plane whilflt the
line of direction falls within the bafe; but it Will

tumble or roll down when that line falls without

Of tbé Properties of Matter; ' 3153

the bafe. Thus, the body .4 will only flide Fig. 4.
down the inclined plane CD, whilfl: the body 3
rolls down upon it. ' .

When the line of,dire&ion falls within the
bafe of our feet, we (land; and mof’t firmly when
it is in the middle: but when it is out of that,
bafe, we immediately fall. And it is not only
pleafing, but even furprizing, to refleé‘t upon
the various and unthought-of methods and pof-
tures which we ufe to retain this pofition, or to

r .. . .

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 f’tairs: and for this
purpofe a man leans forward when he carries a
burden on his back, and backward when he car-
ries it.on his breaf’c; and to the right'or left fide
‘ as he carries it on the oppofite fide. A thou-
fand more inf’tances might be added.

The quantity of matter in all bodies is in ex-

a& proportion to their weights, bulk for bulk.
Therefore, heavy bodies 'are as much more
denfe or compact than light bodies of the fame
bulk, as they exceed them in Weight.

All bodies are full of pores, or {paces void ofAlIbodié’s
matter: and in gold, which is the heaviel’t ofPOFOUS-
all known bodies, there is perhaps a greater
quantity of {pace than of matter. For the par»,
ticles of ‘heat and magnetifm find an eal'y paffage
through the pores of gold; and even water itfelf
has been forced through them. Befides, if we.
confiderhow eafily the raysiof light pafs through
f0 folidra body as glafs, in all manner of direcg-
tions, we {hall find reafon to believe that bodies
are gnuchi more porous than is generally ima-

ine . \ ..
All bodies are fome way or other 3%ng by The ex-
heat; and all metallic bodies are expanded in Panflomf
length, metals.

‘16

The py-

xometer.

Fig. 5.

Of tbe Properties of Matter.

length, breadth, and thicknefs thereby.——The
proportion of 'the expanfion of feveral metals,
according to the. belt experiments I have been
able to make with my pyrometer, isnearly thus :
Iron and f’tee‘l as 3, copper 4. and an half,
brafs 5, tin 6, lead 7. 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
augh't I know) of a new confiruétion, a de-
fcrip‘tion of it may perhaps be agreeable to the
reader. ' ‘

11.4 is a flat piece of mahogony, in which are
fixed four brafs fluds B,C,D,L; and two’pins,
one at F and the other ,at H. On the pin
F turns the crooked index EI, and upon the
pin H the firaight index GK, ag’ainf‘t which a
piece. of Watch-fpring R bears gently, and fo
prefles it towards the beginning of the feale MN,
over which the point of that index moves. This
fcale is divided into inches and tenth parts of an
inch: the firl’t inch is marked 1000, the fecond
2000, and f0 on. A bar of metal 0 is laid into
notches in the top of the finds C and D; one
end of the bar bearing againft the adjul’ring
{crew P, and the other end againf’t the crooked

. index E I, at a 20th part of its length from its

center of motion F.—Now it is plain, that how—
evenmuch the bar 0 lengthens, it will move "
that part of the index E I, againf’t which it bears,
juf’t 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 againl’t
which the bar hears, it will move 20 times as
far as the bar lengthens. And as this crooked
end bears againf’t the index GK at only a 20th
part of the whole length GS from its centerof

motion

<._..—~

Of five Properties of ’Mat‘te’r;

motion 'H, the rpoiht S Twill move thiOugh‘zbt -

times the {pace that the point of bearing near H
does. ~Henc’e,'as 20 multiplied by 20 produces

‘ 4.00, it is evident that if the barle'ngt'hens but a

400th part of an inch, the point S will move a.

whole inch on- the fca-le; and as every inclr'isf
divided into 10 equal parts, if the barlengthens

but the 10th part of the 400th part of an inch;
which is only the 4oooth 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,
firft lay it cold into the notches of the finds, and
turn the adjuf’ting, fcrew P until the'fpring R
brings the point S of the index G K to the begin-
ning of the divifions of the feale at M: then,
without altering the {crew any farther, take olf
the bar and rub it with a dry woollen cloth .till
it feels warm; and then, laying it On where it
was, obferve how far it pulhes the point S upon
the ‘fcale by means of the crooked index E I ;
and the point S will lhew exaétly how much the

bar has lengthened by the heat of rubbing. As

the bar cools, the fpring R bearing againi’t the
index KG, will caufe its point S to move gra-
dually back towards M in the fcale : ‘and when
the bar is quite cold, the index will rei’c at M,
where it was before the bar was made warm by
rubbing. The indexes have {mall rollers under
them at [and K; which, byturning round on

the fmooth wood as the indexes move, make’_

their metions the ealier, by taking of? a great
part of the frifiion, which would otherwile be
on the pins F and H, and of the points of the

‘ indexes themfélves on the wood.

17

_ Befides the univerfal ~properties above‘men- Magne-
troned, there are bodies which have properties “(m-

pecu‘

Eleflr‘i-
city.

30f tbs Properties qf Mailer.

peculiar-to themfelves: fuch as the loadflo'nq
in which the molt remarkable are thefe: I. It
attracts iron and fieeluonly. 2. It confiantly
turns one of its fides to the north and another
to the fouth, when fufpended by a thread that
does not twill. 3. It communicates all its pro-
perties to a piece of Fred when rubbed upon it,
without loling any itfelf.

According to Dr. Helflyam’s experiments, the
attraé‘tion of the loadflone decreafes as the fquare
of the dillance increafes. Thus, if a loadl’tone
be fufpended at one end of a balance, and coun—
terpoifed by weights at the other end, and a.
flat piece of iron be placed beneath it, at the
dif’tance of four tenths of an inch, the {tone will
immediately defcend and adhere to the iron.
But if the lione be again removed to the fame
dii’tance, and as many grains be put into the
feale at the other end as will exaétly counterba-
lance the attraétion, then, if the iron be brought
twice as near the {tone as before, that is, only
two tenth parts of an inch from it, there mul’t
be four times as many grains put into the fcale
as before, in order to beg juf‘t counterbalance
to the attraftive force, or to hinder the {tone
from defcending and adhering to the iron. 80,
if four grains will do in the former cafe, there.
mull be fixreen in the latter. But from fome
later experiments, made with the greatefi ac-
curacy, it is found that the force of magnetifm
decreafes in a ratio between the reciprocal of the '
fquare and the reciprocal of the cube of the di-
fiance -, approaching to the one or the other, as
the magnitudes of the attracting bodies are varied.

Several bodies, particularly amber, glafs, jet,
fealing-wax, agate, and almolt all precious
ftones, have a peculiar property of attraéling

- and

 

 

  
 

 

 

 

 

 

 

     
  
 

   

 

 

 

    

 

   
  

 

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«‘ . 157144011 Jilin.

 

Of central Forces. 1. 9

and repelling light bodies when heated by rub-
bing. This is called elefirz'ml attrqfi‘ion, in'
which the chief things to be obferved are, 1. If
a glafs tube'about aninch and _a half diameter,
and two or three feet long, be heated by rub-
bing, it will alternately attraél: and repel, all light
bodies when held near them. 2. ltfdoes not
attract by being heated witho’Ut" rubbing.
3. Any lightobody being once repelled by the
tube, will never be 'attraé‘ted again till it has
touched fome otherbody. 4.’ If the tube be
rubbed by a moil’t hand, or any thing that is
wet, it totally defiroys the electricity. 5. Any
body, except air, being interpofed, {tops the
eleé‘tricity. 6. The tube attraéts fironger when
rubbed Met with bees-wax, and then with a dry
'woollencloth. .7. When it is well rubbed, if
a finger be brought near it, at about the dif—
tance of half an inch, the efiluvia will fnap
againfi the finger, and make a little crackling
mile; and if this be performed in a dark place,
there will appear a little flalh of light.

L E. c T.“ 11.
Of central Forces.

      

if ,
“"rn

E have already mentioned it as a necef- Motioniolitf‘V: .‘7
fary conlequence arifing from the dead- refleq'ual-ii "
nefs or inaé‘tivity of matter, that all bodies 13' md‘fiie‘
endeavour to continue in the {late they are imgzztiet: a”
whether of ref: or motion. If the body 11 were Plate 1.1.
placed in any part of free fpace, and nothing Fig- I~
either draws or impels it any way, it would for /
ever" remain in that part of fpace, becatife it
could have no tendency of itfelf to remove any
way'from thence. If; it receives a fingle im~

C . . pulfe

 

‘r

20

All mo«
tion na-
turally
rectill.
neal.

Of central Forces.
pull'e any way, as fuppofe fromfl towards B, it
will go on in that direction; for, of itfelf, it
could never fwerive from a right line, nor flop
its courfe.—-When it has gone through the fpace
113, and met with no refii’tance, its velocity

' will be the fame at B as it was at d: and this

velocity, in as much more time, will carry it
through as much more fpace, from B to C; and
f0 on for ever. Therefore, when we fee a body
in motion, we conclude that fome other fub-
fiance mui’t have giVen it that motion; and
when we fee a body fall from motion to rel’t, we
conclude that fome other body or caufe fiOpt it,

As all motion is naturally reé‘tilineal, it ap-
pears, that a bullet projected by the hand, or
{hot from a cannon, would for ever continue to
move in the fame direction it received at firl’t, if
no other power diverted its courfe. Therefore,
when we fee a body move in a curve of any kind
whatever, we conclude it muft be aéted upon. by
two powers at leai’t; one putting it in motion,
and another drawing it Off from the reé‘tilineal
courfe it would otherwife have continued to
move in: and whenever that power, which bent
the motion of the body from a {traight line into
a curve, ceafes to act, the body will again move
on in a firait line touching that point ofthe
curve in which it was when the action of that
power ceafed. For example, a pebble moved
round in a fling eve}~ fo long a time, will fly off
the moment it is fet at liberty, by flipping one
end of the flingcord: and will go on in a line

- mulching the circle it defcribed before: which

line would actually be a firaigh‘t one, if the
earth’s attraction did not affect the pebble, and
bring it down to the ground. This flaews that
the natural tendency of the pebble, when put

1 Into

 

 

l

Of central Farm.
into motion, is to continue moving in a firaight
line, although by the force that moves the fling
it be made to revolve 1n a circle.

The change of motion produced 13 in propor-
tion to the force imprefied: for the. effeé‘ts of
natural caufes are always preportionate to the
force or power of thofe caufes.

By thefe laws it is eafy to prove that a body
will defcribe the diagonal Of.- a fquare or pet'-
rallelogram, by two forces conjoined, in the
fame time that it would defcrihe either of the
tides, by one force fingly; Thus, fuppofe the

body A to reprefent a {hip at fea; and that it is

.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, fuppofe a fiream or cur-

rent of water rUnning in the direction 111), with
fuch a force as would carry the {hip through an
equal {pace from A to D 1n a minute. By thefe‘
two forces, a&ing together at right angles to
each other, the {hip will defcribe the line AEC
in a minute: which line (becaufe the forces are
equal~and perpendicular to each other) will be
the diagonal of an exaél: fquar‘e. To confirm
this law by an experiment, let there be a wooden

2!

The ef
feels of
combined
forces.

Fig. 21‘

fquare 148 CD f0 contrived, as to have the part F10 3,

B E FC made to draw out or pufh mm the fquare
at pleafure. To this part let the pulley H be
joined, f0 ”as to turn freely on an axis, which
will be at H when the piece is pufhed in, and
at 12 when 1t is drawn out. To this part let the
ends of a firaight wire 1% be fixed, fo as to move
along with it, under the pulley -, and let the ball
G be made to Hide eafily on the Wire. A thread

‘ m is fixed to this bid], and gOes over the pulley

to I; by this thread the ball may be chawn up

. an the wire, parallel to the fide 11D, when the

C 3 p211";

22

Of central Forces.

part B EFC is pufhed as far as it will go into

the fqtiare. But, if this part be drawn out, it
will carry the ball along with it, parallel to the
bottom of the fquare D C. 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 fpaces, each

., power aé‘ting equally and feparately‘ 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 /I ~
of the fixed fquare, and the moveable part
B E F G be drawn out, the ball will then be afted
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 carried with its

’ wire k towards the right hand BC, moving all

the while in the diagonal line L”; and will be

found atg when the fliding part is drawn out as

far as it was before ; which then will have caufed
the thread to draw up the ball to the top of the

7 infide of the fquare, jnl’t as high as it was before,
when drawn up fingly by the thread without
moving the fliding part.

If the afting forces are equal, but at oblique

. ”angles to each other, (0 will the {ides 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 twoequal forces aét conjointly upon the

body A, one having a tendency to move it
through the {pace dB in the fame time that the
other has a tendency to move it through an equal
fpace flDg‘it will defcribe the. diagonal flGC
in the fame time that either of the fingle forces
would have caufed it todefcribe either of the

. tides. Home of the forces be greater than. the

other,

 

 

Of central ' Forces.

other, then one fide of the parallelogram will be
fo much. longer than the other. For, if one force
lingly would~ carry the body through the {pace
flE, in the fame time that the other would have
carried it through the fpace A D, the joint action
of both will carry it in the fame time through
the fpace AHF, which is the diagonal of the
oblique parallelogram .4 D E F.

If both forces act upon the‘body in fuch a
manner, as to move it uniformly, the diagonal“
defcribed will be a firaight line, but if one of

the forces acts in fuch a manner as to make the '

body move falter and falter, then the line dc-
fcribed will be a curve. 'And this is the cafe
of all bodies which are projected in reftilineal
directions, and at the fame time acted upon by
the power of gravity; which has a confia‘nt ten-
dency to accelerate their motions in the direction
wherein it aéis. ‘

23

From the uniform projectile morion of bodies in The laws

firaight lines, and the univerfal power of gravity of the

01‘ attraction, arifes the curvilineal mOtiOn of all Plane‘a‘?

motions.

the heavenly bodies. If the body 11 be projeéted .

along the firaight line fl F H in open fpace, Fig. 5.

where it meets with no refifiance, and is not
drawn afide by any power, it will go on for

ever with the fame velocity, and in the-fame '

direélion. But if, at the fame moment the
projectile force is given it at A’, the body 8 be-
gins to attraé‘t it with a force duly adjul’ted 9*,
and perpendicular to its motion at 14, it will then
be drawn from the flraight line-A F H, and forced

* To make the projectile force a jolt balance to the gra-
vitating power, f0 as to keep the planet moving in a circle,
it mul’t 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

See Plate

‘0

0/ central Forces.

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-.7 And if, when

the body is in any part“ of its orbit (as {uppofe
at K) a {mailer body as L, within the Iphere of
attraction of the body K, be projected in the
right line LM, with a force duly adjufied, and
perpendicular to the line ofattrafiion L K; then,
the {mall body L will revolve about“ the large
body K in the orbit N O, and accompany it 1[in

its whole courle round the yet larger body ,5.

But then, the body Kwill no longer move in
the circle 11 T W -, for that circle will now be

Edefcribed by the common center of gravity be;

étween K and L, Nay, even the great bodyLS
will not keep in the Center; for it will be the
common center 70f gravity between all the three
bodies 8,- K, and L, that will remain immove-
able there. So, if we fuppofe S and K connected
by a wire P that has no weight, and K and L
connected by a wire q thatfihas no weight, the
common center of gravity of all thefe three
bodies will be a point in the wire P near S;

i . which point being fupported, the bodies will be

all in eguiiz'lrrz'o as they move round it. Though
indeed, ltriétly fpeaking, the common center of

gravity of all the three bodies will not bein the

.wire 1) but when thefe bodies are all in a right
line. Here, S may reprefent the fun, K the
earth, and L the moon. . .

In order to form anidea of the curves de-
fcribed by two bodies revolving about their com—i
{non Center of gravity, 'whilf’t they themfelves
with a-tnird body'are in motion round the com—
mon center of gravity of all the three; let
us firf’t {uppofe E to be the fun, and e the
earth going round him without any moon; and

‘ i " ' ' their

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

   

 

  

 

 

 

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- 2

Of cerziml Fortes. 25‘

their moving forces regulated as above; In
this cafe, whili’t the earth goes round the fun in
the dOtted circle RTUWX, &c. the fun will The
.go round the circle .48 D, whofe center C is fuigeijdg‘
the common center of gravity between the fun begs; re}:
and earth: the right linefia‘ reprefenting the volving
mutual attraction between them, by which they about
are as firmly connected as if they were fixed arm”
the two ends of an iron bar firong enough toififififi,
hold them. So, when the earth is at e, thegravity.
fun will be at E; when the earth is at T, the fun
will be at [Ts—and when the earth is at g, the fun
'will‘be at G, 8.50.
Now, let us take in the moon g (at the top of
the figure) and fuppofe the earth to have no'pro-
greflive metion about the fun; in which cafe,
whill’t the moon revolvesabout the earth in her
orbit $315639, the earth will revolve in the
circle 8 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.
But the truth is, that whilfl; the moon revolves
about the earth, the earth is in motion about
the fun: and now, the moon will. caufe the
earth to defcribe 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 defcribe 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 defcribe a quarter of her progrefiive, orbit
about the earth in the time that the earth moves
from 3 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 Farms.

will have defcribed the dorted arc R l T, the
earth the curve R 5 f, and the ,moon the curve
9 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 defcribethe dot-
ted arc T 2 U, the earth the curve f 6 g, the
moon the curve r 15 r, and f0 on—And thus,
whili’t the moon goes once round the earth in
her progreflive orbit, their common center of
gravity def-tribes the'regular portion of a circle
R I ‘f 2 U 3 V4 M the earth the irregular curve
R 5f6 g 7 la 8 i, and the moon the yet more.
irregular curve 9 14 M5 5 .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 centertowards the

moon 3 therefore the circie S 13 which the earth ,

defcribes 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 miies nearer the fun at the time of full
moon than at the time of new. [See the earth at
f and at 17.] i‘ ' '

' To avoid confufion in {0 {mall a figure, we.
have fuppofed the moon to go onl twice and a
half round the earth, in the time that the earth
goes once round the fun ; it being impoflible to
take in all the revolutions which the makes in a
year, and toigive a true figure of her path, un-
lefs we fhould make the femidiameter of the
earth’s orbit at leaf’t 95 inches; and then, the
proportional fe‘midiameter of the moon’s orbit

I, would be only a quarter Of an inch.—-For a true

figure of the moon’s path, I refer the reader to
my Treatife of Afi'ronomy.

If the moon made any complete number of
revolutions about the earth in the time that the
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Of central Forces. '. 27‘

earth makes one revolution about the fun, the

aths of the fun and moon would return ‘into
themfelves at the end of eVery year-.i-,and {’0 be
the fame over again: but they return not into
themfelves in lefs than 19 years nearly; in which
time, the earth ' makes nearly =19 revolutions
about the fun, and the moon 2’ 3-5 about the earth;

. If the planet 1? be attraé‘ted-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-
fcribe the are AG by the combined action ofthefe A d

t ,. . p. . oublc
forces, 1n thefame time-that the former would projeétilc
have caufed it to fallffrdm‘jfl to B, or‘ the latter. force ba-
have carried it from 14 to F, ‘ But, if the projec- latices a
tile force had been twice as great, that is, fuch as (1:33:55?
would have carried the planet from 1? to H, in E, ‘

the fame time that now, by the fuppofition, it
carries it only from A to F 3 the fun’s attraction
mul’t then have been 'four times as {thong as fox-'-
m'erly, to have kept the planet in the circle
flTW; that'is, it muft have been fuch as Would
.have caufed 'the planet to fall from A‘ to E,
which is four times the diftance of fl from B, in
the time that the projeétile force fingly would
have carried it from .4 to H, which is only twice
the dil’tance of flfrom 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 {hall foo’n-g‘be confirmed by an
experiment; ' i w -

The whirling-table is a machine contrived‘for Plate IV.

{hewing experimentsof this nature. AA is aFig- ‘-

firong frame of wood, 3 a winch or handle

avity,

* Here the arcs A G, A I mufi be fuppofed to be very
{mall ; otherwife A! hich is equal to H1, Will be more
than quadruple t0 hich is equal to'F G. 1 ‘ ’ .1

‘ fixed

   

28..
The

, whirling
table de-
feribed.

Of central Forces.

fixed on the axis C of the wheel D, round which
is the catgut firing F, which alfo goes round the
fmallw heels G and K, croliing 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 boardd,» to which the“ bearer
M SX may be fafiened occafionally, and remov-
ed when it is not wanted. On the axis of the
wheel H 15 fixed the bearer N T Z and it is
eafy to lee that when the winch B 15 turned, the
wheels and bearers are put into a whirling mo-
tion.

Each bearer has two wires, W X, and 2", Z,
fixed and fcrewed tight into them at the ends by
nuts on the ontfide.b And when thefe nuts are
unfcrewed, the wires may be drawn out in
order to change the balls U and 1/, which flide
upon the wires by means of brafs loops fixed in,-

‘to the balls, which keep the balls up from touch:

ing thewood below them. A firong [ilk line
goes through each ball, and is fixed to it at any
length fiom the center of the bearer to its end,

as occafion requires, by a nut {crew at the top Of
the ball- -, the {hank of the fcrew goes into the
center of the ball, and prelTes the line againfl:
the under fide 01 the hole that it goes through.

..-—-The line goes from the ball, and under a {mall
pulley fixt in the middle of the bearer ~, then 11p

through a focket 1n the round plate (fee S and T)

in the middle of each bearer, then throngh a
.flit 1n the m ddle of the lquare top (0 and P)
of each towe1, and going over a {mall pulley on
the tep, comes down again the fame way, and 13

.at lal’t fafiened to the upper end of the rocket

fixt 1n the middle of the above- mentioned round

p’plate. ihefe plates 8 and T have each four
round hoies 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 conneéted, each by its particular
line, it is plain that if the balls be drawn outward,
or towards the ends M and N of their refpeé‘tive
bearers, the round plates 8 and T will be drawn
up to the top of their refpeétive towers O and P.

There are feveral brafs weights,‘ fome of two
ounces, fome of three,» and fome of four, to be
occafionally put within thetowersO and P, upon
the round plates S and T: each weight having
a round hole .in-the middle of it, for goingupon
the fockets’or axes of the plates, and is {lit from
the edge to the hole, for allowing it to be flipt
over the forefaid line which comes from " each
ball to its refpeétive plate. (See Fig, 2.)

The experiments to be made by this machine
are as follows :

I. Take away the bearer M X, and take the Fig; 1.’
ivory ball a, to which the line or filk cord 6 is
faitened at one end; and having made a loop on
the other end of «the cord, put the loop ever a
pin fiXt in the center of the board 4’. Then,
turning the winch B to give the board awhirling The Pm,
motion, you will fee that the ball does not imme- penfity of
diately begin to move With the board, but, on 1133“"th
account of its inactivity, it endeavours to conti— fiZEEii i:
Tnue in the flate of reft which it was in before—in, ‘
Continue turning, until the board communicates
an equal degree of motion with its ownto the
ball, and then turning on, you will perceive that
the ball willremain upon one part of the boar-d,
keeping the fame velocity with it, and having no
relative motion upon it, as is the cafe with every
thing that lies look upon the plane furface of the
earth, which having the motion of the earth
communicated to it, never endeavours to remove

from

30

Of central Forces.

from that pl ace. But {top the board fuddenly
by hand, and the ball will go on, and con-
tinue to revolve upon the board, until the
friction thereof flops its motion: which Ihews,
that matter being once put into mbtion,
wovuld continueto m0ve‘for ever, if it met

no refii’tance. In like manner, 'ifa perfon Pt

Upright 1n a beat before it begins to move, he
can fiand firm; brat the moment the boat lets
offi he 13 in danger of falling towards that place
which the boat departs from: becaufe, as mat-
ter, he has no na‘tirral prOpenfity to move. But.
when he acquires the motion of the boat let it
be f0 fwift, 1f 1t be fmooch and uniform, he
wil nd as upright and firm as if he was on
the plain fliore , and if the boat firikes againi’c
any obf’tacle, he will fall towards that obfiacle;

~ on account of the propenfity he has, as matter,

to keep the motion which the boat has put him
Into.

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 M‘X, 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-

* Bodies. ‘
movie-gin
orbits
have a
tendency
to fly out
of thefe
orbits.

board to its center.
’ Draw OFF the ball a little from the center, and
turn the winch; then the ball will go round and
round with the board, and will gradually fly 0%
farther and farther from the center, and raile up
the weight below the machine: which {hows
that all bodies revolving in citcles,have a ten-‘T
dency to fly oil“ from thefe circles, and muPt have
Tome power acting upon them from the center of
metion, to keep them from flying oh". Stop the
machine, and the ball will continue to revolve
« - for

 

u

Of central Forces. , . 3!

far fome time upon the board; but as the frie-
tion gradually flops its motion, the weightaéting
upon it will bring it nearer and nearer to the
center in, every revolution, until it brings it
quitéYh’ither. This fhews, that if the planets

w,

w with an refinance in oin round thefun
.r \ ,

gm.

it attractive power would bring them nearer

and nearer to it in every revolution, until they

fell upon it. . i

_ 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 {:13 at:
to the cord, by which means it will go round bits than
and round upon the board. The ing in large
with what velocity it moves, pull the be» “35'
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

falter it will revolve; as thofe planets which are

"neared the fun revolve falter than thofe which

are more remOte; and not only go round fooner,

becaufe they defcribe fmaller circles, but even

move falter in every part of their refpeftive

circles. _ ‘ p

_ 4. Take away this ball, and apply the bearer Their
M X, whofe center of motion is in its middle at centrifi“
w, directly over the center of the whirling-board figfims
d. Then put two balls (V and U) of equal
weights upon their bearing wires, and having as;
fixed them at equal dif’tances from their refpeétive
centers of motion w and x upon their fill: cords,

by the {crew nuts, put equal Weights in :the ,
towers O, and P, Lal’tly, put the catgut firings - ' ‘
E and Fupon the grooves G and Hof thevfmall
wheels, which, being of equal diameters, Willgive
‘equal velocities to the bearers above, Whent-athe
winch B is turned: and the balls, U and K-will

fir

      

32

Of central Fortes.

fly off towards M and N ; and will raife the
weights'in the towers at the fame infiant. This
fl'lCWS, 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 inflead
of them, put a ball of’fix ounces into the bearer
MX, at a fixth part of the dil’tance w z from'the
center, and put a ball of one ounce into the op
polite bearer, at the whole d‘ii’tance xy, which
is equal to w z from the center of the bearer;
and fix the balls at thefe dil’tances on their cords,
by the {crew nuts at top ; and then, the ball U,-

, which is fix times as heavy as the ball V, will ”be i

at only a fixth part ofthe dilliance from its cen-
ter of motion ; and cofnfequently will revolve in
a circle ioflonly a fixth part ofthe circumference

, of the circle in which Vrevolves. Now, let any

equal weights be put into the towers, and the
machine be turned by the winch ; which (as the
catgut firing is on equal wheels below) will
caufe the balls to revolve in equal times; but V
will move fix times as fal’t as U, becaufe it, re-
volves in a circle of fix times its radius; and
both the Weights in the towers will rife at once.- i
This lhews, that the centrifugal forces of revolv-
ing bodies (or their tendencies to fly off from the

’ circles’fhe defcribe) are in direct to ortion to,
Y P

their quantities of matter multiplied into their
refpeétive velocities ; or into their diitances frOm
the centers of their refpeétive circles. For, fup-
pti‘fing U, which weighs fix ounces, to be two
inches from its center of motion to, the weight
multiplied by the dil’tance is 12: andfuppofing
V, which weighs only one ounce, to be 12 inches
dii‘rant from the center of morion x, the weight:
1, ounce multiplied by the dii’tance 12 “inches
~'° is

 

 

Of central Forces.

' is 12. And as they revolve in equal times,’ their
velocities are as their dil’tances from the center,
namely, as I to 6. ,

If thefe two balls be fixed at equal diftances
from their refpeétive centers of motion, they
will move with equal velocities; and if the
tower O has 6 times as much weight put into it
as the tower P has, the balls will raife their
weight exactly at the fame moment. This
fliews that the ball Ubeing fix times as heavy as

the ball V, has fix times as much centrifugal
force, in defcribing an equal circle with an equal

velocity. .
6. If bodies of equal weights revolve in equal
circles with unequal velocities, their centrifugal
forces are as the fquares of the‘velocities. To
prove this law by an experiment, let two balls
U and V of equal weights be fixed on their cords
at equaldiftances from their refpeétive centers
of motion to and x; and then let the catgut
firing E be put round the wheel K (whole cir-
cumference is only one half of the circumference
of the wheel H or G) and over the pulleys 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 V will re-
volve twice as fall as the ball Uin a circle of the

333

A double
velocity
in the .
fame cir-
cle, is a
balance
to a quat‘
ruple
power of
grav1ty.

fame diameter, becaufe they are equidil’tant from .

the centers ofthe circles in which they‘revolve;
and the weights in the towers will both rife a
the fame infiant, 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 attraclive forces in the cen-
ters, a€ting ‘upon, the‘revolving balls; which,

. . ‘ moving

3+

Keeler’s
Problem.

Of central Form.

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-
equal circ=les,\in fuch a manner that the fquares
of the times of their going round are as the
cubes of their dil’tances from the centers of the
circles they defcribe ; their centrifugal forces are
inverfely as the fquares of their dif’tances from
thofe center’s. For, the catgut firing remaining
as in the laft experiment, let the'diftance of the
ball V from the center x be made equal to two
of the crofs divifions on its bearer; and the dill
tance Of the ball U from the center to be three
and a fixth part; the balls the'mfelves being of
equal weights,.and V making two revolutions
by turning the winch, in the time that Umakes -
one : fo that if we {uppofe 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: is only I, and the {quare of
2 is 4; therefore the fquare of the period‘Or
revolution of the ball V, is contained four times
in the fquare of the period of" the ball U. But
the dif’tance ofV is 2, the cube of which is 8,
and the dif’tance 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 difianCes from x and to, which are the cen-
ters of their refpeé‘tive circles. And if the
weight in the tower 0 be four ounces, equal to
the fquare of 2, the dillance of V from the cen-
ter x; and the weight in the tower P be [0'
ounces, nearly equal to the fquare‘ of 3%, the

edif’tance of Ufromirw; it will be found upon turn-

ing the machine by the winch, thatthe balls U

/;and V will raife their refpeétive weights at

5 the.

 

 

' Of cenlml Forces.

the fame infiant of time, Which confirms that

famous propofition of KEISLER, viz That the
fquares of the periodical times 0f the planets
round the fun are in proportion to the cubes of
their dii’tances from him , and that the fun” 3 at-
traction is in’verfely as the fquare of the dii’tance
from his center: that is, at twice the dif’tance,
his attraction is four times leis; and thrice the
diflance, nine times lefs ; at four times the dif-«
tance, fiXteen times lefs, and f0 on, tothe re-
motef’t part of the fyfiem.

8. Take off the catgut firing E from the"
great Wheel D and the {mall wheel H, and let
the firing F remain upon the wheels D and G.
Take away alfo the bearer M X from the whiil‘
ing-board d, and infiead thereof put the ma-
chine .48 upon it, fixing this machine to the,

center of the board by the pins 6 and d, in fuch Fig. 3'.

a manner, that the end ef may rife above the

board to an angle of go or 4o degrees. In the The ab-

35

 

upper fide of this machine are two glafs tubes furdity of
aand b, c10fe fizopt at both ends-,D and eachthe Cartéf

tube IS about three quarters full of water,
the tube a is a little quickfilver, which naturally
falls down to the end a in the water, becaufe
it is heavier than its bulk of water; and on the
tube 5 is a fmall cork which floats on the top
of the water at e, becaufe it is lighter, and it
is fmall enouoh to have liberty to rife or fall
in the tube. While the board 5 with this ma-
chine upon it continues at rei’t, the quickfilver
lies at the bottom of the tube a, and the cork
floats on the water near the top of the tube 5. 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
farthei’c from the center of motion) theiheavieit

D with

I fian vor—
1’1 texes.

I

. 36- F ' .Ofl central Forces.

‘ with the greatef’t 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, becaufe it is lighter
than quickfilverg-but the water in the tube]:
flying OH” to its higher endJe, will exclude the

cork from that place, and caufe the cork to dec

fcend towards the lowermoft end of the tube,

where it will remaimupon the lowei’t end, of the
water near-l}; for the‘heavier body, having the

greater centrifugal force, will {therefore poflefs
the uppermoi’t part of the tube; and thelighter
body Will keep between the. heavier and the
lowermofl part. . . ,
This demonfirates the abfurdity of the Carte~

flan doctrine of ' the planets moving round’lthe

fun‘ in vertexes : for, if the planet be more

denfe or heavy than its bulk of the vortex, it will

fly 01? therein, farther and'farther from the fun 3

' if lefs denfe, it will come down to the lowefi:
.. part of the vortex,“ at the fun: and the whole

, vortex itfelf muff be furrounded with {omething

like a great wall, otherwife it would fly quite ofi'",

planets~ and all together.-——But while gravity ex-

ifls, there is no occafion for fuch vertexes; and
when it ceafes to with a {tone thrown upwards V

will never return to the earth again. . _

If one bo. 9. If a body be fo. placed on the whirling.-
dy moves board of the machine (Fig. i.) thatthe center of
mug: gravity of the body be directly over the center"
:23}, g? of the board, and the board be put into ever f0 .
themmurtrapid a motion by the winch B,_t_he body will
move turn roundwith the board, but will not remove
””2“.“d from the middle of it; for, as all parts of the
’ Lang: body are in egm'lz'brz'a round its center of gravity,
m of and the center of gravity is at reit in the center
gravity. of motion, the centrifugal force of all parts of
" 2 uthc '

;

 

 

\ Of whim! Farms. ’
the body Will be equal at equal dillanees 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 ofi“ towards that lide of the

37

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 fl, and the flat fide e f of
this demi- -globe be laid upon the whirling- board
of the machine, To that their centers may coin-
cide ; if then the board be turned ever it) quick
by the winch, the demi- globe will remain where
it was placed. But if the wire C be fcrewed into
the demi-globe at d, the whole becomes one
body, whofe center of gravity is now at or near
d. Let the pin 6 be fixed in the center of the
whirling-board, and the deep grOOV‘e 5 cut in the
flat fide of the demi—globe be put upon the pin,

fo as the pin may be 111 the center of A [See Fig Fig. 5-.

5 where this groove is reprefented at b] and let
the whirling-beard be tinned by the winch,-
which will carry the little ball B (Fig. 4. ) with

its Wire C, and the demi- globe .4, all round the -

Center-pin c z' , and then, the centrifugal force of
the little ball B, which weighs only" one ounce,-
will be To great, as to draw 01? the demi-globe‘
1 .4, which weighs two pounds, until the end of
the groove at e firikes againlt the pin c, and
f0 prevents the demi-glo‘be A from going any
farther: otherwife, the centringal force of B
would have been great enough to have carried
14 quite OFF the whiiiing-board. Which lhews,

"that if the fun were placed 1n the very center of.

the orbits of the planets, it could not pofiibly
remain there, for the centrifugal forces of the
planets would carry them quite ofir and the fun

2 . _ with

38

Of central Forces.

iwiththem; efpecially when feveral 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 .fubfif’ts- between

them, as the bodies fland B are by, the wire C
which is fixed into themboth. And even if
there were but one fingle planet in the whole
heaventho goround ever f0 large a fun in the
center: of its orbit, its. centrifugal force would
foon carry ofiC both itfelfian‘d the fun, For, the

, greatefl: body placed in any part of free {pace

might be eafily moved ;, becaule if there were no
other body to attract it, it could have. no weight
or gravity of itfelf 3 and confequently,though it
could have no tendency of itfelf‘to remove from
that part of fpace, yet it"might be very eafily '
movedxby any, other fubf’tance. : ' 4.

, 10. As the centrifugal force of the lightbo'dy
B will not allow the heavy body A to remainin
the center of motion, even though it be 24-times
as heavy as B;- let us now take-rhéballflKFig.
6.) which weighs 6 ounces, ,. and conneétvit‘ by
the wire C with the ball B, ,whiehgweighs'only
one ounce; and. letthe fork E be fixed into the

center of the whirlingboardnthen ”hangzthe

balls upon the fork by the wirefiC in finch a man-
nerg, that they may exactly balance each other;
which, will be when the center of gravity between
themz in: the wire a’td, is fuppor’ted by thefqu.
And: this center of gravity is as much nearer to
the centeri-of—the ball 11, than to the center of the
ball 48, ‘as A is heavier than 8, allowing for the

,weight of the wire on each ,{ide of the“ fork.

This done, let the machine be put into motion
bythe winch; and the balls fland B will; go
round their common center of gravity d, keep-
ing their balance, becaufe either will not allow ‘
' 3 the

 

 

Of central Forces.

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 fide of the fork, the center
of gravity 4? would be h): times as far from the
center of the ball 8 as from that of the ball fl,
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 xi has: but then, as B is only one
ounce, and fl fix ounces, the whole centrifugal
force of A? will exactly balance the wholercentri-
fugal force of B :- and therefore, each body will
detain the other fo as to make it keep'in its
circle, This {hews that the fun and planets mui’t
, all move round the common center of gravity
of the whole fyfl‘em, in order to preferve that jufl:
balance which takes place among them. For,
the planets, being as unac‘tive and dead as the
above balls, they could no more have put them-
felves into motion than thefe balls can; nor have
kept in thein orbits without being balanced at ‘
firf’t with the greatefi degree of exaé‘tnefs Upon,
their common center of gravity, by the Almighty
hand.that made them and put them in‘motion. ‘
' Perhaps «it maybe here aiked, that fince the
center of gravity between thefe balls muI’t be
‘ fupported by the fork E' in this experiment,
‘10de prop it is that fupports the center of gra- ,
vity of the folar fyf’tem, and confequently bears
the weight of all the bodies in it; and by what
is the prop itfelf fupported P The anfwer is eafy
and plain; for the center of gravity of our balls
muf’t be fupported, becaufe they gravitate to- ,
wards the earth, and Would therefore fall to it:
but as the fun and planets gravitate only towards
D 3 ‘ One

'46-

Of sentral Hams,
one andther, they have'nothi'ngbelfe to fall to;

~and'therefore have no occalion for any thing’to

topper: their common c‘enter'of gravity : and if‘
they did not move 'roundthat center; and con'l‘e-g
quently acquire a tendency to fly off from it by! ‘-
their motions, their mutual attraét-ions would
foon bring them together; and fo the whole
would become one mafs 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 fim’s attraftion.

But after all this nice adjuf’tment; 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
imprefl:'- Upon them atfirft. For if he fhould

\ once leave them [0, their order would in time

come to an end; becaufe the planets mui’t ne-i
Cefl'arily dif’turb’ 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 attraél: the {Unmare
towardsthat quarter than when they are in a

A manner difperfed equably'around'him, if he was

not at th'at'time made to defcribe a'portion; of a

- larger circle round the common center of gravity;

the balance would then be immediately dc?
firoyed; and as it could never reitore itfelf again,i
the whole fyftem would begin to fall together;
and would in time unite in a mafs at-the fun-47
Of this diflurbance we have a very remarkable
inf’tance in the cometwhicli appeared lately; and
which, in going lai’t up before from the fun, went
{o’near to'Jupiter, jana was f0 afi'eéted by his,
attraction, as to have the figure ofi its orbit much
changed 5 and not only f0; but to have its period
’ ‘ ' f ' thatch;

 

 

 

Of central Forces. _' 2.1;

altered,'and its courfe‘to be difi’erent in the heaa
vens from what it was lal’t before. a
II. Take away the fork and balls from the Fig, 7.

whirling-board, and place the trough fl’B there-

on, fixing its center to the center of the whirl-
ing-board by. the pin H. In this trough are two
ballsD and E, of, unequal weights, connected

'by a wire f; and made. to flide ‘eafily Upon the
wire C firetched from end to end of the trough,

and made rat by nut-{crews on the outfide of the

‘ ends. Let thefe balls be fo placed upon the wire

C, that their common center of gravity g may be
directly over the center of the whirlingboarcl.
Then, turn the machine by the winch, ever fo
fwiftly, and the trough and balls will go round their
center of gravity, fo as neither of the balls will fly

off ; becaufe, on account of the equilibrium, each
ball detains the other with an equal force aéting
againl’t 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 morion; and then, upon
turning the machine, the little ball E will fly oil",
and {trike with a confiderable force againlt the
.end 1?, and draw the great ball 8 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 oh",

and l’trike violently againfl: the end B of the
trough, and will bring thelittle ball E into the
middle of it. If the trough be not made very
flrong, the ball D will break through it. ,

12. The reafon why the tides rife at the fame Of the
abfolutc time on Oppofite fides of the earth, and tides.
' ‘ D 4, confequcntly . 4.

J

4%

Figs. 9:

9

Of the Tides,

eonfequently in oppofite direétions, is' made
abundantlytplain by a new experiment on the
whirling-table. The caufe of their tiling on the fide
next the moon every one underfiands to be owing
to the moon’s attraction: but why they '{hould
rife on the oppofite fide at the fame time, where
thereis no moon to attract them, is perhaps not
f0 generally underfi‘ood. For it would feem
that the moon {hould rather draw the waters (as
it were) clofer to that fide, than raife them upon
it, directly contrary to her attractive force. Let
the circle Iaécdlreprefent the earth, with its fide
6 turned toward the moon, which will then at?
traé‘t the waters f0, as to raife them from c to g.
But the quefiion is, why fhould they rife as high

,at that very time on the oppofite fide, from a to

a? .In order to explain this, let there be a plate
#8 fixed upon one end of the flat bar D C; with
fuch a circle drawn upon it as aécd (in Fig. 8.)
to reprefent the round figure of the earth and
fea; and fuch an ellipfis as efg/o to reprefent the
fwelling of the tide at e and g, occafioned by the
influence of the moon. Over this plate .48 let
the three ivory balls e,f, g, be hung by the filk
lines la, 2', la, fafiened to the taps of the crooked -
wires H, 1, K, in fuch a manner, that the ball "at
.3 may hang freely over the fide'of the, circle 6,
which is farthefi from the moon M (at the Other
end of the bar); the ball at f may hangtfreely
Over the center, and the ball at g hang over the
fide of the circle g, which is nearel’t the moon.
The ballf may reprefent the center of the earth,
the ball g fome water on the lide next the moon,
and the ball 6 fome water] on the oppofite fide.
On'the back of the moon M is fixt the lhort bar
Nparallel to the horizon, and there are three

.lioles in it above the little weights 1), q, r. A

fills

 

Of the Tider.
[ilk thread .0 is tied to‘the‘line k clofe above the

ball g, and pafling 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 72131.

tiedU to the line 2', clofe above the ball f, and
palfing through the center of the moon M and
middle of the bar N, has the weight g hung to
it, which 15 lighter than the weightp. A third
thread m is tied to the line la, clole above the ball

12, and pafiing by the other tide of the moon M, ‘

through the bar N, has the weight r hung to it,
which 18 lighter than the weight g.

The ufe of thefe three unequal weights is to
reprefent the moon’s unequal attraction at diFfe—
rent dil’tances from her. With whatever force
{he attracts the center of the earth, {he attracts

- the lide nexc her with a greater degree of three, '

and the fide farthefi from her with a lefs. So,
- if the weights are left at liberty, they willdraw
all the three balls towards the moon with diffe-
rent degrees of force, and caufe them to make

43‘

the appearance lhewn 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 19,2, k, becaufe the lines would then hang
perpendicularly. This mews, that as the moon
attracts the fide of the earth which 13 nearefl: her
' with a greater degree of force than {he does the
center of the earth, {he will draw the water on
that rfide more than {he draws the center, and f0
caufe it to rife on that fide: and as lhe draws the
center more than {he draws the oppolite fide,
the center will recede farther from the {urface of
the water on that oppofite tide, and [0 leave it as
high there as {he raifed it on the fide next to her.

F or, as the center will be in the middle between

the t

4““

Of the Tides. *

the tops of the oppofite elevations,’ they mutt of
courfe be equally high on both {ides at the fame

. time.

But upon this fuppofition the earth and moon

would foon come together: and to be fore they
would, if they had not a motion round their
common center of gravity, to create a degree of

, centrifugal force fuflicient to balance their mur

tual attraction. , This motion. they have ; for as
the moon goes round her orbit every month, at
the difiance of 240000 miles from the earth’s
center, and of ~2 34000 miles from the center of
gravity of the earth and moon, fo does the earth
go round the fame center of gravityevery month
at the dil’tance 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 di.a—‘
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 itsfarther fide from
the moon 10000. Therefore the centrifugal
forces of thefe parts are as 2000, 6000, and,
10000 5 that is, the centrifugal force of any lidc
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-
pref’t by the number 6000) at the earth’s-center
keeps the earth from flying out of this monthly
circle, it mull be greater than the centrifugal
force of the waters on the fide next her; and

‘confequently, her greater degree of attraction on

that fide isfuflicient to raife them; but as her
attraction on the oppofite fide islefs than. the
centrifugal force of the water there, the excefs.
of this force is fufiicient to raife the water’jult as

high

The Earth’s Motion demonfimted. 454
high on the oppofite tide—To prove this, expe—
rimentally,- let the bar D C with its furniture be Fig. 9.
' fixed upon the whirlingrboard of the machine
(Fig. 1.). by pulhing 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 6, f, g,
and moon M. Now/if the whirling—board and
bar be turned {lowly round'by the winch, until
the ball f hangs over the center of the circle, as.
in Fig. I 1. the ballg will be kept towards the
moon by the heaviefl: Weight p, (Fig. 9.) and
the ball .9, on account of its greater centrifugal
'force, and the lelfer weight r, will fly off as far '

«to the other fide, as in Fig. 1 I. And fo,‘whilfl;
the machine is kept turning, the balls 8 andg
will hang over the ends of the elliplis~ If k. So
that the centrifugal force of the ball 6 will ex-
ceed the moon’s, attraé‘tion jull as much as her
attraction exceeds the centrifugal force of the
ball g, whill’t her attraction jufi balances the cen- ‘
'trifugal force of the ball f, and makes'it keep
in its circle. And hence it is evident that the
tides muft rife to equal heights at the fame time
on Oppofite {ides of the earth; This experi-
ment, to the belt of my knowledge, is entirely
new. . -
From the principles thus; el’tablifhed, it is The
evident that the earth moves round the fun, and can?“
not the fun round the earth : for the centrifugal 23:13):
law will never allow at great body to move round mated:
a fmall one in any orbit whatever; efpeCially‘ ‘ i
when we find that if a fmall body moves round
a great one; the great one mull alfo move round
the common center of gravity between them ‘two.
And it is wellknown that the quantity of matter»
in the fun is 227000 times as great as the quan—
ttty of matter in‘ the earth... Now. as the fun’s

' i i A ~dil’cance

4.5

Fig. 12.

Tire Earl/5’: Motion “demon/1372121. '1 ‘
dil’tance from the earth is- at halt/81,000,000 of’
miles, if we divide that diflante bye-227,900, we
{hall have only 357 for the number ofrnilfi that
the center of gravity between the fun andvearth
is difiant from the fun’s center. And as the
fun’s femidiameter is 7} of a degree, which, at fo
great aidif’tance as that of the fun, muf’t be no
lefs than 381500 miles, if this be divided by
357, the quotient will be 1068;, which ‘lhews
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 hiscenter toward his furface. - I '

All globular bodies, whofe parts can yield,
and which do nOt turn on their axes, mui’t be
perfeét fpheres, becaufe all' parts of their furfaces
are equally attracted toward their centers. But
all fuch globeswhich do turn on their axes will
be oblate fpheroids; 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 quickel’t, they mul’c
have the greatefl: centrifugal force; and will
therefore recede 'farthefi from the axis of mo-
tion. Thus, if two circular h00ps [113’ and
CD, made‘thin and flexible, and crofiing one
another at “right angles, be turned reund their
axis EF by means ofthe winch m, the wheel n, 7
and pinion o, and the axis be loofe in the pole
or interfeflion'e, the middle parts .4, B, C, ,D
will fwell outf‘fo as to' firike againl‘t the fides of
the frame at 'Fand G, if the pole e, in finking
to'the pin E, 'jbe'not f’topt by it from linking.
farther : To that the whole will appear of an oval
figure, the 'equatoreal diameter being confide-r
rably-lohger than the polar. That our earth is
of this figure, is demonfirable from aé‘tual mea-

~ {uremcnt

Of Ibex mechanical Powers.
furement of ferric degrees on its furface,‘ which
are found to be longer, in the frigid zones than
in the torrid : and the diEe'rence .is found to be’
fuch as proves the, earth’s equatoreal diameter
to be 36 miles longerthan its axis.—+Seeing then,
the earth is higherirat the equator than at the
poles, the fea, which like all other fluids natu-
rally runs downward? (or towards the places
which are nearei’t the earth’s center) would run
towards the polar-regions, and leave the equato-
real; parts. dry,.if ,the‘ “centrifugal force of the
water, .' whichlcarriedlitt to thofe, parts, and 'fo
raifedthem, did not -_ detain andk'eep‘ it frbm
running back, again towards the polesof the
earth, 4; , ,

J”...

LE TC T; in

Of the met/ganical Pertinent“. .

47?

, F-we confider bodies in motion, and com-iThc

\ pare them together, we may do thisteither
with refpeit to the quantities of matter they
contain, or the, velocities with which theyare
moved. The heavier any body is, the greater
is the power required either to move it or to {top

its motion : and again, the fwifter it moves, the.

greater is its force. 50 that the, whole momen-

founda‘

tion of
a1 me-

chanics. _

mm or'quantity-of force of a moving, body is the ' ‘

refult of its quantity of matter multipliedlby the
velocity with which it is moved. And when the
yprodufis arifing from _ the multiplication of the
particular quantities of matter in any tWobodies
by their refpeét-ive velocities are equal, the mo-
menta or entire forces are fo too. Thus, {up-
pofe a body, which we {hall call A, to weigh 40
“ pounds, and to move at the rate of Mo miles
. m

 

48 Of the mechanical Poweri‘;

in a minute; and another body, which We {hall
call B, to weigh only four pounds, and to move
20 miles in a minute; the entire forces with
which thefe two bodies wduld {trike againi’t any ‘
obfiaele would be equal to each'other, and there-
fore it would require eqUal powers to flop 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 eafy principle depends the-whole
of ‘ mechanics: j and it hOIds ‘univerfally true,
that when two bodies are fufpend‘ed on any
machine, f0 asto a& contrary to each other; if
the machine be put into motion, and the'per-
pendicular afcent of ~one body multiplied into
its weight, be equal to the perpendicular defcent
of the other body multiplied into its weight,
thefe bodies, how unequal foever in their weights,
" will balanceone another in all fituations: for,
as thewhole afcent of one is performed in the
‘fame time with the whole defcent of the other,
. their refpeétive velocities-mull: be directly as the
{paces they mOVe through 3 _ and the extefs of
. weight in one body is compenfated by the :eTXcelis
How to of velocity in the omen—Upon this principle it
compute is eafy to compute the powero-f any mechanical
$6 POW" engine, whether fimple or compound; for iris ‘
meg?“ but only finding how much fwifter the power ’
cal en- moves than the weight does (2'. 6. how much far-
Sine. ther in the fame time) and jufl: fo much' is the
’ ‘ power increafed by the help of the engine. ‘
In the theory of this fcience, we fuppofe all
planes perfectly even, all bodies perfectly fmooth, 7
levers to have no weight, cords to be extremely
\ pliable, machines to have no friction, and in
fhort, all imperfections mull: be fet afide ungil
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Of the mechanical Powers: \ 49
the theory be el’cab’lilhed; and then, proper ‘
alloWances are to-‘be- made. \ . ,

The fimple mac/nines, ufually called mechanical The .me-
poweri‘; are_fix in number, viz. the lever, the “ham
wheel and axle, the pulley, the inclined plane, the m?“
wedge, and the ferew.—-—They are called mechaj. '
nical powers, becaufe they help us mechanically to ’
raife weights, move heavy bodies, and overcome
refifiances, which we could not effect without
them. ’ _ ' >

1,. A lever is a bar of iron or W00d',90ne part‘The lg.
of which being fupported by {a prop, all the we.
other parts turn upon that prop as their Center. .
of morion: and the velocity of every part or ,
point is directly as its diflzance from the prop.
Therefore, when the weight to be'raifed at one
end is to the power applied at" the other to raife
it, as the diftance of the power from the prep
is to the dillance of the weight from the prop,
the power and weight .will exaétly balance or
counterpoife each other: [and as a common lever
has next to no friction omits prop, a 'very
little additional power will be fufficient to raife
the weight. ‘ l V ‘ ‘ - ’

There are four kinds of levers. V1. The
common fort, where the prop is placed between}
the weight and the poWer; but much nearer to i
the weight’ than to the power. 2. When the
prep 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 firl’t fort, but not .in property. Thofe of—the
firf’t and fecond kindvare often ‘ufed in mechani-~
cal engines; bur there are few infiances in which
the third fort is u'fejd. ‘ ~ ‘ '

i ~ w i - A [0771:

The 6a-
lance.

Plate V.
Fig. 1.
The firfl;
kind of
lever.

Of the mechanical Powers.

A common balance is by Tome reckoned a lever
of the firlt'kind; but as both its ends are at
equal 'dil’tances frOm its center of mOtion, they
move with equal velocities; and therefdre, as.
it gives no mechanical advantage, it cannot pro-
perly be reckoned among the mechanical powers.

A lever of the firfi kind is“ repréfented by the
bar d B C, fupported by the prop” D. Its prin--
cipal ufe is to 100an large {tones in the ground,
or raife great weightsto {mall heights, in order
to have ropes put under them for railing them
higher by other machines. The parts 118 and
B C, on different [ides ot‘the prop D, are called
the arms of the lever: the end 11 of the fhorter
arm AB being applied to the weight intended
to be raifed, or to the refil’tance to be overcome;
and the power applied to the end C of the longer
arm B C.

In making experiments with this machine, the i

/ fhorter arm A B mul’t be as much thicker than

the longer arm B C, as will; be fulficient to ba-
lance it on the prop. This fuppofed, let P re-
prefent a power, whofe gravity, is equal to I
ounce, and W a weight, whole gravity is equal
to IZi'OunCCS. , Then, if the power be 12 times
as far from the prop as the weight is, they will
exactlyicounterpoife; and a fmall addition to
the power P will caufe it to defcend, and mile
the weight W, and the velocity with which the
power defcends will be to the velocity with
which the weight y‘ri‘fes, as 12 to I : that is,
directly as their i‘dil’tan‘ce's'lfrom the prop; and
confequently’, as th‘efpac’es through which they.
move. ‘Hence, it is plain that a man, who by
his natural firength, Without the help of any

‘ machine, could fupport an hundred weight,.w'ill

by the help of this lever be enabled to fupport
twelve

 

1')

Of the mechanital Powers; ’

tWelv‘e 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
raifed to a proportionably greater] height. For

univerfally, if the intenfity of the weight mul. .

tiplied into its diflance from the prop be equal
to the intenfity of the power multiplied into its
difiance from the prop, the power and weight

will exactly balance each other; and alittle ad—,

dition to-the power will mile the weight. Thus,
in the prefent inflame, the weight W is 12
ounces, and its dil’tance from the prop is 1 inch;
and 12 multiplied by 1 is 12; the pOWer P is
equal to 1 ounce, and its diltance from the prop
is 12 inches, which multiplied by I is 12 again;
and therefore there is an equilibrium. between
them. So, if a power equal to 2 ounces 'be ap-
plied at the dif’tance of 6 inches from the prop,
it will jufl: balance the weight W; for 6 multi-
plied by 2 is 12, as before. And a power equal
to 3 ounces placed at 4 inches difiance from the
prop would be the fame; for 3 times 4 is 12;
and fo on, in pmportion. ‘

.51:

The flatem or Roman fleebzzrd is a lever of The fee).

this kind, and is ufed for finding the weights 0014M

difi’erent bodies by one lingle weight placed at
different dil’cances from the prop or center of
morion D, For, if a fcale hangs at A, the ex-
tremity of the ihorter arm AB, 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 11 B,
the fingle weight P (which We may fuppofe to
be I pound) will ferve for weighing any thing
as heavy as itfelf, or as many times heavier as
there are divilions in the arm B C, or any quan:
tity between its own weight and that quantity.

As

.52.

The fe-

Of. the" mechanical Powers;

As for example; if P be I pound, and placed
at the Brit divifion I in the arm BC, sit’will
balance I pound in the fcale 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 ft) on to the end of the arm BC.
If each of thefe integral div‘ifio'n‘s be fiibdivided
into as many equal 'parts‘as a oun'd contains
ounces, and the weight P be placed ,at anyvof
thefe fubdivifions, fo as to counterpoife-Whatvis
in thefcale, the pounds and odd-ounces therein

are by that means afcertained. . i
A To this kind of lever may be reduced feveral
forts of. infiruments, fuch as fciffars, pinchers,
{nu-Hers; 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;
whichgainsgreat advantage, becaufe it adds f0

, mttchito the power.»

A lever of the fecon‘d-‘kind has theweight I

cond kind‘betweenxthe prop and the power] In this, as

of lever.

Fig. 2.

well as the former, the adVantage gained is as

the..dii’tance of the power from the prop to the
difiance of the weight from the prop: for the
refpec‘tive velocities of the power and weight are
in that'proportion {and they will balance each
other when .-:the intenfity of the‘powe‘r multi-
plied by its diftance from the prep is equal to '
the intenfity of the weight "multiplied by its dif-
tance from the prop; Thus, if .48 be a lever’
on which the weight W of 6 ounces hangs at'the
dill‘ance of I inch from the prop G, and a power
P equal to "the weight of I Ounce hangs at” the
end B, 6 inches from' the prop, by the cord
: I ' C

 

.Of the mechanical Power's: ‘ i '53

CD going 'over the fixed pulley E, the, power
will jul‘c fupport the weight: and a finall ad-
dition to the power Will facile the weight, 1 inch
for every 6 inches that the power delcends.

This lever fhews the reafon why two men
carrying a burden upon a {tick between them,
bear unequal {hares of the burden in the in-
verfe proportion of thei1 di fianees from it. For
it‘is well known, that thenearer any of them is
to the burden, the greater lhare he. bearsof it:
and‘ if ,he‘ goes directly under it, he; bears
the whole.~ So, if one man be at G, and the
1 1 Other at P, having the pole or flick flBHrefi—ing
on their fl10ulders; if the burden or weight W
be placed five times as neardthe man 336,535 it
is to the man at P, the ”former will bear five
times as much'weight as the latter. This is
likewife applicable to the cafe of. two _ horfes of
unequal firength, to be {0 yoked, as that each
_gh01fe may draw a part proportionable to his
firength, which 15 done by fo dividing the beam
they pull, that the point of traétiono may be as
muchnearergto the {tronger horfe than to the
weaker, as the l’trength of the former exceeds
that of the latter.

To this kind of leVer may be reduced oars,
rudders of lhips, doors turning upon hinges,
cutting—knives which are fixed at the point of
the blade, and the like.

If in this lever We fuppol'e the power and Thethird
weight to change places, lo that the power may kind of
be between the weight and the prop, it will be- 15V“-
come a lever of the third kind . in which, that
there may be a balance between the power and
the weight, the intenfity of the power mul’t ex-
ceed the intenfity of the weight, iul’t as much'
as the difiance of the weight from the pop ex-

E2 ceeds

'54

Fig. 3.

The,

fourt

A x a Of zbéflmecbaniml Powerr.‘

ceeds the difiance-of the power from it. Thus,
let Else~ the prop of the lever A B, 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 mui’t 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 whenwe lift a
weight by the hand, the mufcle that exerts its

‘ffOI'CC to raife that weight, is fixed to the bone

about one tenth partgasafar below, the elbow as
the hand is. And the elbow being the center
'rorind which the lower part of the arm turns,
the mufcle muf’t therefore exert a farce, ten times
as great as the weight that is raifed.

As this kind of lever is a ,difad‘vantage to the
moving power, it is never .ufed but in cafes of”
inecefiity gsfuch as that of a ladder,- which being

ufixed at one end, is by the firength of a man’s

arm-s reared» againfi a wall. Andin’ clock—work,
where all the wheels may be reckoned levers of
this kind, becaufe.,the power that moves every
wheel, except the.firf’t,7afis Upon it near the

» center-30f motion by means of a {mall pinion,

and, the refillance it hasto overcome,'a€ts againl’t
the‘tpeethj round its circumference.

‘The'fourth kind of lever,diEers nothing from
the firft, but in being bendedi'for the fake of

kind of convenience. 11C B is a leverigf this fort, bended

lever.

Fig. 4.

at C, which is its prop, or ”center of motion.
P is a power, afiing upon: the longer arm A‘C at

- F, by means of, the cord DE going over the

pulley G ; andW is a weight or refif’tanee acting
upon the end B of the {homer arm B C. If the
power be to the weight, as CB is to CF, they
are in egui/iérie. Thus, fuppofe W to be 5
, m / pounds

 

 

Of tire mechanical Palm's; ' 55

pounds acting at the dii’ca’nce of one fact from
the center of motion C, and P to be I paund
aéling at F, five feet from the center C, the
power and weight will juit balance’Each other.
A hammer drawing a nail is-a levéarigof this
fort. ' . '

2. ‘The fecond mechanical power is the pulsed The
and axle, in which the power is applied to the W533] “”47
circumference of the wheel, and the weight is “H'
praifed by a rope which coils about the axle as the

wheel is turned round. Here it is plain. that
the velocity-of the poWer’mult 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 weightwill balance each
other, when the intenfity of the power is to the
intenfity of the weight, asthe circumference of
the axle is to the circumference of the wheel.
Let flB‘ be a wheel, GD its axle, and fuppofe 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 I 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 frie-
tion on the pivots or gudgeons of the axle is
but fmall, a fmall addition to the power will
caufe it to defcend, and raife 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‘f _ace,7‘i‘n the fame time. If the
wheel be pulled fauna by the handles S, S, the _
power will be increafed in proportion to their
length. And by thisi'imeans, any weight may
be raifed as high as the operator pleafes.

~ , E. 3 ‘ T o

56

Of the mechanical Powers;

‘ ",To this fort of engine belong all cranes for
raifing great weights; and in this cafe, the
wheel may have cogs all round it infiead of han- ,
dles, and a {mall 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 Cf thewinch
exceed thole of the axle D, when multiplied
by the excefs of the length of the winch‘above
the length of the femidiameter of the axle,
added to the femidiameter or half thicknefs 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, f0
that the weight W will hang at 6 inchesper— '
pendicular .dil’tance frombelow the center of
the axle. Now, let. us fuppofe the wheel 148,
which is fixt on the axle, to have 80 cogs, and
toibe‘ turned by means of a winch fix inches
long,_. fixton the axis of a trundle of 8 {taves or
rounds, working in the cogs of the Wheel.——-
Here it is plain, that the. winch and trundle.
would make IO revolutions for one of the wheel
:A’B,-and'fits axis D, on which therope K winds
in i-raifing theiweight W; and the winch being-
no longer than thefum of the femidiameters of
the great axle, and rope, the trundle could have,
nomore power on the wheel, than a man could.
have by pulling it round by the edge, becaufe
the winch would haveno greater velocity" than
the. edge of the wheel has, which we here fup-
pofe to be ,tenitimes as great as; the velocity of
the. tiling weight: f0 that, in this cafe, the
p wer gained would be gastto to I. But if the
leigth of the winch be 12 inches, the power

- gained

 

Of the. mama; Powers.

gained will be as 20 to I: if .18 inches (which
is long enough for any man to work by) the,

power gained would be as 30 to I ; that is, a
man, could raife 30 times as much by fuch an
engine, as he could do by his natural firength
Without it, becaufe the velocity of the handle of
the winch would be 30 times as great as the ve-

locity of the tiling weight; the ahfolute force»

of any engine being in proportion of the velocity
'of‘the power to the velocity of the weight railed
by it.—-—But then, juft as much power or advan-
tage as is gained by the engine, f0 much timeis
loll in working it. In this fort of machines it is
requifite to have a ratchet-wheelG 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 workman (bould,
through inadvertency or careleiln'efs, quit his hold
whillt the weight is railing, And by this means,
the danger is prevented which might otherwife
happen by the running down. of the weight
when left at liberty.

757

‘ 3. The third mechanical power or engine con- The Pu!"

lifts either of one mooeable pulley, or a fyflem Qflqy.

pulleys; fome in a block or cafe which is fixed,

andgothers in a block which is moveable, and-

rifes with the Weight. For though a fingle
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, whole arms are of equal length and

weight. *Thus, if the equal weights W and P Fig. 6,

hang by the cord BB upon the pulley A, whole
block 12 is fixed to the beam [-1 I, they will coun-
terpoife each other, jufi: 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 htmg upon the hooks fixt in the pulley at
A? and fl, equally difiant from its center. '
But if a weight W hangs at the lower end of
the moveable block 1) of the pulley D, and the
cord GF 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,
fufiains one half of the weight: and if the cord
at F be drawn up f0 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 intenfity is equal to one
half of the weight will be able to fupport it
becaufe if the power moves (by means of a {mall
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 theipower, without givino any
advantage to it) and hanging on the weight P,
which is equal only to one half of the weight W;
in which cafe there will be an equilibrium, and a
little addition to P will caufe it to defcend, and
rai-fe W through a fpace 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 undermofi:
block. So that, when the upper or fixt block
u contains two pulleys, which only turn on their
axes, and the lower or moveable, b10ck U con-
tains two pulleys, which not only turn upon their

axes, but alfo rife with the block and‘weight;
[the advantage gained by this is as 4 to the

working.

 

 

 

PLATE VI.

   

_.‘. g - : ‘ _‘-— g

1..“
iIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIII.

 

 

 

 

 

 

Of the mechanical Powers}~

working power. Thus, if one end of the rcpe
KMO Qbe fixed to a hook at I, and the rope
palTes 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 if, this weight
will balance and fupport a weight W of four
pounds hanging by a hook at the moveablc
block U, allowing the faid block as a part of the
Weight. And if as much more power be added,

as is fuflicient to overcome the friction of thc‘

pulleys, the power will defcend with font times
as much velocity as the weight tiles, and confe-
quently through four times as much fpace.

The two pulleys in the fixed block X, and
the two in the moveable block 2”, are in the
fame cafe with thofe lal’t mentioned; and theft:

in the lower block give the fame advantage to 7

the power.

As a fyfiem of pulleys has no great weight,
and lies in a fmall compafs, it is eafily carried
about; and can be applied, in a great many
cafes, for railing weights, where other engines
cannot. But they have a great deal of friction
on three accounts : x. Becaufe the diameters of

their axes bear a very confiderable proportion to,

their own diameters ; 2. Beca’ufe in working
they are apt to rub againl’t one another, or againfl:
the fides of the block -, 3. Becaufe of the fiiffnefs
of the rope that goes over and under them.

'59“- 4.

4. The fourth‘mechanical power is the in- The fire

clinedplane; and the advantage gained by it is (lined
as great'as ltS length exceeds its perpendicular-1’1“”?!

height. Let A B be a plane parallel to the hori- Plate VI.
zon, and C D a plane inclined to it ; and fuppofe Fig. I.

the whole length C D to be three times as great

as the perpendicular height G f F: in this cafe,

the cylinder .5 will be fupported upon the plane
. ,. C

z

60

Fig. 2.

Fig. 3.

Fig. 4.

\

Of the mechanical? Powerfl

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 fufiicient 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 l’uflicient; and f0 on, in pro-
portion. Or, if a pillar was to be raifed from a
floor to the height G F, by means of the machine
AB’D C, (which would then act as a half wedge,
where the refifiance gives way only on one fide)
the machine and pillar would be in cgm’lz'érz'o when:
the power applied at G F was to the weight of
the pillar, as G F to CD; and if the power be
increafed, fo as to overcome the friétion of the

.‘ machine againl’t the floor and pillar, the machine

will be driven, and the pillar raifed: and when
the machine has moved its whole length upon.
the floor, the pillar will be raifed 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 0
will keep, at tell: upon any part of the plane
where it is laid. If the plane be foelevated,
that its perpendicular height D is equal to half

‘ its length .4 B, the cylinder will roll down upon.

the planewith a force equal to half its weight ;\
for it would require a power (acting in the di-
rection Of .4 8) equal to half its weight, to keep
it from rolling. if the plane .48 be elevated,
fo as to be perpendicular to the horizon, the cy—
linder C. will defcend with its whole force. of

. . gravrty,

, 0f I796 mechanical, Powers; ' ‘ 6i

gravity, becaufe the plane contributes nothing
to its l‘upport or hindrance ; and therefore, it
would require a power equal to its whole weight
to keep it from defcending. 7
Let the cylinder C be made to turn upon Fig. 5.
flender piv0ts 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. , 1f the weight
of the body I, 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 jul’t fupport the cylinder
upon the plane, and a fmall touch of a finger
will either caufe it to afcend or defcend with.
‘ equal eale : then, ifa 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 Al to B, it will rife through the
whole height of the plane ML; and the weight
will defcend from H to K, through a fpace equal
to the whole length of the plane 178.
If the machine be made to move upon rollers
or friction-wheels, and the cylinder be fupported
upon the plane C B by a line G parallel to the, .
plane, a power fomewhat lefs than that which
drew the cylinder up therplane will draw the
plane under the cylinder, provided the pivots of \
the-axesof the friétion-wheels be fmall, and the
wheels themfelves be pretty large. For, let the ~ ,
machine 148 C (equal in length and height to Fig. 6.
fl 48 Ill, Fig. 5.) move upon four wheels,
whereof two appear at Dand E, and the third
tinder C, whilfi 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
CB, and the line G be extended from the frame
of the cylinder, about llX‘ feet parallel to the
i ' plane

6.1

The

wedge;

fig. 8.

I ’.Fig. 9.

Of #36 mechanical 13mm.- ‘

plane C B; and, in that direction, fixed to a hook
in the wall, which will fupport the cylinder, and.
keep it from rolling oi? the plane. Let one end
or the lint H be tied to a hook at C 1n the ma-
chine, and the other rnd to a weight K, lome-
what lefs than that which drew the cylinder up
the plane before. If this line he 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 C B, the
the cylinder will be raifed to d, equal to the per-f
pendicular height .48 above the horizontal part
at .4. The reafon why the machine mul’t be

~ drawn further than the whole length GB is, be-

caufe the weight F rifes perpendicular to C B.

To the inclined plane may be reduced all
hatchets, chifels, and other edge- tools which
are chamfered only on one fide.

5. T he fifth mechanical power or machine 1s
the wedge, which may be confidered as two
equally inclined planes DEF and C EF, joined
tagether at their bafes eE F0 : then DC is the
whole thicknefs of the wedge at its back ABCD,
where the power is applied: E F is the depth or
heighth of the wedge: DF the length of one of
its fides, equal to C F the length:3 of the other
fide, and O F is its {harp edge, which Is entered
into the wood intended to be fplit by the force
of a hammer or mallet firiking perpendicularly
on its back. Thus, A85 is a wedge driven
into the cleft C D E of the wood F G.

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 refiitance of the wood act-

ing againl’t the two fides of the wedge when the

power is to the refifiance, as half the thicknefz‘ A
o

 

Of the mechanical Powers.”

of the wedge at its back is to the length'of either
of its (ides; becaufe the refifiance then acts per-

pendicular to the {ides of the wedge. But, when,

the reliflzance on each fide aé‘ts parallel to the
back, the power that balances the refil’tanCes 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 difiance before
the wedge (as it generally does) the power im-
‘ pelling the wedge will not be to the refil’tance 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 thecleft, efiimated 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 refif’tance,
as half the length ofthe back of the wedge is to
the length of either of its fides : or, which
amounts to the fame thing, as the whole length
of the back is to the length of 'both thefides.

In order to prove what! is here advanced con-
cerning thewedge, 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 ab c, may be made ufe of as aFi‘g'. 7.

half wedge for feparjating the moulding c d from
the wainfCot A B. It is evident, that when this
half wedge has been driven its whole length vac
between the wainfcot and moulding, its fide as
will be at ed; and the: moulding will be fepa‘
‘rated to f g from the wainfcot. 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 refi-{t- ,
ance of the moulding, the former mutt be to the ~

3 latter,

Fig. 10.

Of we mac/mm; Pom: .

latter, as 45 to at; that is, as the thicknefs ofthe
back which receives the firoke is to the length
of the fide. againi’t which the moulding aets.
Therefore, fince the power upon the half wedge
is, to therefifiance againf’t its fide; as the half,
back a 5 is to the whole fide a c, it is plain, that
the power upon which the whole wedge (where
the whdle back is double the half back) muff be
to the refittance againl’t both its fides, as the
thicknefs 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 fplits at any dif’tance before the ,
wedge. F or, when the wedge is drivenquite

into the wood, and the wood fplits. at ever ‘fo

finall a dii‘tance before its edge, the top of the

,l-wedge, then becomes the acting part, becaUFC-the

Wood does nor touch it any where elfe. And
fince the bottom of the cleft mufl: be con’fidered
ashthatlpart where the whole fiickage or refif’tance

,is accumulated, it is plain, from the nature of

the lever, that the farther the power acts from
therefifiance, the greater is the'advantage.
Some writers have advanced, that the power
of the wedge is to the refiitance to be overcome,
as the thiCknefs of the back of the wedgefis to

the length only of one of its {ides ;, which feems

very flrang'e- : for, if we fuppofe‘ A B to be a
firong inflexible bar of wood or iron fixt into the °
ground at C B,iand D and E to be two blocks of
marble lying on the ground on oppofite {ides of

.the bar; it is evident that the block D may be
,feparated from the bar to the difiance d, equal to

a (5, by driving the inclined plane or half [wedge
a b a down between them; and , the block E may
be feparated to an‘equal difiance on; the other
fide, in like manner, by. the half wedge céo.

- th

Of the" mtc/mm'cal Powérr.‘

But the poWer impelling each'half‘ wedge will'be
to the refiflance of the'block againltrits fide,uas
the thicknefs of that half wedge is to‘ its perpen-
dicular height, becaufe- the block will be driven
off perpendicular to the fide of: the bar .43.
Therefore the power“ to drive both the half
wedges is to both the refiflances, as borh the
half backs is to the perpendicular heightof each
half wedge.- And if the bar be taken away, the

blocks. put clofe together,” and the two-half '

wedges joined to make one; itrwill require as
much force to drive it down between the blocks,
as is equal to the mm of the feparate‘ powers
acting upon the half wedges when the bar was
' betWeen‘them. - . ' .

1:63 i

To confirm this by an experiment, “let two Fig. 1:;

cylinders, as 1178 and C D, be drawntowards'one
' another by lines running over fixedpulleys, and
a weight of ,40 ounces hanging at the lines be-
longing to earth cylinder: and let a wedge of

4o~ounces weight, having its backjuf’t as-thiick as ‘

either of its {ides is long, be put between the
cylinders, which Will then act againl’t each fide
With a refillahce equal'to 40 ounces, whill’c its
owh Weight endeavours» to bring it down and
feparate‘ them. And' here, the power of the
Wedge’s gravity impelling it downward, will be
to the refiftance of both the cylinders againf’t the

wedge, as the thicknefs of-the wedge is to "double , ’
"its perpendicular height; for thereiwill then be .

an equilibrium between the weight of thewedge
and the refillance of the cylinders againf‘t it, and
1tw111 remain at any'height’ between them; re—.

quiring jul’t-as much power to pull: 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 theficylind-ers, it‘will
require twice as-much wei'gh'tto be hung at’the

ends

7, as

Fig. 119

Of the. mechanical Powers}

ends of the lines which draw them together, to
keep the wedge from going down between them.
That is, a wedge of 4.0 oun'Ces, whofe back is
only/equal to half its perpendicular height, will
require 80 ounces to each cylinder, to keep it in
an equilibrium bet-ween them : and tviice 80 is
160‘, equal to four times 40,. So that the power
will be always to the refifiance, as the thicknefs
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 belt way, though perhaps not the neatel’t,
that I know of, for making a~ wedge with its
appurtenances for fuch experiments, is as fol-
lows. Let IKL M 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 3 and let P be a graduated arch
of brafs, on which the faid pieces of wood may
be opened-to an y angle not more than 60 degrees,
and then fixt at the given angle by means of
the two {crews at and 5. Then, I K N 0 will
reprefent the back of the wedge, L M its {harp
edge which enters the wood, and the outfides of
the pieces IKLM and LMNO thb :tWo fides of
the wedge againf’t which the wood acts in cleav«
ing. By means of the {aid arch, the wedge may
be opened {0, as to adjul‘t the' thicknefs 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 itfelf, 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 pufh it down, or hung to its edge to
pull it d0w\n.—Let A B and C D be two wooden
cylinders, each about two inches thick, where

they

Of the mechanical Pawerr

they touch the outfides of the wedge , and let‘

their ends be made like two round flat plates, to
, keep the wedge from flipping oi? edgewife from
between them. Let a fmall cord with a loop on

one end of 1t, go over a pivot in the end of each '_
i « cylinder, and the cords S and T belonging to the-

cylinder/f B go over the fixt pulleys Wand X, and
be faf’tened at theii other ends to the bar to x, on
which any weight as Z may be hung at pleafure.

In like manner, let the cords Qand R belonging
to the cylinderB C go over the fixt pulleys VandU

to the bar 7211, on which a weight Tequal to Z may ‘

’ be hung. Thefe weights, by drawing the cylin~
ders towards one another, may be confidered as’
the refii’tance of the wood aélincr mequally againfl:
oppofite fides of the wedge , the cylinders theme
felves being fufpended near, and parallel to each
other, by the1r 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 flIOUQd never be lels than »

four feet eacli. The farther alfo the pulleys

V,Uand XJ/V are 150111 the cylinders, the truer 7 i '
will the experiments be: and they may turn

Upon pins fixed into the wall.

In this machine, the weights Yand Z, and the /

weight p, may be varied at p leafure, {o as to be
adjufied 1n pmpk'ortion at double the wedge’ 3 per-
'pendicular height t0 the thickness of its back:
and when they are f0 adjuiled, the wedge will be
in equiliéria With the rtfiil’ ance of the cylinders
The wedge is a veiy great mechanical power,
{ince not only wood but even rocks can be fpli t
by it- , which would be impohible to effect by the
lever, wheel and axle, or pulley: for the force

‘ ofthe blow, or firoke, {bakes the cohering parts, 1

and thereby makes them 1ep‘a1ate the more eafily.
v E “ ’ 6. The

6;:

68
The

' flaw.

Fig. 12,
13‘

Of the mechanical Powers;

6. The fixth and lafl: mechanical power is the
forew; which cannot properly be called a fimple
machine, becaufe it is never ufed witho'ut the
application of a lever or which to aflii’t in turn-

‘ ing it : and then it becomes a compoundengine

of a very great force either in prefiing the parts
of bodies clofe together: or in railing great
weights, It may bewiconceiived to be made by
cutting a piece of paper flBC (Fig. 12.) into
the form of an inclined plane or half wedge, and
then wrapping it round a cylinder A B (Fig. 13).
And here it is evident, that the winch E
muf’t turn the cylinder once round befdre the
weight of refifiance D can be "moved from one
fpiral winding to anOther, as from d to c : there--
fore, as much as the circumference-of a circle
defcribed by the handle of the winch‘is greater
than the interval ordif’tanCe between the fpirals, fo
much is the force of the fcre'w. Thus, fuppofing
the dif’cance between the fpirals to be half an inch,
and the length of the winch to be twelve inches 3
the circle defcribed by the handle of the winch
where the power acts will be 76 inches nearly, or
about I 52 halfinches, and confequently I 52 times
as great as the difiance between the fpirals : and
therefore a-power at the handle, whofe intenfity
is equal to no more than a fingle pound, will baa-
lance 152 pounds acting againi’t the {crew -, and
as much additional force, as is fufiicient to over-
come the friction, will raife 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 be made, and the nearer ‘
the fpirals are to one another, fo muth the
greater is the force'of the ferew. '

A machine for fhewing the force or power of
the {crew may be contrived in the following i

- manner.

 

PLAT E V11 .

d

'5

/

 

Of the mechaniml Powers, ‘ 69

manner. Let the wheel C have a fcrew a b on Fig. ,4.
its axis, working in the teeth of the wheel D,

which fuppofe to be 48 in number. It is plain,

that for every time the wheel C and fcrew a & aré’
turned round by the winch X, 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 d be equal to the circumference of a.
groove 6 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 6, and has a weight of 48 pounds hung,

to it bClOW‘thC pedel’tal 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, itiwill
balance a weight of 48 pounds hanging by the

line G; and a fmall addition to the weight H , ’1
will caufe it to defeend, and fo raife up the other ‘ -
weight.

If the line G, Ainfiead of going round the
groove 6 of the wheel D, goes round its axle I 5
the power of the machine will be as much in-
creafed, as the circumference of the groove e
exceeds the circumference of the axle: which,
fuppoling it to be fix times, then one pound at
1-] will balance 6 times 48, or 288 po‘unds'hung
‘ to the line on the axle : and hence the powerior
advantage of this machine will be as 288 to I.
That is to fay, a man,» who by his natural
firength‘ could lift an hundred weight, will be

" ° F 2 ' able

797‘ p . Of the. meebamk’el Powers. -

able to raife 288 hundred; or 14 78—6. ton weight ‘
by,this engine.
. But the following engine is/ {fill 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,
eaten if we take in the balance. For as the axis
PlateVlI- D of the bar/f8 is in its middle at C, it is~plain
f‘g' "i that if equal weights are fufpended upon any two
A combi pins equi- diltant from the axis C, they will couné
nation of terpoife each_other.———It becomes a lever by‘
21:33: hanging a {mall weight P upon the pin 21, and a
nical weightflas much heavier upon either of the pins
powers. 5», 5, die, or f, as is in proportion to the pins be-
ing {0 much nearer'.the axis. The wheel and
axle FG is evident; fois the {crewE which
takes in the inclined plane. and with it the half
wedge. Part of a cord goes roundthe axle, the
rel’t under the lower pulleysK, m, over the upper,
pulleys L, n, and then it is tied to a hook at m
in the lower oranoveable block,’ on which hangs
~the weightI/V. - \f p ’ .
, In this machine, if the wheel F has 30 teeth,~
“it will be turned once round in thirty revo-
lutions of the bar flB. which is fix: on the
axis D of the {crew E: if the length of the bar
is equal to twice the diameter of the wheel, the
pins a and 72' at the ends of‘the bar will move 60
times as fat”: as the teeth of the wheel do: and
confequently, one home at P‘will balancedo
ounces hung upon a tooth at q in the horizontal.
diameter of the wheel. Then, if the diameter ‘of
'the wheelf‘. is to times as great asthe diameter
of the axle G, the wheel will have 10, times the
velocizy of the axle; and therefore ene ounce PI
atthe end of the lever AC will balance to times
6001‘»- 600 ounces hung to the t0pe H which goes'
a? s 7 , _- round

\

 

Of Water-Mlz’r.- ’ 7;;
round‘the‘ axle. Lafilyi», if four pulleysbe added; ‘
they will make the velocity of the lower block
‘ K, and weight IV, four times lefs than the velof
city of the'axle': and this being the lal‘tepo‘wet
in the machine; which is four times as great. as
that gained by‘t‘hexiaxle, it makes the whole
poWer of the machine’q. times 600, or 2400,

' So that a man who could lift one hundred weight

in his arms by his natural firength, wouldbe
able to mile 2400, times as much by this CD?
gine.-+Bu~t .itiis here as: 'infall other mechanical
cafes -, for the time loft is always asmuch as the
power gained, becaufe the Vel-ocity‘with- which

the powerimoVes will ever exceed the velocity
with which the weight rifes,.as much as the in:
tenlity of the weight exceeds the intenfity "of the?
power. , , M, .. i ,

“ The frié‘tion‘of the {crew itfelf is very “confi-
dera-ble ; and there are” few compound 3enr-
gines, but what, upon account of the mam of '
the parts againft one another, will req.u\ire‘.a_t-hitd
part more~0f power to work lthem‘when loaded,
than what 'is »- Tufliciengt to; conri’t-itute ; agbalanee
betwee-nthe weight and the power. 3 7 t n

L. E c T. N.

Of mills, cranes, wheel-carriages, and the engine
~ V for driving piles. ‘

. AS thefe engines are f0 'univervfally/ ufefttl,
. it would be ridiculous to make any apo-
.10gy “for defcribing, them. ' ‘ . i. i * "
. I V in. a common brew-mill, where the fall of {.1335ng
water maybe about ten feet, 11/! is the grea't Fig. 2.
‘ wheel, which is generally about 17 or ~18 feet in A‘wm-
.. L 3 diameter, m mill.

.72..

0f" kaéflMlls.

V diameter, reckoned from the ’outerirhoft edge of

any float—board at a to that of its "Oppofite float at
5. To: this wheel the wateris conveyed through

' a channel, and by falling upon the wheel, turns

it round. ‘ ‘

0n the axis BB of this wheel,and within the
mill houfe, is a'wheel D, about 8 org feet dia-
meter, "having61 cogs, which turn a trundle E

ii containing ten upright/{taves or rounds; and
When thele are the number of bugs and rounds,

‘the‘tr'undle will makeng rev'olvutions for one
revolution of the wheel. ' ' r

" The trundle is fixt Upon a flrong iron axis
called the fpindle, the lower end of which turns in
a brafs foot, fixr at F, in the horizontal beam ST

' called the bridge~tree; and the uppertpa’rt of the

'fpindle turns in a wooden bufhfixt into the nether
millfione Which lies upon beams in the floor T2”.
The top part of the fpindle above the bulb is
fquat‘e, and goes into a fquare hole in a firong iron

' , "crofs 456d, (fee Fig. 3.) called the rynd; under
' which, and chic to the bufh, 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 millilone G_(Fig. 2.) and fo
turns it round in the fame time that the trundle E
is turned round by the cog-wheel D. This mill-

‘ {lone has a large hole quite through its middle, ,

called the, eye of the (tone, through which the
middle part of the rynd and upper end of the
fpindle may be feen ; whilfi the four ends’ of the
rynd lie hid below the {tone in their grooves.
The end Tof the bridge-tree TS (which {up-

ports theiupper millf’tone G upon the fpindle) is

)fixed into a’hole in the wall; and the end S is let

_" into abetting]; called the brayer, whofe end R

remaint

 

Of W were Mills.

remains, fixt,in la mortife: and its other end Q
hangs by. a ftrong iron rod P which goes through
the floor 2")”, and has a {crew-nut on its togat
O; by the turning of which nut, the end Q of
the brayer is raifed‘or depreffed at pleafure; and
confequently the bridge-tree ST S and! upper mill-
fione._ By this means, the upper millf’tone may ‘
be fet as clofe to the under one, or railed as high
from it, as the miller plealES. The hearer the
milll’tones are to one another, the finer they grind
the corn, and, the more remote from one anorher,

the ‘coarfer.

The upper miliPtone G --is inclofed in around
box H, whieh‘does not touch it any where ;- and
is about an inch dif’tant from its edge all arbupd.
On the top of this box {tands a frame for hold-
ing the hOpper kit, to which is hung the {hoe I

by two lines fafiened to the hind-part of it, fixed _

upon hooks in the hOpper, and by one'end-of
the crook~firingK fafiened to the fore- part of it

at i; the other end being twrfiedround thepiirt‘L. .
,As the pin is turned one way, the firing, draws

up the lime clofer to the hopper, and fo leITens
the aperture betWeen them; and as the pin is
turned the other way, it lets down the fhoe, and
enlarges theaperture. r '
If the time be draWn up quiteto the hopper,
no corn can fall from the hopper intothe mill ;
if itbe let a little down, fame, will fall: andzthe
quantity will be more or lefs, according as‘ the
ihoe‘is more or lefs let down. For the hopper is
open at bottom, and there is a hole in the boctom
of the fhoe, not direétly under. thebottom of the
hopper, but forwarder towards the end '2', 'over
themiddle of the eye of the millflOne. .
There is a fquare hole in the t0p of the fpindle,
in’ which is‘put the feeder e : this feeder (as the

F 4. ’ fpindle /

‘i 73

Fig. 3c

74;

heavy; milli’tone is but very-little more th‘mwhet;

Of: Waterq‘ler;

[pindle turns round). jogs the {bee threetimcs in
each revelation, and lb caufes the torn to run
confiantl-‘y down from therhopp’er th rough the (hoe,
into the eye of the mxilli’tone, where it falls Upoh
theitop of’the rynd, and is, by the "metion of the
ryntl, and the leather under it, thrown below the
upper- fione, and. ground between it‘fand “the '
loWer one. The violent motion Of the {tone
Creates a centrifugal force in the. corn going
round with it, by which means it gem farther and '
fartherfrom the center, asvin afipi'ral, in every
revoliition, until \it be thrown quite out,» and,“
being, then ground, it falls through a fpout M,
eallec} the mill-eye, into the trough N.

. ,VVh’en the mill is fed too faf’t, the? corn bears
up the fione, and is ground too 'coarfe; and be-
fides, it clings the mill {0 as to make it. go mo;
flow.“ When the mill is too {lowly fed, it goes
too fafi, and the [tones by their attrition are apt
to {trike fire againft one another, Both which
itigenveniencies are avoided by‘ turning the pin L

“ backWards or forwards, which draws up or let's

down ithe {11063 and In regulates the feeding as.
the, miller fees mnvenient. - , .

_The heavier‘the running'millftone is, and the
greater the‘ quantity of water that :falls. upon the

‘ wheel,rfo‘ much the fatter will the mill bear to be '

fed 5 and confequently f0 much the mone'it will
grind. And On the .contrary,.: the lighter the
ftone, and the let's the quantity of water, fomu’c’h
{lowermufi the feeding be. But when the fiche
is confiderably ~Wore,.,'and become light, the mill
nfiufibe fed {lowly at any rate -,, Otherwife the

/ fione will be too much borne up .by-the com

under it, which wileake the "meal cearfe." ,
The quantity ofepower required to turn a

1.5,

of anW-‘Mz‘lfk:
i‘s fumeii‘e'n‘t'td'tmn’a'light Chef fof' as it is Tu i
ported upon the fpindleby’ ‘th‘e‘ bridgmree ST,
and the end 6f the fpifid'l'emhat‘ ttti‘ns' ’ih‘th'e brafs’
foot therein being ‘but’ fmalhth‘efod‘ds‘ arifing
frOm the weight is but very in’c’bfihdetabie in: its
'aé’tieh agafih‘fi the power or Fore-e'bf the, Water,

And 'befidhs, a heaVy Pto‘he has the fame advan- '

tage as a heav‘y'fiy; namely, that it regulate‘s
themO-tibhF-‘much better than a light one. _ .
' In order to {cut and grind the com, bOth the
upper and under millfioneshav’e 'c‘ha‘nn'e'llsplr
furrows cert into them, proceedingobliqueig froth
the center tOWa‘frds’ the circumference. An‘ thefe
”furrowsare'dut perpendicularly on’one tide and
obhque}y‘ on the other into the fic‘o’nex which
~gives each furrow 1a {harp edge, and ‘in the twp
i’to'nes -they'com'e,t* as it were, againfi one aha-.1:
theriik’e the edges of a pair’of ‘fc‘iffirs : and f0
Cut the com, to ”make it grind the eafier When it
falls Upon“ the places b‘etweeh the furroy’Vs.
Thiefe are Cut the ‘fame ‘way‘in beth'fior‘re's when
they lie‘upofi'ith'e‘ir’backs, which makes them tufi

‘c'tofs Ways ‘té‘eéteh‘ other when‘the upper/{tone ”is‘
inverted by turningits fmjrowed {U'fiface tqwa'rdé .
that of the lower. P or, if the futr'OWS ”of both“

fiodesl‘iay thefam‘e way, a gteh’tfde’ail ofthe co‘th
V .wmld be'di‘WEn"' anard' in the .l‘ower furrows;

and fo'co'me but from between‘ theift'pnm With} ‘ ,

ou't'beihg‘ei-thet cut or'br'uifea. 1' T p ‘ , , .

When the fa rroWs become blunt and ‘fltafl‘qfi
by wearing, the running fiche" ‘m‘lfi’t ”be takflj
.. up, and bdthfiones new dref’cfivith' 'a ch'i'fel’and

hammer. Aha 'e'Vei‘y’ti‘me the fiche is‘t'ak’e‘n u’p; '

there n’mt‘t be 'fome talllow put found the fpint’ile
Upon the bufh, ‘Wh‘ich‘will {ooh be melted :‘b‘y
the'hea't‘the‘Tpihdile acquires'from its taming

andtrubbih‘g-égainfi the bath, find Te will get si'fi"
‘ It 1 4 , betwixt

'73

Of WateroMz'lls.

betwixt them: otherwife the bulhwould take
fire in a very little time. i

The bufh mul’c embraCe the fpindle quite
clofe, to prevent any lhake in the motion, which
would, make fome parts of the fitones grate and
fire againl’t each other; whilf’c other parts of
them would be too far afunder, and by that
means fpoil the meal in grinding.

Whenever the fpindle wears the bulb f0 as to

, begin to [bake in it, the Prone mull be taken up,

and a chifel drove into feveral parts of the bulb;

[and when it istaken out, wooden wedges mull be,

driven into the holes; by which means the bulb
will be made to embrace the fpindle clofe all

around it again. In doing this, great care mui’t

be taken to drive equal wedges into the bulb on
oppofite {ides of the fpindle; otherwife it will
be thrown out of- the perpendicular, and fo hin-

_ der the upper Prone from being fet parallel to the

under one, which is abfolutely necefTary for mak-

..ing good work. When any accident of this
kind happens, the perpendicular pofition of the

fpindle mull: be rei’tored by adjuf’ting the bridge-
tree ST by proper wedges put between ituand

. the brayer SLR.

It often happens, that the rynd is a little

- wrenched in laying down the upper {lone upon

it»; or is made to link a little lower upon one
fide of the fpindle than on the other; and this
will caufe one edge of the upper {tone to drag
all around upon the other, whill’t the oppofite

, edge will not touch. 'But this is eafily fer to -

rights, by railing the [tone alittle with‘va lever,
and putting bits of paper, cards or thin chips,
between the rynd and the Prone. .

The diameter of the upper Prone is generally

about fix feet, the lower {tone about an inch

more:

Of ‘Waz‘er—‘Mz’lls.

more: and the upper {tone when new Contains
about 22; cubic feet, which weighs fomewhat
more than 1900 pounds. A Prone of this dia-
meter ought never to go more than 60 times
round in a- minute; for if it turns falter, it Will
heat the meal; ‘

The grinding furface of the under {tone is a
little convex from the edge to the center, and
” that of the Upper {lone a little more concave: fo
that they are farthel’t from one another in the
middle, and come gradually nearer towards. the
edges. By this means, the corn at, its firfifen»
trance between the fiones is only bruifed; but as
it goes farther on towards the circumference or
edge, it is cut fmaller and fmaller; and at lal’t
finely ground juft before it comes out from be-
tween them. - ' v ,

The water-wheel mul’t not be too large, for
if it be, its morion will \be«too flow; not 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 {lone to turn round once in
a fecond of time.

In order to confirué‘t a mill in this perfect

manner, obferve the following rules : .
1. Meafure the perpendicular height of the
fall of water, in feet, above that part of the
wheel on which the water begins to aél: giand
call that, the height of the fall: -
2. Multiply this confiant number 64.2882by

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 qumient {hall be the velocity of the float.
boards of the wheel; or the number 0f feet they
’ mull:

77

Of Water-Mild
mul’t 'ea‘ch go through in a fecond, when the
water aéts upon them fo, as to have the greatefl:
poWer to turn the mill. -
' 4. Divide the circumference of the wheel 111
feet by the velocity of its floats in feet per fe-
00nd, and the quotient {hall be the number of -

' fhconds 111 which the wheel turns round.

- 5. By this lal’t-nd’mb‘er of fecunds divide 60?;
and the qubt‘ient [hall be the number of turns
ef the wheel in a minute.

6.‘ Divide 60 (the number of revolutions the

- millfione ought to have in a minute) by the num-

ber of turns of the wheel in a minute, and the:
‘tfuotient {hall be the number of 'turns the mill;
Hone ought to have for. one turn of the wheel.
"i '7. Then, as the number of turnsrofthe wheel
in a minute is to the number of turns of the .
'milll’tone in a. minute, 10 Inuit the number of
flaves 1n the trundle be to the number of cogs
in the wheel, in the nea‘refi whole numbers that
Can be found.
' By thefe rules I have calculated the follmving
table to a water wheel 18 feet diameter, which
I apprehend may be a good fize 1n genewral 1
To cont-111161 a mill by this tabie, find the
height of the fall of water in the 111.11 column, and
21152111111 that height, 1n the fixth column, you have
the number of cOgs in the wheel, and Ptaves 1n the
“trundle, for caufing the mil-ll’eone to make about 1
60 revolutions 111 a minute, as near as poliible,
when the wheel goes with a third part of the ve-
106137 of the water. And it appears by the 7th
eolt1m11,tha"t the number of cogs in the wheel and
flames in the trundle, are To hear the truth for the
required purpo-fe, that the leal’t number of 1W0-
1utiohs of the millfione in a minute is between 59 .
and 66, and the greatel’t number never amounts

to 6I._ \
The

_- ’ Of Water-Mills. ;

"The MILL-WRIGHT’STAQLE."

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E . - ' \ . Revolu~‘ C 6 . Rigedf
66‘ Velo- ‘Velor Revoluetions of , ogs 1“ _ .
gr- . . . the .1111“-
.-. 01tyof c1tyof uons of the wheel fione‘ er
59.. the the the mill- d . Pb
r+ ,, an mm. y
2 5- water wheel wheel fione fiavesin thefe
:1 per fe— per {e- per for one * the ' c0 5
9’: cond. ~cond. minute. of the trundle _ angd
1 o ' Wheel. ' ' Ra"
H» 7 ______________ _ . yes.
?..§§§§‘§§w§§53§ Q swag“;
93§§%32?§E?§2? 33.53:”?
0:." 3."; 58 53 [“2
1~ 8.02 2.67 2.83 21.20127 659.92
2 11 .34 3 .78 4.00 15.00105 7 60 .00-
3 13 -89 21.63 4-9I12.22 98 860.14
4 4 16.04 5.35' 56710.58 95 959.87..
* 5 17:93 5-95 6.34 9-46 85 959-84
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, 9593.67
9 24.05 A 8 .02 87.51 7 .05 70 10 ”59.57
10 25.35 8.45 8. 7 6.6.9 67 1060.09
11 26 .59 8.86 9.40 6.38 641060.10
12 27.77 9.26 9.826.141 61 10 59.90
13 28 .91 9 6410.22 5.87 59 10 60.18,
14 30.00 10 00 10 6c 5.66 56 1059.36
15 31 .0510 35 10 99 ‘5 .46 55 10 60 .48.
16 32 .07 10 6911 34 5.29 53 10 60.10
.17 33.0611 0211 70 5.13 51' 1059.67;
18 34.02 11.3412 02‘ 4.99“ 50 10 60.10
519 34.95 11 6512 3 4285 49 10 60.61
*2135661951268 4.73 47 103922 .
I 2 3 4 "5 '6 ' 7

 

 

 

 

80

_ Of Water-J'dillr. \

Such a mill as this, with a fall'of waterabout
7;;- 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
overéome the refiftance arifing from the friction
of the geers and attrition of the {tones in grind-
ing the corn. - ~

The greater fall the water has, the lefs quan-
tity of it will ferve 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 penfiock is drawn up by means ofa
lever, it opens a pafi'age through which the water .
flows to the Wheel: and when the mill is "to be

i flopt, the penfiock is let down," which {tops the

water from falling upon the wheel.

A lefs quantity of water will turn an over‘lhot-
mill (where the Wheel has buckets infi‘ead of
float-boards) than a breaf’t-mill where the fall of
the water feldom exceeds half the height db of
the wheel. So that, where there is but a {mall

‘ quantity of water, and a fall great enough for the'

wheel to lie under it, the bucket (or overlhot)
wheel is always ufed. But where there is a large

'body of water, with a little fall, the breal’t or float-

board wheel mull take place. Where the water I ‘
runs only upon a little declivity, it can aft but

. {lowly upon the under part of the wheel at b; in

which cafe, the motion of thewheel 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; f0 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 millf’tone a fufficient degree ofvelocity.
They who have read what is faid in the firit
lefture, concerning the acceleration of bodies
fallmg

i Of Water-Mills; '

falling freely by the power of. gravity aeting
confiantly and uniformly upon them, may per—

haps afk, Why lhould the motion of the wheel be -

equable, and not accelerated, fince the water aéts
confiantly 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 lhould become fo great,
the power of the water would be quite hit upon
the wheel, and then there would be no proper
force to overcome the friction of the geers and
attrition of the Ptones. Therefore, the velocity
with which the wheel begins to move, ,will in-
creafe no longer than till its momentum or force
is balanced by the refifiance of the working
parts of the mill; and then the wheelwill go
on with an equable motion. '

81 ,_

[If the cog-wheel D be made about 18 inches A Immi—

diameter, with 30 cogs, the trundle asfmall in mill-

proportion, with 10 fiaves, and the millfiones be
each about two feet in diameter, and the whole
work be put into a {irong 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
infiead of the wheel AA: the millfizone 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 lay, the trundle might make a given ,

number of revolutions for one of the wheel,
without a fraction. But as any exa€t number is
not neceiTary in mill-work, and the cogs and
rounds. cannot be fet in f0 truly as to make all

the

 

825

Cf Horfé—MZZ: and Wind-Mills.

the intervals between them equals a fl<ilful
mill-wright will always. give the wheel what he
calls a hunting cog; that is, onemore than what
will anfwer to an exaét divifion of the wheel by
thetrundle. And then, as every cog comesto
the trundle, it will take the next fiafi’ “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 difiances from
one anOther in a little time; and fo make a true -
,u‘niform ymotio‘n throughout the whole work.
Thus, in the above water-mill, the trundle has

‘ Io flaves, and the wheel 61 cogs.

. A 1507:];—
mill.

A wine’-

71M].

Sometimes, wh'erethere is a fufficient qu'an.
tity of water, the cog—wheel .41.? turns a large‘
trundle B B, on whofe axis C is fixed the hOI'l-r

’ zontal wheel D, with cogs all around its edge,

turning two trundles E and F at the fame time;
"whofe axes or fpindles G and H turn two mill—
fiones’I and K, upon the fixed {tones 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 {laves of its trundle, and turning the
vacant place towards the cog wheel _D. And
there may be a wheel fixt on ethe 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, 85.0. , - ‘
If, infiead of the cog-wheel 21A and trundle
B B, horizontal leVers be, fixed into the axle C,
‘below the wheel D; then, horfes may ibeput to
thefe levers for turning the mill : which is often.
done where water cannot be had for that pur—
pofea v~ '
The working parts of a wind-mill diEer very
little fromthofe of a water—mill; only the former
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Of Wind-Mil;

is turned by the aél‘ionéof the wind Upon four
fails, every one of whichought (as is generally
believed) to make an angle of 54.; degrees with
a plane perpendicular to the axis on Which the
arms are fix-t for earrying them. It being de-
monl’trable, that when the fails are‘ let tofuch an

' angle, and the axis turned end-ways toward the

wind, the wind has the greatei’c-power upon the,“

fails. . But this angle anfwers only to the cafe of ’

a vane or fail jul’c beginning to, move*: for, ~
when the vane has a certain degree of metion, "it
yields to the ’Wlnd sand then'that angle mul’t be
increafed to givethe ’wind ’its‘full efi‘eét.

‘ Again, the increafe of this angle fbould be
dinerent, according to the different velocities
from the axis to the extremityof the vane. At
the axis it lhould be 54% degrees, and thence
continually deereafe, giving the vane a twill, and
To cauling all the ribs of the vane to lie in dif-
ferent planes. , , r . ~ »

Lafily, Thefe ribs ought to decreafein length
from the axis to the extremity, giving the vane a
curvilineal form 3 lo that no part of‘the force of
any one rib be fpent upon the rel’c, but all move
on independent of each other. All this is rev
quired to give the fails of a wind-mill their true
form :, and we fee both the twilt and the diminm~

. tion‘of the ribs exemplified 'in the wings of birds.

It is al—mol’t incredible to. think with what
velocity the tips of the fails move when acted

upon by a moderate gale of wind. I have fe« A

veral times counted the number of. revolutiOn‘s‘
made by the fails in ten or fifteen minutes 3, 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 MACL'AUMN’S [Fluxions, near the end.

G ‘ city

83,

(8.4-;

A tfrmze.

Of Grams;

city that it wouldmove if put upon the fail-arms;
it wotild go upwards ofgo miles in an hour. '

As the ends of the fails neared the axis cam
not move with the faine velocity that the tips or
farthelt ends do, although the wind aé‘ts equally
firong upon them, perhaps a better pofition
than that of firetching them along the arms
direétl from the center Dof motion, might be to
have t em fet perpendicularly acrofs the farther
ends of the arms, and there adjufl'ed lengthwifc
to the proper adgle. I or, 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 {0 much the more power:
and then theie would be no occafion for having,
them fo large as they are generally made, which
would render them lighter, and confequently,
there would be f0 much the lefs friétion on the ‘
thick neck ofthe axle where 1t turns in the wall. ‘

A crane is an engine by which great weights
are raifed to certain 23heights, or let down to cer—
tain depths It tonnes of wheels, axles, pul-

PIateV III. leys, ropes, and a gib or gibbet. When the

Fig. 1.

‘ rope H 15 hooked to the Weight K, a man turns

the winch .4, on the axis whereof 15 the trundle ’
B, which turns the wheel C, on whole axis D 18
the trundle E, which turns the wheel F with 1ts
upright axis G, on which the great rope HH-~
winds as the wheel turns, and going over a
pulley fat the end of the arm d of the gib c cde,
it draWs up the heavy burden K; wl11ch,heing_
railed to a proper height, as froin a [hip to the
quay, is then brought over the quay by pulling
the wheel Z round by the handles 2, z, which
turns the gib by means of the half wheel 5 fixt
on the gib- -pol’t c c, and the firong pinion a fiXt
on then aXis of the wheel Z. This wheel gives
the man that turns it an abfolucé command over
, 1 the

AOif’CMnel‘.~

the gib’, foes toAptEVeht'it‘from taking any tn}
lucky 'fWin'g; fueh‘a's .o‘ftenl‘hqppensi when it ié
bnly .gl‘i'id‘cd by‘fa jropéftifid 90' fisarmd; and
people _ a‘re'Treqtiently"httrtg 'fdmetimes‘ killed;
by fueh' 'aécidents.‘ :_ . , ’ . '

The g‘reafl'mpe goes ‘bétWeeh tw‘o‘ upright
follers’z' and k; which cum upon gu‘dgeoné iii.

the fixed'Beeim'sf andg; and as the gibis t‘iir‘n?

ed toWar'd’sfe'ither fide, the rope b‘e’ndé’itpontthé
roller heictjthat 'fide; Were it not for thefé
rollers, ’ the 1 igib Would be qLHEC uhmanédeable 4,
for‘thésmo'rhe‘nt 'it Were turned eve? fo llttleto—
Wards; any fide,,the Weight K would begin to
defcend, beca’ufe, the to 6" would . befhortened
between; the pulley I 'an‘tlpaxiSG 3 and fo‘thelgib

would be" pulled Violently" to that fi'de, and eithei‘:
be btolt‘e‘t'o' pieces, or“ bre'ali'every’ thing that

Cameln’it's Way.- ; Thefe'trollefs mufi‘be‘ip'léjced
fo, thati‘thefidesiof then): found. Which the tepid
bendsg’; n‘fiy’keep the middle ’0)? the bended part
direftlj’. EVER With "the-”center of the hlo1‘e in

which'thé‘ uppe‘p gudgeoh 'of the gib‘: turns in-

the béa'th f. The truer thefe rollets are placed?"
the Ea‘fie‘rthe'giblis nienélged, and‘the‘ Alefs 31.335
{wingeithe‘r Way; by the fOr'eeof the Weight K.“ ,_

A ra'tchetWIieelv‘QI‘is’ fixt Upon the aids D;
near the trundle E ; and into—this wheel tlleeatch
Or elickfR‘l'fa'llé." This hinders theiinzéxchinery
from running dek by the Weight of the, burden

K, if the-man ‘who raifes‘itfl1buldhappen tobel”

Carelefs,‘ anclfiyleewe(3’87iivcjrking1 at thewinclt
fl foon‘er than he ought td'do.‘ ‘ V ‘

\Vhen'the“ burden K is “infill—4d toi‘io't‘iq ‘Pifope; ,
height from the fhip, and brou’ght‘ovet the

quay by shaming. the gib ~zi‘rlaotn':”, it" is letdown
gently upon the qitay, Orin‘to aV‘cart‘ {tending
thereon, in the follOwing manner: A man takes‘

hold of the rogue t t (which goes over‘ the‘pulley \
. G i

2 V ‘v, and

9‘5“

8,5 ‘

’Of Crews.

v, and is tied to a hook at S in the catch 1%) and
foldifengages the catch from the ratchet-wheel
Q}, and then, the man at the winch VI turns it

' backward, and lets down the weight K. ‘ But if

the weight pulls too hard againfi: this man, ano-
ther lays hold of the handle V, and by 'pulling
it downward, draws the gripe U clole to'the
wheel‘f, which, by rubbing hard'againl’t they
gripe, hinders the too quick defcent of the
weight; and [not only 1’0, but even [tops it at
any time, if required. ~By this means, heavy
gons may be either raifed 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
therope is to be let down for more, the catch R
isjfirft difen‘gaged from the ratehet-wheel Q, by
pulling the cord 1‘; then, the handle 9 is turned
Béilfronnd backward, which; by the crank nn
inij'thepieee a, pulls’dOWn the frame. b, between
thejguides m and m (in which it Hides in a.

rooyejandfo difengages the trundlefifrom
thetwheeliC :1 and then,,the heavy hiOOk B at

the; end of the rope lH'defcends by its own

weight, and turns back the great wheel‘F with

its; trundle E, .and the wheel C; and this lafi ~ 7

Wheel acts like a fly agai'nfl: the wheel F and
hook. Qt; andfo hinders it from going doWn too
quick -, whilft the weight‘X keeps up thegripe
U from rubbing againlt'the wheel 2”, by means.
of adeordgoing from. the weight, over the pulley
w to, the hook Win the gripe -, f0 thamhe gripe
never touches the wheel, unlefs it be pulled
down by the handle V; , .

When the cranenishto be fet at work again,
for drawing up another burden, the handle 9 is
turned, half round. forwards 5 which, by the
crank 71 fl, raifes up, the frame b, and'ca‘ufes the

'3 trundle

OfiCi/cmés.
trundle B to lay hol dof the wheel C, and then,
by turning the winch A’, the buideti of goods
K 15 drawn up as before.

The crank n, 72 turns pretty {till 1n the mortife
near a, and from againfi the farther end of it
when itahas got juftb a lit le beyond the perpen-
'1(l cular; f0 that it can never come bac1< of1t~
felf: . and therefore, the t1undle B can nevcr
come away from the wheel C, until the handle
9 be turned half1doun, backwards.

The g1ea t rope 111115 upon rollers 1n the lever
L M WhiCh keeps 11: from bending between the
axle at G and the pulley I. T his lever turns upon
the axis IV by means of the Weight 0, which is
jul’t fuI-liCient to keep its end L up to the repe; fo
that, as the great axle turns, and the 10pe coils
round it, the'3 lever rifes with the rope, and pre-
vents the coil ings from going over one another.

The power ofthis c1 ane may be el’timated thus:
fuppOfe the trundle B to have 13 Faves or rounds,
and the wheel C to have 78 fpur cogs, the trundle
E to have 14 haves, and the Wheel F 56 cogs.
Then, by multiplying the flames of the trundles,
1 3 and 14, mto one anOther, their product will be
182-, and by multiplying the cogs ofthe wheels,
78 and 56, into one another, their produét will be

4368, and dividincr 4368 by 182, the quotient
will be 24; which fhews that the winch 11 makes
24 tums 101 one turn of the wheel F and its

axle G on which the ”teat rope or chain HIH ‘

wmds. So that, if the length or radius of the
winch d were only equal to half the diameter
of the great axle G, added to half the thicknefs
ofthe mm [1, the power of the crane would be
as 24 to I. but the radius of the Winch being
double the above length, it doubles the faid

power, andl lo nukes it as 48 to 1. ° in which '

Cafe, a man may raife 48 times as much weight
G 3, . by

87

6f Cranes,

‘ by this engine as he could do by his natgral ‘ ‘

firength without it, making proper "allowance
for theirié‘tio‘n of the: Working pause—Two
men may work at once? by having “another-
winch on the oppofite end Of the axis of the

. trundle under Bg'zanyd {0 make the power Ptill

double. .

i If this power be thought greater than what
may 'be’generally wanted, the wheels may be
madewith fewer cogs {in proportion to the Ptaves
in the trundlesgyand fo'the power may be of
Whatever degree is judged to be requifite. But i

. if the weight be f0 great as will require yet more

power to raife it (fuppofe a dzouble‘qtiantity)
then the rope H may be, put under "a moveable

' pulley,‘ as c“2 ‘and the end of it tied to a hook in
' thefgib at 5', whieh will give adouble power to

the machine, > and f0 raife a ‘donble weight
hooked to'the block of the moveable pulley.

' When oriiy finall burthens are to be raifed,’
this may be wquickly done by men pnihing the
axle G round ‘by' the handfpokes y, y,‘ y, y; hav-

ing fi'ri‘t difengaged the trundleIB frOm the wheel

C : and then, this wheel. will only aél: as a fly
Upon the wheel F; and the catch R will prevent
its running back,'if the men {hould inadvert-
ently leaye off’pulhing befo're'lthe bttrtheh be

,. imhooked from {3 M

i Lafily, When very heavy burthens are to be '
railed; which’ might endanger the breaking of

' the’cogs' in ithewheel F -, their force againlt thefe
' Cogs may be mueh abated by men pufhing'round

the handfpokes y, y, y, y, whill‘t the man at .4

y turns the 'wmch.‘

I have only {hewn the working parts of this
cranegwithout the whole Of the: beams which
{tippdrt' them; knowing that thefe are ’eafily'
V I '7 i i ' {UPPOfCS-h

.1

Of diam; ‘i

‘fuppofed,1_'land‘that if they had been drawn,
they would, have hidfia great deal of the
working partsirfrom light, and alfo .confufed the
figure: ' , '

Another very good tram: is made in thefoh Another

'lOWing manner. 1124 is a great wheel turn¢diffiflflf-
by men walking within it at H. On the part F’g' 2°

C, of its, axle B, C, "the great rope D is wound as
the wheel turns; and this rupe drawsup goods

in thefame way as the ropeiHH does in the.
above;mentioned crane, the gibwork here beg;

ing {uppofed to be of the fame fort; But thefe
cranes are very dangerous to the men“ in‘athe
wheel; for, if any of the men fhould chance to

fall, the b‘urthen 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. Parlmare of Brif—
.tol, (whofe contrivance the forementioned crane
is, f0 faras .‘I ran remember its, eonl’truétion,
after feeing’it once about'twelve years ago 9“,)

obferving this dangerous .confirnétion, ,eo'n-

trived a method for remedying it, by putting
‘cogs all around the outlide of the wheel, and.
applying a trundle E to 'turn it; which inereafes

the power as” much as the number of’eogs in the, .
wheel is greater than the number of fiavesnin .

the trundle ;: [and by puttinga ratchet-wheel E
on the axis of the trundle, (as in the above-
mentioned crane) with aeatch“ to fall into it, the
great wheel ,is ftoptfmm running healthy
the foreeof the weight, even if all the men in

* Since the firfi edition of this book ‘was printed, Ihave
feen’ the fame crane again; and do find, thatthough-the
working parts are much the fame as above defcrihed, yet
the method of raifing or lowering the trundle B, , and the
gatch R, are better contrived than I had deferibed them. .

G4 - it

90 ~ Of Wheel-Carriages.

itfliould-leaveoE walking. And lay-one man
working at the winch} I, or two menatrthe op.-
pofite winches whentneedfuhthe men in the
wheel are much affil’ted, and much greater
,weights are railed, than could be by men only
twithin the wheel. Mr. Padmore put‘alfw a
gripewheel G upon the axis of the trundle,
which being pinched in the fame manner as de-
leribed in the former crane, heavy burthens
may be let d0wn without the leafl: danger.
And before this contrivance, the lowering of
goods-was always attended with the utmofi:
danger to the men in the wheel; as everyone
mutt be fenlible of, who has feen {tich engines
at work. . . , . _
And it is Farprifing that the mafiersof wharfs
and cranes {haul-d be to regardlefs of the limbs,
or even lives of their workmen, that excepting
the late Sir flame: Creed of Greenwich, and
fome gentlemen at Brillol, there is fcarce an in--
~ flame of any who has ufcd this fafe contri-
' vance.
- WM!- The {trué‘ture of wheel-carriage: is generally
carriages. fo well known, that it would be need/leis to de-
fcri‘oe 'them. And therefore, we {hall only,
point out fome inconveniencies attending the
common method of placing thewheels, and
. loading the waggons. .

In Coaches, and all other four-wheeled car-
riages, the fore-wheels are made ‘of a ,lefs flee
than t‘he'hind ones, both on account of turn-
ingfhorrh. and to avoid cutting the braces:
0thCrWl{€~,t'-fhe carriage would go much ea‘fier if
the fore-wheels were as high as the hind ones,
'andnthe higher the better, becaufe they would

‘ [ink to lefs depths in little hollowingS/in, the
roads, and :be the more eafily drawn out- of
,1 ' them,

Of Wheel-Carriagrfi

then‘n But carriers andcoachmen give another
real'on for making the fore—wheels much lower
than the" hind—wheels ~, namely, that when they
are lb, the hind-wheels help to pufh on the fore
ones: which is too unphilofophical andiabfurd
to deferve a refutation, and yet for their fatiSa
faction we {hall fhew by experiment that it has
noexil’tence but in their own imaginations.

lt iS‘plain that the fmall wheels muf’t turn as
much oftener round than the great Ones, as
their circumferences are Ilefs. And therefore,
when the carriage is loaded equally heavy on
both axles, the fore—axle mull lilllain as. much
more friélion, 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 obf’tinately perfifi, againl’t the clearel’t
reafon and demonfiration, in putting the heavier
' part of the load upon the fore—axle of the wag—
gon ; which not only makes the frié‘tion greateli:
where it ought to be lead, btit alfo prefl‘eth the
fore-wheels deeper into the ground than the
hind—wheels, notwithflanding the fore-wheels,
5 being leis than the hind ones, are with f0 much
the greater difficultydrawn out of a hole or over
an obf’tacle, even fuppoling the weights'on
their axles were equal. For the difficulty, with
equal weights, will be as the depth of the hole
or height of the obftacle is to the femidiameter
of the wheel. Thus, if we fuppofe the {mall

wheel D of the waggon 118 to fall into a hole Fig. 3, '

I of the depth E17, which is equal to theifemi-
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

direélzly againfl the top of the hole; and there-
’ , fore,

..

$ a.

Olel/‘Zefl omega?
fore, all. the pmabf’hiorlEs and nfénil’vlilill not:
be‘able to draw‘it obt, unl'efsthdgtound gives
way before it." “Whereas, if; the hind-Wheel C’
falls into fuch‘ a‘ hole, it' links nOt near to deep
in proportion to its 'femidiameter; and there-
fore, the point C of the large wheelwill not be
drawn direétly, but obliquely, againlt the'top

,, of the hole; and fowill be eafily got out of it.

Add to this, that as’a {mall wheel will often
fink to the bottom of a hole, in ”which a great
Wheel will go but a very littl'e’wvay‘, the l‘mall'
wheels onght in all reafon to be loaded with lefs
weight than the great ones : and then the heavier
part of the load would be lefs jolted tiPWard and:
downward, and the horfes tired fo much the
lefs, as their draught railed the load to lefs
heights, . V g

It is true, that whenthe waggon-road, is

‘ much uprhill, there may be danger in loading

the hind part much'he‘avier than the fore part ;‘
for then the weight Would overhang the hind-

’ axle, e-l‘pecially if the load be high, and endan—

get tilting up thefo‘re-wheels from the ground.
In this title, the fafefl 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
rifts“ from a level below the carriage; Bur as this
feldom happens, and when it’doesfa {mall temw

fiorary weight laid upon the pole between the

orfes would OVerbalance the dangeg; and this
weight might be thrown into the waggon when

‘it comes to level ground ; it is flrange than an,’

advantage fo plain and obvious as would arife
front loading the hind—wheels heavieft, lhould
not be laidhold of, by gomplying with this
method. ' ' \ - . ‘

@13th Céiffiagw;

- ‘To‘confirmt thefe reafonings,by experiment; -

let a {nialltrnodel’ofi a ,waggon .be"‘_made, with

its fore—wheels;airinches.indiameter, andfits ,

hind-wheels 4:57,..‘gthe w'hole,_model weighing
about; 2o ounces, _ “Let this, little carriage be

loaded any how with weights; and have a ftnall .

cord tied to each of its ends, equally high from
the grohndv itmrefis upon; and let'it be drawn
along a horizontal board, firlt by a weight in a
fcale hungto the cord at the fore-part; the cord
going over a pplley at the end of the board-
to facilitate the draught, and the weight jul’c
fufficient to draw it along. Then, turn the

carriage, and hang the fcale and weight to the f ‘

hind cord, and it will be found to move along
with the lameveloeity has at firlt: which fliews,
that the power required to draw the carriage
is all the fame; whether the great or {mall
wheels are foremol’t-V and therefore the great
wheels do not help in the leall: to pulh on the
{mall wheels in the road. . t

Hang the feale to ‘the forelcord, and place

the ‘fore‘wheels (which are the fmalllones) in'

two holes, cut thizee eight parts of an inch

deep into the board; then put a weight of 32 '

ounces into the. carriage, over the fore—aide,
and an equal weight over the hind one: this
done, put 4.4 ounces into the fcale, which will

bejul‘t-fufiieienti to draw out the forefwheels

but if this Weightbe taken out of the leak, 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 necefi'ary to draw-

otit the fere-wheels. This {hewsg that the lat-

ger the wheels are, the leis p0wer will draw -

the garriage, efpecially or; rengh groundr

triad

“l5

" :23" '- ‘

94

Of lVihEEl—Cairr‘z'zzgés.

Put 64. 2ounces'over the axle‘of' the hind;
wheels, and 32x0ver 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 jul’c draw out the fore~wheels; and
when the hind Ones come 'to the hole, .they‘will
find btit very little refiltance, becaufe they link
but a little way into it. ‘ x t ‘

But lhift the weights in the carriage, by put-
ting the 30. ounces Upon the hind—axle, and the
64 ounces upon the fore one; and place the
fore-wheels in the holes : then, if’76 ouncesbe
put into‘the (sale, it will be found no more than

dizlhcient to draw, out thefe 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 demonltration of the ab-
furdity of putting the ‘heaviefi part of the load
in the fore-part of the Waggon. '

Every one knows what ,an out-cry was made
by the generality; if’noc the whole body, of the
carriers, againl’t the broad-wheel aft; and h0w
hard it was to perfuade them to comply with it,
even though the government allowed them to
draw with more horles, and carry greater loads,
than ufual. Their principal objeétion was, that
as a broad wheel mul’t touch the ground in a great
many more points than a narrow wheel, the fric—
tion mull. of-courfe bejuftfo much the great’er;
and conlEquently, there mull: be fo many more
hOrfes than ufual, to draw the waggon. I believe i

that the majority of people were of the fame

t opinion, not conlidering, “that ifthe w‘hble weight

of the waggon and load‘in it bears upon a
great many‘points, each fullaihs a propor-
tionably lefs degree of weight'and friétio-n, than
when it bears only upon a few points 5 {0 that

what

\

l

Of Wb€6[-Cdrr~igggfi

what/is wanting {in one, is made, up in the other;
and therefore will hejuf’t equal under equal de-
grees of weight, .as may be (hew‘n) by the. follow-
ing plain and, eafy Experiment. _.

Let one end of a piece of .paekthread be.
fafiened to a brick, and the Other end‘to: a com»

mon fcale for holding weights: then, haying
laid the'brick edgewife on“, a table, and letthe
feale hang under, the edge of the table, put as

much weight into. the feale as will infl: draw, the .

brick along the table.” Then. taking hackihe
brick to its former place, lay it flat on. the table,
and leave it to be afled upon bythe fame weight
in the feale as before, which will draw it alohg
with the fame eafe as when it lay upon its edge.
In the former cafe, the brick may be confidered‘

as‘ a narrow wheel onthe ground; and inthe'

latter as a broad Wheel. And fince the brick is
drawn along with equal cafe, whether its broad
fide ornarrow, edge touches the table, it fhews
that a broad wheel Sinight be di'awn along the,
ground with the fameeafe as anarrow one (hip--
pofing them equally heavy) even tho-ugh they

‘fhohld drag, Land-not. roll, as they go along.

As nargow wheels are always linking intothq
ground, efpecialilywhgen the heaviel’t part ofsthe‘
load lies upon them, theyimufl; beconfidered 3.3..
going confiantlymnp hill, even on level ground,
And their {ides molt fufiaina greatdeal of frié’tiort

bay/rubbing 'againl‘t the rutts‘inadelby them, But;

both thefe incqnyenieneiesare avoided. by brpad
Wheels; which, inftead of. cutting and plough:
ing up the roads, roll, them fmoorh, and harden.

. them, as experience tefiifies in. places where

they have been tiled, efpecially either on wettilh.

or landy ground : though after all it mul’t be con.
felled, that they will not do infiii? clayey crofs

roads ~,

96

0f Wheel-Carriage};
roads; becaufe they Wou’ld foon ‘gathér tip ii§
much clay as would 'be almol’t'equal to‘ thé
weight of any Ordinary load. , ~
If the wheels’were always to go upon {moan
and level ground, the befliwaywould be to make

‘ the fpokes perpendicular to the haves; that is;

to Rand at right angles to the axles; b'ecaufé
they would then bear the 'Weioht of the load

perpendicularly; which is the f’iiongefi Way'for

' wood. But becaufe the ground is genErally u'n-

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 dilhing-wheels are belt,
becaufe when one falls into a rut, and the other

keeps upon high ground, the {pokes become per:

- pendicular in the rut,.and therefbre‘have the"

greatef’t {trength when the 'obliquity of the load
throws moi’t of its weight upon them ; whilfif
thofe on the high ground have lefs weight to bear";
and therefore neéd not he at their full. firenggth;

. So that the ufual wayof making the Wheels con.”

Cave is by-much the belt. .\
The axles of the wheels ought to, beperfeftly
flraight, that the rims of the wheels may be‘

parallel to each other; for‘then‘ they Will move

eafiel’t, beca'ufe they Will‘be' at liberty to go on ,
firaight forwards. But in the ufual way of pracs

a rice, the axles are bent downward at their ends ;-

whichibrings the fid'ES of the wheels nexththe
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 a much greater power of cruf‘ning‘
them than when they are parallel to each other;

{but alfo endangers the over-turning of the car;

riage when any wheel falls intoa hole or rut; or
when

24.3% 59:13 21:3an gmflhb'
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31’3me

 

 

 

 

 

PLATE

 

% deg—752772 /%e ymf W
ggIZIM/We/fl‘d/g'z. yo.

Of Wheel-Carriages; - 97
when the carriage goes in‘a road which has one
fade lower than the Other, as aldn’g the fide of a
hill. Thus (in the hind view of a waggo-n or
cart) let AE and B F be the great Wheels paral-
lel to each other, on their firaight axle K, and Fig.4.. .
H C I the carriage loaded with heavy goods from
C to G. Then, as the carriage goes on in the
oblique road flex 8, the center'of gravity of the _
whole machine and load will be at (1*; and the *9 see
line of direétion CdD falling within the wheel Page ‘3?
BF, the carriage will not overfet. But if the,
wheels be inclined to each other on the ground,‘F5g-- Sn
as flE and BF are, and the machihe be loaded '
as before, from. C to G, the line of direétion».
CdD falls withouc the wheel 8 F, and the whole
machine tumbles over. When it is loaded with _
heavy goods (fuch as leader 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 ofdi-
reelion C [1 falls "within the wheels -, but if it be
loaded high with lighter. goods (inch as wool- _
packs) from C to L, the center. of gravity is railed. Fig- 5%
from C to K, which throws the line of direction a
K k without the loweft edge of the wheel 8 F,
and then the load overfetst the waggon. , ‘
- If there be; fome advantage from {mall fore-
wheels, on aeeount of the carriageturning more“
eafily and fhort than it can be made to do when
they are large ; there is at leai’t as great'a difad- ,
vantage attending them, which is, that as the;~
axle is below the level of the horl‘es breafis, the»
hories not only have. the loaded carriage to
draw along, - but alfo patt'of its weight to bear .3;
Whieh tires them fooner, and makes, them
grow mach Rider in their hams, than they
would be if they drew on a level with the'xi'or'e-s
axle. And for this reafon, we find coach horfes».

» ' .'f-i>on,
8

Of the Pile- Engine;

‘ foon became unfitfm riding So that on all ac-

Plate IX.
Fig. 1,2

The pile--

angina,

counts it is plain, that the tore—wheels of all car-
riages ought to be to high, as to have their axles
even with the bread of the horfes; which would
not only give the horfesa fair dratight, but like-
wife caufe the machine to be drawn by a lefs de-
gree of power.

We {hall conclude this leé’cure with a defcrip‘

. tion 13er Vaulaue’ s curious engine which was

made ufe offer driving the piles of Wel’tmini’ter-
bridge: and the reader may call his eyes upon
the firfi and fecond figures of the plate, in which
the fame letters of reference are annexed to the
fame parts, in order to eXplain thofi: in the fe-
cond, which are either partly or wholly hid 1n
the fixfi. -
~ A 13 the great upright {haft or axle, on which
are the great wheel B and drum C, turned by
horfesjoined to the bars 8, S. T,he wheel B turns
the trundleX, on the top of whofe axis is the
fly 0, which ferves to regulate the motion, and
21110 to aél; againl’t the horfes, and keep them
from falling when the heavy ram Qis di-fcharged
to drive the pile P down into the mud in the ,
bottom of the river. The drum C 1s loofe upon
the {haft/I, but is locked to the wheel B by the
bolt 2”. On this drum the great rope HH is
wound, one end of the rope being fixed to the
drum, ahd the other to the follower G, to which
it is conveyed 'over the pulleys I and K. In the
follower G is contained the tongs F (fee Fig.
3. ) that takes hold of the ram Qby the i’taple R 1
for drawing it up. D is a fpiral or fu-fy fixt to
the drum, on which IS wound the final] rope T
that goes over the pulley U, under the pulley V,
and is zDfafiened to the tope of the frame at 7. To
the pulley block V is hung the counterpoifehPVh.
w 1c

Of" tim- Péle- Eagz'ééi
Which hinders the follower from accelerating as
‘ it goes downatoitake hold of the ram: for, as
the follower tends to acquire velocity :in its de-
fcent, the line ‘1’ windscdownwards upon the
fufy, on a larger andlarger radius, by which
means the counterpoife W : aets {ironger and
flronger againfl: it; and f0 allows it to come
down with only amoder’ate anduniform velo-
city. The bolt 2" locks the drumto the great
wheel, being pulhed upward by the {mall lever
2, which goes through a mortife in theilhaft 11,
turns upon a pin in the bar 3 fixt to. the great
wheel B, and has a weight 4, which always tends
to pulh up the bolt 2" through the wheel into

the drum. L is the great lever turning on- the y

axis m, and refling upon the forcing bar: 5, 5,
' which goes down through a hollow in the mm:
.4, and bears up the little'leverTz.

\ By'the horfes going rotmd, the great rope H
is wound about the drum C, and the ram 91 is
drawn up byth'e tongs F in the follower G, until
the tongs comes between thefiinclined planes E ;
which, by {butting the tongs at the top, Opens it"

at the foot, and difcharges the ram, which falls ‘

down between the guides b 5 upon the pile P,
and drives it by a few vl’trokes as far into the mud

as it can go; after which, the top-part is fawecl ’

ofi‘ clofe to the mud, by an engine for that puta-
'pofe. Immediately after the ram is difcharged,
the piece 6 upon the follower G-takes hold of the
ropes a, a, which raife,.the.end of the lever L, and
caufe 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 wheelB; and then, the follower,
being at liberty, comes down by its own weight-

to the ram 5. and the lower ends of the tongs llip ‘

QVEI‘

9‘9“

100

*1

Of tbé Pile—Engine.

over the {taple R and the weight of their heads
caufes them to fall outvs'Iard, and {huts upon
it. Then the weight 4 puihes up the bolt 2-" th-
to the drum, which locks 1t to the great wheel

1 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, whili’t the horfes, great wheel, trundle
and By, go on With an uninterrupted motion:
and as the drum 1s turning backward, the couno
terpoife W 13 drawn up, and its r0pe ET wound
Upon the fpiral fufy D. .

There are feveral holes in the under {ide of
the drum, and the bolt 2" always takes the firi’t
one that it finds when the drum {tops by the
falling of the follower upon the ram- , until which
Roppage, the bolt has not time to flip into any
of the holes.

This engine was placed upon a barge on the

. water, and lb was eafily conveyed to any place

defir-ed. —-I never had the good fortune to fee it,
but drew this figure from a model which I made
from a print oft) 1t , being not quite fatisfied with
the View which the p_1int gives. I have been—
told that the ram was a ton weight, and that the
guides & 22, between which 1t was drawn up and

' let fallfldown, were 30 feet high. I fuppofe the

great wheel may have had 100 dogs, and the
trundle 10 faves or rounds , R) that the fly’
would make 10 revolutions for one of the great a
wheel. .3

LECE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

,Of warmth; - tot

_ 4 r; «L Efci V _ g.
Ofloydlrg/‘l‘atzics; and hydrant/iii mac/nines; .271 general

- HE ,fcience of hydro/2min treats of the
nature, gravity, ,prefl'ur‘e, and m'otion of
fluids in general; {and of weighing folids. in
them. ' 1 . 31‘. . 1 7. .
A fluid is a body that yields tothe leait pref- Defini—
[ure or difference of preifures.“ Its particles [are tiou of
{a fmall, that they. :canrnot‘b‘e difcejrned; bythe a fluid:
bef’t microfcppes ; they are hard, fincctno fluid
- except air orfiteam, can be \_’pr.eflied into a ‘lefs
{pace than it naturally pofieffes; and theymui’t be
round and ‘fmooth, ,feeing they 'are fo eafily
moved amongvone another. ~ .
All bodies, borh fluid and folid, prefs down-
wards by the force of gravity : but fluids have
this wanderful “property; that their preffure up»
wards and :fidewife is equal; to their prefl'ure»
downwards -, and this is always in preportion 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
fideon which the p‘re-fl‘ure is leaf’t. And hence,
no particle or quantity of a fluid can beat tell,
till it ise‘very way equally preITed. . ,
‘To'fhew by experiment that fluids prefs up- Plate X}
ward asiwell as down-ward, let AB. be along Fig. i.-
upright tube filled with water near to its tQp; Fluids
and CD a {mall tube open at both ends, and Prer‘ as
. . . . much up:
immerfed intothe water in the large one: if the ward as
immerfion— be quick, you will fee the water rife down-
in the {mall tube to; Ihfifamc height that it fiands ward-
in the great one, pr until the {urfaccsof the
' a" ’ awater

W\

.3102

W ffidroflatz’cr;

water in both areon the fametlevel; whichfliews
that, the water .is prefi‘ed, upward into the
{mall tube by the weight of what is in the great

«one; otherwife it could nevizer rife therein, con-

‘tra‘ryto its natural gravity; unlefs thediameter
of the bore were for finall, that the attraétion of
the tube would raifelthuemater; whichfwill ne-
ver happen, if the tube be as wide as that in a
common barometer. And, as the Water rifes no

._ higher in the {mall tube than till its furface be

\-

g is prefl'ed by the weight of all that i’tands abort: _

911,3 level with the furf'ace of the water in the
great one, this {hews that the prefibre 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 raifed' to the fame height in the {mall one,
as it hands in the great. .

Take out the {mall 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 to the height E -, which {hews that the air is a

body, otherwife it could not hinder the water
from rifi-ng 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 alfo lhews that the
air is a compreflible body, for if it were not f0,
a drop of water could not enter‘into the tube.
The prefl‘ure of fluids being equal in all diw
reétions, it follows that the tides of a vefl'el areas
much prefl'ed bya fluid in it, all arOu'n‘d ina‘ny
given ring of points, as the fluid below that ring

“it. -

Of ’Hjfirtyfatitsf 1133 ‘
it, Hence the preflfure‘upmieVery point in the ‘
fi'des‘, immediately above the bottom, is equal: to ‘
the premiere upon every po‘inf'bf the bottom. ‘To
thew, this by experimeht, let a ‘hole be made ”at Fig. 2.
e in the fide of the tube‘AB'clofe by the b‘ot- ‘
tom}, and another hole Of the fame fize in the
bottom it ’0 g then pour Water, into the tube,
keeping it’full‘asg long es‘youehoofe the holes
{hould run; And have two bafthfeady :‘to. receive ,
the water; that runs "through" thjef‘twoiholes, 7 until
you ‘think‘there is enough in "ea’iéh‘f‘batfoh"; and
you will find by: mieafuting thequ’iimfli‘tie’s, that
» they areeqtialt; Which lhewvsithat‘the‘yVa'tet'run‘
withiequ'al {peed t‘h‘roUgh‘ both holes :7'whiCh it
Could not‘ha‘VjCi'd‘one, if it had not been equally
prefl‘ed "throttgihthemrbmh; For, if a'h‘ol'e‘ of
the {time fi'z-e be made in the fide'of the tube, .as”
about f, and if all three “are permitted to run
together, you will» fifid that the quantity run
through. the ,hole at fins much lefs than what has
run in the. fame timethr‘bugh “either", Of the holes
C or ‘e. ' _ j y "‘ ,_ ' ‘ '

In the‘l'a'me figure, let the fuhe’be'ttirned up
from the bottom: at C into the fltape‘p 1E, and
the hole at C 'be ft‘opt With a cork. ”Then,”pour
water into the tube to any height, as: Agi,’yahdit
will fpout up in a jet E F G, nearly asthigih- as it
is kept‘ in‘t’h‘e tube flB, by Continuing: to poitr
in _as much "there as runs through "the hole E;
which will be 'the'cafe whili’tthe fttrface flg keeps
at the fame height. And if a little ball of cork.
G be laid upon the t0p of thejet, it will be {ups
ported thereby, and dance upon it. The reafon
' why the jet rifes not quite 'fo high as the futface
of the water 21g,“ is owing 'to the refiftance it meets
with in the Open air: for, if a tube, either great
or final}, Was fcreWed ‘upon the pipe; at E, the

H 3 ’ ' Watch:

194».

The by;

droft‘m‘ic

paradox,

Fig 39

\

Of‘ielflrzmfica .
water wank} ; rife-£122it-guhtil ftheffurfa‘ge'g of the
watfilidp bOth tubefiwfle on the fame, level 5. as
Willbcaihewn by:'tbe amtmperhncnc‘. ,

‘ a

-: 1: Any quantity , rot. a; fluid», » thowgfmall- 'lbelier; ,

maybe madeto‘ balance amdtfmpfioréhay quan-
tity, :hOw» 5 great foster.- .A ThtsFtleu defervedly‘
termed the bydmflatiml pgzadox, ,;wh,ich we {hall
firihfhew by anorexperimentg‘and then account for
it uponthe' rinciplelabo'vé mentioned; =namcly,
that. like preflgrev of fluids is direfily; asfzbeir perpenx
dicular bez‘g/at, “without any regard to: ibeir'gudutiqt
.* Leta {mall glalh tube D C G,‘ topmfithfioughoufis '
and bended at B; bejbin'ed’ to the; entdtlofaugreaté
011621 I at :c d, .leetefth‘e great (melt. itlfo-open ~, .
fo that thefe tubes. in their openings amaytfreelyt
Communicate with each ethane Thenlfp0ur‘ wan

' ter thrbugh a 'fnaall".n€cked funnel intoithe {mall
' tube at H; thiswater; willsr‘unfthfiwghlthe join:

ing ofthe tubes a": cd, and rife-“jup into the ngQE
tube; and if you Continue pouring. will the fur-
fac‘eof the water comes to: any pama‘sgfl, in the
great tube, and then leave o'f’f, you will fee; that;
the furfae‘e of the-water in the {mall-tab; 'will‘be
jufi; as high, at D; 110 thatflthe perpendicular
height of the ,waterwill ,sbesthe fame in both
tubes, ’ however {mall the onébein proportion to
theother. This flaews‘, that the fmall column
DCG (balanees and fupports the great column
(1662', whichtit could not do if theirdprellhres
were not equal againl’t one another; in; the re-
curved bettom "at g."'-"If the {mall-tube bemade
longer,’ and inclined in the fituation G E F, the:
furface of the water in it Will {hand a: F, on the
Iam‘elevel with the-furface Al in the great {tube ';
that is, the water will have the fame pergendicular 4
heighttin bot-h tubes,‘ although theficolumn in'the
{mall tube is longerxthan that. in‘ the great one];

‘ ‘ . F S

OfHMfWict.‘
the'AMWr,ib§ingI'»®hqugand the latter per-
‘- Shite then*‘thé'firefl'utrELOffluidsis;direaly as
"their fiefipendi'g' elmz Haghts,’ ' without'hny 'iegard
toot-heir; quantities; it appeai‘s that Whateverfthe
figure or fizp‘ of V'efl'éls be, iftheyvare of balsa:
heights, andif the areas of their'bottoms are
equal. thegprefiute'SOf eons] heights of waterare
equal upon the bottoms of thefe véffels -, ,evefi

'thotigh the ohefifiimijid“ ‘hOid‘ a._tho_ufand 'or-ten

I

lhq'ufa‘ndsti‘m'es as much 'water as w'omfld 831 the

bthCr. . ‘T‘o oonfimi this part Of the hydrofiatical Fig. 4, g.

paradox by Ed experiment, iet two VeITels be
ptepated .f eqtfiiai heights, but very unequal
é’ohtehts,‘ fuc'h as 24.8 in Fig. 4‘. and [YB in Fig.
‘5'} Let each 'vefifl‘elg‘p'e open at both ends,’and
their bottoms D d, Dd be of equal Widths. . Let,
'a; ‘brafs ‘bOttom C C be’exaétiy-fitted to each veil
Tel, not't‘o‘ go'into-‘it', but 'fot itto [land upon;
'a'fid'let'i 'a. piece. of-'Wet ieather be putlbetween
each {zefliei and‘its brafs bottom, for the faker'of

elofehefs. Join "eachybottom to its veflei‘by a 7

hifige D,_fothat it may open like the lid of a
box”; and let each hot-tom be kept up to its
vefi’ei by com} weight-SE and E hung to lines
Which goover‘the-pulleysF and F (Wh‘ofe'blo‘cks
are fixed to the tide; of th‘e‘vefl‘els at f ) _ land «the
lines tied to hooks-at'd'aiid d, fixed in the {brafs
bottoms oppofite to the hinges D and D. Things
being thus ?preparediand fitted, hold the veifel
A 8 (Fig.5?) Upright in. yoUr hands over albafoh
on a table, and caufe water to be poured into the
~veflelflowl§z, till the preffu’re of the water bears

dowh sits boctom at theffide d, and'er‘aifes the _

’w'eight E {and thehii‘pa‘rt’of‘thewiatet’wili run
out at d.“ ” Mark the height htwhich the fur-face

H, of the water floodin the veiIel, when the bots f

4. _ tom

4% i

195

Fig. 4.-

Qf marque“;

item began to give way aL 4,3, and ,then, holding
.up the other veflel 11B (Fig. 4.) in the fame

manner, caufe water to ,be poured 191:9 it at H;
and you will fee that when the watch, rifes to .4
in this veiiel, jul’t as high? as it did 111 the former,
its bottom will alfo giv9 way at d, and it will
lofe par1; oftheiwater

T he naiural teafon of this furpriling pheno-_
menon is,~.that :finee all parts of a fluid at equal
depths below the furface are equally prcfled in
all manner of directions, the water immediately
below the fixed part Bf (Fig. 4. ) will be prefl'ed
as muCh upward againfi 1ts lower furfaCe within
the velTel, by the action of the column Ag, as
it Would be by a column of the fame height, and
of any diameter whatever- 3 (as was evident by
the experiment with the tube, Fig. 3.) and there-
for‘e,E ,fince tuition and reaction are equal and
contrary to each other, the water immediately

_ below the ftgriaee Bf will. be prefled as much

downward by it, as if. it was 1mmed1ate1y touch-
ed and prefiCed by a column Of the height gd,

I and of the diameter B f and therefore, the

water in the cavity 8.29 df will be prefl‘ed as
much downward upon its bottom C C,- as the
bottom of. the other velIel (Fig. 5. .) 1s prefied by
all the water, abbve it. -

To illufirate this a little farther, let. ;a hole be

made atfin the fixed top Bf, and let a tube G
be put, into it, then, ifwater be poured into the
tube fl, it will (after filling the cavity B d) rife
up into the tube G until it comes to a level with
that 111 the tube Al, which is manifetlly owing to
the preifure of the water in the tube 4', upon

: *A'that 1n the cavity of the veifel below the , Con-
fequcntly, that part of, the top B f, m which the

”11.016. is now made, would, it corked up, be

preffcd ,

0f .agaama: ' _»
prefl‘edjupwmd awithta‘yf‘t’grgea equal: to. the weight}
of all the .Waterwhich’ i‘sfuppottedxin the tube G:

and, the fame ‘thin'gwou’lgl hold at; g, if a‘rhole'

were made there; I‘Andrfofifithe whole cover or
top B f ‘ were fullof holes, and had tub‘esas high
as the middle one 11g put [into them, the water
in each tube would rife to the-fame height as: it is
kept into. the tube 1,17, bypOuring mokreinto it,
to make up the deficiency that it fufiains by {up-z
plying the others, until they are all full: and

then the water in the tube 11 WOuld 'fuppor‘t'
equal heights of water in all the reii; of the tubes;
Or, if all the‘tubes exceptvrfl, or any Other one;

were taken av'vay,‘ and. a large tube equal in dia-
meter tothe whole topB f were placed upon it,
and cemented to. it, randthen if water were
poured into the tube -_Vthat was left in either of;
the holes, it would afcend through all the tell of
the holes; until it filled “the large,. tube to" the

fame height that it fiandsip the {mall one, after"

a fuflieient. quantity had been poured'vinto it:
which fhews, that the top Bf was prelied ~‘up-
wa-rd by the water under it, and; before any
hole was made in it, with a force equal. to that
wherewith-S it is now prefi‘ed downward;-1 by the

weightof all ,the water above it in thegre‘at
tube. And therefore, the reaé‘tion of the fixed"

top Bf intuit be as gteatrjn premng the water
“ down-Ward upon the bottom CC, as the Whole
prefi‘ute 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 direé‘tly upon
the water in the cavity B D d f. '

Perhaps the bef’tamachine in the: world for'Fig. 6

i

10;?

demonfirating the'upwatd prelTure of fluids, ,, is The 12)»
the hydroflatic bellows d ; which confifis of two ”If/I'm?"
thick oval boards, each about 16 inches broad, 53‘1”“

and 1.8 inches long, covered with leather, to
' , Open

xo‘8<

Of Ifierirs.'r‘,
Open-mania: like a commoii-lbellows, human.
outsvaIVessr only a «pipe B;2“abol1t 'thr‘ée’feet'

- high,**is-fixed into- the bellows at e; ”‘Eéflotfié

waterbe poured into 'the‘p‘ipe'at é’,-§,Wh’iéh i-v‘v’ill
run'imo‘ithe’ bellows; afi‘él {ep'arate th-é‘bdatds a
little} ‘Thedvlay three" Véei-gh-ts I), c, 4’, each weigh"—
ing Ibo ppufihc‘ls’éh'hpoh thdu’pjxr board: and
pourm‘dfe; vgaler into the pipe B, which" will r‘u‘h" .
into the helléws, and ifiife‘up‘the board ‘withfall
ihew’eig’htsifhpml it“;7 and ‘if: the pipe bexkept
fullilguntililt‘hé’ Vveigh’ts‘» are rail-ed ‘as high as the
leathe’W’vh i-‘ehaeov'ees the bellows wi‘ll alloW‘them;

the water’Wil‘l remain in the pipe, aridflfiipport

all the Weights,‘ eVen‘though it} Iho‘uld ‘iveigh‘no

‘more‘thana oat-“tee dfiia‘"dtind54‘and‘the 00"
fl P Y 3

pounds :1 'thrrwiuan t'héir foi‘ce be ableii'to'iza’ttfc‘
them§'-g9.,dflfcéhd and {maybe ‘w‘a’tetfo'ur at the:

top'ofithefpipe, ~ " 5 “*‘f .
The re'aifiin-Qf'thi'y’will“be made'evident, by

roonfideringiiWhat has‘ bedh‘lalready‘faid of ‘the

refulfiof the prefi‘trl‘e’iof’fluids of Eequaliheights

'wichoutiany regard toithéifi‘quantitieéi" 4For, if a"

hole bfifilflfidéfii the if or board, and anube'be
put-fifiloii‘t‘;f‘the‘wate3r ' fr-ife in the fubé’to the
fameheightgthaflit ddeéiih theplpe; ahd‘wwld
rife'a‘s ’h'lgh ~( by {applyi’fig the~ pipe)- inias many
tubes “as: the 'bOard-eolJ-‘lil :eohtain hole‘si; NOW,
{Uppof‘e only dne‘hole-td'be made 'i any part of
theibfoafie‘l, of an ’equal'diam‘e‘ter wit the bore of
thé‘pip’éfiBi', land that tli'é pipe h01ds jul’t a“ qua;
tef-Ofi'ffa pound of "Watei‘gyif' a perfon‘élaps his
finger {upon the tholegz‘afid the pipe be‘filled with
water, he will find his} finger'tovbe prefl'ed up-

” ward'iivith" a force equal-‘-‘to‘a'*quarter of a pound.
.' And-ias-‘thei'fame ptefliireiS‘equal upon all equal
, partslof the-board, cachpan Whofe area is equal
' 'toxhe are‘aof the‘ holelwill‘k be PFCITCd upward with

g force equal to that of aquarter of a pound : the
i ' ' H .7- H " fum

0f_.Hydrojmzas-:» ' tog
font of allzwhichprefiutes againft theunder tide
of an offal bdardi 16inches bread, and 18» inches
long; will aitnetlnt {0300 pounds; and therefore
{0 much-’weightwv‘i‘ll be r'aifedup and fupported
by a quattemfapound of water inzthe' pipe. .4
~Hence5 “if; mattflands upon the Upper bohrch How a
and blow into the‘bel-lows‘through thezpipe 3,31%“ “lay
he will raife him-felf Upward upon' the beard: ;:11;eu};m- -
and the {mallet the; bore of the. pipesis,nthe e‘afiergward by
hewill be »-able<;to faifehimfelf. w; And then, by his
clapping ,his'fing'er upon'the. top of the pipe; dime-breath-
can fupport himfclf‘as long.- aswhe pleafes -,'. pro-
vided the‘bellows be airrtight,“ f0 as not to loft:
what is blownfin’to it.‘ ' . 3. u. 2 ' l
This figure, 1 confefs; might to have been.
much la’rg‘ér'than any;QtlICf.up¢“n the plate; but
it was nionthohght of, until- an the reit were
drawn ; and it‘could not {0 pmpetly come'intor
any Other plate." i, . . ’
Upon this pit'meiple oflthe UpWaI‘d prefl'ure of How lead
fluids, a p’ie'c'e of lead my be made to {with in mag be
water", by ‘i’mnlerflng it to'a' preper depth,‘ and 3:15;:
keeping; the [water from gettingxabove it. Let-water,
C D be a glafs tube, open throughout, and
E F G a flat piece of lead; exaf’tly fitted to theFig. 7.-
“lewer end of the tithe, not to go within it, but .
for it to fiand Upon ; with a wet‘leather‘ between
the lead and the tube to make clofe work. .Let
this l’eaden betmm be half an” inch thick, and
held Clofe to the. tube by pulling the pack-thread
I H L upward at L with one band, whilfi the
tube is held in the other "by the upper end C.
In this fituation, let the tube be immerfed in
watér in the 'glafs vefiel AB, to the depth of fix
inches below the furface of the water at‘K 3' “and i
then, the lead-en bottom 'E F G will be plunged
to the depth of fomewhat more than eleven times
~ 'tte

w

Q‘Tfiyflrbfldficfl
its" ‘ovm thiCkne-fs' : ' fhbldin‘gfgthc““tube“at that
deptih,".'yoju may, let go thei‘thread", atL ; " and
the lead will'not' fall from the tube”? twill be
kept to it bylthe upward prefl'ure of "the ”Water
below it, occafioned by the height-*o'f the water
at. K above the level of the lead. For as lead is ,
I 1.33 times as heavy as its bulk of 'water,"and is '
in this experiment immerfed to ”a depth {ome-

what more than t1. ‘3 3 times its thiéknefs,’ and

 

. - nofwater getting into the tube betWeen it and
. the lead, the ‘COIumn of water E 'aé’cG'below the

lead is pteITed upward againi’t‘itby thewater-I
KD E GL all around. the tube; ”Which water
being a little more than I 1.3 3 times as high as
the lead. is thitk, is fuflicient to balance andfup-
port the lead at the depthK E. ' If a little” ‘water
be poured into the "tube "upon male-ad; it will
increafe .the'Nveight upon the column Of ,‘water
under the lead, and cant; the lead”"to"fall"fromr
the‘tubeto thebotto’mof the glafs yeah, ' where

it will lie in the fituatibn & 22'," " Orf,‘ if the tube be?

tailed a little in the Water,_ the lfeadei‘Ilffa'll by its
own weight, which’Will théélibé too-great for the

HoWlight
wood may
be made
to lie at
the bot-
tom of
water.

. .,c0lum“n of water below it;

. . . a ((1: Jr»: _ '
prefi'ure of the .water around “themtube upon the

Let two pieces of wood be piaihgdgt‘ne flat, {0
as" no water may get in between themjwagn. they
areput together : l'et'one ofi‘the f p‘ieceé; as 5 d,
be cemented to the bottomlof the” ytii‘é’l'fl B
(Fig. 7.) and the other piecebe laid fla’t'andfidofe
upon it, and held down to it by a flick, Whilfi:
water is poured into the velTel; then remove
the flick, and the upper’piece of wood Will not_
rife from the lower one: for, as the upper one is
prefl‘ed ‘down both by its own weight and the
weight of all‘the.‘ water over it, whili’t the con-
trary preliure of the water is: kept all" by the

. ‘ wood

‘.

\ Of Ibdmulz'ctJ-i , I

wood under it, it will lie as fiill» as a {tone would
do in’its‘ifi’li’tgg ,But, if it be raifed ever foclittle
at any edge; Tome water will then get under~it ;
which being afiefl upon; by the water, above, will
immediately prefs it upward; and as it is lighter;
than its bulk of water, it will rife, and float upon
the furface of the water. 7 _ a V I

All fluids weigh jui’t as. much. in their :0th
elements as they do in Open 'air.’ To prove
this by experiment, let as much {hot be put into
a phia], as,‘ when corked, will make itfink in
water ; and "being thus charged, let it be
weighed, full in air, and then in water, and
the weights in both cafes wrote downs Then,
as the phial hangs ‘fufpended in water, and
counterpoifed; pullout the cork, that water may.
run into it, and it will defe’end, and pull down
that end of the beam. This done, put as much
weight into the Oppofite fcale as will ref’tore the
equipoife ; which weight will be found to anfwer
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 fpouts out at 397m: mo.
hole in the, fide or bottom of a vefTel, is as the tity oi
9* fquare rootof the depth or dif’tance of Etheifpouting,
hole below the furface of the water. ' For, in wate“
order to make double the quantity ,of a fluid. _ i
run through one hole asthrough anOther of the ’
fame fize, it will require four times the prelTure
of the Other, and therefore muft be. four times
the depth of the Other below the furface of p the
water : and for the fame reafon, three times the
quantity running in an equal time: throughthe

1'
- a

3* The {quare root of any number is that which being
multiplied by itfelf produces the [aid number; Thus," axis
the fquare rootof 4, and 3 is the fquare roOt of9 : ‘for 2
multiplied by 2 produces “and 3 multiplied by 3 pro—
duces 9, 8m. ' a . , ‘

‘fame

Of Hydraulic}.

Tame fort of hole, mull: run ivith three times

Fig. ‘8.

the velocity, Which will require nine times the
prefihre; and confequemly mull: be nine times
as deep below the furface of the fluid: and {0
on. -—---To prove this by an experiment, let two
pipes, as C and g, of equal fized bores, be
fixed into the fide of the vefl’el 11 B -, the pipe
g being four times as deep below the furfaCe of
the water at I) 111 the veiTel as the pipe C 15: and
whi’ll’c thefe pipes run, let water he eonfiantly
poured into the veflel, to keep the furface {till ‘
at the fame height. Then, if a cup that holds

,, a pint be {0 placed as to\ receive the water that

fpouts from the pipe C, and at the fame moment
a cup that holds a quart be f0 placed as to receive.
the water that fpouts from the pipe g,- both cups

, will be filled at the fame time by their refpec-

The horic
zontal
difiance
to which

tive pipes. ,

The horizontal difian'ce, to which a fluid will
fpout from a horizontal pipe, in any part of the
lids of an upright veflel below the futface of the

Waterw1ll flu1d, is equal to twice the length of a perpen-

I out
rom

pipes.

Fig. 8.

dicular to the fide of the vefl‘el, drawn from the
mouth of the pipe to a femicircl‘e defcribed upon
the altitude of the fluid: ' and- therefore, the
fluid will fpout to the greatefi diii‘ance pemble
from a pipe, whofe moist-h is at the center of
the femicirele, becaufe a perpendicular to‘ its
diameter (fuppofed parallel to the fide- Of‘fhc
veliel) drawn from that point, is the 'longelt that
can 'poflibly be drawn from any part of the
diameter- to'the circumference of the femic‘irzc-lei
Thus, if’the vefiel AB 'be-tfull 'of water, the
horizontal pipe D be in A the middle of its fide,
and the femicircle N d c (’7‘ be defcribed upon D
as a center, with the radius or femidiameter
Dg N, or be, the perpendicular TD d to the
diameter N D 5 1s the longei’c that can be dlrcawn

rom

Of‘ flydmulics. ' «113 ,

from anyhpart of the diameter to the citeuinfe-i
rence N d 45, And if the veflel be kept full,
thewjet G will {pour from the pipe D, to the
horizontal difiance N M which is double the
length of the perpendiCular D d. :va two other.
pipes, as C and E, be fixed into the lide of the
velTel at equal dii’tances above and below the
pipe D, the perpendiculars Cc‘a‘nd E:, from
thefe pipes to the femicircle, will beethal; and
the jets F and H fpouting from themawill each
go to, the horizontal diitance N K; which is
double, the length of either of the equal pet-pen—
' udiculars Cc or Dd. _ ,2» , ‘ .9 ,t , ‘

Fluids by their prefi’bre may be conveyed over How wa.
‘hills and vallies; in bended pipes, to any height “If my
not greater than the level of the fprings from}: :3”
whence they flow. But when they‘are defigned over him,

to be raifed higher than the fprings, forcing en- and val—
gines muf’te be ufed; which {hall be deferibedhes'.
when we come to treat of pumps.

,A fyp/aon, generally ufed 7 for decanting li-

quors, is a bended pipe, whofelegs are of uns
equal lengths; and the lhortef’t’leg muf’t'always
be pUt into the liquor intended to be decanted,
that the perpendicular altitude of: the column of
liquor in theother leg may be longer than the
column in the immerfed leg, efpecially above
the 'futface of the water. For, if both columns
Were equally high in that refpeét, the‘atmo-
fphere, which prelTes as much upward. as down-
ward, and therefore aéls as much upward
againft the-column .in ,theleg that hangs without
'the velTel, as it acts downward upon. the furs
'face of the liquor in the veITel, .would hinder
the running of the liquor through the fyxphon,
even though it were brought over the bended
part by fuétion. So that there is nothi‘ngpleft- i?
l , ,. can e

 

in.

Fig. 9.

follow.

Of Ifi'cz'mulz‘m

caufe the mbtion of the liquor, but the {aperior
weight of the column, in the longer leg, on
account of its having the greater perpendicular

height. ~

Let D be a cup filled with waterto C, and
AB C a fyphon, whofe lhorter leg BC F is im-
rnerfed in the water from C to F. If the end of
the other leg were no lower than the line A C,
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 11. For
although the fuétion would draw fame water at
firl’t, yet the water'would flop at the moment
the friction ceafed ; becaufe the air would act as
much upward againl’t the water at x], as it acted
downward for it by prefiing on the furface at C.
But if the leg .4 B comes down to G, and the
air be drawn out at G by qution, the water will
immediately follow, and continue to run, until
the furface of the water'in the cup comes down
to F ; becaul'e, till then, the perpendicular

‘ height of the column B 11G will be greater than
that of the column C B ; and confequently, its

weight will be greater, until the furface comes
down to F 3 and then the fyphon will Prop,
though the leg C F {hould reach to the bottom a

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 fuélzion at E, the water int--
mediately follows, and by its continuity brings
away the whole from the cup; jufl: as pulling
one end of a thread will make the whole clue

If the perpendicular height of a fyphon, from

the furface of the water to, its bended top at B,

4 be:

 

 

 

 

" ‘PLAFTE XI.

 

 

 

 

8

Of Hydraulz‘ri; V
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; becaufe‘

the weightof a column of water 33 feet high:
is equal to the weight of as ‘Ithick ‘3, column of
air, reachi‘hig from the furfacef'of’ the earth to
the top of the atmofphere; fothat’thereawill,
then‘ be an equilibrium, and Atonfequently,
though there would be weight enough of air
Upon the furface C to make the water, afcend in
the leg. C B .almofl to the height B, if the fy—s
phon were emptied of air, yet the weight would
not be 'fuflicient 'to force the water over the"
bend ', and therefore, it could never be brought
’over into the leg B 11 G. '

, "115

Let a hole be made quite through the bottom Fig. ,5“
of the cup A’, and the longer leg of the bended Tantalus‘:

fyphon DEBG be cemented into thehol'e, fora?"-

that the end D of the {better leg DE may al-
fnoft touch the bottom of the cup within.

\ Then, if water be poured into this cup, it will

rife in the {hotter leg. by its upward prelfure,
"driving Out the air all the way before it through
the longer'leg: and when the cup is filled ab0ve
the bend of the ‘fyphon at F, the prefi‘ure of
the water in the cup will force it, over the bend

of the fyphon ; and it will defcend in the longer ,

leg C B G,‘land run through the bettom, until
the cupvbe emptied. . ' .

This is generally called fl’amalm’s mp, and
the legs of the fyphon in it .are almof’t clofe toa
' gether; and a little hollow flame, or figure of
a man, is fometim’es put over the fyphon to con:

teal it;:the bend E being within the neck of

the figure as high as the chin. S'ogthat poor . '

thirfly Tan-talus vi’tands up to the chin in water,
imagining itwill rife ‘a little higher, and he
- mar

\

116:

The foun-
tam at
command.
I’late Xl.
Fig. 1.

Of Hydraulics; ,
may drink; but infiead of that,_when the water '
Comesupgto his chin, it immediately begins to’
defeend, and fo, as he cannot {loop to follow?
it, he is left as much pain-ed with thirft as ‘
eVer. , .. i _

The device called the fomt'ain‘ at command
aéts ppon the fame principle with the fyphon in
the cup. ’ Let two vefl‘els 11‘ and B be joined .
together by the pipe C which opens into: them
both. Let 1! be open at top, Belofe bethat
tOp and bottom (fave only a {mall hole at '5 to,
let the air get Ont of the vefl‘el B): and d 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 veITel D, fo that the part DE e may be
with-in the Wild, and F without it; the end D
almol’t— touching. the bottom of the vefiiel, and
the end F below the level of D: the vefiel B
hanging to A by the pipe C (foldered into both)
and the whole fopported by the pillars G and H
upon the hand I. The bore of thep-iip-e muf’t]
be confiderably lefs than the bore of the fy-j
phon, . = p ;7 \~
T he whole being thus confirué’ted, let the'
veflel A’ be filled with water, whieh'will run:
though the pipe C, and fill the velTel- B. When
B isfilled above the top of the fyphonjat 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 fy'phon
will run fatter than the pipe, and will foons'
empty the vefi‘el B ; upon which the water will
ceafe from running through the fyphon at F,
until the pipe C refills the veITeI B, and then it

will begin to run as befbre. And thus the {y-
' phon will continue to run and‘f’mp alternately,-

until all the water in the vefiel.fl has 'rum
_- - through

/

Of HydrauZ/‘r Engines; ' 117
thronghtlie pipe C.—-So’that after a few trials,
‘ "one mavenfilyguefs aboutwhat time the fy-
phon will flop, and when it will begin to‘run :
‘ and then, to amufe Others, he may call out/20p,
or raw, actordingly, . i ' '
.. 'Upon this principle, we [may eafily accountlntermz‘t.‘
for Jim‘éfl’fliflifig or reciprocating firings. Let’mg
’Afl be pg}: of a hill, Withinwhich there is a/Wg“
4. Cavity . BB 7-, and from this Cavity a {Vein on Fig. 2.’
Channel running in the direélzion B CD E. The
rain that falls upon the tide of the hill will fink
' and fiteiin through the {mall pures and cranies
G, G, 6,67, and fill the cavity with water K;
When the water i‘ifes to "the level H H C, the
Vein B C DE will ”be filled to C, and the water
Will tun "throughCDF as through a fyp‘honf',
which running will continue until the cavity be
emptied,an then it will 110p until the cavity
be filled‘again. ‘ ' y “ . ' ' ~
J The common pump (improperly called the fuck— The tome . l \
Ling pump), with which we draw water (out o‘memP' ,
wells, is an engine both pneumatic and hydraulic. ‘ '1' i
It 'confil’ts, of a pipe open at both ends‘,‘ in which
is .al moveable pillar“) 0r bucket, as big _as the
here of theupine in that part wherein it thks;
,and ifs.legtheted rou’n’d, f0 as to fit the bore
eXaéllylj, and {nay be moved up and down, with;
"out fulfering anyair to come between it and the
pipe "or pump barrel. '
W6 Ihall explain the c‘onf’trué’tion both of
this and, the forcing-pump by. pié‘tures‘of glafs
models, in which» ‘bOth the ‘Vaélion of the pifions
and motion Of the valves are fee'nf " , y '
Hold themodel D C B Lupi‘ight in the veiTel Fig' 3'
of water K, the water being deep” e'nough to
rife at leal‘t as high, as from fl to L.‘ T he valve
4 on the moveable bucket G, and the valve 5
‘ . l 2 \ ' ‘ on

11% .

Of Hydraulic Engines; ‘
on the fixed box H, (which box quiteqfills 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 bral‘s, and
lined underneath with leather for clofing the
holes the more exactly: and the bucket G is

railed and deprelled 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'itlelf, 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 firlt firoke, the outward air
will prefs up the water through the notched
fooc A, into the lower pipe, about as far as 6:
this will conden‘fe the rarefied air. in the pipe
between 2 and C to the fame date it was in’be-
fore; and then, as its fpring within the pipe,
is equal to the force or prefl‘ure ofthe outward
air, the water will rife no higher by the fitlt.
firoke; and the valve Z2, which was raifed a
little by the dilatation of the air in the pipe, will
fall, and fiOp the hole in the box H; and the
furface of the water will {land at e. Then,
deprefs the pifion or bucket from C to B, and
as the air in the. part B cannot get back again
through the valve 5, it will (as the bucket de-
fcends) raife the valve 4, and f0 make‘its way
through the upper .partaof the barrel’d into the
open 'air. ‘But upon railing 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 u;

, fil

Of Hydraulic Engines; ‘
fill a larger (pace; and f0 its fpring being again

weakened, the prellure of the outward air on ‘
the water in the vefi‘el K will force more water.

up into the lower pipe from 3 to f; and when
the bucket is at its greatef’t height C, the lower

valve b will fall, and PCOP the hole in the box j

H as before. At the next flroke of the bucket
or pilton, the water will rife through the box
H towards 'B, and then the valve 5, Which was
railed by it, will fall when the bucket G 'is at
its greatel’t height. Upon deprefiing the bucket
again, the water cannot be pulhed back through

the valve &, which keeps cltife upon the hole

whill‘t the pifion defcends. And upon railing
the pifion again, the outward prellure of the air

will force the water up through H, where it will ..
raife 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 5, it will raife the
valve 4 as the bucket defcends, and will be

lifted up by the bucket when it is next raifed.’

And now, the whole ‘fpace below the bucket

being full, the water above it cannot fink when:
it is next depreffed; but upon its deprefliOn,:
the valve 4 will rife to let the bucket \go down;

and when it is quite down, the valve 4 will fall
by its weight, and {lop the hole in the bucket.
When the bucket is next raifed, all the water
above it will be lifted up, and begin to run of?

by the pipe F. And thus, by railing and.

deprefling the bucket alternately, thereis f’till

more water raifed by it; which getting above-

the pipe F, into the wide top I, will fupply
the pipe, and make it run with a continued
fiream: '

I 3 5,0;

.119.

:1 2‘6

Of‘ Hydmzthr EngiyeL

So, at every timerthe bucket is ratified, the
valve 5 tiles, and the valve 4 falls; and atevery

. time the bucket is deprefied, the-yalveé falls,
_ and a-rifes. ‘ ' ' ‘

3 As it is the prefi‘ure of the air or atmofphere
which caufes the water to rife, andifouow the
piltOn or bucket G as it is‘drawn' up; and fince;
a column of water; 33 feet. high is 'of equal»
weight with: as thick '3. column of the atmoL
fphere, from the earth to the very top of. the air; ’

therefore,the'perpendicular height of the pifion'

or bucket from the furface of the water in the
well mull always be'lefs than 33 feet ;‘ otherwife
the water will “never get- above the bucket.
But, when the height is lefs, the preflure of the
atmofphere will be greater than the weight of
the water in the pump, and will therefore raife
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 firength
be employed, to raife it with the weight of the:

water above the bucket.

’ The force required to work‘la pump, will be,
as the height to which the water is raifed, and

a; the {quare of the diameter of the pump-bore,

in that part where the pifion works. 'So that;
if tvszopumps 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 narrowefi: ;' "and will therefore reqtiire four.
times as much ft'rength to work it. i ‘ "i '
The wide'nefs’jor‘ narrownefscf the pump, ' in
any other part befides that in {Which thepii‘ton
works, does not make‘th‘e ‘pt‘imp either more or; -
Iflfsdifficult to work, except ‘what- difference

, may arife from the friélion of the Water lathe,

13°.“ 3

Of Hydraulic Engines,

gbore; which is always greater in a narrow bore
than in a wide one, becaufe of the greater
velocity of the water. “ '

The pump-rod is never railed 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‘i-s applied) generally exceeds the
length of the fhorter arm five or fix times; and,
by that means, it gives five or fix times as much
advantage to the power. Upon thefe principles,
it will be eafy to find the dimenfions ofa pump
that {hall work with a given force, and draw
water from any given depth. But, as thefe
,calcul'ations have been generally neglected by
pump—makers (either for want of {kill or in-
duf’try) the following table was calculated by the
late ingenious Mr. Boarbifor their benefit a“.
In this calculation, he fuppofed the handle of
the'pump to be a lever increafing the power
five times; and had often found that a man can
work a pump four inches diameter, and 30 feet
.‘high, and difeharge 27; gallons of water (Eng-
lifh wine meafure) in a minute. Now, if it be
required to find the diameter of a pump, that
gihall raife water with the fame cafe from any
other height above the furface of the we]! ; look
for that height in the firl’t column, and yover~
.againlt it in the fecond you have the diameter or
‘width of the pump; and in the third, you find

the quantity of water which a man of ordinary .

fi'rength can difch‘arge in a minute,

*V I have taken theliberty to make a few alterations in"!

:Mr. Boat/2’s numbers in the table, and to lengthen it out
from Sqfeet to too." . ’ - /

\

I 4'. ‘ Height

121’

'12:;

F331 4g
'1 he

jbrcz'lzg-,

{Cm/11). ‘

Of Hyfiaufic Ehgz'nes.‘ -

 

 

 

 

 

Height of the Diameter of the W‘aterfiifehhrged'ir
pump above 3 bore where the a minute, Englifh
the furface of ' bucket‘works.» wine meafure.
the welt]. I I ' ‘ w .
H I-a -‘ A
s“: , '2 S ‘ '-"’
IO, 6 .93, 81 V6
15 5 ~66 ‘ . 54 '4‘
20 4 999 > 40 7
25 4 .38. 32, 6
3C) 4. .00 27! 2
35 3 -70 23 3
4O 3 '.46 20 3 t
45 3 27 ' I8 I
50 ‘3 .10 16 . 3
55 ,2 .95 I4 7
60 2 .84 .13A 5 -
65 2 “.72 12. 4
7o _ 2 .62 , II 5;
75 2 é53 » ‘0 Z
‘ 80 »2 L45 » ‘10 2
85 2 ~38 9 5
90 2 .31 9 I
95 2 , .25 8 5
100 _2 .19 -8 t

 

 

 

The forcing-pump raifes water through the
box H in the fame manner as the fuckingopump
tides, when the plunger or pifion g is lifted
up by the rod Dd. But this plunge—r has, no
hole through it, to let the water inétlhe barrel
.8 C get above it, when it is depreifed to B, and
the valve. 1! (which rofe by the afcent of the

fivatee

Of ‘ Hydraulic Engines;
water through the box H ,p when the plungerg‘
was drawn up)‘falls down and {tops the" hole in;
H, the moment that the plunger is raife'd to its
greatef’t 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 L 3; but
has a free pafihge by the cavity around H into
the pipe MM, which opens into the air-veffel
K K at p,’ the water is'forced through the pipe
MM by the defcent of the plunger, and driven
'into the airrveifel; and in running up through
the pipe at P, it opens the valve 4-, which {huts
at the moment the plunger begins to be raifed,
.beeaufe the aétion of the water againf’t the under
fide of the valve then ceafes.
The water, being thus forced into the air-
" veITel K K by repeated firokes of the plunger,
gets above the lower end of the pipe GHI,
and then begins to condenfe the air in the veffel
KK. For, as the pipe GE is fixed’ air-tight
into the veffel below F, and the air has no way
to get our of the ve{l"el but through the mouth
of the pipe at I, and cannot get out when the
~ mouth I is covered with water, and is more
and more econdenfed as the water rifes Upon
the pipe, the air then begins to aét forcibly by
its fpring ‘againi’t the furface of the water at H:
and this aétion drives the water up through the
pipe [HG F, from whence it fpouts in a-jet S
to a great height; and is fupplied by alternately
raifing and deprefiing of the plunger g, which
, conf’tantly forces the water that it raifes through
the valve H, along the pipe MM, into the air-
veffel K K. , i
The higher that the furface of the water H is
raifed in the air-vefiel, the lefs {pace will the
‘ air

:23

:24-

Of , Malta/2'; Engines.

air be condenfed into, which. before filled thaf
yefi‘el; and therefore the, force of its fpring wil

be f0 much the fironger 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 whi‘lfi the plungerg is rifing, the fiream
or jet 5 will be uniform, as long as the action
of the plunger continues: and when the valve 5,
opens, to let the water follow'the‘ plunger up-
ward, the' valve oz lhuts, to hinder the water,
which is forced into the air veflel, from running
back by the pipe M .M into the barrel of the.
pump. . _

" If there was no'air-vefliel to this engine, the
pipe G HIwould be joined to the pipe MMN
at P; and then, the jet S would flop every
timethe plunger'is raifecl, and run only whet;
the plunger is‘deprefined. '

-lVlr. Newficzm’s water-engine, for extinguilh;
ing fire, confifizs Of tvyo forcingpumps, which
alternately drive water into, a clofevellel of air;
and by forcing the water into that wife], the
~air in it is thereby condenfed, and comprefles
the water fo firongly, that it rufhes out with
great impetuofity and force through a pipe that
Comes down into it; and makes a continued
uniform {tream by the condenfationof the air
upon itsfurface in- the veflel. ‘ i, i -

By means of forcing-pumps, water may be

.raifedto any'heigjht above the level of a river

or l‘prin'g; and machines may be contrived
to work thefe pumps, either by ‘a running
fiream, a fall ‘of, water, or by horfes. An

- int-tame in each for; will be futiiicientv to fhew '
5h? whoa: , .

Fir £13

 

 

 

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m 4H m ._ , ,

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Of Hydraulic E: 27165. .125 ,

Firi-‘t, by a running Puccini, or a fall of wacmate x11,
ter. 7 Let .411 be fatwh'eel, turned by the fall {Fig 1
if water B B; and have any nnrnberof cranks "
(fuppofel fix) as C, D,E_, F, \G, H, on its axis,
according to the firength of the fall of water,

'and the height to which the water is intended to

be railed by'the engine} As the wheel turns ‘
round, thefe cranks moire the levers c, d, e, f, gflz A P811115,
tip and down, by the” irony rods 5, [Q], m, n, a -, engi“? t9; ‘
Which altetnately mile anddeprefs the pil’tonehyi‘ig 5;
the 'other iton rod§ «p, q, r,*fi..g, at, w,x,y,. i‘n -; is

twelve pumps; nine Whereof, as‘ L, M, N, O, P,7-»il'

52, R, S, T, appear in the plate; the other thrlee‘il!
being hid behind the world-at V. Andras pipes
may go from all thefe pumps, to convey the
water (drawn up by them‘to a {mall height) into
.3 clofe cifiern, from which the main pipe goes
93‘, the water will be forced into this clftern
by the defcent of the'pil’tons‘fl And as each
pipe, going from‘ its irefpe'etive. pump into the
cifiern, hash valve at its end in the cil’tern,
thefe valves: will hinder the return of the water
by the «pipes-5 and therefore, vyhen the ciltern
is once full, eachvpil‘ton upon. its defCent will
force the water (conveyed into, the ‘lc'ifitern‘ by at ‘

formerfitdge) up the_‘mein ‘ pipe, ,to the ‘

height, the: engine was intended to: raife it: -

which height depends‘ upon the quantity, raifed,
and the, power that turns, the wheel. When
the power upon the wheel is“ leffened by any
defeétfiof the quantityof'wgter turning it, a
proportionable number of; theipnmps may be. ‘
laid afide, by difengaging. ”their todsfromfthc
iyibratin'g‘jilfetrei"s. ' 7 V g ,

p ' 'This figgre is a reptefentation of the engine,
erected at Blenheim for the Duke of Marlbqrougb,
by the late: ingenious Mt. flldeiftza. The waters}, .
,- . . Wh§¢l

1’26 . Of Hydraulic Eflgiaerf
’wheel is 7’; feet' in diameter, according to Mr.
Switzer’s account in his Hydraulics.

When fuch a machine is placed in a fiream
that runs upon a finall declivity, the motion of
the levers and action of the pumps will be but
flow; fince the wheel muf’c go once round for
each firoke 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 flA’, upon its axis, to turn a trundle

‘ upon each fidc; the cranks being upon the axis
of the trundle". And by proportioning the’ eng-
Sizheel-s to, the trundles, the motion of the pumps-
may be made quicker, according to the ruantity
and firength of the water upon the firf’t wheel ;‘
which may be as great as the workman pleafes;
according to the length and breadth of the float-
boards or wings of the. wheel. In. this manner,

. ’ the engine 'for railing water. at Lcfidon-Bridge is,
c‘onl’truéled; in which, the water-wheel is 20 ,
feet diameter, and the floats I4. feet long.

A pump. Where a firearm or fall of water cannot be had,

engine to and gentlemen want to have water raifed, and

80 W brought to their houfes from a rivulet or 'fp'ring ;

horfes' this may be efl‘eéted by a horfe-engine, Working

three forcing-pumps which Fraud .in; a refervoir'
filled by the fpring or rivulet :* the pifions being

moved up and down in the pumps by means of a

triple crank fl'B C, ‘w‘hich, as it is turned round

by the trundle G, raifes and deprell‘es the rods

13,1117. The trundle may be turned by {uch a'

wheel as F in Fig. I. of PlateerIl, having levers

y;y,y._y, on its upright axle, to which horles may i

be joined for working the engine. And if the

wheel has three times as many cogs as the
trundle has Ptaves or rounds, the-;trundle and
cranks will make three revolutions fer every one

of

Fig. 2.

Of Hydraulic Engims; 127,
of the wheel; and as each crank will fetch. a ‘
firoke in the time'it goes round, the three'cranks
will make nine firokes for every turn of the great
"Wheel. _ A 1 i

The cranks {hould be made of caft iron, be-
caufe that will? not bend; and they lhould each
make an angle of 1-20 with both of the others,
as at oz,b,c-, which is. (at it were) a view of their Plate XII. ‘
radii, in looking endwife at the axis :, and thenfig. 2.
there will be always one or other of them going
downWard, which will pufh the water forward
with a continued fiream into the main pipe.
For, when 5 is almol‘t ati‘its loweft fituation, and
is therefore jufi beginning to" lofe its aé‘tion upon
the pifizon which it moves,.c is beginningto move
downward, which will by its pif’ton continue the
propelling force upon the'water: and when c is
come doWn to‘the polition of I), a-will be in the
pofition of c.

The more . perpendicularly the pii’ton rods
move up and. down in the pumps, the freer and
better will their firokes be: but a little, devia-‘
tion from the perpendicular will not be material,
Therefore,‘When the pumprods D, E, and F
go down, into a deep well, they may be moved
direé‘tly by the cranks, as is done in a very good
horfe-engin-e of this fort at the late Sir7ames
Creed’s at Greenwich, which forces up water about
64 feet from a well under ground, to a relervoir
on the top of his houfe.' But when the cranks
are only at a {mail height above the pumps, the
pii’tOns molt be moved by vibrating levers, as in
the above engine at Blenheim: and the longer
it the leversare, the nearer will the firokes be to a.
perpendicular. . ' i

Let ‘us fuppofe, that in fuch an engine as Sir Acalcu—
j’amer Creed’s, the great wheel is 12 feet .diame- lation of ‘
ter, the trundle 4, feet, and the radius or length the quan‘

of [try of

129 Of Hydmz‘ilz‘c Enginér. .
waterfhafof each Crank 9 inches, working a pifion’ in iéé
may be pump. ‘Let there be three/pumps in all, and'thé‘
”He‘lby bore 0,. each pump be four inches diameter:
ahorie- ' ..-- . . » -'.
engine. Then,_1f the great wheel has- three times as many
c0gs as the trundle has fiaves,‘ the trundleand

cranks will go three tiines round for each” revo-

ltition of the horfes and Wheel, and the three
“cranks will make nin‘e firokes Of the pumps in

that time, each firoke being 18 inches (or double"

the length of the crank} in a fouréinclr bore, Let"

the diameter of the horfe-walk be 18. feet,“ find

the perpendicular height to which: th'eWater is‘

raifed above the furfaée of the well be 64 feet.
if the horns go at the rate of two miles an-
hour (which is very moderate walking) they will
turn the great wheel 187 times round in ari
hour. . ' _
‘ In each turn of the wheel the ”pillons rhake 9
firokes in the pumps, which amount to 1683 in‘
an hour. 9 , 7
Each firoke raifes a column of water 1 8 inches‘
long, and four inches thick, in the: pump¥bar-
rels; which column, upon the defcent.;OF the’
pifion, is forced into the main pipe, whole per-
pendicular altitude above the fu‘rface of the welf
is 64. feet. ' ' , .
New, fince a column of water 18 inches long;
and 4 inches thick, contains 226.18 cubic inches,
this number multiplied ,by 1683 (the firokes in‘
an hour) gives 380661 for the number of cubic
inches of water raifed in an hour. ’
'A gallon, in wine meafure, contains 23 1 cubic
inches, by which divide 380661, and it quotes; .
1468 in round numbers, for the number ofgii‘ifh
lon‘s railed in an hour; which, divided b37763;
gives26—; hogflieads.———If the horfes go falter,
the quantity raifed will be fo much the greater.
In this calculation it is fuppofed that no water
- ‘ 1-3

Of Hydraulic Engines;
is walled by the engine. But as no forcing
engine can be fuppofed to lofe lefs than a fifth
part of the calculated quantity of water, between
the pifions and barrels, and by the opening and
fhutting of the Valves, the horfes ought to walk
al—moi‘t 2; miles per hour, to fetch up this lofs.

A column of water 4 inches thick, and 64;

feet high, weighs 3499'? pounds averdupoife, or
42 4-1—5; pounds troy ; and this weight together with
‘the friction of the engine, isthe refil’tance that
limit be overcOme by the {trength 0f the horfes;

The horfe-tackle {hould be f0 'contri'ved, that:

the'horfes mayirather pulh on than drag the '

leversafter them. For if they draw, in going
round the walk, the outfi'de leather firaps will
rub againlt their fides and hams; which will
hinder them from drawing at right angles to the
levers, and f0 make them pull at a difadvantage:
But if they pull} the levers before their breal’ts,

inflead of dragging them, they can always walk

at right \angles to thefe levers. ‘ ,
It ‘is no ways material what the diameterof
the main or conduct pipe be: for the whole

refiftance of the water therein, againl’t the horfes

will be according to the height to which it is
raifed, and the diameter 'of that part of the pump
in which the pil’ton works, as We have already
obfe’rved. ‘ So that by the fame pump,~ an equal
quantity of Water may be raifed in (and confe—

quently made to run from) a pipe of a foot dia-e

meter, withthe fame eafe as in a pipe of five or
fix inches: or rather with more eafe, becaufe its

velocity in a large pipe will be lefs than in a,
fmal'l one; and therefore its. friétion againfi: the '

fidCS 'of the pipe will be lefs alfo.

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
‘ 5 ' above

1’29

330

Fig. 3;

Of Hyzimzziz’c E fighter; ,

above the level of thelfpring. So that. the fame I

farce,‘which would raife mate: to the height AB
in the upright pipe Ai k l m 7104 p q B, will raife it
to the iameuheight‘ or IICVCLBJ H in the. oblique ._
pipe .4 E F G H. {F or the preflhre of'the'water at
the end A of the latter, is no more than its prefg
fure againfi the end A of the former.

The. weight 0t prefihre 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 parallelto the horizon. F or, although the
water‘ in the upright pipe AB would require a,
force appliedvimmediately' to the lower end .4
equal to the weight of all the water in it, to {up
port the water, and a little more to drive it up,-
and out of the pipe; yet, if thatpipe be inclined
from its upright pofition to an angleof ‘80 de-
grees (as in A 80) the .force re‘Quited tofupport
or to mile the- fame cylinder of water will then
be as much lefs, as the fine 80 b is lefs than the;
radius flBgior as the fine of Sol-degrees is lefs
than the fine of 90. And {0, decreafing as the
fine of the angle of elevation lelTens, until it at;
rives at its level AC or place of tell, where the
force of the water is nothing at either end of the
pipe. For, although the abfolute weight of the

a water is the fame in all pofitions, yet. its pref-V

fure at the lower end decreal‘es, as the fine of
the angle of elevation decreafes; as will appear
plainly by a farther con fideration of the figure. ‘
Let two pipes, AB and 1% C, of equal lengths
and bores, join each other at fl; and let the

' pipe 1? B be divided into 100 equal parts, as

the fcale S is; whofe length is equal to the

length of the pipers—Upon this length, as a

radius, defcribe'the quadrant BDC, and divide
it into 90 equal parts or degrees.

Let the pipe 46' be elevated to 10 de‘gree‘s‘

J “P0“

0f v Hydr‘dulz'c' Engines.
upon the quadrant, and" filled with" water;
then, part of the water that is init will rife in
the pipe A73, and if, it befkept full of Watfil’, it
will rail‘ez the water in the pipe 4 B from .flto i;
that is, to a leveli to with the mouth 'of‘ the
pipe atIoE and the Upright line a‘io, equal to
A}, will 'be the fine "of“.“io degrees elevator];
Which—being meafured tampon/the fcale S, _wi ll be
about ~17.4; of'fuch parts as thepipe cb‘ngiains
100 in length : {and therefore, the fofce or pref-

fure of the'water at Al, in: the pipeifl‘to, :will ‘ M

be to thesforcc or pr’eflhre at" A in the pipe
AB, as 17.3 to 100.. f ‘ i' ' ’ f
Let the’fame pipe beelevated to 20 degrees
in the quadrant, and if it be kept full of water,
part of that watbi' will run into the pipe 11 B,
arid rife therein to "the height At,- which is
equal to ‘the‘length of lthe upright line b” zq,‘ or
to the fine-of 230 degrees? elevation-"g iwhich; be—
ing mediated upon the feale S, 'will :be 234."? of
filth parts as the pipe; contains 100 in length.
Aind thetefo-re, :the prefl‘ute Of the vilate‘ir at 1?,
[in the full'pipe: A 20, will. be to its pfefiiirfie, if
that pipe Were raifed to the perpenditular fijtua-
flop/{8; 3934.22 to, 1001 ‘ ' ' ‘3 a 7
. :Elevaoe the pipe to the ‘pofition fl; goonthe
quadrant, and if it be gfupplied with 'wat‘er, :the
water will rife from it, into the pipe £8, to
the height 241, or to thefame level with :the
mouthjof the-pipe at 30.’ The line of this ble-
vation, or of the angle of - 30 degrees, [is c 1‘ o ;

which is jul’tequal to half the length of the pipe, * l

or to 50 of fuch parts of the fcale, as the letiiigth
of the pipe contains Ioo.‘ . Therefore, the pref.
lure of the water at Air? a pipe elevated 30
degrees above the horizontal level, will be equal
to one half of what it would be, if the fame
pipe flood upright in. the fituation flB.
» ‘ K 1 And

' r311

132

Of Hydi'czulic Engines. ‘ 4
‘ fiAnd thus, -by elevating the pipe to 40’, 5’0,
60, 70, and 80 degrees on the quadrant,,the
fines of‘ thefe elevations will be d 40, e 50, f 60,
g 70, and 1780; which will be equal. to the
heights 11m, .472, do, 11;), and Ag :’ and thefe

 

Sins of Parts 'Sine of ' Parts Sine of Parts 4

1i

 

'D-1 '17 D31 515~D.61‘ 875' .
35 32 530 . 62 883 >

I; 2
- 3 52 33 545 63 89I
4 4 70 . 4344.559 ‘ 64» 899
‘ 5 87 35 573» *65‘ 906 t
6 104 - 36 588 - 66,913
,7 122 37 .602 _ 67‘ 920- _
8 139 ,38 616. g 68, 927
9 1564‘ 39 “629 4169- 934 ,

IO, 4 ,’74 40 643 : 7o ,, 940 4

II 191 41 "656 775.» 945
~ ~ .123 208, 42 669 :4 72.. ,"9551 f
“z 13' 2425' '43 682 .73: 956
I4: 242 - 44 '695 74 961
I5 259 45 5707 475 966 r
,164 276 46 719 *5 376- :970. :
' I7 292 47 ‘731 . 77 .974»~
‘Wirv18 “309 48 743 - 78 *978
- 4,.19 325. 49 755 79 V982 ‘>
20 34.2 50 766 80 9815 4’
4::21 ~358- 5I 777 .-‘8r 988 .
2'2 375 52 788» ' 82 990 i
23 39I 53 4799 83 992
24 407 ,54 809 84 994
25 423 55 819. 85 996 r
26 _438 56 829. 86 . 997
27 454. 57 839 87 998
28 469 4 58 848 88 999 .-
29 485 59 857 89 1000 E
30 500 60 866 90 .LIOOO _
heights

 

 

 

 

 

 

 

 

 

 

Of 113611111122 Engines.
heights meafured upon the fcale S will be
_64. 3, 176.65 86 6 9410,: and 98. 5 , which
exprefs the prefixes at A' inell thefe elevations,
contrderimg the prefure 1n the upright pipe .43
as 100.

‘ Becaufe It may be of me to have the lengths
of all the fines of a quadrant from 0 degrees
to‘ 90, We have given the foregoing table, {hew—
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
1 if you fuppofe the length of the pipe to be di»
~vided only into too equal parts, the lai’t figure
of each partor fine mutt be cut ofi“ as a decimal,
. and then thofe Which remain at the left hand
of this feparatton will be integral or whole
parts.-
Thus, if- the radius: of the quadrant (fup-
pofed to be equal to the length of the pipe 117C)

be divided into 1000 equalc 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 7o. .7 0r 70—10— of thefe
parts. For, as 1000 is to 707, f0 is IOO to
‘70 7 ‘ i“

As it is of great iniportance 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, f0 as by
knowing what weight is to be raiied, they may
1 proportion their engines to the force which
they can afi‘brd to work them , we {hall fubjoin
tables Ihewing the number of cubic inches of
water contained 1n an upright pipe of a round
bore, of any diameter from one inch to fix and

K 2 a half;

1‘33?

134

Of Hydraulic Brigitta;

_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-
dupoife ounces. The number of Cubic inches
divided by 231, will reduce the‘Water to gal-
lOns in wine meafure; and divided by 282, will
reduce it to the meafure of alergallons. Alfo,
the troy ounces divided by 12, will reduce the
weight to troy pounds; and the av‘oirdupoife
ounCes divided'by 16, will reduce the Weight
to avoirdupOife pounds.

And here I, mul’t repeat it again, that the
weight or prefl'ure of the water acting *againl’c- 4
the power that works the engine, mutt always
'be el’timate‘d . according to the perpendicular
height to which it is to be raifed, Withoutiany
regard to the length of the conduétjpipe, When
it has an. oblique pofition; and as if the diame—
ter of that pipe Were juf’t-equal' to the 'diam'erer'
of that part of the pump in which the Tpif’tonr
works. Thus, ’ by the following tables, ‘ the
prefihre of the water, againl’t an engine whofe
pump is ‘of a 4.;— inch bore, and the perpendi-
cular height of the water in the conduét-pip’e is
80 feet, will be equal to 8057.5 troy ounces,-
and , to. 8848.2. avoirdupoifeounces; which
makes 671.4 troy pounds, and 553 avoi‘rdu-
poife. , _ ' i t '

For any bore whofe‘diameter KexCeedis'égl
inches, multiply the numbers on the following

- page, againfi any height, (belonging to I inch
diameter) by the fqu'are of the diameter'of the
given bore, and'the products Will‘be'the num-

ber of cubic inches, ~ troy ounces, and 'avoird-u-
- po‘ife ouncesof Water, that the given Bore Will

Contain.

J Inch

IZydrq/iatz’ml T526135.

 

”“7.in Inch" Vdiarhetéf. 7

 

s“

 

 

 

 

 

 

 

 

.r 5? ', EQIantirty ' " Weight [In avoir‘
1 g. in Cubic _'in'troy dupoifc.
' 03' 'i‘inch‘es. ‘ ounces. ounces.

1 9-42 4-97 4 546

2 18.85 9.95 10.92

3 5 28.27 14.92 16.38

4 37.70 ‘ 19.89 21.85

5 '47-!2 24.87 27-3.1

6 _ 56.55 . 29.84 32.77

7 9 65.97 34.82 38.23

, 8 75.40 39-79 43:69

/ 9- . 84-82 44-75 49416

10 ' ‘ 94.25 49.74 54.62,

20 . 188.49 99.48 109.24

30 v 282.74 - 1149.21 163.86

" - 40 376-99 @9895 218-47

50. 471.24 3,248.69 - 273.09

60 565-49 ~ 298-43 327-71

70 659-73. 348.17 382-33

80 753-98 39790 436-95

90 :848-23 447-64 4-91-57

109 942.48 497.38: 546-19

200 J , 1884.96 994.76 1092.38

 

 

EXAMPLE, Re'qm‘red tbe numéér of cubic inrbes, 'dfld‘ t5:
(weigbt {3}“ flat water, in an tying/2t pipe 278 feet bigb, and ,

I; 2'an diameter ?

Here the muck fingle
decimal figure is only
taken into the account :
and the'whole being re-
duced by diviflon, a—
mounts to 25—;— winc‘galg
Ions in meafure ; :02;ng
pounds troy, andco 213;~
pounds avoiIrdupoife.

 

’ - Cubic Troy Avoird. ‘
Feet inches 02. oz.
zoo-«4241.1--2238.2--24‘57.8

70-44844» 783.3» 800.2

8-- 169.6--

89-5--

 

Anf. 278--5895.I—-3I I x.o--3416.3

 

K5

Thefe

135

Ebdrvffatzml- Table:

1% Inch diametcr

it"A-flvml' 4n

 

 

 

Qjantity

 

 

 

 

 

 

 

 

 

 

E37 j Weight, ' Iri aVoir-
;: in cubic Vin troy’ dupoxfe
03' ' inches. ' ounces.w ’ 0Linces.
ET
1 21:21 ' 11.19 12.29 .
.2 42.41 22.387 24.658
'3. 63: 52 33-57 35-87
, 4 84.82 44.76, 49.16
5 16663 5 55-95 61:45
8 6 ~ 127-23 67-15 ~ 73-73 V
7 147.44 78.34 86.02
4 8 ' 169.65 89.53 98.31
9 190.85 100.72 110.60
10‘~ 212.06 111.917 7, 71.22.89.
'20 424.12 1 223.82 245.78
307 6362.17 335-73 ' _' 368.68
40 848:23, 447- 64, 491.57
’ 50 [1060.29 559. 55 ’ '9 614.46
66 1272-35 ,' 67I 46 [737-35
70 1484.40 783. 37 9 860.24
‘ 80 1696.46 895. 28 7 983.14
. 90 1908.52 1007.19 3 1106.03
100 2120.58 1119.10 1228.92
”260 4241-15 “22-38-20 2457-84

 

 

Thefe tables were at £319: calculated to fix
decimal places for the fake of exaEtnefs, but
111 tranfcribing them there are no more than
two decimal figures taken into the amount, and
fomccir'ncs butbon9,bctj:aufethere.1s no necemty

for

wdrgflatical Trifles;

 

2 Inches diameter..

 

20
30
40
50
60
70
8-0
.90
100
200

 

[Sb oox'rm'm-pmp... I'q81q2aafl_

 

 

 

 

 

 

 

 

i Qy-antity W eight 7 Ina‘voir‘;
_in cubic in troy' dupoife
. ”inches. ounces. ounces.
637-70 19:89 21-85 i
75-40 3979 43-69 ,
113.19 5968 65-54. i
150.80 . 79.58 87.39 ’
188,50 ‘ 99.47 109.24
226.19 119.37 f 131.08 =
263.89 : 139.26? 152.93
301.59 159.16‘ 174.78
339.29 179.06 196.63
376.99 198.95 218.47
753-98 39790 436-95
1130.97 596.85 655.42
1507.97 795.80 873-90
1884.96 994.75 1092.37
2261.95 1193.70 1310.85
2638.94. 1392.65 , 1529.32
3015.93 1591.60 91747380
3392.92 1790.56 1966.27
3769.91 1989.51 2184.75
7539-82 2979-00

' .4369-50 ._

 

 

for computing to hundredth parts of an inch or
'of an ounce in praé‘tice.
appeared in print before, it may nopbe famifs *
‘ :9 give the'reader an account of the principles

And as they never

upon which they WCXCQQHRW<36¢ . _

K4

137; ‘

34:38 .

[1922.72.22.21 2452:;

 

 

 

9 2% Inches; diameter.
p? anntity 'Weji'ght ,. Inavoir-
1% g. in-cubic , in troy dupbife
03' inches. ounces. 4 ounces.
' I 58.90 31.08 34.14
2 117.81 62.17/ "68.27
_3 176.71 93.26 102.41
4 r 235.62 124-34 If36~55
‘ 4'5 294.52 1355.43 . 170.68
6 353.43 186.52 204.82
7 412.33 217.60 238.96
8 ‘ 471.24 248.69 273.09
4 9 530-14 . 279-477 307-23
10 589.05 310286 . 341.37
. 20 1178.10 621.72 682.73
, 30 1767.15 932.58 1024.10
40 2356-20 124344 1365-47
'50 2545.25 155430 1706-83
60 3534.29 1865.16 2048.20
70 4123.34 2176.02 2389.57
80 4712.39 2486.88 2730.94
190 5301244 2797-744- 3072-30
100 5890.49 3108.60 2413.67
1L 200 11780.98 6217.20 4827.34

 

 

 

 

 

 

 

 

 

J

The fplidity of cylinders are found bymuL
tiplying the'areas ’of' their bares by4thcir alti-
tudes. ’And ARCHIMEDES gives the following
proportion for finding the area of a circle, and

1h; foljdjty pf a cylinder raifgd upon tha; circle:

As

wirwdfflalifafilmv '

N... .2. .. my... 1...

 

 

 

 

 

 

 

 

 

 

 

 

 

. 31.;1fiches Tclfif‘stifit’,fsini" 4 , .

E? "‘Cflléntity 1|~Weight - "In‘a‘voit—

g. ”in cubic ' it!= troy“ — dupoifc

. .03” inches. ‘ “O'unices. ‘ '0unces’.‘
7; '1 ‘ 84.8 L l 44.76 49.16
2 169.6 89.53 98.31
3 254-5 134-29 ’ I47*47
4 1. 239.3 179.06 196.63
5 424.1 223.82 245.78
W6 508.9 268.58 ' 294.94
7 593-7 313-35 344-10
8 698.6 358.11 393.25
‘9, 763.4 402.87 ' 442.41
10 848.2 447.64. 491.57
20 1696.5 895.28 983.14
'3‘0' 2544.7 , 1342.92. 1474.70
40 73392.9 ' 1790.56 1966.27
‘50 4241.1 2238.19 2 ‘ 2457.84
60 5089.4 2685.83 : 2949.41
79 ,_ 5937-6 3133-47 3449.98
80 6785.8 3581.11 3932.55
90‘ .7634.1 4028.75 4424.12
100 7 8482.3 - 4476.39 4915.68
200 16964.6 28952.78 9831.36

As 1 is to 0.785399, {0 is the’fquare of the
diameter to the‘are'a of the circle. , ‘And 'as 1 is
to 0.785399, To is the fquare of the diameter
multiplied ”by the height. to the folidity off the
cylinder. By this analogy the folid inches and

partg

I39

\

Hydrcflatiml Tables;

 

 

 

 

" i I 33%‘5-Ih0hes diameter. d
S? ngantity ,Weigh: - Inlayoir-i ‘
g. in' cubic - introy dupoife
0'5" inches.’ ounces: _ 01m¢es.
I 115.4 “ 60.9 9 66.9
2 230.9 -- 121.8,, 1333.8
3 346.4‘ 182.8 ‘ 2.90.7
\ 4 461.8 243.7 267.6 .'
5 577-3 304-6 334-5
6 692.7 «365.6 401.4
7.. 808.2 ,. 426.5 468.4
' 8 923-6 487-4 535-3
9 ‘ ' 1039.1 548.4 602.2
‘10 1154.5 609.3 . .. 669.13
i 20 2309.1 1218.5 1338.2
Q 30 3463.6 1827.9 2007.2
‘ 40 4618.1 2437.1 2676.3
. 50 , 5772-7 3046-4. . 3345-4
7: 60 6927.2 3655.7 , _ 4014.5
70 8081.8 __ 84265.0- 4683.6
80 9236-3 4874-3 5352-6
90 10390.8 5483.6 6021.7
100 31545.4 6092.9 _ 6690.8
1200 23090.7 12185.7 i 13381.5

 

 

 

 

 

 

 

 

 

 

 

parts of an inch in the tables are calculated to a

'. cylinder 200 feet: high, of any diameter from I
inch to 6;, and may be continued at pieafure.-.’

And as to [the weight ofa cubic foot of running

water, it has bcgnvoften found Upon trial, by:

.7 , ' ' Dr.

Hydrafiatical Tables.

 

4. Inches diameter. .

 

 

‘ ‘1

 

 

 

 

 

 

 

 

 

 

 

 

 

Pg? (luantity ‘ Weight In avoir—
E;- in cubic in troy ‘ dupoife
0; inches. ounces. . ounces.
I 150.8 79.6 87.4.
’ 2 30126 159.2 . 174,8
‘ 3 452-4 238.7 262.2
L4. 603.2 318.3 34.9.6 ’
5 754.0 397.9 43629
6 ' 904-8- 477-5 524-3
7 1055.6 557.1 , 611.7
8 * 1206.4 636.6 699.1
9 1357.2 716.2 786.5
10' 1598.0 795.8 873.9
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 15079.7 7958.0 8739.0
200. 30159.3 15916.0 17478.0 _

 

 

Dr. Wyberd and o
troy, which is equa
Therefore, fince t
inches in a cubic foot,
contains 1,8949 cubic inch 5- and an av

poife.

thers, .to be 76 pounds

1 to 62.5 pounds avoirdu-The
here are 1728 cubicWeightof
running

-a troy ounce of water
water.

\

oirdupoife
ounce

141

.142.

fzfildrojiaz‘z'cdl T251425.

 

4—;— Inches diameter.

*i

 

i

 

 

 

 

 

 

 

 

 

 

 

 

 

3'? Quantity Weight. Irravoir-
; in cubic. in troy dupbife
0; inches. ounces. 1 ounces.
1 190.8 ‘ 100.7. . ” 110.6
2 381.7 201.4 221.2
3 572.6. 302.2 4331.8
4 763-4 4029 442.4
5 954-3 503-6 553-0
6 1145.1 . 604.38 663.6
' 7 1338.0 705.0 774.2
» 8 1526.8 805.7 884.8
‘ 9 1717-7 9065. 995-4
10 1908.5 1007.2 . 1106.0
20, 3817.0 2014.4 _ 2212.1.
30 5725.6 3021.6 _ 3818.1
40 7634.1 4028.7 4424.1
50 9542.6 5035-9 , 5530.1
60 ' 11451.1 6043.1 6636.2
70 13359.6 7050-3 77142.2
80 15268.2 8057.5 8848.2
90 I7176-7 9064-7 9954-3»
4 100 19085.2. 10071.9 11060.3
1 200 38170.4 A 20143.8 22120.6

ounce of Water 1.72556 cubic inch. Confe-

quentiy, 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 weigbt

‘5.

Hydmflafiml Tables.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_ .14.:3
'5 ' Inchesfiiameten “‘1
E (luantiey vWeight In avoir-
, g— in cubic in troy : dupoife
0:01; inches. ounces. ounces.
1 235.6 124.3 ‘ 136.5
4 _ 2’. 471.2 248.7 273.1
,3" 706.9 373.0 409.6 _
a 4* -942-5 497-4 9 546-2
i 5 : 1178.1 9621.7~ 682.7 .
i 6- 1g13.7 746.1 819.3 ;_
7 , 1 49-3 870-4 . 955-8
8 1885.0. 994.8 ' 1092.4. 1
9 2120.6 1119.1 1228.9
10 2356.2 _ 1243.4. . 7 1365.55i
20 4712-4 . 82486.9 2730.9
. 30 7068.6 3730.3 .1 4096.4 :
s: '40 9424-8 4973-8 ‘ 5461-9
fl 50' 11780.0 6217.2 ‘ 6.82.7.3
Z 60': 14137.2 ‘ 7460.6 9 8192.8 1
70 16493-4 . 8704-1. 9553-3 j
° 80.. 18849.6 9947.5 10923.7‘
2 90 21205.8 11191.0 12289.2-
?' 100‘ 23562.0 12434.4 13654.7 '
3 2901471240 243683 ‘ 27599-39!

 

in avoirdupoifesounces. By this method, the ‘
.weights .ihewnjn the tables were calCulgted ;
randare near enough for any common praéhce.

The fire—engine comes next in order to be eX- The fire-
plained 3 but as it would be difficult, ~even 1131‘)! engine.
_ . i r t e

 

 

 

 

 

 

 

 

 

 

 

‘ .144. Hydro/iatical I T615165.
5—; Inches diameter.
9? V Quantity i .Weight i In avoir-
; in cubic in troy dupoife
65’ inches. ounces. . ounces.
5-" _ _
1 285.14 150.5 164.3.
2 520.2 300.9 328.5 7
3 855 3 451-4 492.8}:
4. 1140.4 601.8 ' ' 657.1 2;
5. 1425-5 _, 7521-3 821-3 -
6 1710.6 902.7' ‘ 985.6 ‘
7 1995.7 . 1053.2: '- 1149.9 ,
8 2280.8 * 1203.6: ' 1314.2
'9 2565-9 1354-1 . 1473-4 »
. 10 2851.0 ‘ 1504.6 1642.7
‘20 5702.0 83009.1 ' 3285.4 4
30' 8553.0 4513.7 4928.1
40 11404.0 6018.2 6570.8 V
50 14255.0 7522.8 8213.5 ‘
- 60 ”17106.0 9027.4 9856.2 _’
70 19957.0 10531.9 11498.9 5
80 22808.0 12036.5 13141.6 .
9.0 25659-0 13541-1 14784-3 .
100 28510.0 . 15045.6. 16426.9 1
1:00 57020.0 30091.2 32853.9 ,

 

 

 

 

 

the beft plates, to give a particular defcription
. of its feveral parts, f0 as to make the whole
f intelligible, I {hall only explain the principles
.upon Which it is confirufied.

_1. Whétf

derdidtiealz’ébieii ~

 

 

 

 

 

 

 

 

 

 

 

 

' 6‘Inehes diameter.
’ E . Quantityi weight In avoir-
; . in Cubic 7 in troy dupoife
113' inches. ' ounces. ounces. ‘
1 339.3‘ 179.1 196.6
2 678.6 358.1 393.3
3 ~ .191719 537.2 589-9 * '
4 . 1357.2 716.2 3 786.5. A
~ 5 1696-5 895.3, .9837}
v 6 2935.7 1074.3 1179.8
7 2375.0 1253.4. 1376.4.
8 2714-3 1432-4 1573.0
9 9953.6 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 16964.6 8952.8 9831.4
60 20357.5 10743.3 11797.6
70 237150-5 12533-9 I3763.9
80 27143.4 14324.4. 15730.2 '-
. 90 30536.3 .16115.0 17696.5
100 33929.2 17905.6 19662.7
zoo [67858.4 35811.2 39325.4“

 

1. Whatever weight of water is to be raifed,‘
the pump-rod mufl: be loaded with weights fuf-
ficient for that pLirp'ofe, if it be done by a
forcing-pump, as is generally the cafe; and the
poweg

”145

514.6

~ 15.215724112212251“:

 

 

 

 

 

 

 

 

 

 

 

 

 

6;. Inches diameter. ~ 7
p? Qiantity Weight ' In gvoiro
g. ,in cubic . in troy dupoife
03‘; inches. . ounces. » ounces.
1 398.2 210.1 230.7
2 , 797-4 4203 461.4 ?
3 1195.6 630.4. 692.1
. 4. 1593.8 840.6 92228
i 5 1991.9 1050.8 1153.6 ;
6 2390.1 1260.9 -'1384.3
7 2788.3 1471.1 ' 16115.0
8‘ 3186.5 1681.2 1845.7
9 3584-7 1891-3 2076-4
10 13982.9 . 2101.5 - 2307.1
, 20 7965.8 4202.9 :: 4614.3
30 11948.8 6304.4; 1 6921.4 ,,
40 15931.7 8405.9 ~ 9228.6 3
50 19914.6: I0507-4L 11535-7 E}
60 23897.6 12608.9 13842.9
70 27880.5 14710.4 16150.0
80. 31863.4. 16811.8 18457.2
90.. 35846.3 18913.3 20764.3 5
1001 39829.3 21014.8 23071.5
2001 79658.6 , 42029.6 46143.0

to 15 pounds upon every fquare inch.

power of the engine “muff he fuflicient for’thc
weight of the rod, in order to bring it up.

2. It is known, that the atmofphere _.prefl"es
upon the fiirfaee of the earth with a force equal

3. When

7 Of Hydraulic Engine;

t3. When water is heated» to a-certain, degree,
the particles thereof repel one anOther,‘ and con.-
fiitute an elallric fluid, Which, isgeherally "called
flea’m or vkpo‘zir. , ' ' _ .
4‘". Hot/{team is very elal’tib; and When it is
cooled by any means; particiilarly by its being
. iniiced With Cold Water; its elai’tiCity is defiroyed

immediately,.,a’nd it is reduced to water again;
‘5.llf a veffel be filled With hot (learn; and
\then cldfed; f0 ‘as to keep out the eXternal air,
and all other fluids; when that l‘team is by any
means coride'rifed, Cooled, or' reduced to water,
their water will fall to the bdttOm of the v‘efl‘el ;

and the cavity of the vefi’el will be almoi’t a per-' ‘

feel: vacuum.

6. WheneVCr a-v‘aéuum is made in any vefl'el‘, '

the air by its weight will endeavour to rufli into’
the V‘efl‘el, or to drive in any other body that
will give ,way to its prefl'ure‘; as may be eafil’y
feeri by a common f’yring‘e‘. ‘For, if you {top
the bottom of a fyri'nge, and then “draw Up the
pillori, if it be {0 tight as to drive oUt all the
air before it, and leave a vacuum'within the
fyringe, the pifion being "let go Will be driven
down with a great force. '*

7. 'The force with Which the pifion is drove
”down, When there is a Vacuum under it, will be
as the fquare of a diat’neter'of‘ the bore in the
'fyringc. That is'to fay; it will be driven down
with four times as m‘Uch force in a fyrin-g’e Of a
two-inch bore, as in a fyringe of one inch: for
the areas of circles are always as the {quares of
their diamétErs. -

8. The prefl'ure of the atmofphere being
equal to‘ 1'5 poUnds Upon a‘ fqua're inch, it
Will be almol’t equal to 12 pounds upon ,‘a cir—
CLilar inch. 50 that if the bore of the fyrirge
' L be

:47

top of the boiler within.

'

Of Hydraulzc Engine5

be round, and one inch in diameter, the pil’ion
will be prefi down into it by a force nearly equal
to 12 pounds: but if the bore be two inches
diameter, the pii’ton will be preit down with
four times that force. 1 V
And hence it is eafy to find with what force

F the atmofphere preiles upon any given number

either of fquare or circular inches. 1

Thefe being the principles upon which this
engine is confirtiéted, we {hall next defcribe the
chief working parts of it: which are, I. A
boiler. 2. A cylinder and pil’ton. 3. A beam
or lever.

The boiler is a large velTel made of iron or
capper, and commonly f0 big as to contain
about 2000 gallons.

The cylinder is about 40 inches diameter,
bored f0 fmooth, and its leathered pifizon fitting
f0 clofe, that little or no water can get between
the pifion and {ides of the cylinder.

Things being thus prepared, the cylinder 13
placed upright, band the {hank of the pifton is
fixed to one end of the beam, which turns on a.-
center like a common balance.

The boiler 15 placed under the cylinder, with
a communication between them, which can be
Opened and {hut occafionall. ‘

The boiler 18 filled about half full of Water,
and a firong fire 18 made under it: then, if the
communication between the boiler and the cy-i
linder be opened, the cylinder will be filled with
hot fieam, which would drive’the pifion quite

out at the top of it. But there is a contrivance

by which the pifion, when it is near the top of
the cylinder, {huts the communication at the

This

Of Ibdmulz'c‘Engimr;

This is no rfooner (but, than another is opened
by which a little cold water is thrown upwards
in ajet into the cylinder, which mixing with the
hot fleam, condenfes it immediately; by Which
means a vacuum is made in the cylinder, and
the piflgon is prelfed down by the weight of the

atmofphere ; , and fo lifts . up the loaded pump--

rod at the other end of the beam.
If the cylinder be 42 inches in diameter, the
pil’ton will be prelfed 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 muf’t 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 more5than'8 pounds 0f prefl'ure
mof’t be allowed for, on every circular inch of
the pifion in the cylinder, that it may make
about 16 firokes in a minute, about 6 feet
each. ' ‘ /

Where the boiler is very large, the pifion
will make between 20 and 25 firokes in amie
nute, and each {troke 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 109 yards long: and hence we
can find the diameter and length of a pump,
that can be worked by any other cylinder.

' L a For

349

150

.Of Hydraulic Engines. \ ’
For the conveniency of thofe who would
make ufe of this engine for railing water, we
Ihall fubjoin part of a table‘calculated by Mr.
Brig/arm, Ihewingr how any given quantity of

water may be raifed in an hour, from 48 to 440 -

hogfheads; at any given depth,- from, I 5 to
100 yards; 'the machine working at the rate
of 16 firokes per minute, and each firoke being

' 6 feet long.

One example of the ufe of this table will

‘make the whole plain. Suppofe it were required

to draw :50 hoglheads per hour, at 90 yards
depth'; inrthe‘ fecond column from the right

hand, I find the ’nea’reft number, viz.‘ 149 hogf—

heads 40 gallons, againfi: Which, on the right
hand, I find the diameter of the bore‘of the pump
muPt be 7 inches -, and in the fame collateral line,
under the given depth 90, I find 27 inches, the
diameter of the cylinder fit for that purpofe.-—-
And f0 for any Other. ’ ‘

I

A Table,

 

 

 

‘ PLATE XIII.

 

~ [(3

 

 

 

 

 

f Ida/nae, f .

 

,

ea

 

A Table fhewing the power of the engine for raifing water by fire.

 

 

 

.1931;le

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

, '_ Diam. g

Thedepthto be drawn in yards. . In one hour. of’ 5» g

. ‘ ‘ pump. a a.

1; 20 25 30 1 35 40 452 5‘0 60 .70 80 90 1‘00 Hogih. Gal. Inches. 1;) g

E 18% 2‘3 24 26% 28; 30% 32:2- 34? 37-31 40 ‘-*-, -- ~-- 440 12 2:“
‘5 17 19% 22 34-3: 26:: 28 29‘: 31: 234% 37 39:. r— 369 33 11 gfa
2 155‘ 18 20 22 ' ‘23:} 25-}; 27 28% 31% 33%: 36 38%; 40 304. 48 , 10 E'g
'; I4 16% 18 20 21-;- 23 24% 25 28 30% 33 _ 35 i 36% 247 7 * 9 29.:
,3 13% 15% 17%, 19 20.}; 21% 23 24 26% 28% 31 32% 45% 2“ 15 8% 50° 8‘
._._‘E 12% 14% 16% 18% 19 20%. 21% 23 ' 25 27 . 29 ‘ 30% 32—;— 195 22 8 ‘ '2 3
{3‘ 12 .14 15% 17% 18.}. 193 21 22 24—1; 26 28 , 2937!: 31% 182 I3 7%,; 1: g-
2 11 13—} 15 16% 18 19 ‘ 20 21-}; 23: 25 27 28; 30% 172 30 _ 7-;— a;
g 10% 13 14 1.1% 16% 18; 19 20% 22 24 25% 2.7I 28% 149 40 7X 3 g
E 10 12 >13 14. 152;— 16i 18 19 20 22 23- 24; 26,; 128 54, £6; ' Ed
33 9% 11 12 13 14 15-;- 16 17 19 20% 22 23 24% no 1 6 “a;
“g 10 11 12 13 14 1; 155‘; 17 19 20 a 21 225 94. 30 5% g
.E 1/0 11 ”"23: 13 137} 14' 15% 16% 18% 19% 20L4 65 >61 ,, 5 93.;
Q 10 10 > 11; 12 13:5: 14 15 16 .17 18$; 60 60 a ' ‘4’; a:
q to 11 11%: 12 13% 14» 15 16 '48 51 4 9,3-

 

 

 

211% 9.11anpr '

 

 

 

I91

’152

Of Hydraulic“ Engines,

PlateXIIl. . Water may be raifed by means of a firearn
The Per- A B turning a wheel. C D E, according to the

flan
wheel.

order of the letters, with buckets a, a, a, a, &c.

. hung upon the wheel by firongv pins 5, b, b, b,
‘ &c. fixed in the fideof the rim: bUt the wheel

mull he made as high as the water is intended
to be raifed above the level of that part of the
firearm in which the wheel is placed. As the
wheel turns, the buckets on , the rightzhand go
down into the water, and are thereby filled, and
goup full on the lefehand, until they scome to
the tor; at K -, where they firikeiagainf’c the end
73 ofthe fi..ed 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 dcfigned 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 prring r,
which going over the t0p or crov‘m'of the bar 772
(fixed to the trough ‘M) raifes the bottom of the
bucket above the level of its "mouth, and fo ~

caufes it to empty all its water into the trough.

Sometimes this wheel is made to raife water ‘
no higher than. its axle; and then, infieaddf
buckets hung upon it, its fpokes ,C,'d,e,f,g, b
are made'of a bent form, and hollow within;

lthefe hollows opening into the holes C, D, E, F,

in the outfide of the wheel, and 'allb 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 hOIlow fpokes, c, a", ‘&c. and runs
out in a fiream Pfrorii the holes at O, and falls
into the trough Q, from whence it is conveyed
by pipes, And this is 2} very eafy way Of raifing ,
‘ - . . water,

a: _,. -~ -'J', .
- “3? *4: :, ‘
'r’. '

Of tbe/fim'fic Gm'vfiz'es of Bodies. ' I 53

water, becaufe the engine requires neither men
nor horfes to turn it. e x y .

The art of weighing difi‘erent bodies in Water, Of the '
and therebylfinding their fpecific gravities, or {peeifig
weights, bulk for bulk, was invented by Ania???
CHIMyEDES', ofwhich we have the following 9 165',
account : i , ‘

Hiera, king of Symmfi’, having employed a
.goldfmith, to make a crown, and given him a
mafsrof pure goldforv that purpofe, fufpeéted
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. Butlgthe
king not knowing howikto find out the: truth of \
thatflmatter, referred it to flrcbimedes; who
having fiudied a long time in vain, found it out
at 121?: by chance. .‘Ffior, going into abathi'ng
tub of water, and obferving that he thereby i
raifedthe water higher in the tub” than it Was
before, he~ concluded Linl’cantly that he had raifed
itJuflashighv as any thing elfe could havedonc‘,
th‘atzwasexaéhly of his bulk: and confidering
that anylother bodyof equal Weight, and of lefs ' ' "
bulk thanlhimfelfiflconlclmot have raifed‘ the
wanerxfolihigh :as he did; he immediately tOld
the king, ,that, hehad found a method by which
‘ he could difcover whether there were any cheat
inlthe, crown. For, {ince gold is the heaviel’c
of‘all’known metals, .it mull be of lefs bulk, '
according ,toyflits weight, than anyorher‘metal.’ "
‘And therefore he defired that a mafs; of pure
« gold, equally heavy with the crown when
.‘weighed in air, 'fhould be weighed a‘gainfi:
it in water; and. if the crown was not allayed, '
.it would counterpoifemthe mafs of gold when
they were both immerfed in water, as well as it "
(lid when they were weighed in air. But Upon

‘ , 4, . ' making

154

Of the @196sz Cavities of Bodies,

._ making the trial, he found that the mafs of

The 17}-
droflatz'c
Zia/ante.

,How to
find the
{pacific
gravity 0

any body

gold weighed much heavier in Water than the
crown did. And not Only f0, but that, when
the 1112115 and crown were immerfed fep‘arately'
in one veITel of Water, the crown raifed the
Water much higher than the mal's did; which
Ihewed it to be allayed with fome lighter metal
that increafed its bulk. And 1o, byl making
trials with dilieren't metals, all equally heavy
With the crown when weighed 111 air, .he found
out the quanti ty of alley 1i) the crown "

The fpecific gravities of bodies are as their
weights, bulk fdr bulk 5 thus a body 13 laid to
have two or thlee times the fpecifi'c graVity of
another, Wheh it contains two or thiee tunes as
much matter in the fame {pace '

" A body immerfed 111 a fluid will fink to the
bottom, if 1t be heavier than its bulk of the
fluid.- If it be fufpended therein, it wrll lofe
as much of what 11 weighed 1n air, as its bulk
of the fluid weighs. Hence, all bodiES bfequa‘l
bulks, which would Iink in fit‘iids, lofe equal
weights when fufpended therein. And unequal
bodies lofe in proportion to their b'ulks

' T he hydro/latte éa/czme differs Very little
from a common balant‘e that is nicely made
Only" it has a hook at the bottom of each fcale,
on which fm'all Weights may be hung by home-
hair‘s, Or by {ilk threads. SO that a body, Inf-
pended by the hair or thread, may be immerfed
in water without wetting the Icale from which
it hangs.

" If the body thus fufpended under the fcale,
at one end of the balance, be firI’t COUnterpoifed‘
fin air by weights in the oppofite fcale, and then,
immerfed in Dwater, the equilibrium will be 1m-
mediately del’tmyed. Then, if as much weight
. , , ’ be

Of- tlae‘jfieclfic Gravitz'es’ of Bodies;

be put into the'fealefijom which the body hangs,
‘35 will irel’c‘ore‘theieqfiihbrium (without altering
the weights. in *thejoppolite feale) that weight;
'which refiores the eguiilibrium; 'Wlll be Tequal to
the Weight Ofa quantity! of‘ water as bigias the
immerfed body. '3 Aha if the weight 0f the. body
in air be divided“ by What it loies in water, the
quotient Will {heyv "how much that body is‘h‘eal
yier than its bulk of Water. h-Thfm, if a guinea
‘fiifpe‘nded ‘ in ' aif, be” eoun‘terbalaneed by :29
giains in the opp’ofite {Cale ‘of the balahc'e; and
t‘henj‘fipOh'it‘S‘hei-hg"i'mmerfed in Water: it 'be-'
tomes lb finich lighter, as Ito'i'e'q'ui'rei'yg. giains
'piut intoth‘e fc‘ale’ OVEf-‘itf to 'rel’cbre’ the equili;
brium’,’ ”it ‘flieWé‘ Athat ”a" quantity‘of "Wafer, of
'equal b‘ul’k’withw the guinea, Weighs 7i} grains;
of ‘7.“2‘5"; by "which 1diyidc ’~ 129 (the-Weight'of
"the“ guinea“ in‘aii‘f and ' the quotient Will bé
17.793 3 which'ihews'fiat the guinea is‘ 17.793
tinies'as' heavy as' it'SlSrollt‘of water. ' ‘An‘d‘thusé
«any'piece 'of gOId--' ‘rri‘ay‘ He" tried; by weighingl'i;
firfit iri' ail"; an'd" their in Water; Vaind-gif ppori
f*dividi'rig the weight in air" by the lOfs in Watef,
ith‘é‘q'iu'fitienic Comes obt'ito' be 17.793,“ the gold
isgoodgeif" the’lQUotikm~'be 1'8, or'between 18‘
and 19, ~ the‘gOld‘i'efi‘Wry fi-he; but‘i‘f it be lefs
than 17; "th'efigold3 is too much allayegi, ‘ by be-
ing? mixed with{Effieotherirritétal,~ ’ , ‘-

’ *lf filver ebeiti‘ie‘d" in this manner and found
to been ‘timeaasfihea‘vyas water, it-“is‘vérjr
fine-{7 if .it‘be*‘1*o—,E-"l:iines'jas heavy, it is fiand-
ard ;" but “if it be of any lefs'weight compared

with-Water; if is miXed ”with foyme lighter me!

tal', fudhwas tin; 4 - ,
' By~~thi~s method; he fpe'cific'gijavities of all
'bOdieskhat ‘will‘lin-k iii *Water, may be found.
Eat'asto‘xliofe WhiChare lighter than water‘, a‘sy
gm A . mOfl;

555

Of the fpea‘fic Gravities of Bodies.

molt forts of wood are, the following method
may be taken, to fhew how 'mnCh lighter they
are thantheirrefpeétive ibUlksfloif water. , , ,
Let an upright flzud jbei'fixed into a thick flat
piece of. brafs, [and in» this find let a finalllever,
whole arms are equally long, turn upon a fine
pin as anaxiS'. Let the. thread which, hangs
from the fcale 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 thebrafs‘ and lever into a vefl‘el; then pour
water into the veITel, and the body willrife. and
float upon, it, and draw._dow_n the. 9‘“de the
balance from which it hangs :“ then, put asvmuch

/ weight in the oppofite {cale‘as will raife that end

ofzthebalance, fo a§ ”to pull the body down into
thewater by means of - the lever; and this
weight in the fcale will fhew‘hqw much the. body

' is lighter than its bulk of watch,

' VThere-n are 7 form: things Which cannot be
weighed in.,thi§'_rmannp“er,, Inch asquickfilver,
fragme'n'tstpf diamonds, &c. A becaufe they‘can-
not be fufpended in; threadse, and mdi’t therefore
be put into a glalisxbucL‘ket, hanging, by a thread
from the hook of one fcale,‘ rand’counterip'oifed

’

by weights put into thetoppdfitelcjale.‘ Thus; ‘

fuppofe you want to know; the_:fpecific.gravity
of quickfilver, with refpeétftogthat of water; let
the empty bucket bevfirft counterpoifed in-rair,
and then the quickfilver put into itand Weighed.
Write down the weightyofithe bucket, and alfo
of the quickfilver; which done, empty \the
bucket, and let it be immerfed in water as it
hangs "by the thread, and counterpoifed therein
by weights in the oppofite fcale: then,.pour

the quickfilver into the bucket in the water, i

which _will caufeiit to preponderate; and put as
i ’ much

I ' Of the flwa'fic' Gravitz'es of Bodies;
much weight into the oppofite fcale as will re—

I’tore the balance to an equipoife; and this
Weight will be the weight of a quantity of water

equal in bulklto the quickfilver. Lal’tly, di— "

vide the weight of the quickfilver 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, glafs, lead, or filver, be '

immerfed and fufpe‘n’ded in different forts of
fluids, the different loffes of weight therein will
{hew how much it is heavier than its bulk of the

fluid 5 the fluid .being lighteli: in which the im— ,

merfed body lofes lealt of its aerial weight. A
folid bubble of glafs is generally ufed for finding
the fpecific gravities of fluids. ' .

Hence we have an eafy method of finding the

fpecific gravities both of folids'andfluids, with
regard to their refpeétive bulks of common
pump water, which is generally made a f’tand—i
ard for comparing all the others by. ~‘
, In confiruéting tables of fpecific gravities with
accuracy, the gravity of water mul’c be repre-
fcnted by unity or 1.000, where three cyphers’
are added, to give room for exprefling the ratios
of other gravities in decimal parts, as in the
following table. ' " i

a Table

157',

Of the/pacific Gravities of Bodies;
A Table of the fpecific gravities of feveral folid

and fluid bodies.

 

 

 

 

 

 

 

 

 

‘ 1 . Troy weight. Avoirdup. Compa-
4 A cubic inch of - - .rati‘ve
. oz. pw. 4 gr. oz. drams. welght.
" Very fine gold - 10 7 3.83 1 15.80 19.637
Standard gold - 9 19 6.44 10 14.90 18.888
.Gginea gold- - 9 7 17.18 10 4.76 17.793
Moidore gold - 9 O 19.84 9 14.71 417.140
;Quickfilver - - 7 7 171.61 8 1.45 14.019 l
{Lead - - 5 19.17.55 6 9.08 11.325
'Finc filver - - 5 16 23.23 6 6.66 11.087
Standard filver — 5 11 3.36 6 1.54 10.535
Copper - - 4 13 7.04 5' 1.89 8.843
,‘Plate-brafs ‘ - 4. 4. 9.60 4 10.09 8.000
Steel - _- - 4 2 20.12 .4 8.70. 17.852
Iron 1- - - 4 0 15-20 4 6-77 7645
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
Glafsof'antimony- 2 15 16.89 3' 0.89 5.280
Germanantimony -2 2 4.80 2” 5.041 4.000
Copper ore - -. 2 1 11.83 2 4.43 3.775
Diamond 7- - 1 15 20.88 1 15.48 3.400
Clearglafs - 5- 1 13 5.58 1 13.16 3.150
Lapis lazuli - - ,1 12 5.27 1 12.27 3.054
Welch afbef’cos ‘- 1 10 17.57 110.97 2.913‘
White’ma’rbl‘e - 1 8 13.41 1 9.06 12.7077
Black (litto - 1 8 12.65 1 .902 2.7041
Rock cryfial - 1 8 1.00- I 8.61 2.658
Green glafs - - I 7 15.38 1 8.26 2.620
Cornelianflone — 1 7 1.21 1 7.73 2.568
Flint - — 1 '6 19.63 1 7.53 2.542
Hardpavingfion 1 5 22.87 1 6.77 2.460
Live fulphur - 1 I 2.40 I 2.52 2.0008
Nitre - '- - 1 0 1.08 1, 1.59 1.900
Alabai’ter — - o 19 18.74 1 1.35 1.875
Dry ivory - - 0 19 6.09 1 0.89 1.825
Brimflone - - 0 18 23.76 1 0.66 1.800 -
Alum - - -_- 0 17 21.92 0 15.723 1.714
8. The

 

Of tbefibec’z‘fic Gravit’ies of Eadie}? 159
The Table concluded. ‘ \

 

 

 

 

 

 

 

 

 

' ‘ Troy weight. Avoirdup. Compad
Acubic inch of ‘ -—--«—-—-—---- —-——- rative '
~ oz. pw. gr. oz. drams. weight.
r____—---—--..——-—......——--. ....——-...'.~———- ._, .. ____.....——-
Ebony - - 0 11 18.82 0 10.34 ' 1.117
Human blood - 0 11 2.89 o 9.76 1.054;.
Amber . - - - 0 10 20.79 0 9.54. 1.0307
‘Cow’s milk - 0 10 20.79 0 9.54. 1.030
Sea Water - - 0 10 20.79 0 9.54 1.030
Pump water - 0 10 13.30 0 9-26 1.000-
Spring water - o 10 12.94 0 9.25 0.999
Difiilled water —‘ 0 10 11.42 0 9.20 0.993
Red wine - - o 10 11.42 0 9.20 0.993
Oil of amber - 0 10‘ 7.63 0 9.06 ' 0.9781
Proof fpirits - o 9 19.73 0 8,62 ‘ 0.931
Dry/oak - - 0 9 18.00 -0 8.56 0.925
Olive oil — - ‘ o 9 15.17 0. 8.4.5 0.9'13,“
Pure fpirits -, - 0 -9 3.27 o 8402 0.866
Spiritofturpentine. o 9 2.76 0 79.99 0.864
Oil of turpentine 0 8 8.53 0 7.33 0.772
Dry crabtree -\ o 8 1.69 0- 7.08’ 0.765.
Saflaftas wood - o 5 2.04 0‘ 4-46 0.482
Cork -; - o 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
{hew how. many ounces avoirdupoife are con-
tained in a Cubic foot of each body.

The ufe of the table of fpecific gravities will How to
belt appear by an example. Suppoie a body to find out
be compounded of gold and filver, and it is re- :15: 3.3“”
‘quired to‘find the quantity of each metal in aniiltera-
the compound. . ' tioh in;

Firlt findthe fpecific gravity of the com. meralS-
pound; bylweighing it in air and in water, and
dividing its aerial weight by what it. lofes there-
of in water, the quotient will {hew its fpecific‘

' gtaVIty,

:60»

Of tbe‘fpérific‘ Graeme: of Bodies.

‘ gravity, .or how many times it is heavier than

its bulk of water. Then, fubtraét the-fpecific
gravity of filver (found in the table) fromithat
of the compound, and the fpecific gravityfof the
compound from that of gold ; the firfl: remainder

i fliews the bulk of gold, and the latter the bulk

of filver, in, the whole compound: and if thefe
remainders be multipliedby the refpeétive {pe-
cific gravities, the produé‘twwill fliew' the pro-
portion of weights of each metal in ”the body.
Example. , ' . . ’
Suppofe the fpecific gravity of the compound-
edbody be 13-, that of fiandard 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 whom 19.63, remains
6.63 the proportional bulk of filver in the com-
pound. Then, the firll: remainder 2.5, multi-
plied by 19.63, the fpe‘cificgravity of gold,
produces 49.075 for the proportional Weight of
gold; and the lait remainder 6.63 multiplied
by 10.5, the {pecific gravity of filver, produces

, 69.615 for the proportional weight of filver in

How to
try {piri-
tubus li-
quors.

the whole body. So that for every 49.07 ounces
or pounds of gold, there are 69.6 pounds or
ounces offilver in the body. / '-

Hence it is eafy. to know whether any fufpeéh
ed‘metal be genuine, or allayed, or counterfeit ;'
by finding how much it; is heavier than its bulk
of water, and comparing the lame With the
table: if they agree, the metal is good 5 if'they
difl’er, it is allayed or counterfeited.

A cubical inch of good brandy, rum, or other ‘
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

’ weight

Of t/yé fpm’fir Gratuities of Bodies. "i 6::
weight in fpirits, the‘y'are above proof ’; if it lofes,
more, they are under. , 'For, the better‘ the
fpirit‘s are, they are the lighter -, and the worfe,
the heavier. All bodies expand with heat and
contraét with cold, but fome more and fome'lefs
than others. And therefore the fpe'cifi‘c 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 10 grains heavier in wine
ter than in fummer 5 as much fpirit of nitre, 20
grains; vinegar 6 grains, and fpring-water 3.
Hence it is mo’fi: profitable to buy fpirits in
Winter, and fell them in fummer, fince they are
always bought and fold by meafure. It has
been found, that 32 gallons of fpirits in winter
will make 33 in fummer. p

The expanfion 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 thefe principles depends the confiruc- The it”.
tion of the thermometer, in which the globe or momm-
bulb, and part of the tube, are filled with a

fluid, which, when joined to the barometer, is

fpirits of wine tinged, that it may be more eafily

feen in the tube. But When thermometers are

mad-e by themfelves, quickfilver is generally

ufed. ' ‘ ‘

In the thermometer, a feale is fitted to the
tube, to fhew the expanfion of the quickfilver,
and confequently the degree of heat. And, as
Fabrenbeit’s fcale is mofi: in efieem at prefent, I
{hall explain the confirué‘tion and graduation of
thermometers according to that fealé.

Firi’t, Let the globe or bulb, and part of the
tube, be filled with a fluid; then immerfe the
bulb in water jufl freezing, or fnow jufi: thaw;

ing;

:6;

=11 Of the @ecific Gratuities of 3047285";

ing , and even with that part in the fcale wheré
the fluid then f’tands 1n 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, To that it may
acquire the fame degree Of heat With your flgin- -,
and when the fluid has rifen as far as it can bv

‘ that heat, there place the number 97: then-

divide the fpace between thefe numbers into 65
equal parts, and continue thofe divilions both
above 97 and below 32, add number them ac—
curdingly.
' This may be done 1n any part of the world;
for 1t is found that the freezing point is always
the fame 1n all places, and the heat of the human
bOd‘y differs but very little, fo that the thermo-
meters made 1n this manner will agree with one
another , and the heat of feveral bodies Will be _
'ihewn by them, and exprciled by the numbers
upon the fcale, 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 fummer fun, from 86 to men Butter
jul‘t melting, 95 Alcohol b‘oils‘w‘ith 174 or”
175. Brandy with 190. Water 212. Oil of
turpentine 55o. Tin melts with 408, and lead

~with 5.40 Milk freezes about 30, vinegar 28,
and bl lood 2 ,
A body fpecifically lighter than a fluid will
fwim upon its furface, in fuch a manner, that a
quantity of the fluid equal in bulk with the
immerled part of the body, Will be as heavy as

the Whole body. Hence, the lighter a fluid is,
4 the deeper a body will fink 111 it, upon which
depends

Of- ?lse fiecz'fit Gratiz’tiés of Beam." ‘ :63
depgnds thec’onl’truétion of the bydromefzr or- '
water-pdife; 1- .' ‘

F rem this we c‘an‘eafily find the weight of quw the
lhip, or any other" body that floats .in waters WEghE 0"
For, if We multiply the number of cubic feet gag m
which are. under the furface, by 62.5, the may be
number ofpeunds in one fooc of frefh water ; ellimatedt
or by 6.4.4, the number of pounds in a foot of
‘ falt water; the'.produé‘t will be the weight of,
the Ihip, and all that is in it. ’ For, , fince his
the weight of the (hip that difplaces the water,
it mul’t continue to fink until itihas removed as-
much water as is equal to it in weight; and
therefore the part immerfed muft be equal in,
bulk to fuch a portion of the Water as is equal. ’
tothe weight of the whole «fliip. _ i

To prove this by‘ experiment, let a [bal‘lid
fome light wood, fuch as fir or pear—tree, be
put into water contained in a glafs veffelg‘ and
let the vefi'el be put into a fcale at one end'of a
balance, and counterpoifed by weights in the
oppofite fcale : then, marking the height of the “
water in the velTel, take out the ball; and ,fill
up the veffel with water to the fame height that
it flood at when the ball was in it; and the fame
weight will counterpoife it as before. \

From thevellel’s being filled up to the fame
height at'which the water Ptood when the ball
was in it, it is evident that the quantity poured
\in is equal in magnitude to the immerfedparft.
of the ball; and from the fame weight coun-
terpoifing, 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 pennyweight makean ounce, and '
12 ouncesa pound. In avoirdupoife weight, '
E6 {drains make an ounce, and 16 ounces a

. ‘ poundt

I64.

' more than 37 avoirdupoife;

Of the mafia Gram-ties of Bodies;

I yound. The troy pound. contains 576o grains;

ahd the avoirdupoife pound 7000-, and hence,
the avoirdupoife dram _weighs'27.34.375 grains,
and‘the avoirdupoife ounce 4’37. 5. , '
Becaufe it is often of fe to know how' much
any given quantity of goods in troy weight do
make in avoirdupoife weight, and the re'verfe;

_ We {hall here annex two tables 'fOr converting

thefe weights into one anather. Thofe from
page 13 5 to page 14.6 are near enough for com-

— \ mon hydraulicpu'rpofes -, but the two following

are better, where. accuracy is required in com-
pari‘ng‘the weights with one another: "and. I
find; by trial, that ”5. troy ounces are preeifely
:equghto: 192 avoirdupo‘ife ounces, and» I75 troy
pounds are equal'to “i44. avoirdupoife'. Andi
ahh't‘mgh thereir‘are i'feveral lefl‘er integral num-
bers,- which come‘very- near to agree together,
YEL’EI havefou‘nd none lefsthan the above to
agreetexaétly. Indeed ,4; troy ounces are fo
nearly equal to 45 avoirdupoife ounces, that the
lattereontains. only 7% grains more than the for-e
mer’: and 45 troy pounds weigh only 75% drama

‘A Table

72.96.169.56! 5124.292 290460242206

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Avoirdupoife. . Avoir.
. Troywcight. :——-—-—-— _Irovaejg_h_t_.‘. --—~
9 ‘1.'b oz. drarq$ {Ln-11:97am; ,
—-———-—-- 9—1—1— . if; ‘
" Pounds-+4000» 3291 6.1.3.685 Pennywt. 19416.67.
' 3900 2528 9. 325.316 {:‘1‘ 4 18 $15.79
2000 164151 131 .62/84;, 1..-. ”51771" ' ‘1‘499’2 .
1,3 .9 10004322 13.11.42 ) ‘ - 16‘ “1142104 .,
:50“ 900 740 19 *2. 28 ‘ 15 13.16
a .806 6‘5 .3497? "‘"” :2?! 552-29.
3‘ .799 575. 9'. 9-99 . “143-2141.
1.2? 9" 600 493 $1: 6. 85? ‘9 _“* -‘ 4:1?2 10.53 3
‘5- '560 411 ’6” 13 71' I, ‘151 9.6;:
E- 460 329 2 457 ? "' {I'D 8-78;
.6" ~ 300 246 §3 1.1.212“ » '74 9 7.90;
.t.“ ‘200 164919 2-. 28? ‘4‘ ’ 8 7.02 i
8‘ :1‘00 82 ;4 9.19 ’37 6.143
<9“ ‘90 74 9 13:?62‘ __ ‘6 954-27
o" .89 65 2:3 4‘- H - '5 4-39:
E: -r- .79 57. ’ 96°, "‘4 3-51
'2: 69 49 :5 15-98 1 34 2-63
95.5} .‘59 4| 2 457 . ‘ ‘2 I-75_
.—- ‘ 4o 32 1‘4 1005 .4 .4 ~.1 0.88
g? -,39 24 5.9 I5 54' 31761655" 23 ~84
>442 72.9 .16.. 7 5,93 [22 ~89 ‘
.2; , 10 48 :3 10.52 ' 121 .77
2 .- 1 1
E4 9 7 6 7.86 20 .73
.6065 1:8 6 19 521 19 .69
,8: ,. .7 5 1/2 256 318 .66
3g: ; ,6 4.134 15. 90 1g .62
”U: 5 4 1 1325 I ~58
.3... 4 3 :4 10.60 I1; .55
1‘5; . 3 2 7 795 ~14 -51
“H" 5:2 1 11° 5 3° , ‘3 «47
".32.. ‘ i 1 o 13 2.65 1‘ 12 .44
5-3“ Ounces —-,- 11 12 1 .09 I1 .40
{—4 1 L 19 1.91954 10 -39
h} 5 i9 1 - 9 9 -'3
‘4? 3 5812.23 8 .29
‘ 7 {736.88 ' 7 .26
6 36' 9.32- 6 .22
5 ;5 7-77' 5 -18
4 9 {4- 6.22 . 4. .15
3 3 4.66 3 .11
‘ -2 2 3.11 2 ~ .07
1 1 LC: 1 . .04
M 2" A Table.

1-6,.

166

ZwoirJupoife Weigbt'reduced‘z’nto Troy: __ ,1

Tro‘yi‘weigh‘t.’

‘ A Table ‘for redu'cing» Avoirdupoife weight 'into

 

 

 

 

 

 

 

 

. . Tray weight. . Troy weight.
Avou‘dupod'c: - 1 Avmrd. 1 _____
weight. , _ - weight. ~ 1 " ' '

lb. oz. pw. gr. 1b. oz. pw. gr.

vPounds 6000 7291 8 0 0 Ounces 1; 1 1 13 19.50
50006076 413 8 141 o 15 35 .
.4000 4861 1 6: 16 13 11 16 213-50.
3°00 364-5 10.0 o .12 10 18 1’8 .
2000 2430 6 1" 1’ ,8 U 10 0 12.50

10001215 3_ 6 16. .19 9 2 7

9001093 9 :0 o: 9 '- “-8 4 1.50
800 972 2.13 8 8 1.7" 5 2’0
700' 850 8 6 162 -' 7 6 7 14.50

600 729 2 o. o" 6 5 9 9 ,
500‘ 607 7’ 13 3, 8 '5 4 11 23.50

400 486 1 6 16 ,4 . 3 12 22

300 364 7 0.. 0 .. 3 2 14. £6-50}

200 243 0 13 ‘8 Q2 1 16121 ;

100 121 6 _6 16 V 1 O 18 5.50

90 109 4 10.. 0‘ Drams‘ 15 17 52.10

’80 97 “ 2 13 8 . “I4 15 22.76

.70 85 o 16‘ 16 13 14. 19.42

60 72 11 '0‘ 0 12 13 15.08

50 6o 9 3 8 11 12 12.74

40 48 .7 6.16 10 11 9.40

30 36 5 1o 0 9 106.06

20 24 3 13 8 8 9 2.72

10 n 1 16 16 7 8 23.38

9 1011 '5 0 '6 720.04‘

8 9 8 13 8 5 6 16.70

7 8 6 1 16 ‘4‘ 5 13,36

6 7 3 10 o 3 3 10.02

,5 6 0 18 8 2 1 2 6.68

4 4 10 6 16 1 l 3.34

3 3 7 15 q % 0 20.51

2 2 5 3 8 . g 13.67

1 1 2 11 16 f; 6.83

 

 

.The.‘

fl‘voirdupofl'W/eifbt; rzidilzed info Tray;

The two following examples will be fuflicient
to explam thefe tWo tables and-{hew their agree-

ment.

Ex. I. In 6835 paunds 6 22mm: 9 pennywengu

6 grain: Troy, Q29.

 

 

; . Avmrdupoxfe

* lb. oz. drams.
{40003291, 6 13.68
12000; 1645 11 "6.984:
Pounds< 800 658; 4 9.14;
troy—’— 20 .16‘ 7 5.03
~ ' 10 >8 3 10.52

5 4 *1 I3-25

-oz.- 6 6 9.32
pw. 9 97.90

3. gr. - 6 ; .22
Ailfwei‘. "[5624 10 i190

Ex II. In 5624. pounds 10 ounces 12 dram

 

 

Mg

dvoirdupoz'fe, Q99 How mug/9 Troy weiglaz‘. ?
' . (See page 166)
x i . Troy.
1b.. oz. pw. gr.
. 5000 6076 4 ’13 8
Pounds: 600- 729 2 o o
avoird. 20 24. 3 ’ 13 8
' 4 4 IO '6 16
02. IO 9 2 7
dr. 12 13“ 15.08
’ Anfwer. 16835, 6 9’ 6.08
LECI

How 17999972 flmairdupoz'fe
. weigh. ? '(See page 165.. ) .

f: 67‘

in

of mama.

LECTaw.
‘ Of Pneumatics.

' HI 5 fcie’nce;treats of the nature, weight,
firefi‘ure, and fp’ring of the air, and, the

- efl’eétsai‘ifing therefrom.

The pro— 1 ‘ ' H ‘
f which welivé and’b‘re the. ' It encompafi‘es the

Parties 0
W?

The air "is that thin Etranfparent fluid body in .

wholegearth t'o a‘confi erable height; and, to-
gether- with the clouds and“ vapours that float in
it, it is called the atmoi‘phere; The airis juflly
reckoned among‘the nhmber of fluids, becaufe
it has *all the ‘prope’rties by which a fluid is dif-
tinguiili‘ed‘. For, it. yields to the leafl force
imprefl'ed, its parts are eafily"moved among one
another, it memes according t'Q'i‘tS p‘ETpendicue
‘lar height; and its prefihre is every way equal.
That the air is a fluid, confifling of fuch
articles as have-no cohefion betwiXt tlfem, but
ealily glide Over one another, and Yield to the
flightefi; impreflion, appears from thatyeaufe and
freedom with which animals breathe in it, and

. move through it without any diflic‘tilty,qr fen-

fible refif’tance. ~
3th it differs from all other‘fluids in the four

following particulars, 1'. It can be comprefl'ed
into a much ,lefs‘ fpace than {what it naturally
PQITCfl'et‘h, which no other fluid'can. 2. It cannot
be congealed or fixed, as Other 'fluids may, 3.. It
Iis'bf a’different denfity 'in every part, upward
from the earth’s furfafice _ ‘d’e’c’re’afing in its weight,
bulk for bulk, the higher it tiles; [and therefore
muft alfoj decreafe in denfity. 4. It is of an.

- ‘4, ' elafiic

ii?

Of . Pfi‘efl‘maticr.

elafiie or fpringy nature, and the three of its
* fpring is‘equ'ai to its weight.

That air is a body, is; evident from its ex-
cluding all other bodies out of the {pace it- pof-

feffes: for, if a glafs jar be plunged with its -

mouth downward into~a~veflbl of water, there

will but very little water get into the jar, becaufe

the air of which it isfull keeps the water out.
As. air is a body, itmui’t needs have gravity

or weight ~: and that it‘isj weighty? 1’3 demon‘ -

firat‘ed by r-exp'erirnent. " For, let the air be
taken duttof a vefTel by means of the air-pump,
then, having weighed the vtefl-‘el, let in the air
again, and upon weighing it "when ”re-filled with
air, it will be fotlnd confiderably heavier. Thus,

a bottle that holds a Wine quart, being emptied ,
of air and weighed, is found to be abbut 16 .

grains. lighter than ”when the air is let into it
again .5 which Ihews that a quart of air weighs
17 :grains: (But a quart of water Weighs i462»:
grains; this divided by 16, quotes 914 in round
numbers; which't’hews, that water is 914 times
.as heavy as sit near the furfa’ce bf the earth.
_ Asthe air‘rife's above the earth’s furface, it
lgroWs rar‘er, and confe’quently lighter, bulk for
bulk. FOr, beeaul‘e it is of an elal’tic or fpringy
. nature, and its lowermofi parts are preffed with
the weight of all that is above them, it is plain
that the air mufi be more denfe or compaé‘t at
~ the earth’s furface, than at any height above it;
and gradually rarer the higher up. For, the
denfity of therair is always as the force that
cor'nprelTeth it; and therefore, the air towards
the upper parts of the at’mofphere being leis
prefi’ed than that which is near the earth, it will
. expand itlelf, and thereby become thinner than
at the earth’s furface. ~ t .
‘ M 4 ' ‘ a Dr.

159

170 Of fwumatiw.’

Dr._(,‘az;25~ haSgdcmonfirated, that if altitudes
in the‘air: bletaken inarithmet-iCal. proportion,
:thcrarity70f thqair will be int-geometrical pro-
,_portion.- . Forinfcance, .. . ' ,

 

 

 

 

 

-r 71-.” » .41 8

' 14.. “g - ,-._- - "- - - -*"-\~- .16 Lg

. 21’; --~~-¢*-’64J£Ei

. . 28 1% . ------ ~ .7256 :2

' 35 .;—----- 1024-71“?

., 42 g «e ----- .4096 u

3-H 49 8 -—..--u 16384;?

43 56 _g ----- - 65536 g

'5: 63 c. ----- 262144. E:

E 4.: 7o >8< ------ 104-8570 7’5

:3 77 e - - - -.—, 4194304- 2:

,5 .84 “g - '- -:.;~.9:rt:;zv’;>r_16t777216 .3

_ 2H ; 91 ‘F" 7- 9.7 .,- ‘67108864— :2?

<1 98 g .9 -1 - ”268435456 72

«.105. g. -.r- - 1073741824. st

112 .8‘”. -:-..—‘ 4294967396 E

. 119 cc - -- ., 4117179869.I;84;,.E,S
126 3:3 -_ :- 68719476736. '5; 2

. 133* g e - 274877906944; E

«14.0» s t-p» 10993511627776; .5

2 And hence it ris- eafy: topr'o’ve byralculation,~
that a'cub‘ic inch of . quh-‘air "as‘7we"7br‘e'athe,
. would be f0 much: rarefied at theialti‘itude of 50d
miles, “that it would fill a fphere equal in diae
meter’to the orbitt'of Saturna * '
_ ,. T he'weight' or." ‘prefiure of theuair xis»exa&ly
, determined by the following experiment; "
The 97,. ‘ Taken glafs tube abOut three feet long, and
ricellz‘fzzi open at one end ;’ .fill it with quiekfilver, {and
”Pet” putting your finger upon the open end, turn
{$168+ ’ thatgendr'elownward, and immerfezitintO-a {mall

Ycficl ' '

.0)" ~- Pneumatics:

Veflbl of quickfilver', « without letting in any air:
then take away your finger; and the quickfilver
‘ ~ will remainfufpended in the tube 29% inches
0 above its furface in the velTel ; ~ fometimes more,
and at other times lefs,‘as the weight of the
air is varied by; winds and other caufes. That
‘the quiekfilveriis kept ‘up in the, tube by the
preflbre of the atmofphere upon that in the ba-
fon, is evident; for, if the bafon and tube be
put under a glafs, and the air be then taken out
of the gl‘afs,;.all the quickfilver in the tube will
fall down into the bafon; and if the air be let in
again, the, quiekfilver will rife to the. fame
height as before. 7» Therefore the air’s prefi'ure
,on the furface 0f the earth; is equal to the
weight of .29.;— inches depth of quickfilver all
«over the;=earth’s furface, at a mean‘ra-te,
quuatre column of quickfilver, 29.;— inches
high, and i» pne inch thick, weighs jui’c 15
pounds, which is equal to the prefl‘ure of air
upon every fquare . inch of theearth’s furface;
andng-times as much, or 2160 pounds, Upon
. every fqttaretjfoot‘; becaufe a fquare foot con-
tainsf144‘fguare inches. At this rate, a middle-

- fized mamwhofefurface may be about 14fquare _

feet, fufiains a preliure‘of 30240 pounds,
when, the , air is of amean gravity : a prefi'ure
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 dimmed through the whole body ;

and reads With an‘equal force againfi the out--

ward preITure. ,

Now, ,fince the earth’s furface contains (in
round numbers) 200,000,000 fquare’ miles,
and every fquare mile 27,878,400 fquare feet,
there muI’t be 5,575,680,000,000,ooo fquare

/

feet.

37$

172

The 5a-

7017161773

water to afcendwin the Slut

0f Pneumatic}; ,
feet on the earth’s furface ; » which multiplied by
2160 pounds (the pref-Tut's on each fquar’e foot)
gives 12,04’3,4.68,8oo,ooo,oeo,ooo potmds for

.the prefi‘ure or weight of the, "whole atmo-

fphere. ~. , , . -

When the end of a pipe is ii'nmerfed in water,
and the ari’i‘ 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
3 3 feet‘above the furface of the well: and unle-fs
the bucket goes within that difiance from the
well, the water will never get aboveit. Now,
as it is the preffure of the atmofphere, on the
furface of the water in the‘well, that caufesthe

7 '_ and follow the
piii-‘on or bucket, when theé‘ié‘tr abbve it is lifted
up; it iii-evident, that a‘i‘c‘olumn of, water 33
feet high, is equal in weight (to aw‘columnrot’
quickfilver of the fame diameter, 29—;— inches
high; and to as thick a column of air, reach-
in-g from the earth’s- furface to the top of the
atmofpher‘e. - ' - -

In uferene calm weather, the air has weight
enough to fupport a column of quickfilver 31
inches high; but in tempeftuous fiormyrwea- ‘
thér, not above 28 inches. The q—uickfilVer,
thus fupportedin a glafs tube, is found to,‘ be a
mice counterbalance to the weight or prefl‘ure of
the air, and to ’fhew, its alterations at difi'e-tent
times. And being now generally ufed ito'de-
note the changes in the weight of the 7air—,_ and
of the weather co'nfequent upon them, it is
called the barometer, or "weather-glafs.~

'The preiTure of the air being equal “on all
“tides of-a body expofed to it, the foftef’t pogieS

. u am

 

0f Pneuniatz'cs. 173
fut’cain this prei'fur‘e without fufi'ering any change,
.in their figure ; and fo do the melt brittle bodies
without“ being broke. ' _ ' » z
The air, is rarefied, or made to ifwell with
heat; and of this property, wind is a neceffary Thecaufe
confequence. For, when any part of theyair‘is of wind:-
heated by thei'fun, or- otherwife, it will fwell,
and thereby afiee‘t the adjacent air: and To, 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 atmofphere, and
the adjacent air will rufh in to fupply its place;
~and therefore; there will be a fiream or current
of air from all pa ggowards the place where.
the heat is. And»; 43"”,‘we fee’the r'eafon why
the air ruih'es '- Orce into a glafs-houfe,
or towar‘dsany :isi‘vvhere a great fire is made.
And alfo, why {make is carried up a chimney,‘
and Why the air rufhes in at the key-hole of the
doom Or "any fmall Chink, when there is a fire
in the room.- Sowe may take it in general, that
the air will prefs towards that part of the werld _‘ 7
where it is moi’c heated. . ’
Upon this principle; we can eafily account for The
the trade—winds, Which blow co'nfiantly from eafiirqa’e-
to Well about the equator. For, when the fun WM"
{hinesp‘erpendicularly on any part of the earth,
it Will heat the air very much in that part, which
airswi‘l'l therefore rife upward, and when the fun
withdraws, the adjacent air will rufh in to fill its
place; ‘and confeqUently will caufe a dream or
current ofl’air from all parts towards that which
is molt heated by the fun. But as the fun,.with
refpecl to ‘Fthle earth, moves from call to well,
the commontourfe of the air Will be that way
too ,; continually prefling after the fun : and
' therefore,

   
 
 
 

The mom
fiom.

Of Pneumatics:

therefore, at the equator, where the fun fhines
firongly, there will be acOntinuaI- wind from.
theeafi; 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 feveral 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-‘
tiesr'of rain, caufing thereby a fudden conden—
fation or contraction of the air. 3. By burn-
ing'fands, that often retain the folrar. heat to a
degree incredible to thofe who havenot felt it,
caufing a more than ordinary rarefafiion of the
air contiguous to them. By high moun-
tains, which alter the direélion :of’the winds
in‘firiking againf’t them. 5... By the declina-
tion of the fun towards the north or. fouth,
heating the air on the northror fouth fide of' the
equator. ., .

To thefe and fuch like caufes is owing, I. The
irregularity and uncertainty of winds-in climates
diflant from the equator, as! in molt parts of

.Eurape. 2. Thofe periodical winds, called

and places.

monfoom, which in the Indian feas blow half a
year one way, and the other half another.
3. Thofe winds which on the coall of Guinqy,
and on the wefiern . coails of America, blow al-
ways from well to call. 4.. The {ea-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 lhort,
all thofe fiorms, hurriCanes, whirlwinds, and
irregularities, which happen at difi‘erent times

a , All

Of Pneumatics; ~ ’1 75
”All. common air is impregnated witha cer-Them'cvi-
. tain kind of viwifyz'ng fiairz'z‘ or quality, which isflingfli-
neceITary to continue the lives of animals :1 and m "‘ am
this, in a gallon of air, .is fuflicientfor one man
during the fpace of (a minute,‘and not much
\ longer. ‘ ~ ~ .
‘ This fp‘iriti in air is defiroyed by paffing
through the lungs ofi-animals : and, hence it is,
that-an animal'dies foon, after being-put under
a VeITel whichadmits no-frefh air to come to it.
This fpirit isvalfo i‘nithe' air which is in water;
for fifh die when they are excluded from freih
air, as in afipond that is clofely frozen over.
And the’littl’e eggs of rinfeéts, , flopped upv'in a,
*glafs, do not produce their young, though
aflified by a'xkindlyawarmth. - The feedsalfo of
lants mixed withiiggood earth, and .inclofed in;
a glafs, will not grOw. 1 > , >
This en'livening quality in air, is alfo dc?
.{iroyed byt-he air’s pafling .ithrough‘fire; parti—
cularly charcoal fire, or the flame of fulphur;
iHence, fFFlOleg chimneys muft be very un-a
.wholefome, efpeciallyif the rooms theyrare in

V

'be'fmall and clofe. 1 i A .

. Air is alfo vitiated‘yby A remainingnclofely
pent‘up in any place for a confiderable time;
or perhaps, by being mixed with malignant
.fleam‘s and particles» flowing from the neighbour-
ing bodies ~,_ or lai’tly, by the corruPtion of the
vivifying fpirit; as in the holds of - Ihips, in'
oil-cii’terns, ' or- wine-cellars, which have been
{but for a confiderabletime. 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 beca-ufe it'is ' filled with humid
or moii’t vapours, but bec’aufe it deadens fire,
3 ,extin:

(a 76 ‘1 0f Pnemetirn

extinguifhes flame, and, ,defioys life. " The
dreadful .elfeé‘ts ,ofda-mps are. {efficiently known
to ,fuchas work. in mines. : ~ 7- .
ifpart of the vivifying fpinit of air in any
country. begins to 'prutrify, the inhabitants .of that _
country will be fubjec't to an epidemical ,difeafp,
which will Continue until ,the’, putrefaéliion is
rover.» And. as the,,putrefying fpirit‘ oceafions
thedifeafe, fo if the difeafed.~ body contribgtes
towards the putrefyingof the air, then the, dif-
, teafe will not only 'beepidemical, abut _.pel’tilential
:andrcontagious, , - u ' ,
‘ The atmofphere is the,common receptacle of
,all therefliuvia or vapours .arifing. firom ~ different
bodies} of the {teams and fmoke of thingsburnt
lorrmel ted 3 thefogs or vapours proceeding from
rdamplfwatery ,pla'ces -, .andgof JthC;CfliU.Vla from
fulphureous, nitrous, acid, and alkaline bodies‘.
/~In flidrt, .iivhatever may be called volatile, irifes
«inthe {air to greater or ,lefs.:heights, according
toitséafpecifiegravity. . ., i : . .
per-3,3“, 'When the efi’luvia, whieh arife from acid and
rim, salkaline bodiesfirneetleaehvother in the .air,
there will be a firong confliélzor fermentation be-
tween them; whiCh iwil'l-fometimes be Io, great,
z~asrto produce a fire, then‘if the effluviagbe
;combufiible, the fire Willi-run fromJoAne- part
.to another, jult as the inflammable matteréhap-
,, pens to lie. ~ ~ . ' .
Anyone may be convinced of this, by mixing
an.acid,.,and an ,alkaline fluid together,_as,. the
'fpirit of, nitre and oil of cloves; 5 , upon, the doing
of. which, a fudden fermentr with a fine flame,
will arile; and if the. ingredients be very pure
. andfirong, there will be a fudden. explofion.
Tbunfier thoever confiders the efi‘ecftswofwfermentav-
and 118"”- tion, ~cannot be at a lofsi to account for the

”iflg‘ . . , dreadful

Of Pneumatics.

dreadfulefi'eéts of‘ :1»de and lightning : for the"
efiluvia of fulphureiOus and nitrous bodies, and'
others that may rife into the atmofphere, will ‘

ferment with each Other, and'take fire very often
of themfelves; fometimes by the affiftance of the-
funfs heat. « ‘ - ' ' ‘5 ‘

If the inflammable matter be thin and light;

“will rife to the upper part of thelatmofph‘erei

where it. will flafh without doing any harm':‘
but'if it be denfe,‘ iti-will lie near the "fur-4
face of the. earth, where taking fire, it will-ex-
plode with a furp‘rifing force; and by its‘heat:
rarefy and drive a‘way’the air, killmeh- and“
cattle, fplit trees, walls, rocks, 82c; :and-be ae-
companied with terrible claps of thunder.

, » Thefheat‘ of lightning appear-sto be quite"
different from that-of other-"fires °, for it has
been known to run through wood, leather,
cloth, 8m. without huvting- mama-while- it has‘
broken and melted iron, flee-l, filver, gold, and
other hard bodies. T husit has melted or bu‘rnt‘
afunder a fword, without hurting thefcabbard'v‘;
and money in a» man’s pocket, "without hurting
his cloaths: the’reafon ofthisfeems to be,» that?
the particles of tbat fire are fo fine; ‘as topafa
through fofta loofe bodies without diH'olving
them ; whilfi they {pend theit'whole force upon
the hard ones.‘ , ' - '3‘ ' ' -’
1 It is remarkable, that knives and ferks which
have been {truck “with lightnih‘g 4 have a very
{trong’magn‘etical virtue for feveral’ years after;~
andl have heard that lightning {hiking upon
the mariner’s compafs, will fometimes turnit
round, and often make it l‘tand the Contrary
way -, or with the north-pole toWards the fouth.

Much of the famevkind with lightning, are Fire-

177'

thofc explofions, called fulflziizating or firedamps, dawflv

which

5178-

Earz‘lJ- _

gunk“.

Of Pneumatics. "
which fometim‘es happen in' mines; and are
occafioned'by fulphureous and nitrous, or ra-a.

‘ 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 ufe of. The fire being kindled will
run from one part of the mine to another, like
a train of gunpowder, as the combufiiblej matter-
happens to lie. And as the e’laflieity. of therair'
is increafed «by heat, that in,_the mine will con—'

‘ fequcntly fwell very much, and fo, for want of

room, will explode with a greater or lefsdegree
of force, according to the denfity of the com-_

bufiible vapours. It is fometimes f0 flrong, as

to blow up the mine; and—tat "other times fo

weak, that when it has taken‘fite 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 exhaufied a
receiver of the air-pump, lest the air run into it
through the flame of theoil of turpentine, then.
remove the cover of the receiver, and holding a
candle to that air, it will take fire, andbuprn’
quicker or flower, aCcording to the denlity of
the oleaginous vapour. _ '

When fuch combui’tible matter, as is above~
mentioned, kindles in the bowels of the earth,
where there is little or no vent, it produces
earthquakes, and violent Prorms or hurricanes. of

, wind when it breaks forth into the air.

An artificial earthquake may be made thus;
Take 10 or I 5 paunds of fulphur, and as much
ofthe filings of iron, and knead them‘ with
common water into the confifience of a pafie:
this being buried in the ground, will, in 8 or
10 hours time, burl-l out in flames, and cautfe

t 3

 

 

 

PLATE XIV.

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Of r152 , flirt-Pump:
the earth to tremble all around to a co‘nfiderable‘
tiifiance. ‘ ,7 .

From this eXperimen’t we haVe‘a Very natural
account ‘of the fires of, mount Ema, Vefuevz’ul,
and other volCanos, they being probably fet
bn fire at‘fi‘rl’c’ by the mixture of fu'ch metallihe
and fulphiJreous particles.

9

The air—pumpbeing cbnftruéted the fame way PlateXIV.

as the Water-plimp, whoever underf’tan‘ds the Fig- ‘6

Jone, will be at no 1ch to Underfiand the other.

Having put a wet leather on the plate LL The air-r

Of theair-pump’, place the glafs'feceiver MPWP‘

Upon the leather, f0 that the hole 5 in the plate
may be withiriffthe glafs'; 'Then, turning the
handle F back-Ward and forv‘vard, the air will be
pumped oUt Of the recei'Ver; which will theh

be held dowh to the plate by the preffure of the }
external air, or ‘atmofphere. For, as the handle F

(Fig. 2.) is tumed backwards, it miles the piiZ
tonrde in the barrel BK; by meansof the
wheel E and rack Dd : and, as the pil’ton is lea-
,thered fo "tight as to fit the barrel exa‘étly, no
air can get between the pifion and barrel; and
therefore, all the air above ’51 in the barrel is
lifted Lip towards B, and a vacuum is made in

the barrel from e to 5-, upon which, part of the. ‘

air in the receiver M.(Fig. i.) by its fpring‘,
'rulhes' through the hole}, in the brats plate
LL, along the pipe GCG (which cammuni-
Cates with both barrels by the hollow trimk [H K
(Fig. 2.) and pulhing up the valve é, enters
into the variant place a e of the barrel 8 K. For,
wherever the relifltance or prefl‘ure is taken oil;

the air will run to that place, if it can find \a.
pall‘ager—Then, if the handle F be ttirned'

forward, thg pif’ton dé Will be deprefled in the
barrel; and, as the air which had got into the

N» ‘ barrel ‘

18o

. Of the "flirQPfirnjb.

barrel cannot be pu‘fhed back through the valve
5, it will afcend through-ahele in the pifion,
and efca'pe through ‘a va'l'v/e atwéz’; and be him—
de‘red by that valve from "returning into ‘the‘b’ar—

’rel, when the ‘pi‘fton is. again 'rai‘fed.‘ "‘At the

next raifing of the pifion, a ‘vacut‘rm is again ~

. made in the fame manner as .‘laiefore, between ’22

and 2-. upon which'more-of thel‘a‘i’r, --whiéhlwas
‘left ‘in the receiver M, gets out thence by its
fpr‘ing, and runs into the ‘barrel‘BK, "through-

"the valve B. The fame thing is tor-be under-

flood with regard to the other? barrel )1]; anél. .
as the. handle F is turned baCkWar‘ds "'a‘nd for-
wards, it alternately raife’s andiaepr‘e'fies the pi-
f’tons in their barrels; always railing "one whiltt
it deprefies the Other. And5.as there is a va-
cuum made in each barrel when :its pifio’n is
raifed, every'particle 0f air ’in- the ‘r-eCeiver M
pufhes- out anOthe‘r, by,its fpring' Ore’l‘afiicity,
thrOug‘h the "hole 1', and pipe GG into the~bar~

4 rels; until at hit the air in the receiver‘comes to

bevfo much dilated, andits "fpringifo‘far weak-
ened, that it can no longer get through the

valves; and then no more can be. taken out.
,Henee, there is no fuch thing as making aper-

feé‘t vacuum in the receiver; ‘for‘th'ezqua‘ntity of
air taken out at any' one'f’troke, will alWays be- as
the denfity thereof‘ in the receiver :. and there-
fore it is impoffible to take it all out, becaufe,

‘fuppo-fing the receiver and barrels, of equal ca~
Vpacity,’ there will be always as much left as was 7

taken out at the lai‘t turn‘. of'ihe- handle. "
There is a cock 1e below the pump-plate,
which being turned, lets the air into the receiver

again; and then the receiver becomes loofe, and

may be taken 08‘ the plate. The barrels are
fixed to the frame Eee'by two {crew-nuts ff,
a . , which .

0f the Air- Pump.

which prefs down the top-piece E upon the bar—
rels: and the'hollow trunk H (in Fig. 2..) is
{Overed by a box, as 'G H in Fig; 1.

:‘There'is a glafs \tube mema open at both
ends, and about 3-4 inches long; the upper end
~ communicatingwith the hole in the pump-plate,
and the lower end immerfed in quickfilver at n
in the veflel IV. To this tube is fitted a wooden
ruler mm, .ealledthe gage, which is divided into
inches andpartsof arr-inch, from the bottom at
n (whereit is even with t‘hefurfa'ce of the quick-
. 'filver) and cohtinUed Up to the top,- a little
below 1-, to goer 31 inches. '

As the airispumped out of the receiver .M, it is
likewife pumpedogut of the glafs tube [m n, be-
caufe that tube. opens into the receiver through
the pump-plate; and as the tube is gradually
emptied-of air, the quickfilver in the velTel Nis
forced up into the tube by the prefiure of the
atmofphere. And ifthe receiver could be per-
“feétly e’xhaufied of air, the quickfilver would
ftand as high in the tube as it does at that time
in the barometer: for it is {Upported by the
, fame power orvweight of the atmofphere in
s both. i .

The. quantity of air exhaui’ted out of’the re.-
ceiver‘ on'eaeh 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 defeft of
the height of the quickfilver in the gage, from
what it is at that time it) the, barometer.

l {hall now give an account of the experiments
made with the air-pump in my leftures; thew-
ing the reliance, weight, and elallieity of the
am i

N 2:. 1T“-

‘18;

182

Fig. 3.

Fig. I.

Of the flir-Punip.‘

I. To [haw the rtflfld’me oftie air.

1. There is a little machine, confiflzing Of two
mills, a" and b, which are of equal weights, inn
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 I; have their planes parallel to
it. Therefore“, as the mill 6; turns round in com-
mon air, it is but little refii’ted thereby, becaufe
it’s fails cut the air with their thin edges: but
the mill [7 is much refitted, beCati-fe the broad»
fides of it’s fails move againi’t the air when it
turns round. In each axle is a pin nearthe
middle of the frame, which goes quite through
the axle, and fiands 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
firong {pring c is fet on bend againfi the oppofi‘te.
ends of the pins; ‘

Having fet this machine upon the pump-
plate L L (Fig. 1‘.) draw up the flider d to the
pins on one fide, and fet the fpring c at bend
Upon the oppofite ends of the “pins : then pufh
down the flider d, and the fpring acting equally
firong upon each mill, will fetthem both a going
with equal forees and velocities :' but the mill 4
will run muehlonger than the mill [2,,becaufe the
air makes much lef‘s refiflanee againfi the edges
of its. fails, than againft the fides of the fails
of b. ‘

Draw up the flider again, and fet the fpring
Upon the pins as before; then cover the ma;-
chine with the receiver M upon the pump—
plate, and having exhaufied the receiver of air,

’ puih’

Of tine flir- Pump;

pulh down the wire PP (through the collar of
leathers in the neck 9) upon the flider; which
will difengage it from the pins, and allow the
mills to turn round by the impulfe of the fpring:
and as there is no air in the receiver to make any
fenfible refifiance againf’c them, they will bOth
move a confiderable time longer than they did
in the open air; and the moment that one ltops,
the other will do fo too.—This fhews that air
refil’ts bodies in motion, and‘that equal bodies
meet with different degrees of refiflance, 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 b upon
the brafs'flap 6, turn up the flap, and {but it into
the notch d. Then, putting a wet leather over
the top ofthe tall receiver 143 (it being open both
at top and bottom) 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 wirefa 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 pumpvplate at the
.fame inl’tant. N. B. In this experiment, the
'obfervers ought not to look at the too, but at the
bottom of the receiver; in order to ice the gui-
nea and feather fall upon the plate: otherwife,
on account of the quicknefs of their motion, they
will efcape the light of the beholder , "

N 3 \ Ii. Ta

Of‘ the Arr-P717112?

II. To flame {he weight of the 1211*. "

.Elaving fitted a bra‘fs cap, 'with a Valve
tied OVer it, to the 111011 th of a thin bOttle Or
[31’ 19757766 flaflc, whole Contents are exaéfl'y 1411115117'11-3,~
{mew "the neck of thisf‘cap‘ into the hele 7‘ 0f the
pump plate: then, havina exhaul’te‘d the air Out
of the Balk, and taken 1t 01%? from the pump, let
it he fhfp'ended at one end ofa‘ balance, and mcely
counte1p‘oifed by weights in the lcale at the other
end: this done, raife up the valve with a pin, and
the air Will rulh into the 'flafk with ah'audible
hoife 1 during which time, the flafle will defcend,
and pull down that end of the beam. W hen the
noife 18 over, put as many grains into the fcale at
the other end as will ref’tore the equilibrium- ,
and they will thew exaélly the weight of the
quantity of. air which has got into the Balk, and
filled 1t. If the flafk holds an exaft quart, it,
will be found, that 16 grains Will rellore the

equipoife of the balance, when the quick filver
{lands at 29;. inches in the barometer: which
Ihews, that when the air 13 at a mean rate of den.

fity, a quart of it weighs 16 grains: it weighs

j‘more when the quickfilvcr fiands higher, and
leis when it {lands lower.

7 2. PIuCC the {mall 1eceiverO(Fig. 1. )over the
hole 1' in the pump plate, and upon exhaul‘ting
the air, the recewer will be fixed down to the
plate by the prefl'ure of the air on its outlicle,
Which 15 left to ac't alone, without any air in the
receiver to aél: againfi 1t: and this prelfitre will
be equal, to as many times 15~pounds, as there
are {quare inches in that part of the plate which
the receiver covers, which will hOId down the '
receiver f0 fall, that it cannot be got or}; until

the

szfbe dz’fifamp. ' . 185

the air he let into it by turning the cock 1%; and
then it becomes loofe. 4 '

3. Set the little glafs flB (which is open at Fig. ;,
bOth ends) over the hole z'upon the pumpplate '

'L, and put your hand clofe upon the top of it
at B : then, open exhaul‘ting the air out of? the
glafs, you willhnd your hand preffed down with
a great weight upon it: 12) that you can hardly
releafe it, until the air ‘1' e re-admitted into the
,glafs by turning the cock lea, which air, by aft-
ing as {tr-ongly upward againl’t the hand as the
external air acted in prefling it downward, will
releafe the hand from its confinement. . . i ,,

4. Having; tied a piece of wet bladder 5 over Fig. 6.
the open top of the vglafs fl (which is alfo openat
bottom) fet it to dry, and then the bladder will
be tight like a drum. Then place the open end
,4 upon the pump-plate, over the, hole 1', and

, begin to exhault the air out of the glafs. A‘s.
' the air is exhaul’ting, its fpringin the glal's will
be weakened, and give way to the preITure of the
outward air on the bladder, which, as it is pref-
fed down, will put on a fpherical coricaye figure,

\ which will grow deeper and deeper, until the
fi-rength of the bladder be overcome by the
. eightof the air; and then it will break with a
report as .loud as that. ofa gum—If a flat piece
. of .glafs be laid upon the open tOp of this re-
l ceiver, and‘joined to it .by a flat ring of wet
3 leather between them; upon pumping the air
out of the receiver, the prellttre of the outvifard'
“ air upon the flat glafs will break it all to

pieces, p
‘5. lmmerfe the neck ,c d of the hollow glafs Fig. 7.
,ball e b in water, contained in the phial a a; then
r,fetit uponthe purpoplate, and cover it and the
hole 1' withthe clofe receiver [2 3 and then begin
i N 4, i , ' to

l
l

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 ofjthe hollow ball eé, through the
neck dc, and rife up in bubbles to the furface of
the waterin the phial -,1 from whence it will make
its way, with the tell of the air in the receiver,
throngh the air-.pipe G G and valves 4 and 5, into
the open'airg When it has done bubbling in
the phial, the ball is fufliciently exhauf’ted; and
then, upon turning the cock 1:, the air will get
into the receiver, and prefs fo upon the furfacé
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 almofi full of water: The
reafon why the. ball is not quite filledxisbecaufe'
all the air c0uld nOt be taken out of it; and the
{mall quantity that was'left in, and had expanded
itfelf fo as to fill the whole ball, is now Condenfed
into the fame hate as the ontward air, and re-
mains in a {mall bubble at the top of the ball;
and fo keeps the water from filling that part of
"“the ball.’ I i ' ' " ”
Fig. 8.3 " 6.- Pour fome quickfilver into the jarD, and
” ' fet it on the ipump~platey near 'the hole 2'; then ,
let on the tall open receiver 118, To as to be over
the jar and hole", and’ cover the receiver with the
brafs plate C.- Screw the open glafs tube f g’ l
(which has a brafs tOp on'it at [2) into the fyring’e 3
H, and putting the tube through a hole in the 1
middle of the plate, {0 as to immerfe the lower ‘/
end of the mbe'e in the quickfilver at D, fcgew ,x
the end b of the fyringe “into the plate. This?
done, draw up the pifton in the fyringe by the}
ring I, which Will make aiva‘cuu'm in the fyringeg‘
below the pifion 5 and as the upper end of the...)i
tube opens" into the fyringe, the air will be di-l
lated’in the tube, becaufe part of it, by‘it's fpring,"

get;

Of the Air-Pump; ‘ ‘

gets up into the fyringe; and the fpring of the
undilated 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 pifion in the fyringe? in the fame
way, and for the fame reafon, that “water follows
the pifion of a common pump when it is raifed
in the pump-barrel; and this, according to fame,
is done by fuétion'. But to refute that erroneous
notion, let‘ the air be pumped mat of the receiver
AB, and then all the quick‘filver in the‘tube will
fall down by its own weight into thejar; and can-
not be again raifed 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 prefl‘ure, let- the air

into the receiver by the cock It (Fig. I.) and its;

action upon the furface of the quic‘kfilver .in the
jar will ’raife it up into the tube, although the
pifion of , the fyringe continues motionlefs.—lf
"the tube be about 32 or 33 inches high, the
’quickfilver will rife in it very near as high as it
frauds at that time in the barometer. And, if
the fyringe has a {mall hole, as 772, near the top
or it, and the piflon be drawn up above that hole,

the air will rufh through the hole into the fy- ‘

ringe and tube, and the quickfilver will imme-
diately fall down into thejar. If this part of the
apparatus be air-tight, the quickfilver may be
pumped up into the tube to the fame height that
it l’tands in the barometer; but it will go no
higher, becaufe then the weight of the column in
' the tube is the fame as the weight of a column of
[air of the fame thicknefs with the quickfilVer,
and reaching from the earth to the top of the
heathen ' " ‘ ‘ ‘ ’ ' .

" 7. Having

187

188
fig. 9.

Of the flirt-Pump:
,7: Having placed- the jar A, with fome quick-

. filver in it, on the pump-plate, asjn the lali:

experiment, cover itrwith the receiver 8; then.
pufh the; open end of the glafs tube de through
the collar of leathers in the brafs neck. C (which
it fits 1b as to be air-tight) alr‘noi‘t down to the
quickfilver in the, jar. Then exhaufl: the air
out of the receiver, and it will alfo come out of
the tube, becaufe the tube is clofe at top. When
the gauge mm lhews that the receiver is well
exhaul’ted, pufh down the tube, fo as to immerfe
its lower end into the quickfilver in the jar.
Now, although the tube be exhaufied of air,
none. of the quickfilver will rife into it, becaufe
there is no air left in.,the receiver to prefs upon

its furface» in the jar. But let the air into the

receiver by'the cock k, and the quickfilver will
immediately rife in the tube; and Rand as high
in it, as it was pumped up in the lai’t experi-
ment. a. .

Both thefe experiments flaew, that the quick-
filver is fupported in the barometer by the pref-
fure of the air on its furface 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 quickfilverrife; and, on the contrary,
the thinner and lighter the air is, the more Will
the quicklilver fall. For if the handle F be
turned ever f0 little, it takes fome air out of the ’
receiver, by railing one or other of the pil‘tons in
its barrel; and confequently, that which remains
in the receiver is f0 much the rarer, and has f0
much the lefs fpring and weight ;‘ and thereupon,
the quickfilver falls at little in the tube: but
upon turning the cock, and readmitting the air
into the receiver, it becomes as weighty as be-
fore,.and the quickfilver him again to the fame
‘ ' height.

Of _ rife flit—Pump;

mighty-Thus we fee thexreafon why the quick-
filver in the “barometer falls before rain or fnow,

cafe, the air is too thin and lightto bear up the
vapours, and in the latter, too clenfe and heavy
to let them fall. '

N. B.' In all mercurialaexperiments with the

‘ air-pump, a fhort pipe m‘uf’t be fcrewed into the .

hol'e‘z', fo as to rifeaboutran inch above the plate,
to prevent the qu‘icléfilver from getting into the
air-pipe and barrels, in cafe any of itlhould be
accidentally fpilt over the jar: for if it once gets
into the pipes or barrels, it fpoils them, by
loofening the folder, and corroding the- brafs. .

8. Take the tube out’of t-he‘receiver, andput
one end of abit of dry hazel branch, about an
inch long, tight intothe hole, and the other end
tight into a hole-quite through the bottom of a
{mall wooden cup: then pour fome quickfilver
into the cup, and 'exhaul’t the receiver of air, and
the prefl‘ure 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 fhower into a glafs cup placed under
the receiver to catch it. » '

. Put a wire through-the collar of leathers in t

the top of the receiver, and fix a bit of dry wood
on the-end of the wire within the receiver; then
exhauf’t the air, and pulh the wire down, f0 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 fplitting it, .

its pores will be found full of quickfilver, which
the force of the air, upon being let into the re-
ceiver, drove into the wood.

and tiles before ”fair weather; for, inthe former,

:89.

10. Join the two brafs hemifpherical cups A and Fig. 19.

B together,with a wet leather between them, hav-
, , mo
{3

1'90 ,

Of 1126 diePump."

ing a hole in" the middle of it; then {crew the
end D of the pipe CD into the plate of the
pump at i, and turn the cock E, f0 as the pipe
may be open all the way into the cavity of the

’ hemifpheres : then exhauf’t the air out of them,

and turn the cock a quarter round, which will
{hut the pipe CD, and keep out the air. This
done, unfcrew the pipe at D from the pump;
and fcrew the piece Fl? Upon it at D, and let
two {hang men try to pull the hemifpheres afun-
der by the rings g and la, which they will find
hard to do: for if the diameter of the hemi-

'lpheres be fOur inches, they will be prefled to-.

gether by the external air with a force equal to
190 pounds. And to {hew that it is the prefl‘ure
of the air that keeps them together, hang them
by either of the rings upon the hook P Def the
wire in the receiver M (Fig. I. ) and upon ex-
haui‘ting the air Out of the receiver, they will fall
afuncler of themfelves.

II. Place a fmall receiver 0 (Fig. 1. ) near the
hole z on the pump- -plate, and cover both it and
the hole with the receiver M, arid turn the
wire ft)» by the top P, that its hook may take
hold of the little receiver by a ring at its top,
allowing that receiver to {land with its 1 own
weight ’on the plate. Then, upon working the
pump, the air'will come out of both receivers .3,_
but the large one M will be forcibly held down
to the pump by the prefi-“ure of the external air;
whilf’t the {mall one 0, having no air toiprefs up-

' on it, will continue loofe, and may be drawn up
‘ and let down at pleafure, by the wire PP. But,

upon letting it quite down to the plate, and ad-
mitting theb air into the receiver M, by the cock
Jr, the0 air will prefs f0 firongly upon the fmall

receiver 0, as to fix it dOWn to the plate; and at

8 the

(9f the flirt-Pump:

1the fame time, by counterbalancingthe outward
preITure on the large receiver M, it. will become
loofe. This experiment evidently {hews,'that
‘ the receivers are held down by preffure, and
not by fuélion, for the internal receiver conti-
nued loofe. whill’t the operator was pumping, (“and
the external one was helddown; but the former
became faf’t immediately by letting in the air
upon it.- '

191

. 12. Screw the end-fl of {the brafs pipe dB.FFig.u.‘

into the hole of thepump—plate, and turn the
cock f," 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 GH,
which is clofe at top: then exhaufi: the airout
of the receiver, and turn the cock e to keep it
out; which done, unfcrew the pipe from the
pump, and fet its end 11 into a bafon of water,
and turn the cock 6 to open the pipe; on which,
as there is no air in the receiver, the preITure of
the atmofphere'on the Water in the bafon will
drive the water forcibly through the pipe, and

make it play up in, a jet tothe top of the re-~

ceiver. » .

I 3. Set the fqzuare phial fl (Fig. ’14.) upon the
pump-plate, and having covered it with the wire
cage B, put a clofe receiver over it, and exhaufi:
the air out of the receiver -, in doing of which,
the air will all?) make its way out of the phial
through a {ma-ll hole in its neck under the valve
5. When the air is exhaufied, turn the cock
below the plate, to re-admit the, air into the

receiver ;, and as it cannot get into the phials‘ '

again, becaufe of the? valve, the phiaI Will be
broke into fome thoufands of pieces by the pref-
fure of the air upon it. Had the phial been
of a round form, it would have fuf’tained this

prefiure

:92

Of the i‘fz'r-kpmflfi;
preflhre Ilke an archr,~'without breaking“; “but ae
i’tsxfi‘des; are flat, it cannot. ' ,: 5 97’

fq‘ flew the kid/firm!" qr firifig of fly: air. '

14, Tie upa very'fihall/ quantity of air- in' a

bladder, and put it under a receiver; then exhaufl‘?
the air but of the receiver; and theifmall quan-
titywhich is confined in the bladder (having no-
thing to aft ag‘ainfi: it) will expand itfelf TO by
the force of its'fpring,‘ as to fill the bladder as
full as it could be blown of com-mohair.” But
11an letting the air into the recei‘i’rer‘again, it
will overpower the air in the bladder; and prefs
its fides almof’t clofe together. * ' ~ -» P -
' 15‘. If the bladder 1’0 tied up" be pot into a

, wooden box, and have 20 or '30 poiijrrd weight

of lead put upori it in the box, and‘t-he box be

~ covered with a clofe receiver; uponexhaui’ting

Fig. 70

Fig. 11.

the air out of the receiver, that air which, is con-
fined in the bladder will expand itfelf f0, as to ra-ife’
up all the lead by the force 0f its fpring.

16. Take the‘glafs ball mentioned in the fifth
experiment, which was left full of water all but
a {mall bubble of air at top, and having; fet it"
with its neck downward into the empty-phial ad,
and covered it with a clofe receiver, exhaufi the.
air out of the receiver, and the fmall bubble of
air in the top of the ball will expanditfelf, f0 as
to force all the water out of the ball into the
phial. '

:7. Screw the pipe _/1 B into the. pump—plate,-
place the tall receiver G H upon thte‘pl'ate ed, as-
in the twelfth experiment, and exhaul’t the air"
out of the receiver; then, turn the cock e to
keep out the air, unfcrew the pipe from the
pump, and {crew it inte the mouth of the copper

yefl'el;

Of the HirLPump.‘

VelTel CC (Fig. 15.) the vefl‘el having firfi been
about half filled with water; Then open ”the
cock 6 (Fig. '11,.) and the fpring of the air which
is confined in the c0pper'vefi'el will force the
water up thrbugh the pipe .47 B in a jet into the
exhaufted receiver, as firongly as it did by its
prethire onthefurface of the‘water‘in a bafdn, in
the twelfth experiment. ' V ’

18. If afowl, a cat, rat, moufe‘, or bird, be i

put under a' receiver, ~andthe' airgbe exhaui’ted,
the animal will be at firl’tjopprefl'ed as ,with a
4 great weight, then grow-convulfed,’ and at lall';

expire: iii-“all the agonies of a molt bitter and '

cruel "death. “But as this» experimtnt is too
‘ihocking to every fpeé‘tator whohas the leai’t de-
gree of humanity, We fubflitt‘ite a machine called
the lungs-giafi in place of the animal. . ,

19. If a butterfly be fufpended inpa receiver,
‘ by‘ a fine thread tied to one of its hows, it will fly

about inathe receiver, as long as‘ the receiver .

‘ continues fullof "air; but if" the air be vex’haurfized‘,
though the animal will not die, andwill continue
to flutter its wings, it cannot remt'we itfelf 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. ' ' ' ‘

I93

20, Pour fome quickfilver into the {mall bottle Fig. 12.

A, and {crew the brafs collar c of the tube B G
into the brafs neck 50f the, bottle, and the lower
end of the tube will be immerfed into thequicl —
filver, f0 that the air above the quickfilver in the
bettle will be confined there, becaufe it cannot
get out about the joinings, nor can it be draWn
out through the quickfilver into the tube. This
tube is alafo open at top, and isto be covered with
the receiver G and large tube E F, which tube is
fixed by brafs collars to the receiver, and is "clofe

3E

4/,” ___,_._-—
l

. Maw- -. M

 

£94

Fig. 130

Of (be AirePump.

at the top; This preparation_ being made, eiée?
hauflz‘ the air both out of the receiver and its
tube]; and the air will by, ' the fame means
be eXhaufied out of the inner. tube BC, through
its Open top at .C; and as the receiver and tubes
are eXhauftin‘g, the air that is confined in the glafs
bottle .4 will prefs f0 by its fpringvupon the
Turface of the quiékfilver, as to force it up in the
inner tube as high asitwas railed in the ninth
experiment by the prefi'ure of the atmofphere :7
which demonfirates that the fpring of the air is
equivalent to its weight. . ‘ _ , .

. 21. Screw the end C of the pipe C D into the"
hOIC of the pump-plate, and turn all the three"
cocks 0’, G, and H, fo as to open the communi-
cations between all the three pipes E, F, DC,
and the hollow trunk AB. 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, [hut the pipe F by turn-
ing the cock H, and exhaul’t the air our: of the
receiver I. Then, turn the coCk d to {hut out
the air, Linlcrew the machine from thepump,
and having fcrewed it to the wooden foot L, put
the receiver K upon the plate la; 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 V
the pipes F and E, through the trunk flB -,. and
then the air in the receiver K, having nothing to
act againl’t its fpring, will run from K into], un-
til it be fo divided between thefe reCeivers, as to;
be of equal denfity in both, and then they will
be held down with equal forces to their. plates by
the preliure of the atmofphere; though eaelr
receiver will then be kept doWn but with on?

_ ‘ hali

Of zze atm-

hal‘f'of preli‘u'r'e upon it, that the reCeiver I had,

when it was exhaulted of air; be‘caufe it has now
one half o'f‘the commoh air inwitjwhich filled
the receiver K When it Was fet' upon the plate ;'
and therefore, a force .‘eq‘uaI-to half the force of
the fpring‘of Common air, Will? :15: Within'vthe
receiversiagai’nl’t the whole prefTure of the com“-
mon air ‘upoh their outfides. "This “is called
transferring the air Ont of one'veffeljinto anoL
ther. i ' ‘
fix it-in with Wax Or Cement ;‘ put thephial Upon
the pump-plate ”with the Wire cage 3 ‘o‘Ver it,
and cover the cage with a clofe-receit/er. Theh,
exh‘aul’t the air out of the reééiiier, and the air

that was Co‘rked Up in, the ‘phial Will break the “

phial outwards by the force bf its fpring,‘becaufe
there is, no air left on th‘etoutfide of the phial to
act againi’t the air Withih it. ' ‘ _

22. Put a» {hrivelled apple under a clOfe re-
_Ceiver, and exhaurt the air;- then the“ ‘fpring of
the air within the apple will plump it ottt, f0 as,
to caufe all the wrinkles difappear; but upon
letting the air into the receiver again, to prefs
upon the apple, itfivill inltantly return to its
former decayed and thrivelled fltate. ’

23. Take afrefh egg, and cut ‘ofi' a littleof
the {hell andlfilni from its {mallefi end, then ”put
the egg tinder‘ a receivergvand pump out the air ;
upon Which, all the Contents in the egg will be
forced out into the rCCeiver, by the expanfibn Of
a {hall "bubble of air'COntained in the great end,
betweenthe {hell and filth. " i p ‘

.24. Put fome V'varin beer in a glafs, andhav-
ing fet it on the pump, “cover it with a clofe‘re-L

Ceiver, and then exha‘ufl; the air. Whill‘t this ié"

doing, and thereby the prelTure in'ore arid more
0 taken

195

22. Put a cork into the {quare phiadl,fl,iaii7d Fig. :4.

196‘

Of the [fir-Pump.

taken off from the beer in the glafs, the air there-
in will expand itfelf, 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,
hauf’ted, the air in the’beer, which could not
difentangle itfelf quick enough to get of? with
the refi, will now expand itfelf f0, as to caufe
the beer to have all the appearance of boiling ;
and the greatef’c part of it will go over. the
glafs. "

25. Put fome warm water in a glafs, and put

habit of dry wainfcot or other wood into the

water. “Then, cover the glafs with a clofe re:
ceiver, and exhaui’t the air; upon which, thelair.
in the wood having liberty to expand itlélf, will
come out plentifully, and make all the water to
bubble about the wood, efpecially about. the
ends, becaufe the pores lie lengthwife. A cubic
inch of dry'wainfcot has f0 much air in it, that
it will cbntinue bubbling for near half an hour
together.

szcellcmeous Experiments.

V 26. Screw the fyringe H (Fig. 8.) to a piece

of lead? thatweighs one] pound at 16213:; and,
holding the lead in one hand, pull up the pifionv
in “the, fyringe’ . with the other; then, quit—
ting hold of the lead, the air will pufh it upWard, ‘
and'drive back the fyringe uppnfthe pil’ton,~
The reafonof this is, that the drawing up of the
piflon makes a vacuum in the fyringe, and the
air, which prefies every way equally, having
nuthing to refill: its preITure upward, the lead is
thereby. prefled upward, contrary to its natural
tendency by gravity; If the fyringe, fo loadegl,
. , , e

 

Of the dirt-Pump; ,
be hung in a receiver; and the air be exhanf’ted,
the fyringe and lead will defcend open the pillon-
rod by their natural gravity; and, upon admit-’-
ting the air into the .retceiVer; they will, be drove
upward again, until the pifton be at the Very
bottom of the fyringe; -, _ i _
, 27. Let a large piece of cork be fiifp‘ended
by a thread at one end of a balance, 'and coon;

terpoifed by a leaden'weight, fufpended in the ,

fame manner, at the other. Let this balance be
hung to theinfide of the-top of a large receiver;
which being fet on the pump, and the air ex-
haufied, the cork will preponderate,' and {hem}
itfelffto be heavier than the lead; but u‘pori
letting in the air again, the equilibrium will be
refiored. The realon. of. this is, that firice the
air is a fluid; and all bodies lofe as mach of their
. abfolute weight in it, as is equal to the weight

of their biJlk of ’ the fluid; the cork being the
larger bOdy; lofea mere Of its real weight than

the lead does; and therefore mutt in fact be '
heavier, to balance it Under the difadvantage of

lofing fome of its weight: which difadVantage
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,‘ ibeWs itfelf’to be heavier‘i‘whe'n in
mam, , ,- " ”

28. Set a lightedvcahdle upon the “pump, and
cover it with a tall receiver. If the receiver
holds a gallon, the candle‘will burn a minute;
and th’en,~_ after having gradually decayed froni
the full ini’tant, itwill go our: which fhewé, that;
a confiant'fu’pply of frelh air is ne'eeflary to feed
flame; and fo’ it ,alfo'is ‘for animal life. \For a
bird kept under a [clofe receiver will form die,
althdUgh no air be pumped out; and it is;

O a ‘ found

"971

198

Of the flir-Pump; .
found that, in thediving-bell, a gallon of air is
fhflicient only for One minute for a man to breathe
in.

The mement when the candle goes out, the
fmoke will be feen to afcer‘rd to the tap of the
receiver, and there it will'form a fort of clo‘ud:
but upon exha‘uf’tin’g the air, the fmoke will fall '
down to the bottom of the receiVer, and leave it
as clear at the terms it Was before it was fet upon
the pump. This IheWs, that fmoke does‘not
afcend on account of its being pofitively light,
but becaufe it is lighter than air; and its falling
to the bottom when theair was taken away,
ihéws, that it is not ‘del’titute of weight. So
inoi’t forts of wood afcen’d or fwim in Water;
and yet there are none who doubt of the Wood’s
having gravity or weight. g

29. Set a receiver, which is open at top, 11 on
the air-pump, and cover it with a brafs hate,
and w‘e‘t'leather -, and having exhaui’ced it of air,
liegt the air in again: mp through an iron pipe,
making it pals throq”‘h 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
mOUfC or bird into the receiver, and the burnt
air willi‘mffiediately kill it. If a candle be'let
down into the air, it' Will go out directly; but“,
by letting it down .gently, it will purify the air to
far has it goes 5'; and To“, by letting it dtmnmore
and more, all the air in the reCCiver will be
purified. . ' y 7 7
i gt“). Set a bell upon, a cufhibn on the pinup-
plate, and coVer- it with a receiver; then lha‘ke
the pump to make the clapperfirike againl’t the

bell, and the found will be very well heard: but,

éXhaufi the rCCEiV€Y.Of air, and then, if the
Clapper be made to (trike erer f0 hard againft‘
‘ i I ‘ the

Of 1795 Air—Pump;

the beli, it will make 110 found at all; which
them, that air is abfolutely neceITary for the
propagation of found. ‘ ‘

i 31. Let a candle be placed" on one {ide of a
receiver, and viewed through the receiver at
fome dif’tance; then, as foon as the air begins to
be exhaufized, the receiver will be! filled with va-
pours which rife from the wet leather, by the
{pring of the air in it; and the light of the
candle being refraéled through that medium of
vapours, will have the appearance of circles of

various colours, of a faint refemblance to thofe

in the rain-bow. ,

The air-pumpwas invented by OtiooGuerz’cé
of Magdeéurg, but Was much improved ,by Mr.
Boyle, to whom we are indebted for our greateft
part of the, knowledge of the wonderful proper-
ties of the air, demonflzrated in the above expe-
riments. ‘

The elaf’tic air which is contained in many
bodies, and is kept in them by the weight of the
atm‘ofphere, may be got out of them either by
boiling, or by the aircpump, as Ihewn in the
25th experiment: but the fixed air, which is by
much the greater quantity, cannot be got Out
but by difiillation, fermentation, or putrefac-
IIOQ. ‘

‘ ‘If fixed air did not come out of bodies with
difliculty, and {pend fome time in ektricating
itfelf from them, it would tear them to pieces.
Trees would be rent by the change of air from
a Ext, to an‘elaf’tic Rate, and animals would be
buri‘c in pieces by the explofion of air in their

' food. ~

Dr. Hales found by experiment, that the air
in apples is f0 much condenfed, that if it were
let out into the common air, it would fill a fpace

O 3 48

"1-99

209

Of the {fir-Pump.

:48. times as greatas the bulk of the apples them-,4
(elves; f0 that its preffure outwa'rds was equal
to 11776 lb. and, in a cubic inch of oak, to
19860 lb, againft its lides. So that if the air
was let loofe at once in thefe fubl’c’ances, 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 l’tomach, otherwife, an apple
would be immediate death to him who eats it.
:The mixing of fome fubfiances with others,
.will releafe the air from them, all of a fudden,
which may be attended with very great danger,_
Of this we have a remarkable infiance in an ex-
perimentmade by Dr, Slate, who having put'
half a dram of oil of carraway-feeds into one glafs,
and admin Of compound f irit of nitre in ano_- '
ther, covered them both on the air-pump with a
receiver fix inehes‘wide, and eight inches deep, '
and then exhaufled the air, and continued pump-
ing until all that could polllbly be got borh out
of the receiver, and out of the mo fluid-s, was
extricated: then, by a partieular contrivance
from the top 9f the receiver, he mixed the
fluids together; upon which they produced
l‘uch a prodigious quantity of air, as inflantly_
blew 'up the receiver, although it was prelTed
tlown by the atmofphere withpupwards of 500;
3299991 wsisbte ' - ‘ '

LECT:

wank/X

 

 

 

 

 

' “vx‘fi‘w-

Of Optics; .201.

L 'E C T. V111,.
Of Optics.

- IGHT confil’ts of an inconceivably great
number of particles flowing from a luminous
body in all manner of directions; and theft:
particles are fo finall, as to furpafs all human
COmprehenfion.
I~»"That the number of particles of light is in.
conceivably great, appears from the light of a
candle; which, if there be no obllacle in the
way to obl‘truét the palTage of its rays, will fill
all the fpace within two miles of the candle every
way, with luminous particles, before it has loll:
the lealt fenfible part of its fubf’tance.

A ray of light is a continued flream of thefe
particles, flowing from any vifible body in a
itraight line: and that the particles themfelves
are incomprehenlibly final], is manifel’t from the
following experiment. Make a fmall pin-hole
in a piece of black paper, andrhold the paper
upright on a table facing a row of candles l’tand—
ing by one another; then place a {heet of pafte— '
board at a little dillance behind the paper, and
fome of the rays which flow from all the candles
through the hole in the paper, will form as many
fpecks of light on the palteboard, as there are
candles on the table before the plate: each fpeck The am,
being as difiiné‘t and clear, as if there was only zing
one lpeck from one fingle candle: which lhews, fmalnefii
that the particles of light are exceedingly fmall, 0f “lie!
otherwife they could not pafs through the hole $3221:
from f0 many different candles without confu- '
fion.—-Dr. Nie'wentyt has computed, that there
flQVVS more than 6,ooo,ooo,ooo,ooo times as

‘ A Q 4. many

2.0%

' Plate XV.
Fig. I .

/ 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. »

Thefe particles, by falling direé‘tly upon our
eyes, excite in our minds the idea of light.
And when they fall upon -b0dies;and are thereby
refleéied to our eyes, they excite in us the ideas
of thefebodi‘es. Andras every point of a vifible
body reflects the rays of light in all manner of
gireftions, every point will be vifible in every
part to which the light is reflected from it.
Thus the object/ZCB is vifible to an eye in any
part where the rays fla, flb, flc, A’d, 11g, B a,
85, Br, 34’, Be, and Ca, C17, Cc, Cd, Ce,
come. Here we have fliewnthe rays as if they

, were only reflected from the ends A’ and B, and

'Refiefled
‘ light.

from the middle point C of the objeét; every
other point being fuppofed to reflerft rays in the
fame manner. 80 that wherever a fpeétator is
placed with regard to the body, every point of
that part of the furface which is towards him will

~be vifible, when no intervening objeél fi0ps the

pafiage of the light. .
Since no object can be feen through the bore .

_ ofa bended pipe, it is evident that the rays of

light move in flraight lines, whilf’t there is, no-
thing to refraét or turn them out of their reé‘ti-s
lineal courfe. ‘

Whili’t the rays of light continue in any 9* me-
dium of an uniform denfity, they are firaigh‘t,
but when they pafs obliquely out of one medium
into another, Which is either more denfe or more ,

* Any thing through which the rays of light‘can pafs, is
Called a medium ; as air," water, glafs, diamond, or even,
a vacuum.

rare,

"' Of Optics.
rare, they are refracted towards the denfer me-
dium :' and this refraction is more or lefs, as the
rays fall more or lefs obliquely on the refraéting
furface which divides the mediums.

_ To prove this by experiment; fet the empty
velTel A B C D into any placewhere 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 veITel with water,
and»the’{hadow will reach no farther than c;
'which Ihews, that the ray aBE, which came
firaight in the open air, juPc over the edge of the
veflel at B to its bottom at E, is refracted by

2.03

Fig, 2,

falling obliquely on the furface of the water at Refraaed
B; and inl’tead of going on in the rectilineal cli- light. ‘

reé‘tion 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 ft) of all the other rays
4 b c. » '
If a flick be laid over the vefl'el, and the fun’s
rays be reflected from a glafs perpendicularly
into the veITel, the lhadow of the [tick will fall
upon the fame part of the bottom, whether the
veflel be empty or full; which fhews, that the
rays of light are not~refra€ted when they fall
erpendicularly on the furface of any medium.
' The rays of light are as much refraéled by
pafiing out of water into air, as by palling out of
air intqwater. Thus, if a ray of light flows

from the point 3, under water, in the direétiori‘

e B -, when it comes to the furface ofthe water at
B, it will not go on thence in the rectilineal
courfe B d, but will be refracted into the line B 61.;
Therefore, 7

To an eye at 6 looking through a plane glafs
in the bottom of the empty velTel, the point a
cannot be feen, becaufe'the fide Bc of the velTel

inter: '

204

Of Optics.

1 interpof'es; and the point d will jolt be feen over

The days

are made

‘ ‘ longer by

the re-
fraflion
of the ,
fun‘srays,

the edge of the 'VelTel at B. But if the veITel be
filled with water, the point a will be feen from 6;
and will appear as. at d, elevated in the direé‘tion
of the ray (2 8*.

The time of fun-tiling or fetti‘ng, fuppoling’
its rays fquered no refraélion, is eafily'found by
calculation. Bot obfe'rvation proves that the
fun rifes fooner, and lets later every day than the

calculated time; the reafon of which is plain,

from what was faid immediately above. For,
though the {unfs rays do not come part of the
way to us through water, yet they do through the
air or atmofphere, which being a groller medium
than the free fpacebetween the fun and the top
of the atm'dfiphere,the rays, by entering ob-
liquely into the atmofphere, 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 fuller no refraélion at that
time, becaufe they come perpendicularly through
the atmofphere: yet there is no place to‘which

'the- fun’s rays do not fall obliquely on the top of

the atmofphere,- 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 fetsin it: and the longer or fliorter, as
the atmofphere' is more or lefs replete with va—

Fig. 3.

pours. For, let .480 be part of the earth’s
furface, DEF the atmofphere that covers it,

* Hence a piece of money lying‘at e, in the bottom of‘an
empty veffel, cannot be few by an eye at a, becaufe the edge

of the vellel intervenes; but let the veflel be filled with

water, and the ray ea being then refraé’ted at B, will {trike
the eye at a, and {o render the money vifible, which will
appear as if it were railed up tof in the line 43f. .\

' a ‘ ‘ and

 

Of Optics.
and E B G H therfenfible horizon of an obferver

at B. As every point of the fun’s furface fends"

out rays of light in all manner of direé‘tions,
fome of his rays will conl’tantly fall upon, and
enlighten, fome half'of the atmofphere; and
therefore, when the fun is at I, below the hori—
zon H, thofe rays which go on in the free fpace
Ik K preferve a reétilineal courfe until they fall
upon the tOp of the atmofphere; and thofe
thich fall fo about K, are refrafted at their
entrance into the atmofphere, and bent down
in theline KmB, to the obferver’s place at B :
and therefore, to him, the fun will appear at L,
in the direction of the ray B m 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 refraé‘ting furface, is

205

called the angle of'z'rz'cidmce; and the angle con- Angle of
tained between the fame perpendicular, and the incidenct.

fame ray after refraélion, is called the angle of

refrafiz’oiz. Thus, let LBM be the refraéling Fig. 4_
furface of a medium (fuppofe water) and d B C Aflglezf
a perpendicular to that furface; letDB be animal-9'”-

ray of light, going out of air into water at B,
and therein refracted in the line B H ; ,the angle
d B D, is the angle of incidence, of Which DF
is the fine; and the angle KB H is the angle of
refraclion, whole line is KI. < .

When the r‘efracling 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, q "

- Defcribe the circle D /I E C on a plane fquare
board, and crofs it at right angles with the
firaight lines £80, and LBM; then, from
the interfeétion .4, with any opening of the com-

‘ i ’ patties,

 

206

Of Optics.

pafTes, let off the equal arcs AID and AE, and i

draw the right line DFE: then," taking Fa,
which is three quarters of the length FE, from
the point a, draw 01 parallel to A B K, and
join K1, parallel to B M: {o Kl will be equal
to three quarters of FE or of D F. This done,
fix the board upright upon the leaden ipedefial
O, and flick three pins perpendicularly into the
board, at the points D, B, and I; ‘then let the
board upright into the VefTel TUV, and fill up
the yellel With ‘water to the line L BM When
the water has fettled, look along the line DB,
f0 as you may fee the head of the pin 8 over the
head of the pin D; and the pin I will appear in
the fame right line produced to G, for its head i
will befeen jul‘r over the head of the pin at B:
which fhews that the ray [3, coming from the
pin at I, is to retracted at B,las to proceed from
thencein the line B D to theeye of the obferver;
the fame as it would do from any point G in the
right line DEG, if there were no water in the
yellel: and alfo {hews that K], the (inept. re-
fra€tionin water, is to DF, the fine of incie
dence in air, as 3 to 4*. '

Hence,.if DBH were a crooked flick put
obliquely into the water, it would appear a

‘ firaight one, as D B G.; Therefore, as the line

B H appears at B G, fo the line B G Will appear
at Bg; and ‘confeguently, a liraight {lick DB G
put obliquely into water, j will feem, bent at the
furface of the water in B, and crooked, as

1333'.

When a ray of light pafies out of air into
glafs,’ the fine of incidence is to the fine of re-

* This is firié‘tlyitrue of the red rays only, for; the other
coloured rays are difierently refracted ; but the difference is
{,0 fmall, that it need not be ‘co‘nfidered in this place. .

~ fraftion,

Of Optics; 207

fraction, as 3 to 2; and when dut of air into a
diamond, as 5 to 2. ~

Glafs , may be ground into eight different Fig. 5.
lhapes at leafl, for optical purpofes, viz.

I. A plane glafi, which is flat on both fides,
and of eqUal t’hicknefs in all its parts, as 11.

2. A piano-comm, which is flat on one fide, Lenfes.
and convex on the other, as B.‘ .

3. A double-tamiex, which is convex on both
~fides,asC. ' . , ,

4. A planolconmm, which is flat on one-tide,
and concave on the other, as D. A P

5. Adouble concave, which is 'concave On both
fides, as E. . .

6. A menifcus‘, which is concaVe on one fide, ,
and convex on the other, as F. . ., ; ,

7. A flat plane—convex, whdfeiconVex tide is
ground into feveral little fiatfurfaces, as G. , 3

8. A prifin, ,which has three flat fides, and
when viewed endwife, appears like an equilateral ' "
triangle, as H. 3 , . _ 1 ,

GlalTes ground into anyaof the fhapes B, C, D,
E, F, are generally called Zenfizs. »

, A .right line 'L I K, going perpendicularly
through the middle of a lens, is called the axis 1%
oft/ye lens. ~ ’ ~ ~ ._ , ~

A ray of light G b, falli‘ng‘perpendiculalrly on
a plane glafs, E F, ‘will pails through the glafs Fig. 6.
in the fame direction bi, ,and go out of it" into
the air in-tlie fame right courfe iH. .

\A ra‘ of light flB, falling obliquely on a.
plane g afs, Will go Out of the glafs in the fame
dire‘é‘t'ion,’ but not in the fame right line; for in
touching theg‘lafs, it will be refracted in“' the
line B C,- and in leasing the glafs, it Will be re:
fraéled in the line C—D. \ ' ~ > V.

f ' A rag

208 Of Optics.

Fig. 7. A ray of light CD, falling obliquely on the
middle of a convex glafs, will go forward in the
fame direction DE, as if it had fallen with the
fame degree of obliquity on a plane glafs; and
will go otit of the glafs in the fame direétion
with which it entered: for it will be equally

K refraéted at the pointsD and E, as if it had palied

through a plane furface.‘ But the rays CG and

C I will be f0 refracted, as to meet again at the

point F. Therefore, all the rays which flow

from the point C, fo at 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 (ides of the middle ray

. ' CD‘E F, to what they werein approaching it in
i the directions HF and KF.

Fig. 8. . When parallel rays, as ABC, fall directly

The pro~ upon a piano-convex glafs DE, and pafs through

PFrtieSOf'it‘, they will befo refracted, as to unite in a

$3532th .pointf behind it; and this point is called the

' principal focus; the diftance of which, fromthe
middle of the glafs, is called the focal rig/fame;
which is equal to twice the radius of the fphere.
of the glafs’s convexity. , And, .
When parallel. rays, as 11 B C, fall directly
upona glafs DE, which is equally convexon
both fides, and pafs through it; they will be f0
refr’aétéd, as to meet in a point or principal focus-
f, whofe difiance isequal to the radius or femi.
diameter of the fphere of the glafs’s ennvexit‘y.
But if a glafs be more convex on one fide than
on the Other, the rule for finding ,the focal

, dil’tance is this; as the fum of the-femidiameters

of both convexities is to the femidiameter of

either, to is double the, feniidiameter of the
other to the difiance of the focus. Or, divide

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the double product of the radii by their fum,
and the quotient will be the dif’tance fought.
Since all thofe rays of the fun Which pafii
through a convex glafs are collected together
in its focus, the force of all their heat is col—
let‘led into that part; and is‘ in prepor-tion to

the common heat of the, fun, as the area of the 4'

glafs is to the area of thefocus. Hence we fee
the reafon why a convex glafs caufes the fun’s
. rays to burn after pafling through it.

All thefe rays crofs the middle ray in the fox
cus f, and then diverge from it, to the contrary

fides, in the fame manner F f G, as they con- -

verged in the fpaee DfE in coming to it. -

If another iglafs F G, of the fame convexity
as DE, be. placed in the rays at the fame dili-
' tance from the, focus, it will refraét them {0,
as that after going 'out of it, they will be all
parallel, as aha; and go on in the fame man—
ner as they came to the firi’t glafs DE, through
the {pace ’flBC; but on. the contrary 'fides of
the middle ray Bfé: for the ray flDf will go
on fromf in the direction fGa, and the ray
CEf in the direitioanc; and fo of the refit.

The rays diverge from any radiant point, as
from a principal focus: therefore, if a candle
. ”be placed at f, inthe focus of the convex glafs

FG, the diverging rays in the fpace FfG will
be [0 refracted by ,theglafs, as, that after going
out of'it, they will become parallel, as f‘newn
in the fpace 'céa.

If the candle be placed nearerthe glafs than

its focal :difiance, the rays will diverge after '

pafling throughtheglafs, more or lefs, as the

candle is more or lefs diftantfrom the focus.‘
If the candle be placed farther from the gl‘al's
than its focal dil’tance, the rays will converge
3 ' ‘ after

"209‘. -

2 id

PlateXVI.

Fig. 1.

a:

Of Opticrl \

after paffing through the glafs, and meet in a
point which will be more or lefs dif’tant from‘the
glafs, as the candle is nearer to, or farther from
itsfocus; and where the rays meet, they will
ferm an inverted image of the flameofvthe
candle; which may be fecn‘ on a paper placed
in the meeting of the rays. -

Hence, if any object ABC be~placed beyond
the focus F of the convex glafs d e f, mee of
the rays which flow from every point of the
objeét, on- the fide. next the glafs, willfa’ll upon
it, and after pafiing "throughrit, they will, be

'Converged into’ as many points oh the oppofite

fideof the glafs, where the image of every point
will be formed: and confeqUent‘ly, the image

_ of the Whole objeét,’ which will be inverted.

Thus, the IraySQ/Id, A e, A f, flowing from the” '

. point A, will COnverge in the [pace daf, and by

meeting at a, will there form the image of the
point A. The raysBd, Be, B f, flowing'vfrom
the point B, will be‘united at} by the refrac¢
tion of. the glafs, and will there fcrvm'therimage
of thehpOin’t B'. And the" rays C d, C e, C f,
flowing from the point C,1 will be unitedhat 6,2
where they will form the image of the "point C. v
And f0 of' all the other intermediate ploi-nts be-
tween A and C; The rays whieh’ flew from.
every particular point of the objeé‘t,,-and are
united again by the glafs, are called pencils of
rays. ' 'g

'If the object AB C be brought nearer to the.-

‘ glafs, the piéture 4126 will-be removed to a

greater difiance. For then, more rayeflOvVing ’
from every fingle point, will fall mOre diverging
upOn the glafs; and therefore "Cann’otlbe to foon °
colleéted into the correfponding points behind
it. Confequently, if the dill-ante of the 335%

, Of Optics; ' , ' arr
A B C be equal to the difiance e B of the ~focusPlateXVI.
of the glafs, the rays of each pencil will be f0 Fig- 2-
refraéted by palling‘ through the glafs, that they
will go out of it parallel to each other; as d I,
all, fit, from the point C; dG, e K,‘ fD,
from the point B; and dK, e E fL, from the
point [1: and therefore, there will be no pic:

ture formed behind the glafs.
If the focal diftance of the glafs, and the .

‘ ‘ difiance of the object from the glafs, be known,

' the difiance of the pieture from the glafs may

be found by this rule, viz.‘multiply the diflance

of the focus by thedifiance of the object, and

divide the product by their difference; the

quotient will be the dillzance of the picture. .-

- The picture will be as much bigger or lefs Fig. I;

than the object, as its difiancelfrom the glafs is' a

greater or lefs than the difiance of the object.

. For, as “Be is to eh, f0 is AC to ca. 80 that

> if A B (Che/the object, 5 b a will be the picture ;

or, if‘céa be the object, flBC will be the

picture. ‘ '
Having defcribed how the rays of light, Them“.

flowing from objects and pafling through con- net of vii \

vex gl'afl‘es,= are collected into points, and form {mm

the images of the objects ; it will be eafy to un-

derftand how ether rays are affected by pafling

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

’difl'erent humours of the eye, and particularly

the chryi’talline humour, are to be confidered

as a convex glafs ; and the rays in pafling

through them to be afi‘eéted in the fame manner

as in pafling through a convex glafs,

I? The

212i

IPl'ateXVI.
tthree. mats and -t.hteé;"'=hu~mours. The 'part

Figo, ‘3.

The eye
defcribed.

Of Optics.
, .‘Theye‘yenis nearl-yz globular. flt confifl’s‘ of

Dh’rH Gof the outer coat, is called the falc-
rotica,,;the_.'refi DE F G-thexarnm. Next-with.
ingthis .f'coat {is that called: the ckoroides,-,Whitih
{CY‘VCS'aSg-iE;WCrC for a'lining to the other, :and,
joins with the iris min, min. , T he iris is com-h
pofed of two fets offlinfcular fibres; the one of
a circular form, whiehcontra‘é’ts the hole in'the
middle called the pupil,twhen the. light would
otherwife :be too firong for the eye;:.and.the
orher‘p’f radial fibres, tending every where from
thecircumference of the iris towards the middle
of the pupil; which fibres, by their contraction,
dilateand enlarge the pupil when the light is

: Weajk,.in-orde‘r to let, in themore of its rays. 4
' The” third coat is only a fine expanfion of the

optic nerve L, which ifpreads like . network all ,
overfthe infide of the choroides, and is therefore
called. the retina; uponiwhich are painted (as it,
were) the images of all vifible objects, bythe
rays of light which either flow or are ‘refieéted
romthemirw» Q ; f ., ‘ : , .‘3
Under the cornea; is ;a fine tranfparent fluidi
like water, which is therefore called thetagiueaus
humour. It gives a protuberant: figuretotuthe
cornea, fills the two cavities m m and 1211, which
communicate by the pupil P, and has the fame '
limpidity, fpecific gravity, and refractive power-
as water. 7, At the back of this lies the ckry/iallz'ne ,
humour I], which is fhaped like a double 00n—
vex glafs -,1 and is a little more convex On the
back. than the fore-part. lt converges therays,
which pafs through it from every vifible object
tolits focus at the bottom of the eye.. This
humour is tranfparent like chryfial, is much of

. the confii’tence of ard jelly, and exceeds the

fpecific‘

. _ 9‘

OijSz‘iés. , s ‘ ‘ J 213

mail
11 to 10. It is inclofed iii a. fine craftfparent.
membrane, from which proceed 1, radial-fibres,
oo, 'Called'it'he lz'gammtum Mime, all around-its;
edge 5 and join. tothe circumference of‘the iris.
Ehefe fibres have, a power: of contracting'and

ilating‘ occalionally, b‘yL which means! they alter
the fliape or convexity of the Chryfiallinejh'u-
mour, and alfo fhift it a little backward orfor--.
wardflinthe eye, (0 as to adapt its focal diltance
at the bottom of the eye to the different dil’tanc'es
of objects; without which provifion, wecould
onlyrfee thofe objects dil’ti'nftly, that were all at
one'dil’tance from the eye. . ‘ -. . _

. At the back of the chryf’talline, lies the wire,
oasi‘laumour K K, which is tranfparent like glaFS,
and is largel’t of all in quantity, filling the whole
orb of the eye, and giving it a globular fhape.
It is much of a confidence with the whiteof an
egg, and very little exceeds the fpecific gravity
and refractive power of water.‘ , . . W

Asgevery point of an object 11 B C {ends out
rays in all directions, forne rays, fromevery
point on the lide min the eye, will. fallauppn
the cornea between E and F; and by paffinglon
through the humours and pupil of the eye,
they will be converged toas many points on
the retina or bottom of the eye, and will thereon
form a dif’tincl: inverted picture c [2 a of the ob—»
ject. Thus, the pencil of rays gr 5 that flows
‘ from thespoint A! of the object, will be con-
verged to the point a on the retina 3 thofe from
the point B will be converged to the point (5;,
thofe from the point C will be converged to the ‘
point c ;and f0 of all the intermediate points: by
which means the whole image a be is formed,
and the object made vilible; althoirgh it mult

' P 2 ‘ . be

fpecific gravity of water in the prop-e; ti

114

Of Optics;

be owned, that the method by which this fenfaa
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 efi'eéted in this manner,
may be demonl’trated experimentally. Take a

* bullock’s eye whilfl: it is frefh, 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 objec‘t upon the paper. ‘

Seeing the image is inverted, many have
wondered why the objeét appears upright. But
we are to confider, I_. 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 profpecft are painted upon
the retina, they ‘are all right with refpeé‘t to one
anorher, as well as the parts of the profpeét.
itfe‘lf; and we Kean only judge of an object’s
being inverted, when it is turned reverie to its
natural pofition, with refpeé‘t to other objects
which we fee and compare it with.-’—-If we lay
hold of an upright Rick in the dark, we can tell
which is the Upper orlower 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 mufi: 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 y,

' . and

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gl’LATE XVII.

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Of Optics: '2 :5

and as the judgment ,is‘informed by the motion
of the hand in one cafe, fo it is alfo by the mo-
' tion of the eye in the other.

In Fig. 4. is exhibited the manner of, {eeing Fig. 4. _>
the fame object A B C, by both the eyes D and ‘
E at once. a
. When any part of the image 6 b 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 ; {0
that whatever part of the image falls upon the
optionerve of one eye, may not fall Upon the
optic‘nerve of the other. Thus the pointa of
the image 5 b a falls upon the optic nerve of the
eye D, but not of the eye Esand the point e
.falls upon the optic nerve of the eye E, but not
of the eye D 2 and therefore to both eyes taken
tagether, 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 is feen, and XVII-
the magnitude under which it appears._ Thus F‘g° "
to the eye D, the object A B C is feen under the
angle A PC; and its image cba is very large
upon the retina:' but to the eye E, at adouble
diltance, the'fameobjeét is feen under the angle
A p C, which is equal only to half the angle
A P C, as is evident by the figure. The image
c b a is likewife twice as large in the eye D. 'as
the other image 6 ha is in the eye E. In both
thefe-reprefentations, a part of the image falls ~
on the Optic nerve, and the object in the corre-
fponding part is invifible. ,

As the fenfe of feeing is allowed to be occa-
fioned by the impulfe of the rays from the vilible
object upon the retina of the eye, and forming

P 3 the

216

Of Optics.
the image of the object thereon, and that the

“retinas only the expanfion Of the optic nerve all

over: the choroides , it {hould feem furprifing,
that the part of the image which falls on the

optic nerve fl10uld render the like part of the

objeft invifible , efpecially as that nerve is al-
lowed to be the infirument by which the impulfe
and image are conveyed to the common fenfory

'in the orain. But this difficulty vanifhes, when

we confider that there is an artery within the
trunk of the optic nerve, which entirely ob-
{cures the 1mage in that part, ahd conveys no
fenfation to the brain.

That the part of the image which falls upon
the middle of the optic nerVe is loll, and confe-
quently the corréfpcinding part of the object is
renderedinvifible‘, is plain by experiment. For,
if a perfon fixes three patches, 1?, B,'C, upon a
white Wall, at the height of the eye, and the
dif’tanceof about afoot from each‘other, and
places himfelf before them {butting the right

, eye, and directing the left towards the patch C,
j he will fee the patches 12’ and C, but the middle '
1' " patch B will dilappear. Or, if he {huts his left '

eye, and directs the right towards 11, he will fee
both A’ and C, but B will difappear , and if he
directs his eye towards B, he will fee both '8 and
A’, but not C. For whatever patch is direé‘tly
oppofite t0" the optic nerve N, vanifhes.‘ This
requires a little practice, after which he will find
it eafy to direct his eye, {0 as to lofe the-fight
of whichever patch he p l.eafes

‘ We are not commonly fenfible of this dilap-
pearance, becauie the motions of the eye are
10 quick and inflantaneous, that we no fooner
lofe the fight of any part of an objeél, than we
recover it again , much the fame as in the
twinkling ofour eyes, for at each twinkling we
. . , . , t . . . are

Of Optics. . 4 *2 1.7
are blinded; but it is {'0 Ibon over; that We are
' fcarce ever fenfi-ble of 1t. '

Sbm‘e eye's require the afiifianc’e of convex Fig yo4
.glalTes to make them fee objects dif’tinétly, andvv (Oi, e C's
others of concave. If either the cornea (1' h, 1: o'r regain; '
“chryflfalline humour 6, or both of them, be too fpeétacles.
flat, as 1n the eye fl, their focus will not be on
the retina, as at d, where 1t ought to‘ be, in or.
der to render vifion diftiné‘t, but beymd the
'eye, "as at f. Confequent‘ly thefe‘ rays which .
flow from the object C, aad pafs through the
humours of the eye, are not converged enough
7to unite at d; and therefore the 'obferver Can
have but a very indil’tih‘ét view of the object.
This is remedied by placing a conveX glafs g h
before the eye, which makes the rays converoe
fooner, and imprints the image duly on the
retina at d.

If either the cornea, or chryfl'ailine humour,
or both of them, be too convex, as in the eye
f, the rays that enter in froml the object C, Will
be converged to a focus 1n the vitreous humour;
as atf; and by diverging from thence to the
retina, will form a very confufed image thereon:

‘and fo, of courfe, the obferver will have as con- "
fufed a view of the objefl, as if his eye had been
too ‘flat. This inconvenience is remedied by
placing a concave glaisg la before the eye, which
glafs, by caufing the lays to diVerge between it
and the eye, lengthens the focal dillance 10,
that if the glafs be properly ehofen, the rays
wi Ill unite at the retina, and form a dil‘tinft pic-
ture of the object upon it. ‘

Such eyes as have their humours Of a due
\ convexity, cannot fee any objeé‘t difiinftly at a
lefs dif’tance than fix inches ; and there are
numberlefs objects 100 final] to be feen at that
' P 4 di fiance,

\

Q18" Of Optics;
difiance, ‘be'caufe they cannot appear under any
fenfible angle. The method of viewing fu-ch‘
minute objects is by a microfl'ape, of which there
are three forts viz. the fingle, the double, and
the folar. . ' , ,
Fig. 5. The fingle mirrofcope is only a {mall convex
Thefi'zgk glafs, as and, having the objeét a b placed in its
may“? 3' focus, and the eye at the fame difianceion the
other fide ; it) that the rays of _ each pencil,- flow-
ing from every, point of the objefi‘ton' the fide
next the glafs, may. go onparallel inthe {pace
~ between the eye and the «glefs; and then, by
entering the eye atC,‘they will be converged
to as many different points onthe retina, and
form a {large inverted piéiure 21 Btupon it, as
in the figure» - V ‘. . _
. To find .howmuch this glafs magnifies, di-
vide the leafl: difiance (which is about fix inches)
at which an objeél: can be feen difiinétly with
the bare eye, by. the focal dii’tance of the glafs ;
and the quotient will vflnew how much the glals
magnifies» the diameter of the obje-ét. _
Fig. 6. The double or compared 'mirrofcope, eonfil’ts of,
The . an obieét-gla-fs c d, and an eyeeglafs c f. The
iii/Z}?- fmall object ,4 bis placed :at a little; greater dif-
- ' tance from the glafs r dthan its. principal focus,
f0 that the pencils ofzrays flowingfromxthe dif-
ferent points of the objee‘c, and. paflingi through
the glafs, maybe made to converge and unite
inflas many pointsbetweengandb, where the
image of the objeét will be formed : which
image is viewed by, the eye through the eye-
glafs e f For the eye-glafs being f0 placed,
that the image gb may be in its focus, and the
eye much about, the fame difiance on the other
‘fide, the rays of each pencil will be parallel,
after going out of the eye-glafs, has at e and f,
, till

Of Optic: 219

till they come to the eye at k, where they will
begin to converge by the refraé‘tive power of
the humours; and after having crofl'ed each
other in the pupil, and pafl'ed through the chryil
talline and vitreous humours they will be col-
Jetted into points on the retina, and form the
large inverted image “A B thereon

The magnifying power of this microfcope is
as follows. Suppoie the image gM/a to be fix
times the difiance of the obg'eét 316 from the .
objeét- glafs 5d,. then will the image be fix times
the length of the objeét: but fince the image
could net be feen’ diftiné’cly by the bare eye at
a lefs difiance than fix inches, if it be viewed
by an eye-g olafs e f, of one inch focus, it will
thereby beD brought fix times nearer the eye;
and confequently viewed under an angie (ix times
as large as before, f0 that it will beD again mag-
nified fix times , that IS, fix times by the objeét—
glafs, and fix times by the eye glafs, which mul-
tipli'ed into one anOther, makes 36 times , and
[0 much is the object magnified 1n diameter more
than what 1t appears to the bare eye; and confe-
quently 36 times 36, or 1296 times in furface.

But, becaufe the extent or field of View is
very fmall in this microfc0pe, there are gene-
rally two eye-glafi'es placed fometimes clofe
together, and {omctimes an inch afunder; by
which means, although the objeét appears lefs
magnified, yet the viiible area is much enlarged
. by the interpofition of a fecond eye—glafs; and
confequently a much pleafanter View is ob—
.tained.

The folar micro/hope, invented by Dr. Zie- pig
’ berkbzm, is confirué‘ted 1n the following manner. The war
Having procured a very dark room, let a’ round 7’1“" 5" We
hole he made 111 the window- Ihutter, about three

incheg

220

Of Optics.
inches diameter, through which the fun may eafl:
a cylinder of rays .4 A into the room. In this
hole, place the end of a tube, containing two
convex glafles and an objeét, viz. 1. A convex
glafs a a, of about two inches diameter, and
three inches focal dii’tance, is to be placed in
that end of the tube which 18 put into the hole.
2. The objeét b I), being put between two glaITes
(which mui’t be concave to hold it at liberty) is
placed abOut two inches and a half from the glafs
a 11.3.A little more than a quarter of an inch

from the objeét 1s placed the fmall convex glafs
. c c, whofe focal diliance IS a quarter of an inch.

The tube may be fo placed, when the fun is
10w, that his rays fl 1% may enter dire€tly into
it: but when he is high, his rays B B muf’t be
reflected into the tube by the plane mirrour or

looking-g1 als C C.

Things being thus prepared, the rays that
enter the tube will be conveyed by the glafs a 1.:
towards the objeEt h h, by which means it will
be firongly illuminated ; and the rays 51’ which
flow from it, through the magnifying glafs c C,

will make a large inverted piéture of the objefl:
at D D, which, being received on a white paper,

will reprefent the objeét magnified in length, in
proportion of the diltance of the picture from
the glafs c c, to the difiance of the object from
the lame glal’si T hus, fuppofe the dif’tance ofthe
objeét from the glals to bcm3 3 parts of an inch, “
and the dii’tance of the difliriét picture to be 12
feetor 144 inches, in which there are 14.40 tenths

- of an inch; and this number divided by 3~tenths,

gives 480; which is the number of times the
pitiure is longer or broader than the object, and
the length multiplied by the breadth, {hews how

much the whole furface is magnified.

_ Before

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Before We enter tipioh the d§fcripti0n 0f~ t31337‘31’Lj/Eapax.
limp“? it “’1.“ be PYOPCUO 'fhéw how] the ray? , '

- . of light are affeé‘ted by'pafilng‘ through cone-ave

glafles, and (allorlby falling upon concave mir- - i '-
“rburs. — ' _ . , , . a r
' - When parallel rays, assert a 6 lid 6 f g 17,, apafs Plate
directly through a glafs AB, w'hich'is equally XVIII:
concave. on both fides, they will diverge after F 1g. "
pafling through the glafsl, as if ”they hadcome ,
from a radiant point C'g'in 'the center; of the.
_ glafs’s concavity; whichwpoint‘is‘ called thehneé
gative or virtual'foeus of theglafs, I Thusthe
ray a, after ‘pafiing through theglafs; A B, Will i
go on in the‘direé‘tion k I, as if it had proceeded
from the point C, and n‘oglafs been in theway.»
The ray b will go on in‘ the direétion 124377: -,‘ the; ,
ray c in the'direétion o p, &C,g—-—1The rjath,‘ -
that falls direftly upon the middle of the gl’afsg ,
{offers no refraétion. inmpafiingfithrough it; but
goes on in" the fame reé‘tiline'al dire’étion, ‘jaslit; ‘
no glafs had been in its way. '
., If the, glafs had been concave only-onfonfei
fide, and the ether fide qu‘iteyplan‘e, the rays,
wo’ul‘d'have diverged, after pafhn'g othroughit;
as if they had tome from .a ‘radiant pointiat
double-the dil’tance of C from thefglafsj, that-is” ‘
as if the radiant had been at the dif’tance ofaf
Whole diameter of the’glafs’s‘concavity.
If rays come 'moréConverging to fuclh a glafs,
than parallel rays diverge after paflihg’ through?
it, they will continue to converge after pairing;
through-it; but will no: meet f0 form as iffno, 7
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 raysfand la, going in a converging
fiate towards the edge of the glafs at B, and
con-

fig. 2.

_ 0f .‘Cpticst

I converging theft: in their way to it than‘the a-

rall‘el rays diverge after palfing thrOugh it,» t ey
Will go on converging after they pafs through
it, though in a lefs degree than they did before,
and will meet at 1:” but-if no glafs had been in
their way, they would have met .at i.» A a
When the parallel rays, as d f a, 02:22 5, e l a,
fall upon a concave mirrour A B (which is not
tranfparent; but» (has only the furface A 5 B of
a Clear polifh) they-will be reflected‘back-front
that mirrour, and meet in a point :49, at half the
eliflance of the furface'of the mirrout 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 mlrrour, as they fell
upt‘m it, with regard to that perpendicular ; but
on the other fide thereOf. V Thus, let C be the

center of concavity of the mix-tour A b B, and '

let the parallel rays df a, C m 5, and e I 5; fall
upon it at the points (z, a, and 5. Draw the

‘ lines C 1' a», C me, and C b c, from the center C

to thefe points ; and all thefe lines will be per-
pendicular tothe furfaee of the mirrour, becaufe
they proceed thereto like fo'many radii or {pokes
from its center; Make the angle C a 5 equal

to the angle 4’ a C, and draw the linea at; 12,. I

Which Will be thedireé‘tiomof the my a! f a, after

[it is reflected from the pointtasof the mirrour r

its that the angle of incidence d a C, . is equal to
the angle of reflec‘lionC a 17-, the rays making
equal angles with the perpendicular C i a on its
oppofite' «fide’s. _

Draw 3116 the perpendicular C I) e to the point

e, where the ray e I: touches the mirtour -, and,

having made the angle C t 1', equal to the angle

,(2‘ e e, dtav'v‘ the line 6 m 2', which will be the

. courfe

ta 'as-néfl‘” "y“. t" "‘

Of Optzcs.

courfe of the ray e! c, after 1t is 11111111 from
the mirrour. ‘ '-

The ray C 1115 p11fiésf through the center of
concavity of the 1111110111, and falls upon it at
iv, the perpend1cular to it; and 15 therefore re-
fleéled back from It in the fame line '5 m C. .

All thefe refleét’ed rays meet 111 the point m;
and m that poi11t_ the Image of the 'bOdy Which
emits the parallel rays 4‘ a, Cl»; and ac, will be
formed“: Which point is dil’ta-nt from the mir-
four equal to half the radxus 5: m C of its con-'-
cavity .. -

The rays wlnch proceed from arly celeftxal
objefl' may: be efieemed parallel at the earth;

and therefore, the wages ‘cs'f that o‘bjeét will be
formed at m, whew the «refleétmg furface of the
' concave 'mirronr ’19. tamed dneétly tGWards the
objeét. Hence, the focus 7% 01" parallel rays

is not 1:11 the center of- the m1rrour s concavity, -

but half way between the m1rrout and that

center. ~

1 The rays;-wh1ch proceed from any 115111011:
terrefirial object are nearly parallel at the 11111;

roar , not-1111116115: f0, but’ Vc0n'1e tixvergmg to it,

in feparaté pencxls, or", as it Were, bundles 0f

raYs, from each point 0f the fide of the Object
. next the 1111110111 and therefore they will not

be converged: to 1a"; perm, a: the dxlltnce of half

the radius of the rumours concawry frenn its.

refleéting furface, but 11110 feparate 11011113 at a

little greater dillance from the mirronr. And.

the nearer the Objeét is to the mirrour‘, the far-1
ther thefe points will be from it; and an in-
verted image of the obje’ét will be formed in
them, wh1ch will feem to hang pendent 1n the
air- , and will be feen by an eye placed beyond
it (with regard to the 1111110111) in all refpeé‘ts

like

2 2:3

aa6

Of @ptics'

If the ohjeék be 1n the center of. the mirrour’ s
concavity, the image and objeél: will he coinci-
dent, angel equal 111 haulk

If a man plaees himfelf direétly before a large

’ tonnage mirtonr, but farther from it than its

center of: concavity, he will: fee an inverted
image of himfelf in the air, between him and
the mirrour, of ar- lefs fize‘ than 'himfelf. And
if he holds out his hand towards the mirrom,
the hand of the image will come out towards
his hand, and coincide with it, of an equal-
bulk, when his hand 1s in the center of conca-
vity; and he will imagine he may lhakehands
with his image.- Ifthe reaches-his hand farther,
the hand ofthe image will pals by his hand, and

come betweenhis hand and his; body: and if he

moveshis hand towards either fide, the hand of
the image will move towards-the other; {0 that
whatever way the obj-eel moves, the image will
move the contrary.

All the while a by— l’cancler will lee nothing of
the image, becaufe none of- the refleéted rays
that form 11: enter his eyes.

If a fire be made in a large room, and a
fmooth mahogany table be placed at a good
dillance near the wall, before a large concave
mirrour, fo placed, that the light of the fire
may be refleéted from the mirrour to its focus -
upon the table ; if a perfon {lands by the table,
he Will fee nothing upon it but a longilh beam
of light: but if he {lands at a difl‘ance towards
the fire,. not direélly between the fire and
mirrour, he will fee an image of the fire upon
the table, large and ereét. And if another per-
fon, who knows nothing of this matter before-
hand, fhould chance to come into the room,
and {hould look from the fire towards the table,

4. he

, . 0f Optics; 2 2 7

he Wodld be I’tartled at the appearance; for the Plate

table wo'uld 'feem to be on fire, and. by being XV 11L

hear the wainfcot to endanger the whole hbufe.

In this experiment, there fhould‘ be no light

in the mono but What proceeds from the fire, ~

and the mirrour ought to be at leafl' fifteen

inches 1n diameter. 1 1- 1
If the fire be? darkened by a fcreen, and a.

large candle. be placed at the back of the Icreen , _

a perfon handing by the candle will fee the

appearance of a fine large llar, or rather planet,

upon the table, as bright as Venus or Jupiter.

And if a fmall wax taper {whore flame IS much,

lefs than the flame of the candle) be placed neat

the candle, a fatellite to the plane: will appear

on the table; and if the taper be moved round

the candle, the fatellit'e will "go round the planet;

. For thefctwo plear’ing experiments, I am in-

debted to the late reverend Dr. LONG, Lotvn‘des’ s

profefi’br of altronorny at Cambridge, who 11.

voured me with the fight of them? and many

more of his curious inventions. .
In a refrafiz'ng tale/rope,- the glafs which is The f‘e- 1 U

nearefi: the object in viewing; it, 18 called llflefraéi‘ing i ..

objefiglafs, and that which is marred the eye, t/fwfl- i

is ‘called the eye glafr. The objeét-g o‘lals molt ' i

be convex, but the eye glafs may Dbe eithe1

convex or concave: and generally, in looking

through a telefeope, the eye is in the focus or

the eye-glafs ; though that 13 not very material;

for the difianCe of tohe eye,- as to difiinet vifion,

is indifferent,- prdvided the rays of the pencils

fall upon it parallel: onl V5 the nearer the eye

is to the end of the telefcope, the larger rs the

{cepe or area of the field of View.

. Let cd be a convex glafs fixed 1n along tube, Fig 4,

. and have its focus at E. Then, a pencil of rays

g .12 z,

   
    
 

I 228'

Of Optics;

- ‘ , g bi, flowing from. the upper extremity A of the

remote object A B, will be f0 refracted, by pamng

through the glafs, as to ~Converge and .meet in

the point f -, whili‘c the pencil of rays It 1m, flow-
ing, fromthe lower, extremity B, of the fame ob;
jeet A‘ B, and pafling through the glafs, will con-

.vergeand meet in the point erand the images'

of the points 14 and B, will-be formed in the
points f and e. And as all the intermediate
points of the object, between A and B, fend out:
pencils of rays in the fame manner, a fufiicient
number of thefe pencils, will pafs through the
objeétglafs c d,.'and converge to as many inter—-
mediate points between 6 and f ; and-f0 will form
the whole inverted image e E f, of the difiinft
object. But becaufe this image is final], a con-
cave glafs 72 a is f0 placed in the-end of the tube

. men the .eye, that its virtual focus may be at F.

And as the rays of. the pencils pafs converging,
through the concave glafs, but converge lefs after
palling through it than before, they go on for-

~ther, as to b and a, before they meet; and the

pencils-themfelves being made to diverge. by
pafl’mg through the concave glafs, they enter the.
eye, and form the large picture a & upon the
retina, whereon it is magnified under the angle

But this telefcope has one inconveniency'which

' renders it Unfit for molt purpofes,-which: is,-tihat '

the penciis of rays being made to diverge by
pafling through the concave glafs no, very few
of them can enter thepupil of the eye; and
therefore the field of view is but very fmall, as
is evident by- the figure. F 0r, 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 fiopt by falling upon the iris

_ above

Of Optics:

‘above and ‘be‘lowthe popil :~ and therefdre, only;

the middle pa‘rt‘of the» objeét’can be ’feen when
the telechpe lies direcfliy towards it, by means
of thofe rays which proceed from the middle of
the objeét. [So that to fee the Whole of it, the
telefCOpe mutt be moved upwards and down-
wards, Holds the object be very remote; and
then it is never feen dif’tinétly. ’

. 229.

This incOnvenience is remedied by' fubfiitut- Fig. 5.

ing a convex eye-glafs, as gla, in place of the
concave one»; and'fixing it f0 in the tube, that,
its focus may be coincident with the focus of the
objeEt-giafs '6 (1,35 at E. For then, the rays of

the pencilsflowing from the objeét A? B, and '

paging—through the objeé‘c—giafs c d, will meet in
its focus, and form the, inverted image 771 E’p:

and as-the image is formed? in the focus of the

eye-giafs gb, the' rays of each pencil will bepa-
railel, after pafling through that glafs ; but the
- pencils themfelves will c-rofs in its focus, on the
Other tide, asate: and the pupil of the eye
being in this focus, the image will be viewed

through theglafs, underthe angie‘g e Z2; and

beingat E, it wii'i‘appear magnified, f0 as to fill
the whole {pace C 'm e p D. ' '

But, ‘as this tele‘fcope inverts the imagewith,

refpeét to the objeét, it gives an unpleafant View
of terrei’triai objeéizs 3, and 'is only fit for viewing
the heavenly‘bodies,‘ in Which we‘regard not‘their
petition, became their being inverted does not»
appear, on account of their being round. But
whatever way the objeél-er’ems‘to move, this tel-ea

' {cope mutt be’moved the contrary way, in ‘order .

to keep fight of inter, time the objeét is in:

i > vetted, its-motion will be {0 too‘.

The magnifying power of this telefcope is,
asthe focal .dii’tan'ce of the objeét-giafs to the
‘ ‘ Q2 focal

230

Of Optics.

fOcal diftan‘ce of the eye-.gl orlafs. Therefore, if the

former be divided by the latter,- the quotient

will exprefs the magnifying power 1 .
When we fpeak of the macrnifying of a tele-

‘fcope or microfcope, 1t is only meant with regard
, to the diameter, not to the area or folidity of the

object. But as the infirument magnifies the ver-
tical diameter, as much as it does the horizontal,
it is cafy to find how mil-ch the whole vifible area

for furface 'is magnified: for,1if the diameters be
’multiplied into one another, the product will

exprefs the magnification of the whole vifible
area. Thus, {upppofe the focal diftance of the

‘objeéb glals be ten times as great as the focal

diftance of the eye-glafs; then, the objeét will
be'magnified ten times, both in length and
breadth: and IQ multiplied by 10, produces
.;100 which fhews, that the area of the object

will appear 100 times as big when feen through

fuch a te‘lefcope, as it does to the bare eye.
Hence it appears, that if the focal dittance of
the eye- g—lafs, were equal to the focal difiance of
the objectoglafs, the magnifying power of the
telefc0pe would be norhing.
This telelcope may be made to magnify in any ’

:given degree, provided it be, of a .fuflicient

length.1 For, the greater the focaldiftance of

‘ the objeé’t-glafs, the. lefs - may be the focal

difiance of the ”eye olafs; though not directly in
proportion 1 Thus, an object Dglafs, of 10 feet
focal difiance, will admit of an eyeb Olafs whofe
focal difiance is little more than 21 inches;

1WhiCh will magnify near 48 times: but an obs

jeét-glafs, of 100 feet focus, will require an eye-
glafs fomewhat more than 6 inches- , and will

therefore magnify almol’t 200 tithes.
A telefcope for viewing terref’trial objects, {hould
be in confirué‘ted, as to fhew them 1n their natural
pofiure.

Of Optics. ‘ 231

pol‘ture, ' And this is done by one objeé‘t-glafs Fig. 6.
c d, and three eye-glaifese f, g/o, He, fo placed,
that the dii’tance betweenyany two", which are
nearef’t'to each other, may be equal to the fum
of their focal difian’cesi; as in the figure, where
the focus Of the glaifes c d and ef meet at F,
thofe of the glaffes‘efanclvg [9, meet at l, and-of
g 19 and 2'- le, at m; the eye being at 72, in wheat
the focus of the eye-glafs z' k, on the other fide.
Then, itis plain, that thefe pencils of rays,~which
flow from the objeft fl 8, and ipaf‘s through
the objef‘t-‘glafs c :1, Will meet and form «an in-
verted'irn’age C F D. in the focus of that 'glafs;
and the image being alfo in the focus of the, glafs
’ e f, the rays of the pencils will become parallel,
after paffing through that glafs, rand ctofs at l,
in the focus of the glafs e f; from whence they
'pafs on to the next glafs g In,“ and" by going
through it they are converged topoints in-its
Other focus, where they form an ereé‘c‘image
E 772 F, ’of the objeét flB :7 and as this image is
alfo in the focus of‘the eyev-glafsi hand! the eye
on the oppofite fide of the fame glafs; the image
is viewed through the eye-glafs in this telefcoPe,
in the fame manner as through theeyeglafs in
the'f'ormer one; only in a contrary pofitiOn,
that is, in the fame pofition with the objeét.

The three glaffes next” the eye, have vall'their
_ focal difiances equal 2 and the magnifying power
of this telefcope is found theffameway 'as that
of the lait above; viz. bydividing the-focal
diitance of the o'ojet‘bglafs c d, by the focal
, ~ dii’tanee of the eye-glals i It, or g 10, or e f, fince
all thefe three are equal. i , :

When the rays of light are feparated by rea
fraflion, they become coloured, and if they be
united again, they will bea perfeét white. But
’ i Q g \ thofe

2 32 Of Optics.

Why the thoi'e rays which pafs through a convex. glafs,
obieél ap- near its edges are more unequally refraétedb than
fearsco‘ thofe which are nearer the middle of the ghfs. .
oured . .
when {em And when the rays of any penal ale unequally
through arefraé‘ted by the glafs, they do not all meet
§€l¢fCOPe again in one and the fame point, bUt 1n feparate
points , which makes the image indif’tinét, and
coloured, about 1128 edges. The remedy is, to
have a plate with a {mall round hole in its mid-
die, fixed in the to be at m, parallel to the glalles.
For, the wandering rays about the edges of the
glafihs Will be flopt, by the plate, from coming
to the eye. , and none admitted but thofe which
come through the middle of the glafs, or at leait
at a good t,dil’ta111c,_e from its edges. and pafs
through the hnle 1n the middle of thepla‘te. But
‘this circumfcribes the image, _ and lTelTens the
field of View, which wouldb be much largei if
the plate could be difpenfed with. "
The ré- - lhe great inconvenience attending the ma-
flefimg nagement of long telefc0pes of this kind, has
”UMP" bretight them much into difufe ever fince the
rtyi’ezfiz'ng telefia’pe 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 Ifaat Newton, but has received confiderable
improvements fince his time , and is now gene-
rally; confitufted 1n the following manner, which
was 11:11 pro‘pofed by Dr. Gregory.

:At the bottom of the great tube T79”? is
placed the large concave mirrour DUI/F, whofe ~
principal foeus 18 at m , and in its middle is a
round hole P, onofite to which is placed the
{mall mirrour L, concave toward the great
one; and fo fixed to a firong Wire M that it

_ may be moved farther from the great mirrour,
Q; nearer to it, by means of a long fcrew on the
out:

Of Optics;

outfide of “the tube, keeping its axis {lill in the
farhe line ‘Pmn with that of the great one.»-
‘ Now, fince inviewing' a very remote objeét, we
can fcarce fee a point ”of it but what is at lea-fleas
broad as the great mirrour, We may confiderthe
rays of each pencil, which flow frpmfevery point
of the obj'eé’t, to be parallel toe-eaCh‘ other, hand
to cover the 'whole reflefting‘ furface D U—V F.
But to avoid ”confufion (in the figure, we fliall
only draw two: rays of a pencil flowing fronieaCh
extremity of the object into the: great-tube, --a:nd
' trace their' progrefs, through‘all' their re‘fleet‘ion's
and ~refrat‘ftions, to the eye f, at the endof the
{mall tube H, which is joined to theggreat one:
Let us the'rf fuppofe' the objeft A B to: be at
fuch a difiance, that the rays Cl'may-flowyfrom
its lower extremity B, and the rays-E from its
upper exttéfn‘ity d. Then the rays: C‘ falling
parallel upon the great (mirrour at'Drwi‘ll be
thence refleéted, converging in, thedireé'tion
D6; and by crOfiing rat/I in the principal‘ifocus
of the mirr‘our, they will form the upper extre'»
mity I of the ihverted ima‘ge‘I'K',‘ ‘-fimilar'~tothe

lower extremity B of theobje-‘ét .24 B: and paf- /
fing on to the concave mirrom‘ 'L (whofe focus .

is at 7-2) they will fall upon it» at g, and be thence

reflefled‘cOnverging, in the direé’ciongN,‘ 'becaufe '

g m is longer than g ‘71; and pa’fling‘ through-the
hole P in the large min-our, they-wouldmeet
fomewhere abbut r, and farm the‘lower extremity
d of the ereét image a d, ‘fi‘milar to the loWer-ex-
tremity'B "of the‘ objeétfl B, But» by pafiing
throngh the plano-convex' 'g-‘last in their way,

they form that extremity of the ,. image at e.
' In like manner, the rays E, which come from the
top of the objeél d B, and fall parallel Upon the
great mirrour at F, are thence refleéted converg-

Q4 mg

233

“S4

: Of‘ Optzcs.
ing to its focus, where they form the lower- 6X3

tremity Kof the inverted image 1K, fimilar m
the upper extremity def the objeét x13; and

~-th'ence pafling on to the {mall mirrour L, and
falling upon it 211: la, they are thence reflected 111
1111: conVerging {tare b O; and going on through

the. hole P of the great mirrour, they will meet
fomeWhere about 9, and form there the upper
extremity a of the eree‘t image a d, fimiiar to the
upper extremity flof the objeft .48: but by

, pafi’i'ng through the convex glafs R in their way,

they meet and crofs fooner, as at a, where that
point of the crest image is formed -T he like

“being underflood of all thofe rays which 6011,!

from the intermediate points of the oblest, be-

tween 12’. and B, and enter the tube Til”, all the
'li'ntermediate points of the image between a and
”b will be formed . and the rays pafiing onfrom
the image through the eye» aglafs S, and through
a lmall hole 19 in the end of the leFer tube 1‘ t,
« they enter the eyef, whilch fees the image a d
‘(by means of the eye-b «fl afs) under the Dlarge
angle 6 e d, and magnifif: d in length, under that

angle from c to d
‘ In the belt refleéting telefcoipes,‘ the focus of

» the {mall mirrour is never coincident with the
.focus m of the great one, where the hilt 1mage
:I K 15 formed, but a little beyond it (with refpeft

to the eye) as at n: the confequenee of which 15,
that the rays of the pencils will not be parallel
after refleétion from the {mall mirrour, but con-
verge fo as to meet in points about g, e, r- , where
they will form a larger upright 1mage than a d,
if the glafs R 11a mm 111 their. way . and this.
image might be viewed by means of a fingle
eye~g olafs properly placed between the image
and the eye: but then the field of View would be
' lefs,

10191010112691
' let’s, and confcquently not It) pleafant for which
1eafon, the glafs R is 11111 retained, to enlarge
the {Cope or area of the field.

To find. the magnifying power of this tele-
feepe, multiply the focal difiance of the great
mirrour by the difiance of the {mall mirrour
from the image neXt the eye, and multiply the

, focal difiance of the fmall miriour by the focal
difiance of the eye- glafs: then, divide the pro-
dufl of the former multiplication by the pro-
' duct of the latter, and the quotient W111 eXprefs
the magnifying power.

I {hall here fet down the dimenfions of one of
Mr. Sbort’ s refieéling telefcopes, as defcribed 111
Dr. szt/J’ s Optics. .

The focal difiance of the great mirrour 9. 6
inches, its breadth 2. 3 , the focal difiance of the
fmall mirrour 1. 5, its breadth o 6: the breadth
of the hole m the great mirrour 0.5-, the dif‘tance
between the frnalfJ mirrour and the next eye—glafs
I4. 2 , the difiance between the two eye-glaflEs
2 4 , the focal difiance of the eye—glafs next the

(metals 3. 8- ; and the focal dif’tance of the eye-,
glafs next the eye 1.1.

’ One great advantage of the reflecting tele-e
{cope is, that it will admit of an eye}3 orlais of a
much {better focal dil‘tance than a refracting
telefcope will -, and,confequent1y, it will mag-
nify fo much the more: for the rays are not
coloured by reflection from . a concave nurrour,
if it be ground to a true figure, as they are by
palfing through a convex— —glafs, let 1t be ground
ever {0 true.

The adjufiing fcrew on the outfide of the
great tube nts this telefcope to all forts of eyes,
by bringing the {mall mirrour either nearer to
(the eye, or remoying it farther: by which

‘1 ° 1 I ' i ' mans.

235,

‘ 236

Of Optics. ‘

means, the rays are made to diverge a little for
fhort- lighted eyes, or to converge for thofe of a
long fight. '
The nearer an object 18 to the. telefcope, the
more its pencils of rays will diverge before they
fall upon the great mirrour, and therefOre they
will be the longer of meeting in points after re-

. fieétion , To that the firf’t image I K will be

0

formed at a greater difiance from the large mir-
rour, when the object IS near the telefcope, than
when It is very remote. But as this 1mage muft
be formed farther from the {mall mirrour than
its principal focus 12, this mirrour mui’t be always
fet at a greater dif’tance fr om the “large one, in
viewing near obJeélts, than in viewmg remote
ones. And this IS done by turning the icrew on
the outfide of the tube, until the imall mirrour
‘oe fo adjul’ted, that the objeét (or rather its
image) appears perfect.

In looking through any telefcope towards an
objeét, we never fee the object itfelf, but only
that1mage of it which 18 formed next the eye in
the telefcope. For, if a man holds his finger or a
flick between his bare eye and an objeé‘t, it will
hide part (if not the whole) of the object from
his View. But if he ties a flick acrofs the mouth
of a telefcope, before the objeEt- glais, it will hide
no part of the imaginary objeé‘t zshe faw through
the telefc0pe before, unlefs It covers the whole
mouth of the tube : for, all the effect Willbe, to
make the objeé‘t appear dimmer, becaufe it in-
tercepts part of the rays; Whereas, if he puts ,
only a piece of wire acrofs the infide of the tube,
between the eye- -glafs and his eye, it will hide

1 part of the obJeét which he thinks he fees: which

proves that he fees not the real obJeEt, but its
image. This is alfo confirmed by means €16 the

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. PLATE XIX.

 

‘7. 1W deli/2,.

Of Optics. ' - 4 237

fmall .mirrour L, in the refleélzing teledfcope',‘ '
. which is made of opake metal, and fiands di-
rcélly between the eye and the objeétntowards
which the telefcope is turned -, and will hide the
whole objeé‘t from the eye at e, if the two glalfeé
Rand S are taken out of the tube.

The multiplying glafs is made by grindingplatexxx;
down the round fide 6 iii of a convex glafs A B, Fig. 1.
into feveral fiat furfaces,'as‘ J: b, 5ch, d k. An obi The ML
je€t C. will not appear magnified, when "feen tz'plyz'ng
through this glafs, by the eye at H ; but it willglafi-

- appear multiplied into as many difierent objeéts
as the glafs containsplane furfacesz. For, fince
rays will flow from the objeé’t C to all parts of
the glafs, and each plane furface will refraét thefe
rays to the eye, the fame objeét will appear to
the eye, in the. direé’tion of‘the rays which enter
it through each furface. _ Thus; a ray g i H,
falling perpendicularly on the middle furfa-ce,
will go through the giafs to the eye with-out ruf‘
fering any refraEtion; and will therefore {hew ,
the objeét in its true place at C: AWhllfi: a ray a5,
flowing from the fame objefi, and falling ob-
liquely on the plane furface b Is, will he refraéted
in the direction 5 e, by palling through the glafs ;
and upon leaving it,'will go on to the eye in the
direétion e H 3 ‘which will caufe the fame o’bjeé't
C to appear alfo at E, in the direétion ofthe ray J
He, produced in the right line H e 72. ' And the
ray Ed, flowing from the objeét C, and falling
obliquely on the'plane furface a’ k, will be refraét-
ed (by pafiing through the glafs and leaving it
. atf) to theeye at H; which will caufe the fame
objeét to. appear at D, in the direétion Hfm.——
If the g-lal‘sbe turned round the line g Z H, as
an axis, the object C will keep its‘place, became
the ‘furfac‘e 5 Id is not removed; but all the:
' ' other

238.

Pi g. /2.‘
The ta-
were 06-
fiam.

Of Optics.

other objects will feem to go round C, becaufe
the oblique planes, on which the rays a £2, c’d‘
fall, will go round by the turning of the glafs.
The camera oéfczrm is made by a convex glafs
C D, placed in a hole of a windowofhutter.
Then, if the room be darkened fo as no light
can enter but what comes through the glafs, the 1
pictures of all the objects- (as fields, trees, build-
Jngs, men, cattle, 82c.) on the outfide, will be
’flieWn in an inverted order, on a white paper

placed at GHin the focus of the giafs; and

will‘afford a theft beautiful and perfect piece of
perfpeétive or landfcape of whatever is before,
the glafs; efpeciallyif the fun {hines upon the
Objects. .

If’the convex glafs C D be placed in a tube in
the fide of a fquare box, within which is, the
plane mirrourvE F, reclining backwards in an
angle of 45 degrees from the perpendicular It 9,
the pencils of rays flowing from the outward Ob?
jeéts, and pafiing through the convex glafs to
the plane mirrour, will be reflected. upwards
from it,’ and meet in‘ points,- as I and K (at the
fame diflance that they would have met at Hand
G, if the mirrour had not been in the way) and
Will form the aforeiaid images on an oiled paper--
firetched horizontally in the direction I K ; on
which paper, the out-lines of the images may
be eafily drawn with a black/ lead, pencil ; and
then copied on‘a clean Iheet, and coloured by
art, as the” objects themfelves "are byvnnaturel—
In this machine, it is ufual to place a plane glafs,
unpoliflied, in the horizontal fituation I K, which
glafs receives the images of the outward objects ;
and their outlines may be traced upon itby a
black-lead pencil. ‘ '

- N. B.

Of Optics.

N. B. The ttibein which the Convex glafs
CD is fixed, mul’t be made to draw out, or pulh
in, f0 'as to adjul‘t the dif’tance of that; glafs from
the plane ,mirrour, in proportion to the dil’tance
of the outward objeé‘ts», which the Operatordoes,
until he fees their images dilliné‘tly painted on
the horizontal glafs at I K. . ‘

The forming a horizontal image, as IK, of an
upright objeé‘c A B, depends upon the angles of
‘ incidence of the rays upon the plane mirronr

EF, being equal to their angles of refleélion from
'it. For, if a perpendicular be fuppofed‘to be
drawn .to the furface of the‘plane mirrour at a,

where the ray Ari, Ce falls'upon it, that ray will '

be refieé’ted upwards in an equal angle with the
other fide of the perpendicular, in the line ed I.“
.Again, if a perpendicular be drawn to the mir-
rour from the point f, where the ray/i h f falls
upon it, that ray will be refleéte'd in an equal
angle from the other fide of the perpendicular, in
the line fit) I. ‘ And if'a perpendicular bedraWn
from the point g, where the ray flcg falls upon
5 the mirrour, that ray will be refleéted in an equal
angle from the other {ide of the perpendicular,
in the line gz' 1.‘ So‘ that all the rays of the pencil
a 19 c, flowing from the upper extremity of the
objeét A B, and pafiing through the convex glafs
C D, to the plane mirro‘ur’ E F, will be refleéted

from the mirrour, and meet at I, where they will.

form the extremity ,I of-kthe image I K, 'fimilar
to the extremity/1 of the obje€t A B. The
like is to be» underfloodrof the pencil q r 5, flow-
ing from the loWer extremity of the objeél‘fl B,
and meeting at K (after refleé‘tion from the plane
mirrour) the rays form the extremity K. of the
image, fimilar to the extremity B of the ob‘jeét:
and In of all the pencils that flow from the in‘

termediate

éfas

v opera-

240 ‘ i . Of Optics;

termediate points of the object to the mirreur,
through the convex glafs. .
if a convex glafs, of a {hort focal diltance, be
pllaced near the plane mirrour, in the end of a
fhort tube; and a convex glafs be placed in a
hole in the fide’ of the tube, f0 as the image may
be formed between the hit-mentioned convex
glafs, "and the" plane mil-rout; theimagebeing
viewed through this glafs will appear magnified.
-—-In this manner the operaglafi: are confiruét-
ed; With which a gentleman may look at any
lady at a difiance in the campany, and the lady
know nOthing of it. ’ .
The image of any objeél: that is placed before
The com a plane mirrour, appears as big to the eye as the
men [amobjec‘t itfelf; and is erect, dii’tinét, and teeming-
mg 346%, 1y as far behind the mirrour, as the objectis be-
fore it: and that part of the mirrour, which
reflects the image of the object to the eye (the
eye being fuppoled equally dil’tant from the glafs
With the objectlis juft half as long and half as
Fig. 3, broad as the object irfelf. Let .4 B be an ob-'
. jeél placed befOre the reflecting furfa’ce glaz' ofl
the plane mirrourC D ; and let the eye be at o. ‘
‘Let Alb be any of light flowing from the tap
.,A of the object, and falling upon the mirrour at
it: and Z2 M be a perpendicular to the l‘Urface of.
' the mirrour‘at Z2 : the ray .419 will be reflected
from the mirrour to the eye at 0, making an
angle m ,6 0 equal to the ”angle A’ b m :- then will
the top of the image E appear to the eye in the
direction of the reflected ray 0 la produced to E,
where the right line zip E, from the top of the
objeét, cuts the right line a [7 E, at E. Let Bi
be a rayxof light proceeding from the foot of the
object at B to the mirrour at i 5 and m’ a per-
pendicular to the mirrour from the point z',
where

The
slat/h

Offlptz’m 241:
where the ray B i falls upon it :\ this ray will be
reflected in the line i o, - making an angle 72 in,
equal to, the-angle; Bi 7:, with» that perpendi-
cular, and entering the eye-aw : the-n willgthe
foot F of: the-image appear in theadireétion of
the reflected rayojg producedutoF, where-the
right line B F cuts. the reflected ray produced to
P. All the other raysthat flowfromthe interv- a
mediate points of. the object {1 B, and fall upon
the mix-tour. betweenb and i,‘ will: be reflec’tedto
the eye at o -, and all theintermediate points of
the image E F will appear touthe. eye in.the,.-di-'
rec’tion-line of thefe reflected ,rays produ-ced.f
But all the rays, that flow from‘the,objc€l,"and
fall upon the mirrour above it, will be refleéted
back above. the'eye ‘3: a ; and all the rays that
flow from the object, and fall Upon themirrout
below 2', will be reflected back below the'eye at
a : {0 that none of the‘rays that fall above 19,,01'
below .2", can be reflected totheeye at 0-, and
the dlfiance between band i is equal to half the
length, of», the object .4 B. , I ‘ ~

Hence it-appears, that if a man fees his whole A man
image in a-plane alooking-glafs, the part of the w_iu_fee
_ glafs that tefleétsrhis imagemufi be jult half as im "gage
long and half as broad as. himfelf, let him fiand $01aner
at, any difiance from it whatever; and that his glarsghag
image mul’t appear jul’t as far behind the‘glafs as is but _ ..
he is before it. Thus, the man A B viewing hzlfhiéls
. himfelf in the plane mirrour C 'D, which is juft Fig 4:
half as long. as himfelf, fees his whole image as
atEF, behind the glafs, exactly equal to his
own fize. , F or, a ray A C proceeding from his
‘ eye at d, and. falling perpendicularly upon the
furface of the glafs ,at C, is reflected back to his
eye in the fame line C .4; and the eye of his-
image will appear at E, in the fame line pro-
duced

242' ‘

Of Optici.’

(luced to E, beyond the glafs.’ Arid a My B D,
flowing from his fOOt, and falling obliquely or?
the glafs at D, will be reflefted as‘obliquely on
the other fide of the perpendicular a F D,- in the
direétion Dfl; and the f'OOt of his image will ‘
appear at F, in the direétiOn of the refleéted ray
11D, produced to F, where it is cut by the right
line B G F, drawn parallel to the right line/10E. 1
Jul’t the fame as if the glafs Were taken away,
and a real man flood at F, equal 111' fize to the
man {tanding at B: for to his eye at fl, the eye
of the other man at E would be feen 1n the di-
reé’cion of” the line A C E , and the foo: of the
man at F Would be feen’ by the eye 11, in the
dire‘fiion of the line [1 D F.

If the glafs be brOught nearer the than 11 B,-
as {Uppole to c [7, he Dwill fee his image as at
C D G :' for the reflefied ray C /1 (beingo petpen’g
dicular to the glafs) will then: the eye of the
image as at C; and the incident ray B 5, being
fefleeted in the. line b .4, will thew the foot ofhisf
image as at G; the angle of refleétion a 5/1 being
always equal to the angle of incidence B 5 a‘:
and f0 of all the intermediate rays from A to B; .
Hence, if the man 14B advances towards the
glafs C D, his image will approach towards it ,
and if he recedes from the glafs, his image will
alfo recede from it.

Having already fhewn, that the rays of light
are refraéted when they pafs obliquely through
different mediums, we come now to prove that
Tome rays are more refrangible than others; and
that, as they are differently refraéted, they ex:
cite in our minds the ideas of different colours,
This will account for the colours fe‘en abOUt the
edges of the images of thofe objeé’ts which are -
viewed through fome telefcopes.- ,

z, , Let

1‘”

Of 01mm. 243

Let the fun {hine 1ntIo a dark room through a Fig. 5.
{niall 11611: as at e_,e in a w1ndow {hutter5' band
place a trianou at prifrn B0111 the bean‘1‘. of rays
14,111 inch a manner, that the beam 11131316111111-"
liquely 6111 one of the iid‘es abC of the" 111111.
The rays}, W1 11 fufier d1ffe1ent refraétions “by; paf- The
{ing hrouvh the prifm, fo_'_ that infiead 6? 601110 Fri/77h
all out o‘i“ it 0151 the fide dc (if in 61‘16 direétion
they will 6n £16m it" in’ the (lili‘erent d1reé‘t1ohs
reprefente by the lines f, g, ii, z,k,' '1, 772,71, and
fglhncr u'p6n the oppolite (16661r the room, or
on White paper placed as at £612,111. receive thet‘h,
they Will paint up’on it a iienes of 111611 beautiful
:liIvely coTours ( not to 1:56 EQfialled by art) in this The m.
'6r6er, Iinz. th'o‘fe rays which are leafii refraéted by [ours (f
the prlfm, and Will' therefore go on betW'een the”? 113/7"
‘li'nes n and ”'4, Will be‘ 6? a very bright intenfe
red at in, deceneratincr from thence gra‘diially
into an orange colour, as they are nearer the” line
m the né'x't' Will be 6'? a fine orange colour at
m, and from thence degenerate mm a yelloW e6-
Iqur tOWards I: at Z they Will be Of a fine yelloIW,
Which will incline towards a green, more and
mote, as they are nearer and nearer k . at It they
Will be a pure green, but from thence towardg 1'
they Will incline gradually to’ ‘a blue: at 2' they

‘ will be' a 'perfeét blue, inclining to an indigo Ico-l

lour from thence towards la: at 12 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. 1
There 13 not an equal quantity of rays in each
of thefe colours; for, if the oblong image pg
be divided into 360 equal parts, tiie red b‘fpace
R R Will

[244

Fig. 6;

Of Optics.

R will take up 45 of thefe parts ‘3 the orange 0,
27; the yellow 2", 48-; the green “G, 60; the
blue B, 60; the indigo I, 40; and the violet V,
‘80 : all which {paces are as nearly proportioned in
thevfigure as the {mall ifp'ace gp would admit of.

' If all thefe colours be blended together again,

they Will make a pureewhite; as is proved. thus. ,

Take away the paper on-whichthe colOurs p q
fell, and place a large convex lal§1D inithe rays _

r f, g,‘ b,.&c. Whichvwillrrefraél: t ”em f0, as to make

them-unitetand crofs each other atW: [and if (a
white paper. be plaCed .to receive them, they will
excite the idea of a (bong lively white. But if

’ the paper be plated'qfartheir fromrthe glafs, as at

m, the different colours will appear again upon

it, in 'an‘ inverted order, occalionedubys the rays

.crofling atWZi ' .

As white‘is’ a, .«compofition ,OflaanO‘lOLll'S, ['0
black is a privation of them all, and, therefore,

properly no colour.

Let two concentric 'circles-~\be-:6rawit on a
fmooth round board ABCDEFG, and the
Outermofl' of them: divided. into "3:60 (equal parts

' V or degrees: then,udrawxfeven right lines, as G) A,

' QB} 8am, from the center tothebutermol’t Circle ~,

making the lines 0 24 and. Q B include, 80 de-
grees’ of that Circle; the lines‘Q‘B and (DC 40

a degrees; 0 C and. G D 60; Q Dctmd O E 60‘;

.0 E and 0 [7 48;-0 Fahd-3Q G327 3201C? and '0‘ A
i45.'- Then,'betwcen thefe (WOCil’Qlfifi-fpalnt the

’fpa'cer/I'G red,:inclining7to,orange Bear-G; G F
orange, inclining to .yellowaneargf'y FE yellow,"
inclining to green'n‘ear E 3 ED griten,._ inclining

.to blue near-'D;-.;DVC blue,~ inclining toiindigo

near C”; .C B indigo, inclining tovi’olet near B ; ‘

'and BA violet, inclining’to a {loft red near A.
This done, paint all that part of the. bo'art‘zl' black
, V which

. Of Optics. 245
"Which lies 'within the i’nner"~circlei-, and putting All the
‘an axis throttghthecenter of 'ther'board, let it Prifmatic
be turned. very fwiftly mood that: axis, for as the 3:22 :1
rays proceeding :from‘the .abovevcolours, maybe together;
all blended! and mix: together incoming to make a
the eye; and then, the whole-Coloured pari: 'willWhltci
appear like a white ring, a little greyifh; not
perfeétly'white; becaufe no colours prepared by
art are’perfeét." ' r '* “ '. ,
Any of ,thefe'colours, except red and.Violer-,
may be made by mixing tOge'ther the:tw0‘con-
'tiguous prifmatic colours: Thus, yellow is made
by mixing together a-due' prepo'rtion of orange
and green; and green may be made by a mix-
ture of yellow and blue. f » - - ~ ‘ >
‘ "All bodies appear of that Colour; whofe rays
they refle&- mol’c; as a body appears: red ”when
it reflects-melt of the red-making rays, and" ab
forbstherefl. . .. - p '.~’ \ .
’Any turn or more colours that‘are quitetranf- Tranrpa-
parent by themfelves; become topake when .:put {em Cg;
together. Thus; if water or usfpiritsof virinebe 3;: . "
tinged red, and put in'a phiah'eVery objeét feen opake it
‘ through ' i‘twill “appear red, becaufe‘it. lets only put to—
‘ the red rays ipafs 'throughkit, and fiopsall the gather“
'refl. If water or fpirits-be tingedfblu'e, and put .
in a phial, allobjeéts feen through. it will appear
blue, bee’aufe’it tranfniits only .theiblue rays, and
[tops all the.“ re‘fii But if thefe‘ two phials are A
held clofe together, ifo as :borh of them may be
' * betweenthe eye-sand objeét; thenobjeét will no
rfiore be {rich through their: than through a plate
of metals? for Whatever rays ‘ are "tranfmitted
through thekfluiid invthe phial. next the objeét,
are {topped by that ‘in the phial, next the eye.
In this exPeriment, the ‘phia'ls ought not to be
round, but fquarc; becaufe nothing but the
R a light

‘ .
y ‘K ‘ n
24.6 , .. _ .Of OptidsL >
light litfelf can be» {eenghrwéugh a ronndwt’féhfl
. parenthody, at anydifianee. ‘ ‘ A x
As therays of light .fnfl’h: different (TegreES
of ‘refraétion byhf‘qufing ohliq’nelyifthrqujgh'7”a
, prifm, or through 3‘4FIODV¢X;.-g1,af3,_3f}din“? thierehy
. feparated . into all the-ifeyengqr‘iginalkgr'pn‘rnaiy—
goolaursiexfg {theyualfo‘ fgfig; jéiffereng degféés‘ibf
refraftion by paflfing through dng§jnhf‘fgilling
‘ mm, a’ and Inhen,— being igeflewékefijtowards ,‘the eye,
~ from the: rides _ ofxlrthef'é gnaw which“. are ifatighef’c
: from :the ,‘eye,_an~d again-trefggéfqd bngamflg-éfit

ofxtbe'fe: drops inqé Elli-3.; airy. “in. WhiCthéfya‘QEd
~.dir.e&iqns».t.h€y emeéo £59m?seth'éygmake all

the colours to appeé. inv‘tfiegfpgm‘ of; firietaiiéh

in the heavens; which ‘iscalledighejféz’éhfgowg A
There are alwa‘yzsvtwqirgln-gbéws: feen tqge‘ther,
‘ -». the) interim: of :vyihighggijst. iggmeld; by gthejraysl db,
which fall'ing"'hpon the upper paregolvg/pfltherdebp
:Eig. 7. 'zficd; are,- refrafledainnnbeéin? -é,¢;9%315<3¥5€5f€r
" . th e dwfiahd ‘ are; gefleétegi {{qu the; haek nf itgat
‘ c, inehe line ~c d, and themtbyggflingimytvbf‘the
-..,d‘rop,into air, they {are again i'efraéledafi J; and
. ,ifromrhenee they pra{‘s,.on $9 thjeeye ‘at é}; R) that
' .3 to lform‘ the inceziohhowyfihege. § fufl‘ermome-
;(.:f‘raiélions,- as. at. érand'dgyand ,one/refiefli‘op, ,Ias
T he exterior bowis. fqrnied bygrays“ which
-, "fuffen'eltwol rxefleé‘t’iOnsggangLfitwog re’fracéfions ;
6. giwhich is the ioec‘afion ~ of itgbeing let‘s; yivicf Ehan
, zthe interior, and alfo'of:itseofllonrs’gbei‘ng“ invert-
:‘Jze’d; with‘wr‘efpeé’c to thofehof. ,the interior.“ ‘F or,
n f. ’ whenaxay. ab falls -;upon"the lowe; partpffthe
Fig. 8.¢.‘.12d2170p'12‘cdve,i it is fefr-Vaéte‘ci‘r infigthejdireé‘tiqn b e. _
.;',j:)y:.-Jénteringi the“ di‘gpgg; and; Bailing; pp t9”_the
;. '. backadf :the: dropyae :6, it: is ,thenee reg‘ejé’geyckliin ghe
.:.5]inez cigdh Whichdii‘eéfiqhit is imqufihlefor it
«’56 enter the eye at f: but by being 'again re-
“ Megs:

\

Of 72777 T 71777194777771 (31051177.: , 247

fieéTed from the point 71’ of the drop, it goes on in
the drop to 7, Where it pafl‘es out of the “drop mto
the a1rj, and 18 there refraéte'd downward to the
eye, in the d1re€110n cf.

L L C T V111; AND‘ 1X; ”

T be defthpizm and 77f? of, the glows, and 77777777]:
[777757 fp/oere.

IF :1 map of the 1170‘er be accurately. delineated The m.
on afphericaT ball, the furface thereof will “75"”!
re refent the furface of the earth: for the highel’cg [‘05‘
hiTTs are f0 inconfidérable with relpeébto the bulk

of. the earth, that they take off. 1110 more from its
rOundnefs, than grains of land do from the
roundnefs 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 111 per-
pend1cular height-'71- "

That the earthI is {phencal or round l1ke a Proofofjs
‘globe, appears, - F~170m its cafiing a round ESE???
mado‘w Upon the 11noon, whatever fide be turned globular:
towards her when The 13 echpTed. 27. From its
11mg been failed round by feveral p'erfons.

From our feemg the farther, the higher we
Raid 4 From our feeing the mafis of a fh1p,
Whilfi the hull 1s hid by the convex1ty of the
water. . And that-

The attraétwe power of the earth draws all 1t may be -
terrefinal bodt-es towards us center; as:is evi- Peopled
dent from the defcent of bod1es in Tmes per 31251132163
‘penclicolar to the -’earth 3 furface, at the places any one, .
whereon they fall; even when they are thrown being 111
”153‘ from the earth on~Qppof1te Tides, and con- danger 0f
fequently, in oppofte d1re€t1ons. So that the faumg a”
T R

, way from
.ieartn

243;

Up and
down,
what.-

All oh~
jeEls in
the hea-
ven ap-
Pear e-f
qually
35.13%“?!

of tag-HammadManama.
earth may be compared to a great magnet rolled.

V in filing; of fiee‘l, which attraé‘ts— and keeps them

equally fall to‘its 'furface on all fides. ‘Hence,
as all terrefirial bodiesare attraéted toward the

earth’s center, they can be'in nodangerroffall-

ing ‘frorn‘any fi'de'ofs the earth, more than from
any Other. 5 , . a . ,V

' The heaven or- Iky furrounds the whole earth:
and‘when we {peak of up, or down, we mean
only 'With regard toourfelves; for no point,
either in the heaven, or on the furface of the
earth, is above or below, but only'with' refpeél:
to ourfelves. ‘ And let us be (man what part of
the earth we will, we {land with our feet ‘10?

' wards its ‘center, and our headstoward the iky;

and to we» fay, it lie-up toward the iky, and dngz
toward the Center? of the earth. '

To an obfer-ver‘ placed anywhere in the in,
definite fpace,'wwhere there is nothing to limit
his ~v’iew, I all- remote objeéts appear equally
difiant from himgifvahdffeem to be placed in a
van concave'fphere, of which his eye is the
center; Every- al’tronomer ~c’an demonl’trate,
that the moon is much nearer tousthan the fun
is; that {time of the planetsaare- fometi‘mes
nearer tom, and , fometimes farther from use,
t—‘hanthe {tin-g that Others, of them never come {0

‘ near uses the: fun-always is; that the remotefi
“planet in our! fyflem, is beyond ,comparifon

The face
of the ‘

nearer'to ,u's thaniany of thefixed flars are; and
that it. is highlyi‘probable fome flats are, in a
manner, 'infinit’ely'more dxfiant from us than '

others; - And yet'a'll thefe’celel’tialobjeé‘ts ap-

pear-eqUal'lydifiant from us. Therefore, if we
imagine a large hollow fphere of? 'glafs to have

heaven" as many. bright finds fixed to its infide, as

andeunh the“: 3.“?5 {jars Y'ifiblfi ’m the heaven, and thefe

find:

affix-Heaven; (2224112; Earth. 249

finds to be~ofdifiierent magnitudes, and placed reprefent.
at the fame anghlar dii’tancesf‘from each otheted in}
as the! flats: are; . the fpherewill be a true ire-maChme'.
prefentation of the {tarry heaven, to an eye {up-
pofed to be-in its center,» and viewing “it all
around. And if a fmall globe, with a map of.
the earth upon‘it, be placed on an axis in the,
center of-this {tarry fphere, and the f here be
made to turn round on this axis, it wi l repre-
fent the apparent: motion of the heavens round
“the. earth. ,' . i a 7 _
. 'If a great, circle be {'0 drawn upon this’fphere,
’as to divide, it into two equal parts, or hemi»~
fpheres, and the-plane of the circle be perpen:
dicul‘ar to'theaxisof the fphere, this circleiwill
reprefent the equinafiz’al, which divides the; yhea- The equi.
ven into two equal parts, called the nartbernandmélial.
the foulbmz bemz'flJber-es; and every point ofthat
circle willbe equally difiant from the poles“, .orThe 2,1”.
ends of the axis 1n the fphere. - That pole which
is in the middle of the .northern hemifphere,
will be called the ”only pole of the fpbere, and
that which is in the middle of the fouthern hemi—
fphere, the four/a pole. . * , . . '

If another-great circle be drawn upon the
fphere, in fuch a manner as to 'cut the equinoc-
rial at an angle of 2 3; degrees ’in two oppofite
points, itiwill ,reprefent the ecliptic, or. circle of'rhe “1,3,.
the fun’sapparent annual motion :. one half oftz‘c.
which is on the north» fide of the equinoétial;
and the other half on the fouth. ., , ' .

If a large fiud be made to move eaf’tward in
this ecliptic, in; fuch. a manner as to go quite
' round it, inthe time that the fpherc , is turned
round wel’twatd 366.. times.,upon»its' axisgfihie
find will; reprefent the fuzz, changing his place The/m;
every day a 365th pair: of the ecliptic-Land

' , 4

going

230‘ r ' Of tbé Heavens am? ihé Earth

gomg round wei’tward the fame Way as the
flats do‘,‘ but WIII) a motion f6 mueh flower than '
the morion 6f the 1321‘s,; that theX Will make 366‘
revolutions about the axis of the fphere, in the-
time that the fun‘ wakes onlv 365.’ Dutit'ig1 one
half of theft: revolutions” the fun" WiII be oh the‘
myth fide of the equmoéba duhnar the other '
haif, on the fouth and at the end 6f eac‘h haif, '
in the etiumoeti 1i

Themrtb If we fupptiIe the terrefirial gldbe 3in this mao_
chine to be about one inch 111 diameter; and the‘
diameter of the {Iariy fphere to be :11b6ut five
or fix feet, a {his II infeé‘t on the globe WOu‘l‘d fee-

only a 'very little portion of its zDIutfa‘ce4-, but it
would fee one half of the I’tarty lphete the coh-f

vex1ty of the £316? 1e hiding the other haIf from its

The ap- VI€W. "If the Iohe‘te be turned weflward r0und
Pa‘ent fthe globe, and the infuft could judge 6f the af-
3:120 ¥eafahces which arife from that mOtion; it WOu d
ee mee flats I‘lfi'ig to its vieW in the hafieth

fide‘ of the fphef'e, Whiiit others Were fetting on
the Wei’tern: but as all the flats are fixed to the
fphere,‘ the fame {tats WoulCi aIWays rife in the
fame points of VICW on the eai’t fitie, atid fet in
the fath‘e points of VieW Oh the Wéfi fide. With
the ”fun it hiViOliilyd 6e otherw1fe, becaufe the fun
i§ not fixed to. any point of the f here, but
moves [16wa along an oblique Circle in it. And
if the infeé‘t flic’iui‘d look toWards the fouth, and
Cali that point (if the globe, Where the equi-
noé‘tial 1n the I here feems to Cut it 66 the left
fde, the 325/13 pom;- , and Where it Cut—‘3 the globe
iori th6 richt fide, .the wtfl point; the lItII‘e’b ani-
mal Would fee the fun rife north of the ehf’t, and
fet north of the 'Wefi', {61' 185—3— reif6lutions,

’ after whieh, for as many mOre’, the fun woold
fife :foUth 6f the eafi and Iet fouth of til’te

we

V6115.

oftanHeaWr-mtartar»; 25,:
weft;- .A'nd‘ tar the whale '36‘5; rerlt'itio'ns, the
tan: Would mean-1y Vt-‘v’siicefiri’ the? e‘a‘i’tf point, and?
fé’tptwice lathe-welt} A“11"4‘_th'e‘fe appearances: ’
wolild‘ be: the fame, if thel'fia‘rrf fpherevfiood:
fifill (the fuu'oh‘lyim‘ovingi iriwthe—ieelipt’ic) and};
the earthly globe were turned round the axis; in
the "fph‘éré eal’tWaird'. F or,“aS"the infeét would:
be? iearfree!" "roj‘ulrid’i‘ With the globe, ‘he’ would. be}
qtiite'inknfi‘ble iof- its traction ;7 and the fun and?
liars would appear to move wel’tward. ‘

‘ - We are but very fn‘ia'll' beings-when Compared
With -‘oureearthly-globe, arid-the gloée ill/24f is but
a dikmenfionlefs point compared With‘the mag-
fiitu’de of ' the Afiarr‘y heav’éfis‘. Whether the.
earth be at rei’t,«5and the heaven turns round it;
or the h-eaVen be at remand th’e'earth turns
round, the appearance to us will, be exactly the
fame. And becaufe the heaven- ié ‘fo imm’enfely
large, in copmparifon“ of ”the: 'e'ar‘th,<W‘e fee one
half of the heaven as Well from , thelea’rth’s furs
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 defc‘ribed Circlesf
a Upor’l the earth» as we pleafe; and we maybe/1’77”"?

imagine the plane of any circle defcribed upon ,
the earth to be continued, until it marks a circle
in‘ the concave fphere of the‘heavens. . 1

' The horizon is either flmflble or rational. The The gm.“
feigfléle horizon is that circle, which a man {land-2m.

irrg up‘Onf a large plane, obferves to- terminate
his view‘all ’ar‘ou‘nd, where the heaven and earth
feem'to-r‘n’eeté.L The ’plane of our fenfible horie- . ,
z'on contihiied’ropthe heaven, divides it into (two
'hemifphereslgiene vifi-ble to us, the other hid by
the cdnve‘xity ’of‘the'earth. - a
r, ~ The

252 1 Of‘ 'tli‘e"‘HeatJ‘en:;aud :tbe‘Eartlz-g

“ The plane of the rational borizonyis {uppofed ,
parallel tOthe““:plane of the fenfible;~=to pafs
through-the center of the earth, and to be
continued to the-heavens. And although, the
planeof ‘ the fenfible ,4 horizon touchesi the :earth
in the place of. the'obferver; yet tbirplane,
and. that of the 'ratiOnaliihorizon, will, fcem to
coincide inrthe heaven, became the whole earth
isbut a point Compared to the fphete of the;
heaven. . ‘ . ,-

The earth being ,a fphericalrbody," the hori-
zon, or limit of our‘view, mull: change as we

I

v

change our place; , A r a . .
Falls. The pole; «of the earth, are thofe two points on
‘ its farface in which its axis gterniinates.. The
one is ,. called [thermrtb pole, and‘the other the

foutbpole. w ' r ~.~ .. ,
The pole: of tlae heaven, are: more two points
in which the earth’s axis produced terminates in

the heaven : f0 that the north palevof thehe‘aven

is directly over the north pole of theearth; and
the foutb pole of the heaVen is direétly over the

fouth pole of the-earth. ; ; 1 ,v; _ ,

39mm The equator :is a great. circle upon-the earth,
every part of which is equallyd‘iflant from
either of the poles. 'It divides "the earth into
two‘equal parts, Called the northern and foutbern
.bemz'fpberes. If wefuppofe the plane of this
eircle to be extended tothe‘ heaven, it will
mark the eguitzazfi‘ial' therein, .ah‘dwill divide the
heaven into two eqnal'parts,“ called.‘the.zzartbem t

and feat/9m: hemifphcreevof the lzieave‘n. r ,
Merifiam The meridian of ahy place is, a. great circle
.pafiing through that place and the p’qlesxof the
earth, -.We may'imagine as; many .fuch meri-
dians as, we pleafe-y becaufe any Place that is _‘
. l V. , _,Hi‘ CVCY

Of tbéf’Hea'UEns. and we Earth. ',

lever fo little to the leaf]: or weft of any Other
place, has a differentmericiianhfrom that place 5
for ’no onecircle canpafs” through any 'tWO fuch
places and—the poles of the earth,- - , »
, The meridian of any place divided by the
oles, into two femici‘rcleS'txirthat which paITes
through“ the place is called the geographical, or
upper meridian; and thatwhich pafl‘es‘. through
the oppofite place, is called the lower meridian;
When the rotation of the earth brings; the
plane of ' the geographital meridian to the fun,
it is man or :mz'deday to, that, place; and when
[our lower meridian comes to thefun, it is mid-
mlglvt. 7 ~ ‘ - 4 ~ . .1 ~ ,
. 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 {aid to have the fame'longz’tude, becaufe
no one of them lieseithet eafivVard or wei’tward
from any of the rei’c. '

253

Now: and
mid‘ 711kb,-

lf we imagine 2¢xfemicirc1es, one of a which Hour err.
is the geographical meridian-of a given placed“-

to meet at "the poles, and to divide the equator
into 24.,»equaljparts; each of theft: meridians
will comero'undto the fun in 24 hours, by the
earth’s equable motion round its axis in that
time. And, as-the equator-g contains 360 de-
grees, there. will bet}; degrees contained be—
tween anye-tw'o of thefe; meridians which are
neareft‘to .oneeanother: for24'times r 5 is 360.
And-astheflearth’s motion is eafiward, the fun’s
apparent motion will be wefiward, at the rate
of I5 degreeseach-hour. Therefore,

Theyl ,whofe 'eographical meridian is 15
degrees cafiward rom us, have noon, and every.
., other hour, an hour foonerthan we have. They
whore meridian "is fifteen degrees wef’tward from

' us,

Larzgz'iua’e.

agar , 0f 1&6:me «Wkfiiét’és

us; have noon; andfiVSW other hquruaihhghlfl
later-thaniwe have: and, {none in. PEQRdlngllfl
reckoning onehour for ever fifteen degrees,

As the earth tutns, roup~ ., its. axis ghee in' 24.

hOlflFSif and fllfigws" itfelf all round tothefgniin‘
thattim'm; {9 it. gcefiz roundthe fun onlcélga yeag

’Eclzpic, in) ajgreatmc;itcle cal-(ledtheyflzptjc, whichiq‘toffesg
the-squidaflial‘ in two .QPPQfi-te ‘pdinfsg; hiking

an angle-Of 4.2.31; clearsswith the cquinéfiia’l‘jon.

t. . . ‘eachfidet Sothathohehhal‘fiof .thejeclliBtid is'ir‘i
.4 - ‘ the northern hemifpherezgantl ' the othetginfthe
fonthetn.. it contains. 360; equal" ‘af'rtsgl‘c‘all’ed "
degreesjasall other circles“ tip, 'w/ ether great”;

[or fmall) and as the earth goes onceround’it
everyfyearl the fun will.._ap,p,ear to clothe fame;
changing h’i‘sjplaee almoflgiadegree, ta'tla meat}

‘ rate, every 24. hours. so that whatevei’ffilaCei
or degree ofrthe ecliptic, the earth is” in a‘t'any
time, the fun will then appear in the‘oppofite.
And as one half of the ecliptic is' On the north
fide‘of‘therequinoflialiand theother‘half on. the
foutheytihefuvn, asfeen‘fr‘om. theearth; will be .
half a,yearfbn the/fonthficle offthelequinoé‘tial,
and, half . a year on the north}: and twice a year
in-the‘ equinoétial itfclf, ', .' “ i M ‘

3,-gmafid The ecliptic is di—videdfjby‘ afiron’oiners into
degrees. 12 eqi-Jal~ parts, calledgflgngeach fign into 39
degrees, and! each degree: into :60- ’mizzutgsfhibut
in ufingdthe globes, wefeldoniwan’t the Inn’s
place nearer than halftaclegre‘e. of the truth. ,
. \The {names and characters pf'the 1,2.li’gns are '
as follow.) beginning atthat point of thé‘;eclip-
tic where it crolTes the~ gevqguginoftial to the north-
ward, ~and reckoning eafiward round ¢_3:.,'o,the
fame point again. And the :Clays'of‘the‘ months
on which the fun nowenters thefignsgare'fet
down below them. i . f ' .i ' ‘
' ' ‘ 'IIr‘z'as, -

aft-beaymmmndMagma: ' «555

” "'klries, Taurus, ' Gemini; . Gamer, 9‘
{March ‘Ap‘ril , may I-V‘ii‘Junc
.» :=--. 20 A ”‘20 ' ?_ 12]} . 22]} 1‘

’L’eo,~ . Vikgo, ”3’ ‘Lz‘ém, '. W IScérpio,‘
ju'ly" Anguf’t September OEtobet,
’3 Edgitmrz'm, VCaprz'Lco’rnfi Aquarius, i Pifies,‘
. ., ’,‘ ’ . :'- j g M... . x

7 No'vember 'Déé‘etmber January 9. February
' g 22 '§1 10"” 18W
”” " By" remembering: err What day: the; fun; enters
,any particular Efign, ‘we may ueafily findxhis
place ' any: day"firaf'terwardyfitwhilvf’c' he is» in that: r;
fffign,-by ‘_reck0ning-‘-‘a degree‘ffor each day .;
"Which”wilf o‘ékiafiejri-fifi error- ovaOnfequence in
"1 “fing the globes.~-7"~' . - m " ' ' _,
‘ 'A When the. funiSrat the beginning of Aries;
"he is‘ih the .equi'nbétial; ‘and from‘that “time he
“declines 'n‘OrthWard "every day; untiiwhe comes
mm the beginning‘Of-‘JC‘omcer,“Whi'eh}istszzgé dc-
' ”gree‘sfrom' the equ’inoélial:~'fmmfthente he re'a
"cedes‘ fouthward everyday, for halffra year-3' in
the middle of-Whiéh4-h-alf,-vheficroffesjthe equi-
‘noc'tial‘ at the’be‘ginning‘ of Libra“, and rat] the .
end l'of that half‘year, hefts atghié greatefi fouth
. %' \deflin‘ation, inithe beginning ovaaprico‘rn, which
‘ i’selfong; d‘egree3'frb'm the equihoétial; Then,
he'te’turnls northward from Capriw‘m every day,
‘. for'half a year; in the middle of'which éha1.f,rhe:

"C'téiTe/s the equi’n‘é‘é‘tial at the'be’g.'inining 6f Aries;
,_ _ and at the end-of it he-h‘rrivesitatrfiancer; ,
"‘ ' ’ T he

255

Tropic»

Polar dr-
(/0.

- Of the“ Hcawm’ arid; tiaeiEartih.
The fun’s meti-on» in the‘recliptict‘i‘s not perch-
fe‘é‘tly equable‘, «for.- he 'pcontinuesfeight days
longer in the nor-them; half of the ecliptic, than
in the fouthernt' fobt-‘hatfthefommer half “year,
in' the northern- hemifphere, is eight-days longer
than the winter half year; and lithe «contrary in
the fouther‘n hemi’fphe‘reafiiv” ' '3‘ -' T - '
The tropics are lefl'er circles in'the' heat/en,
parallel’to the equinoétial; one on each tide of
it,‘touching the ecliptic in thepoints of its
pgre’ateil: de-eli'n‘ationy'fo that each ’-‘tropic is,
23;. degrees from's-the equinoc’tial, ope-Lon- the
north-Y. fide of it, and the other; on -thc"ll)uth.
The northern tropic touches 'theeclip’tic‘ at: the
beginning of Cancer, the foutherfi ‘afithe begin-
ning of Capricorn ; for which’re‘afon-«th’e former
is, called the tropic of Cancer, and the latter the
tropic of Capricorm-“ij ' i ‘ ti-"f‘e‘ ~
v The polar circ/er'in the? heaven,i~are» each
2 3.; degrees from the poles, all‘arou‘n'dl‘ That
which goes round the north pole, is‘ca‘lled the
arfiz’c circle, from o’a’gx7@e, which fignifies‘ a ‘bcar;
there being a col‘leétiOn orz'groupe of flats near
the north pole, which" gees byth’at name. The
fouth polar circle, is called, the‘antartfi‘ic circle,
from its being oppoiite tO'thelarft‘ic.‘ ‘ -
The ecliptic, tropics, and polariclircles, are
drawn upon. the terrei’trial globe, 1 as well as
upOn the ce-le'l‘t'ral, -, Bot the ecliptic, being a
great fixed circle‘in the heavens, cannot pro-
perly be {aid to belong to the terref’ttial globe;
and‘is laidtdown open it only for the conveniency
of {olving 'fome problems. _ ‘Sotha‘t, if this
circle on the terreltrial globe was properly din
vided into the months and days of the year, it i
would not only fuit the globe better, but would
alfo make the problems thereon much eafier‘, l
. « fl

‘ _ Ofdae Hammad the-Earth.

In orderto form a true idea of the earth’s
,motion round; its axis every 24 hours, Which'is
the caufe.’of day and night; andof. its metion
,~ in the ecliptieround the fun every year, which
is the caufe of . the different lengths of days and
nights, and of the vicillitude offeafons; take
the following method, Which will be both eafy
‘ and pleafant,‘ '

157

Let a {mall terrei’trial globe, of about three An idea
inches diameter, be fufpen’ded by a long, thread 0‘ the

\ of twilled filk, fixt to its north pole: then hav—
ing placed a lighted candle on a table, to repre-
fent the-fun, in the eenterof a hoop of a large
calk, which may reprefent the ecliptic, the hOOp
making an angle of '23;- degrees with the plane
of the table .3 hangfthe globewithin the hoop
near-.to-it; andif the table be level, the cotta-
, tor of the globe will be parallel to the table,

and the plane of‘ the h00p will cuc the equator .

at an angleof 23.3,. degrees; {0 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-wof the-globe, as the fun
enlightcns,:oneflhalf’ ,of-the‘earth, whilft the
“other half-,istin, the dark. . . .

Things being. thus prepared, will the thread,
towards the; left hand, that it.may turn the
globe thefame way by. untwil‘ting; that is, from
well, by fouth, tos’eal’t; Age. the globe turns
round,itssaxis-er«thread, the different places of
(its furfac’ettwill goregulatly through the light
andaldark»;rand have,.as it'were, an alternate
return ofada'y and night in each rotation. As
' the iglorbeeontinues to turn round, and to lhew
.itfelt’ all around to the candle, carry it {lowly
round the hoop by the thread, from well, by:
ibuth, to call; whichiis the way that the earth

. ’ moves

feafons.

~32 58 x / 3:012zéeltfkmm«Msétefidttfio
gmoves »rpqu_.g¢tihe .3 {9311,} 995:6. gym; Jill: the

~r:e.Cl.iP?iC =.:;an,d»1yéfi' will,-f6¢»thétzwhilfi-fi, 6 $1qu
semi-mics intherlovyer part-pith: hqoprthe Eggin
«€1.16. (’bsiipg. then-awzthfif :thcgtguat9tilhfllfi9fi‘

. 33 {tantlygjhjne round3 Ihe(.:q,0}‘th; pole 5:; and'gall the
»_.notthetn-3_pliaces which go, thgomxlgh , 39y part 991'.

~ thedzarkmwillgo thwugbakf’syortiqn p‘firthan
they do of the light; anfld'tlie‘ more'fogwmheQ gr—

:1 thcr they.:.at¢. 39m the #619549“ ;;§dififéqfi4€hilya
- 239?“; days glare, them-longer:than-fiber21112431168-
When ‘ the -globe tomes to anoint .5 in the 19%,
.‘mideayg-bctwecn thehighsfhanfi lowdhpdints,

l the» gaggle yvill (be, direélly Wetthe}: iiam‘r,,mid
will enlightmtbqglobcJuli-#9111120 cm Pblés
and thenT everytplace. on, \tlg'enég‘lohe‘; Williéo
throggh £99.31: pettionwféiéght; afldndarknbi,
was-it runsrwndlitsfaxis s;- ahdwtaftquentlh the
gelay and night-will be, of,,.,equ'glf,3.,length_vat.€111
.plhcgs uponlt. -. Asthe globe: adyapcesthegge-
3.,forWard, towards thetrhighefiipart offthe‘ hoop,
the gentilelwigllfbe onthe foht'hggfifie. of the'equa-

. ltornlhinuigg; farther and figtherlroondgthe {ohm
p9le, as the globegrifes, highegaqd hIgherm the

. 11009 ; leaving» thehorth polegfa§.much intlark-
nefs, as the {oath pole;is then in the light, iapd

f making long days.gndi.3f3hotjtgggightsgpill/the fébth
fidg of; the . equator; and ,_ ghe'3‘9on3t‘tary, on._,¢he.
’north‘ fide, whilf’c jthei’galpbeizcggtinges .i,h3.;gthe

1 northerhorthighet fide of the hoop} and .LWhien

- it comesto the shighefli pointntheday; will. beat ,

_. the longefiflndflthe‘n‘ightg qtltheyflxortefl, in the

3 . fouthern. hemifphere; and, the_,reverfe ,in the
. northern. Asthe globe advances; and defeends

, in the hoop, ‘the light will graduallyreeede from

.. the fouth pole, and approaph towards thefnorth
pole, which will craufe the .northen'i’day's' :to

. lengthen, and the. fouthem days to {horten in
l l t C

Of the Heaven: and the "Earth.

the fame proportion. When‘ the globe comes to
the middle point, between the highefi: and lowef’t
points of the hoop, the‘candle will be over the
equator, enlightening the globe jul’t from-pole
to pole, when every place of the earth (except
the poles) will go through equal portions of
light and darknefs; 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 demonfizrative view of
the caufe‘of days and nights, with their gradual
increafe and decreafe in length, through the
Whole year together, with the vicifiitudes of

fpring, fummer, antumn, and winter, in each-

annual courfe 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 highel’t point of the
hoop, and reckoning eal’tward (or contrary to

the apparent motion of the fun) you will fee \

how the fun appears to change his plane every
day in the ecliptic, as the globe advances eal’c-
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 mull appear in a high

fign, as at Cancer, oppofite to theearth’s real‘

place : and that whill’t the earth is in the
fouthern half of the ecliptic, the fun appears in
the northern "half, and vice verfa : that" the far‘
ther any place is from the equator, between it
and the polar circle, the greater is the difi‘erence
between the longelt and fliortef’c day at that
place; and that the poles have but one day and
one night in the whole year. “

~ Thefe things premifed’, we {hall proceed to
the defcription and ufe of the terrel‘crial globe,
' . and

259

\

' 2/60, The; Terrqlifial Gloée a’efcrifiecii

and explain the geographical. terms as they. deem" \
in the Problems. -
The far. This globe, has the boundaries of land and-
r61/275621 " water laid down Upon it, the countries and
€313};ch- kingdoms divided by dots, and coloured to
i L ' dif’tingui-tfh them, the iflarids properly fituated',
the rivers and principal towns inferred, as they
have been afcertained Upon the earth by meaé
furement and obfervation. . ‘ .

The equator, ecliptic,'tropics, polar circles,
. and meridians, are laid down upon the globe in
the manner already defcribed. The ecliptic.“ is
divided into. 12. figns, and each fign into 30
degrees, which are generally fubdivided into-
halves, and into quarters if theglobe is large.
Each tropic is 23% degrees from the’equator,
‘and each polar circle 23%: degrees from its
refpeé‘tive pole. Circles are drawn parallel to
the equator, at every 'ten degrees dif’cance from»
it on ._each'..fide to the poles: thefe circlest'a're
called fimllels of latitude. On Iange globes
there are circles drawn-l perpendicularly through
every tenth degree of the equator, interfecting
each other at the pOIes: but on globes of or,
under ,a £001: diameter, they are only drawn.
through every fifteenth degree of the equator -,
thefe circles are generally called "meridians, Tome-
times cycles of longitude, and at other times bour-
circlw, \ ' ' '

. The globe is. hung in a brafs: ring, called the‘ 4
bra/m meridim;,. and turns Upon a wire in each
pole funk half its thicknefs into one fide of the
meridian ring; by which means, than" fide of»
the ring divides the globe into two equal parts,»
called the??~léczflém and eve/fem bemifp/aeres; as the
eqtiator'divides it into two equal parts, called the
moniker” and four/gem bemifpberes. This ring "is
8- \ divided}

The Ternfirml GloZe deftfiéel
dmded into 360 equal parts or degrees, on the

flde wherein the axis of the globe turns. One 1

half of thefe degrees are numbered, and reck-

’oned, from the equator to the poles,- where _

they end at 90: their me Is to {hew 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 thew how to elevate either the north or
fouth pole above the horizOn, accOrding to the
latitude of any given place, as it is north or
fouth of the equator.

The brafen meridian is let 1nto two notches
made in a broad flat ring, called the woodeié
horizon, the upper furface of which divides the
globe 1nto two equal parts, called the upper and
iawe‘r’ bemiflbberes. One natch is in the north
point of the horizon, and the other 111 the fouth.
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 gradtiated tide of the
brafs meridian lies towards the eaf’t fide of the
horizon, and {hould be generally kept toward
the perfon who works problems by the globes.

There IS a {mall bomry circle, f0 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 brafen meridian ;
which is the contrivance of the late ingenious Mr.
7ofepla Harris, matter of the aiTay- -oi‘hce in the
Tower of London; and makes it very conve-

S a nient

26f

262

The Terra/trial Globe- defcrz'ééd.

nient for putting thepole's of the globe through;
the horizon, and for elevating the pole to fmall
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-r
dram‘ of altitude, which is'dividecl into 90 equal
parts or degrees, anfwering exaftlyto fo any
degrees of the equator. It is oecafionally fixed
to the uppermol’t point of the brafen meridian
by a nut and fcrew. The divifions end at the
nut, and the quadrant is turned round upon it. ‘

'Asthe globe hasbeen feen by molt people,
and upon the figure of which, in a plate, neig-
ther the circles nortcountries can be prOperly
exprelTed, we judge it would fignify very little
to refer to a figure of it; and {hall therefore
only give fome directions how to choofe a globe,
and then defcribe its ufe.

Direélions I. Seeflthat the papers be well and neatly
for choof- pafied on theglobes, which you may know, if

ing of
globes.

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 fh’orf, 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. a _ a >

3. See that the ling“? hang evenly between
the brafen meridia“>3’nd the wooden horizon;
not inclining either? to one fide Or to. the
Other. 3 7 i

4. See that the globe be as clofe to the hori-
zon and meridian as it conveniently may 3 other-

 

yyife, you will be too much puzzled to'find

againfl:

'Dz'refiz'amfir tbaq/z'ng Globes: 263
ainfl: whatpart of the globe any degree of the ‘ "

ac
niperidian or horizon ice _

5. See that the equinoétial line beeven with
- the horizon all around, when the north or fouthr'
pole is elevated 90 degre’es‘above the horizon.

6. See that the equinoftial line cuts the hori-
zon in the eaf’c and Welt points, in all elevations
of the pole from o to 90 degrees. ‘ ‘

7 See that the degree of the \brafen meridian
marfied with o, be exactly over the equinoftial
line of the globe. ‘ ‘ ,

8. See that there be exactly half of the brafen
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 90 in the.
Tomb point. , ' \

. 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 ofvthe qua—
drant reaches juit to, the plane furface of the
horizon. ,

10. See that whill’t the index'of the hour—
circle (by the motion of the globe) paffes from
one hour to another, 15 degrees of the equator
p'afs under the graduated edge of the brafen
meridian, A i '

II. See that the wooden horizon be made
fubi’tantial and firong: it being generally ob-
ferved, that in mof’t gloggs, the horizon is the
{Mt part that fails, on. count of its having
been made too flight. “i , i

In ufing the globes, keep the eaft fide of the Directions
horizon towards you (unlefs your problem re- for “fin:
quires the turning of it) which fide you may men“
know by the word Eui’c upon the horizon; for
/ . S 3 ' then

 

12.64r

The ‘Ufl: 01‘ the T enreflrz'nl Globe,
then you have tie graduated fide of the meri-
dian towards you, the quadrant of altitude before

hyou, and the globe 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 i
that you may look on the weft fide thereof:
which turning will be apt to jog the ball fo, as

to fliift away that degree of the globe which

was before fet to the horizon or meridian:

to avoid which inconvenience, you may thrufl:
in the feather- end of a quill between the ball of
the globe and the brafen meridian; which, with-

I . out hurting the ball, will keep it from tUming.

in the meridian, whili’t you turn the weft fide of-
the horizon towards you. '

PROBLE'M I

To find the * latitude and 1- longitude of any gzzzm
place upon (/93 gloée.

Turn the globe on its axis, until the given
place cumes exactly under that graduated fide of

i the brafen meridian, on which the degrees are

numbered '

* The latitude of a place 15 its diflance from the equator,
and IS north or foutli, as the place 1s north or {outh of the '
equator. Thofe who live at the Equator have no latitude,
becaufe it is there that the latitude begins. '

' 'f The longitude of a place is the number of degrees
(reckoned upon the equator) that the meridian of the {aid
place 15 difiant from the meridian of any other place
from which we reckOn, either eafiward or wei’tward, for 180
degrees, or half round the globe. The Englifh reckOn the '
longitude from the merid1an of London, and the French

. now reckon 1t from the meridian of Paris. The meridian
of that place, from which the longitude 1s reckoned, is;

called

9°52 life 22/” the Terreflrz'al Glob;
numbered from the equator, and obferve what
degree of the méridian 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 polition, the
degree of the equator, which is under the
brafen meridian, is the longitude of the place
(from the meridian of London on the Engl2%
globes) Which is eafi or well, as the place lies
on the call; or wef’t fide of the firfl; meridian of
the globe.—'-—Ali the flikmtic 022422, and 122222222222,
' is on the welt fide of the meridian of London;
and the greatefl: ’part of Europe, and of 12119222,
‘ together with all flfla, is on the eaf’t fide‘ of the
meridian of London, which is reckoned the firfl
~ meridian of the globe by the Englg'fla geographe1s
and aftronomers.

PROBLEM IL

The longitude 2222223 l222‘22‘22de of 22 place 52mg gwm, 2‘0 i

find M2222 place 022 2/22 globe

Look for the given longitude in the equator
(counting it eal’tward or wel’tward from the firlt
meridian, as it is mentioned to be ealt or weft ,)
and bring the point of longitude 1n 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 fomh, and under that degree of lati-
tude on the meridian, you Will have the place
required.

called the firfl 2222222122122. The places upon this meridian

have no longitude, becaufe it 18 there that the longitude

begins.
, S 2t“ P R 0 B3

2‘65

266

D

‘1’ he 'Ufe of the Teflefiriel Glohe.‘

PROBL-EMIII. .
To find the deference of longitude, or' dzhfl’renee of

latitude, hetween any two given places:

\ Bring each of thefe places to the brafen "me—I,
ridian, and fee what its latitude is: the lelier
latitude fubtrafted from the greater, if both

. places are on the fame lide 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 thefe'places, reckoned on the equator,
when they are brought feparately under the
brafen meridian, is their difference'of longitude ;
if it be lefs than 180: but if more, let it be fubi
traéted 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, pal’r over by the index, will
give the longitude in time; which may be eafily
reduced to degrees, by allowing 1'5 degrees for
every liour, and one degree for every four mi:
nutes. A .

’ N. B. When we fpeak of bringing any place
to the brafen meridian, it is the graduated fide of

!

the meridian that‘is meant.

PROB:

The Ufa of the Terrylrz'al Globe.‘

P R‘O'B L E M IV.

.179» place hing given, to find all Ibo/2’ place: that
[maze tbe fame longitude or latitude wit/a it.

Bring the given place to the brafen meridian,"
then all thofe places which lie under that fide of
the meridian, from pole to pole, have the fame
longitude with the given place. Turn the globe
round its axis, and allrthofe places which pafs
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 firi’t meridian, it is evident, that the point of
the equator which is cut by the firi’t meridian, has
neither latitude nor longitude—The greatefl:
latitude is 90 degrees, beCaufe no place is more
than 90 degrees from the equator. And the
greatefl: longitude is 180 degrees, becaufe no
place is more than 180 degrees from the firi’c

meridian7 3

PROBLEM V.

To find the * antoeci, + perioeci, and j: antipodes,‘
of any given place.

i _ 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

‘5 The tmtmz‘ 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 alfo 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,

.257 '

268‘

The Ufl’ of the Term/Erin! Glofie.

degrees of latitude from the equator towards the'
contrary pole, and where the reckoning ends,
you have the am‘am' of the given place upon the
globe. Thofe who‘live at the equator have no
antarcz'. ~ ‘ .
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 perimz' required. Thofe
who live at the poles have no perimcz'. ’

As the globe now {lands (with the index'at
the lower XII) the am‘z'podes of the given place
will be under the fame point of- the brafen me-
ridian where its antwci flood before. Every
place upon the globe has its antipodes. j

tor, they have different or Oppofite feafons 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 diEerent poles.

. 1- The perimrz‘ are thofe people who live on the fame pa-
rallel of latitude, but on oppofite meridians : f0 that though
their latitude be the fame, their longitude differs 18o‘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 fame feafons. ’ But being on'oppo-~
lite meridians, when it is noon to the one, it is mid-night

to the other.

I The amijiode: are thofe who live diametrically oppo-
fite to One another upon the globe, fiandin g with feet
towards feet, on oppofite meridians and parallels. ’ Being on
oppofite {ides of the equator, they have oppofite feafons,
winter to"one, when it‘is fummer to the other; being equally
diftant from the equator, they have the contrary poles equally \
elevated above the horizon; being on oppofite meridians,
when it is noon to the one, it mutt be mid-night to the other;
and as the fun recedes from the one when he approaches to
the other, the lefih of the day to one mutt be equal to the.
length of the night at the fame time to the other. '

mos:

‘

. g‘ae’ Ufa of gin Terra/trzaiezdag,

‘P R O,B_,_L,E M VI,

9’? find 1196 di/tame Zetween any two places on the

Lay the graduatedtedge ,of ,_-_the quadrant of
altitude over both the places,=x.:and ., count the
number of degrees intercepted between them on
the quadrant, then. multiply thefedegrees by
60, and the prodqp‘t will give the dii’tance in
. geographical miles :‘ but to find the dii’tance in
Euglilh miles, multiply the degrees by 697}, and
the product will be the number of miles required. t
Or, take the dif’tance betwixt any two places
with a pair of compafl'es, and apply- that extent
‘ to the equator; the number of degrees,inter~;
cepted between thepoints of the compafles, is
the dillance in degrees of a great circle “E 5 which ,
may be reduced either to geographical miles, or
to Englilh miles, as above.

_ *tAny ”circle that divides the globe into two equalparts, Great
’ is callé‘d a great cirglg, 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 legfir circle. New, Lgflér
as everycircle, whether great or fmall, contains 360 degrees, circle,
and a degree upon the equator or meridian contains 60 geo- '
graphical miles, it is evident, that a degree oflongitude upon

the equator, is longer than a degree of longitude upon any
parallel of latitude, and mull therefore contain a greater
number of miles. So that, although all the degrees of lati-

tude are equally long updn an artificial globe (thoughinot
precifeLy {/0 upon the earth itfelf) yet the degrees of longi-

tude decreafein length, as the latitude increafes, but not in

the fame proportion, The following table fhews the
length of a degree of longitude, in geographical miles, and,
hundredth parts of a mile, for‘every degree 'of latitude;

item the equator to the poles: a. degre , on the. equator;
heing 60 geographical miles, . 7'- 1% ' ' '

@5012:

.369,

276

The U]? qf the Tern/trial Glehe.

P R‘O B L E M xVII.

2! place on the glohe heiag given, and it: .elzflahee
from any other place, to find all the other place:
‘apan the glohe which are. at the fame a'z'flaaee from
the given plate, , _‘

Bringyithe' given place to the brafen meridian;
and {crew the quadrant, of altitude to the meri-
dian, .direétly 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 dif’tant with it
from the given place. ' . _

This is' the fame as if one foot of a pair of \
'compafi‘es was fet in the given place,-and the
other foot extended to the fecond place, whofe
diftance is known; for if the compafi'es be then
turned round the firl‘t place as a center, the
moving foot will go over all thofe places whi'Ch
are at the fame dil’tance with the fecond from
it. -

'A'TABLE

Tbe U]: of (be. Terra/trial Glaze; 2 7 t

H TA B L E flaming 1796 number of miles in 4 deg
gree of Iohgitude, in any‘givén degree bf [aritudcfi

U Sw-U a? 6.33

 

o 2.92
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01
.‘9. . . . _
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an Ufi: of In fem/inn can;
P R o B L EM’ VIII.

Tee hour of "the day at any place being given, tofinJ
all elaofle plages where it is noon at that time. .

Bring the given place to the brafen 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 [lands for noon, 3
and when the bringing" of any place to the brafen
meIidian Is mentioned, the fide of that meridian
on which the degrees are reckoned from the
equator is meant, unlefs the contrary fide be

mentioned.

PROBLEM IX.

The hear of fine day at any place My given refine!
what 0 ’a’joek it then 2.9 at any et/aer place.

Bring the given place to the Ibrafen meridian;
and fet’ the index to the given hour; then turn
the globe, until the place where the hour 13 re—
quired comes to the meridian, and the index will
point out the hour at that place.

PROBLEM Xi

fa‘find lbe fan’s place in the ecliptic, and 121's 9* alga
elination, for any given day of line year.
Look on the horizon for the given day, and
right againfi it you have the degree of the fign
In which the fun is (or his place) on that day

* The fun’s declination in his‘difiance from the equinoé‘tial
in degrees, and is north or fouth, as the fun is b’etWeen the
equinetiial and the north or fouth‘ pole.

- m

~

T he (1/2 of the Terrcytrz'al Glohe.‘

at'nloon. Find the fame degree of that fign in
the ecliptic line Upon the globe, and having

brought it to the brafen meridian, obferve rwhat "

degree of the meridian fiands over it 5 for that
islthe fun’s declination, reckoned from the
equator.‘ \

P R‘O BI‘L E-M XI.

if he clay of the month heiteg given, to final all thofi
, places of the earth over which the fan will pafe
vertically an 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 thofe places which pafs .under that ,pointhof
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 mul’t be
direétly over head to eaeh of them at its refpec:
nve noon.

PROBLEM XII.

leace helng given m the * torrid zeae, to fitza’ the/2!
two days of the year, on whz'eh the fun [hall he
vertical to that place.) ‘

Bring the given place to the brafen meridian,”
and mark the degree of latitude that! is exactly

OVCE’

\

*1 The glolie is divided? into five ‘zbnes ;' one torrid, two ‘

temperate, and two frigid.The torrid zone lies between the two
, tropics, and is’47 degrees in breadth, or 2 33,: on each fide of
the equator : the temperate zone: lie between the tropics and
polar circles; or from 23»; degrees of latitude, to 66%, 0“;
eac

2-73

£74

The U]: of the Terreflriol Glohe.

over it on the meridian; then turn the globe
round its axis, and: obferve the two degrees of
the ecliptic which pafs exaétly under thatdegree
of latitude : laf’tly, find on theywooden horizon,
the two days of the year on which the fun is in

,thofe degrees of the ecliptic, and they are the

days required : for on them, and none elfe, the
fun’s declination is equal to the latitude of the
given place": and ConfeqUCntly, he will then be
yertical to 'it at noon. ‘ ‘

/P R on L E M‘ XIII.

To find all thofl: places of the north frigid zone,
where the fun hegin: to floz’ne eon/I'ono‘ly without
fitting, on any given day, from the 2 I ft of March
to the 23d of Septen‘zher. ‘ K ‘

On thefe two days, the fun is in therequinoc-

' 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

7, places of the earth. But as the fun declines

from the equator, towards either pole, he will
fhine jufl' as many degrees round that pole, as ‘
are equal to his declination from the equator;
fo that no place within that dif’rance of the pole
will then go through any part of the dark, and
confequently the fun will not fct to it. Now, as

each fide of the equator 5 and are each 43 degrees in breadth:

the frigid zone: are the the {paces included within the polar
circles, which being each 2 3% degrees from their refpeé‘tive
poles, the breadth of each of thefe zones is 47 degrees. As
the fun never goes without the tropics, he muft every mo.- '
mcnt be vertical to fame place or other in the torrid zone.

3 ' the

The Ufa» offhe Tamara; Globe: ,
ihé fun’s declination isnorthward, from the 21H:
'of March to the 23d of September, he zm'ul’t con.
fiantly ihine round the north pole all that time ;
and on the day that he is in the northern tropic;

\ he Ihines 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 brafenmeridian, 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 polelwhere the
reckoning ends: then, turning the globe round
its axis, .obl’erve What places in the north frigid

Zone 'pafs direétly under that mark; for they "

'are the places required. ‘ :
The like may be done for the Youth friOid
gone, from the, 2 3d of September to, the 2111? of
March, during which time the fun fhine‘s cons:

- flantly on the fouth pole.

To find ”the place over which the fun is quarried], at
My 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 meridianrthen bring. the place-

Where you are (fuppofe London) to the brafen

meridian, and fet the indexto the given hour;

which done turn the globe on its axis, until the

index points to XII at noon ; and theplace on

[the globe, which is then directly under the point
T

9?

275 '

276

The Ufi of the Term/trial Glohei

'of the fun’ 5 declination marked 113311 the meri-~

dian, has the fun that moment in t e zenith, or
direélly overhead.

PROBLEM XV.

The day 222221 hour 222‘ any place heim ggineh, to 152221 all.
the/e places where the fun 25 the22 ryz'hg, or fitting,
or 022 the meridzem: eo22feque22tly, all thofie places
which are enlzghtened at 222222 time, and 222/2» which
are 222 the dark.

This problem cannot be folved by any globe
fitted up in the common way,w with the hour
circle fixed upon the brafs meridian , unlefs the ’
fun be On or near tome of the tropics 0n the
given day. But by a globe fitted up according
to Mr. yofeph Harrzs’ s invention (already men-
tioned) where the hour-circle lies on the furface
of the globe, below the meridian, 1t may be f01ved
for any day in the year, according to his meé
thod; which 13 as follows.

Having found the place to which the fun is_
vertical at the given hour, if the place be 1n the
northern hemilphe’re, elevate the north pole as
many degrees above the horizon, as are equal to
the latitude of that place , if the place be 1n the

_ fouthern hemifphere, elevate the f0uth pole ac-

com‘ingly- , and bring the faid place to the brafen
meridian. Then, all thofe places which are in
the wel’tern femicircle of the horizon, have the
fun rifing to them at that time, and thofe 1n the
eaf’tern femicircle have 1t fetting1to'th0fe under
the upper femicircle of the brafs meridian, it is
noon , and to thofe under the lower femicircle',
it is mid- night. All thofe places Which are.
above the horizon, a1e enlightened by the fun,

and;

97” 076’ 0f the Terrcfirial Globe;

i and have the fun jui’c as many degrees high to
- them, as they them-{elves 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 {aid place and the horizon.
In all thofe places that are 18 degrees below the
wefiernfemicircle of the horizon, the morning
twilight is jufi' beginning; in all thofe places that
'are I8 degrees below the ealtern femicircle of
the horizon, the evening twilight is ending; and
all thofe places that are lower than 18 degrees,
have dark night. . . a ‘

If any place he brought to the upper femi—
circlezof the brafen meridian, and the hour index
be let to the upper XII or noon, and. then the
. globe be turned round eaf’tward on its axis;
when the place comes to the Wefiern femicircle
of the horizon,” the index will fhew the time of
fun—tiling 'at that place; and when the fame
place comes to the eafiern femicircle of the hori-
zon, the index. will fhew the time, of fun-fer.

To thofe places which do not go under the

horizon, the fun fets hot "on that day: and to .

thofe which do not come above it, the fun does
not rife. '

V’P‘ROBLEM XVI.

The day and boar of a lmiar eclz'pfiz 56mg given; to‘
- find all t’laofe places (if like earl/9 to which it will
he :aiflb/e. \ »

' ‘The'moon is neirer eclipfed but when fheis
lull, and f0 directly Oppofite to the fun, that the
I 2 earth’s

/

277

278

fig life of the Terr‘efiriel Globe. -

earth’s {hadow falls upon her. Therefore, what~
ever place of the earth thefun is vertical ,to at
that time, the moon mutt be vertical to the anti-
podes of that place: fo that the fun will be then
.vifible 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 ofthat place, and bring the ‘place
to the upper part of the brafen meridian, as in
the former problem: then, as the fun will" be
vifible to. all’pthofe parts of the globe which are
above the horizon, the moon will be vifible to all
thofe parts of the globe which are'below it, at ,7
the time of her greatefi obfcuration.

. But with regard to an ecliple of the" fun, there
is no fuch thing as fhewing to what places it
will be vifible, with any degree of certainty, by
a common globe; becaufe the moon’s fhadow
covers bur a {mall portion of the earth’s furface;
and her latitude, or declination from the eclip-
tic, throws her ,fhadow f0 varioufly upon the
earth, that to determine the places on which it
falls, recourfe mul’t be had to long calculations.

PROBLEM XVII.

To refiify the glohe for the laiitude, the *5 zenirh,
and the fan’s place. a

Find the latitude of the place (by Prob. I.) and if
the place be in the northern hemifphere, raife the ..
north polerabove the north point of the horizon,-

* The zenith, in this fenfe, is the highel’t point ofth‘e bra-
fen meridian above the horizon; but in the proper fenfe,
it is that point of the heaven which is direé‘tly vertical :0
any given place, at any given inflant of time.

\ a5”

The 1/72 of the Terra-firm] 61056.}

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 \fouthern
\hemifphere, raife the fouth pole. above the fouth
aim 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 brafen
meridian, and fallen the quadrant of altitude To,
that the chamfered edge of its nut (which is
even with the graduated edge) may be joined
to the zenith, or point of latitude. Thisdone,
_ 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 uppermoi’t XII on the
hour-circle ; and the globe ,will be reétified.

279

The latitude of any place is equal to the ele- Remark.

vation of the nearel’t pole of the heaven above '

the horizod of that place ;‘ and the poles of
the heaven are direc‘ily 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 {hall 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 {hall fee the correfponding

ole of the heaven rifing gradually above our
liorizon, juf’t as many degrees as we have gone
frdm the equator: and if we were at either of

the earth’s poles, the correfponding pole of the,

heaven would be direé’tly over our head. Con-
;fequently, the elevation or height of the pole [in
T 3 degrees

280 The U]; of the‘Teeezé/trinl Glehe.
detrrees above the horizon, is equal to the

number of degrees that the place is from the
equator.

PROBLEM XVIII.

The [etitztde of any place, not exceeding * 66— de-
grees, and the day of the month, heing given, to
find the time effnn- refing andfetting, and eenfio
getentb the length of the day and night.

Hating re6?:i tied the globe for the latitude,
and for the {1111’ 5 place on the given day (as di-
re6ted 11-1 the preceding problem) bring the fun’ 3
place 111 the ecliptic to the eal’tern fide of the ho-
rizon, and the hour index will {hew the time of
ion 1ifing- , then turn the globe on its axis, until

the fun’ 3 place comes to the wel’tern tide of the 1 ,

her zon, and the 1ndex will lhew the time of fun—
fetting.

The hour of fun- fetting doubled, gives the
length of the day, and the hour of fun-tiling
doubbled gives the length of the night.

"P R OB L E M XIX.

if he latitude of any place, and the day of the month,
heing given- , to find when the manning twilight
hegins, and the evening twilight ends, at that
place.

This problem IS often limited, for, when the
fun does not go 18 degrees below the horizon,
the twilight continues the whole night , and 1‘61“

*5 All places whofe latitude 13 more than 66' degrees, are
in the frigid zones: and to thofe places the fun does not
fet 1n {umbmen for a certain number of diurnal revolutions,
which occafions this limitation of\latitude.

I‘ ‘ ‘ ' feveral

qjae Ufa of we .Terreflrz'zzldGlaéc-ti

feveral nights together in fummer, between 49 ’

and 66% degrees of latitude: and the nearer

to 665, the greater is the number of thefe nights. "

But when it does, begin and end, the foliows
ing method will fhew the [time for any given
’ da '. , , *

yRetftif‘y the globe, and bring the fun’s place in
the ecliptic to the eal‘rern fide 0f the horizon;
then mark that point of the ecliptic with a chalk
which is in the wef’tern tide 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 eal’tward, keeping the
quadrant at the chalk-mark, until it is jui’t 18
egrees high on the quadrant; and theindex
will “point out the time when the morning twi-
light begins: for the fun’s place will then be 18
degrees below the eaf’tern tide of the horizon.
To find the time when the evening twilight
ends, bring the fun’s place to the weftern fide
of the horizon, and the point oppofite to it,
which Was marked with the chalk, will be rifing
in the eafi: then, bring the quadrant over that
point, and keeping it thereon, turn the globe
weltw'ard, until the faid point be 18 degrees
above the horizon oh 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 wei’tern fide of the horizon. '

i 281

282

'fne Ufl: of the Torreflrial Glade;

PROBLEM XX.

Sfo find on what day of tloe year the fun begin:- to
jnino confiantly ‘wz't/oont fitting, on- any given
place in the nortlo frigid zone 5 and how, long be
toniz‘nnes to do fo. ‘ ‘

Reé‘tify the globe to the latitude of ' the place,
and turn it about until fome point of the eclip-
tic, between Arie: 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 theday on

‘which the fun begins to {hine confiantly on the

given place,~without fetting. This done, turn
the globe until. fome point of the ecliptic, be-
tween Cancer and Liana, 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 confiantly {hining on the faid place, and rifes
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 Confiantly above the horizon without
fetting: for all the portion of the ecliptic, that
lies between the two points which interfeé’c the

.hOrizon in the very north, never lets below it:

and there is juft as much of the oppofite part of
the ecliptic that never rifes; therefore, the fun
will keep as long confiantly below the horizon
in winter, as above it in fumrner..

‘ ‘ " Whocvsr

The Ufe ‘of we Terreytrz'nl eta/32;

Whoever confiders the globe, will find, that
all places of the’earth do equally enjoy the bene-
fit of the fun, in refpeét 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 g

oppofite feafon.

'PROBLEM XXI.

' To find in what latitude the fun jhz'nes cenflnntb
withont jetting, for any length of time lefi than
* 182-;- af our day: and nights. ' ’

Find a point in the ecliptic half "as many de-
grees from the beginning of Center (either to-
wards flrie: or Lihm) as there are 1- natural days

in the time given; and bring that point to‘the .

north fide of the brafenlmeridian, on which the
degrees are numbered from the pole towards
the equator: then, keep the globe from turning
on its axis, and tilde 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. :

"“ The reafon of this limitation is, that 132.; of our day;
and nights .make half a year, which is the longelt time that
the gun lhmes without fetting, even at the poles of the
cart . ’

:f A natural day contains the whole 24 hours: an arti-
fiual day, the time that the fun is above the'horizon.

PRO-g

283

a

The Ufe of the Tare/treat Glah_e.- - i :
\P R o B L E M \XXH,‘

The latitude of a place, net exceedingx 66-5 degrees,
and the day of the meath-heiug given; ate find
the fua’: amplitude, or point of the eompaft on
'(owhieh he rife: erfeti.

’ Reé‘tify the, globe, and bring the fun’s place-
to the eaf’tern fide of the horizon, then obferve
what ‘point'of the eompafs on the horizon {lands
right againi’t the fun’svplaee, for that is his
amplitude at rifing. This done, turn the globe
wefiward, until the fun’s place comes to the
wefietn tide of the horizon, and it Will cut the .
point of his amplitude at fi‘etting.‘ Or, you may "
count the tiling amplitude in degrees, from the
wit point of the horizon, to that point where
the Iun’s place cuts it; and the fetting ampli- ‘
. tude, from the weft point of the horizon, to the
fun’s place at letting.

PROB‘LEM XXIII.

T he latitude, the fan’s place, and his * altitude, V
heing given; to find the hour of the day, mid the ‘
fun": azimuth, or uumher of degrees that he i;
di/taat from the meridian. ' '

Refiify the globe, and bring the fun’s plaee _
to the given height upon the quadrant of alti-
tude; on the eafiern fide of the horizon, if the
time'be in the forenoon; or the weltern fide, if

* The fim’s altitude, at any time, is his height in degrees
above the horizon at that time. ' '
' ~ ~ it

m Ufl: aft/he Terrqirial ezoae‘;

it be in the afternoon: then, the index will
{hew 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 1n 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 ‘lhewn by the c‘ompafs, if they
agree, the compafs has novariation in that place :

_ but if they difl‘Er, the compafs does vary, and.

the variation is equal to this difference.

P R OB L E. M XXIV. ’

' The/latitude, [war of the day, and {be fim’s place,

being given; i0 find the fun’s altitude and
azimuth

Reétifyi the ”globe, and turn it until the in;

dex points to the given hourythen lay thequa— ‘
*‘ldrant of altitude over the fun-’s place in the
(ecliptic, and the fiegree of the quadrant cut by

the fun’s place is is 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. ’

PRO:

28.5-

~.286

The Ufl’ of the “Tet're/irial Glole. _

PROBLEM XXV.

The latitude, t/Je flin’r altitude, and lair azimuth
aeing given; to find his place in the ecliptic, the
day of tlae manta, ana’ laanr of the day, tlaoagb
27%;}! lead all leen lo/l.

Reétify 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; andithe day of the month
anfwering 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 {hew the hour.

Any two points of the, ecliptic which are
equidil’tant 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 mifiaize both the month,
and the day of the mOnth; to avoid which,
obferve, that from the 20th of” March to the
exit of June, that part of the ecliptic which is

”" By reé’tifying the globe for the zenith, is meant
fcrewing the quadrant of altitude to the given latitude on
the brafs meridian. _ ' . a
, between

The Ufe of tlae Terreflrz'al Globe."

between the beginningof Arie; and beginning of
Cancer is to be ufed: from the 2111 of June to
the 23d of September, between the beginning
of Cancer and beginning of Libra: from the
23d of September to the 21ft “of December,
between the beginning of Liara and the begin-
"ning of Capricorn; and from the 21ft of Decem-
ber to the 20th of March, between the begin-
ning of Capricorn and beginning of dries. 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;

\‘I’o. final five length of Ike lengefi day at any‘gi‘ven ,

place.

'If the place be on the north fide of the equal-7
tor, find its latitude (by Prob. I.) and elevate
the north pole to that latitude; then, bring the
beginning of Cancer 23 to the brafen meridian,
and fet the hour—index to XII at noon. ‘ But if
the given place be on the fouth fide of the

equator, elevate the fouth pole to its latitude,‘

and bring the beginning of Capricorn 19° to the
~brafs meridian, and the hour-index to XII.
This done, turn the globe wefiward, 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 midday and fun-fet;

3 ‘ . ’ ' which

287,

288

{rte Un afcne Terrenmz Glace.

which length of time being doubled, will give
the whole length of the day, from l‘unwrifing to ‘
fun-fening, For, in all latitudes, the fun rifes
as‘long before mid-day, as he fets after it.
, / .

‘PROBLEM XXVII.

'To find in what latitude t/ac langcfl day 2': of' any

, given length Zcfs clean 24 hours.

4 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; becaufe the longefl:

day in north latitude, is when the fun is in the

firf’c point of Cancer; and in fouth latitude,
when he is in the fitf’t point of Capricorn. Then
fet the hour-index to XII at noon, and turn the
globe wefl'ward, until the index points at ‘half‘

the number of hours given ;which done, keep ,
‘the globe from turning on its axis, and flide'the

meridian down in the notches, 'until‘ the afore-
faid point of the ecliptic (Vi-z. Cancer .or Capri—
corn) comes to the horizon; then, the elevation
of the pole will be equal to the latitudere:

quired. '

“.' V PRO:

TheUfi of tbe'Terre/irz’al Globe;

-1) R o B L E M ‘XXVIII,

'Tbe latitude, of any place, not exceeding 66% de—
grees, being given; in find in what * climate flee
place is. ,

Find the length of the longel‘t 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
anfwer to the climate in which the place is,

PROBLEM XXIX,

The latitude, and tlae day of the month, ageing given;
z‘efind the hour of the day when the fan f/aines.}

Set the wooden horizon truly level, and the
brafen meridian due north and fouth by a ma-
— riner’s compafs : then, having rectified the
‘ globe, flick a {mall {Ewing-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
brafen‘ meridian, and fet the hour-index torXII

"f A climate, from the equator to either of the polar'cir—
cle‘s, is a traé’t of the earth‘s furface, included betWeen two
fuch parallels of latitude, that the length—of the loragelt day

in the one exceeds that in the ,other. by halfan 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 cirq
yes; and fix from each polar circle to its refpeétive pole.

at

'2 89

290

TheU/Z’ of the Terreflrz’al Glahe.
at noon; then, turn, the globe on its axis, until

the needle points exaé’tly towards the fun (which
it will .do when it cafis no ,fhadow on the globe)

‘ hand the index will Ihew the hour of the day.

PR 0 BL E M XXX.

.2! plea/ant way of flaewing all thofi" places of thé
earth which are enlz’ghtemd hy the/1m, and alfa‘
the time of the day when the fun jhz’nes.

Take the terref’trial ball out of, the Wooden
horizon, and alfo out of the brafen meridian;
then fet it upon a pedef’tal in fun-fhine, in fuch
a manner, that its north pole may point direétly
towards the north pole of the heaven, and the
meridian of the place where you are be direétly
towards the fouth. Then, the fun will fhine'
upon all the like places of the globe, that he
does on the real earth, riling to fome when he
is fetting to others; as you mayperceive 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 thofe“
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 thine exactly to the two XII’s; and at
one o’clock to the two 1’s, &c. 80' that the

' ‘ 7 Place,

Oh/ernations concerning it;

place, where the enlightened half of the globe
is parted. from the fh'aded half, in this circle of
, hours, will [how the hour of the day.
rThe principles of i‘dialing‘ {hall be explained
farther on, by the. terrel’trial globe. At prefent
we [hall only add the following obfervations
upon it; and then proceed to the ufe of the ce-
. leflial globe. .

I . T he latitude of anyplace is equal to the ele-

vation of the polexaho've the horizon of that place, ,

and the elevation of the equator is equal to the cone-
plement of” the latitude, that is, to what the latitude
wants of 90 degrees. .

2. Tho/e places which lie on the equator, have no
latitude, it heing there that the latitude hegins; and
tho/h places which» lie on the fir/t meridian have
/ no longitude, it heing there that the longitude he-
gins. Configuently, that particular place of the earth
where the firjl meridian interflehls the eauator, has
neither longitude nor latitude. .

3. In all places of the earth, except the poles,
all the points of the compafi may he di/lingui/hed in
the horizon : hut from the north pole, every place
is flouth ; and front the- [oath pole, every place
is north. Therefore, asthe’ fun is conflantly aho‘ve
the horizhn of each pole for half a year in its turn,

he cannot he fizid to depart from the’nuridfan of ‘

either pole for half a year together. .Con/hquently,
at the north pole it may he [did to he noon every
moment for half ”a year-,‘and let the winds 'hlow
from what part they will, they mu/t always hlow
from the fouth; and at the [oath pole, from the
north. , -
' 4‘. Becaufe one half of the ecliptic isahe'oe the
horizon of the pole, and the fun, moon and planets,

move in (or nearly in) the ecliptic 5 they will all ,
. U .

rzfig

2,9 t

'29:

Ohfirvations concerning the ,

rife ‘ and ' jet to the poles. (But, hecaujZ’ the flars
never change their declinations from the equator (at
leafl not finflhly in one age) thofe which are once
ahove the horizon of either pole, never fet helow it;
and tho/e which are once helow it, never 'ri/E'.

1;. A’ll places of the earth do equally enjoy the he-
tuft of the fun, in rupee; 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 mic/t always continue ahove the
horiZon for one half a diurnal revolution ahout the
earth, and for the other half helow it. ,

7. When the ficn’s declination is greater than the
latitude of arm place, upon either flde of the equator,
the fun will come twice to the fame azimuth or point
of the compo/s in the forenoon, at that place; and
twice to a lihe azimuth in the afternoon; that is,
he will go twice hack every day, whil/t his declina-
tion continues to he greater than the latitude. Thus,

fuppofe the glohe rettified to the latitude, of Barhau

does, which is 13 degrees north 5 and the fun to he
any where, in the ecliptic, hetween the middle of
Taurus and middle of Leo; 2f the quadrant of al-
titude he fit to ahout * I 8 degrees north of the eajll
in the horizon, the fun’s place he marked with a’
chalk upon the ecliptic, and the glohe he then turned
wcflward on its axis, the [aid mark will rife in the
horizon a little ”to the north of the quadrant, and
thence afcending, it will croft the quadrant towards

"‘ From the middle of Gemini to the middle of Cancer,
the quadrant may be fer 20 degrees.

- the

l T erre/trzal Glohe.

the/oath; hut hefore it arrives at the meridian, it
will era/3' the quadrant again, and pafi Ever the
meridian northward of Barhadoes. [find if the
quadrant he fet ahout 18 degrees north of the weft,
the fun’ 3 place will crofi it twice, as it defcends from
the meridian towards the horizon, in the after-
noon.

8. In all places of the earth hetween the equator
and poles, the days and nights are equally long, viz.
12 hours each, when the fun is in the equinottial
for, in all elez ations of the pole, /hort of9 0 de—
grees (which is the greate/t) one half of the equator
or equinottiol will he ahove the horizon, and the
other half helow it.

9. The days and. nights are never of an equal

length at any place hetween the equator and polar .

circles, hut when the fun enters the f gns <r dries
and a Lihra. For in every other part of the
ecliptic, the circle of the fun’ s daily motion is divided
into two unequal par ts hy the horizon. ,

10. The nearer that any place is to the equator,
the lefs is the diferen‘ce het ween the length of the days
and nights in that place, and the more remote,
the contrary. The circles which the fun defcrihes
in the heaven every 24. hours, heing cut more
nearly equal in the former cafe, and more unequally
in the latter.

11. In all places lying upon any aiven parallel
of latitude, however long or /hort the day or night

he at any one of thefe places, at any time of the“

year, it is then of the fame length at all the rejt‘ ,
for in turning the glohe round its axis (when refiiq
fied according to the fun’s declination) all thcyh
places will keep equally long ahove or helow the
horizon.

12. The fun is vertical twice a year to every
place hetween the tropics , to tho/e under the tropics,
' U 2 once

293'

2%

Ohfernations concerning the

once a year, hut never any where elfl. For, there
can he no place hetween the tropics, hut that there
will.7 ee two points in the ecliptic, whofe declination
from the equator is equal to the latitude of that
place- , and hut one point of the ecliptic which has a
declination equal to the latitude of places on the
tropic which that point ofthe ecliptic touches, and
as the fun never goes without the tropics, he can,
never he vertical to any place that lies without
them. .

i 3. To all places in the ‘* torrid zone, the dura-
tion of the twilight is lea/t, hecaufe the fun’ s daily
motion is the mojl perpendicular to the horizon. In
the frigid TL zones, greatejl, hecaufe the fun’s
daily motion is nearly. parallel to the horizon; and '
therefore he is the longer of getting 18 degrees he—
low‘*it (till which, time the twilight always con-

‘ tinues.) find in the i temperate zones it is at a

medium hetween the two, hecaufe the ohliguity of
the fun’ s daily motion is [0.

14.. In all places lying exattly under the polar
circles, the fun, when he is in the neare/t tropic,
continues 24 hours aho'oe the horizon without fit-
ting ; hecaufe no part of that tropic is helow their
horizon. And when the fun is in the fartheyt

tropic, he is for’ the fame length of time without

rifing; hccau/e no part of that tropic is ahove their
horizon. But, at all other times of the year, he
rifes and fets there, as in other places; hecaufe all
the circles that can he drawn parallel to the equator,
'hetween .the tropics, are more or le/s cut hy the
horizon, as they are farther from, or nearer to,
that'tropic which is all ’aho've the horizon : and

‘ Between the tropics.
1* Between the polar circles and poles.
I Between the tropi‘cs and polar circles. \

4, when

Terreflrial Glohe.

when. the fun is not in either of the tropics, his
diurnal tour/e inn/l, he in one or other of theft:
circles. ‘

I 5'. To. all place! in the northern hernifphere,
from the equator to the polar circle, the longe/l clay
vandflortflt night is when the fun is in the northern
tropic; and the jhorte/l clay and longe/l night it
when the fun is in the fouthern tropic; hecaufe no
circle of the fun’s daily motion is fo much Move the
horizon, and fo little helow it, as the northern tro-
pic; and none fo little aho've it, and fo much helow
it, as the flouthern. ' In the fliuthern hemifphere,
the contrary. '

1-6; In all places hetween the polar circles and ~

poles, the fun. appears for fame another of days ( or
rather diurnal revolutions) without fetting -,_ and at
c the oppoflte time of the year without riflng; hecaufi:
fome part of the ecliptic never fets in the former

cafe, and as much of the oppo/i‘te part never rife: in '

the latter. A’ncl the nearer unto, or the' more re-
mote from the pole, thefe places are, the longer or’
fhorter is the fun’s continuing prefence or ahfence.

17, ff afiflpip fit: out from any port, and fails
round/the earth eajtwarcl to the foam port again,
let 'her tahe what time /he will to do it in, the
people in that fhip, in reckoning their time, will
gain one complete clay at their return, or count one
day more than tho/e who rcflde at the fame port“,
hecaufe, hy going contrary to the fan’s diurnal motion,
and heing forwarder every evening than they were
‘ in the morning, their horizon will get fo much the
foone'r above the jetting fun, than if they had kept.
for a whole clay at any particular place. 5 And thus,
by cutting of apart proportionahle to their own
motion, from the length of every clay, they will
gain a complete clay of that [ort at their return“;

without gaining one moment of ahfolute time more a
- 3 . g than

egg

>296 ‘The Ufe of the Cele/tint Gnu.

than it elapfi'a’ during their tour/e, to the people at ,
the port. ,_ If they fail weflwaru', they will reckon
one day lefs than the pee-pie a’o who rzyiele at the [aid
port, heeaufe hy gradually. following the apparent
diurnal motion bf the fun, theywili heep him each
,. particular day fo much longer above their horizon,
_ as an/wers to that day’s oourfe; andohy that means,
they cut of a whole day in reckoning, at their re—
turn, without lofing one moment of aofolute time.
Hence, if two [hips fhould fit out at the fame
time from any port, and fail round the glohe, one
eaflward and the other wefiward, ,fo as to meet at
the jame port on any day whatever; they will a’zfier
‘two days in rec/zoning their time, at their return,
If they jail twice round the earth, they will' defer
few 46215;, 2'f thrice, flewflx, €36: '

, L E c: 1‘. IX.
9'5? ufe of‘the eele/tialglohe, and armillary @hergg.

The «1%,HAVING done for the, prefent with'thg
gielglate. terrcfirial globe, we {hall pr06¢¢d to thc
” ufe of the cclcfiials firfi premifing, that as, the
equator, ,ecliptic, tropics, pglar circles, hogié
zon, and bggfcg meridian, are gxgfily glikc on
' bOth glqbgs,all ghe former problems concern:

ing the fun .arc‘falvcd chc fame way by bath.
Torcé‘ti- glpbesg" ‘TthmCthogi' alfo of rfiétifying thfi
filisz Cel¢fiialg19b¢ is the fame as rcfiifyiflg £111? rm“.
rcfirial, {42, Elcyatg: the pole; gecordingi'to thc'
latitude; Of War plaice, then fercw the Quadrant;

Of altigudg g9 thg: genit’h, or} the brgfs meridian;

bring the fun’s place in the eclipticko .thé
gradeewd Side-ac 9? tbs? beefs Wide?» on. [‘36

~ W LE

/

‘Tlve Ufi ‘of the Cele/tie! Globe,

tide which is above the fouth point of the
wooden horizon, and fet the hour-index to the
uppermof’t XII, which fiands‘for noun.

- N. B. The {un’s place for any‘ day of the
yearfiands directly over that day on the hori-
zon of the celeftial globe, as it does on that of

the terrefirial,

'297

The latitude and longitude of the f’cars, :and OfLafimjg
all other celeflial phenomena, are reckoned in aand longi-
very different manner from the latitude and’m’ “the

longitude of places on the earth: for all terrefr
trial latitudes are reckoned from the equator;
and longitudes from the meridian of fome re-
markgble place. as of London by the Englifli,
and of Paris by the French; though molt of
the French maps begin their longitude at the
meridian of the ifland Ferro.-———:-But the allro-
nomers of all nations agree in reckoning the
latitude: of the moon, fiars, planets, and comets,
‘ from the egliptig; and their longitudes, from the
a * equinottz'al colure, in that femicircle of it which
euts the ecliptic at the beginning, of Aries 6r ;
and thence eafiward, quite round, to the fame
femicircle again. Confequently thofe {tars which
lie between the equinoétial and the ”northern
half of the ecliptic, have north declination and
{outh latitude; th'ofe which lie between - the
equinoétial and the fouthern half of the ecliptic,
have {out}; declination and north latitude; and

* The great circle that pafl‘es through the equieac‘lialpaz'nt: '

at the beginning of <Y‘ and a}, and through the pole: cf
(be (warld (which are two oppofite points, each 90 degrees

from the equinoé‘tial) is Called the eguz‘noiiial calure : and the 091”“,

great circle that palfes through the beginning of 5 and 19°,

'and alfo through the pole: af tlze ecliptic, and poles of the '

world, is called the folflz‘tial colure.

U 4 > i hi

298 p The U]? of tbe Celcylz'al Claim

all thofe which lie ”between the tropics and poles,
have their declinations and latitudes of the fame
denomination. 7 i
‘ There are fix great circles on the celefi’ial
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.
‘Thefe polar poihts diyide thofe circles into 12
femicircles ; which cut the ecliptic at the begin-
nings of the 12 figns. They refemble {9 many .
meridians on the terreftrial globe; and as» all
places which lie under any particular meridian
femicircle on that globe, have the fame longik.
tude, f0 all thofe points of the heaven, through
which any one of the above femicircles are
drawn, have the fame longitude.-—~And as the
greateft latitudes on the earth are at thenorth
and fouth poles of thecarth, fo the greateft lati-
tudes in the heaven, are at the north and fo‘uth'
. poles of the ecliptic. , ’ ‘
Cofieflw In order to dif’tinguifh the flats, with regard
rim. ’to their fituations and pofitions in the heaven,
,the antients divided the whole vifible firmameflt
Of flats into particular fyf‘tems; whichthey called
canfle/[atiamg and digel’ted them into the forms
'of fuch animals as are delineated upon the celefl
tialglobe. And thofe {tars which lie between A
the figures of thofe imaginary animals, and
could not be brought within the compafs of any
of them, were called unformed/fdrr.

Becaufe the moon and all the planets were
obferved to move in circles or orbits which crofs
the ecliptic (or line of the fun’s path) at fmall

, angles, and to be onthe north fide of the eclip-

' ' tic for one half of their courfe round the hea.
ycn‘of firm, and on the {curb fide of it for the-

' ' ‘ other

we Ufa of tbe cum: Globe; . 299-.

other half, but never to go quite 8 degrees from
it on either fide, the antients difiinguilhed that
fpace__by two leiTer circles, parallel to the ecliptic
(one on each fide) at 8 degrees difiance from it.
And the fpace included between thefe circles,
they called the zodiac, becau‘fe ‘ molt of the 12
confiellations placed therein refemble fame living

’ . creature.-—Thefe conf’tellations are, I. flrz'es ‘1’,Its.figns,,

the ram; '2. Taurus 25 , the bull; 3. Ge.“ diVifi‘s
mim' n,“the twins; 4. Cancer es, the crab 5°“ -
5. Leo 5),,“the lion; 6. Virga m, the virgin;
7. “Liém a, the balance; 8. Scorpio m, the
fcorpion'; 9.,Sugitturiu: 1 , the archer; 10. Cu-
prz'coruu—s 19°, the goat; II. Aguurz'u: 3:, the
water bearer; and 12. Piftes 3E , the fillies.

It is to be obferved, that in the infancy ofRemark,
afironomy, thefe twelve confiellations fiood at
or near the places of the ecliptic, Where the
above charaéterii’tics are marked upon the globe:
but. now, each confiellation has got a whole fign
forwarder, on account of the receflion of the
equinoétial points from their former places,
80 that the conf’tellation of flutes, is now in the
former place of Taurus ;‘ that of Tuurut, in the
’ former place of Gemini; and f0 on. '

The fiars appear of different magnitudes to
the eye ; probably becaufe they are at difl‘erent’
dif’tances from us. Thofe which appear brightf-
eft and largefl, are called flur; of the firji‘ mug-
uitude; the next to them in fize and ‘luf’tre, are
called flaw of tine fitoud magnitude; and f0 on
to the fixtbfwhich'are the fmallefi that can be
difcerned by the bare eye. ‘

Some of the moi’t remarkable {tars haire names
given them, as Cuflor and Pollux in the heads of
the Twim, Sirius in the mouth of the Great
Dag, Proqyou in the lide of the Little Dog, Rigel

. in

3:229

T be Dye of the Celrflz'nl Clone,
in the left‘foot oflOrinn, flrfinms near the right
thigh of Banter, &‘c. ‘ g r y . i
. Thefe things being pre’i‘nifeld,“ which I think.
are all that the young Tyrg need' be acquainted
with, before he begins‘to work any problem ‘by

this globe, Wefhall now proceed to the molt
i tifeful ofthoi‘e problems; emitting feveral which
arc of little or no confequence- I

PROBLEM I,_

T a find tine,ale rig/5t nfrenfinn and Jr dalmatian of
‘ the fin, or any fixed/3dr.

Bring the fun’s place in the ecliptic to the
brafen meridian, then that degree in the equi:
noélial which is cut by the meridian, is the fun’s
right afrenflon; and that degree of the meridian
which is over the ”fun-’3 place, is his declination,
Bring any fixed fiar to the meridian, and its
rig/9t nfcenfion will be cut by the meridian in the
eqtiinoétial ; and the degree of the meridian that
fiands over it, is its dec'lz'nntz'on. , ,
_ So that right afierfian and declination, onthe
celefiial globe, are found in the fame manner
as [angitnde and [ntz'tndg ,on the terrei’trial.

. * The degree of the equinoflial, reckoned from the bear
ginning of Aria, that comes to the meridian with the fun or
liar, is its right aflenflan. ' ' .

+ The diltance of the fun or flar in degreesfrom the equi-
noélial, towards either of the poles,- north or fouth, is its

declination, which is north or {oath aceordingly,

"P R Qt

2%,: 0/2 of tbe cam: 610173,

F R O B LXEM ‘II.
To find the lafitude and longitude of any/24;»...

' If the given {tat 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 {ethicireles meet; which di-
vide the ecliptic into the 12 figns: but if the
l’tar be on'the fouth fide of the CCllpth, place
the 90th degree of the quadrant on the fouth
pole of the ecliptic ; keepihg the goth degree of
the quadrant on theproper pole, turn, the qua-
drant about, until its graduated edge cuts'the
flat: then, the number of degrees ih the qua-
draht, betweeh theeeliptic and the {121353 its
'latithde; and the degree of 'the‘ecliptic cut by
the quadrant is the fiar’s longitude,_reckoned
according I? Ch? fign in. which, the quadrant
lb“! .15: J

BROBLEMIm

2'0 reprefmt the face of tlée flarry firmamenl, a;
few from any given place of {lee earth, at any
740??” 0f W 7212/??- ‘

Reé’tify the celei’tial orlobe for the ’ given lati-
tude, the zenith, and Llaunfs pléme, in every re-
fpefk, as tgughtby the 17th problem, for the
'terrel’trial; and; tom it about, until the index.

hints to the given hour: then, the upper he-
tttilphereof the globe will reptefent the vifible
half 0? the heaven. for that time: all thefiars
_ ,. ,. QPQH

39E

362

The 07?: of the Celefliel Globe;
upon the globe being then in fuch fituations, as

_\ exaétly corre‘fpond to thofe in the heaven. And

if the globe be placed duly north and fouth, by
means of a {mall fea-compafs, every flat on the
globe will point toward the like {tar in the hea-
ven: by which means, the confiellations and
remarkable fizars may be eafily. known. All
thofe {tars which are. in the eaftern lid; of the
horizon, are then riiing in the eaflern fide of
the heaven; all in the wefiern, are fetting in
the wefiern fide; and all thofe under the upper
part of the brafen meridian, between the fouth
point of the horizon and the north pole, are at
their greatefl: altitude, if the latitude of the

\ place be north: but if the latitude be fouth,

thofe {tars which lie under the upper part of the
meridian, between the north .point of the hori-
zon and the fouth pole, are at their greatef’:
altitude.~

PROBLEM'IV.

‘ The latitude of the place, and day oft/9e month,

éeing given; to find the time when any known
jtezr will rife, er’ée on the meridian, or fet.

‘ Having refiified the globe, turn it‘about un-
til the given fiar comes to the eafiern tide of the
horizon, and the index will Ihew the time of
the fiar’s rifing; then turn the globe weflward,

“and when the {tar comes to the brafen meridian,

the index will ihew the time of the f’tar‘s coming,
to the meridian of your place ;‘ lafily, turn on,
until the {tar comes to the weflern fide of the
horizon, and the index will fhew the time of the
fiar’s letting. ' '

. N. B.

7%} .U/qofibé Celqflihl.Globe.'
N. B. In northern latitudes, thofe {tars-which

are lefs dii’tant from. the'north pole, than the

quantity of its. elevation above the north point
of the horizon, never fet; and'fthofe which, are
lefB dif’tant from the fouth pole, than. the num-_
ber of "degrees by which it is deprefl'ed below

M the horizon, never, rife : and vice wrfcz in fouth~ "

ern latitudes.

’v

PROBLEMVQ

To find at what time of 2:191; year” oz givenflar will
, he upon tbe_merz'dz'an, at a given/your of the
" wig/9r. ' ' , ‘

Bring the‘gi'ven flat to the upper ”'femicirele /

of the brafs 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-
mieircle of the meridian will then cut the fun’s
place, anfwering to the day of the yearfought';
Whieh day may-be eafily found againl’c the like
plaee'of the fun among the figns on the wooden
horizon. , " " "

PROBLEM-VI.

'Tbe latitude, day of like month'ande“ azimuth

of (my known. flar hing given g. toflfind the hour .

oft/be night.

» Having refiified the globe for the latitude,

zenith, and fun’s place; lay the quadrant of

* Thehumber of degrees that the fun, moon, or any
altar, 1e from the meridian,‘either to the call onweil, is called
Its 42175145. '

altitude

3°:

w . /

.’ l

. \/‘
.. /

sot

rte we write 06142542 Glehé.
altitude t'oth'e given degree of azimuth in the ho;
rizon :' then turn the globe on its axis, until the ~

fiat comes to. the graduated edge of the qua;

drant; and when it does, the index will point
but the hour of the night. ‘

PROBLEM VII.

T he latitude of the place, the clay of the month, and
altitude 9* of my beaten flat"; heing given; tofind
the hour of the mght.

Rec’tify the globe as in the former problem;
guele at the hour of the night, and turn the
globe until the index points at the fuppofed
hour; then lay the graduated edge of the qua-
drant of altitude over the known (tar, and if the
degree of the flar’s height in the quadrant upon
the globe, anfwers exaétly to the degree of the
fiar’s obferved altitudein the heaven, you have
guefi'ed exaélly: but if the fiar 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 fiar, ‘
until its center comes to the obferved altitude in
the quadrant; and then, the index will fhew the
true time of the night.

’ * The number of degrees that the flat is above the hori~
min, as obferved by means of a common quadrant, is called
its altitude. "

PRO,~

 

Ernie Ufe oft/fie Celefliel Glade. _ ,
_\ ' P-R O'B‘L E M vnt.
flit eafi method for findz'zeg the [your of thetfiight I?)

any two. known/tars, witbom knowing either their.
‘ altitude 0r azimuth; and 119m, effizgdz'ngth‘
their: altitude and azimuth, and thereby the true _‘

meridian.

. Tie one end of a thread to a common mui’ket
bullet; and, having reétified the globe as abOve,

hold the other end of the thread in your hand, a

and carry it {lowly round betwixt your eye and
the fiarry heaven, until you find it cuts any two
known f’tars at once. Then, guefling at the
hour of the night, turn the globe until the index
points to that ‘time in the hourvcircleg which”
‘done, lay the graduated edge of the quadrant
over any one of _ thefe two flats on the globe,
which the thread cut in the heaven. If the faid
edge of the quadrant cuts the otherfiar alfo, you
have guefled the'time exactly; but if it does
not, turn the glObe'flOwly backwards or for-g
wards, until the quadrant (keptupon either fiat)
cuts them both through their centers :. and then,"
the index will point out the exaé‘t time of the
night; the degree of the horizon, cut by the
quadrant, will be the true azimuth of both. thefe
fiars from the fouth; and the liars themfelves
\Wlli cht their true altitudes in the quadrant. At
which moment, if a common azimuth compafs
be f0 fet upon a floor or level pavement, that
thefe flats 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 ,

I

5 will

30':

306

m Ufi of (A: Celeflz'al Glaze;

' will be directlan/the plane of the meridian: "
and if a line be drawn upon the floor or pave-

ment, along the courfe of the thread, and an up—
right wire be placed in the fouthmofl end of the
line, the {hadow of the wire will fall upon that ’

line, when the fun IS on the meridian, and fllines

Upon the paVement.

PROBLEM IX.

1 ,. To find the place of the mom, or of any planet; and ‘

Ibereéy Ito/126w the time of It: rgfing,foutbing, and
fetlmg.

Seek in Parker’s or Weaver’s Ephemeris the
“E 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 {hewri ‘
by the Ephenaeris, mark the fame with a chalk
upon the globe. Then, having rectified the
globe, turn it round its axis weltward ;— and as
the {aid mark comes to the eaftern fide of the
horizon, to the brafen meridian, and to the
Wefiern tide of the horizon, the index will fhew
at what time the planet rifes, comes to the meri-
dian, and fets, 1n the fame manner as it would do
for a fixed fiat.

P R o B L E M X.
:70 explain the pkenomemz‘ of the‘ harvefl-mom.

In order to do Ithis, we mull: premil'e the fol.-
lowing things. .That as the fun goes only

"" The place of the moon or planet, as feen from the
earth, is called its geocentric place.

ORCC

The Ufe qf the Celeji‘izzl Gloée.

once a year reund the ecliptic, he can'be but
once a year; in any particular point of it: and
that his motion 'is almofl: a degree every 24.
hours, at a mean rate.3 2-. »That as the moon
goes round the ecliptic once in 27 days and 8
hours, {he‘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 roundit, the moon cannot at any time
-be either in conjunction withthe fun, or oppofite
to him, in that part of the ecliptic where {he was
To the lai’t time before; but mufi travel 'as
much forwarder, as the fun has advanced in the
{aid time; which being 29% days, makes almolt
a Whole lign. Therefore, '4.- The moon‘ca‘n be
but once a year oppofit’e to the fun, in any
particular part of the ecliptic. 5. That the
moon is never full but when {he is oppolite to
thefun, becaufe at no other time can we fee all
that half of her, which the fun enlightens. 6. That
when any point of the‘ecliptie rifes, the oppofite
point fets; Therefore, when the moon is oppo—
fire to the fun, {he mui’t rife at * fun-fer. 7, That
the different figns of the ecliptic rife at very dif-
ferent” angles 'or degrees of obliquity with the
horizon, elpeCially in canfiderable latitudes; and
' that» the-finaliler this angle is, the greater is the
porrio‘fi’Of ’tliefecliptic- that rifes in any fmall part
,of time; and vice oerfci.‘ 8.‘ That, in northern
latitudes, and part of the- ecliptic rifesat fo-~fmall
an'angle with’the horizon, as 5-P‘ifces and flries do;
therefore; at greater portion of the ecliptic rifes in
"* This is not always firiétly true, becaufe the moon does
not keep in, the ecliptic, but crofl‘es it twice every month.
However, the,dififerencellneed not, be regarded in a general
' enplanation. ’

XV .‘one

307

308'

The" Ufia‘of the Ceigzz'aerlttfir.

one hour, aboutjthcfe figns, than; about any of
the refi. 9. That the moon can _.never be full
in szces and Aries but-in our autumnal months,
for at no other time of the year is the fun in the
oppofite fignsl/z'rgo and Libra. ~ , 7 . - r V
Thefe things premifed, take Igfirdegrees of
the ecliptic in- your compafl'es,‘ andgbeginnin-g at
Fifties, carry that extent all, roundithe ecliptic,
marking the places, with afichalk, "where the
points of the compafle-s fucceffively‘ fall; So
you will have the moon’s dailymotion- marked
out for one compleat revolution in the ecliptic

(according to § 2‘ of the 13?: paragraph”) .
; Reétify the globe for any confiderable-northem .
latitude, (as fuppofe thatgof».1;.ondon.)xand then,
turning the globe-round, its axis, obfervethow

‘ much of the hour—Circle the index’has gone over,

at therifing of each particular mark; on the
ecliptic; and you will find that feyenof the
marks (which take in as much of the ecliptic as
the moon goes through in a weekywi‘ll all rife
, fucceflively about Pifres and firm,“ in the time

. that the index goes over two hours. .. Therefore,

.whilf’t the moon is in Pifres and/fries,»- [he will nor:
difi'er in general above twohours; in her filing
for a whole week. r But if. youatake. notice of.
the marks on the oppofitefigns, Virgo and Libra,
you will find that [even of them take nine hours
to rife; which fhews, thatylwhenthe moon is in
thefe two figns,yihe differs. nine hours in her '
rifing withinthe compafs of ayiweek, And f0
much later~as every mark isof tiling than the
one that role next "before it, formuch later will
the moon be of tiling on any day than {hewas on
‘the day before, in the correfponding part of the
heaven, The marks about Cancer and Capricorn

' . _. ' rife

0:

3?”??? (if? of the cagzmzczobe:
‘rifé at a mean difi'e‘rencfiof time between thol'e'
about fifties and-'*I.‘z'»&-m.”i V :
Now, a‘lthongh the moon is LinfiPifces and Arie:

every month,- and" therefore muf’t rife in thofe

figns within therfpace of two hours later for a
whole Weeks: ot-‘only, ab0ut717/ minutes later
every day than {he did .on the former ; yet {he
is 'never"‘~fijll“in t‘hefe figns, abuitr’tin our antumnal
months,‘rflug‘ufi'and September, when the fun is in
Virga‘and Libra. ~Therefore, no full moon in
the year Will'eontinueto rife f0 [near the time of
fun-{ct for a-week' forfo, 'asgthtfe' two full. moons
do, which fallii‘n th'e'time of harvei’t.

-“In the‘l'win’ter' months,» the moon , is in Pifm
‘ and flrz‘miaboue her firi’t quarter ~, and as thefe-
_ figns tifeabwttnocn in'wi'n'ter', the moon’s tiling
in them, 'paffefs-i nnobferve’d. - In the fpring
months”, ‘the moon changes in thefe figns, and
“Confeqn'ently rife’s at thefame time with the fun ;
fo that it is irn'poflible to fee her at that time.
In the fn'mmermonths {he is in thefe figns about
her' third quarter, and rifes not until mid-night,
1 when: her filing is but very little taken notice
.fof -, efpecially as {he is on the decre‘afe. But'in
“the harVeft months {he is at the full, when in
thefe-figns, and being oppofite to the fun, {he
rifes when the fun fets (or foon after) and “fines
all the night. ' ‘

A I n {Outhern latitudes, Virgo and Libra rife at as
fmall angles with the horizon, as Pifces. and A’rz’es
do in the northern -, and as our fpring is at the
time oftheir harvel’t, it is plain their harvef’t full
moons mni’t be in Virgo 'and Libra; and will
therefore rife with as little difierence of time, as
ours do in szm and rifles. .

_X 2 i ' For

309

.310

flee Ufle of use Gimmick».

~ ‘, For —a fuller account of this matter, I m‘uit‘
refer the reader to my AfironOmy, in which it is

defcribed at large. - _

‘P'Ro BL'E M XI.

:To explain tine equation of time, or dzfierenee of time,

between well regulated clocks and true/im-dials.

The earth’s motion on its axis being perfectly
tequable, and thereby caufing an apparent
equable motion of the {tarry heaven round the

.fame axis,‘produced to the 'poles' of the heaven;

it is plain that equal portions of the celei’cial
equator pafs over the meridian in equal parts of
time, becaufe the axis of the world is perpendi-
cular to the plane of the equator. Andthere-

,fore, if the fun kept his annual courfe in the

celei’tial 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 bothito the plane of the equator and axis
of the world, he cannot always revolvefrotnthe
meridian to the meridian again in 24 equal
hours ; but fometimes a little fooner, and at
other times a little later, 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 {h‘ew this by a globe, make chalk-marks
all around the equator and ecliptic, at equal
difiances from one another (fuppofe 10 degrees)
beginning at flrz'e: or at Liem, where thefe two

circles interfeft each other. Then turn the _

i ' globe

 

PLATE XX.

 

 

 

_—4———“

 

8".l-v-u-a.

., ‘3’!

 

 

 

Iv
a.

 

[Err/fin

 

we Ur: pf the warm; Globe.

globe round its axis, and you will/fee that all
the [marks in the firfl: quadrant of the ecliptic, or
from the beginning of ‘Ar'z'e: to the beginning of
Cancer, come fooner to the brafen meridian than
their correfponding marks do on the equator:
thofe in the. fecond quadrant, or from the be-
ginning of Cancer to the beginning of Libra,
come later: thofe in the third quadrant, from
Liam to Capricorn, fooner; and thofe in the
fourth, from Capricorn to Aries, later. But thofe

at the beginning of each quadrant come to the .

meridian; at. the fame time with their correfpond-
ing'marks on the equator. , - '
Therefore, whilft the fun is in. the firl’t 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
fatter than a well regulated clock, which always
keeps equable or equatorial time: and whill’c he
is in the fecond and fourth quadrants, he comes
later 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 1
intervals of time between them. But as the =

moves faf’ter at fome times than at others (being;
eightdays 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. .

tothe equator,'makes up that difierence, which
islhewn by the common equation tables to be“
between good clocks and true fun-dials.

- ' * X 3 ‘ - . 7776

31 t

31.4.

Plate XX.
Fig. 1.

The are
miller}
fpbcre.

_ ' Of 1196’, 471114147}. Sphefé.’
'- ,7 -- [i ’ .iii tr 5, V‘lskgl’ii‘iigi’vi!
.5,

The dcfcriptz’m and at]? of the armzZlmy [231mm,

\Vhoever has {can a common armzllary fibers,
and underitands how to ulté 1t, tnuft be fenfible
that the machine here referred to, is of a very
diEerent, and much more advantageous con~
firuétion. And whoever has feen the curious
glafs fphere invented by- Dr. LONG, or the figure
of it in his Ai’tronomy, mLLPt know that the fur-
niture of the terrei’trial globe in thxs machine,
the form of the pedefial, and the manner of
turning either the earthly globe, Q1; the circles
which Dfurround it, are all copied from the
Doctor’ 3 glafs fphere , and that the only difi‘e-
rence is, a parcel of rings inflead of a glafs celef-
tial globe, and all the additions are a moon
within the fphere, and a fem1c1rcle upon the
pedef’tal. ‘

‘ The exterior parts of this machine are a corn.
pages of brafs rings, which repreient the princi-
pal circles of the heaven, viz. I. T he equinoé‘tial

.4.4, which is divided into 360 degrees (begin-r
ning at its interfcétion with the ecliptic 1n flrzer)

. for ofhewing the {1111’ 3 right afcenfion 111 degrees; .

and alfo into 24. hours, for lheWing 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 111 which the fun 15, on any given
day, {lands over that day 1n the cirCle 0f months.

:3. T he tropic of Cancer C C, touching the eclip-

tic at the beginning of Cancer in e, and the

tropic of Capricorn D D, touching the ecliptic at
the beginning of Cap; mm inf; each 2 3%: degrees
from

0f. the drmz'llary Sphere.
from the eqUin'ofiial'tirele; '4. The arftic circle
' ,E, and the antarétic circleF, each 23; degrees
from its refpeétive :pole at'N and S. 5. The
eq'uinoétialf :col‘u're: G G, :paffing through the
north and ‘fouth poles of the heaven at N and S,
and .thi‘OU‘g'h 'the equinoé‘tial points flries, and

Libra, .._ii't'th'e ecliptic, 7'6. Thefolf’t’iti‘alcolure .

H H, pamng thi‘onghthe poles ofath'e heaven", and
thrOugh the folfiitial points Cancer and Capricorn,
in theieeliptic. ’ ' Each quarter of the former of
thegfe corms ié‘tlifidedinto 90 degrees, from the
equinoftial to‘the“ poles of the-werld; for {hew-
ing theidediination‘of the fun, moon, and liars;
and 'each‘SQUarteriof the latter, from the ecliptic
at e and'f, to its poles ,5 and d, forvfhewin'g the
latitudes oft'he l’taré. , ~» = -
In the ’hérth‘pole‘of’the ecliptic is .a nut &, to
whic'he-iefixeélione‘end of a quadra'ntal wire, and
to the "Other én‘da "finallfun 2", which is-carried
round the ecliptic B B, by turning the nut: and
in the fouth-pole of the ecliptic is a pinat d,‘ on

Which: is 7_'an0ther ,qu‘adrant’al wire, with a‘fmallr

moonQZ 'upo'n'it,‘ which may be moved round by
handi ’b‘ut’there-is a particularcontrivancefor
rcaufing the” inoon to move in-an orbit which
.crolTesth-ee‘cliptic-at an angle-01:51,r degrees, in
two oppdfité points called the man’s. nodes; and
alfo fot fh‘ifti‘ng’ thefe points backward in the
ecliptic, as the m’aon’s nodes {hift in the heaven.
Within], thefe circular -.rings is a-fmallterref»
trial globe 1,. fixt on an axis K K, which extends
from the north and fouth’ poles of the iglobe‘at n
, and it, to thefeof the celeltial fphere-at‘N and S.
on this axis'is fixt the'fi'at celelli'al meridian LL,
which may‘be'fet direétly Over“~the meridian of
any place on the-“globe; andgthen turriéd'roti‘n‘d

with the globe, *fo as to keep over the fame-

X 4. meridian

3'3

‘3 14' of ”22’ flrhaillary Sphere;

meridian upon -it.; This flat meridian is gra-
duated the: fame wayrlas the brafs meridian of
a common globe; and its ufe is much the fame.
. To this globe is fitted‘the moveable‘ horizon
MM, fo as. t0»turn~'up0n two firong‘ wires pro-
ceeding from its fall: and‘wefi points to the
globe, and entering theglobe at oppofite points
of‘itsequator, which is: a moveable brafs ring let
into» the globe in a groove all around its equator.
The globe "may be turned by handwithin this
ring, fo as to'place any given meridian upon, it,
direétly under the celeflial meridian LL. The
horizon is divided into 360 degrees all around
its outermoft edge, within which are the points _
of the compafs, for.‘ fliewing the amplitude of
the fun and moon, both in degrees and points.
The 'celef’tial meridian L L pafl'es 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. Atthe fouth pole of the
fphere is a circle of 24 hours, , Ext to the rings,‘
and on the ”ax-is is an index which goes round
that circle, if the globe be turned round its
aXIS.‘ ~ “ ’-‘ ‘ x .
The whole fabric is fupported on a pedefial
VN, and may be elevated or depre‘fled upOn'the
joint 0, to any number of degrees from o to 90,
by means of the are P, which is fixed in the
firong brafs arm 52, and flides in the upright”
piece R, in which is a {crew at r, to fix it at any“
proper elevation. . ~
In the box 51” aretwo wheels (as in Dr. Long’s
fphere) and two pinions, whofe axes come out
at Vand U; either of which may be turned by
the fmall winch W When the winch is put
upon the axis V, and turned backward, the ter-
* , refirial

3

Of the drmz‘flary- Sphere. A
refirial globe, with its horizon and celel‘tial me.
ridian, keepat‘ reft ;" and the whole fphere of

circles turn-s round from call, by ‘fouth, to weft,

carrying the fun 2”, and mOon Z, round the fame
way, andcaufing them to rife above and fet be-
low the horizon. But when the winch is put:
upon the axis U, and turned forward, the fphere
With thefun and moon keep at refi; and the
earth, with its horizon and‘meridian, turn round
from‘wel’t, by fouth, to eal’t; and bring the fame
poin‘tsof' the horizon to the fun and moon, to
which thefe bodies came when the earth kept at
tell, and th‘eywere carried round it; fhewing
that they rife and fet in thefame points of the
horizon, and at the fame times in the hour-Circle,
whether the motion be in the earth or in the
h‘eaven.‘ 'If the earthly globe be turned, the
hour~index goes round its houncircle; but if
the fphere be turned, the hour-circle goes round
below the.index. '

And {0, by this‘conl’trué‘tion, the machine is
equally fitted to {hew either the real motiomof

the earth, or the apparent morion of the»

heaven. ‘ . .

To rectify the fphere for ufe, firit flacken the
{crew r in the upright fiem R, and taking hold
‘ of the arm 92, move it up Or dawn until the‘
given degree of la’titudofor any place be at the
fide of the item R; and then the axis of the.
fphere will be properly elevated, lb as to {land
parallel to‘the axis of the world, if the machine
be fer north and fouth by a {mall compafs: this
done, count the latitude from the. north-pole,
upon the celefiial 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 2” comes to the given’day of the‘year in"

- ' ‘ the

315

 

316

Prelimi-
varies.

' farther upon it," t

* Qffiieiiflge

theoriecliptiehandj theftm will! hey-{ago ita'pin‘opet
elm-for, thacgdayx findixhe place‘e-inihenaeén’s
aleending node, and alfo the place ’offhegghoon,
hie-9:1.Ephsmcrisxand {ct them filghcfiiCWYd-
ingly.~lail1y,»tur:n.ihc Winch. mentil either the 7
59439011365 to the-meridianL L,.ot unt;il;the- me—

ragidjame‘omes to the fun (accordingas ycuwam

the fphere or earth to move) and EtthchOLir-
index‘tov theXll, marked noon,~ agagthe whole
machine will; be , refitified. 7. Then turn the
winch, and obiIerve when the {unflior'nfoon rife
and let in the horizon, and the hoii’reindefx will
fliewithe times thereoffor the givehfday, . , _

«Asrthol‘e who underfiand the life Gillie glObes
will be at nolofs to work many;otheftilroblen'is
by this fphere, it is. needlel’s toil enfirge any

 

The pzjmzplm and/1r! (5f dialing;
’ Diél‘is a plane, uponwhiehlifies' are deg.
I. _ dfcfribed in fuch a manner, thanthéflaadOw
of [a wire; or of the upper edge of afplate Pti'le,
ereé‘ted perpendicularly on the planeof the dial,
mayfhew‘thetrue‘vtime of‘the day.” .. _
. .The edge Cf theplate by which theotime of
the dayis found, i‘s‘called the fine golf" the dial,
Whieh m’ul’t be parallel to the earth’s 'aXis; and
the line on which the {aid plate. .iseteé‘ted, is
Called the fubflile. ' i . g . '_ .

, Theangleincluded between 'the'i'ftibl’tile and
fine, is'ca-lled the elevation, orfhei'ght of the
fille. \ ' . , ’ ' I \
Thofe dials whole planes are parallel to the '
plane of the horizon, are called horizontal dials 5 /
‘ ' and

Of -;"Dz'“alz'ng;
and thofeid‘ials whOfe planes are perpendicular
to the plane'ofthe horizon, are called vertical,
or erect "dials. ' ,

Thole area dials, whofe planes‘ direétly front '

‘ the north or‘ fouth, are calledidireéi: north or
"fouth dials; and all other ereé‘t dials are called
decliners’, "becaufe their planes are turned away
' from the nnrth or fouth.

Thofe dials who-f6 planes are neither parallel
nor perpendicular to the plane of the horizon,
are callhd inclining, got reclining dials, accord-
ing as their planes make-acute or obtufe angles
with the'horizon;,and if their planes are alfo
turned "afide from facing the-fouth or north,
, they are called declining-inclining, or declining-
reclining dials. ‘

Theinterfeé‘tion of the plane of the dial, with
that of the meridian, pafling through the ftilc,
is called the meridian Qf the dial, or the heur—
line of XII. '

Thofe meridians, whofe planes pafs through
the Ptile, and make angles of 15, go, 45, 6Q
75, and 90 degrees with the meridian of the
place (which marksthe hour-line of XII) are
calledhour-‘circles; and their interfeétions with
the plane” of the dial, are called hour-lines.

In all declining dials, the fubftile makes an
angle with the hour-line oleI, and this angle
is called the :dii’tance of the fubf’tile frbm the
meridian, .

The declining plane’s difi'erence of longitude,
is the angle formed at the interfeétion of the
fiileand' plane of the dial, by! two meridians;
one of which paITes through the hour-line of XII,
and the other through the fubfiile. '

This

31 7..

318'.

Plate XX.
Fig! 2.

The uni-

verfal

principle
on which
dialing

depends,

Horizon;

- m1 dial.

29'

£1)

Of Dialing. .

This muck'nez’ngw premifea’ concerning dial: in g3;
new], wefltnll now proceed to explain the dzflrent
methods of their confirnfiion. - . _

" If the whole earth 2: Pr 1) were tranfparent,
and hollow, like aifphere of 'glafs, and had its
equator divided into 24 equal parts, by fo many
meridian rfe-micircles, a, 6, c,.-d, e, f, g, &c. one
owahich is the geOgraphicalrmeridianof any:
given place, as'London (which is fuppofed to
be at the point a ;) "andvif the hours ,of XII“
were marked at the'equator, both upon- that
meridian‘and the Oppofite- one, and all“ the roll:

.of‘ the hours in order on the refl: of the meri-

dians, thofe meridians would be the hour-circles
of London: then, if the fphere had an opake
axis, as, P E p, terminating in the poles P and . ,
p, the ihadow of the axis would fall upon’every
particular meridian and hour, (when the fun
came to the plane of the oppofite meridian, and
would confequently thew the time. at London,
and at all other places on the meridian of
London. ‘ ' i '
lf‘this fphere was cut through the middleby
a folid plane 113 C D, in the rational horizon of
London, one half of the axis E P wohld be ‘
above the plane, and -the~ other half below it ;4
and" if firaight lines were drawn from. the center
of the plane, to theft: points where its circum-r
ference is cut by the hour-circles of the fphere,
that]: lines would be the hour-lines of: abode
Zontal dial for London : for the {hadow of the
axis Would falli‘upon each particularhounline

/ of the dial, when it fell upon the like hour~circle ,

ofthe-‘fphere; - ~ ' ‘ . t -
If the plane- which cuts the fphere be upright;
asfl F C G, touching the given place (London)
at F, and direcily facing the meridian of Lon-
don,

Of Dialing. . 3:9

don, it will r.thert’becorne the Blane of, an ereé't
d1re€t {Outh (1131:“ and ifflght lines. be. drawn Vertical
from its-Center. E, to t'ho‘feflpoirtt‘s of its.cireum,- dial'
:ference where the hourfcirc‘les" yofsthe fphere cut '
:it, thefe.Will be thehhour-‘linesfi.of”a..vettic‘a’l or

dir‘eé‘t [fouth‘ dial for London, to W‘hieh‘ the hours

are to be“ fet as it) the figure (echtrary; to thofe

on a horizontal dial) and the. lowerhalf E1: of

the axis ‘willleaf‘t a thado‘w' on. the hour of the

day in this dial, at, the fame time that it Would

fall upon; theiljke‘ “our-circle of the fphetfe, if

the dial-plane Wasmnotiu the wéyf v‘

s f the: Plane ‘ ('{till facing thei'metfidian); be Ifldiningf
made to incline, Ottccline» by any given} numbfirrafid."‘ '

,3 .‘ _. . \ r t, .V .V‘ .r .. ”mg

of d¢gr¢cs, the bout-CWCECS 95m? fpherc Wilma.
Vfiillr cutthe edge oftheiplane in thofe'points to '
which the ‘.hour;1;nes ‘ mutt be 1 drewui‘ firefight

frOm the Center; ‘a‘ndth‘e’ éx'i’s of'thfe fpherefWiil

r-cafl a {hadow on: thefe lines ’étthel‘refpeft‘ive ‘
hours. Iheli’lketwill {till hold; if the plane be Dam”
'made to decline by any, given number of ngYCCSdfalg‘ 7’ .
from the meridianihtovvards the eafl: or weft! '
provided the declination he lefs than 90 degrees,

or the reclinatiortsbe Vlefs, than the lee-’latitud‘e

of the place: _and the axis of the {phere will be
,_av guomon, or fitletvfor theiydiel’. But it cannot
the a gnomon, “when. the ‘deelination’ isf'q’uite 9;)
degrees; “01““!th the reelinatioh is equal to

the co~latitudegdbecaufe ‘in :thefeitwo :cafes,

the axis has no elevation above the plane of the

vdiah ' ‘, . d, _, . .1
And thus it appears, that the, plgneof "eVefiy

dial reprefents. the; plane of ‘fome . great: circle
upon the earth _§, and‘the gnomOd the earth’s

axis, whether itibe afmall wire, as inthe above
figures, or the'edge “of a that plate, ’as in? the
‘ comm-on horizontal dialst~ _ -

AlThe.

‘329 Of :Diala'hg.

' I The Whole earth, as tto its=btill<,*is' but 31’
point, if compared-to its :d‘illanc‘e from the fun:
and therefore, if a fmall fphere of glafs be‘placed
Upon any part of theeart‘h’s‘ 'furfaeez, «f0 that
itS’axis be parallel’to thie‘axis‘o’f' the'earth, and
the ‘fphere have fuc’h lines upon irrand fuch
planes within" it, as'above ‘deferibed; it will
{he'w the hoursof' the'day as ‘trulyaz’s’= if» it were
placed at theearth’s center, and-'thelhell of'the
ear-th‘Were-as tran‘fpare'nt as gran; . '

\ But bec'au'f'e it is i’mpofli’ble to ”hate 3‘ hollow
‘ fphere of glafs 'perfeftly truegblown round a
"Fig- A} ‘folid'plane; or if it was,”we ‘c‘o‘uld‘ not get at
the plane within theglafs’ td‘fet'it in any given
pofition ; * we make me of a "wire-{phere to ex-
plain the principles of dialihg,‘”by‘ joining 2‘4.
femicircl‘es’ together at the'poles, and putting a
thin flat plate of brafs within it. _ ' g
Dialing A common globe, of ‘12 inches'diameter, has
by the generally'24 meridian femicirele‘sg ‘dr'awnu'po‘n
gigs; it. If fire-h a globe be elevated toithelatitude of
31056,. ‘ any given place, "and turned about until any one
of 'thefe meridians Cuts the ~hori20n in the north
point, where the hour of 'XHT-is fitppo’fed to
be’marked,=fthe ref: of’thei ‘méridians"'will cut
the horizon at the refpeétive‘dii’taneesof all the
other hours from XII. Then, if'th'efe points of
diflance be marked "on the‘horizon, and the
globe be taken“ out of I the” horizon; and- a flat
board or plate be put into its’pla‘ce, even with
the furface of the horizon 3' and if l’tra'ig‘ht lines
be drawn from the center of the board, to thofe
points of dil’tance on the horizon which were
cut by the 24 meridian femieircles’, thefe lines
will be the hour-lines of a horizontal dialfor
that latitude, the edge of whofegnomon mull
be in the very fame fituation that the axis of the
’ 5 . globe

 

Of. Dialing“ '

' globe was, before it was taken out of the her]-
zon: that is, the gnomon mul’c make an angle
with tJ1;e plane of the dial, equal to the latitude
of the place for which the dial 13 made. -

If the pole of the globe be elevated to the
*eo-latitude of the gwen place, ahd any meri-
diau be brought to the north point of the- hori-
zen; the refitof the meridians will cut the horizon
in the r’efpeétiv-e dil’tances of all the hours from
XII, for‘ a direélzfouth dial}, whole gnomon mui’c
make" an anghe- with the plane of the dial, equal
to the eo- latitude of the1pl_ace,an’d the hours
mul’t be fees the centraty way on this dial, to
what they are- on the horizontal

But if your. globe have more than 24 men-
dian femicit-cles upon it, you muf’c take the
following methed- for making- horizontal and
fowl) dmfs. -

Elevate the pole to the latitude of your place, To com
and turn the glbbe until any particular meridian flrué’t a
(fuppofe the fitl’t) eomes to the north point of “WWW
the heriZon, and the oppolite meridian will cut
the horihon in the fouth. Then, ice the hour-
index to the uppermol‘c XII On its circle, which
done, turn the globe welt-ward until 15 degrees
of the equator pafs under the brafen meridian,
and then the: ham-index will be art], (for the fun
moves 1 5 degrees every.h01Jr)vand the firll: meri-
dian-.Willicu-tvehez horizon,_in;,;the number of de-
grees from the north point, that I is dil’tant from
XII. Turn £9113} until other I .9 degrees of the
equator pafs under the brafen meridian, and the
hour-index wilI then be at II and the firl’c me-

05
be
u

‘5,

"‘ If the latitude be fubtraeled from 90 degrees,_ the re-
mainder 1s called the co-latitude, or complement of the
latitude. " .

ridian

 

322

Of Dialing.

ridian will cut the horizon in the number of
degrees that 11 is dii’tant from XII : and f0, by
making 15 degrees of the equator pafs under
the brafen meridian for every hour, the firi’t me-
ridian of the globe will cut the horizon in the
dif’tan’ces‘ofall the hours from XII to V1, which
is jul‘t 90 degrees; and then you need go no
farther, for the diflances of XI, X, IX, VIII,
VII, and VI, in the .forenoon, are the fame
from XII, as the diflances 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.0ther half of the dial:
/ but no more of thefe lines need be drawn, than

what anfwer to the fun’s continuance above the

horizon of your place on the longeil clay, which
'may be eafily found by the,26th problem of the

foregoing leclure. .

Thus, to make ‘a horizontal dial for the latif
tude of London, which is 51-; degrees north,
elevate the. north pole of the globe 51»; degrees

above the north point of thehorizon, ,and then

turn the globe, until thegfirfl meridian (which
is that of London on the Englifh terrei’trial
globe) cuts the north point of the horizon, and
fet the hour-index to XII at noon.

‘ Then, turning the-globe wei’tward until the
index points fucceflively to I, II, III, 1111, V,
and VI, in the afternoon; or until 15, go, 45,
60, 75, and 90-degrees of the equator pafs under
the brafen meridian, you Will find that the firit
meridian of the globe cuts the horizon in the
following numbers of degrees from]. the north
towards the call, viz. 11.}, 24%, 38%,, 53%,
7 H25, and 90 'gWthh are therefpeé‘tivc’: dil’tances
of the above hours from XII upon the plane of
the horizon. ‘ "

a - 4. , ' To

 

 

 

 

PLATE XXL

 

 

 

 

 

 

 

 

 

 

Egg. ‘2.

171’
.I.

 

 

 

 

 

 

 

 

 

 

‘ITI'V
v1

 

 

 

 

 

ca’

.2.

 

 

 

 

 

 

 

 

Of Dialing; ‘ '323
To transfer thefe,‘ and the ref‘: of the hours, PlateXXIz
. to a horizontal plane, draw the parallel right Fig. 1.
lines at and bd upon that plane, as far from '
each other as. is equal to the intended thicknefs
of the“ gnomon or {tile of the dial, and the {pace
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
g 19, and fetting one foot of your compafl‘es in the
interfeétion a, as a center, defcribe the quadrant ,
g e with any convenient radius or opening of the
compafl'eszxthen, fetting One foot in the inter-
feétion Zr, as a center, with the fame radius de-
fcribe the quadrant f b, and divide each qua-
drant into 90 equal partsor degrees, as in the
figure. .
Becaufe the hour-lines are lefs dil’tant from-
each other about noon, than in any other part of
the dial, it is belt to have the centers of t‘hefe 1‘
quadrants at a little dil’tance from the center of
the dial-plane, on the fide oppofite to Xll, in
order to enlarge the hour-difiances 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. ' *
Lay a ruler over the point 5 (and keeping it
there for the center of all the afternoon hours in ~
the quadrant fb) draw the hour-line of 1,;
a through I 1; degrees in the quadrant; the hour-
line of II, through 24;; degrees ; of Ill, through
3811,- degrees; 1111, through 53—5, anth‘hrough '
71—2—5: and becaufe the fun rifes about four in
the morning, on the ’longefl: days at London,
continue the hour-lines of III] and V, in the
afternoon, throngh the center 5 tothe Oppofite "
tide of the dial.—-—This done, lay the ruler to the

center a, of the quadrant e g, and through the
' Y like

1324,

f V Dialing.

like divifions or degrees of that quadrant, 17in

HT , 24%;, 38T,, 53;, and 7IT‘T, draWthe fore-

.noon hour lines of XI, X, IX, VIII, and VII;

and becaufe the fun fets not befme eight 1n the
evening on the longett days, continue the hour-

\ lines of VIIandVIIl 1n the forenoon, through the

Gen-tern, ’tonl and VIIIin the afternoon; and-

all the hour-lines will. befinifheds on~this dial -,

to which the hours may be fet, as in the figure.
Lafily, through 51T degrees of either bquad-

. rant, and from its center, draw the right line tag

for the hy pot henufe or axis of the gnomon erg z' ,
and from g, Iet fall the perpendicular g 2, upon
the meridian line a z, and there 11111. I be a triangle
made, whofe Iides are a g, g z, and z a. If a
plate fimilar to this triangle be made as thick as
the diftance between thelines a c and [1d, and fet
upright between them, touching at a and. 5, its

' hypothenufe ng will be parallel to the axis of the

world, when the dial IS 111th fet , and will cafi a
fl1adoiv on the hour of the day/._. —

N. B. The trouble of dividing the two quad-
rants may be faved, if you have a feaIze with a. _
line of chords upon it, fuch as that on the right,
hand-of the plate: for if yen extend. thecom-V
pai’fes from o to 60 degreesof the line of chords,
and with that extent, as a radius, defc'ribe the
two q t1adrants upon their refpeétite centers, the

, above diltances may be taken with the com-

Pig. 2.-

10 C05‘
ruét 313

6:653/01535

dial

‘ pal lies upon the line, and fet ofl' upon the quad—

rants.
To matte cm eVeEZ cIZ'V'efi fautb dzczl. Elevatethe
pole to the co latitude of your place, and pro- ‘

_ ceed- in a II iefpee‘ts as above taught for the hori-

zontal d1al, from VI in the morning to VI 111
the afternoon,o only the hours mull: be reverfed ‘

. as in the figure, and the hypothenufe a g, of the

gnomoo '

 

\ Of Dialing:

gnomon a g f,‘ mul’t make an angle With the dial; ,

plane equal to the co-la-titude of the place. As
the' fun can ihine-no' longer on this dial, than
from fikinthe morning until fix in the evening,
there 'is no oecafion for having any more than
twelve hours upon it. ‘-

325

‘To make rm area“ dial, declining from the four/y'To con-

tritvards t/ae eafl‘ or wéfl. Elevate the pole to the
latitude of your place,- and {crew the-quadrant of

clines towards the eaf‘t (which we {hall fupp‘ofe

i‘t‘to do- ,at prefent) {count in the horizon the.

degrees of declination, fromthe eal’t 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 fuppofe the

fi'rl’t‘meridian) direétly under the graduated edger

. of the ,‘u‘pper'part of the brafen meridian, and

fet the hour-index to XII at noon. Then, keep-,
.i-ng the quadrant of altitude at the degree of

declination in the horizon, turn the globe ealt—
ward on its axis, and obferize the degrees cut by
the firit» meridian in the quadrant of altitude
(Counted from the zenith) as thehour-index’
comes to Xi, X, IX, 8m. in'the forenoon, or as

1 5, 30, 4 5, &c. degrees of the equator pals under V

the brafen meridian at thefe hours ‘refpeé’tively ;
and the‘degrees then cut in the quadrant by the
- firfl: meridian, are the refpeé‘tive diltanees of the
forenoon hours from XII on the plane of the
dialeuThen, \for the afternoon hours, turn the
quadrant of altitude round the zenith until it
' comes to the degree in the horizon ovpp‘ofite to
that where it was placed before; namely,“ as far
from- the weft point of the horiZon toWards the

fonth, as it was fet atfifirl’t from-the eal‘t point ten»

wards the north 5 and turn the globe wei‘tward
,, ’ Y 2 ' on

firuét an
ereé? de-
. t _ .- ‘ ,, _ (lining
altitude” to the zenith. Then, If your dial de- dial.

i 326

Of Dialing: .

on its axis, until the firft meridian comes to the
braan meridian again, and the hour- index to
XII: then, Continue to turn the globe well-

‘ward, and as the index points to the afternoon

hours I, II, III, 85¢. or as 15, 30, 45, 8“; de-
grees of the equator pafs under the brafen meri-

‘ dian, the firl‘t meridian will cut the quadrant of

altitude in the refpeétive number of degrees
from the zenith, that each of thefe hours is from

‘ XIIon the dial.-——And note, that when the firft

1‘

meridian goes off the quadrant at the horizon, in
the fOrenoon, the hounindex fhews the time
when the fun will come upon this dial: and
when it goes olf'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-difiances 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 direéled.
In all declining dials, the line on which the,
frile or gnomon fiands (commonly called the
fun/Malina) makes an angle with the twelve
o’clock line, and fal lls among the forenoon hour-
lines, if the dial declines towards the end , and
among the afternoon hour-lines, When the dial
declines towards the weft, that is, to the left
hand from the twelve o ’clock line 1n the former
cale, and to the right hand from it in the
latter.
, To find the difiance of the fubfiile from the
twelve o’clock line, if your dial declines from
the fouth toward the cafe, count the degrees
of that declination in the horizon from the call:
point toward the north, and bring the lower end
of the quadrant of altitude to that degree of
declination

, Of Dialing;
declination where the reckoning ends: then,"
turn the globe until the firl’t meridian cuts the
horizon in the like number of degrees, Counted
from the fouth point toward the eafi; and the
quadrant and full: meridian will then crofs one
another at right angles, and the number of de-
grees of the quadrant, which are intercepted
between the firi’t meridian and the zenith, is
equal to the diftance of the fubl’tile line from the
twelve o’clock line ~, and the number of degrees

of the firi’t meridian, which are intercepted be— .

tween the quadrant and the north pole, is equal
to the elevation of the {’tile above the plane of
the dial. ' _ ‘ '

If the dial declines wet’tward from the fouth,
count that declination from the call: 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 dii’tance of the fubf’tile
from themeridian’: and for the afternoon hours,
bring the quadrant to the oppofite degree in the
horizon, namely, as far from the weft towards

the north, and then proceed in all refpeéts as '

above.”‘~

Thus, we have finilhedour declining dial;
' and in ID doing, we made fOur dials, viz.

1A.,north dial, declining eafizward by the
fame number of degrees. 2. A north dial, de-
clining the fame" number wei’t. 3. A fouth
dial, declining eaf’c. And, 4.. a fouth dial de-
clining wef’t. Only, placing the proper number
of hours, and the {tile or gnomon refpet‘iively,
upon each plane; For (as above-mentioned)

in the fouth-wel’t plane, the fubfiilar-line falls '

among the afternoon hours; and in the fouth-
eal’t, of the fame declination among the forenoon
' Y 3 hours,

327':

328 ,

Aneafi
rnethod
fbr con-
‘ flrué’tin g
ofgfiak.

Fig? 3.

' Of Dialing;

hours, at equal dilianees from XII. And Io,
all the morning hours on the weft decliner will
be like the afternoon hours on the eal‘t deeliner:

‘the fouth eafl: deeliner will produce the north-

weft deeliner ; and the f011th-W6fl2 decliner, the
north- eaft decliner, by only extending the hour-
lines, {tile and fubfiile, quite throughb the center:
the axis of the {tile ( or edge that calls the lhadow
on the hour of the day) being 1n a l dials what-
ever parallel to the axis of the world, and come-
quently pointing tOWards- the north pole of the

1 heaven 111 north latitudes, and towards the foutlt

pole, in fouth latitudes 'See more of 111211121111
fo Mowing Zefiure. ,

But becaufe every one who would like to make
a dial, may perhaps not be provided with a globe
to afiil’t him, and may probably not underfiand
the method of doing 1t by logarithmic calcula—
tion- , we ihall lhew Dhow to perform it by the
plain dialing lines, or (cake 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 lcales commonly fold
by the mathematical infirument makers.

This 13 the eafief’t of all mechanical methods, .
and by much the belt, when the lines are truly
divided: not only the half hours and quarters
may be laid down by all of them, butevery fifth
minute by mof’t, and every fingle minute by
thofe where the line of hours is a foot in” length.

Having drawn your double meridian line a 5,
c d, on the plane intended for a horizontal dial,
and croIIed 1t at right angles by the fix o’clock line
fa (as in F113. 1. ) take the latitude of your place
with the compafles, 1n the Icale of latitudes, and
Iet that extent from c to e, and from a to f, on
the fix 9 ’elocl; line: then, taking the whokle fix

.. QUI5

\

 

. Of Dialing. .
hours between the points of the com-pallet in "the

fcale of hours, with that extent let one foot in the »

point r, and let‘the other font fall where it will
upon the meridian line c d, as at (2?. Do the fame
fromf to [9, and draw the right lines 6 d andfbt
each of which will be equal in length to the whole
{Cale of hours. ' This done», letting one foot of
the c-ompalles in the beginning of the fcale atXII,
' and extending the other to each hour on the
feale, lay of? thefe extents from 43 [0‘16 fer the
afternoon- hours, and from 5 to f for th-ofeofthe
forenoon: this will divide the lines de‘ and 5f
in the fame manner as the hour—{cale is divided»,
at 1, 2,3, 4, 5 and! 6-, on'which the quarters
may alfo be laid down, if required. Then, lay-
ing a ruler on the point 6, draw the firlt five
hours in the afternoon,rfrom that point, through
the dors er: the numeral figures 1, 2, 3, 4, 5, on

the line d e; andr’continue the lines ofllll and V ,

throughthe center 6 to the other fide of the dial,

for the like hours of the morning; which done, _

lay the ruler on 'the point or, and draw the lal’t

five hours in the forenoon through thedors ’

5, 43 3,2, I, on the ,linefZi; continuing the‘
hour-lines of VII and VIII through the centera
to the Other fide of the dial, for the like hours
of the evening; and fet the hours to their re-
fpeétive lines as in the figure. Laltly, make'the
gnomon the fame way as taught above for the
horizontal dial, and the whole will be finilhed. "

i To" make an ereét fouth dial, take the co-la-
titude of your place from the fcale of latitudes,
and then proceed in all refpeéts for thehour—
lines, as in the horiZontal dial; only reverfing

the hours, as‘in Fig. 2 -, and making the angle; ’

9f the {"tile’s height equal to the co—latitude.
' Y 4 ' ‘- . I have

s]

.329

.330

Of Dialing."

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 praftice, to every quarter
of an hour. ' This fcale may be cut off from the
plate, and paf’ted on wood, or upon the infide of

i ‘One of the boards of this book 3 and then it will

Fig. 4.

_ Horizon-
?! dial.

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 fhrinks as the
paper dries: but when it is wetted again, it
firetches to’fthe fame fize as when newly printed;
and if paf’ted on while wet, it will remain of that
fize afterward. ,9 -

But left the young dialift fhould have neither .
globe nor wooden i fcale, and {hould tear or ,
otherwife fpoil the paper one in pai’ting, we {hall
now fhew him how he may make a dial Without .
any of thefe helps. , Only, if he has not a line
of chords, he mui’t divide a quadrant into 90
equal parts or degrees for taking the proper angle
of the f’tile’s elevation, which is eafily done.

With any opening of the compafles, as Z L,-
defcribe the two femicircles L F It and L 5216,
upon the centers Z and z, where the fix o’clock
line croITes the double meridian line, and divide
each femicircle into 12 equal parts, beginning at i
L (though, fitic‘tly fpeaking, only the quadrants
from L to the fix o’clock line need be divided) :
then connect the divifions which are equidif’tant
from L, by the parallel lines K M, IN, HO, G P,
and F Q; Draw 1/ Z for the hypothenufe of the
fiile, making the angle VZ E equal to the lati- ‘
titude of your place -,4 and continue the line VZ to
R, Draw the line R r parallel to the fix o’clock
line, and fet off the dii’tance a K from Z to i” ,_

3 ~ It

 

 

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PLATE XXII.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Of Dialing. , 331 N
the dil’tance b [from Z to X, c H from Z to W',
dG from Z to T, and eFfrom Z to S. Then
draw the lines 8 5, €17, Wm, Xx, and Ty, each
parallel to R r. Set oil” the dil’tancey Tfrorn a
to I 1, and fromf to I 3 the dillance forom Z)
to to, and fromg to 2 ; lefrom c to 9, and
from b to 3,9; t ETfrom d to 8,. and from 2' to
4, s S from e to 7, and from n to 5. Then lay-‘
ing a ruler to the center Z, draw the forenoon
hour—lines through the points 11, lo, 9, 8, 7;
and laying it to the center 2, 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
1111 and V through the center 2, to the oppofite
fide, for the like morning hours. Set the hours
to thefe lines as, in the figure, and then erect
the {tile or gnomon, and the horizontal dial will
be finiihed.
To conflruét a fouth dial, draw the line V Z, «Tomb
making an angle with the meridian Z L equal dial‘
to the co-latitude of your place; and proceed in”
all refperfts 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 coni’trué‘ting the dialing lines, and
ionic others; which is as follows.
1 With any opening of the compafies, as E A, Plate.
according to the intended length of the feale,XXH°“
defcribe the circle AD C B, and crofs it at right
angles by the diameters C'E fl, and D E B. Fig. 1.
Divide the quadrant z! B firl’t into 9 equal parts, $415713 .
and then each part into 10'; f0 {hall the quadrant fgdilrizlg‘iv '
he diyidecl into 99 equal parts or degrees. Draw ed. '
a " J ‘ i ., the

33'2- \

,Of Dialing; ..

the right liner! F B for the chord of this quad-s
rant, andrfetting one foor of “the compafl'esin
the point, fl, extend the Other to the feVeral divi-
fions of the quadrant, and transfer thefe divifion's
to the lineflFB by the arcs 10 m,‘ 29 20, &C.
and this will be a line of chords, divided into 90
unequal parts 5 which, if transferred from'the ‘
line back again to the quadrant, will 'di’videfic
equally. lt‘is: plain by thefigure, that the dill
trance from d to 60 in the line of‘ chords, is jut-t
equal to flE,*the radius .of the circle from Which
that line «is made ; _ for if the are 60 60 be con-
tinued, of which 11 is the center,gitrgoes exactly
through the center E 'of' the are 22 B. . i

, And therefore, in’laying down any number of
degrees on a circle, by the line‘of chords, you \
muf’t firfi: open the compailes f0, as to take in
qut 60 degrees: upon that line, as from d to 6‘0:
and then, with that extent, as a radius,,de{cribe
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 compaf'fes in’ the
beginning of the chord line, as at 21, and extend
the other to‘ the numberlof degrees you Want
upon the line, which extent, applied to the circle,
will include the like number of degrees upon
it. >
Divide the quadrant C D into go equal parts,
and from each point'of divifio‘n dra'wiright lines,
as}, k, 2, &c. to the line CE; all perpendicular
to that line, andkparallel to D E, which will di-
vide E C into a line of fines; and although thefe
are feldom put among thedialing lines on a fcale,
yet they aflifi: in drawing the line" of latitudes,
For, ifa 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,
‘ . 2.5:

. i Of Dialifig.

as B a, a 5, 85¢. {hewn by the right lines 10 a,
20 Z, 30 c, &C. drawn along the edge of the ruler.

Ifrthe right.- line B C be drawn, fubtending thist

quadrant, and the nearet’t dif’tances B a, B b, B c,
Sac.» be taken in, the compafles from B,’ and fet
upon this line in the-fame manner as direéted for
the line of chords, it will make a linebf latitudes
30; equal inilen‘gth to the line of chords flBg
and of-an eq a1 number of divifions, but very
unequal as to their lengths. , ‘

Draw the right line'D G A, fubtending’the.

quadrant D A -, and parallel to it, draw the right
line ‘7" s, touching‘the quadrant D A? at the numeL

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 line rs, whieh will divide it ‘a’tithe points
where the fix "hours are to be placed, as in the
figure. If every fixth part of the quadrant be
fubdiyided into four equal parts,- right lines,
drawnfrom the center: through thef'e points of
divi-fion, and continued to the line M, will divide
each hour upon it into quarters.

as;

In Fig. 2. We have the reprefentati'o'n of a Adialm
portable dial, which may; be eafily drawn On a a card’-

card, and carried in a pocket-book._ The lines
a 22’, a b and b c of the gnomon muft be cut quite
through the card; and as the end a b of thergno-

men 'is raifed occafionally above the plane of the ‘

,. dial, it turns upon the uncut line ed as on a
hinge. The line dotted AB mutt be flit quite
through the card, and the thread mull 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 {mall plummet D,
and on the middle of it a {mall bead for {hewing
the'hour of the day,

To,

3,34

‘ 0f Dialing; ~

To rectify this dial, fet the thread in the
flit right againf’t the day of the month, and
firetch the thread from. the day of the month
over the angular point where the curve lines
meet at XII ; then, fhift the bead to that point ,
on the thread, 'and the dial will be rectified.

To find the hour of the day, raife 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 uppermofi: edge of the lhadow
of the gnomon may jul’t cover the fiadow-lz'ne;
and the bead thenplaying freely; on the face of
the'dial, by the weight of the plummet,»iwill
{hew the time of the day among the hour-lines,
as it is forenoon‘ or afternoon. -

To find the time of fun-tiling 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-rifingamong 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 fon’s declination, firetch the thread

a from the day of the month over the angular

point at XI], and it will cut the fun’s declina-
tion, as it is north or fouth, for that day, in the
arched fcale 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’ih the fcale of months.

The confirué‘tiOn of this dial is very cafy,
efpecially if the reader compares it all along ,
‘1 - » Wit,

with Fig. 3. as he reads the following eXp-lana:
tion of that figure. ‘ , A -
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 C D 3‘ then upon C, as a center, '
with the radius C A, defcribe the femicircle A EL,
and divide it into 12 equal ‘parts (beginning at
A) as Ar, A 5, &c. and from» thefe points of
divifion, draw the hounlines r, s,‘ t, u, ‘v, E, w,
and or, all parallel to the fix o’clock line EC.
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 D 0, making the angle S AB equal to the
latitude of your place. Upon the center A de—
fcribe the arch R S T, and let olic upon itthe arcs,
S R and ST, each equal. to 2 3% degrees, for the
fun’s greatef’t declination ; and divide them into
23-; equal parts, as in Fig. 2. Through the
interfeé’tion D of the lines E C D and A D o, ‘
draw the right line FDG at right angles to
A D 0. Lay a ruler to the points A and R, and ,1
draw the line ARF through 23—;— degrees of
fouth declination in the are S R 3 and , then lay—
ing the ruler to the‘ points A and T, draw the line
A T G through 23% degrees of north declination.
in the are S 7’: f0 {hall the lines AR F and;
A TG cut the line FD G in the proper length
for the fcale of months. Upon the center D,
with the radius D F, defcribe the femicircle ,
F o G; and divide it into fix equal parts, F m, _
m 72, n o, &c. and from thefe points of divilion.
draw the right lines 772 In, 721', 1) la, and g Leach
parallel to o D. Then fetting One foot of the
compall‘es in the point F, extend the other to A,
and defcribe‘the are A 2 H for the tropic of 15- :
with the fame extent, fetting one foot in G, de-

— 7 ‘ fcribe

— 336

Fig. 4. ~

' Of Dialifigfifi

fcrihe the are ’11 E O for the tropicjof' 63., Netti:
fetting one foot in the point b, and extending
the other: ‘to if, defcribe. the arc flCI for the
beginnings of the figns :3: and 1‘ ’; and with the
fame extent, fetting one foot in the point I, de—
fcribe the are flN for the beginningsh‘of the
figns 11 and .51. Set one foot in the‘point i, and
having extended the other to A, defcribe the arc
dK for the beginnings of the figns ,x and n1 ;
and with the fame extent, fet one'foot in it, 3 and
defcribe the are .4 M for the beginnings of the
figns 3 and 1112.. Then, fett‘ing one foot in the“
point D, and extending the other to 1!, defcribe
the curve AL for the beginnings of no and '4; 4,
and the figns will be finilhed. This done, lay a.
ruler from the point A! over the fun’s declination
in the arch R S T (found by. the following table)
for every‘fifth day'of the year; and where the
ruler cuts ,the line FD G, make marks," and »
place the days of the months right againi’t thefe
marks, in the manner {hewn by Fig. 2. Lafily,
draw the fhadow-line P Qparallel to the occult _
line'flB; make the gnomon, and fet the hours
to their refpeétive lines, as in Fig. 2'. and-the dial a
will be finiihed. ' " ‘

There are feveral kinds of dials, which are
called univerflzl, b‘eeaufe they ferve for all lati-
tudes. Of thefe, the heft One that I know,vis
Mr. Pardz'e’s, which confif’ts of three principal
parts ;. the firf’t whereof is called the horizontal

An ma plane (12), beea-ufe in the practice it muf’t be p‘aa

wet/ZZZ
dial.

mile! to the horizon. In this plane *is'fixtian
upright pin, which enters into the edge of the
fecond part B D, called the meridional plane;
which is made of two pieces, the lowef’t whereof
(8) is-ealled the quadrant, becaufe it contains a
Quarterofa «circle, divided into goudegtees 5 ant!-
‘ ' 1t

Of Dialing“; ' ,
, it is only into this; part, near B, that thepin enters.
The other piece is a femicz'rcle (D) adjufied to the

quadrant, andturningin it by agroove, for raifing ,

or depreflingthe diameter (E F) of the femici‘rcle,

_which diameter iscalled the axis of the infirur‘

ment, The third piece is a circlev(G), divided

On both fidesinto 24. equal parts, which are the,

hours. This circle is put upon the meridional
plane fo, that the axis (E F) may- be perpendim-

lar to. the circle; and the point C be the com”- '

rn'on center of the circle, femicircle, and quad-
mm. The firaight edge of the femicircle. is
chamfered on bOth fides to a [harp edge, which.
paITes through the Center of the circle. On one
fide of the chamfered part, the firi’t fix months
of the‘ year are laid down, according to the funls
declination for, their refpeétive days, and on the
other fide the hit fix months. And againl’t the
days on which-the fun enters the figns, there are
firaight lines drawn upon the femicircle, with the
characters of the figns t’narked upon them.
There is a black line drawn along the middle of
the upright edge of the quadrant, over which
', hangsa thread (H), with its plummet (I), for
levelling the infirument. N. B. From the, 2 3d
of September to the 20th of March, the upper
furf’ace of the circle mutt touch both the center

C of the femicircle, and the line of an and a.» ,-

and from the 20th of March tomthe 23d of Sep-
tember; the lower furface of the circle mull:
, touch that center and line. ‘ ~ ‘
. ; To find the time of the day b ' this dial. , Hav;
ing fest iton a level place in fun-Thine, and ad;
\ jui’ted it by the leveling {crews/e and 1, until the
plumb-line hangs over the black line upon, the
edge of the quadrant, and parallel to the faid
edge; movethe femicirclein the quadrant, until
, z ' . _ the

'33:?

Fig. 50:

Of Dialing,

~ the line of M and £5 (where the circle touches)

comes to-thelatitucle of your place in the quad-
rant: then, ‘turn the whole meridional plane
B D, with its circle G, upon the horizontal plane
A, until the edge of the {hadow 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 EFwill be
parallel to the axis-of the world, and will caft a
ihadowrupon the true time of the day, among
the hours on the circle.

N. B. As,'when the infirument is thusreéti-
fled, the quadrant and femicircle are in the plane
of the meridian, fo the circle is then in the plane
of the eqUinoEtial. Therefore, as the fun is above
the equinoé‘tial in fummer (in northern latitudes)
and below it in winter;~ the axis of the femi-
circle will caft a fhadow on the hour of the day,
on the upper furface 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
fhadow of the femicircle, upon the lower furface .
of the circle. In the former cafe, the {hadow 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 fl C 8, equal to the diameter of the
femicircle A D B, and crofs it .in the middle at,
right angles with the line E C D, equal in length
to AIDE; then EC Will be the radius of the
circle F C G, which is the fame as that of the
femicircle. Upon E, as a center, defcribe the.
circle FC G, on which fet ofi'the arcs C la and
C 1', each equal to 23—3: degrees, and divide them
accordingly into that number, for the fun’s de-

~ clination.~

Of Dialling; ,
elination. Then, laying the edge of a ruler.
over the center E, and ”alfo over the fun’s declié
nation for every * fifth day of' each month (as in
the ‘card dial) mark the points on the diameter

~ J B of the femicircle from a to g, which are cut

by the ruler; and there place the da 3 of the
months actordingly, anfweringthe fun s de‘clinai
tion. \This done, fetting one, foot of the com;
pafi‘es in’Cg and extending the other to oz or g;
defcribe the femicircle a é c d e f g ', which divide
into fix equal parts, and through the points of
divifion draw right lines‘, parallel to C D, for the
beginning of the fines (of which one half are on
one fide of the femicirc’le, and the other half on
the other fide) and fet thecharaé’ters of the figns
to their proper lines, as in the figure.

The following table fhews the fun’s place and
declination, indegrees and minutes, at the noon
of every day of the fecond year after leap—year;
which is a mean between thofe of leap~y_ear it;
felf,‘and‘the firi‘t and third years after. It is
ufeful for infcribingéthe months and their days
on fun~dials; and alfo for finding the latitudes
of places, according to the methods prefcr’ib‘ed
after“. the table.

* The intermediate days may be drawn in by hand, if
the {pace be large enoughto contain them;

' Z A Table

339

g ' t

 

 

 

 

 

 

 

 

 

 

 

@3446 Tables of 2222 8222’ 3 Place 22222! Decli22252'o22.
/ A Table fhewing the fun’ 3 place and declination
,January. 1 tibruary.

,Sun’sPl. Sun‘s Dec. Sun‘s 1‘1, Sun's Dec.
I). Ed. 1). b4. ' 1). Ed. I). Dfl. ‘,
11199 ‘5“ 235—— 1: 1292*3'8 1/3 2“
1,2,. ,6. 22 55 I3, 39 I6 45
13 8 ‘22 49 14-:40 .16-‘27 ‘
14 .922 43 15 41 1610‘
153510‘.22 37: r161 4? 15-.5L
I6 I! 22 29 1:7 42- i5 33:.
17 121 22 22 18 43 15 I4 .
I8 13.22 14- I9 43 I4 55

20' 44 I4“ 32"
2: 145; 14- 17~
23 46 I3 37 ‘
24, 46? 13 I7
25 47 12 57"
26 47 12 36..
27 48 [12 '15 ”
28 48 11' 54% .1

19 14‘ 22 t 5"
2o 16: 21 56'.
217 17 121 47’
22 18' 21 377'~
2'3 19' 21 27
24 20 21 17
25 2:1 ‘21 '
26 22 20 54
27 .24 20‘ 43

 

 

 

 

 

1532:; 33:15; 1; make ow 514.133.» 42522“

 

 

 

 

 

 

 

 

 

 

 

 

 

28 . 25 20 go ' 29‘ 48' 11 '33”

29 26 20 18 ‘0}{49’ 11- 12;
1. £5231 20 i 1 49 IO 50
21 1\28 19 52 21 ‘2 50 10.29
22 2 29. 19 38 22 3 50 10‘ ‘7.
23 3 30 I9 24 23 4 5O 9‘ [£5
24 4 31 19 ‘10 24 5 51 9 ’23
g_5 5 32 I8 55 2__5_ 6 5l 9 0
26 6 33 18 4o 26 7 51 8 38
27 7 34 18 24 27 8 51 8 16
2883518928951753
29 9 35 17 53 in thcfe TablesNfig—
323 IO 36’ I7 36 nifies north declina-'
31‘” 37 I7 19- Horn, and S fouth.

 

A Table

Taéles cf the 822’: P1266 and Declinafz’onfi .

 

I 'A T2131: {hewing thle fun’s Place and declination.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

—March. ' April.
E) Sun’s Pl. Sun’sDec. g Sun’s Pl. Sun’sDéc.
E D. M. D. M. ‘5‘; D- M. D. M.
7103652 7830 11161038 4N36
21152 7 4 7 2 12 37 4 59
43.12. 52“ 6. 44 3 13 36 .5 22 C
413 52 6 21 414 35 -5 45
314' 52, . ,5. 58 315 34 6 8
615 52 5 .35 616 33 6 31
716 5‘51 5 12 *7 17“31 6 53
8 17 51 4 48 8 18 30 . 7 16
9 18 51 4 25 9 19 29 7 38.
10 19‘ 51 4 2 10 20 2‘8 8 o
11 20 51 3 38 11 21 27 8 22
1221 50‘ 3 14 12 22 25 “8 ‘44
13 22 5o . 2 51 1323 24 9 6 '
14.23 50 2 27 14 24. 23 9 28
£22242 2.4 15.25 21 9 49
16 25 49 I 40 16 26 20 IO 11
117126 48 1 16 17 27 18 10 32
18-27 48 o 53 18 28 17 10 53
19 28 48 o 29 19 29 15 ,11 14
2029 47 o _ 5 20 0814. 11 34
’21 om47 0N19 21. 1 12 11 55
.22 1 46 o 42 22 2 11 12 15
23‘ 2 45 I 6- 23 3 9 12 35
.24. 3 45 1 29 2. 4. 7 12 55
35 4 .44 I 53 fig 5 6 12 I4
26 5 43 z .17 26 6 4 13 34
27 6 42 2 40 27' 7 2 13 53
2‘8 7 ‘42 3 3. 28 8 70 14 12
29 8 41 3 .27~ 29 8 59 14 30
80.9 40 .4 3 50 3‘3 9 57 14 49
3110 39 , 4‘ '13
Z2 4 ATablc

5341?

. vzv:

{Tables of tée Sun’i Place and Dalmatian!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2342
‘ A Table {hewing the (1111’s place and declination.
May. June.
9 S'un‘s Pl. Sun‘s Dec. ~ g P’Sun’s Pl. Sun’s Dec.
‘21). M. D. M. . :‘11. M1 1). M.-
710855 15N 7 7101144 MN ‘5
*2 11 53 15 25 2 11 41 22 2.13
' 3,12 51 15 423 ' 3 12 39 22 .21..
413’ 49 16 o 4.13 36 22 28
“5.2.2216 1.1. .514 s4 35.
6 I5 45 16 35 6 15 3.1 .22 4-1
9‘ 7.16 43‘ I6 51 7 16 28122 47‘
‘ 8 17» 41 17 8 817 26 22 53;
9 18 39 17 24 918 2'3 22 58'
1019 36, 17. 40 10 19 2O 23 3
11 2o 34 17 55 11. 20- 18 23. 7.
12 21 '32 18 1o 12 2'1 15 23 11
13 22 30 18 25, 13.221 12 23215
14 23 '28 18 4O 1 14. 23, ,9 23 18
15 24 25 18 5,4 15 24 7 23 20
16 25 23 .19 8 T625 423 22'
17 26 21 19 22 17 26 1' 23. ‘24‘
1827 19 19 35 18 26 58 23' 2-6
19 28 ’16 I9 48 19 27 56 23'. 27
29 29 14 2o 1 20 28 53 23 28
21 01171 20 13 21 29 '50 23> 28
'22 1 9 20 25 22 06.2547 23: 28
23 2 7 2o 37 25 1 45 23‘28
24; 3- 4 20 48, 24 2 42 23 “27
35:4'22059553392326
26 4 59, ‘21 7101 26 4. 36 ' 23 24‘
27 5 57 21 20 "27 5 33 23 21’
28 6 54 21 30 28 6 31 23 19
29-7 52 21 39 29 7 28 23 16
30! 8' 49 2—1 49 30 8 25 23 12 *
531} 9 47 21 57

 

 

 

 

 

 

7 / 4 . 77 A‘ Table

/

Table: of fine Sam’s Place 2112’ Declination. .

 

A Table 1hewing the fun’s place and decimation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Za

J'uly. Augufl.
9 Sun’s Pi. Sun’s Dec. 9 oun’s Pl. Sun’s Dec.
‘; [I DA: [1 DA. ‘5' [L DA. [1 DA.
”1,92522 23N‘18 1 851.58 18N2
’2 ‘0 I9 23 4 2 9 55 I7 47
3 11 16 23 . o 3 10 53 17 32
4’12 .14» 22 55 ‘ 4 11 5o 17 16
5 13* 11 22 49 5 12 48 I7 0
6'14 8, 221 43 6 13 45 16 43
7 15 5 22 37ii 7‘14 43 16 26
’8 I6 ' o 22 30 8 I5 41 16 9
9 17 2 22 23 9 16 38 15 15;
IO 17 57 22 16 10 17 36 15 25
11 18 54 22 8 11 18 33 15 17
212 19 51 .22 , o 12 19 31 14 59
13:20 49L 21 52 13 2.0 29 I4 41
'14 21 46 21' 43 14 21 26 14 23
15 22 43 21 33 15 22 24 14 4
16 23 4o 21 22 16 23 22 13 45
17 24 38 21 14 17 24 20 13 26
18 25 35 21 3 18 25 17 13 7
19 26 2 20 52 19 26 15 12 47
20 27 29 2o 41 20 27 13 12 27
21 28 27 20” 39 21 28 11 12 7
22 29 24 20 18 22 29 9 11 47
23 05121 20 6 23 cum 7 11 27
124 1 19 19 54 24 1 5 11 6
25 2 16 19 41 25 2 3 10 46]
26 3 13 19 28 26 3 1 10 25
27 4 11 19 14 27 3 59' 1o 4
285819.128457943
29 6 6 18 46 29 5 55l 9 21
3437 3 I8 32 29.6.12‘223
31 8 ' 0] 18 17 31‘ 7“ 51 8' 38
‘ Arable

 

(144'.

T 2526.140]? the Sun’s Placé’and Declination.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AvTable ihewing the/fun’s place and ,deélination.
September. 4' ' Oétober.
U Sun’s P1. Sun’s Dec; E7 Sun’sPl. Sun’s Dec.
1» ___..__.._-————— ——————- _.__._.—.—‘
‘E I). Rd. [1 D4. ‘E [L BAP I} D41»
7 8111249 8N16 1 821-.“ 8 3814.
‘2 9 47 7 55 ._2 9 7 3 37
3 IO 46 7 33 ' 3 IO 7 4 I
4 II“ 44 7 10 4 11 6 4 24
_§ 12 42 6 '48 _§ 12 5 4 47
6 13 4o , 6 26 6 13 4 5 10
714 39 6‘3 714 44533
1815 37 541,815 3 556
9 I6 35 5 18 9 16 3 6 19
1o 17 34 4 55 10 17 2‘ 6 42
11 18 '32 4 32 11 18 1 7 5
'12 19 31 '4 9 12 19 1 7 27
13 20 29 3 46 13 20 o 7' 50
I4 21 28; 3 23 14 21 ' o 8 12
15 22 ‘26 3 o 15 22 'o 8 35
16 23 25 2 37 16 23 o 8 57
I7 24 25 2 14 I7 23 59 9 19
18 25 22 1 5o 18 24 59 9 '41
19 26 21 1/ 27 19 25 58 10 , 3
20 27 .20 I 4 20 26 58 10 24
21‘28 19 o 40 21 27 58 10' 46
22 29 17 o .17 22 28 58 11 '7
.23 0&16 oS 6 23 29 58 11 28 A
24 1 15. c» 30 24. on158‘11v 49
25 2 14 o 53 25 1 58 12 ,10
26 3 13 1 17 26 2 58 12 31
27 4 12 1 4o '27 x3 58 12 51
28 5 111 2 4 28‘ 4 58 13 12
29 6 10 2 27 29 5 58 13 32
39 7 9 2 5o 30' 6 58 131 51
' <1 13175851411.
' ' ' ATable

,/

‘I'aéle: _of the Sun? 5 Place and Declinatim.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WA Tablé fhewing the {1111’s place and declination.
Nave nber. ‘ December.
FSun '3' Pl Sun’s Dec. ,g Sun’sPl. Sun’s Dec.
€31).M. D.M. TDDMDM.
#1 811158 148 o 1 9316 21852
2 .9 58 14 5o 2 10 17 ;22‘ I
3 1o 59 15 . 8 3 11 18 22 10.1
4 11 59 15 27 ‘_4 12 19 22 18
" 5 12 59 15 45 5 13 20 22 26
._ 6 13 ,59 16 ' 3 6 14 21 22 33
j 7 15 o 16 ‘21 7 15 ‘22 22‘ 4'0.
- 8 16 o \ I6 39 8 16 23 22 46
9‘17 0 16. 56 917 24 22 52
10 18 1 17 13 10*18 25 22 58
11 19 1 17 3o 11 19 2-6 23 3
2 12 20 2 .17 46 12 20 27. 23 8
13 21 2 I8 2 13 21 28 23 12
14122 3 18 18 14 22 29 23 15 -
I5 23 4' 18 34 ‘ I5 23 30 23 18
16 24 4 18 49 16 24 31 2'3 21'
I7 25 5 I9 4 I7 25 33. 23 24
18‘ 26 ,5 19 18 18 26 34 23 26
I9 27 6 I9 32 I9 27 35 23 27
20 28 , 7 19 46 20 28 36 23 28
2129 ’ 7 I9 59 21 29 37 23 28
22 03 8 20 12 22 01538 23 28
23 1 9 20 25 ' 23 1 4o 23 . 28
24 2 10 20 37 24 2 41 23 27
’25 3 11 .23... 49 25 3 42 23" 25
26/ 4 11 21 I :6 4 43 23 23
27 5 \ 12 21 12 27 5 44 23 ~21 ,
28 ,6. 13 21 23 28 6 46 23 18
29 7 I4 21 33 29 7 47 23 I5
30 8. 15 21 43 3o 8 48 23 11
31 9 49 23 01
Z 4. ‘ \Ta

3'45;

3 4g Rule: fvr‘findz'flg 11,96 Latitude? i

570 find the latitude of any place ,5} oéfirwtz'm,

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 flat was
fixt' in the pole, there Would be nOthing re:
quired to find the latitude, but to. take ‘the al—
titude of that Ptar with a good infirument. Bu‘t
although there is no flat in the pole, yet the
latitude may be found by taking the greatefl:
and leaf“: altitude of any Prat that never fets : for
if half the difference between thefe altitudes bev
added to the leaf: altitude, or fubtrafied from
the greatefl, the {um or remainder will be equal
to the altitude of the pole at the place of obfer-
vation. , '
~ But becaufe the length of the night muft 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 equinoélial above
the horizon,“ and if this complement be ‘I'ub-
tracked 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 meridianfand to'the fouth' of your place,
fubtrafl the declination from the meridian alti-
tude (taken by a good quadrant) a‘ndthe re-
mainder is the height of the equinoétial o‘r coin: ,
Plement of the latitudenorth. " " ‘

EXAMg

Rulé: for finding tba. Latitude.

EXAMPQE

S ofe The fun’s‘ meridian altitnde 4.2"- 20’ South
.9131? {And his declination, fubt. IO 15 North

 

Rem. the complement of the lat. 32 5‘
Which fubtraét from --- —- 90 o, ‘

M

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 ifrthe fum exceeds 90 de-
grees, the latitude is fouth; and if 90 be taken
from that fum, the remainder will be the la—
titude.

EXAMPLES

The fun’s meridian altitude —-— 65° 10" South
\ The fun’s declination, add —- 15 30. South

, o-—-——‘
Complement of the latitude 8o 40
Subtract from ' -,- —— go o
Remains the latitude -— 9 20 North
The fun’s meridian altitude 80° 40’ South

KThe fun’s declination, add —-- 20 10 South
The-fumis '.' - - - 100 50

From which fubtraEt - - - 90 o

Remains the latitude -_-: -—.- .10 50 South;
. , ’_ 3*“:

3n

343

I Rules for finding 25552 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 lefs than 90 degrees, is the complement of
the latitude fouth :2 but if the fum is more than
90 degrees, fubtraét 90 from it, and the reg .
mainder is the latitude north. .

EXAMPLES

Sun’s meridian altitude —— 60° 30’ Norih
Sun’s declination, add -,—- 20 10 North

Complement of the latitude - 8o 40
Subtraé’t from - — _ - .. 9 o
Remains the latitude - - . 19 20 South
Sun’s meridian altitude —. - 70° 20’ North
Sun’s declination, add _ - — 2 3 20 North
The fum is - - - - - 93 40

From which fubtraét - -’ - 90 o‘
Remains the latitude .- - - 3 40 North’.‘ «

t 4. If the fun has fouth declination, and is north
of your place at noon, fubtraét the declination
Trom'the‘ north meridian altitude, and the re‘-..

mainder is the complement of the latitude
fouth.

EXAM

"Rules for finding tbevLm‘z‘m‘de'.
EXAMPLE

Sun’s meridian altitude _- - 50° 30' North

Sun’s declination, fubtraé’t' - 20 10 SOuth

Complement of the latitude - 32 20

Subtraét this from _ - — - 90 o
”oil—d

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 " - - 38° 30’ South
Subtraé’t from — — - — ‘-’ 90 o ‘
Remains the latitude - -. 51 30 North
Sun’s meridian altitude — ,- 38° 30' North
Subtraét from — ~ - - - 90 o
Remains thMatitude - — 51 30 South:

'6. If you obferve the fun beneath the pole,
fubtraé‘t’his declination from 90 degrees, and
add the remainder .«to his altitude; and the furn
is'the latitude,

EXAM:

349

350

Rules for finding the Latitude;

EXAMPLE.

Sun’s declination ' - - - - 20° 30'
Subtract from - - - - - 90 o
Remains - - - - - - 69 go i
Sun’s altitude below the pole - IO 20 Eadd

The rum is the latitude - - 79 5'0.

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 feen 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 equinoétial, and f0 have no lati-
tude.

8. If the fun be in the zenith at noon, and
has declination, the declination is equal to the
latitude, north or fourth. Thefe two cafes are
f0 plain, that they require no exanjiplfis° , .

L E c T. XI.
~ Of Dialing.

HAVING fhewn in the preceding Lec-

ture how to make fun-dials by the allift-

ance of a good globe, or of a dialing fizale, we
{hall now proceed to the methOd of conl’trufting
dials arithmetically; which will be more agree-
able to thofe who have learnt the elements of
WC:

Of Dialing:
trigonometry, becaufe globes and fcalesca‘n

never be. f0 accurate as the logarithms, in find- _

.ing the angular dillances of the hburs. Yet, as
a globe maybe foundexaé‘t enough for fome
other requifit‘es in dialing, we {hall take it in
occafionally. ’ '

The confirufiion 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 underfiovod. For there is
no plane, however obliquely fituated with re-
fpeét 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-
blet'n on the terrei’trial globe, or by a trigonome-

trical calculation, and confiruét a horizbntal dial. '

for it; that dial, applied to the plane where it is

to ferve, 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 51—} degrees
north latitude, which falls in with 38; degrees
of fouth latitude. But if the upright plane de-
clines from facing the fouth at the given place,
it would {’till be a horizontal plane 90 degrees
from that place; but for a different longitude:
which wohld alter the reckoning of the hours
accordingly:

CASE 1.

1. Let us fuppofe that an uprigthlane at
' .ILondon declines 36 degrees wei’twar‘d 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.

Reftify

3‘52”

, Of Dialing.

g Reftify the globe to the latitude of Londoii',
and bring London to the zenith under the b‘rals
meridian, then that point of the globe which lies
in the hori‘zdn atthe given’ ”degree of declination
(Counted. Wefi'Ward' from the‘fou‘th point of the
horizon) is, the place at which the above—men'-
tioned plane wkjuld be horizontal.~—-Now, to
find the latitude and longitude of that place,
keep your eye upon the place, and turn the
globe eaftWard, until it comes under the gradu-
ated edge of the 'brafs meridian; then, the do:
gree of the brafs meridian that {lands diredtly
over the place, is its latitude; and the number
of degrees in the equator, which are intercepted
between the meridian of London and the brafsz
meridian", is the place’s' difference of longitude. .

Thus, as the latitude of London is 51%- ode“-
grees north, and the declination of the place is

36 degrees wef’t -, I elevate the north pOIe 51—;~ , ‘
‘ 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 weflzward' from the]

"ibuth point, and make a mark on that place of
the globe over which the reckc‘ming ends,'an_d

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,1courrt
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;
weft‘ward from the fouth, would be a horizontal-
”plane at that place, whofe latitude is 30;:— degrees
fouth of the equator, and longitude 4.2% degrees!
Weft of the meridian of Londom

V i ' " ‘ Which

V
549‘
4

R‘fi

if

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

JM 0.

. Of Dialing;
Which diH‘erehce of .. longitude Being jgalaxi-
fverted into time, is a hours5r rriiniites,
The vertical dial declining ,weflward 36 dc,-
greesat London, is therefore to be drawn in all
ref‘peétswas a horizontal dial for fouth latitude

[0; degrees; fave on-l ,‘ thatthe ,reckoni-n of
3 4 D Y g

the hours is to anticipate the reckoning on the
herizontal dial, by 2 hours 51 minuteszjfor fo
much fo‘oner will the fun come to the meridian
of London, than to the meridian of any place
whofe longitude is 42%. degrees weft “from Lon:
don. - fl '

2-"iB'U¥.§9 be more exact than the globe’will
fhew us, we lhall ufea littlertrigonometryu »

Let NE 8 W ‘ be the horizon , of London,
whofezf’enith is Z‘, and P the north pole” of the
fphere .; andzlet Z b be thegpofitioneofga vertical
* plane'at Z, declining .wefiWard from}? (the
fouth) by" an angle of 361d‘egrees; [on whicg

lane an ereél: dial for London at Z isito be
' defcribed. Make the femidiameter Z-D penpen—
Ldicular tO-Z la, and it will cut the horizon in D,

.kfi‘!‘
353

Plate
XXIII.
F 1g. I 3

36 degrees well: of the fouth‘S, Then, a plane .,
in the tangent H D, touching the fpher‘exin D, i

will be parallel to the plane Z In; and theaxis of
the fphere will be equally inclined to both thefe‘
planes. ‘
Let W QE be the equinoéti‘al, whole elevae
tion above the horizon of Z (London) is 38;
degrees; and PRD be the meridian [of " the
place D, cutting the equinoé‘tial-in R.- 1: Then,
it is evident, that the are R D is the latitude of
the place D (where-the plane Z 79 would be ;~hori.-
zontal) and the arc RQ is the diflerence of
longitude of the planes Z la and D H. -. '
g In the fpherical triangle W D R, the-arcW D
"is given, for it is the complement of the. plane’s
‘2 , ‘ ' decli-

'354‘

Of “Dialing. , ~
declination from ‘S the fourh; which coniple-i
ment is 54° (viz..9o°-—r36°:) the angle afR,
in which the meridian of the place 1) cuts the
equator, is a right angle; and the angle R WD
meafures the elevation of the equinoétial 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, [0 is the co-
fine of the latitude of th the fine of‘R D the
latitude ofD: which is of a different denomi.
nation from the latitude of Z, becaufe Zand D
are on different [ides of the equator. A . « ‘

~As radius - V-’ -' - -- - jio.ooooo
To co—fine 36° 621192) 9.90796

So co~fine , 51° 30’,:’_QZ 9.79415

 

To'fine 30° 14’ : D R ~ (9.70211) ::
the latitude of D, whofe horizon is parallel to -
the vertical plane Z I: at Z.

IV. B. When radius is made the firi’t term, it
may be omitted, and then, by fubtraéling it
mentally from the fum of the other two, the
operation will be fhortened. Thus, in the pre;
fent cafe, ~ 7

0

To the logarithmic line of WR=* 54° 0’ 9.90796
Add the logarithmic fine of R. D: 1* 38° 30’ 9.79415 “

 

Theirtfum —— radius — .‘ - - 9.7021 x
gives the fame folution as above. And we ihall
keep to this' method in the following part of the
work;

a [The eofihe of 35° 0", or of R g;
1* The co-fine of 5 1° \30’, or of Q2.-

To

,/

0f Dialing;
iTO‘find the difi‘erence of longitiid‘e Ofthe
places D and Z, fay, as radius is to the co—fine

of 38—;~ degrees, the height of the equinoétial at '

Z, f0 is. the cotangent Of 36 degrees, the plane’s
declination, to the cotangent of the difi’erence
of longitudes. Thus, ‘

To the logarithmic fine of * 51° 30’ 9.89354.
Add the logarithmic tang. of T 54° 0’ 110.1 38 74.

 

Their {um—radius - - 910.0322?

is the nearei’t tangent of 47° 8'2WR; which'

is the cotangent 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

V and longitude of the place D, to whole horizon
the vertical plane at ’Z is parallel, we {hall pro; .

ceed to the confiruEtion of a horizontal dial for
the placevD, whofe latitude is 30° 14’ fouth;

but anticipating the time at. D by 2 hours 51

minmes (neglecting the % minute in praétice)
becaufe D is f0 far wef’tward in longitude from

the meridian of London; and thiswiil bera i

true vertical dial at London, declining wef’tWard
36 degrees.

355

Aflhme any right line C S‘L for the fubfiile Fig. '2;

of the dial,’ and make the angle KC P equal to
the latitudeof the place (viz. 300 14’) to whofe
horizon the plane of the dial is parallel; then

C R P will be the axis of the fiile, or edge that ,

cafis the lhadow 0n the hours ofthe day, in the
dial. This done, draw the contingent line E Q,
wtting the fubfiilar line at right angles in K,

* The co-fine of 38° 30’, or of WD R.
'l‘ The co-tangent of 36°, or of]? WI

4

A a . and

356

Of Diazzags.‘

- and from K make K R perpendicular to the axis

C R P. . Then KG(::K K) beingmade radius,
that is, equal to the chord of 60° or tangent of
45° on a good feé‘tor, .take 42" 52’ (the differ-
ence of longitude of the places Z and D) from
the tangents, and having fet it from KtoJW,
draw C JVIfor the hour-line of XII. Take KN
equal to the tangent of an angle lefs byll5
degrees than K M -, that is, the tangent 27° 52’;
and through the point N draw C N for the hour-
line of I. The tangent of 12° 52’ (Which'is
15° leis than 27° 52’) fet offthe 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° 87 (the (inference between 45° .and
42° 52) placed on the ether fide of CL, 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 fetofl‘” from-K towards,Qon the line
E Q, will give the point for the hour-line of
1111 : and fo of the ref’t.-'--The forenoon hour-
lines are drawn the fame Way, by the continual
addition of the tangents 15°, 30°, 45°, &C. to
42° 52’ (:the tangent of KM) for the hours
of XI, X, IX, 8m. as far as necefiary; that is,
until there be five hours on each fide of the
fubi‘tile. The fixth hour, accounted from that
hour or partof the hour on which the fubi’tile
falls, will be always in a line perpendicular to
the 4fubilile, and drawn through the centenC.
.In all credit dials, CJVJ, the hour- line of
XII, is perpendicular to the horizon of the
place for which the dial is to ferve: for that
line IS the interfeétion of a vertical plane with
the plane of the meridian of the place, both
which are terpendicular to the plane of the
, horizon .

0

Of Dialing?

horizon: and any line H O,'or Into, perpendie
eular'toC M, will be a horizontal line on the
plane of the dial, aloncr which\ line the hours
may be numbered; an C M being fet perpen-s
dicula‘r to the horiZon, the dial will have its true
ofiuon. ' ' ' i ‘ ‘
5. If the plane of the dial had declined by an
equal angle toward the eaf’t, its defcription' Would
have difi‘ered only in this, thatthe hour4line of
Xll would have fallenon the other fide of the
fubi’cile CL, and the line H 0 would haVe a
fubcontrary polition to What it has in this

figure. ,
6. And thefe two dials, with the upper points
of their {tiles turned toward the north-pole, will

ferve for the other two planes parallel to them ; i

the one declining from the north‘to‘ward the
call, and the Other from the north toward the
\wefi, by thefame 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.

‘357‘

7-. If the plane of the dial not only détlz'nes, Fig 3;

but alfo recliner, or inclines. Suppofe its declina—
tion from frontingthe fouth S be equal to the are
S D on the hurizon ;. and its reclination be
equal to the are D d of the verticle circle D Z :
then it is plain, that if the quadrant of altitude
Zd D, on the globe, cuts the point D in the

horizon, and the reclination is counted upon the .

, quadrant from D to (1-, the interfeé‘tion of the
hour-circle? R d, with the equinoétial W (2’12,
_ mill determine R d, the latitude of the place d,

’ ' ' Ana 2- ‘ - whole

35$

_ Fig. 4.

Of Dialing.

whofe’ horizon is parallel to the given plane .2 b at
Z; and "R Qwill be the difference in longitude
of the planes at d and Z. " '

Trigonometrically thus : ‘let a great circle
pafs throughpthe three points W, (I, E; and in
the triangle W D d, right-angled at D, the fides
WD and D d are given ; and thence the angle
D W5! is found, and f0 is the hypothenufe Wd.

‘ Again, the difference, or the fum, of D Wd

and 1) WR, the elevation of the equinoflial
above the horizon of Z, gives the angle d WK ;
and the hypothenufe of the triangle WR d was
juf’t' now found ; whence the (ides R d and WE
are found, the fOrmer being the latitude of the
place (1, and the latter the complement of R Q,
the difference of longitude fought. »
Thus, ifthe latitude of the place Z be 52° IO
north; the declination S D Of the plane Z b
(which would be horizontal at d) be 36°, and
the reclination be 15°, or equal to the are D d;
the fouth latitude of the place d, that is, the
arc Rd, will be 15° 9’; and R Q, the dill}:-
rence of the longitude, 36° 2’. From thefe
data, therefore, let the dial (Fig. 4.) be de—

I

_ fcribed, as in the former example.

8. Only it is to be obferved, that in the re—
clining or inclining dials, the horizontal line
will not {land at right angles to the hour-line of
XII, as in erect dials 3 but its pofition may be
found as follows. '

To the common fubl’tilar line C K L, on
which‘the dial for the place d was defcribed,
draw the dial C rp m 12 for the place D, whofe
declination is the fame as that of d (viz. the are
S D -,) and H , perpendicular to Cm, the hour—
line oinl on this dial, will be a horizontal line
on the dial GP 1% M XII. For the declination

- of

 

Of Dmlmg.

of both dials being the fame, the horizontal line
remains parallel to itfelf, while the erect pofition

of one dial is reclined or inclined with relpeél: to

the polition of the other.

Or, the polition of the dial, may be found by i

applying 1t to its plane, fo as to mark the true

hour \Ciof the day by the fun, as fhewn by another -

dial; or by a clOck, regulated by a true meri-
dian line and equation table. 1

9. There are leveral Other things requilite 1n
the practice of dialing the chief of which I
{hall give in the form of arithmetical rules,
, {impleb and eafy t‘o thofe who have learnt the elep

merits of trigonometry. Forin practical arts of i

this kind, arithmetic fhould be med as far as
it can go; and {calesnever truf‘ted to, except in
the final confiruétion, where they are abfolutely
necefi'ary in laying down the calculated hour-
dillances on the plane of the dial. And ala-
though the inimitable artif’ts of this metmpolis
have:3 no occafion for fuch infiruétions, yet they

may be of fome ufe to f’tudents, and to private ‘

gentlemen who amufe thgmfclve‘s this way,

,RULEL

To find the angles which the hour-Zines on any dial
’ - Maize with t/chué/iz'le,

To the logarithmic line of the given latitude,
or of the fiile’s elevation abOve the plane of the
dial, add the logarithmic tangent of’thehour
*9 dil’tance from the meridian, or from the

* That is, of 1;, 30, 4g, 60, 75°, for the hours of I,
II, III, IIII’, V in the afternoon: and XI, X, IX, VIII,
VII in the forenoon.

Aag fub—Li

359

360. 0

Of Dialing. . ,,
+ fubfi‘ile; and the fum minus radius will be the
logarithmic tangentof the angle foilght. ‘ ‘ ”
, For, in Fig. “'2. KC is to KM in the ratio
compounded of the ratio of K C to K .G (:K R)
and, of K G to KM ; which, making CK the
radius,__10,000000, or 10,0000, at 10, or r,
are the ratio'of 10,000000, or of 10,0000, or.
of,10,0rof1,tt0KGxKM‘ _
Thus, _. in a horizontal dial, for latitude
51° 30’, tofind the angular dii’rance of XI in
the_forenoon, or I in the afternoon, from XII.

' To the logarithmic fine of 51° 30’ 9.89354 1;,
Add the logarithmic tang.‘of 15° 0' 9.4.2805 ,

 

F

H The {um—”radius is i- - , 9.32159:

the logarithmic tangent of 11° 50', Or of the
angle which the hour-line of X1 or I‘makesi
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, IIL-jIIII,

and V in the afternoon; or of X, IX, VIII,

and VII in the forenoon; you will find their

angular difiancesfrom XII to be 24° 18’, 38° 3’,
53" 35’, and 719 6’; which are all that there
is occafion‘ to compute for. ' And thefe dif-
tances may be let OH‘from XII by a line of"
chords; or rather, by taking 1000"fr0m a fcale

 

of equal parts, and fetting that extent as a ra-

dius f'rom'C 10,311., and‘then, taking 209 of

91» 731.1 horizontal dials, theeret‘ft north of (limb dials,
"'the fa fiile and meridian are the fame: but in all declining

” ‘ dials, the {ubfiile line makes an angle with the meridian.-

yintp 1000000 equal Parts, ,

I In-Which‘cafe, the radius C Kis fuppofedfi to be divided 1

" the _.

O

 

Of Dialing. ‘ 361'

the fame, parts (which, in the tables, are the
natural tangent of 11° 50') and fetting them
from Xll to XI and to I, on the line is a, which Fig. 2,
is perpendicular to C XII : and £0 ’for the melt of
the, hour-lines which, in the table of natural
tangents, ag‘ainfi: the above difiances, are 4.51,
' 782, 1355,: and 2920, of limb equal parts from
XII, as the radius C XIl contains 1000; And
‘lal’tly, fet ofi" i257 (the natural tangent 'of 51°
30’) .for the angle of the ftile’s height, which is 4
equal to the latitude of the place. .

The reafon why I prefer the, tile of the tabu-
lar numbers, and of a fcale decimally divided,
to that‘of the line of chords, is becaufe there is
the leal‘c chance of mifiake and error in this way 3 ,
and likewife, becaufe in fome cafes it gives us
the advantage of a nonius’ divifion. ‘

In the univerfal ring-dial, for inflance, the

divifions on' the axis are the tangents of the
angles, of the fun’s declination placed on either
fide of the center;” But inl’tead of laying them
' down from a line of tangents, I would make a
{tale of equal parts, whereof iooo {hould an-
fwer exaét‘ly to the length of the i‘emi» axis, from
the‘centef: 10 the infide of the equinoétial ring;
and then lay down§434 of thefe parts‘toward.
each end from the center, which would limit all
, the divifions on the axis, becaule 434; are the
natural tangent ofng0 29'. And thus, by a;
720mm affixed to the Hiding piece, and taking
the fun’s declination from an Ephemferis, and
the tangent of that declination from the table of
natural tangents, the Rider might be always fet
(true to within two minutes of a degree. j
And this l‘ca»le.of~434 equal parts Qmightbe
placed right againl’t the 231,- degrees of the {un‘s
declination, on the axis, inltcad of the. l‘un’s
’ A a 4. ‘ place,

0

$62

Fig! 3.

@f‘ 5 Whlzfig.’

place, whichivisethete ofvvery jittleru'fe; . For-

then, the flider Hemight be fet inuthe ufual. way,
.tnéthe-day'of ~:the.mnnth,.for common ufe; ,but

9

to the natural tangent of the declination, vwhen

_ great accuracy is required.

. {1“ he like may .be'done. wherever-get .l‘cale of

rmes or tangents is re'quired on any inl’trument.

‘le U“'\L‘E‘ II. v

‘flae latitude of the place, the fan’s decimation, 4m!
hi5 hour diflame from tlae meridian, being given;
" :to find 7(1)) his ultimate; (2.) leis azimuth. ..

"I. Let ‘a' be «the fun’s place, JR, his decli-‘
nation ; and in the triangle P Zd,"‘P d'the fum, .
or the difference, ,ode, and the quadrant PR,
being given by the fuppofition, as alfo the com-
plement of the latitude P Z, and the angle
at P Z, which meafures the horary dif’tance of d

I from the meridian; we {hall (by Cafe 4.‘ of—

KeiZl’s. Oblique fpheric Trigonometry) find the
bale Z d, which is the fun’s dif’cance from the
zenith, or the “complement of his altitude.
" Andi(2.j)As fineZd: fine'Pd :2 finedPZ: .
at Z P, or ofits fupplement D Z S, the azimuthal
diflanCe from the fouth’.‘ ' ’ ‘ . ' ’
Or, the praétical rule may be as follows.
'Write 2% for the fine of the fun’s altitude, L
and i’l for the fineand co-fine of the latitude, D
and d‘for' the line and CO—fin'e of the fun’s de-
clination, and H for the fine of the horary dif-

tance from VI.

iiiiThi‘Ern théifol-ffiltionibf H to ,fljwill have three

Varieties. " _ .
1;. When

 

‘ Of Healing;
. 1. Whenlzthedeclination is‘towardtheele»
vated. pole, and the hour of the day is between
XII and V12, .it is.fl,:LD.+ Hal d, and
__A-»L.D. » r ‘ . t

H"— ld , .. K * j; ..- f , ,
2'. ’When‘threihOur is after VI, it isdz-JL D

LD+A ~ p‘,“*

t

-_—H l d, and H: “—2-.

- 3; When thedeclination is toward .the'de-

.4 LD , ,
H:‘+“ ‘

 

Id .0 . t _ ,
Which theorems will be found ufeful, and
expeditious enough ,for folving thofe problems
in geOgraphy and dialing, which depend on the
relation of the fun’s altitude to the hour of the
day. » , V . _ —

*EXAMPLEL

,Suppofe the latitude of the place to be 51-:~

degrees north -, the time fivevhours dil’tant from V

XII, that is, an hourafter VI in the morning,
or beforeer in" the ,evening; and the fun’s de-
clination 20” north. Required tbefzm’s altitude .?

Then, to log. L: log. (in. 5i° 30’ 1.89354*
add log. Dzlog. fin. 20° 0’ 1,534.05
Their fum .._— 1- - — - - I. 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, infiead of the index 9 we have—1, as
above ; which is of no farther ufe, than making the work
a little eafier. *

And, .

prelled pole, we have A ::.\_H I d --L D, 'and.

3%

cafe, H:
478°): .743145, and L D: .26-7664, fl—L’D

9f Dialing.” . .
And, to .log.- lava-10g. fin. + 15° 0’ 1.413200

z . s log. 1 2 log. fin. 1 38°, 0’ 1.79414.
}add{ 101g. 4— 3 log. fin. H 70°o’ 1.97300-

Their {um - - - - - b- -‘ 1.18015
give-s H [d :: logarithm of 0.151408, in the
natural fines. ' ' - - ‘

,And thefe' two numbers (0.267664. and
0.151408) make 0.419072 :: A; which, in

, the table, is the neat-ell natural line of 24°47;

the fun’s altitude {Cu-ght. >
The fame hour-difiance being affirmed on the

. other fide ofVI, then L D—Hld is 0.1116256,

the fine of 6? 40% 3- which is, the fun’saltitu'de
at Vin the morning, or VILin the evening,
when his north declination is 20°.

But when the declination is 20°‘fouth‘(or
towards the deprefied pole) the difference
HZci—LD becomes negative, and thereby
.fl16WS that, an hour before. VI in the morning,
or pafi: VI in the evening, the fun’s‘ center is:
6‘? 40% below the horizon. A ‘

EXAMPLEIL»

. an the fame latitude and northideclination,
- fromthe given altitude to find the hour.

Lot the altitude be 48° ; and beeaufe, in this
Ae—L D
[4’

 

, and flfthe/ natural line of

. . i-f The difiance of one hour from VL.

‘ 1‘ The co-latitude of the place. ,
> H The co—declination of the fun.‘

will

 

_ 0f 3523357133: ‘ ’ ‘
' will be 9.47548 1, whofe logarithmicw a ,

from which taking the logarithmic-

 

' fineoflxd: -' - - -- ‘ 1,767I354.
Remain-s - - - '4 ‘ 'h "' ill-9559,9977

the locatithmic fine of the haundii‘tamee fought,
viz. 0' 54‘? 227-, which, reduced ‘tlo time, is
3 hours 371,: 'min. that is, 1X h. 37:— min. in
the forenoon, 0’r TI 11. '21-;- " m.“ in the after—
noon. ‘ " ‘ “

Put the altitude: 18°, hofe 'natuiiil fine]

. is” .3090-1701; and thence file—L D will be
2.0491953»; Whitfi'dividEd' by”! er, gives
.o7i7179, the fine of 406%, in time 16: imi-
nutes 'neatly, before VI in the morning,70r
after V1; in the evening, fwhen‘the fun-’3‘ altitude-
i518°. . ‘ -~ ,
. And, if the de’clinat‘iOn 20° had been~ towards
the fou'th pole, the fun Would have been de-
prefied 18" below the horizon sit-16% minute‘s;
. after VI in the evening; at? which time, the
twilight. would end ; Which hap ens about the
22d of November, and 39th of anuary, in the
latitude of5t°—;~ north. The fameway may the
end of twilight, or beginning of da‘Wn, be found
for any time of the year. , ~ 7 ,
NOTE 1., If in theorem 2 and 3» (page 3.63)
A is‘put :: o, and the value of H is computed,
we have the hour of fun-rifing and letting for
any latitude, and time of the year. And if we
ut H: o, and compute .4, We have the fun’s
altitude or deprefiion at the hour of VI. And
lafily, if H, x1 and D. are gieen, the latitude
' may he found, by the reiuiution of a quadratic
equation 5 for 1::‘/ 1 __. L ,

 

‘ NOTE

4

“6‘5?“ ' ' " " I'd-677133!

. 3165

365

V Take the leg. tang. offi23° 29’ 1.6379562

6f Dialz‘figi .

NOTE za'Whenjfl is equal 0, H tismequa—l
{7?— : TL x T D, the tangent of the. latitude
multiplied by the tangent Of the declination.

’As,xif-it Was required, what is flog greate/i
leagtbiyflday z'zz latitude 51° 30/? _ ,
To the log. tangent of 51° 30’ 0.0993948 -.
Add the log. tangent of 23° 29’ 1.6379563

~—

 

Theirnfum; 1 - - -‘ - - 1.7373511 is
the log. fine of the hour-dif’tance 33° 7’, in"
time 2 h. 12—; m. The longel’t day therefore is
12 h. +g4 h. 25 m. : 16 h. 25 In. And
theflwrtefi: day 'is 12 h.-—_.— 4h. 25 m. .2: '7’ h.
35m- I' i, -- , , , i

'Andif the longeft day is given; the latitude
of the place is fODndyq—gb— being equal to T L.

Thus, if the longefi daynis qtggfihours :: .2 x 6
h. + 45 m. and 45 minutes in time being equal
to 11:;- degrees. ' ‘ ‘ . ' 4

From the-110g. fine of It" 15’ 1.2902357 -

 

_ ._,.,.,
Remains '- - \— - -— - 1.6522795 ‘
zithe 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 afiigned in authors from the length of their
days, may beexamined and correé‘ted. ‘ ,
NOTE “3. The fame rule forlfinding the
longefi day in a given latitude, dil’tinguifhes the .
hour-lines that are necefi‘ary to be drawn onany
dial from thofe which would be l‘uperfluous.
In lat. 52° 10' the longel’t day is 16. h. 32 m.
and the hounlines are to be marked from 44/ m.
' . after

Of Dialing;

after, III in the rimming, to 16 m. after VIII in
the'evening. ' ‘ . -

In the fame latitude, let the dial of Art. 7.
Fig. 4. be propofedg and the elevation of its
fiile (or the latitude of the place d, whofehori-
zon is parallel to the plane of the dial) being
159 9'; the longet’t-day at dythat is, the longefi‘
time that the fun can'illuminate the plane of the
dial, will (by the rule H : T L x31" 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° 27;
in time, 2‘ hours '24. minutes; and the. declina-

tion of the plane was from the fouth to’Wards the .

welt. Adding therefore 2h. 24 min. to 5. h.‘
3 m. the earlieft tun-tiling on a horizontaldial

367.

at d, the fum 7 h. 57 m. fhews that the mornv Fig 3.

ing hours, or the parallel dial at Z, ought to _
begin at 3 min. before VIII. And to the mat
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 latel’t fun-fetting at Z, by 35, m.
{hews that -none of the afternoon hour—lines are
fuperfiuous. ‘And the 4 h. 13 m. from III h.
44 m. the fun-rifing at Z to VII h. 57 m. “the
fun-tiling at cl, belong to the other face of the
dial ; that is,‘ to a dial declining 36° from north
' toeafi, and inclining 15°.

, EXAMPLEiu
From the fame dam to find the fun’s azimuth

If H, L and D are given,‘ then (by- Art. 2.
of Rule ll.) from H having found the altitude

and its complement Z d 5 and the arc Pd (the
dif’tance

3.68

\
Of Dialing.
difiance from the pole) being given ; fay, As
thelc0~fine of the altitude is t_o_t‘hefine of the
diflance from the pole,’ ft) is the fine of'the honra
difiance from the meridian to the fine of» the
a'zimunh-difian cc from the meridian. '

g ' Let the latitude be 51° 30’ north, the decli-

nation 15° 9’ (both, and the time 11 h. 24 m.
Tin‘at‘he afternoon, when the fiin begins to illumi‘
new a vertical wall, and it is required" to find
the pofition of the veall. ,

Then, 'by the foregoing theorems, the com:
vplementeof the altitude will be 81° 32%, and

_P d the difia’nce from ’the pole being 109° 5’,

and the library difiance from the meridian, or
the angle (1 P Z, 36". i -
Tolog. fin. 74° 51’ - - 1.98464.
Add log. fin. 36° 0’ - - 1.76922

”——

 

_‘ And frorn the {um - - 1.75386.

Take ”the log. 1311319327»; 1.99525 -

Remains -» - - - - ' 1.75861 :: log.
1311.3 °,. the azimuth dif‘tan’ce fonth. . _

Wlfen the altitude is given, find from thence
.the hour, and proceed as above.
This praxis is of fingular ufe on many dc-
cafions; in finding the declination of vertical
planes more exactly than in the common way,
e'fp'ecially if the tranfits of the fun’s center is ob—
ferved by applying a ruler with lights, either
plain or telefcopical, to the wall or plane, whofe

declination is required—Jo 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 difiance from it being obferved,
together with the. altitude and hour.-—-And

.4 . . thence

/
A Of Dialing; '

thence determining frnall dii’ferencesof longi-
tude.-1_-In ob‘fe’rving the variation at fea, 81c”,

The learned Mr.“ AndrewReid invented an
infirument feveral years ago, for finding the
latitude at fea from two altitudes of the fun, ob-
ferved on the fame day, andthe interval of the
obfervations, meafured by a common watch.
And this inflrument, whofe only fault. was that
of its being fomewhat eXpenfive, was made by
Mr. y‘ackfon. Tables have been lately computed
for that purpofe, . ,
, But we‘may often, from the foregoing rules,
refolve the fame problem, without much trouble;
efpecially if we fuppofe themafier of the {hip to
‘know‘within 2 or, 3 degr‘ees what his latitudeis.
Thus,

Afiume the two nearef’t probable limits of the
A+LD

latitude, and by the theorem H:—————— com-_
pute the hours of obfervation for both fuppo—
fition‘s.‘ If one interval of thofe computed
' hours coincides with the interval obferVed, the
quefiion is folved. If not, the tWo dif’tances of
the intervals computed, from the true interval,
will give a 'roportional part to beadded to, or
fubtr-aéted rom, one of the latitudes afl'umed.
And if more exaélnefs is required, the operation
' may be repeated with the latitude already
found.

But whichever way the uefiion is folved, .a
proper allowance is to be made for the difference
of latitude arifing‘from the fhip’s courfe in the
time between the two‘obfervations.

0f

359’

376/

Fig. 3.

'0f Dialing;
Of the ddflbie horizontal dial; and the Babylonian
- . v and Italiandials.

To the g‘n‘omom‘c projection, there is fometimes :
added a fler-eogmpbz'c projection of the hours

. 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, {land-

. ing perpendicularly over the center of the pro-

jeétion : fo that the dial, being in its due pofition,
the {hadow of that perpendicular edge is a verti-
cal circle pafl‘mg through the fun, in the fiereo~
graphic projection. ~‘ '

‘ The months being duly marked on this dial,
the fun’s declination, and the length of the day at
any time, are had by infpeétion (as alfo his alti-
tude, by means of a lcale of tangents). But its
chief property is, that it may be placed true,
whenever the fun fhines, without the help of any
other inl’trument. \ -

Let 4’ be the fun’s place in the fiereographic-
projection, x rly z the parallel of the fun’s decli-
nation, Z d a vertical circlevthrough the fun’s ~
center, P cl the hour-circle; and it is evident“,

, that the diameter NS of this projection being

placed duly north and fouth, thefe three circles
will-pafs through the point 6!. 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 projeétion coincides with that marked
bythe hour-circle P d, which palTes thr'Ough“ the
interfeélion of the fhadow Z d with the circle of
the fun’s prefent declination. _
The Baéylom'an and Italian dials reckon the“ V
hours, not from the meridian, as with us, but?
from?

3

0f Dialing: ‘ '37:
from the fun’s rifing and‘fettingi' Thus, in Plate
my, an Hour before fun-{ct is reckoned the 23d XXIH'
hour; two hours before fun-fet, the azdhour;
and lb of the reit. V And the {hadow that marks
them onthe hour-lines, is that of ‘the point of i3.
fiile. This cecafions a perpetual variation be-
tween their dials and clocks, which they mui’t
correct from, time to time, before it arifes to any a
feniible quantity, by fetting their clocks fo much
fafter or flower. And in Italy, they begin their
day, and regulate their clocks, not frOm fun-fer,

"but from about mid-twilight, when the‘dve -Mczrid
is {aid 3 which corrects the difference that would
otherwife betbetween the clock and the dial.
The improvements Which have been made in
all forts of inf’truments and machines for meafur—
ing time, have rendered fuch dials of little
aCcoxufnt. » Yet, as the theory of them is ingez
nious, and they are really, in fome refpe’fts, the ' »
bef’t contrived of ‘any for vulgar ufe, a general idea “
of their defcription may n0t be unacceptable. -
Let Fig. 5. reprefent an ereét rdireét fouth
wall, on which a Babylonian dial is to be drawn,
fhewing the hours from fun-tiling; the latitude
of the place, whofe horizon is parallel to the
wall, being equal to the angle K C R. Make,
as for a common dial K GzzKR (which is, per-
pendicular to CR) the radius of the equinoétial
[E Q, and draw R S perpendicular to C K for
the fiile of the dial 3 the fhadow of whole point
R is to’mark the hours, when S R is fet upright
on the plane of the dial. - . \ h
Then it is evident, that in the contingent line
zfi' .923 the fpaces K I, K2, K 3,f&c. being
taken equal to the tangents of the hourodifianccs
from the meridian, to the radius K G, one, two,
three, 81c. hours after funLriling, on the equi-
iioétial'day; the lhadow of the point R will be *
_ . B b. found,

.3 72"

Of Dialing.

-found, at thefe times, refpeétively 1n the points

I, 2, 3, &c. .
Draw, for the like hours after fun- -rifing, when

the fun is in the trOpic of Capricorn k? V, the
like common lines CD, CE, CF, 81c. and at

thefe hours the fhadow of the point R will be
found in thofe lines refpe€tively. Find the ftm’ s
altitudes above the plane ofthe dial at thefe
hours, and with their co- tangents S d S e, Sf,
8m. to radius 8 R, defcribe ares interfeéting the

,hour- lines 1n the points 51,3, f, &c. fo {hall the

right lines 1 d, 2 e, 3f, &c. be the lines ofI, II,
III, &c. hours after fun- rifing.

The confiruétion is the fame 1n every other
cafe, due regard being had to the difl‘erenc‘e 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 necefi‘ary; which may be done
partly by the rules already given for determin-
ing the time that the fun Ihines on any plane ,

' and partly from this, that on the tr0pical days,

the hyperbola defcribed by the fhadow of the

point R, limits the extent of all the hour-lines.

The mof’t ufeful however, as well as the
fimplefi of fuch dials, is that which 13 defcribed
On the two fides of a meridian plane.

That the Babylonian and Italzc hours are truly
enough marked by right lines, is eafily fhewn.
Mark the three points on a globe, where the
‘horizon cuts the equinoé‘cial, and the two tropics,
toward the call: or well, and turn the globe on
its axis 15°, or I hour; and it is plain? that the
three points which were in a great circle (viz.
the horizon) will be in a great circle fiill; which
Will be projected geometrically into a firaigh't
line. But thefe three points are univerfally the

fun 3

 

Of Dialing:
fun’s places, ‘one hour after fun-fet (Or one hour
before fun-rife) on the equinoétial and foll’titial
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 ‘

flraight‘ lines limited by the projections of the

foregoing example.
Note I, The fame dials’may be delineated

Without the hour-lines C D, CE, CF, &c. by ‘

letting 0E«the fun’s azimuths on the plane of the
dial, from the center 8, on either fide of the {ub-
fiile C S K, and the correfponding co—tangents of

altitude from the fame center 8, 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
equinoétial and foll’titial daysi ' ~

, 2. One of thefe dials has its name from the
hours being reckoned from fun-tiling, the be-
ginning of the Baéylom'an day. But we are not
thence to imagine that the egzml hours, which it

fliews, were thofe in which the al’tronomers of»

that country marked their obfervations'. Thefe,

' we know with certainty, were unequal, like the .. .
yewz‘fl}, as being twelfth parts ofthe natural day :
and an hour of the night was, in like manner, a '

twelfth part of the night; longer or lhorter,
according to the fe‘afon of the year. So that an
hour of the day, and an hour of the night, at the
.fame place, would always'make ,1 of 24, or 2

i‘

_ equinoétial hours. In Pale/line, among the

Romans, and in feveral other countries, 3 of‘thefe
,unequal nocturnal hours were a-w'gz'lia or watt/9.

And the reduction of equal and unequal hours-

into one another, is extremely eafy. ' If, for “in-
fiance,rit is found, by a foregoing rule, that in a
certain latitude, at a given time of the year, the

B b 2 length

tropics ; and which are rightly drawn, as in the ,

' 27's?

374

Of Dialing. »

length of a day is 14. equinoétial hours, the
unequal hour is then 2;; or % of an hour, that
is, 70 minutes; and the nocturnal hour is 50
minutes. The firf’t watch begins at VII (fun-
fet) ; the fecond at three times 50 minutes after,
viz.’ IX h. 30 m. the third always at midnight;
the morning watch at —;— hour paf’t II.

If it were required to draw a dial for fhewing
ghefe unequal hours, or 12th parts of the day,
we inufl: take as many declinations of the fun as
are thought necelTary, from the equator towards
each tropic : and having computed the fun’s
altitude and azimuth for T‘T, 7“,, 72th parts, 81c.
of each of the diurnal arcs belOnging to the de-

‘ clinations aflumed: by thefe, the feveral points

in the. circles of declination, where the {hadow

"of the fiile’s point falls, are determined: and

curve. lines drawn through the points of an
homologous divifion will be the hour-lines ref
quired.

Of the rig/bf placing of dials, and having a true
meridian line for the aegalalz'ag 0f clocks and
wan/yes. '

‘ The plane on which the dial is to tell, being
duly prepared, and every thing necelfary for.
fixing it,.you may find the hour tolerably e‘xa&
by a large equinoétial ring-dial, and fet your
watch to it. And then the dialmay be fixed by:

’ the watch at your leifure.

If you would be more exaét, take the fun’s

A altitude by a good quadrant, noting the precife

time of obfervation by a clock or watch. Then,
compute the time for the altitude obferved, (by

a the rule, page 364) and fet the watch to agree

with that time, according to the fun. A Had/qy’s, '
‘ , A quadrant

How to make a Meridian Line.

quadrant is very convenient for this purpofe;
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
bell: done in fummer, and the nearer the fun is
to the prime vertical (the eaf’t or welt azimuth)
when the o‘bfervation is made, {0 much the
better. -
Or, in fummer, take tWo equal altitudes of the
fun in the fame day 3-0116 any time between 7 and
:0 o’clock in the morning, the other between 2
and 5 in the afternoon; noting the moments/of
thefe two obfervation—s by a clock or watch : and
if the watch {hews the obfervations to be at
equal dil’tances from noon, it agrees exactly
with the fun; if not, the watch mull be cor—
rected by half the difference of the forenoon and
afternoon intervals; and then the dial may be
fet‘ true by the watch. 1- '
Thus, for example, fuppofe you have taken
the fun’s altitude when it was 20 minutes pail:
VIIIl-‘in the morning by the watch ; andjound,
by obferving in the afternoon, that the fun had
the fame altitude 10 minutes before 1111 -, then
it is plain, that the watch was 5 minutes too
fal’t for the fun: for 5 minutes after XII is the
middle time betweeen VIII h. 20 m. in the
morning, and 111 h. 50 m. in the afternoon; and‘
therefore, to make the watch agree with the fun,
it mul’c be let back five minutes.

375

A good meridian line, for regulating clocks or A mm;
watches, may be had by the following mead,” 1m, \

thod.

Make a round hole, almof’t a quarter of an
inch diameter, in a thin plate of metal; and fix
the plate in the t0p of a fouth window, in fuch a

B b 3 manner,

37.6.

How to make a Mfidz’afl Line:

manner, that it may recline from the zenith at“
an angle equal to‘ the co-tlatitude of your place, as
nearly as you can guefs; for then, the plate will
face the fun directly at noon on the equinoéltial
days. Let the fun lhine freely through the hole
into the room; and hang a plumb-line to the
ceiling of the room 3 at leafl: 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 havingmarkedthe faid place on the ceiling,
take away the line. '
Having adjul‘ted a fliding 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 p the above-mentioned place on the
ceiling, 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 almofi to the floor; and the whole
will be prepared for farther and proper adjul’c—

' n‘ient.

This done, find the true folar time, by either

of the two laft methods, and thereby regulate

your Clock. ’I hen, at the moment of next noon 9
by the clock, when the fun lhines, move the
fli'ding bar in the groove until the fhado‘w of the
plumb-linebifeéts the image of 'the‘fun (made
by his rays tranfmitteti through the hole) on the

afloor,‘ wall, 'or ori a white lcreen placed on the

northfide Of the line 3 the plhmmet or weight
at the end of the line hanging freely in a pa‘il of"
water placed below iron the flown—But becaufe

~ this may not be quitecorreél: for the-firfi time,
on account that the plummet, will not fettle im-

mediately, even in water, it may be farther cor- - '
' ' , - ' -_ reéted

{be Calculation of mean New and Full Meme!

reeled on‘ the following days, by the above
method, with the fun and (clock; and {0 brought
to_a very great exactnefs. , a ’ ,

N. B. The rays tranfmitted through the hole,
will calf but a faint imag‘eof the fun, even one
white {'creen, unlefs the room be fogdarkened
that no fun-{hine may be allowed to enter, but
what comes through the finall hole in the plate.
And always, for fome time before the obferya-
tion is made, the plummet oughtto be immerfed
in a jar of water, where it may hang freely ;‘ by
which means the line will foon become Ready,
which otherwife would be apt to y’tontinue
fwing‘ing.‘ ‘ , g . ‘

As this meridian linerwill not only be fuffi-
cie’nt for regulating of clocks‘and watches to the

true'time by equation tables, but alfo for moi": '
afironomical purpofe‘vsJ {hall fay nothing of the;
magnificent and eXpenfive meridian lines at,

Bologm‘and Rome, nor‘of the better methods by
which afironomers obferve precifely the tranfi‘ts
of the heavenly bodies, on the meridian.

\LECTQML

Sleewz'ng 120w to calculate theme/m time ofidny New
" ‘or Full 'Meen,i or Erlz'pfla, from the creation: of the
week! to ,zf/eeyeeref CHRIST 5800.

N the'following tables, the mean lunation is
about a 20th part of a fecond of time longer
. than its meafure as now printed 'in the third
edition of my ‘Afironomy -, which makes a diff~
~ference of an hour and 30 minutes in 8600

years.-.-'-.-B,ut this is notfmaterial, when only the ,

mean times are required.

Bb4 . 7 RREf‘“

3,72

378 Tee Celettlatz'on of meek New and-Full Moms; ,

PRECEPTaV

To find the mean time ef any New or Full Moon in
My given year and mom/a after ibe Clare/lieu
(fire.

I. If the given year be. foUnd in the third
column of the Table of the moon’s mean motion from
, Me fem, under the title Tear: eefore am! after
CHRIST; write cat 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 lefTer one to .it that you find, in the fame
column ; and thereto add as many compleaiyeezrs,
as will make up the given year :' then, join the
given month, and all the refpeéti‘ve mean mo-
tions. ‘

2. Colleét thefe mean motions into one fum of
figns, degrees, minutes, and feconds ; remem-
bering, that 60 feconds (M) make a minute, 60
minutes (’) a degree, 30 degrees (°) a fign, and
12 figns (5) a circle. When the figns exceed
12, or 24, or 36 (which are whole circles.),reje&
them, and fet down only the remainder; which,
together with the odd degrees, minutes, and
feconds already fet down, mufl: be reckoned the ,
whole fum of the colleétion.

. 3. Subtraét the refult, or fum of this collec»
tion, from 12 figns; and write down the remain-
der; . Then, look in the table, under Days, for-
the next lefs. mean motions 59 this remainder;i

. an;

The Calculation If mean New and Fall‘Moam.‘ , 379

and fubtraét them from it, writing down their
remainder.

This done, look in the table under boars
(marked H.) for the next lefs mean motions to a
this 121?: remainder, and fubtraét them from it,
writing down their remainder.

Then, look in the table under minute:
(marked M.) for the next lefs mean motions to
this remainder, and fubtraét them from it,
writing down their remainder.

Laf’tly, look in the table under . feeonds
(marked 8.) for the mean lefs mean motions to
this remainder, either greater or lefs ; and againi’t
it you have the feconds anfwering thereto.

4. And thefe times colleé’ted, will give the,
mean time of the required new moon; which will
be right in common years, and alfo in January
and February in leap-years; but always one day
too late in leap-years after February.

EXAMPLE

380

The Calculatim :of mean New and Full Means.
EXAMPLE I. '

V Required tbe time of new moon in Septeméer, I 76.1. P

(a year not inferted in the table.)

\‘ Moon from fun;

. To‘thé year after Cbrzfl’s ‘ ‘. s 0 ' ”

birth -—— -— 1753 10 9 24' 56
Add compleatyear‘s ., -,t. ,1: - 0 [0,1420
1. ~ (mm-1764.) 4 r .‘ 7.
And join September - - 2 22 321 8
The firm of thefe mean motions is 1 12 ' o 24,
Which, ,being fab. from a circle, -

 

 

 

 

or. __- - V - «g - 12 to" o ‘0
Leaves remaining , - - IO 17 5936
NleE lefs, mean mot. for 26 days, ..

fub. - - - - IO 16 57 34.
And there remains - -— -' , , I 2 2
Next lefs mean mot. for 2 hours,

fub. _‘-, — - :—~. ‘I!_o,57
And the remainder will be ‘- - I 5
Next lefs. mean mot. for 2 min. -

f‘lbo "' - " k "' ‘ I I
Remains the mean mot. of 12 fee. , 4.

Thefe times, being colleé‘ced, would {hew
the meantime of the required new moon in,
September 1764, to be on the 26th day, at; 2 '
hours 2 min. 12 fee. pai’c noon. But, as itis in
a leap-year, and after February, the time is one‘
day too late. 80, the true mean time, is Sep-
tember the 25th, at 2 m. 12 fee. part II in the
afternoon. . t x ‘ ~

I 'No B.‘ ',

 

grbe Calculation of mime New and Full M00725;
N. B. The tables always begin the day at

noon, and reckon thence forward, to the noon
of the day following.

Tafiml the mean time offal] mean in any gzoen year ’

and Monte after Ike Clare/flan [Eran

Having colleéled the moon’s mean motion
from theb fun for the beginning of the given
year and month, and fubtraé‘ted their fum from
' 12 figns (as in the former example) add 6 figns
to the remainder, and then proceed in all re-
ipeéls as above.

EXAMPLEII.

Required tbe meme tzme ‘of full moon in September

1764?
Moon from fury, 'i
To the year after Cerf/3’s s o ’ ”
birth —- — 1753 10 9 24 56
Add cempleat years - u 0 IO 14. 20
(fum'1764)
And‘join September - - ' 2 22 21‘ 8

 

 

The fum of thefe mean motions \

lS - - - — y I 12 o 24.
Which, being fubt. from a Cir.

 

 

 

cle,or:- - - 12000
Leaves remaining ‘ - - - l i 10 17 59 36
Towhich remainder add ' - ‘6 o o . 0
And thefumwill be : r: I 4 17 ‘59 36

Brought.

38$

 

’ {382

The Calculation 0f mean New and Full Meow;
Mbon from fun. 7

/\ I [I

S O

Brought over " -- ' -'- 4 17 59 36

‘ Next lefs mean mot. for It

 

days, fubt. - - 4. 14.3 5 54
And there remains - . «g 3 53 .42
Next lefs mean mot. for 7 <

hours, fubt. \ - - 3 33 20
And the remainder will be - , 20 2?.
Next lefs mean mot. for 40 a .

min. fubt. - - - - / ' ‘20 19

 

Remains the mean mot. for8

fee. - - - - , 3

M

So, the mean time, according to the tables,
is the I 1th of September, at 7 hours 40 minutes
8 feconds paft noon. One day too late, being

”after February in a leap-year.

And thusmay the mean time of any new'or
full moon be found,- in any Year after theChrilL

tian fEra.

Tofind the mean time of new or full mbon in any
given year and month éefore the Clariflian fire. ' _
If the given year before the year of CHRIST
I‘ be found in the third column‘of the table,
Under the title Years éefore 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
{till 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 refpeéts as above.

EXAM.

We Calculation of mean New} and Full Moms;

EXAMPLEIE.

Reqitz'red the meantime of new moon in May, tbe
year aefare Cari/t 585 .3

The next greater year in the table is 600;
which being 15 years before the given yeai“,
add the mean motions for I 5 years to thofe of

600,, together with‘ thofe for the beginning of ’

May.

Moon from fun;

I II

S 0
To the year before Cari/i 600 - X 5 It 6 16
Add‘comple‘at years motion I 5 - 6 o 5 5 24,
And the mean morions for May 0 22 53 2 3

 

Clu-I‘

., The Whole fum is .-

 

 

. . .' ° 4 55 ’3
Which, being fubt. from a err-
cle, or -‘ - a - '12 o o 0
Leaves remaining - ; II 25 4 57
Next lefs mean mot. for 29 . g '
\days, {Ubl'a V - .- _11 23 31 54 .
And there remains , . - - . I. 33 3
Next-lefs mean mot. For 3 hours
’ fubt. - — - I 31 26
And the remainder will be ; 1 37
Next lefs mean mot. for 3 min.
fubt. - - . -‘ I 31:

mm

Rem. the mean mot. of 14 fe- 7 _
conds 3 g - 5

m “fist—V—

So,

. _

282;:

$335

-'1
V435

$34 The'CalenItitz'on of Eclipfig

So, the mean time by the tables, 'was the
29th of May, at 3 hours 3 min. 14 fee. pafl:
‘ noon. A day later than the truth, on account
of its being in agleap-year. For as the year of
CHRIST I was the firf’t after a leap-year,
the year 585 before the year I was a leapoyear
of courfe. ' -

If the given year be after the Chrif’tian fEra,‘
divide its date by 4, and if nothing remains, it
is a leap-year in the old fiile. But if the given
year was before the Chrifiian IEra (or Year of
CHRIST 1)fubtra€t one from its date, and
divide the remainder by 4; then, if nothing

remains, it was a leap»year ; otherwife not.

To find whether the fun is eeh'pfld at the time of any
given change, or the mean at any given full.

Ofeclz'pfit. From the Tnhle‘ of the fim’: mean motion (or
dif’tance) front the moon’s nfcendz'ng node, colleé’c
the mean motions anfwering to the given time ;

n- and if the refult lhews the fun to be within [8
degrees of either of the nodes at“ the time of
new moon, the fun will be eclipfed at that time‘

i Or, if the refult {hews 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. . ,.

,EXAMf

 

,,’

EXAMPLE. 1V.

-« be mean changes mike 26th of Septeméer 1764;
at 2 l2. 2 m. (neglefiing tloe fleeands)‘ after new.
'(See‘Example I.) Qu. Whether the few will
be eclipflzd at that time .? V _

V _ _ Sun from node.”
To the year after Clm'fl’s ' s o ’ ”

~ birth —- —..\ . 1753, ' I 28 o 19
Add compleat years - I I ,7 2 3 56
‘ (111111 1764.) L I
September 1 - — 8 12 22 49
And 26 days - — - 27~ o 13
, . 2 hours —. - - 5 12
2 minutes - -‘ - , 5 ~
Suh’s difiancc from the afcend- ‘ (I? w

ping‘node - - — 6 9" 32 34.

pan-WM

' Now, as the defcending node is jufi oppofite The time
to the afcending, (viz. 6 figns dii’cant from it) and thereof.
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 mufi be ecliptbd -,

being then only 9° 32’ 34.” fhort of the de-
fcending node.

EXAM—

3'86

Sun’s diflance from the afcend-

\ Em Calculatim‘of my”;

EXAMPLE V.‘

Tl»: man will he full on tine I lib of "Septemler’;
1764, at 7 b. 40 min. pajl noon. '(See‘Exam-
ple II.) ' Qu. Whether flu: will be eclz'g/ezl at
that lime .?

Sun from node;

a:
1 b
O

To the year after .Cbrz' ’s ’
birth -- —- 1753 1 28 o 19
Add eompleat years *- 1 I 7 2 3 56

(fum I764.) ‘
September - , — 8 12 22 4‘9

11 days - - II 25 29
And 7 hours - - - ’ 18 II
40 minutes - -‘ , I 4.4.

mm‘

ingnode - - - _- 52412 28‘

n—n-u—u—m

Which being I'ubtraéted from 6 figns, leaves
only 5° 47’ 32” remaining; and this being all
the {pace that the fun is Ihort of the defcend-
ing node, it is, plain that the moon muf‘c then
be eelipfed, beeaufe {he is jui’r as near the con-
trary node. ,

EXAM:-

 

f5? Calculation qucZz'pfis.‘

EXAMPLE VI.‘

Q Whether the fun was eclz'pfed ”in May, the year
fiefore CHRIST 58.5 .9 (See Example Ill.)

Sun from node.

,. s o ’ ”

To the year before Clara/15 600 - 9 9 23 51
Add the mean motion of I 5 '

complete year’s - .. 9 19 27 49 1
‘ May ‘d - - - ‘4 4 37 57
, 29 ays - .,. .I o 7 10
And 3 hours .- .. ,7 74,8

3 minutes (neglecting

the feconds) - , .. .8 i

 

m

Sun’s difiance from the afcend~ ~

ingnode - . 7- ' o 3.44 43‘

 

‘Which being lefs than 18 degrees, fhews that
the fun was eclipfed at that time.

382'

This eclipfe‘ was foretold by Thales, and is Tbales’s
thought to be'the eclipfe which put an end to “5993.

the war between the Medes and Lydians.

The times of the fan’s cpnjunflz’on with Vibe When

”04165, and Cdnfequently the eclipfe womb: ,of any:€€11P/er
given year, are eafily found by the ‘T able iof them/1MP-

fun’s mean motion from live moon’s afcendz'ng node 5‘
and much in the fame way as the mean con-
juné’tions of the fun and moon are found by the
table of the moon’s mean motion from the fun.
,For, colleét the fun’s mean motion from the
:node (which is the fame as‘ his dil’tance gone
,frOrn it) for the beginning of any given year,

and fubtraét .it from 12 figns; then, from the ”

C c genuindex,

' f”.

383

' (Remains nearly) the mean mo-

‘Ia fiigd when there tau/2:519 EclipjéLJ'

remainder, fubtraét the next lefs mean motions "
belonging to whatever mom/2 you find them 1n
the table- , and from their remainder fubtraét the
next lefs mean motion for day5, and f0 on for '
1mm and mimm: the refuit of all which will
fliew the time of the fun’s mean conjunflion
with the afcmdz'ng node Of the moon’s orbit.

EXAMPLE VII.

Reguired the time of five fun 5 coizjzmfiz'm wit/9 the

cf ending node in flye year I764. ?

t 7 Sun from node.
I .7 .- i ,3; ‘0 I II
To the year after, Chg/E’s ‘1 ~

birth ‘, ‘ -' ”1753- I 28 o 119
Add compleat years - 1 1. ' 7 2 a 3 55

Mean dift. at beg. ofA. D 1764. 9 o 4 I5
Subtraé’c this dii‘cance from a cir- '

 

cle, (or «- — - .12 “0'0 0
And, there remains - ’ -i 2 29.55 4.5
Next lefs mean motion for 1 1

March fubtraéi; . - ~- .2 I 16 39

And the remainder will be - do 28 39' 6 - _
Next leis mean mot1on for 27 ~
days, fubtraét .- . - f 'o 28 , 2- 32 ,

. Andthere remains - - . /' 436 34..
.Nextx/lefs mean motion for 14. 1

. hours, fubtraéted ' -\ - 36 21~

tion of5 minutes 3 g- , 13

w~—n—- .—

7 ._ 7 _ I Hene‘e’

 

 

I

i 37."? Period and Return of’EcZipftes.‘ i\
.Hence it appears, that/the fun will ,pafs by

i the moon’s afcehdz'ng node on the 27th of March, ‘

at 14 hours 5 minutes paft noon -, viz. on the
28th day, at 5 minutes pai’t 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. pai’t II in the morning on the 27th day ;'
atwhich time, thedefcending node will bedi-
redfily oppofite t0 the fun.

If 6 fignsbe added to the remainder arifihg ‘
from the firfi fubtraétion, (viz.. from 12 figns) . ,

and, then the Work carried on as 'in the 139:
example, the refult'will give the mean time of
the fun’s co'nju'nétion with the defcending node.
Thus, in ’ , ,

EXAMPLE VIII.‘

Tafind when the fuzz will he 2'72 conjmzfiion with
’ the defcending node in rheyear 1764?

Sun from node,»

I II

' i 'i s 0‘
To the year after Chrifl’s ,
, birth - - . 1753 I 28 o .19
Add cqmpleat years — II 7 2 3 56 1

 

M. (1. fr. afe. n. at beg. of I764. 9 o r 4 15
’ Subtraé’c this ~difiance from a cir’- \
cle, or ‘ - > - - 12 o o d

 

And the remainder will be » - 2 29 55 45
Tolwhichadd half a‘ circle, or -‘ 6 "o o o

 

cs.— nun—u.

'And the fum‘ will be - ; 8 29 55 45'

“' Ccz _Next

"339;

396 . The Period and Return of Eclipfer.

 

 

‘ Sun fr. node.

, s o I, ,,

Brought over i - ‘ 8 29 55 45

Next lefs mean mot. forSept. fubt. 8 I2 22 49

And‘there remains - ‘ - o 17 32 56
Next lefs mean mot. for 16 days, A .

fubt. — - - - o 16 37 4

And the remainder will be - 55 52

Next lefs mean mot. for 2 1 hours,
fubtraéted. - » - - 54 32

\ MW“
Rem. (nearly) the mean mot._<_)_f
31 min. - - - I 20

_—-

 

H

80 that, according to the tables, the fun will
be in conjunfiion With the defamdz'ng nodelon the
1 6th of September, at 21 hours 3 1 minutes pafl:
noon : one day later than the truth, on account
of the leap-year. -
The li- When the moon changes within 18 days be-
mits of fore or after the fun’s conjunction with either of
et/ipfir. 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, {he will be
7 eclipfed at that full : otherwife not.
Their _ If to the mean time of any eclipfe, either of the
pe . ,
riod and fun or moon, we add 557 Julian years 21 days
reftitu- 18 hours II minutes and 51 feconds (in which
‘ion- there are exactly 6890 mean lunations) we {hall "
have the mean time of another eclipfe. Form:
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 endaf
‘ the i,

 

r

a,

5179;! Period and Return of Eclipfir.

, the {aid time, than he was at the beginning of
’ it; as appears by the following example *.
The period. Moon fr. fun. Sun fr. node.
8 I I/ I II

0 S 0

” 1 500—53 5 32 47-—10 14 45 ,8
“25;“? 40—8 26 50 37-— 1 2‘3 58 49
y 17——3 2 21 39——10 28 4o 55

days, 21-1—8 16 0 21—3 21 48 38‘

hours I8-——» 9, 8 35»- 446 44.
minutes 11—— ‘ 5, 35—— » ‘29
feconds 51—— 26— ‘ 2

 

Mean motions -—o o o o-—— o o o 4.5

 

And this period is fo very near, that in 6000
years it will vary no more from the truth, as to
the refiitution of eclipfes, than 8-6; minutes of a
degree; which may be reckoned next to nothing.
It is the fhorteft in which, after many trials, I can.
find f0 near a conjunC‘tionof the fun, moOn, and
the fame node.

3* Dr. HALLEY's period ofeclipfes contains only 18 years
n clays 7 hours 43 minutes 20 feconds; in which time, ac-
cording ‘to histables, there arejufl: 223 mean lunations: but,
as in that time, the fun’s mean motion from the node is no
» .more than 115 29° 31' 49”, which wants 28’ t i” of being
as nearly in-conjunétion with the fame node at the end
of the period as it was at the beginning; this period can-
not be of confiant duration for finding eclipfes, becaufe it
will in time fallquite without their limits. The following
tables make this period 31 feconds fltorter, as appears by the
following calculation. _

The period. Moon fr. Sun. Sun fr. node.
\ s o I // S o r I II
Compleat years 18—7 11 59 4—11 17 46 18
, days 1.1—4 I4 5 54-:- 1.1 25 2.9

 

hours 7-— 3 33 20—— y 38 11
mm. 42—— 21 20—,- 1 49
fee. 44.—-~ 22—- 2
Mean‘motions —-o o 0 0—11 29 31 49

 

C c 3 I This.

391‘

. / ’

392"

A Table of Mean Lunatiom.

This table 13 made by the continual addition -

h .
of a mean Innation, viz. 29d12 44’11 3 6t 21‘:
140 2411i ovii

 

M. S. Th.

 

 

In 100000 mean lunax

 

 

 

 

 

 

 

Lun. Days..H.
_ -—- tions, there arei8085Julian
1 29 12 44 3 6years 12 days 21 hours 36
Y z 59 1 28 6.13 minutes. 30 feconds__ -
‘ 3 g) 88.14 12 9 192053059 days 3' hours 36 1
4 g 118. 2 56 12 25 minutes 30 feconds. ‘
5 3147.15 40 15 32 ProofofI/ae Taéle;
6 ' I7‘7 4' 24 1.8 38 . Moon from fun.
7 206 1.7 82144 7, In s 0 r n
'8 . 236 552 24 5“? 4000 114 22 12
9 . 26s 18 36 2757: 4000 1 14 22 '12
‘10 295 7 2° 3" 3 g 80. 5 23 '41 15
20 590‘441273'3 5-10 01828
' 3C >885 22 l 33 11Days .12 4 26 17 20 *
40 118‘ ‘5 22 4 l4Hours 21 ’ '10 4o 1
50 1476 12 42 35-18 Min. 36 13 ‘7
‘00. :2953 I 25 ’0 35 Sec. 30 I;
200 5006 2 50 21 11M fr fun 0 0 '

/ 300 8859 4153146 _'" 1 ° °
400 11812 .5 4o 42 22 haiung by the former»
goo, 14765 '7 5 ‘52 57 precepts computed the

H1000 29530 14 11 45, 54 mean time ofnew moon in
2000 59061 4 2'3 31 .48 January,_foranygivenyear,I
3000 88591 18 35 17 421t15eafy, bythis Table, to

- 4030 111812258 47 3 36find the meantime ofnew
5000 147652 22 581149 goznoon in lanuary for any '
10000 295305 21 57 39 onumberofyearsafierward:

20000 590611 19 55 18 oand by means of a {mall _'

. 30000 885917 17, 52 5-7 otable of-lunations for 12 or ,

400001181223 15 50 36 013 months, to make age- - ‘

500001476529 13 48 15 oneral table for finding'the

100000 2953059 3 36 30 omean time of new/.01 full

, - . moon in any given yearand
month whatever. ‘4
D. H. M. S. Th.u'
In 11 lunations there are 324 20 4 34 10. .'
In leunations 354 8 48 37 16. ._-
In 13 lunatio’ns --—--' 383 21 32 40 23.

But then it would be befi to begin the year with March, to

1void the inconvenience of lofing a day by miflake 1n leap
$76er

 

 

 

. 'Years

/

' y’fl Table of £122 Moon-’5 mean Morimflom' the Suit; 1393‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

hYearsg; . ‘ 1 1 , , 4
of the 4Years Yea" before» Moon from fun. Com- Moon from fun.
Julian .of the and after ,‘ pleat ‘
period.'W°’ld‘ 011111512/5 o 2 II yearsg s o I u \

706.\ 0 ‘ 4008 .528 1 1; 11 0 1014 20
714 8 .3. 4000 g 9 23 24 12 5 2 3 11
171,1 1008 ‘14 300011, 20 28 57 13 9 11 4o 35 . . 1 '
2711 2008 a 2000 6 '1 34 30 14 1 21 18‘ ‘0 4
3/14 3008 m 10000 12 4o 3, 15 6 .o 55 24
38113108 E: 90010 19 46-36 '_1610 22 44 15
3914 3208 0 800 8 26 53 9 I7 '3 ‘2 21 39
4014 3308 3700 7 3 59 43 - 18‘ 7 1159211
4114 3408 >1 600 5' 11 6 16 19 1,1 21 36.27
4214 3508 g 500 3 18 1‘2 49 .4 20 4 13 25 19-
43143608 is 400 1 25 19 23 7 40- 8 26 50 37
4414 3708 :0“ 300 o 2 25 5‘0 '60» 1 10 15 56>
4514 3808 £3 20010 9 32 2g; 80 5 23 41 15
4614 3908 _. 100 8 16 39 3 100 10 7 6 33'
4714 4008 11> 1 6 23 45 30, 200 8 14 13 7
4814 4108 '3‘ ‘101 45 0‘52 9 300 6 21 19 4:
49144208 F) 201 3 7, 53 431 40° 4 28 26 13
5014 4308 m 301 I I; 5 16 . 500 ‘3 5 32 47
5114 4408 E 40111 22 11 49 1000 611 5 33»
5214 4508 1:31 501 9 29,18 23 42000 0 22- 11 6
5714 5008 1001 1 4 51 9 3000‘ 7 3 16 39
6414 5708 1701 0 24 3742121000 1 14122 12
64.66 57604 ' 175310 9 24. 56‘ l ‘Moonfrom {1111.
6514 5808 1801 6 '5 2015 3Months. s o ’ ’3'

“a :3": :3 1 Compleat Moon'from fun. Jan. 0 O 0 O 1
8,38% ,gyimi—‘ 3 ° I ”. Feb 0' I7 54 4? '
kK—gfi .325 I 4 9 37 24 \Mar. 1129 15 16: ~
9%81E15 $13. 2 83121448 April 01710 3

180103 1...“: 310252213 May 0225323

tagging 2-1;: 4 S 20 4' 4 June 1 10 4811
3:0“; . ":3 510 018 28 july 11631323
u“$"=¢=2~m.62955‘52 Au.‘ 2 6o
“34’82 “\00 «g« 42 2'.
0% “>50 g %M% 7 6 19 33117 bept.~ 2 22 21 8
fi;%%g gE—c 8111122 7 03;, 228 ‘4’ 29
fiapgi‘g—c‘é93205932 Nov. 3155917

22.33335 H ‘0 8 F? 26, 5:5 De1:.1321-42‘_7‘1
g Q :3 .33 “g This table agrees with the old/file until the year "9
41-4' \ ' 1753; and after that, with the new.

 

C c .4 R 4 ‘ ' Days.

394

’44 574516 0f the Moon’s mean Matianfrém the Sum;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E Moonfromfun: Moonfromfun.‘ Moon from fun.
‘g ,S O r I’ H. O , 1/ M. I 7, I”;
_'___ ______! _____~_ M. I II II] S. I] I” I”!
I y. 0 I2 I! 27 S. If III III! Th. III [I], v
2- o 24 22 53 '— 4—...— __ .___..
3 I 6 34 20 -1_ 0 3o 29 31 Is 44 47
41184547,21057 32161516
5 2 0 57 13 3 I 3t 26 33 16 45 44
6213840 42154 34171613
7225207 523223 35174642
8373134 63252 36181710
9319430 733320 37184739
10 4 I 54 27 8 4 349 3819 18 7
II 4 I4 5 54 9- 4 34 I8 39 I9 48 39
12 42617 20 IO 5 446 402019 5
I3 5 8 28 47 'II 5 35 I5 41 20 49 33
14 5204014 12:16 543 42 2120 2
15 6 2 51 4o 13 6 3612' 43 21 5o 31
.16 61537 “4704144222059
I7 627I434I5 737 9 452251281
18 7 92611 16.8 738 46 232156
19 7‘ 21 37 27 17 8 38 6 47 23 52 25
20 8 3 48 54 18 9 8 35 48 24 22 54
21 8 16 o 21 19 9 39 4 49 24. 53 22
22 8 28 II 47 2010 9 32, 5o 25 23 ,51
23 9 10 23 14. 21 10 4o 1 51 25 54 19
24 9 22 34 41 22 11 IO 30 52 26 24 48
25 10 4 46 7 23 11 4o 58 53 .26 55.17
26 1o 16‘ 57 34 24 12 11 27 54 27 25 45
27 Io 29 9 I 25 I2 4I 55 55 27 56 I4
2811 It 20 27 26 1312 24 56 28 26 43
29 II 23 3I 54 27 I3 42 53 , 57 28 57 II
30 o 5 43 21 28 14 13 21 58 29 2740
31 0 I7 54 47 29 I4 43 so 59 29 58 3
g 1 o_ 6 15 30 1514 18 60 3o 28 37
1 Lunation :29?I 1.2h 44m 35 6t“ 21“ 14" 24vi 6V“

 

In leap years, after F ebruary,3 a day and its motion innit
be added to the time for which the moon’s mean diflance
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 muff be {ubtraflezd from the mean time thereof, as

 

found by the tables. In common years they give the day
right;

 

' Years

Mfablé of ' 1b? Sun’s mam .Motz'on from the ,Moan’s' 395

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Aftendz’ng Node.
Years ‘Y Y h f '
.. 1 cars ears 0 '
31111:]: of the an d 3min $1111 from node. :113‘ Sunfwmnoae,
Pfiiéd‘ World. CHRIST. S 0 I II years. S 0 VI II
771: <81 .1 4:08 7 6 17 g 11 712 3 56
1714 1008 h 40:: 011 4 SS 12 7 22 11 3.9
2714 2008 2 2000 210 35 II 13 8 >11 ‘7 2
3714 3008 am4 1000 3;) S 28 '4 9‘ o 22 25
3814 3108 U 00 35 44 15" 9 19 27 49
- 3914 3208 % 300 7 24 32 46 16 [O 9 35 3]
4014 3308' 3 700 0 29 ‘22 48 I7 10 28 4o 55‘
4114 3403 g‘ 600 4- 4 2 49 18 11 I7 46 I8
‘4 4214 3% o 9 923 51. I9 0 .6 s1 43
J ,5: 500 1 24 20 20
4314 3608 I; 400 6 9 17 g: 40 3:6 5% 24
1 a 8 .‘* 3 S 4
:41: £828 Lag) 2:: 10 24 I4 56 60 2 20 58' I:
4614 3908 c—Q— 100 3 29 ‘8 58 8° ‘3 ‘7 S7 37
471/f 4008 > 1 o g 6 5:) 100 4 I4 57 2
4814 4108 E? 101 2 20° 8 29 5‘4 3
149144208 " 201 4 '4 3 3 300 l I4 5! 5
5014 4308 Q 301 3 29 O 4 400 5 29 48 7
51.4 4103 2: 401 6 $31 3 123° ‘3 ”’ 45 8
_ m o
5214 4508 .3 50110 23‘ 1 2 o 29 3o 17
@714 5008 ' 1001 9 8 :6 13 320: g :3 o 33
"e o
61;: :22: 13?; 1:; *5 30 “ 28 °’ 56
/ 3 0 I
3} 1455308 ‘ 1801 ‘8 2g 44 43 .Months. Sgn {20111 godet.’
2:1: «:1 ’2“‘;‘""1°de,-, Jan. 0 o o o‘
3:5 mu .0 o 1 1 Feb. I 2 1148’
2 8,53% “2'5 o 19 523 Margh 2 116 39
33-55 3—2 2»: 812 4.7 Apnl 3 328 27
80:23 ~53; 3227*10May 443757
“2,5“: M? 4 1%235; June 5 649 45
lhlgggé {a g3 29NJu1Y 6 75914
3332.2330- 325344OAug- 7 911 I
zfiig§ >390; 414 40 gSepc. 812 22 49
°§§§§3§§€ggzgg46§& 9133218
0 _ h o .4 <:- I 9 av. 10 15 4
3:63:33 31".”) 6 ‘2 58 33 Dec..1116:33,§r
:50 43g 0 lhls table agrees with the oldfli/e Until the
N {-4 year 1753 ; apd after that, with the new.

 

Days.

8 96 A 722516 of the Sun’ 5 mam Motion from 2‘56 Moon’ 5

 

 

 

 

 

 

 

 

 

 

 

 

 

Afiendz'ng Node.
E” Sun‘fr'o'm node: ' Sun from node. Sun from node
Fso”’fi.“3+7MTfi—TT.
..... —-—--—-—-,- M. ’ ” ”’ S. II I]! [III
I O I 2 19 S. ” ”I ”H Th. III/[III V
202-438— .-——- ——..—.——- '
303657.10236N'31 12031
404.916.20512-321237
50511336 30743 33125433
6061354 401023 34 128 9.
‘70 71613 5 01259 35131.55
80181832 6 015 35 36 13331“
*9 o 9.20 51 7 o 18 11 .. 37 1 36 "6E
10 o 10 2'3 10 8 o 20 47 38 1 38 42'
11 o 15 .25 29 9 o 23 23 39 1 41 18
: 1'2 0 12 27 48 3 10 o 25 58 4o 1 43 54f‘
13 o 13 30 7 11‘ o 28 33 41 1 46 36;
§ 14014322612 031 9 42 149 5f
15 o 15 34 15 I3 0 33 45 "43 I .51‘41‘
16 o 16 37 4 14 o 36 21 44 1 54 17.
, 170173923 1510385745 15653
1; 18 018 4141 16 04132 46 159 29‘
'- 19 019 44 o 17 044 8 47 2 2 5
‘20 0 2o 46 >19 18 0 46 44 48 2 4 41
2’1 02I‘48 38 I9 049 20 49 2 7-17
22 022 5057. 20 05156 50 2 953,
. 23 0,23 53‘ 1’6 21 o 54 32’ 51 2.12 29
12402415535220.5723 522155
‘25 0 25 57 54 23 0 59143 -53 2 I7 4-1 ,
26027 013 24 .1 219 54 22017\
127028232 251455 55 22253
2810 29 451 26 1 731 56 225 29
29 1' o ’7 10 27 1 10: 7 57 228 4"-
.30 1 I 9 29 28 I 12 43 58 2,30 40
31 1 21148 29 115 9 59 23316
32 1 3 I4 7 30 1 17 554 éq 2“ 35 52
In leap- years, after February, add one day and one
day’. s motion to the time at which the fun’s mean dif-
tance from the afcending node IS required.

 

 

J ,

1NDEx

 

 

w—

1’

I f N ~ D I E X.

 

 

' Dulteration of metals, to deteét \ ’page I 59
_ Air, its properties 168"
Air-pumpE - ' t . I79
. experiments upon it 182—209 ,

jllderfea (Mn) his engine 'for' railing water 125
Angle, of incidence . ‘ 205'
of reflefiion ‘ 24.0
——-’———'-of refraé’tion ' 20 5
flntam' I v . . 267
Apparent motion of‘ the heavens i ‘ ' ‘ 250

flrcbz‘medes, phis propofition for finding the area of a
circle, and the felidity of a cylinder raifed upon that

» circle ‘ V. ' 1'39
fer finding the deceit in king Hicro’s crown I53
Armillary fphere , l 'T ‘ 312
At'mofphere, its whole weight upon the earth 170
- Attraélion, of cohefion ' ‘ L ' 6

 

 

 

 

 

of gravitation I x ' 8
of fnagnetlfm ‘ ' ' 17
. of eleétr-icity . i - , ' ‘ 18
Azimuth . ‘ 7 303
1 B , '
Balance . so
Barometer . ’ ' , ' \172
,Bodies moving in orbits have a tendency to fly off
. ’,from their orbits _ p ' 7 30
‘ Bodies moVe fafter in fmall orbits than in large ones 31
, ——-7-—their centrifugal forces ib.
_~Burning-glafl'es, the force of their heat . 208
. t C
‘ Camera obfcura' . ’ 238
Cartaflan vertexes, abfurd ‘ 4 / = 35
Center of gravity , 13
'the curves defcribed by bodies moving round
It ‘ ' ' 2
Central fOrces i h ' . ’ , ’19—45
' 'Circles of the fphe‘re - , ' _ 251‘
Climate , 7' v 289

Coloured

, I N D 13 xi
Coloured bodies, which are tranfparent, become opake

 

if put together 245
Colures ' 297
Combined forces, their efi’eél: 21
Common plump , _ 117
Confiellations 29,8
Cranes . ’ 84—89

D
Damps ’ I75
Danger of people’s rifing haflzily in a coach or boat

when it is likely to be overfet 1/ 14.
Days lengthened by the refraélion of the {un’s rays 204.
Declination of the fun and flats 300
Defcending velocity, gives a power of equal afcent I2
Dialing _ - 316~377
Double projeéiile force, a balance to a quadruple

' power of gravity E 27
Earth, its motion demonfirated 45
proof of its being globular ‘ f 247
Earthquakes . . 1 7-8
Eclipfes 384.
Ecliptic . ' 249
Electricity ' 18

Engine (any mechanical) how to compute its power 48'
for working pumps by water ' 4 125
for raifing water by the firengthlof hor{es 128

 

 

 

Equation of time 310 "
Equinoé’cial . . , 249
Eye, defcribed 212.
Face of the heaven and earth, how reprefented in a
Machine 1 248
Fermentations ‘ p I 76
Fire damps I 77
Fluids, their “prefl'ure 101
Fire engine 143
Forces, central 19-—:4.r
Combined ' 2r
Forcing pump » " 122 - '
Foundation principle of all mechanics 47
Fountain at command , 116

‘F rigid zones 274.
. Gold,

 

INDEX;

Gold, how much heavier than its bulk of water 155
Gold—heaters, to what a prodigious extent they can
, hammer out gold 4
Glafs, the ihapes into which it is generally ground for

 

 

 

optical nice “A . 2'07
‘ ‘Globes, their ufe 24.7
Gravity ‘ I 8
..._——decreafes as the fquare of the Idif’tance increafes IO
Hand-mill ' 8!
Harvei’tm moon \ i 306
Heaven‘s, their apparent motion 2 5°
Horizon, fenfible and rational - 251
Horfe-mill “ 82
-‘—-.-—-Pump 126
Hour-circles 253
Hydraulic engines 1 12—1 34.
Hydroi’tatics , 10 1—1 10
Hydroi’catic balance 154
.— -—paradox - 104.
._——-—--—-—bellows ’ 107
-—-—-tables . I 135—146
Inaé’rivity of matter _ 2
Inclined plane ' 59' ‘
'lnfinite divifibility of matter 5
Intermitting fprings K ‘ 1 1]
Kepler’s problem concerning the-fquares of the periods
and cubes of the difiances of the planets 34.
Latitude, how found 346
Laws of the planets motions 23
Lead, how it may be made ‘to fwim in water 109
Lewenboek, his account of the number and [126 of the
fmall animals in the milt of a cod-fill] 4.
Lenfes, their properties .20]
Lever, its ufe 49
Light, the amazing fmallnefs of its particles 201
reflected ' ‘ 202
-—--——-—- refraéied 203»
Line of direé’rion ~ 13
Loadflone, its properties 17

I Ng‘p E x.‘

Lang (Rev. Dr.) his curious 'eXperiment with a con.- i

; cave mirrour» . ‘ '22'7
_'.__.—his glafs ‘fphere , , . V 312
Looking—’glafs ' ' 24.0
-—-————- need be- only half the length ‘and half‘the

breadth of a man, to fhew him his whole image 24:

Magnetifm .V I7
\ Man, how he may raife himfelf up by his breath 109
of a middle fize, how much he is prefl'ed by the

 

 

 

 

 

 

 

 

atmofphere . p I 7 I
Matter, its properties ' . “1—49
Mechanical powers ' 4.9- ,

‘ all combined in one engine - , 7o
Metals, expand by heat ' . 4 15
-——--—- their fpecific gravities . l , 158
Microfcope, fingle \ x ‘ . .. 218
double , ' ib_. .
, , folar , ‘- . _ 219‘
Mills for grinding corn , 71—80
Mirrours, how they refleé’r the light ' 221"
Monfoons _ . 174.
Moon, the law of her motion l 3, 2'4, 23
Motion (all) naturally reétilineal \ p ‘ 20
Multiplying glafs N " i“ 237
New/[Jam’s engine for extinguifhing fire ‘124
0 . g .
Objeéts, how their images are formed by means of
glaifes , V , . , 210
‘ why they appear ereé’c, notwithftanding their ‘

images are inverted in the eye 214.

-——--— why they appear coloured when {ecn througiv
- fome telefcopes ~ ‘ , 232

Opera-glafs ‘ 240

Optic nerve, why that part of the image which falls

upon it is lofl: 215
Padmore (Mn) his improvement of cranes 89
Periwci pf ‘ ‘ 268

' Perfian wheel , 152
Pile engine . _ ' 98
Planetary motions (the laws thereof) , , 2 3’

-' . I Poles

 

/ .

IiiN DE X9:

Poles of the earth and heavens " 249.452
Polar circles * ~ 256
Porofity of bodies . _ 15
Precepts for calculating the mean times of new and

- full moons and eclipfes , - , 377
Prifmatic colours ' ' .. 243

_—-....—__-——- make a white when blended together 24 5 ,

 

‘ Pulley _ _ 57’
Pump, common ‘ 1 I7
...._..._.. fercing ' 122
——-——- engine to work by water 125
7+ by horfes ' 126

’ \Pyrometer ' 16

Quantity of matter/in bodies, is in ‘exaét proportion

, to their weight 10
Qrickfilver its weight ’ ‘ 171
Rainbow ' 246

_ Rays of light ‘ / 291
; Repulfion , " . r 7
Right afcenfion 300
Running water, its weights ‘ I41

Sails ofawindmill, their proper, form and angler \ 82 ,

 

 

\ ‘ —-——-- their incredible velocity 83, 84.
Screw, its pOWer , . 68
—-‘——-——- {hewn by a machine , ib.
Seafons, how they may be {hewn by a {mall globe 257
Signs of the zodiac 2 5 5
Silver, how much heavier tha'n its bulk of water 155
Slare (Dr.) his dangerous experiment 200

‘ ‘ Solidity of—matter I _
Specific gravities of bodies , ’ 1'53 -
Spectacles, why fome eyes require them 2 177
Spirituous liquors, to know Whether they be genuine»

, [or not 160
Spouting fluids » ~ r. I I I ,
Steam (or fire) engine 143 "
Steel yard ‘ I 5 I
Sun,~ appears above the horizon when he is .really be-

. low it _ ' 204.
Syphon ' 4 i - I 13

Tamalm’s

~

INDEX.

 

or T ,
Tantalm’s cup ‘ 1 I 5
Table for mill-wrights.’ 80
-—-—--—of the quantity of water that may he raifed to any
given height by a common pump ‘ 122
.———--—of fines for the elevation of water-pipes I 32
.———-—-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 {team-engine 1 51
—-of fpecific gravities 158, I 59
--—----of troy weight reduced to avoirdupoife 1 65'
.—————of avoirdupoife weight reduced to troy 166
.———-—-of the rarity and expanfion of air ' ' 170
-———-—of the miles in a degree of longitude in all
latitudes 27 I

-—-—-3—- of the fun’ 5 place and declination 34o~345
T ablesfor calculating newandfull moons and eclipfe5384.

Telefcopes, refraéting and refleé‘ting 227—232
Temperate zones 274.
Thermometer ' 161
Thunder and lightning ' 1,76
Toricellian experiment ‘ I 70
Torrid zone 274..
Trade winds 17 3
Tropics 2 56 ~
U V 1
Up and down, only relative terms 248
Velocity of fpouting fluids III
Vifion, how caufed 211
Vivif in f irit in air ' J
.Y g P W 75‘
Water, how conveyed over hills and valleys 1 1 3
Waters mills 7 I
Wedge ‘ V 1 .62
Wheel and axle 55
Wheel-carriages ’ 90
Whirling—table ‘ 123
Winds, the caufe of 173
Wind—mill ‘ ' ~ 82
"M ood, though light, may he made to lie at the bottom
of Water 1 IO

Warld, hasa tendency of “Elf to come to an end 40,41

Zodiac '2 9,9 '
Zones ' 274
a A 5 U of:

 

l “A
s U P P L E M E N T
>To Mr. Fsacuson’s Book of

LECTURES.

Dd

 

 

 

"s U P P EEM ENT
MR. ‘E ERGU s om
BOOK of LECTURES.
G'I‘MEC‘HANI’es.‘

The Defcriptian of a new and fafe Crane, 'wbz'cb‘
1945 four dz'fizrmt Powers, adapi‘ed to dzfiermt
\ Weights. ‘

‘HE common cranehconfil‘ts only of a

l ‘ large wheel and axle; and the rdpe, by

which goods are drawn up from fhips,

or let down from the quay to them, winds or
coils mund by the axle, as the axle is turned by ‘
men walking in the”_whe‘el. But, as there “

engines have nothing to flop the weight from

running down, if any of the men happen to trip

'or fall in the wheel, the weight defcend’s, and

turns the wheel rapidly backward, and toffes the
men violently abouc ‘within it; which has pro- '

duced melancholy inl’cances, not only of limbs -
' D d 2 ' brolfc,

M E C H A N I C S
broke, but even of_ lives loft, by this ill-judged

'conftruétion of cranes. And belides, they have

but one power for all forts of weights , to that
they generally {pend- as much time in raifing a
fmall weight as in railing a great one.

Thefe imperfeétions and dangers induced me
to think of a method of remedying them. And
for that purpofe,4I contrived a crane with a
proper flop to prevent the danger, and with.
dilTerent powers fuited to different weights , {(1
that there might be as little lofs of time as pof-
fible: and alto, that when heavy goods are let

down into lbips, 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
f’taves, 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 largei’t trundle 24 (faves,
the next largel’t has 12, and the fmalleft has 6.
So that the largeit trundle makes 4 revolutions
for one revolution of the wheel ; the next makes
8, and the fmallef’t makes 16. ,A winch is
occafionally put upon the axis of either of theft:
trundles, for turning it, the trundle being then

,ufed that gives a power bei’t fuited to the weight:

and the handle of the winch defcribes a circle 1n .
every revolution equal to twice the circumfe-

- rence of the axle of the wheel. 80 that the

,r length-

 

MECHVANICS.

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 eafily
eflimated, and they are as follows.

If the winch be put upon the axle of the
largef’t 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, doublethe
circumference of the axle, when the thicknefs of
the rope is added thereto 3 the power goes
through eight times as much fpace 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 itrength Without it: the power,
in this cafe, being as eight to one.

If the winch be put upon the axis of thepnext
trundle, thepower will be as fixteento one, becaufe.
it moVes to times as fall as the weight moves.

I If the winch be put upon the axis of the
vfmallel’t trundle, and turned round -, the power .
’willbe as 32 to one.

But, if the weight {hould be too great, even
for this power to raife, 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 m0veable block, which.is hooked to the
weight below the arm of the glib; aggl then the
- . D d 3 ., ' power~

MECH‘ANI'CS.
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 raiie by his natural
flrength 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
move-able block that rifes with the weight, the
rope being doubled over and under thefe pullies,
the power Dof the crane ‘will be as 128 to one.
And f0, by inmeafing the number of pullies, the
power may be increa fed as much as you pleafe:
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 fucceflively into them, and f0 hinders
the crane from turning backward, and detains
1 the weigh t in any part of its a cent, if the man .,
who works at the winch lhould accidentally
happen to quit his hold, or choofe to relt him-
‘ felt before the Weight be quite drawnup. 1

In order to let down” the weight, a man 'pfulls
down one end of a' lever of thegfeoond kind,
which lifts the catch of the ratchet-wheel, and
gives the weight liberty to defcend. But, if the
defcent' be too quick, he pulls the lever a little
farther dov17n, f0 as to make 1t- rub again-it the
outer edge of a round wheel; by which means
he lets down the weight as {lowly as he pleafCSe .
1 and, by pulling a little harder, he may flop the

weight,- it nee iii, in any part of its defeent
, . , ' I

 

 

 

 

 

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MECHANICS,

If» he accidentally quits hold of the.;l,ei£er,gthe
catch immediatelyfalls,‘ and flop-snhoth the
weight and the whole machine; .~ ;,

This crane is reprefented in- P L A T E. l.‘
where A is the, great wheel, and‘B itsiaxle 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'tou‘n‘dp His the largef‘t trund-le,t..Lthe ' \

next,-- and K is the ads of the {mallefittrundlfi
which isflfuppofed to be hid from view by the
upright {appotter L. . A trundle M is turned
by the great ,wheel, and on the axis of this
trundle is fixed the ratchetnwheel 1V, into the
[teeth ofwhich the catch 0 falls; _P is the lever,
from which goes a rope QQ, over a pulley R
‘ to the catch 5 one end of the rope beingfixcd
‘ to'the lever, andthe other end to the catch? S
is an elafiic 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)th the
further end of the lever, beyond the pin or axis
on which it turns in the upright fupportjep T
The ufe of this bar is tokeep up theulever, from
rubbing againfit the edgeof the wheel U, and to
let the catch keep in the teeth of the ratchet-
wheel : But a weight hung- to the farther eradiof
the. lever would do full as well as the elai’cic‘ bar
and rope. ' :

When the lever is pulled down,:it"lifts the.
’catch Out of the ratchet-wheel, byrmeans ef the
7 gope Sig; and gives the weight F liberty!»

[defcendz but if the" lever P‘be ‘fiulleda‘little
\ farther down than what ‘is‘fuflicient to, lift the
catch 0011: of the ratchet-wheel N, it will rub

- D d 4 againfi:

eii

MECHANIcs
againl’c the edge of the Wheel U, and thereby
hinder the too quick defcent of the weight; and

will quite [top the weight if pulled hard. And
if the manwho pulls the lever, lhould happen

inadvertently to let it go; the elaf’tic bar will

fuddenly pull it up, and thegcatch will fall down‘
and flop the machine.

W W 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 firetched clofe by their utmol’t

fides, the half thicknefs 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
pofitiflons 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
OE from the wheel, after the pin ngar the axis of-
.the trundle is drawn out, and the thick piece of
wood is raifed a little behind the outward fup-
porter of the axis of the tmndle. But this is
not material : for, as the trundle has no friétion
on its axis but what is occafioned by its weight,
it will be turned by the wheel without any fens
fible tefiftance in working the crane.

A Pyroe ‘

I“; ‘i‘iixjsia €335 ‘
figural? 56 if)"

 

 

 

 

     
     
  
   
     

 

    
    
   

     
          
    
 
    

  
   
  

   
  
 

      
  

 
 

   
  
 
 

    

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Jim 52..

MECHANICS.

A Pyrometer, that makes the Expmg/z'on of Metals
by Heat rvz'flble to tbefi‘ve and forty t/aoufandtb
Part of cm Inch. ‘

The. upper furface of this machine is rcpt-e.
fented by Fig. I. of Plate II. Its frame AB C D
is made of mohogany wood,.on which is a circle

divided into 360 equal parts; and within that

circle‘is another, divided into 8 equal parts. If
the {hort bar E be puihed one inch forward (or

toward the center of the circle) the index 3 will »

be turned I 25 times round the circle of 360 para;
or degrees. As 12 5 times 360 is 45,000, ’tis evi-
‘ dent,thatif the barE 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 vifible to half a degree, which'anfwers to the
ninety thoufandth part of an’inch in the motion
or pufhing of the fliort 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 againf’t the end of

the fhort bar E, over; the fupporting crofs bar t

H I‘: and, as the endfof the long bar is placed
clofe againli the end of the lhort bar, ’tis plain,
that if F expands, it will puih E forward, and
-.turn the index (2.

The machine Hands on four Ihort 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
cxPands the bar, and turns the index.

There

‘év

30'

_ s
M E C H‘A N‘IC S.
_ There are bars of ‘difi’erent metals, as filver,‘
bralzs, andiron; all of the fame length as the
bar F, for trying experiments on the diEerent
expanlion of different metals,- by equal degrees
of heat applied. to them for equal lengths of
time; which may be meafured by a pendulum,
that {wings fecorids. Thus, ‘ '

Put on the brafs bar F, and fet the index to
the 360th degree: then put the lighted lamp
under the bar, and count the number of feconds
in which the index goes round the plate, from
J360 to 360 again; and then blow out the lamp,
and take.away the hat.

‘ ‘\

This done, put onan irombar F where the .
brafs 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 jufl:
as many feeonds as it did under the brafs one;
and then blow it out, and ybu 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
expanfion of difl'erent metals may be found, '

 

The bars ought to be exaétly of equal fize ;
and to have them To, they lhould be drawn,-likc

‘ wire, through a hole.

‘ When the lamp is blown out, you will-fee the
index turn} backward; which fhews» that the
metal contraéts‘ as it cools.

The infide of this pyto‘meter is conl’truétedras
follows. -~

In

\

MECHANtos
In Fig. '2. A a is the fliort‘bar, which moves
between rollers; and, on the fidea 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'Cpf IOO teeth, which take into the 10.

leaves of the piniOn D,. on whole axis is the

.wheel E of too: teeth, which take into the 10
leaves of the pinion ‘F, on the tor) of whofe aXlS,

is the index above- mentioned.

a , Now, {as the wheels C and E have too teeth
each, and the pinions D and F have ten leaves
each; ’tis plain, that if the wheel C turns once
round, the pinion F and the index on its axis
will turn 100 times round. But, as the firl’t
pinion B has only 12 leaves, and the bar Aa

that turns it has 15 teeth in an inch, which is

12 and, a fourth part more; one inch motion of

thebar will caufe the lal‘t pinion F to turn an '
hundred times, round, and a fourth part of an. .

hundred over and above, which is 25. 'So that,
if 14 a be pufhed one inch, F will be turned 125

times round. .

- A, filk‘ thread’b is tied to the axis of the pinion

ID," and wound ‘feVefal times round it; and the
Other end of-the thread is tied to a piece of.

flender watch-{tiring Gwhich is fixed into the
fiud H. So that, as the bar f eyepands, and
pufhes the bar A? a ferward, the thread winds
round the-axle, and draws out the fpringg and
as the barfeontraéls, the fpri‘ng pulls back the
thread, and turns the work the contrary way,‘
which'pulhes back the (hon: bar .4 a againl‘tthe

I

long barf. ‘This fpring always keeps the teeth
‘of‘ the: wheels in contact with theleaves of

the

m3

u

MECHANICS

the pinions, and f0 prevents any {bake in the

teeth. ' '
i‘ I I

In Fig. I. the eight divifions of the inner

circle are f0 many thoufandth parts of ‘an inch

in the expanfion or contraction of the bars;

which is juft one thoufandth partof an inch for,
each divifion moved over by the index.

'2! ”war-Mil, invented by Dr. Barker, that 124:

”cit/yer Wheel nor Trundle. '

This machine is reprefented by Fig. I. of
Plate III. in which, .4 is a pipe 01' channel that
brings water to the upright tube B. The

/ water runs down the tube, and thence into the

horizontal trunk C, and runs out through holes
at 2! and it 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 crofs ,
bars at f: fo that, if the tube B,and trunk C
be turned round, the fpindle D will be turned

alfo.

The top of the fpindle goes fquare into the
rynd of the upper mill-{tone H, as in common
mills; and, as the trunk, tube, and fpindle turn
round, the mill-{tone is turned round there—
by. The lower, or quiefcent mill-{tone is re-
prefented by I ; and K is the floor on which it
refis, and wherein is the hole L for letting the

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‘MECHANIC&

meal run through, and fall down into a trough
which may be about M, The hoop or cafe
that goes round the mill-{tone refts on the floor
K,‘ and fupports the hopper, in the common.
way. .The lower end of the fpindle turns in a
hole in the bridge-tree G F, which fupports the
mill-Prone, tube, fpindle, and trunk. This

tree is moveable on a pin at b, audits other end . ‘

is fupported by an‘iron‘rod N fiXt into it, the
top of 7 the rod going through the fixt bracket ,
O, and having a {crew-nut 0 upon it, above the

“bracket. By turning this nut forward or back-

ward, ’_the mill-{tone is raifed or lowered at
pleafure,

Whilfi the tube B is kept full of water from
the pipe 1, and the water continues to‘ run out
from the ends of the trunkythe upper mill-
fione H, together with the’trunk, tube, and
fpindle, turns round. But, if the holes in‘thc
trunk were Item, no motion would enfue; even
though the tube and trunk were full of water.

F or,

If there were no hole in the trunk, the prefi-
fure of the water would be equal againfi all
parts of its fides within. But, when the water
-has free egrefs through the holes, its preffure.
theregis entirely removed: and the prefibrc
againfi the parts of the {ides which are oppofitc
to the holes, turns the machine

L14» 1*
HYDROSTLAATICS.

)1 Machine for demonflmting that, on, equal Bot-
tom, the Prqflure 0f Fluidt. is in Proportion ta

_ their perpendicular Heights, without any regard
to their ngantflz’es. '

V _ HIS is termed 779a [firdrofliztiml Paradox:
. and the machine for {hewing it is reprer
fented in Fig.“ 2. of Plate III. In which A is a
box that-holds about a poundof water, , a b w! e
a glafs-tube fixt— in the top of the box, havi'ng'a
{mall wire within it; one end of thewite being
hooked to the end F‘of the beam ofa balance,
and the other end of the wire Ext to a mov‘eablc
bortom, on which the water lies, within the
box ; the bottom and wire being of equal
weight with an empty fcale (out of fight in the ,
figure) hanging at the other end of the balance.
If this feale be pulled down, the bottom will be
drawn up within the box, and. that mOtion will
caufe the water to rife in the glafs-tube.

, Put one pound weight into the fcale, which
will move the bottom a little, and caufe the
water to appear jul‘c‘in the lower. end of the
tnbeat (2‘; which fhews that the water preffes
with the force of one pound on the bottom: put
anothei' pound into the fcaJe, and the water will
rife from a to b in the tube, jul’t 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 prefl'ure‘
on the bottom is then equal to two pounds.

Put a third pound weight in the kale, and the
‘ water

HYDROS TAT'I CS.
water will be,raifed‘fr0m {2th c in the tube,
th‘ree'times as high above the bottom as when

it began to appear in the tube at a; which ~

Ihews, that the fame quantity of water that
prefled, but with the force of one pound on

the bottom, when raifed no higher than 51,.

‘prefi‘es with .the force of three pounds on the
bottom when raifed three times as high to c in
the tube. ’ Put a fourth pound weight into the.
feale, and it will caufe the water to rife in the
tube from c to 4’, four times .as. high as it was
when it (was all contained in. the box, which
fliews that its prelTurexthen upon the bottom is
four times as great aswhen it lay all within the
box. Put a fifth pound weight into the feale,
and the water will rife in the tube from d to 3,
five times as high as it was above the bortom
before it rofe in the tube; which fhews that its
prelfure on the bottom is then equal to five
pounds, feeing that it fupports {0 much weight
inithe feal'C. And f0 on, if the tube was f’till

longer; for it would, {till require an additional.

p0und’ put into the foal-e, to raife the water in

the tube to an additional height equal to the-

{pace dc; even if the bore of the tube was f0
fmall as only to let the wire m0ve freely within
'it, and leave room for any water to get around
the wire. .

‘Hence we infer, that if a long narrow pipe
or tube was fixed in the toptof a .call; full of
liquor, and, if as much liquor was poured into
the tube asiwould fill” it, even though it were
fofmall as not to hold an ounce weight of.li-
qUor; the prefi‘ure arifing from the liquor in
the tube would be as great upon the bottom,

» ' , . and

:6

HYDROSTATICS;

and be in as much danger of buri’ting it out, as»! i
if the caik was continued up, in its full fize, to '
the height of the tube, and filled with liquor. '

In order to account for this furprifing affair,
we mull: confider that fluids prefs'equally in all
manner». of direétions ; and confequently that
they prefs jufl: as. firongly upward as they do
downward. For, if another tube, asf, be put
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 0E pouring,
when the water is at r, or any other place in the
tube a 22 rd e, you will find it jufi; as high in the
tubef: and if you pour in water to fill the firfl:
tube, the fecond will be filled alfo.

Now it is evident that the water rifes in the
tube f, from the downward preITure of the wa-
ter in the tube abode, on the furface of the
water, contiguous to the infide of the tap of the
box; and as it will [land at equal heights in
both tubes, the upward preITure in the tube f is
equal to the downward prefi'ure in the other tube.

But, if the tube f were pu: in any other part of

the rep of the box, the rifing of the water in it
would i’till be the fame: or, if the tOp was full
of holes, and a tube put into each of them, the
water would rife as high in each tube as it was
poured into the tube aécde; 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 i

HYDROS T‘ATICS.

And feeing that the water'is preH'ed upward
‘into each tube, ’tis evident that, if they be all
taken away, excepting the tube abcd e, and-
the holes in which they {lood be fiopt up ; each
part,vthus fiopt, will be prelTed as much up-
ward as was equal to the weight ofwater in each
tube. 80 that, the upward prefi‘ure againl’c the
infide of the top of the box, on every part equal
in breadth ‘to the width of the tube a 5 c d 6, will
be preffed upward with a force equal to the
whole weight of water in the tube. And confe-
quently, the whole upward prelTure againfl: the
top of the box, ariling from the weight or
downward prei’fure ofthe 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 thicknefs as the width of the infide of the
box: and this upward prellure againlt the top
will react. downward againl’t 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
wateril’tands in the tube.‘ And thus, the para:
dox is folved.

. The movea-ble bottom has'lno friflion againl’c
the infide of the box, nor can any water get,

between it and the box. ' The method of malts .

ing it f0, is as follows :

In-Fig. 3.,flBCD reprefents a feétion' of‘the ,

box, and a 5 cd is the lid or top thereof, which

goes o‘n‘tight, like the lid of a common paper

fnLIEbox. E is the moveable bottom, with a

groove around its edge, and it is put into a

bladderfg, which is tied clofe around it in the
’ e

' groove

.17

18

'HYDROSTATICS.

groove by a {troyng waited 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 prefi‘ed on. So that, if water be
poured inthrough the hole I l of the lid, it will V
lie upon the bottom E, and be contained in the ’
{pace f E gb within the bladder 3 and the bot-
tom may he raifed by pulling the wire 1', which
is fixed to it at E: and by thus pulling the
wire, the water will be lifted up in the tube it,
and as the bottom does not touch againfi the ,
infide 10f the box, it moves without frié‘tion. ‘

, Now," fuppofe 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 5 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 moveabl'e
bottom be raifed only the'1'44th part of an inch,
the Water will thereby be railed a whole inch in
the tube -, and confe‘quently, that if theibottom‘
be raife‘d one inch, it would raife the water to:
the top of a tube 144. inches, or 12‘ feet, in

height.

N. B. The box muff be Open below the‘
moveable bottom, to let in the air. Other-
wile, the prelTure of the attmofphete would be
f0 great upon the moveable bottom, if it be

three inches in diameter, as to require 108

pounds in the fcale, to balance that prefi‘ure,
before the bottom. could begin to move.

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HYDROSTATICS.’

.4 Machine, to be fab/filmed in Place of [be come
man wdroflatz'ml Bellows.

In Fig.1. of PLATE IV. AB CD is an
oblong fquare box, in one end of which is a.
round groove, as at oz, from top tobottom, for
receiving the upright glafs tube I, which is bent
to a. right angle at the lower end (as atz' in Fig. 2.)
and to that part is tied the end of a large blad-
der K, (Fig. 2.) which lies in the bottom of the

- box. Over this bladder is laid the moveable
board I. (Fig. I. and 27.) in which is rfixt an up- V

right Wire M; and leaden weights, NN, to
the amount of 16 pounds, with holes in their
middle, are put upon the wire, over the board,
and prefs upon itwith all their force. -

The‘crofs barp is then put on, to fecure the
tube from falling, and keep it in. an upright pofi-
tion : And then the piece E PG is to be put on,
the part G fliding tight into the dove-tail’d
groove H, to keep the weights N N horizontal,
and the wire Mupright; there being a round
hole at in the part E F for'receiving the wire.

There are four upright pins in the four cor-
‘ners of the box within, each almof’t an inch long,
for the board L to tell upon , to keep it from‘
prefling the tides of the bladder below it clofe
together at firf’t.

The whole machine being thus put together,
pour water into the tube at t0p-, and the
water will run down the tube into the bladder
below the board ; and after the bladder has been

E e 2 filled

1§

,20

HYDROSTATIcs

filled up to the board, continue pouring water
into the tube, and the upward prelTure which it
will excite in the bladder, will raife the board
with all the weight upon it, even though the
bore of the tube {hould be fo fmall, that lefs
than an ounce of water would fill it.

. This machine acts upon the fame principle,
as the one lafi; defcribed, concerning the Moira-
flatz'cczl paradox. For, the upward . preffure
againft every part of the board (which the
bladde1 touches) equal in area to the area ofthe
bore of the tube, will be prefied upward with a
force equal to the weight of the water in the
tube; and the fum of all thefe prefi‘ures, againfi
fomany areas of the board, will be fuflicient to
raife it with all the weights upon it.

In my opinion, nothing can exceed this fitn-
ple machine, in making the upward prefihre of
fluids evident to fight. '

The Caufi of reciprocatmg Spriflgs, and of ebZing
andflowing Wells, explained. '

In Fig.1.of PLATE V. Let a b c dbe a hill,

~wi: hin which is a large cavern Affl near the

top, filled or fed by rains and melted fnow 0n
the top (2, making their way through chinks
and crannies into the {aid cavern, from which
proceeds a {mall fiream cc within the body of
the hill, and ifTues out in a fpring at G on the
fide of the bill, which will run confiantly whilfli
the cavern is fed with water.

From the fame cavern flfl, let there be a

fmall channel D, to carry water into the cavern

 

 

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HYDROST Africa“, P
B ; and from that cavern, let there be a bended
channel EeF, larger than D, joining with the

former channel 6 c, as atfbefore. 1t comes to the
fide of the hill: and let the joining atf be

b low the level of the bottom of both thefi: ,

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 c, it will run down
the part 6 F G, and make a {well in the fpring
' G, which will continue till all the water is drawn
OE from the cavern B, by the natural fyphon
E e F, (which carries ofi the water fafier from B,

than the channel D brings water to it) and then

the fwell'will fi0p, 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 ‘beingyat the top e of the channel
E e P, that Channel will act again as a fyphon,
and carry oilf all the water from B to the fpring

G, and lo make a fwelling flow of Water at G as '

before.

To illuf’trate this by a machine (Fig.9z.) lgtgfl
be a large wooden box, "filled with water , and
let a {mall pipe CC .(the upper end of Which 15
fixed into the bottom of the box) carry water
from the box to G, where it will run OFF Cen-

fiantly, like a final] fpring. Let another. {mi-all}

pipe D carry water from the fame box to the
, ”box or well B, from Which let a fyphon :EeF

proceed, and join with the pipe CC atf: the;
‘ bore of the fyphon being larger than the bore of.

the feedingopipe D.. As the water from this
pipe rifes in the well B, it will alfo rife as high
in the fyphon E e F, and When the fyphonb' is

E e 3 full

23'.

H Y'D-R A U L PC 8.,

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 fljream at
G : and that fiream will continue, till the fyphon
hasicatricd off all the water from the well 8;
the fyphon Carrying ofl’ the water falter from B
than the pipe 1) brings water to it: - and then
the {wellth G will ceafe, and only the water
from’jtjhe {mall pipe CC will run off at 'G, till,-
the pipe I) fills the Well B again; and then
the fy'phon will run, and make a {well at G as,
before; '

And thus, we have an artificial reprefentation
of an ebbing and flowing well, and of a red:
procating fpring, in a very natural and fimple
manner.

HY‘DRAULics,

'Jn Account of the Principles by whit}: Mr. Blakey
propofl’s to wife Water fram Mines, _or from,
River: to [apply Towns and Gentleman’s rvSeats,
by his new invented Fire- Engine1 for which be;
be: received His'MAJESTY’s Pntenl.

' LTHOUGH I am not at liberty to. de:

“‘ ifcribe the whole of this fimple engine, yet

l’haxfe the patentee’s leave to defcribe fuch a,
one as will {hew the principles by which it aé‘ts,

In Fig. 4.. of PLATE IV. let A be a large?
firongxclofe vefi'el; immerfed in water up to
the-COEk n, and” hailing a hole in the bottomz .
With a valve d Open it, Opening upward within;
Witcfiglz A Pix“: 5 Q ¥ll¢§ item the hqtmgf’

 

~HYDRAULICS."
of this vefl‘el, and has a cock c in it near the
top, which is fmall there, for playing a very
high jet 22’. E is the little boiler (not {0 big as”
a common tea—kettle) which is‘ connected with
the vefl'el A by the {team-pipe F; and G is a

funnel, through which a little water mull be A

‘ occafionally poured into the boiler, -tO yield a

prOper quantityvof i’team. And a fmall quantity .
i of water will do for that purpofe, becaufe Ream?

poffefi’eth upwards of 14,000 times as much

{pace or bulk as the water does from which it

proceeds,

The vefibl A being immerf‘ed in water up to I

the cock 5, open that cock, and the water will
,rulh in, through the b0ttom of the veflel at a,
and fill it as high up as the water {lands 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 .5. . When the, ,

water has done rulh‘ing into the veITel, (but the
cock k, and the valve 4 will fall down, and hin-
der the water from being pulhed out that way,

by any force that ptefi‘eth on its furface. All
the part of the vefi‘el above 5, will be full of '

common air, when the water tiles to Z».

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
theboiler; and then {hut the cock 4, and leave
. the cock eaopen,

This done, make a fire under the boiler E,
and the heat thereof will raife a {team from the

water. in the boiler; and the (learn will make _‘

its,_ way thence, through the pipe F, into the
' E e 4 vcffel

d4

iH-YDR‘AULICS.

vefi‘el A; and the {team willcomprefs the air!
(above 5) with a very great force upon the fur-

‘face‘of the water in A. ‘

When the top of the vefl‘el A feels very hot
by the {team under it, open the cockc inthe

pipe C; and the air being firongly comprefled

in X, between the [team and the‘water therein,

‘ will drive all the water outiof the velTel fl; up

the pipe BC, from which it will fly up in ajet
to a very great height.——g——In my fountain,
Which is made in this manner after Mr. Blakey’s,
three tea—cupwfulls of water in the boiler will"
afford {team enough to play aijet‘ 30 feet high.

When all the Water is out of the vell'el .4, and

t the comprefled air begins to follow the jet,

open the cocks Zzandd to let the fieam out of
the boiler E and veilel fl, and {hut the cock 3
to prevent any more. {team from getting into fl;
and the air will rulh into the Vefl'el fl through-
the cock 5,, and the water through the valved;
and {o the vefTel will be filled up with water to
the'sacock b as before. Then (but the cockél
and the, cocks c and d, and .open the cocke;
and then, the next {team thatrifes in the boiler
will make its way into the velTel 11 again 3 and

the operation will go on, as above.

When all the water in the boiler E is evapo:
rated, and gone off into-fieam, pour a little
more into the boiler, through the funnel G.

'In order to make this engine raife water‘ to
any gentleman’s houfe; if the houfe be on the
bank of a river, the pipe B C may be continued

UP.

HYDRAULICS.

up to the intended height, in the direction HI.
,. Or, if the houfe be on the fide or top of a hill,
at a dif’tance from the river, the pipe, through
which the water is forced up, may be laid along
,. on the hill, from the riVer or {pring to the houfe.

The boiler may be fed by a {mall pipe K,
from the water that rifes in the main pipe
BC H]: the pipe K being ofa very fmallfl bore,
{0 as to fill the funnel G with water in the time
that the boiler E will require a frelh fupply.
And then, by turning'the cock d, the water will
fall from the funnel into the boiler. The fun-
nel lhould hold as much water as Will about half

fill the boiler. \ I

When either of thefe methods of railing water,
perpendicularly or obliquely, is ufed ; there will
be no occalion for having the cock c in the
main pipe 8 CH]: for fuch a cock is requifite
only, when the engine is ufed as a fountain.

A contrivance may be very eafily made, from

a lever to the cocks b, d, and e; fo that, by
pulling the lever, the cooks b and 4 may be

opened when the cock e muf’t be fhut; and the

cock ebe opened when 5 and cl mutt be 1’hut.

The boilerE fhould be inclofed in a brick wall,

.at a little 'difiance 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 coverng the funnel G) the force of the
fieam will be prodigio‘ufly increafed by the heat
round the boiler; and the funnel and water in
it will be heated from the boiler; {0 that, the
‘ ' ' boiler

‘ .

25

36

HYDRAULIC$>
boiler will not be chilled by letting cold water

into it; and the tiling of the {team will be {q

much the quicker.

Mr, Blakey is the only perfon who ever thought
of making ufe of air as an intermediate body
between fieam and water: by which means, the
{team is always kept from [Ouching the water,
and confequently'fmmbeing condenfed by it;
And, onthis new principle, he has obtained a
patent : {0 that no one (vary the engine how he
Will) can make me of air between fleam and
water, withotlt infringing on the patent, and
being fobjeét to the penalties of the law. ‘

iThis engine may be built for a trifling 6X-

(pence, in comparifon of the COmmon fire engine

now invufe: it will feldom need repairs, and'
will not confnme half f0 much fuel. And as it;

has no pumps with pif’tons, it is clear of all their

fri'é‘tion: and the effeé‘t is equal to the whole,
firength or comprefiive force of the {team ‘:

which the effect of the common fire engine never:
is, on account of the great friction of the pii’tons

in their ptimps. ' ‘

A R, C H I M E D E 8’: Screw-Engine far miflflg
" Water.

Ian‘g. I. ofVPLATE VI. flBCD isa
wheel, which is, turned round, according to the '
order of the letters, by the fall of water E F,
which need n0t be more than three feet. The
axle Gof “the wheel is elevated f0, as to make ‘
an angle of about 44. degrees with the horizon ;

, and on the topof that axle is a wheel H, which

turns fuch/another wheel I of the fame numhe‘n

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HYDRAuLtcs

of teeth: the axle K, {Of this hit wheel being

parallel to the axle G of the two former wheels.
The axle G is cut into a doubleethreadecl

fcrew (as in Fig. 2.) exaétly refembling the forew-

on the axis of the fly of a common jack, which ,

' Inuit be (what is called) a right-handed-fcrew,
like the wood-ferews, if the fir-It wheel turns in
the direction .43 C D; but mutt be a left-handed
fereW, if the firearm turns the wheel the contrary
‘ way... And, which-ever way the fcrew on the
axle G be cut, the {crew on the axle Kmult be
cut the contrary way, becaufe thefe axles turn
in contrary-directions. '

The fcrews being thus cut, they mul’t be

covered clofe over with boards, like thofe of a
cylindrical calk; and then they will be fpiral
tubes. Or, they maybe made of tubes of fill?
leather, and wrapt round the axles in fhallow
grooyes cut therein; as in Fig. 3.

The lower end of the aide ‘Giturns conl’tantly“
in the {tream that turns the wheel, and the lower.

ends of the fpiral 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'rL, through the holes M, N, as they come

about below the axle. Thefe holes (of‘ which

there may be any number, as four or‘fix)‘ are in
a broad elofe ring on the top of the axle, into
which ring, the water is delivered from the

~ upper open ends of the {crew-tubes, and falls."

into the Open bpx N,

The lower end of" the axle 'K turns on ad

ggdggon, in the water in N 5 and the fpiral
- 1 tubes

@717 .

28

Hut;
,3.

_HYDnmULIcs

tube;~ in that axle take up the water from-Ni,
and deliver it into fuch another box under the
t0p of K ; on‘l’which there may be fuch another

wheel as, I, “to turn a thirdi‘axle by fuch a wheel '

upon it.---—-—And in this manner, water may be
raifed to any given height, when there is a‘

" fiream fufficie‘nt for that purpofe to act on the

broad float boards of the firi’t wheeL

A" gzzaa’mple Pumpfl/Jz’flfor mi/z‘izg Water.

This engine is reprefented in P LA T‘E VII.’
In which AVE CD is a wheel, 'turned‘ by water
according to the order of the letters. On the
horizontal axis are four fmall Wheels, t00th'ed
almoi’t half round : and the parts of their edges
on which there are no‘ teeth are cot down fo, as
to be even with the bottOms‘of the teeth where
they Fraud} ‘ i ‘ ‘ -

The teeth of thefe four wheels take alternately
into the teeth of four racks, which hang by two
chains over the pullies Q and L; and to the
lower ends of thele racks there are four iron
rods fixed, which go down into the four forcing
pumps, S, R, Mand 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 laf’t tooth ova jufl: leaves the‘
uppermofl: tooth of I, the firl’t teeth of His
ready to take into the lowermol’t tomb of the ~
rack K and pull it down as far as the teeth go ; ,

and

fi‘r‘4‘f *3

59‘

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' H ,YDR AU L'I'C s.
and then'the rack I is' pulled upward through

the whole {pace of its teeth, and the wheel G is
ready to take hold of it, and pull it down again,

and f0 draw up the other. ' In the fame ‘

 

manner, the wheels E and F work the racks O
and P. ‘ .

Thefe four wheels are fixed on the axle of the
great wheel in fuch a manner, with refpeéi: to
the pofitions of their teeth; that, whilfi they
continue turning round, there is never one
, infiant of time in which one or Other of the
pump-rods is notgoing down, and forcing the
water. So that,_ in this engine, there is no
occafion‘ for having a general air-veilel to all the
pumps, to procure a confiant {tream of water
flowing from the upper end of the main pipe.

The pii’tons of_thefe‘pi1mps are folid plungers,
' the fame as defcribed in the fifth Lecture of my
book, ”to which this is a Supplement; See
PiLATE XI. Fig. 4.. of that 500k, with the

defrrzptz'bn of tine figure.

' From each ,of thefe pumps, near the lowef‘cj
end, in the water, there goes ofica pipe, with a
rvali/e On its farthei’t end from the pump; and
thefe ends of the pipes all enter. Gne clofe box,
into which they deliver the water: and into this
box, the lower end of the main conduct pipe is
fixed. 80 that, as the water is forced or pufhed
into this box, itis alfo pufhedlup the main pipe
to the height that it is intended to be raifed.

’ ' There [is an engine of this fort, defcribed in
anqlli’s Work: but I can truly fay, that I
* ‘ \ ‘ never

729'

 

.33

DIALLINQ

flever {aw it till fome time after I had made this
model.

The faid model is not above twice as big as,

V the figure of it, here defcribed. I turn-it by a

winch fixed on the gudgéon of the axle behind
the water wheel; and, when it was newly made,

- and the pifions and Valves in good order, I put

tin pipes 15 feet high upon it, when they were
joined together, to we what it could do. And
Ifound, that in turning it moderately by the
Winch, it would raife a hoglhead of water in an
hour, to the height of 15 feet.

DIALLINQ
frag univerfal Dialling Cylinder.

N Fig. 11.0f PLATE VIII. flBCD re;
1 pretents a cylindrical glafs tube,/ clofed at
both ends with brals plates, and having a wire or ‘
axis EFG fixt 1n the centers of the brafs plates
at top and bottom. I his tube is fixed to a ho- ‘
rizontal board H, and its axis makes an angle v
with the board equal to the angle of the earth’s
axis with the horizon of any given place, for
which the cylinder 13 to ferve as a dial. And it .
Inuit be fet 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 particnlar latitude.

There are 24 firaight lines, drawn with 3 dia-
mend, on the outfide of the glafs, equidil‘tant
from each other, and all of them parallel to the
axis. T hefe are the hourflines , and the hours

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DIALLrNGQ
are fet to them as in the figure: the XII next 3

{lands for midnight, and the oppofite XII, next
‘ the board H, f’tands for mid day or noon.

1 The axis being elevated to the latitude of the
place, and the foot-board fet truly level, with the
black line along its middle in the plane of the
meridian, and the end N toward the north, the
axis EEG will ferve as a {tile or gnomon, and
calt a {hadow on the 110m of the day, among the
parallel hour lines when the fun {hines on the
machine. For, as the fun’ 3 apparent diurnal
motion is equable in the heaVens, the {hadow of
’the axis will move equabl y in the tube, and will
always fall upon that hour—line which is Oppofite
to the fun, at any given time.

The brafs plate A D, at the top, is parallel to
the equator, and the axis E F G is perpendicular
to it. If right lines be drawn from the center of
this plate, to the upper ends of the equidifiant
parallel lines on the outfide of the tube , thefe
right lines will be the hour- lines on the equi-
noélial dial 1! D,- at I 5 degrees dif’tance from
each other: and the bout—letters may be fet to
them as in the figure. Then, as the {hadow of
the axis within the tube comes on the hour-lines
of the tube, it will cover the like hour- lines on
the equinoétial plate A D.

If a thin horizontal plate 8 f be put within the
tube, [0 as its edge may touch the tube all
around, and right lines be drawn from the center
of that plate to thofe points of us edge which are

cut by the parallel hour lines on the tube, thefe,

right lines will be the hour-lines of a horizontal
dial, for the latitude to which the tube is elen.
" vated.

3::

32'

DIALLIING.

vated. For, as the lha‘dow of the axis comes"

fuccefi’ivelyto the hour-lines of the tube, and'
covers them, it will then/cover the like hour-
lines on the horizontal plate e f, to which the

' hours may be fet, as in the figure.

If a thin vertical plate g C, be ptit within the“
tube, 10 as to front the me1idian 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 thole points
of us edge which are cut by the parallel hour-
lines on the tube -, thefe right lines will be hour-
lines ofa vertical fouth- dial: and the lhadow of

‘ the axis will cover them at the fame times when p i

it 'c0vers thofe of the tube.

If a thin plate be put within the tube {0, as to
decline, or incline, or recline, by any given num- “
ber of degrees- , and rioht lihe‘s be d1aWn from
its center to the hour- lines of the tube thefe right 1/
lines will be the hour-lines of a declining, inclin-
ing, or reclining dial, anfwering to the lil:e nu 11-
her of degrees, Dfor the latitudeD to which the tube‘
is elevated.

And thus, by'this {imple machine, all the
principles of dialling are made Very plain, and
evident to the fight. .And the axis of the tube‘
(which is parallel to' the axis of the world in
every latitude to which it is elevated) is the fiile
or gnomon for all the difi‘erent kinds of fun-dials;

And lafily, if the axis of the tube be drawn,
out, with the plates 17 D, ef, and g C upon it,
and fet 1t up in fun-fhine, 1n the fame polition as‘
they were in‘ the tube -» you will have an equiw

noétial .

"otALLING;
team dial AD, 2 horizontal dial efif‘and a ver;
'tical fourh dial g C ; on all which, the time of the
day will be fhevvh by the lbadow of the axis or
g'nom‘On E FG. ‘ ,

Let us now fuppofe that; infiead of a glafs
tube, A B C D is a cylinder of Wood 3‘» on which
the 24 parallel hour-lines are dravlm all around,
at equal dif’tances from each Other; and that,
from the points at tOp, Where thefe lines end,
right lines are drawn toward the center, on the
flat furface A D : Thefe right lines will be the
hour-lines on an equinoc'tial dial, for the latitude
of the place to which the cylinder is elevated
above the horizontal foot or pedel’cal H ; and

they are equidil’tant from each other, as in Fig. z.‘

which is a full view of the flat furface or top
A D of the cylinder, feen obliquely in'--"Fig. I.
And the axis of the cylinder (which is a flraight
wire E F G all down its middle) is the (tile or
gnomon; which is perpendicular to the plane
of the equinoétial dial, as the earth’s axis is pets-J
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 ate la f g, parallel to the horizontal
board H, and take on“ the top part a A D f e 5 and
r the feétion e k f g 6 will be of an elliptical form,
as in Fig. 3. Then, from the points of this
feétion (on the remaining part (:3 Cf) where
the parallel lines on the outfide of the cylinder
meet it, draw right lines to the center of the
feétion; and they will be the true hour-dines for
a horizontal dial, as a b c dd in. fig. 3. which may
be included in a circle draWn on that feé‘tion.

" F f Then

'33;

3% if

(of the day, on that dial. 30;, ,E (Fig. 3&1:ng
‘ Us:

l

DIA-LLING.
Then put, the :wire into its. place again,, audit. .
will 138,3, fiile forpcal’ting a fhadow ohthe- time

t

fiile 9f the horizontal dial,‘ parallel tome
of the cylinder. - w - i

To myakeyavertical fonth diai’byi the cyliin;

' t der, drawing; the axis,» and cut the cylinder:
‘ perpendicularlyto the horizontal‘bOard H,,,as'a§
gi C leg, "beginning at} the; hour line (8g a die?

XII. and, making the leétion at right angles "to,
theline S H N on the horiznntal board. Then,
take olft’henpper part-g fl’D C,,an_d the face. of '
the fe'éti‘en ?tl1,,él=épn will be elliptical, as {hewg'inf
1923.4; 4 Fremithe points in the edge Of this fece‘
tinn', Where'fhef parallel heurilines on the'round,
fu’rface, (Sf-the Cylinder puree: it; "draw right lines;
to the center Of the feéti‘on; and they Will be
the true horn-lines on a'ver'tical direct fou-th dial,’ ‘
for the latittide to Which" the cylinder was ele—f

' Vated: and will appear as in Fig. 4. on which ,

the vertical dial may be made of a circular fhape,’
or of a' fquare lhape as reprefented in the figure."
And F will’be its ftile parallel to the axis of the.

,eylinder, a p , ,

And this, by cutting the cylinder any way;
f0 as its feétion may either incline, or decline, or
recline, by any given number of degrhe‘s ; and '
frgm thofe points in the edge of the friction
where the outlide parallel: hour-lines niiéet it,
draw right lines to the center of the feétion; and
they will be the true hour-lines, for the like de-s
dining, reclining, or inclining dial: And the
axis of the cylinder will always be the gnomon’é
or {tile of the dial. For, which-eyer way the A
plane of the dial lies, its fiile (or the edge thereof

':
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1, ‘ -

 

 

 

PLATE IX. _ V ‘ . ’ ,. ' ‘ ' ' \ . ‘

 

DIALLPNG;
that cal-ls theilhadow on the hours of the day)

mull be parallel to the earth’s axis, and point
toward the elevated pole of the heavens.

To delineate a San-Dial mt Paper; which, when
pa/Zed round (1 Cylinder of Wood, flaallfbew the
Time of the Day, the Sun’ 5 Plate m 111% Ecliptzr,
and lair flltz'mde,‘ at any Time of Obferwtzon
See PLATE IX. ‘ _

Dtaw the right line aflB parallel to the tOp
of the paper , and, with any (convenient opening

of the cempafi'es, let one feet in the end of theline .
at a, as a center, and with the other foot defcribe

the quadrantal are A E, and divide 1t into 90 equal
parts or degrees. Draw the right line A C, at
right angle-sb to d z! B, and touching the quadrant
fl E at the point 14. Then, from the center a,
draw right lines through as many degrees of the

Quadrant, as are equal to the fun’ 5 altitude at

'noon, on the longell: day of the year, at the
place for which the dial is to ferve; which alti-
tude, at London, is 62 degrees: and continue

thefe right lines till they meet the tangent line.
14C; and, from thefe points of meeting, draw ’

firaight lihes acrofs the paper, parallel to the
firl’t right line A’B, and they will be the parallels

of the Ci’fun s altitude, 1n whole degrees, from fun- _

rife till fun let, on all the days of the year.
Thefe parallels of altitude muf’t be draWn out to
the right line BD, which mul’t be parallel to
if C and as far as is equal to the intended cir-
cumference of the cylinder on which the paper
is to be palted, when the dial 15 drawn upon it.

 

Divide the {pace between the right lines 14 C
and B D (at tap and bottom) mto twelve equal

f 2 parts, .

' aa-

DIALLI'NG.~

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 A C and
B D; and place the characters of the 12 figns in
there twelve fpaces, at the bottom, as in the figure:
beginning with he or Capricorn, and ending
with )6 or Pil'ces. The {paces including the
figns Ihould be divided by parallel lines into
halves; and if the breadth will admit of it
Without confufion, into quarters alfo. I

Atthe t0p of the dial, make a fcale of the
months and days of the year, f0 as the days may
ftand over the fun’s place for each of them in
the fignsofithe ecliptic. The fun’s place, for
every day of the year, may be found by any
common ephemeris: and here it will be belt to
make ufe of an ephemeris for the fecond year
after leap year; as the nearel’t mean for the fun’s
place on the days of the leap-year, and on thofe

of the firfl‘, 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
thefe computed altitudes among/the horizontal
parallels of altitude, reckoning them downward,
according to the order of the numeral figures let,
to them at the right hand, anfwering to the like
divifions of, the quadrant at the: -left. And,
through'thefe marks, draw the curve hour—lines,
and fet the hours to them, as/in the figure,
reckoning the forenoon hours downward, and

, the

 

 

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DIALLING.

the afternoon hours upward.-————The fun’s alti-
tude lhould alfo be compuced for the half hours -,
and the quarter lines may be drawn, very nearly
in their proper places, by efiimation and accu-
racy of the eye. Then, cut off the paper at the
left hand, on which the quadrant was drawn,
clofe by the right line 11C, and all the paper at
the right hand clofe by the right line B D; and
cut it alfo clofe by the tOp and bottom horizontal
lines; and it will~be fit for patting round the
cylinder.

This cylinder is reprefented in miniature by

Fig. 1. PLATE X. It ihould be hollow, to _

hold the fiile D E when it is noc ufed. The
crooked end of the {tile is put into a hole in the
t0p A D of the cylinder; and the top goes on
tightifh, but mull be made to turn round on the
cylinder, like the lid of a paper fnuff-box. The

ftile muf’t l’tand firaight out, perpendicular to the * '

fide of the cylinder, juft over the right line AB
in PL ATE IX, where the parallels of the fun’s
altitude begin : and the length of the (tile, or
dif’tance of its point e from the cylinder, mul‘t be
equal to the radius a d of the quadrant A E in
P L AT E IX.

6279:: wetland ’of uflng this dial‘z's as follows.

Place the horizontal footB C of the cylinder
on a level table where the fun fliines, and turn the
a top 14 D till the {tile fiands jui’t over the day of
the then prefen-t 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 lowefi: end

Efg" of

37..

'33 '-

DIALLING.

of the fl13dovv,vyill fall upon the time of the
day, as it is beforebr after noon, among the curve
hour- lines -, and will {hew the fun’ 3 altitude at
that time, among the crofs parallels of his alti-i
‘tude, which go round the cylinder: and, at the
fame time, it will thew 1n what fign of the eclip-
tie the fun then is, and you may very nearly
guefs at the degree of the fign, by efiimation of
the eye.

The ninth plate, on which this dial 1s drawn,
may be cut out of the 11601:, and pal’ted round a
cylinder Whofe length is 6 inches and 6 tenths
of an inch beloW Dthe move-able top, and its
diameter 2 incnes and 24 hUndred parts of an
inch—-—Or, I fnppofe the copper-plate prints
of it may be had at Mr CadeZZ’s, bookfeller 111
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

i be hung by the ring F at the top. ' And when it;’

is not nfed, the wife that ferves for a fiile may
be drawn out, and put up Within the eylinder ,
and the machine carried 111 the pocket.

To make three San— dial: upon three dfireizt Planes,
f0 as they may all/Few the Time of the Day 1131
‘ one Gnamm. '

On the flat board A! B: C, defcribe a horizontal
dial, according to any of the rules laid down 111
the Leéture on Dialling ,_ and to it fix its gnomon
FGH, the edge of the fiiadow from the fide

_ EG being that Which {bews the time of the day;

To this horizontal or- flat board, join the
upright hoard E D C touching the edge G H of '
the gunmen hen, making the top of the

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DI'A 1:1:1‘N G1 ’
'gnomon at H the center of the vertical {ouch
dial, del'cribe- a {011th dial 011 the board E D C.

Laftly, won a circular plate [K defcribe an
eqtiinoctial dial, all the hours of which dial are
equidillant from each other; and making a flit
Cd in that dial, from‘its edge to its center, in the
XII o’clock line 5 put the faid dial perpendicu-
larly on the gnomon F,G as far as the {lit Will
admit of; and the triple dial will be finilhed ; the
fame gnomon ferving all the three, and fhewing
the fame time of the:3 day on each Of them.

An univerfal Dial on a" plain Croft.

This dial is reprefented by Fig I. of PLATE
XI, and IS moveable on aJoint C, for elevating
,. it to any given latitude, 0n the quadrant C090,

as it {lands upon the horizontal board A. The -

arms of the crofs {land at right angles to the
middle part; and the top of 1t, from a to 71, is
- of equal length with either of the arms 72 e ormk.

Having fet the middle line t u to the latitude
of your place, On the quadrant, the board A
level, and the point Nn01 thward by the needle,
the plane of the c1ofs will be parallel to the
plane of the equator , and the machine will be
refiified.

Then, from III o’clock in the morning, till
VI, the upper edge 1% l of the arm 2 0 W111 call“ a
fliadOW on the tune of the day on the lide of the
arm 6 m: from VI till IX, the lower edge 2' of
the arm 2 a will call a fhadow on the hours on
the fide 0 9.1710111 IX 11: the morning to XII at
noon, the edge a b of the top part a :2 DWill call a

(fliadow. on the nours On the arm n ef: from XlI‘

{,9 .111 in the afternoon, the edge 6 d of the top
F f 4- v ‘ part

355

DIALLING

par3: will wit a {hadow on the hours on the

arm klm: from Ill to V1 in the evening;
the edge g]? will caf’t a {hadow on the hours
On the partpg , and from VI till IX the fnadow
of the edge efwill {hew the time on 3136 top
parent/1..

The breadth of each part, a b, ef, &c. mul’t
be fo great as never to let the fhadow fall quite
Without the part or arm on which the hotirs are
marked, when the fun 13 at his greateft declina-
tion from the equator.

To determinethebreadth of the {ides of the
arms which Contain the hours, . fo as to be in juf’t
proportion to their length, make an angle
flBC (Fig. 2.) of 23; degrees, which 15 equal

to the fun’ 3 greateft declination. and fuppofc

the length of each arm, from the fide of the long
middle part, and alfo the length of the 30p part
above the arms, to be equalo to B d

Then, as the edges of the fhadow, from each
ofthe arms, will be parallel toBe, making an angle ,
0f 23; degrees with the {ide B d of the arm when

- the fun’ 5 declination is 2 32 degrees , ’tis plain,

that if the length of the arm be Bd, the leaf:

breadth that 13 can have, to keep the edge B gt of
3he lhadow B e a d from going all" the fide of the

arm d e before it comes to the end ed thereof, '
mull be equal to ed or dB. But in order to

keep the Ih-adOw within the quarter divifiqns of
the hours, when it comes near the end of the

arm, the breadth thereof lhould be {lill greater,

{0 as to be almof’c doubled, on account of the

d1f’tance be3ween the 31335 of the arms, '

T8

 

I

‘pther foor defcribe the quadrantal are e f

DIALLING.

To place the hours right on the arms, take the
following method. ' » -

., Lay down the crofs a chd (Fig. 3.) on a fheet
pf paper; and with a black lead pencil, held
clofe to it, draw its fhape and fize on the paper.

‘ Then taking the length \a e in your compaiTes,

and fetting one foot in the corner Al, with the

 

Divide this are into fix equal parts, and through
the divifion-marks draw right lines ag, a 17, &c.
continuing three of them to the arm c e, which
are all that can fall upon it; and they will meet
the arm in t‘hefe points through which the lines
that divide the hours from each other (as in
1Fig. I.) are to be drawn right acrofs it.

Divide each arm, for the three hours it con.

tains, in the fame manner; and let the hours to
, their proper places gun the fides of the arms) as

they are” marked in Fig. 3. Each of the hour
fpaces fliould be divided into four equal parts,
for the half hours and quarters, in the quadrant
,é’fi and" right lines lhould be .drawn through
thefe 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 mui’t be marked.

This is‘a very fimple kind of univerfal dial;
it is very eafiIy made, and will have a prettyun-
common appearance in a garden.———‘-I have fern
a dial of this fort, but never faw one of the kind
that'follows. \_ '

,. J72

4'3

{12

DIALLING;

flit univerfal Dial, fhewihg the Hours of the Day hy
a term/trial Glohe, and hy the Shadow: of feveml
Gnomem, at the fame Time ..- together with all
the Pieces of the Earth which are then enlightened
hy the Sim ; and the/eta which the Sim it then
ring, or on the Meridian, or Setting. ‘ i

This dial (See PLATE XII.) is made of a
thicquuare piece of wood, or hollow metal,
The fides are cut into femicircula‘r hollows, in
which the hours are placed; the l’tile of each
hollow coming out from the bottom thereof,
as far as the endsof the hollows projeét. The

, comers are cut out'into angles, in the infides of

which, the hours are alfomarked ; and the edge
of the end of each fide of the angle ferVES as a
{tile for cai’ting a lhadow on the hours marked
on the other fide. -

In the middle of the uppermoit fide or plane,
there is an equinoétial dial -, in the center where- ‘
of, an upright wire is fixt, for cal’ting a fhadow on
the hours of that dial, and 'fupporting a fmall

., terrefirial globe on its top.

The whole dial flands on a pillar, in the
middle of a round horizontal; board, in which
there is a, compafs and magnetic needle, for
placing the weridea {tile toward the fouth. The
pillar has aj'oiht with a quadrant upon it, divided
into go degrees (fuppoléd to be hid from light
under the dial in the figure) for fetting it to the
latitude Of any given place; the fame way as
already defcribed in the dial on the crofs.

The equator of the globe is divided into 24
equal parts, and the hours are laid down upon it
' ' at r

 

PLATE XII.

 

 

 

 

 

 

 

 

 

 

 

 

BIALLING

atthefe parts. The time of the day may be»
known by thefe‘ hours, when the fun lh‘ines upon ‘
the globe. ,

To reéiify and Life this dial, fet it on a level
table, or fole of a window, where the fun fhines,
lacing the meridian {tile clue fouth, by means
(if the needle; which will be, when the needle
oints as far from the north fleur-dealis toward
the Well, as it declines weflward, 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 refiified, the plane of
its dial-part will be parallel to the equator, the
Wire or axis that fupports the globe will be paral-
lel 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 lhewn in fev'eral‘
of the hollows, by the ends oflthe fhadows of
their refpeétive {lilesz The axis of the globe
will calla ihadow on the fame hour of the clay,
in the equinoétial dial, in "the center~ of which it
is placed; frotn the 20th of March to the 23d of
Septembersand, if the meridian (if-your place
)on the globe b'e‘ fet even with the meridian fille,
”all the parts of the globe that the fun lbines
upon, will‘anfwer to-tho'fe places of the real
earth which are then enlightened by the fun.
Theiplaces where the lhade is juft coming upon
the globe, anfwer to all t'hofe places of the earth-
to which the fun” is then fitting; as the places
Where it is going off, and the light coming on,
anfwer to all the places of the earth Where the fun
' ' - " lS

 

«:44

DIALLING.

is then rifing. And laftly, if the hour of. VI be
marked on the equator in the meridian of your
place (as it is marked on the meridian of Lon;
don in the figure) the divifion of the light and

‘ ihade’ on the globe will lhew the time of the day.

The northern [file of the dial (oppofite to the
fouthern or meridian one) is hid froni fight in
the figure, by the axis of the globe. The hours
in the hollow to which that flile belongs, are
alfo fuppofed to be hid by the oblique view of _
the figure: but they are the fame as the hours
in the front-hollow. T hofe alfo in the right
and left hand femicircular hollows are moltly
hid from fight; and f0 alfo are all thofe On the
{ides nexc the eye of the four acute angles.

' The confiruétion of this dial is as follows, Ste
PLATE XIII. ‘ ~ ' '

On a thick fquare piece of wood, or metal,
draw the lines a r and _& d, as far from each other
as you intend for the thicknefs of the {tile 4 b c d 5
and in the fame manner, draw the like thick-
nefs of the other three (tiles, 6 f g b, Hahn. and
22 o p g, all {landing outright as from the center.

With any convenient opening of the com— .
pages, as afl (fo as to leave proper firength
of Pcufi‘ when KIis equal. to ad) fet one foot
in a, as a center, and with the other foOt de-
fcribe the quadrantal arcflc. Then without
altering the compafl'es, fet one foot in h as a,
center, and with the other foot defcribe the qua-
drant (18. All the other quadrants in the figure
inuf’t be defcribed in. the fame manner,‘ and with

' ’ the

£7.
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DIALLING‘.

. the fame Opening of the companies, on their
centers e,f-, i, It; and n, o : and each quadrant
divided into 6 equal parts, for f0 many hours,
asin the figure, each of which parts mul’t be
{uh-divided into 4, for the half hours and
”quarters. ' —

At equal diflances from each corner, draw the
right lines Ip and K3), L g and M 9, Nr and.
O r, P s and Q,“ to form the four angular
hollows 112K, Lg M, Nr 0, and P: Q; mak-
ing the dittances between the tips of thefe hol-
lows, as IK, L M, NO, and P Q, each equal
to the radius of the quadrants g, and leaving fuffi~
cient'ro'orn within the angular points, 1), q, r,
and s, for the" equinoé‘tial in the middle. ,

- ' To divide the infides of- thefe angles properly,
for the hour-{paces 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, defcribe the arc K t : then, with-\
out altering the compafl'es, fet one foot in K,
and with the other foot defcribe the are I t.
DiVicleeach of thefe arcs, from I and K to their
‘interfeétion at t, into four equal parts; and
from their centers I and K, through the points
of d’ivifion, ’draw the right lines I 3, I 4, I 5,
.16, I7; and K2, K1, K12, K11; andthey

will meet the fides K1) and [p of the angle [39 K ,

‘where the hours thereon mui’t be placed. And
thefe hour~fpaces in the arcs mui’t 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
' V hours,

 

 

oIALLING.

hours in the infides where thofe lines meet them;

as in the figure: and the like hour— lines will be
parallel to each other 1n all the quadrants and 111

a all the angles

Mark points for all thefe hours, on the upper ’
fide , and cut out all the angular hollows, and '
the quadrantal ones quite through the places

, where their four gnomons mufi {and ; and lay

down the hours 'on their infides, as in PLATE

’Xll, and then fet in their four gnomons, which

mufl: be as broad as the dial is thick , and this
breadth and thicknefs mufl; be large enOUgh to ~
keep the fhadows of the gnomons from; ever
falling quite out at the tides of the holloWs, even
when the fun’ 3 declination is at the greatellz.

.. Laflly, draw the equinoé‘tial dial in the mida
dle, all the hours of which are equidifiant from
each Other , and the dial will be hnifhed.

As the fun goes round, the broad end of
the fhadow of the {tile a & c d will fhew the hours
in the quadrant .4 c, from 11111 rife till VI 111 the
morning , the fhadow from the end M will lhew’

the hours on the tide Lg from V to IX 1n the
morning; the {hadow of the llile efg la in the;
quadrant Dg (in the long days) will thew the“
hours from fun- rife till VID in the morning , and -
the lhadow of the end N will Ihe'w the morning” _
hours,o on the fide O r, from III to VII.

Juli as the fhadow of the northern [tile :2 5 c 63
goes ofi‘ the qUadiant .45, the {hadoW of the ~
iouthern fiile i k [m begins to fall within the
quadrant F], at VI 1n the moming , and lhews
the time, in that quadrant, 130111 VI 1111 XII at:

.noon,

D I A L L ‘I N G.
noon 3 and from. noon till VI ‘ in the. evening in
the quadrant m E. Andthe {hadow of the end
0, fhews the time. from XI in the forenoon till
III in the afternoon, onythe fide rN; as the
fhadow gfthe endP {heats the time from IX in

the- morhing till 170?ka in the afternoon, on
theflfide £25.

At noon, when thefnadow of the eaitern f’tiie
efgb goes 03‘ the quadrant 19C (in which it
fhewed the time from VI in the morning till
noon, as it did in the quadrant g D fromfun—
rife till VI in the morning) the {hadow of the
wel’tern {tile 71 op g begins to enter the quadrant
Hp; and {hows the hours thereon from XII at
noon till VI in the evening; and after that till

fun-fet, in the quadrant g G; and the end Q -

cafts a fliadow on the fide "P: from V in the
evening till IX at night, if the fun he not fet
before that time. '

The fliadow of the end I fliews. the time on
the fide K1) from III till VII in the afternoon ;-
and the {hadow of the fiiie a é c d {hews the time
froin VI in the evening till the fun fets.

The {hadow of the upright central wire, that
{apports the‘giobe at top, fliews the time of
the day, in the middle 0r equinoftial dial, all
the fi’immer half year, when the fun is on the
north fide of the equator. '~

« In this fupplement to my book of Leétures,
all the machines that I have added to my appa«

rams, fince that book was printed, are de- '

feribed, excepting two; one of whieh isa model
- ~ Oi:

if

3.8

DIALLING; f
of a mill for fawing timber, and the other 1§ 8
model of the great engine at London—bridge;

for railing water. And my reafohs for leaving
them out are as follow.

Firl’t, I found it impoHible to make fuch a

. drawing of the {aw-mill as could be «11111121110ng

becaufe, in whatever view it be taken, a great
many parts of it hide Others from light. And,
in order to {hew it in my Leétures, ID am obliged
to turn it into all manner of pofitions.

Secondly, Becaufe any perfon who looks on
Fig. I. of PLATE XII in the book, and readfi
the account of it in the fifth Leéture therein,
will be able to form a very good idea of the Lon-
don bridge—engine, which has only two wheels

and- two trundles more than there are in Mr._ 1
Aldeifiaz’ 5 engine, from which the faid figure was
taken.

Ftitle;

 

 

2'”

‘4,

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