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!
Pbilofophia Britannic a :
A New «md CoMPREftENsivB
S Y S^T EM
NewtomanVmYb?>OnV{,
ASTRONOMY and GEOGRAPHY*
I N A
Course of Twelve LECTURE S,^
With N O T E Si ^
containing"'
The Physical, M£chanical, Geometrical, atid jk
Experimental Proofs and Illustrations' ••
of all the Principal Propofitions in every Branch of '
NATURAL SCIENCE. ,
ALSO
A particular Account of the Invention, StructorEj
Improvement and Uses of all the coniiderable ■ ;,
iNSTRtJMENTS, ENGINES, and MACHINES,
With new CtdcuLtthm relating to their
Nature, Powsr, and Opiration. T
liie Whole colle£led and methodized (rom all the pfiadpal
Authors, and public Memoirs to the prefenc Year ;
And niibiUifli-d -mth StwHtj.Jh* COPPERPLATES.
By B. M J RT J N, '
j^<r hthi Jttimos nfettrum Mfent StfboniM -^ -
S^^que ^cholas firufira rauco Cert amine fuexemt^ ,':i
Obvia coA/picinms, Nuhempellente Mathefi. Ha l . in N 8 vr T . Prini ^'
VOL. 11,
RE A V IN G, }
Printed by C. Micklbwricht ahd C**. for the AUTHOft i «^1
and for M. Cooper, in Pater-nofier-ronv^ Lomkm R. RAiKijf
at Ghmcefteri fi. Collins zt Saujhurj i and J. Learb^ titA
Bath. MDCCXLVII.
»A .^ t -^ »* ,.j. /t **- ^ •. / .
■ fc ■ » •
T O T H E
Right Honourable
J O H N
Ezvl o£ORRERK
My LORD,
I Beg Leave to make Your Lors-^
SHIP the humbk OfFering of
thoie Lectures you have here«
tofore been pleafed to approve and
honour with your Prefence. Your
Lordship will not difdain to caft aii
a 2 Eye
-V
DEDICATION..
Eye on this Endeavour 'to difplay
fome of that wondrous , Worth and
matchlefs Sagacity which has fo
much ennobkd Human Nature, and
dignified it with almoft Divinity it-
felf. I doubt not but fome Sparks
of that Celefiial Fire^ which in-
form'd the Soul of NEWTON,
will ftrike upon and mingle with
the like congeneal Flame that glows
in Your Lordship*s Breaft.
The Dodrine of Sounds prefents
us with the Philofophic Grounds of
Music and Harmony ; The Colours '
of Light, in regard to Quantity, ob-
ferve the Harmonic L,aw\ not a
fingle Ray can be- rcikdcd, but ty
Hs^^ Jmi^ Dknne Rule : And there
is fometMng extremely lite Mufic
yi the Motions and Order of the
Spheres. , Confonant, therefbre> it is
wi^ the higheft Reafipjj, that thefc
^Jiar-
D E P I C A r I O N.
«
Harmonious SubjeSis (hould be re-
commended to the World under the
Auspice of One fb well known by
tuneful Accents^ and Skill to firth
the Lyre,
Again, Mv Lord,. Does Pbilo-
fophy breathe Religion and Devotion^
and furnifh us with the bcft Wea-
pons againft Vice and Immorality ?
Then let it be fan^on'd by the di-
ftinguifh'd Name of that Boyi,e,
who in the early Years of Life fet
fuch an illuftrious Example of Magf
nanintity and Chrifiian Heroifm^ in
the following Refolution^ as truly.
piousy as the Numbers are poetical
va. which it flows.
Mature in Tears ^ if e'er 1 chance to llread
Where Vice triumphant rears aloft her Head,
Ev'n there the Paths of Vi r t o e 1*11 purfue.
And the Glory of making it good
is ^Very Day Your Lordship*s Due.
a 3 But
■V
DEDICATION.
But I dare not longer infift on
't'hemes of Praife, (though ever fo
fleafiog) to a Mind poffefs'd and
enrich'd with every Virtue, as well
as native Innocence,
Every thing, Mv Lord, may be
over-valued, and. become the Sub-
jed: of Flattery, except Goodnefs and
Wifdom- The Encomiums of the
Great, the Wife, and the Good, admit
of no Hyperbole ; thcfe Jbining To-
pics ought to plead Excufe for pro-
lix Admiration wherever we behold
them, efpecially in an Age fo little
produdive of fuch Phenomena' So
^OMETS, when they appear, fet all
Mankind a gazing j and fuch unu-
fual Splendor detains our Eyes all
the Time of their Appearance,
The general Dejfign of this Trea-
tifc being to facilitate the Way to
DEDICATION.
real Science, will, I hope, render
it fo much the more acceptable to
Your Lordship, in regard of Mf
Toung Lord Boyle, who bids fo
fair to deferve and continue the Pa-
ternal Honours and Title of a Fa-
mily that will always be had in Re-
nown, while the Records oi Englijb
Nobility, and the Annals of Heaven
fhall laft. I am,
Mr Lord,
With RefpeSI and Duty^
Your Loudship x
Mofl Obedient Servant^ •
-V
B. Martin.
I
I'
ERF- A'T A in Vol. I,
206 36, r^4<^P]. XV. Fig. X^. iji $he Margin,
W 240 30, tf//£r through, r^/ the abovcmcntionMSpacCf
r. 304 20^ Jor Weight, read Height^
E R R A T A //^ Vol. IJ.
'■ ^^le. luip.
23 30, i7//^r Plate XXIX. ^y^^Fig, 5.
27 32, ovn/^ Plate XXIX. Fig. 7. in the Margin,
35 20, /or I to 12, r^/?i^ I to «.
61 22, ^ 26, read i6.
82 14, wriVf Plate XXXIII. fig. 2. X* /i&r jJ4i2r^/>,
302 1% far Liberklum, r^o^ Liber khan.
^43^ Lif ^SioiibiH rM/^SimpA>n,
/
^
A
TABLE
O F
LECTURE VI.
PNEUMATICS.
W
CONTENTS i
1
I.
flETHER Air it properly aFluid^ 2
ff^^rein it differs from the general
Nature of Fluids, ibid.
Of tke Creation and Generation of
Air, si
0/ Artiffcial or Faftitious Air, iUd. I
Several Experiments producing the fame^ 4, 5 [
Xbe ^antities thereof in divers Sorts of Bodies '^
tabulated^ 6-^8
Its' vaft expanjhe Force calculated^ S
Of the fVeigbt of common Air, 9
Of the Nature and Theory i/Barof^eters in genenJ^
10
Qfthe Common Barometer^ xo, n
CONTENTS.
Of the Diagonal Barometer, iz
Of the Horizontal Barometer, I2> 13
Of the Pendent Barometer, 13
O/" /i&^ Wheel Barometer,' '3» '4
Of a Barometer, with an infinite Scale of Variation^
by Mr. Rownino, 14, 15
7J<? Properties of the heft Barometer, Mi bow
madey 16, 17
^e Scale of the Common Barometer improved^ by
adding thereto the Nonius, -. 1 7
J^he Nature of the Nonius explain^ d^ ibid.
The U/e of Barometers in meafuring the Heights of
Pldees^ &c. 17, 18
TMes calculated for that Purpofe^ 19
Of the Spring of the Air and its Denfity, 20
^he Rcpulfive Force of the Aerial Particles by
Calculation^ 20, 21
fhe Air^s Denfity proportional to the compound
Force fhewn by ^Theory and Experiment ^ 21, 22
^e Heights to which Mercury will rife in Tubes
with Air J 22, 23
The Nature and Theory of the Sea Gage, 23 — 25
The prodigious Degree of Compreffion of the Air,
and Force thence artfingj 26
y2^^ Height of the Atmofphere, fuppos^d uniformly
denfe^ determined by Experiment ^ 27, 28
Calculations relating to the Height of the Atmofphere^
29—32
T!he fame determined by Aftronomical Experiment^ 33
T'he fVeight of the Atmofphere on a Square Inch
computed, 33» 34
■!■*■■ on the Surface of the whole Earth, ibid.
A Calculation of the Thicknefs of a Metalline Globe
f that Jhall float in Air^ 35, 36
Fifty Experiments on the Air-Purnp» fhewing the
Gravity^ Elafticityy and all other Properties of
the Air, ' 37^51
Of Condenfation of Air by Experimenty 5 ij ?2
/- - "^
CONTENTS.
Of Papik*s Digefter, 52
Of the Diving-BcU and its Tbeary^ SZ^^S^
Improved by Mr. Triewald, 56
Of Thermometers and their general Theory^ 57
Cy Newton's Oil and Spirit Themiometers,
Of Mercurial Thermometers in general^ 58 1
Of Fakekheit* s Mercurial "Tbermometer J ibid.
The Nature and Ufe of a Standard Thermometer '
exen^lified^ 59, 60
The Newtonian Scale of Degrees of Heat^ from
FreeT^ng to Fire^ 61
Dr. Hales*s Thermometer /57r Hot-Beds, 62
The Nature and Theory of the Hygrometer, 63
The hejl Way of making them^ ibid.
The Theory of the common Air-Gun, 64
Of Col BE* J Magazine Air-Gun, ^S^^Sj .
The Theory and Strufture of the Air-Pump,
63-^66
Of a New Portable Air-Pump of the Author's
Inventionj 66 — 68
Of the Rarefailion of the jlir in the Recipient by
Calculation^ 68 — 71
Of the Gage of the Air-Pump and Concjenfer, 71
LECTURE Vn.
Of WINDS and SOUNDS,
or W I N D.
f\F the Nature tf Wind, and bow produced, 73
^ Dr. Hallet's Theory of the Winds,73 — 7^
The Equilibrium of tbf AVno/pberCy bow defireyedhy
Heat and Coldy 76, 77
P/
CONTENTS,
Of the perpetual Currents cf Air from the -Eift,
North, and South, 77, 78
•• The fame exemplified^ 79
//Im? the Trad«- Winds 0*e produced^ ^ 80
'^be Reafon of the Monfooi^, 76, 77
0//A<? Aerial Tides, 78
Of the Motion of Air or Velocity of Wind^ 8 1
Of the Mola alata of Dr. Hook, ihid.
Of the Stru&ure of a new Anemofcope, 82
A more particular Calculation of the Forjce oflVind
upon the Sails of a Mill, 82—87
A "Theory of Mr. TriewaldV «W fVattr Bel-
lows^ s 88
0/ S O U N D S.
Of Sound in general^ and how produced^ 82 — 89
Of the Make and StruSfure of the Ear^ and its
fevered Parts defcrihed^ 89 — 93
Of the Tremors^ Sounding Bodies^ 90—94
^be Newtonian Theory ^Vibrations ^/Elaftic
Strings, t^c. 93"7t9^
\ Of the Waves of Water compared with the Vihra^
\ tions of the Cycloid J g6 — 99
Of the various Properties of Aerial Pulfes or
Waves of Air, 97 — 103
Of the Diftance to which Sounds are audible, ff
Experiments^ 99, loq
Of the Vdocky of the Pulfes a priori, lot
the fame by Calculafion^ 102
> Experiments to afcertain the fame^ 103— -107
The Nature and Theory of Echoes explained^
107, 108
Their Ufe in meafiiring Dijiances^ 109
The Depth of a Wettj no, in
. yi? Nature 4nd T-^eory of Qtacouftic Inftru-
_ - ilfientSj^ loS^i-r-m
Of the Stentorophonic Tube, mr Speaking Tinirt-
pet, ' III — w^
GROUNDS^MUSIC.
Of^ the Nature of the Note, Tone, or Tuncj)/
Sounds, III, 113
Of /Atf Magnitude, Length, and Tenfion of Mu*
fical Strings, 113— 1 18
Mathematical Cgkntatims relating tbereto^iid^^^til
Of the Nature of the Spinet or Harpfichofd, 115
' v.nV I -i ■ . of the Fkne, Oigan, fij'r. ikid.
—• — ~— of Concords and Difcords, 116
Of^ the Diatonic Soile and its Divifidtts, si 7
0/ /& &eaccr and Lefler Notes of Mufic;
117, fi8
Of MtloAj and Harmonf ^^ 1 1 %
O/Harnionic Proportion i» iViwi^^i, 119— 12 1
. ^bi fame in Lines, .123
Vhe Mathematical Theory of Mufical Pn^rtion,
122 — 127
A wonderful Property of a Mufical O>ord by Ex-
periment^ 124, 125
LECTURE Vni.
0/ LIGHT and COLOURS.
0/* L I G H T.
f^F the Nature of Light ingeneraly 129
^' S[be moKthabte Smsllncfs 'of itr 'Particles.,
• ' - i?o
Tbeit
I fl
CONTENT 5.
.^eir different Magnitudes, ^ / ibid.
The prodigious Velocity of Light, 131 — 133
^e Method of determining the fame by R£ aumer,
Amoji-exaEt Method hy Dr. BradleV, ^36
The Velocity of light and of the Earth com-
^ partd, m
The Newtonian Deftrine of Fire and Heat,
Varicus Kinds of Phofphori, 139
fThe Nature of Freezing co^/ider^d^ 142
fn>e Force of Burning iy Gkffes^ v 143
Experiments made with Mr. Villette'j MhrMr^
' . 145
Its Power, efBunti^ cdmputed^ I46
ff^iy fhe Moon's Light gpves no Heat in the Foots
ill of Burning Glaffesj 147
j Of the Opacity and Tranfparcncy of Bodies^ 148
I;; ^ Of the Refledion of Lights I49
-'^ ' ' ^he Lxsff thereof demonfiratedy 151
Of the Refracting Power of Mediums, 15a
Of the Refraftion of Lights 153
Of the Sines of iHcideme and Refrdlfioti iH Water^
Glafs,&cc. 154
The Phyfical Caufe ofRefraSion explain*dy 156, 157
Of the different Refrangibility of UghK 156, £s?r.
The Mathematical Theory of RefraSion^ 158, 159
An Inftrument that pews the Ratio of the Sines of
Incidence and RefraSim conftmit^ 161
^ yf Table of thofe Sines in various Medii, 162
The RefraSii^e Power of the Air determined^ 163
Of the Apparent Place imd Figures of OljeEtsfkn
through Media^ 1 64, 1 6$
Of C O LOUR S.
91>^ different Colours of the Sun^i Lights 166^ &t.
/ HffWy and why /hewn by a Prifm, 167, C^c.
The
CONTENTS/
The Sines of iQcidence and Refraftion in every Sort
of Rays determined^ 168 — 173
Of the Harmonic Proportion of the coloured
Spedlrum, 173
Of Vifual Mufic, or an Ocular Harpfichord,
> • - • • • ibid.
The Reafon of 'the ImperfeSIion (^ refraSing Tele-
fiopesjhe^nj . ^ 174 — 17S
Of the different Reflexibility of Lights mi ibe
Caufe thereof " 179—^184
Tbf Fits of cafy-Refleftion tf»i: Txanfmiflion,
Of the Rings of Cdlbuf'd Light, explained from
Sir I. Newton, 187 — -'ipS
The TJieory of the Colours of natural Bodies
thence deduced^ ' ^ 19*9-^269
The Mathematical Theory ., ef the - Rainbow,
• /" '• , . 'Z' . . . ' .: ±i^,(Sc.
Its various Phxnomem aciountea for^ sLiy-^zz\
4 curious Theorem relating to the Bows, ^25
Of the Produliion ^/ Hdo's, Parhelia, 6?^. 22>
LECTURE IX, X. ;
; Q p TICS.
0^ M I R R OV^Sand L t N S E S.
/1| F /i&« Catoptrics <}»</ Diop£rics» 231
0/ ]iuenfes:<^ Mirrours, ibid.
Tbtir Effc^s ittveftigattd iy Fluxtms, 232 — 234
- 0/
r
. 0 0 N T B N T 8/
Of spherical. Elliptical, Parabolic, (^c. Lcnfc4<
.234— -1:36
^beorems^fdf the fame Sofi of Mrrours^ 2 3 6'^2^(i
ST/fe Harmpaical Refleftion in Mirroun explained,
240
jitgebraic Theorems for all DidpJfic Cafes^z^o — 243
Oftht Manner in which the Images cfOijeBsari
firmed by. Mirrours and Lenfes^ 244, :^5
Varioits Algebraic Theorems relating theretCj
fhefame in Glotfts arid Heniilpherts, 248^, 1249
r^i 1 I in the Conic Lcnfes, ^49^^ 250
Of thiJE t-E and VIST ON,
5*i&i? /r^^. Theory ^/ Vifion, 250—263
\/tpdrttcular, Defcnption ^/ the%yQ^, • 25i> 25a
y2>^ DiWcnfidns ^/ ifs^feveral Parts^ < ; 253
f2»^ Ratjo ^/ Refrai£^;ivc Vo^txin ih Jj^jolHtir
' mdurs^ , ^. . j . , ^^^^ ^^^
Calculations for the true Focus i?//i6f Eye^zg^ 255
!rt<? Diftance 17/ ObjeSls for Diftind Vifion,
0/ /i>^ D^^iSTj <?/ /^^ ^j^^ and Vi/ion^
Of the Purblind Eye or Myops,
Htm rtfAediedby Concave ^pe^iUcIe^ ..
BefeU of A Flit ot Old Ejte^ [. ; ^
f/iwi; remedied by Convex Spedacles^
The Nature of Roading G^^exflain%
258
ibidi
/^. 261
s6i
OPTIC I N S T R U M E N T S.
Of Microfcoptt ingtiuraty H^
Of Various Sorts of Single iMcM^xiptB, 06^*^26 §
:■ : •■...■..■.yv. : . V •:.- -^
CONTENTS,
0/ Double or Com^Una Microfcb^l; 265^^2fi
Calculations of their Power of M^ifying^
267 — 269
^eory ofb Cata-dioptric Microfrope, z6^
As CatofJtric ^ RcfleSing Microfcopc^ 276
The Theory of a c^ous one by Dr. Smith,
, . • . - 270, 271
The theory of another of the fame Sort^ 271, 272
S^he Nature and Ufe of a Micrometer, 272
Applied to n new Pocket Microfcope of the Author'S
Jnyentioh, ^ 272
Of the Nature and StruSbure of Rcfrafting Tele-
fcopes 268—273
Sr*fe Theory of RcHefting Telefcopes at large from
Sir I. Newton, 274 — 280
ne Imperfemon of Telefcopes, how Remedied, 286
srfo Properties of Lcn{t:s for Telefcopes conJUer^d^
281
Cfthe NKgnifying Poirer, Diffindnefsi nkd Am-
plification, f^ctn Tcjcfcopes, aSx, 291
0/ the different Porms by Gr£oory, Casse-
ORAiN, Newton, and Hkoi^zr of RefteSing
Telefcopes^ 2^1, 29*
^e Camera Obfcura defcribed^ 292
The feverdl Phasnomena thereof explained^ 295, 296
^he Solar Telefcopc andjts Ufes^ 297, 398
^e Solar Microfcope of feverdl SortSy and their
jJ^fi^* . ^99 — ioi
the newinfoentedH^Xxo^u, hy s^GRATESANDf^
with the Reafon thereof^ 30a — ^304
Vol.il
h^c^
CONTENTS,
LECTURE XI.
ASTRONOMY.
QF tbe Univcrfe, or PhtraUiy cf JKerlds^
306 — 308
7be Ptolomean Syftcm e^tpUdid^ 508— -310
fbe Syftcm of Tycho Brahe exploded^ 31^
The Copemican or Solar Syftem difcrihd^ 313, t?r.
AfamUat Idea thereof^ 314^
j: Ihe Periodical Times of the Planets, 315
I ^heir Mem Diftance^^ iHi^
Their Nodesy Eccentricities^ &c. 316 — ^218
Their apparent Dismetersj and real^ 319
Of the Sun and its Maculae or Spots, 320, 321
The Maculae.^?/ other Planet s^ 5 22
Of the Satellites or Moons, 323
0/ the Magnitude, Motion, Diftance, Pferiod, Wr .
of our own Moon^ j 23, 6ff.
jVi Atmofphere in the Moon^ 324
ffV meafun the Heightrof a Mountain in the Moon^
325
Of the Spots i» /A^ ^^«r, what they are ? 3 2 5
Of the Motion and Libration "J?/ the MooHy 327
^i&if Phaics of the Moon defiriked, 32*
Of the Moons (7r Satellites of Jupiter, 3*9, 6?r.
rAi?/r Motion, Diftances, Eclipfes, ^c. 330, &?r.
Tbe Method of finding the Longitude by tbem^ 331
The Moons of Saturn, by whom difcover^d^ 33^
Of Saturn'i.Ring and its Phsenomena, 332, 333
The Greaf Law of the Planetary Sy&cm defcribed
and explained^ ^. 334, 33'*
The Reafonablenefs of tbe Solar Syfiem^ 3 3 4—3 3 7
, Infallible
CONTENTS.
XafidKUe Arguments, and Mathematical Demon-
. ftratioRs rf Us Truibj 3 3 7 — 3 44
From tie Conjan&ibns, Oppofitioos, Apparent
M^nitudes, Stations, /md Rctrogradations of
the Planets^ ibid.
Wbin Venus is moji enlighten*d by CMlcukiion^
J40
Qf the Form of the Planetary Orbits, 346
9W ^ the Earth in particular, 347
lyby the Summer Half- Year is lofiger than the
, Winter^ ibid^
The Newtonian Theory of the Planetary Mo*
ixQtiS explained at large^ 348 — 363
Exemplified by Calculations^ 361 — 363
Of the Orrery and its Invention, 364, 6?r.
^be Grcles of the Armilliary Sphcrt defcriiedj 366
— 37«
Different Forms of Orreries and Planetariums,
368, 369.
Of tb^ Equinoxi, and ibeir Retrogrellmn, 3 70
The Caufe ti^ereof exphin^d^ 37'> 37^
The Motion of the Stars in Antecedentia, ibid.
The Great or Platonic Year explain* d^ ibid.
The Caufes ofT>zy and Night explain* d^ 372, £*fr.
The Realbn of the Vicifitudes of^be Scaioos, 3 75
—385
Calculations of tbe Degrees of Heat in Winter,
Spring, W Summer, 381 — 3^4
Calculation of Time of tbe greateft HeM on as^ D^
propofed^ 38 T
Tbe Do<arine of Eclipfes explain* d^ 3 86—388
Qf Solar Eclipies (tnd tbeir Phenomena explain* d^
388—393
Tbe Pbanomena ^ Lunar Eclipfes, 393, 394
Tbe Doftrine of Comets, 394, (^r.
Tbe Caufe, i^c. of tbeir Tz\\s^ 395
Tk( Nature of a Cometary Orbit, 396
b 2 Tb^,
G ON TENTS;
^e Aftronomical Theory tberetf^ S97'^?99
Jftronomical Calculations of the Mean Anomaly,
Place, Node, Diftance, ^c. of a Comet j 399
^ * ■ ' ■ " ^ —40?
fbe Geometrical Theory of an Elliptic Cometary
Orbit explain* d^ 403-— 406
^b(^ Patb of tbe Comet of 174! afcertain'4 by Ok-
fervation^ ' 4^7
JNe^ Method ofQtmfiruaing tbe Otiits of£om€ts
exemplified in tbat of ;/j^i^ ibid.
^ New Cometarium defcribedj 587 — ^94
AN
APPENDIX
t - • f •
OP
CHRONOLOGY.
.^.
/J F Time in^eneraU and i/s Mcafarc^ 4H
' Of tbe Year, Periodical ^^^Tropical, 412,41;
Tbe Beginning of tb^ Year detetmin'd by Obferoa^
tion, , . . ^^^
By Mathemntical Calculation of tbe Time of tbe
Summer Solftice, 41. — iS
©/■ Days, So,Jar'/i»i Sidereal^ ciZ
Of tbe Equation of Tio7e, • 419—7421
Th' Manner of equating Days, 4221
o/^vy^ck/ ^ ^^ ■ • ihid.
^ . Of
CONTENTS.
0/ a Month* F^riodictl aud SynoAca], 4t)'
Of Civil, Lunar, m^ Soli-Lunar Tears^ 423, 424
Of the JuKan Year and Calendar, 424
Of$b$ Gregorian Correftion, or New Style, 425
0/ the various Epochal or JEn\ Ma.
Of various Cycles, 425
Of tbo Cycle of the Sun, aud Dcxninical Letter^
426,427
Of Biflbcdle, m Leap-Year, 427
Of the Metonic Qyplci ^r Cyc;k of the Moon^
42S
Of the Gqldep Nuipbers, ^ their Vfty 429
Of tho Cycle of Indiftion, and its Ufe^ 43d
Of 'the Dionyfian Period, iU4.
Of the Julian Period^ 43 r
The /^rommical Principles of Sir Ifaac Newton'i
Chronolc^ explain dy 451, C^r.
Sir liaacV Chrondogy vor^ed^ 433, 4^^
LECTURE Xa
the Use of the GLOEES.
,^HE Swfaet tf iU Cefefti*! GIdbe McriM^
^ 43«
Of the various Gonftcllabons.tff Stt^*, 437
Caulc^es </■ tbe Stars, , 43^
(pottflellatwu of tbe Zodiac, 439
1 ~ if /At JJor^cfp Hpmi^lieft, 440,
441
j.'^j .."■ - of tbe Soutbero HdnUJdier^ 44s, 4<i3
CONTENTa
ne Number tf all the Stars^ it>idi
Jfiranomcdl £Xrfinicbns 43 8 — ^448
A Compcnd tf the Aftronomy of the Stars, 437
"^448
t2rf imrtenfe t)iftance of Jke Suri, 445
Of. Nebulous SiarSj 446
^e iVpparent Motioa oflh Staff expUUrid, 446
^ —448
(>/ a Direft, Parallel, aitd ObKqfie 5/sfc#rr, 448
... -^450
Gnpmonics, or the Art of Dialling explain^ d^ 45b
Various Problemft on tbeCdd^ Globe, 449""^
45^
^ronomical Problems reprefented on 4bo ^hro
.' StertagrapbieaUy proj^Sedy 456—463
^.ke^on of the Harveft-;Moon ^xplain^d^ 463,
'-V ' ;■.' ; ^ ' . ' . ... .•' 4^4
9T&* Mianner of drawing a Meridian line, 465,
466
Various Geographical Problems on the Terreftrial
Globe] • " 457—4^9
Ti>^ Velocity of the EarthV Annual and Diurnal ,
Motions, 468, 469
^e Mithai of meafurkiga Degree * /fer Emh'f
Surety ' ' 465, 47Q
0/ the Voyage to the Arctic Circle by the French
JpW,r^^hcnKtticvaAs, . ^ ,47 1 , fl^r,
S^hetrjlmbo^ of meafuring a Degree particularly
defcribed and illuftrated^ , 47a»473
ti^ Ji^ibo'd of determining ' the true figure of the
'^r Earth from thence^ . 474-4-478
n?^ MatheiftaticalXhcory /i^^^ . 4^4 — 470
Tafeles of the Meafures of a ^^^ai^antal Arch in
V t^e Sphere and Spheroid, 478, 479
Geogra^hkaJ Problems frojeHed in Pl^no, 480
th¥ Sphere prpjeSled qrtbograpbii^alfyt ^^^^*
CONTENTS.
ne Stereegrapbkal Projeffion of the Sphere, 481,
Mcrcator'j Projeaion expUutfd^ Jga
3ViWiftf/ Meridional Piits/w^/W^d; '483*484
SaiUng upon the Rhumb-Line expUttn% 485
3'abU of Meridional Parts f&r the Spheroid, by the
Rev. Mr. Murdoch, 486, 487
APPENDIX.
Of the Lunar Motions, ^c,
Y "The threefold Force of AttraaJon. 496, 49?
|^^''f't^"8'^««»^Laritude. * iJo
EUtpttc Figure of the Orbit, ' S?
' The Motion of the Linea Apfidum, roi— ^o?
^ev^MEcc^rieityof^the&t, ^Sop^l
ne Acknation thereof ^,^* §1^
Theoify of the Lunar Motions «k/ IiTegulariti«;
Motion of the Earth's y&isexpiain'd, ?i, /-/
7;&tfRcceffioflof theEquinojres, '^' Z.;
Method of confuting the dianoty of Matter
Denfity and Weight of^hdie^ in tTsZ'
Earth, Jupiter, and Saturn, 52,, ^;
LECTURE
{«)
L t C t U R E VI.
ty Pneumat icsj pr DoElrine of the Aik, or
Atmosphere iH general. Of Artificial or
Faftitious Aiii ; the great Quantity sheriof in
Kitural Bddiei ; various Ey^ifhents reldtisig
thereto. Of the Weight /?/ the AtR •, of the
Nature of the Barometer for, efiimating the
fame I an Accotrnt tf the feveral Kinds^ viz. the
Perpendicular, Diagonal, Horizontal, Pcndeht,
Wheel, and Water Barometers, *!tbt b'eft
Way of making the Common Baronicter. The
Nature and Ufe of the Nonius, applied thereto^
explain* i. fhe Ufe of the Barometer in meafur-
ing the Heights of Mountains, fcff. ithe
Spring or Ela^ticitv of the Air accounted
for^ and explaitfd. The Nature of the Sea-
Gage explained. 7i&^ Altitude of the At-
mosphere determined. The Art of Sailing
iW the Air proved impofpble. The Absolute
Weight of the Air ditemAn^d ty Experiment.
//J variable Prelture bH Hi/mAn doDiis ; the
Quantity thereof computed. An Account of fifty
£,xperimnts of the AiR-PuMi» relating tt> the
iVeigbt^ Springs and other Properties of the
Air. A particular Defcription bf the Air-
Pump; ah AiR-PuMP of a hew Invention:
The Di»»iiofiBLi< explained. The Nature and
tJfe t>f Thermometers ^x/fomV. TheUcvr-
Vol: ft/" A t#nhitt
fsiT'
2 P N E U M A T;l C S.
tonian Standard Thermometer. Faren-
heit'i. new. Mercurial Thprmnmprpr titphiir^d.
"Hygrometers oJ' fever al ^oris exphttTdJ^lTBe
Common Air-Gun ex^luin^d. The Magazine
AiK'Gvii fartifhlin^ defiMedi '*- -
' fTir\^A^. fart of^ Natural Pbilofofbj
, I. . wliich trea^ts of the' Na/urej Properties,
■ -•* i^^^ E^eps of the Atmosphere, or
' . . Body of. Air cncompalfing, the Earthy is
c^rd PNEUMATICS,...A^^ Greek
W^ord for Wind of Breath. , \ . .
,The Air is gen^aJJy eliecmed a Fluidj but
yiCt differs fron), tlie general Naturcrof Fluids in
tftfee Particulars, viz. (i j In that it is compreffi-
ble^ ' which Property no pthcr .Fluid has. (2.) It
cannot be eongedVd^ or any hoMvfxedy as all other
Fluids may, (3.) It is of a dijferent Venjity in c-
very Part, deVreafing from the EartV% Surface
upwards ^ whereas other Fluids are of ajn uniform
Denfity throughout.' The Air is.thereTore a Fluid
Jut generis, if, it be. properly any Fluid at ail
>i . • : ^ . ■,-...■» ^ . . ^
(LX^XV.) Wlmt IS liei« faid of thci incon^alable. Q£a-
]i(^'^of the Air, relates to the Jippoflibilay^of. changing it
fropi a fluid to a fixed State by Cold, a» witcr is congealed
o'^coQ verted 'into Ice; and melted Atfeitalsave brought to their
jRxed State : Arii^^ fn #fhis p^rticubr limiced Senfe, the Air is
incongealahUy or uncapable of Fixation. * fiut yet it is not aib-
foldtely fo ; for we find ^y vai^ous £bq)cr|meiK9y tb^t Air has
a &ced. State.in the Comnofitian of «i^ral fiodiei, from which
when fet at Liberty, 4t becomes a fluid ejailic Air, like the
common Air; and this 4gain, from^ Tluid^ may be redoded
x6z/fix^36tate 111 Gbmpwitioa with Other Matter, tjio' Bot
ferjej, foj-.iye kii8^y^^^.|t^ 9f.y)jS*'d Body confining tti-
«i«Iy of Air. ^ - -• . ..
Pn fi U.M.A T I C ».
That the Air was created at firft witli the
Earth 4tklf,i^ not to be doubted j find that ever
fmce there has been a conjtant Generation of Par-
tides of Air by the^ mutual Aftion of Bodies upoit
e^Ch otl^er, ^s \nJ^ermentations^ and all- Kinds of ^
^ natural j and arlifiafit Cbemiftry^ Sir IJiidc NewtoH
thinks very reafortable to fuppofe; and Mx. Boyle
h<u /given numetoM& . £]|^periments relating to'
tfie Produdion foi artificial ot fa^itiHis Jin
(Lxxxvi). ;;Vv . ;
'■ - ^^■' ' ■ ■ / ' ' • ■ . ■ ; J
(LXXXVI.) Since Ab is Motattly necc^ fot the Li(&,
of Man^ and moft Animals^ yet, and Vegetables too, it wai.
ifeceiTary at the firiV Porniadon of the £tith td render it a:
Habitation for Aniitiats, tuid a proper Matrix for the Pko**
do^fon of Plants. Now ifince there is a oooAant Geneiuioar
of Air frbm all terreflriafl Snbftances (as m^o ihaUlbew by and
by) it follows^ thilt che ori^nal Atmbfphere mnftibe alway*
increafing m Qiiantity and Sb11c^> unleft vre iuppoie aU ihat it
generated is again abforbM or refixM in the Snbftance of Bo4
difes. And this alternate Tranfttanidon of Lthe State of Air
is extremely manifeit from munberlefs Expenm^ta which ha?#
been made by Mr. Boyle^ uhi Dr. U^Ua^ of* which I (hall
hd-e give an Account 4>f (bme of the pincipal of both Kinds^ '
as folu)wsi. ? . . ....,-,■'■
2; The n-oduaioa of artjCdal or hStbrn Air is ctdedt
eitfter fi:> by flow Degrees firom Patrefiiaiofi8.aBd Fermen-^
tiJdoDs of all Kinds; or (2.) more ezpedhSoiifly.byibBe.Sartl
oTcfa^rmlcal DiAblutiontf ofBodies; or (3l.^aodMly» almoft
inftaxitaiieottfly Sy the E«plofioa of Gmqpowder, ^ the Mixt
VM of fome Kinds of Bodies. Thoa^ if^Pafle or Gougl^
with Leaven be placed in an exhaufted Receiver^ it will« after
fome Tinne, by Fermentation, produce a confideraUe Quan-*
fity of Aifi which Will appear very phunly by the Sinking the
^icldilirer in the Gage. Thus alfo any Animal or Vegeta*
ble SubHance, putrifying ijr yacuo^ will produce the fiune £f«
fca.
3. Gunpowdef, indiMFaan, inlfamtly geneiata a large
Quantity of Air in the Receiver, which caufes the Qgickfilver
to fubfide. And in the remarkable Experiment of Dr. Slant
MC^a^ Drachm of Oil of GarrawaySeed, poar'd upon 9
A Z THAt
That the Air is a heavy or ponderoUs &dd^^
' inuft follow from the Nature of the Matter of
t^rachm of the Compound Spirit of Nitre, produced fach s.
jfif odigious Qaantity of Air, as inftantly blew up the Receiver,
' which was fix Inches in Diameter, and eight Inches deep.
I'he PreiFure, therefore^ of the Atmofphere on the exkaufted
Receiver, which it ov^eicame, wns above 400 /j. reckoning
15/$. to a fquare Inch.
Plate 4* But Dr. Hales, in his Ve^etaik Statics^ has greatly ex-
Axxvi II. ^^'^ >A lus Experiments of this Kind,, and. in the Methods of
Fig. I. making them : One of whk:h was by DifiillatioHy the other
by femunmiw. That by Diftillation is as follows : The Mat-*
ter to be diftiird is put into the Retort r, and then at a is
cemented -v^ry £ift the Gia6 VeflS^l '4hi which was very ca-
pacious at i, and had an Aperture ti, or Hole at the Bot-.
lom. > The Bolt-head a h being thus immerfedin Watery witk
one Leg of an inverted Syphon put up as far as »» the Water
would rife in the Bolt*h«uil, and drive out the Ahr through)
the Syphon, Vhich being taken oat^ the Water wiJl remain io,
the Veifel to the fart % ; at.the (ame Time, wjkile. the Bolt-
head is under Water, it is placed in the Veflel kx, whid^
with the Bolt-head and Retort is carried to the Chymical Fur--
ikaQe, where the Retort his the Heat and Fire gradually com-
mcibicated to it, and the Bolt-head « ^ and VeiTei xx well
&]ten*d from the Heat of the Fire.
« 5. As th& Master difUll'd, . all except the Air, would go
doy/n into the Water of the Bolt-head and Vcffel ; the -fir
that was generated or deftroy'd by tiie. Frocefs would be ihewn
by caufing the Surface of the Water in the B^t-head to liand,
below or above the Point «, as at jf, when all was fipt afide till
it became (|«iite cold. Thus if thie Body diftilling generates
Air of an elafiic Quality, that added to the former will not
permit the Water y to riie fo high as jc, an$l the Space be<i^.
tween % and y below will (hew how Kmek Air was produced
from its lix'd Sute.
6. But if, when aU is cold^ the Surfaice of the Water j^ be
feen above the Foint «, it then fhews that the diiliU'd Body did
dedroy, that is, imbibe or abforb, a Part of the natural Ai^ above
% ; and the Space between « and y^ fifl'd with Water, will
(hew what Quantity was changed from a repellent elaftic to a
^'d State, by the ftrong Attraction of the abforbing Particle*
of the didill'd Body. This Qaantity of generated or abforbed
Air it is eafy^to meafure in Cubic inche5| by (lopping the £nd
erf the JBok* head with a Coxk^ and then from a Quantity of
— . ' which
JP If nv 14 A T I c s. 5
yfh]chit doth Gonfifl:; and fince thofe Particles
arife fronj ^cxjjps of every Kind ip or upon the
Water of a known Weight«to i|I| It M to 5B» and afterwards
tojp ; and the Difference of Weight in the two Bulks of Water
gVes the Kumber of Cable Inches from a Table of ipeciiic
ravities, in the Manner we have formerly fhewQ.
7. The other Method which the Doilor made ufe pf fqr ^«
fBmating the furprizing Effeds of Fermentation atr&ni from
yarioas Mixtures of fdid and fluid Subftances, in generating
and abforbing^Air, was as follows : He pat the Ingredients
into the BoU-head b, and then run the long Neck thereof in-
to a tall cylindric Gb& aj, and Inclining both almoft horizon- ^^
tally in a large Vcifel of Water, the Water ran into the Vef- ^>^VIff^
iH ay, and driving out Part of the Aif » would po^efs its ^^S* ^
Pla^ upon turning them up ai^d placing'both in a Veflbl of
Water xx,9s yotf fee in the f igure, where the ^urfa^ce ojf th#
Water tends in the inverted Glafs li jr at the Point s.
8. If the Ingredients generated Air, then the Wafer would
fall from x toj, and the taj^ty Space ky was equal tp the
Quantity of generated Air^s but if on Fermentation (hey ab-
forbed or fix'd the a^ve Pankles o^ Ah*, then the Sur&ce
of the Water would afcend from le to » 1 and the Cylinder z n
wbiild be the Balk of Air abforb'd> whlc^h is eafily known in
Cttl^ic Indies.
9. When the Subjefts for trying thefa Experiments were a
burning Candle, burning Brimftone» Nitre, Gunpowder lired;|
living Animals; ^^. the DoAor ufed to make uie of a Pede-
fial, on the Top of which was a Pbte Whereon he laid the
Matter to be firod } then inverting the tall cylindric Glafs over
it, i^nd drawing the Water up to«» with an inveited Syiten,
he '{tt fire to the Matters lying on the Plate by means q^\ Fig. 3*
^rmng'Glafs, concei^tring the Sun's Rays in i^ Focuyupon
' tl|e (ame. See the Figure.
10. Bntthif Way that I make ufeof, an4 ifvhj^ is the moft
leafy an^ expeditious poffible, is ii^ftpad of having the cylin-
(drie GuTs* dofe upon the 1 op at b b, tq have it open by a
fmall Neck, on which a brafs Cap is cemented with a Femide-
Screw to receive a Stop-Cock, to take off the Commu*
nifiatipfi of the external Ai^ when pccafion requires. * Thus
the Ufe and Trouble of the Syphon is (uperfeded ; ' and
in cafe of noxious Fumes, Vapours, isfc. from J^ua //rih,
' burning Brimilone, ti'r. a Syrinee fcrew*d on to the Stop-
Cock will draw ofF the Air, and raife the Water to what
^Hefg^t you pieafe, ^yithQut the cumberfome Ufe of a large
'''A3 Ea«fi,
Earth, 'tis evident the coriftituent Parts of ^jr are
of" a moft b^terogmoHs Nature^ and infinitely
;^\ II.. J fl^l].)iieru fiibJQia the<5aa»tJty of Air wWdi varioat
^ubuanc^s ^pco^opf . hy, DilUlarioiu .which I hstve coUeAed
.from the,P>6ator's Ej^p^fiiiicnts, am) r.^ia|{jcd to CMjiic inches.
4 9*ip.li»ch^oC«ftg:5 Blood.
Tallow.
; Peer's Ham ,
' Qyner-ShcU.. . .
; HeartLCWfc .v.
:>rOil pfAimif^ .
T0iJ9C!ClQV,e^x::*u
..3i •
iti nSVv.iJ vfiii-;
u.
ye.lJow:feif».W^ ... -rr^
Coarfoft S*mftn . . '..t — r- .
. UnAfcofile Co4 • ' : - T ■> ,^
^•r^^fh £a(tb-i k'I . ; , , , — ^ • ,
sAiHimooy .".;> i>r •.;«:''"' ■'■ *. •:
; r'pjrriteji ....:., -: mm. . ■ : _; . i,:?3„
SearSalt mixed with Bone-Ca];( : 0-64.;
:> .'fj '^liiMf^Jk'T'^nfm ' » -^^ :' r §P4 i
; . , !St«w,in t)>^.CallTBladder , , _• .<S4^/i
Ttefe ara ;^l^./pri!ic#p%l,Ex|yriment$ ty J?i(till^tipi^
Others wi»re;inad«t(y Fermezitatipii ^nv^jioMS Mixu^fpvf^^
xpf^iivbi?hAg^Bjer4te4 'iAiri..othfi(5 ;j^h?5*b'd it,,and)f9mc 40
peithtr generate nor abforb Air., - T^c, principal Subjc^,
fwhicb of th^$)|elve8 3ibi<tb. Airk» nveth^Ffiines ,pt bui^ping
Bwmfton^ror .M:nches, ^be flame and pum^s of a, Iwinwi^
JC^wile^tl^ftrJ?4thJof living and ^irwig A9HPaiff». ?» §a^»
^cc, cTf,,:., : . ; f» .. ^ ; r, \ .. ■ o . ' y,, ;• •
., -13., T\yi% t)i0 DoOor found, that ,tinfin Malichfs^^ippcdin
,;|DPlted Bri«iftQnc;^,^d fired und^i? a:.Qlafs ip, a Qufjf^i^py 9f
:|^4 Cubiclnche^^ abforbM ijp.Vwhjch w^ fall o%? $'o^2;t^
of the WJ|iq!^> .:A Quidle burning till it went out,, jtsFi^es
afterwards coafilna^ a tt Fart of thr whole Quantity of ^ir,
which WW 594 Oi^Ihc focfcei/ , A half-grown Rat expired ift
the confined Air in ttm Hojir*, and abforb'd 45 Cubic Inchei
pf 4if^ which Y^as a tt ^^^ 9^ the whole 594,
various
V'Ut VMAV tC'Sl
vkriaus in dictr .fpedi$c 'Oraviriest 'Wlie^cfr'^klfii^
\t wiUlblloi4r,,ijiao:^ the Matter Which compoH^
. ^ r^. From whar Uh be«ir Bu3 we tte^fkh how much Re««
foQ Sir ^c Newun^ynhfophbotd on this Sabjed in 'dfifjbl-
lo^in^-Words:* - *^ ^Trae-pennancntJAir artfeyBy p0meftta«
'< rdon or Heat fr^m thqfe BodiM die5Cli)Milhr ciat'>^44
*' whojfe FarticTes adhere by a ftron/Attadioa; 'and ire noc
*' ;thefef<^' repar^t)e4 -tmd' ranged iwithootr^Ftimeniardon ;
' 'thofe Particles recedinf^ from one •lothc^'-i^rii'the grtateft
^'* v^ : Sora of ;^) teftT chit AV by PertteotaHon/ nA
^MbniBtiiiies without k; tret(inifiiiito'€«ttAifiililit>.*' See m
^. > ri^jtMoWOindb Air n a«lKar)rBody; il eUblc'hch Whe^f
iMshr teryp Mnr'^ibf ^4 Gyain» klbboWft^-^fhaYAir liP itt
-fo*d^taie in BodierandbB%U'PlBAt.of^h«fr StftAtace, and in
iprikfc«(>tbem*i^ very great Tart ioo| asli icAoWn from tlie
C^AAdi^ ahd Weight <^ the Air difcharged Uponthfc Anaiytii
oiftiMrifiQdies. ' Thib^lias'tfcaped the 0)»fervkcibR of -Oiyl
^fls,i!«ho haveUthetflotaught r]iatilKBodfes Were'dthnate*
l^dU9kable^Mta«rha0iheycalIiF0iit''£A»Mr/4^ HriKrA^t.
/^, Oil, SaU, and £tfr/i&. Bat by the following Table it Will
i^fsar/ that Air i^itf-Bleinont of Natund^Bomi^ ui as firp.
f^r.&^ibireasaDy4ifiC3ie4Xher. v^ ' >
. t^^ Ja thb fii^ €oliimn'of this TiMryoa hsre th^ Bblk
t»f>4lie Body in Oibc Inihes and Pant; ^ th« ^^cond; tli^
'd^lNlf^r of 'CofaicJ Indies of generated > Air $ in the thiitl k
^e.' Wei^t of therfiddy in Grains, iii the fooith is the
<Wcightof the geaeMtcd Air ; Vind the fifch'fliews whdt fin
«f«lto Whole thelAimiakes.
CiM. CLicL 6rs.' Grs. Frop^
/ PeffsHom^ i — 117 -^'±4.1 ~ 33—1
.^ Oyflw^SheU,. i^ - i — 162 --i 266 — 46 — |
fk^i Heartof Oadc, -j *— 108 -^ 13$ -^ 30 -.. j
v^IhKtVm Wheat, *-^ 270 — 58« .:— 77 _ j.
^'»'?«afei I*—. 396 — ' ji'8-^— iij — \j
r.j Muftaid-Seed^ : — 270 --* 437 — 77 — »
' "'J^^V • ' ' -J — »3S — «3y — 38 — 1?
1 •1>ry Tobatco,: ' — 153 -^ 14*'— 44 ^^ i
Honey with C«^7 . ' ■ '^
5'. vrrof iones. ' ' ^- * ~ '44 — KB m, ^ ^i ^ i
r uVcUow Waa^' V — » 54 — ^43 — ' ij -^^tV
A 4 the
^
P N B U M A T I CS.
^ Body of Air, or Atmofpherc, is always vari^
4biCt ifl wil| it9 Weight or Gtavity be likcwife|f
ahek ChA.
,1—
504 -r
ZU
Grr. Fmp.
3<^ — A-
51-4
t6 — i'
- Coarfe Sugar,
Ji/ifTv^^^/' Coal,
, RTitrc wi* G0P
- of Booe^k
, Rbeniji T^xX^tt l — 504 -r 443 -r 144 — t"
. Qalcuf^ihffumm, -^ — 516 r- 250 —^ 147 — 4 *
17. Thus vi^ fe^ tbat difl^rcBt Bodies contain diffbrent
Qganuti^ of fix*d Air, fcom a Sq^nthio onefMf.of the
wi^ole Subi^n^fi. Frcmi henor we may i^e :fMy^ fitMed of
the Tm^ of ^ir I/aac Niwimi'$ R^ofih% jn the sift^wipy
pf feis OptUu v^ t^fe Wordi: *• TJif Pattid^, when Agr
'* are ihaken off* from Bodies by Heat -or Fenoent^pD, w
f . foon-as they lire beycwd the Reach .bf me AttniaiQii of
** the Body, recede from it, and aUb btm oac another, widi
V g^eat Strength, and keep at a Ditece, lb as fomethnes JtQ
f< t^e up al>ove a MiUtoa of Timer more Spaoa than ihey
< V di^ ^fpre in thf: Form of a deofe Body : Which vsft Con^
V trai^ion and ^piinApn fems unincrlligible by feigtungthai
V Particles of , Air to: b^ fpringy an^l jramoiia, or lolild of^
a* 111^ Hopps» Of by any otl^er Mcam than fc^ a repdfivi
?« Ppwer.. - , ■..,'•.'• /; ,.v.
. I i. T]ii| "(he Particles of Air omnot be t|ras coflM 1^ and
detained in thejf elafti^ State in the Subftaucr pf Bodies; ip
faTy CO be l(he!NVfi froiii Calculation. Thtis, for Inftance, one
.Cubic Inch of Oak yields 216 ^Uc Inches pf Air: Now
fuppofe the Pr^Qlire of the Atmofphere hf» on every Sqnar^
Inch a|}ou( 1 5 H^, (a$ ^e fhall fhewy thoi in order to compreft
%\6 Cubif Inches into, onf Cpbic Inch, the Weight of a 16
Times 1 5 Ih, or 3240/^. which woiddlie the Force to confine
itoa each Side the Cube, whi€h,^aSi it has fix Sides, will re<
quire ^ X 3 240 =- 1 9440//^. or near twenty thonfand Wi<i|rhr»
;o cooiine this. Air in its eiaftic ^tatf in one CuImc Indl« Sip*
ppfiog i^ ^ be-all Air; but, as-it ^ not, (ho Fprce''will d«
greater ilill. \ Tttis Fojxe therefore of 1 944,0 Ik xfixA bo ex-
erted in 'qvfjry Cubic In^h of the Oaken Tree, whiph wuld
Vend.i( in picxes with Ivail ExploTion. It i^tbtfefore not to,
be d^ul^ted bat Air in Bodies doe^ ^ifi in a fix*d and u^elaftic
Sta(e I and that ic i; coufed, and put into an aftive repellent
State by means of Fire and Fermentation. * '
19. ThejTwhb would fee the riumberlefs Ufes that may b<i
fnadeof thiuo:)pomiuDo^rineof arti£ciiilAir» and the fur-
Pneumatics. q
u we confttntly txpcricncc by the Barom^tck^
of various Kinds ap4 5pi#Hrc. (LXXXVH),
prtniiff Seeocf of Ktio wbdge whkh it Uj% open in the moA
abfbm aad tlificult Pam of Pi^xfia^ vuy combic all the latter
PMof the invaluable Bo<rfcabote-mentioned, 'viit. l>T.Hmlts^%
FigitMi atiJ Qymc^'Staikal Ej^ferimmN^ ibmeof vvUchwe
Audi take notice of alfo in th^ $^ael of thefe Nofei.
. (LXXXVII) I. The Weight of the Aiv it nanilefl^ fiooi
jtenTott and various Experiaientf . The Ftftides «te affeded
by the Boiver.of the £aiith*a AttiaAion* and muft theidbm
nU gravitate or tend towa|:da its Centre, which 'it wiutcon*
ftitatet Weight in them, aid ^UotherBodiet. TheEjfperanenu
to (hew the Weight of the Av art finmcront wiuch we ihov
on the Air*- Pomp, among which one is abfolote and v^iy ex-
•ift, bjr.weighiag it in a Balance, in the Time manner as all
«lb^r heavy. Bo&s are weigh*<l«
. a, Tfae.Method I take torthiii is, I helievf, the moft ezr
n& and niee that can po^bly be thought of. For itnce (at
«re iiave fliewn) the FnAion of .the Balance is in Proportion
to the Weight with which it is charged, the Icfs the Weight
is, the lefs will be tbe Fri6tion« aid confeqnently the more
nice and arqoifite will be the Ej^etimenc In order to this I
'take a very thin large FlgrmciFUik^ whofe Capacity is exa^*
ly known in Cnbic Inches : This I exhauft lof ail the Air at
near as cai^ be, and ^^n hang it to tbe End of a very fine and
cmA HydroAttic Balance, js^h J oounter-balMce by Grains
'Welghtt in a ^e hanging from the other End. When the
£qnflibrim» ia nicely Mitain*d, I lift up the Valve, and let
the Air raft into the Fkik, which it feniibly heard, liid feeni
to gnsrkate'nii the Ula&, by.amiing it gradually to •dcfeend
tfil it be fxll'4 with Air, and will then preponderate greatly.
Then to reftore the Equilibrium, J find by Ejcperience *tis ne-
cei&ry to add about 8 Gsaina f^r every Pint the Flaflt coq«
tains ; which &ews that a Gallon ef Air weighs about a I>nim,
and a Buihel an Oance ffvp i and becaufe one Pint = 28
Cubic inches nearly, therefore one Cubic Inch of Air weighs
•i^i^^ of a Grain, at a Mean*
%. At,the Air ba hetexx)genCQMS Fluid, it will vary in its
Weight according to its difiSrent component Parts, and alio
sccoraing to its different Altitudes, which it mult have as an
elafhc and flaAoating Fluid. Since few Bodies are lighter
than Water; and that Water is moft^ eafily rarified into Va-
pour, it follows, that the Acmof^ere fiiPd with aqueous Pat-
j15 P N fiO Kf A T re's.'-
i ^ ^iNCE^ the ParticfesJ bf Air are fbch a^ bting
fepairtated frdm Bodios-beyond tke ^ Sphere* of eor^
iiCles ^1 lie flgllteft; ai #»%6ii^i<aIl)F titidf i^>is% nibiftru^
Wtothet^; inAdaKb thac icin^^oltener bt ffii thubli|ht thaa
In a heavier Sut^: ' Atid'thfttJn^tiiiient wliieH' iiiowi theVi*
9i«tlb»:of th6 Atf^s. @n^ityv-^r* <t^ clHFarent Wetgfat mr 4if^
ferent TimM,''. kcaird) k^^^<mtTE9L4"of >whidi> cfacte jui
various Kinds, which are here defcribed ; but I fhall firft pve
«r AcfoMPof the^nioft'^dj^d'^'fiare or Fofni ef thtfe In-
ftrMnbnt^y'^^A^iiich is &$ fellows; A GbikTobi^heniedcall|^
ieaiTdat^^i^find, ^stOibriUl^ wkk^(^uxkfilM"^;«^defeI.
Brifot^thtti4daftf!araGlifac)f-iAlr>^^niitttdi t¥e Ttbe is im
wsrtsrd; vabd 'carefully- imftii^fiid' #itbj the JFinger Qn^ tthe opea
End iit'41 &fon o^. ch4$ ittne' f^pdred Moxqm^i Jilien^ opoa
reniu/ing the Finger, theMefcairyiirtlicBaiiMM^^^ii^bit
intlieTubtt); andbie laid C<i]amn of Merodf^ri^.the Tnbe
«^lU>e^feen Imatediat^ca idbfide, ^or Mc do«m toawrtaui
Pitdror Altitude, if the Tube be aboiie 51 Inches tMg, m
. lt.9rQgKttto*be. ' •! . ;:f.-J-::^ . r :. > '/ - .1
4; Let AB be fuch a'Tuhe«f 54^ Inchea^ Lengthy aadj^ of
an ladi in Diameter, (tf:k>oti^hir.t(>bd!fm'tliii^v^e)Sri(-
metioRHy<real1d at A> €nd 4wen at B; kt C D bi^ theBafqii
of -MeMSdry^^iar which' the Tiibe it immtrfed^iiurcrnali 'thb
Sotface nf^tha Mercmyia theiBaibn £F, aadiintiHs Tube
0>Hs> Kvmi hh eafy tobndeiiland, that ifaittias cbilMbe
iperforio^ in'J^cuoi as foon as tfie Tube> was idviuaed/aU' Ae
Meccttryk wodld defcend- intaithtt.:Bftlbn, b0aHdir>arTa bca^V
Body^ii ihiift tend towards the O^ntiedf <the £aith/ti}llk
inecti^'wMi'roRie O^ftack^'^^tbi B^n, to AAnA-miAa^
.tibn; ifnd ^fa^^ort it. ' 1 fay; cUi this wdidd htifjpin 4i Karm§^
^tCs ^re'Can fuppofe any Power in the Tnber^MMcieHtaofur-
•tain theCddAin of Mercury f now there cancbe iib'foch(Fower
.boti^hat^of -G^i^^xr, whidb Meed, In Tnbet4tf)a fteU Bore,
<ha$ been found able toTdftttin«it; but k ibiarge^'^Bore, j^
«we fep)^e4l|l9 Tube ta kt«6^>thatiV>wer irbyftrrtboifinaU
to fupporc fo heavy a Column^ which 4nuft therefore of &urle
eiinl6:jiiCtfii^iJBafen,i and ib flaiad upon the iadielJiisbl in the
'tBafoHy-^^nd^ihit^Tubiv:^ ^ - . ^ :>: j>^. :.
r f. ~jB«t Tuice the McWuiy>does itot toadly iubfidc^hen thia
1 Experiment >is ^ade-lnehe^Air^ the Qolnmn oithich remains
in th^irfTiibeimuft WeUt^ Stffp<»ifion to the Ai^-SBitsOaofe,,
fi^^e -mtl^m^^ withm <iOjt WithQlll'^the Tube can ' ))e fuppof^
s - . ^ * " pufculaj
Plate
XXVJII.
rig. 4.
Pk^E U'M A Tie sr.
puj^Ulai- AttraflJon, ate •ftrohgly rcpelTcl hnm
thdfe- Bodies; this ' -RejIeHency being mutual
f ^Itfe^^Sifew of RcaAr^ tb proddce ftch im Mffbfe,* befidH
ftftffi' f(d^ fflldwing. thc:Alr*f6 be a gi^tttiifg nuid, k
taiiSiifcMBHIjr.drafeiii^ ih 'EffM, ii» di^^(^^oh bfMet*
'qirjr m'ftd Vbbe ; ftrtjPftiJ-Gfavityi Fofcc of'Pftfflhre moft
¥l
^.ari&cr. Vthe MtTtm K'tiif tefim; itfnr-A) tte Onfioe of
the 'Tbbe; moft Hi^^Aua,%r^«)eV e6dM Wbdi^eadi
i^if fbfiub*a bjr tM ChmWr-frMAt Of "JilGdltnDii of Air
of the^rame^Bafe, ia^'mSlh Altkiide'isif^ cef tiiiit^if te
Atiriofohere, ''^ .->i . / i •
6, TNmeWdghf\tf.Ae'(Mldhitl>f<d^vi>
Ve have jfoVbcen ftcalflfiff JCaHs'jprefciftl^ «^Arl to etch
other;%ai!1)i Urther'ifiaSiff.Wi^ confiabr;*aftnnKm 8iip.
pofititan- Ae QutekfiWf *weit ^roronghljr^pifrg*d from Ak,
wh«a it fub/i^es ^ (Ije Tube, it mod lertfcvVaantm in «It
'tiiat f art c^tlK TiJbe abovie it,' and Co there is nodmig to aft
upon hrtrppcr-Sorftce to dethrfs itrk ^ff therefore witwtfs
fin^ 6^ rHe* to foch ah ARimde, as the^ various 6tavitj of tlo
Air .te^uiies, ai]tf'of^^di"it is therefore aft a2ffc]ftiate St-
prefS6h or Meaftire, as iti^KatvEre imports. 'T^lnirentioii
was' owii}^ ^b that ha^y'/Z/rif/w •G^niite TM-kM, iDiftii^Io
of the fstmQirs Galileo. * k^fi hence it Is very oAM id*d the
7'orrii}tllA*tuh, BXi& the' fof^rttliim Exferimenf;'€^: '
'' ' 4:.'Sfifce,'as*<i^e havett^iyfaVthUfoibctt^ CoSttmn of
Mercury exaftfy inait!ajj^-ihc>(^rav?ly of the Ailr at'all Times.
It has employed the AttenHmrof all Maiiktrilf, itrho^^ry feti-
fibly ifiid thiftnTelVes alRHrf wiA tte difitrent Sta^ -of the
'k^l but m'ore efpedalljPM'fft;faktited the CotifiAemioo of
^hlloltoph^, *who haW Mftl'airc^pornpiiief T^ -explore,-
Iby this* Means/ the two Eir^raWi of the Air'r Onrvity, w«,
wh>klt1s'leaft and greattftdPWF/by qbfernDgitli^ leaft and
^^'mti^^i^^ or^h m^aria! Cofcum; wjiich by long
l^cpencii we'Shd to be vtry nearly betweeft'iS and 51
Jflaics,''itj)emgveiy.iarfefylds or more tfias'thoffi^ heights ;
>yhenpe 2$| Inches is fix'd^^n as the Nfean-AIfitiide, ex-
Jrjlfivc of tjiV Mean-Qiavlrtf of the Air, which therefore let
{? f epirefcnVd I7BK1 and ^ct the greatcft Afetn^ be FI,
between
J4i "^ P N E U. M A T I C »^
by, anyitt^prds'd Force torapproach nearer to each
other, xh^repujfivi Power wiU rc-^(9: or.refift th^
Plate
xxvnr.
Fig. 9.
G very Tmidly • tke Motkm :of tbe*' Qokkfihrerv ud tdiiA»»
quently of » the A^ G, will at Bottpm be very ooafidctable ; hot
fts the Weight QntoTcsiipiaaddHiwi)/ it tiini»thejPuttey CD^
and that a Habd'or Index KL, byicbe Divifioiis :o£ a largf
graduated CirdeMNOP ; byvvhick.aetis tkeminoteft Va-
riations of the^Air are plainljr ihewa,: if the Inftnunent be fit
very accomtelv -made tJiat-tfae FridiOn of the {everal;Pait9 be
hiQonfideniblei TJdsisoncof th0BiaUiycurioiia.Ikivciti6AliQ£
Dr, Hooh, .> ■ ■ ■ ..; .^,, ,., , ,'. .,.•..'
13. Tkefe arethepnnctpalCbBCrivaneeahitbeftoiiivvD^
forenlai^Agthe Scale of Variafioiciti fimple MeituJrial Baro-
meters. There are other invcntian of compound :fiiromfe-
ttw, tuku flick as are made of > Nfoouy and Water,, or other
I^iiors Ibr that Purpofe ; blit they^ari fo difficult to. make^
ib faulty when* laade, and fo troilbkibme toi de«, that it is boc
worth while to defcribe diem, i ;HowcTer, as the Header^may
have an Idttft'tyf ooeof the heft. Soft^ 'l ihali heie give ban
that whkrhowev itti inireution>t6' the Reverend Mr. Ibvmhgf
together with his DemondratioB of Its iThedry.
' 14*. ABC isia compoand Tdbe Teafd «t A, and open at
C, em|)ty firdm A to D, filled «vithijyiertu^ from thence to
B, and from ihence to £ Witii Water ; let G, B« H, be.:hi a«
borissoD^l jynoy then ir4s' plaim 60m the Natsre^xsf theSy«
phon, that all the compoondFhiiflhcontain'd ilk? the Part be*
tween ti and &,- iaoSt ever be. in SpuhSn^ 'with > itfelf be the
Wdghtof the Airwhat/iC'Will, becaufe the>Prdiitrcf«t:Haad
G ii)ttflalway9.boe«[uar; - Whence <^tkevident, that/the €o*
tunm of Merctti^ D H it in Bqiu/iMo'^f'tth the Colnma of Wa^
ter GS^;^ 'andittOrfumnf of- (Air of the^tine Baf^ oabjointlyy
and'wiN^H^i^fbrevaiQrrwkh^th^fScmivpfthe V;u»aoi^
tbf^lsCt'; all^Mcbitfuftnoiv^bi^^ciompnt^. • . ' ^ > . '
W^.^i^h^ Vfit^^dift^f the W«]gh^thK Ah-^wiackii^ wU
call y, is meafured by the Space which the Mercury movet
in 'the <toim!iw^afoitieieritr«g»ftirTime; ^^Let'Jk^ be .the
SplSte^^AAd^n}l^^^tK€t at: S*m6ve6 thixir in the £no ITimev
aiiS^^^tMiiidtcr^iht Tube. A F be to that of khe Tube
FCasDtb'rvJhed^Will^heSpcio^rabi^cdthioagh :at.B beaa
f^» andtiieref6reG£ the JKlfeic^cepf tjhel^^ E K f^dL^^
' .'"^ \ " ' • ' " '■' X ■ ■ • ''■'■ '^ '
K B, wHl vajy Ift'lts Weight bjt^ 4./^. >Alfo fince th«
Pneumatic s. «"
laid Force with an eqtiiU Momentum i and .thus,
caufe what we call the Renitency, Elasticity,
M
Space mov'd through by the Mercaiy at B and D iiu.~,
the Diffierence D H will vary it« Wc^ht by — . But thb Fa-
f^ati§a of Weight Is equal to both the fbnner, and fiace x ^
j^ n an Alqtude of Watery if we poe m to i ai the Specific
GnyixyoftSercury to 'Water, we fhsdl hare m : i :: x ^
^ = Altitude of Mcrcfory of the fame Weight,
which Equation^
VD*m
gives * =s ■■ K\t.__' » which ghrcs this
V ::.)•. D*: 2« — D*— i. fo is the Scale
'confeqcently,
when reduced.
Analogy; mx :
of Variation in this, to that in the common Barpmeter.
16. Hence if /«= 14, andD=:: 11 wchave;r: V :: 14:
26 :: 7:135 which ihews that when the Tubes. A F and FC
are of an equal Bore, the Variation in this is Ids than thatoF
the common Barometer in the Ri^o of 7 to 13. If 2j»-« *'
!)• — isro, or2« — i -zzD*, then D = V^ 2« — i :==
5,2 1 whence it appears that when the Diameter of A F is to
that of FC as 5,2 to i, the Variation x ml\ be infinity; ii^^
refpedloftiiatin the conoimon 'Bai:ometer. Iffii z:z $, then
X*: V :: 175 : i ; which (hews how rery large the Sc^c of.
Variation in this Barometer noiy be made in comparifon ol" th« '
common one. Btt( I believe inch a Strudlure as this wiU af-
ford more Pleafure in Speculation than.in Fiance i and When .
ail is done the Barometer of the common Form, as it is moft
fimple, fo it will be found themoft eafy and accurate, of all
otfaers. . /
17. Bdfore-I conclude Urn Artide, I ihall jull mentiomthe
B&rometer invented by the Rev. Mr. Oi£wtlloi Oxford, Sup-
pofe ABC0 be a Bucket of Water,, in which, is placed Utiit
Barbfcope xre^ygsm^ which confifts of a hollow Body xrsm^ thut
and TxihtiKyo, madp of Biafs, Tin, GJafs, (sTc. IheBoc- XXJX.
torn of the Tube se jr has a Lesid- Weight. to.fink it, {0 that pj^^ ^^
the Top of the Bo^y maf jaft iWim.CY€a v^ the Surface pf '^ *
> - ". or
l6 i^ N E tJ M A * I C S.
6r Spr iNG of the Air ; which is fo fcnfible by th«l
Water, by the Addition of fome Grain- Weights. As the In-
ffatment is pat into the Water, with the Moath dov^nWards;
the Water aucends into the Tube to the Height ofju; there
^ is added on the Top a {baU concave Cylinderj or Pipe, to
fofiain the Infbrument from finking to the Bottom when the!
Air becomes heavier; mJ isa Wjre, and ms^ dg, are two
Threads, oblique to the Surface of the Witter i of thefd
Threads there may be feveral ; and as the Water juft touches
Che Top or Crown of the Infbrument, when the Altitude of
the Mercury is leaft in the Common Barometer, fo as the Ait
increafes in Weight, the Inihiuient finks in the Water, and a
finall Bubble is rorm*d on the Thread, which continually af>
cendsand de&ends thrO" all the Length of theTl\jread. From
aCalcuUtdon on the, Theory, it appears, that this Barometer
IS Hbove 1 200 Times more exa£i than the Common Baro-
ifietef.. See the Whdle Calculation in the ProfeiTor's own WOtk
in the Phii. Tranfa^ionj*
1 8. Though I have made and tried the Barometer above
drfcribed, and find it to anfWer the Theory very* well, yet is
it not fit for common Ufe, becaufe it can only Ih^^ the ex-
treme minute Variauons of the Air^s Gravity for the frefent
^imtj by rcafon it is afffcded by the Heat as well as Weight
of the Air. , While the Degree of Heat remains the (ame^^
nothing can exceed this Inftrument as a Barometer ; but as the
Heat of tl^e Air varies, fo will the Elafticity of the included
Air, which dierefore will caufe the Infirument to vary its Gra-
vity, while thsit of the Ait remains the fame, and fo cannot
be of conftant Ufe.
19. I have already hinted that the Common Barometer^'
after all, is the beft Irifb-ument to meafure the Air*s Gravity t
iVhich that it may do to the greateil Perfedlion, the following.
Things arc neccffary . ( i .) That the Tube be at leaft of i <>f
«n Inch Bore ; -| of an Inch is a gbod^ize. (2.) The Tube
ought to be new, clean, and dry within when fill'd 1 in or-
der to this, the Tube (houid be hermetically fealcd at both
Ends at the Glaf$-Hoa& when made ; one End of which may
be ctt off with a File wheh you mtcnd to ufe it. (3:) The
Diameter of thtf CiHem that holds the Mercury,- in which the
Tube is immerfed, (hould be as large as conveniently may
ibe, that the Mercury therein spay have neariy at all times
the fame Altitude; otherwife the Index will not be truc^
(4 ) The Mercury muft be very pure, and free from any Mix-
tare of Tin, Lend, or other Metai, (j ) Jt. ought to ^
many
10.
Pn e v ma 1 1 b». 17
cbxhtnon Experiment of a Miwh Bladder :^ an4
Wgeid from. Air entirely^ as it v^y W by (>oiling it,. ifi<! bU*
mg the Tube with it wkile boiliofe-Hot nearjy. (6.) The
Tubemaft be heated hpc wbffi (ill*^ to ivold breakipe tf
the boiling Mercory. (7.) It fli6uld be tubb'd vpry ^hardr, tp
excite t^e ^ledric Virtue, which vM eac{Spl the I>rticlet of
Air from tKe ^arface within. (8.] Tl^ere ought to be a TiTf-
mus [ai i^U .call*d)^,aj>pljje(! \^ the Index of the grad^ed
l^ate, to ineafore more accurately t£e Rife and Fall of the
Mercury. • • ^ '
20. This Artifice is of fingnlar Ufe m thisand many other
Cafes. It bears the Inventor Nomus*% Name, and its Natoid ^ ^
auid Manner i>f applying it u is fbfiows. A B is the upper p|^M . . .
Part of th^ Parometer, in vliich \^ Surfiice of tbft Meicuiy xXVtti
3S. at C. FG is the ufual Plate of 3 Inches Extefi&t, from 3t8 p^^
CO 3 i ; and.Ofi iis the final! Plaie called the Namus, lb con- ^
trived as to Jlide by the other in fuch manner thlk its Index p
snay Be always Jet on one Part to the ^ai6ce of the Mercury,
abd on the other End pointing to the Divifion m the Scale of
Inches correfpqnding Uiereto. Again^ the Nomim is divided
into 10 equal Parti, which tfigetKer are equal to 11 of the
Divifions of the, Scile i tbat is, DE =: 11 Tenths of ap
Inch ; and confeq^^i^^l}^ ^^b fmall Divifion of theNomiu is
bqoal to 1,1 s tw6 bi* them to 2,2 ; three of .the^tito 3,3 i
and JTo on. Wiience *tis eafy to obferve^. that if the Index D
pomto betweeiiany two Diviilonsof tKe,Scal^» as here be-
tween 29.7 and 29, 8, we need only hM.^xk to fee what
Divifion of the No/iius coincides with a, Dififi^n of the ScaJe,
^nd that will (hew how many Tent& of a Tenth, that is» ho«r
inai^ Ij^enchs beyond 29,7. m the prefent Caft; : But you ob-'
ierve the Noniw coincides with a Divifion of the Scale at the
fifth Divifion i confequently, .flie Meitory ll^s. at 29,7$
Inches in the Scale ; and u> yoa proceed with the greateft
Eafe to the hundredih Ito of an Inch, which is a great De-
gree of Exa^eis. • , . 'I
21. From what has tleenfaid we ifftf €My (be tike excel-
lent U(e ofM ttrometo* in mci(fuxitig the Heights of Flacet:
as Motinumsj Towers, (ffr. Forfince (as we (hall (hepir) thi
fpe^cific Gravity of Air (fuch, as is near, the £arth*s Snrftce) i^
to that of A^ercui'y as i fo 12040^* .*tiis ph^n 12040 Inchies
of Air in Height w^ b^Unce one Inch Height.of Men^ury X
confequentlyji 1204 inches, or too Feet,.aniwers to t^ of an
J}ftl| oS, Mercury. Therefore if a good Barometer be; caniec^
to the Top of a Mountain, or other high Place, the Mercury
V©L. 11/ • B' tttiftf
f 1 1
'< ill
1l^
i
m
i8 . Pneumatics.
nuny others on the ^ir Pump. (LXXXVIII.)
will ri4>fide near one Tenth of an Inch for eveiy too Feet
of perpendicular Afcent, and fo will be a proper Index of the
whole Height afcend^d.
22. But iince Mercury is not quite 14 timet heavier than
* Water, the Number 12640 is fomewhat toe large, and there-
fore a lefs Height than 100 Feet wHl anfwer to ^^ of an Inch
D^fcent of Mercury in the, ^ometer ; and what that is will
1)e Ihewn from the Experiments made by Dr. NettUtou vezy
exadly^ as in the Table below.
Altitude of iJ. ^
i ^ ri
Haght, Bottom. Top. Dtfftrenee. for ^^
Irbwer o£Hatjfu9c loz — > 29,78 — 29,66 ^ 0,12 — 85
' » Coal IVlinc . 140 — 29,48 — 29,32 ^0,16 — 87^
Another, Mttd 236 — 29,5:0 — ?9,?3j — o>*7 — 8% .
A fmall Hill . 312 — ; 29,8 1 — 29,45 "~ ^»3^ — ^K .
JiaUfa'x Hill - 507 — 30,00 — 29,45 — 0,55; — 9.1
\ 23. Havii\g the Height, jto which the Meicoiy will (land
at any one JSlevadon, it is eafy to find at what Height it will
iland at any other propofed. For finc^ the Denfity of the Air
decreafes in'a Geometrical Ratio^^ as the Altitudes incfieafe i|i
^ Arithmetical one, the latter will be as the LogaritKins of
the former reciprocally : But the Weight of the Air is s(s the
BenHty,' and the Height of the Mercury in the Barometer tt
as the Weight, therefore the Elevatic^ns are as the' Loga-
rithms of the Height of the Mercury reciprocally; and oonfe-
quently, 'if >ve t^e 30 Inches for the Standard Altitude, and
S5 Feet for th<^ Altitude requiiite to make it fall -^ of an
Inch ; then by faying. Aft the Logarithm of -^- is to 85/fo
29»9
is the L<»;arithm of to the Elevation which wiB make
29,5
it fidl 4 an lach's and fo for any other.
24., A^(er this Manner^ the X)o^\or bascoxnpuQed theibi-
Jowiflg Tables. • ^
A TA^
Pnbuwatics.
19
A TABLE ihewing the Niun
ber 9f Feet sUceoding* required
CO make the Mercury "^1 Co Miy
• given Height in the Tube, ffom
36 to 26 Inches. As alfo the
Number of Feet defcegkling, re
; jqnir'jl jto make the M^rciuynfe*
from 30 to 3 1 Inches.
^'b
3*:
30
JO 8
30 7
^o 6
.30 .4
39 ,3
30 2
30 I
JO o
29 .^
29 7
29 6
^9^ 5
29 4
^9 3
29 2
29' I
29 o
28 9
28 8
r ?
334 79
670 01
.587 21
^20 82
337 «»
28
28
28
28
28 i
zS 2
28 r
2S o
7M
89
2?3 ^2
169 10
84 72
00 CO
' 85 00
17^ ?9
25s 87
34'
427
SH 34
601 q8.
688 II
775 44
863 08
951 01
039 25
127 8c
216 6(
30s »3
395 32
485 »3
575 26.
665, 70
75<^ 47
r
li ,T<
S
A TABLE fliewiog the
Number of Feet requjr*d
to make tJle Meicory fail
, one Tench of an Inch
' from any given Height
in the TubCf from 3.1 Co
26 l»c^
?7
27
27
*7-
*7
f7^
27.
27
27
26
26
26
26
26
26
26
25
26
26
?
I
%/^47 55
1938 97
2030 72
'2122 80
2215 ^*-
?307 95
2401 o^
H94 44
2588 29
z6%z 33
2776 80
2871 62
?966 79
3062 32
3VsS 21
3254 4^
3f335' 07
2 344« c>5
,3545 4»
J643 14
rr
34
30
30
30
30
30
30
30
30
30
30
29
29
^9
^29.
»9
29
29
29
2f
29
28
28
28
z8
28
28
28
28.
28
28
r?
i
82 z6
82 53
82 79
83 06
83 33
83 61
$3 .89
34. 16
•4
i:?
7-«
00
29
58
86
16
36 45
86 74
»7 03
87 33
9763
o .87 93
83 24
88 55
88 86,
89 17
,'«9+9
89 81
^ 13
90 45
90 76
91 <w,
»7
^7
27
*7
27
*7
27
27
*7
a?
26
26
26
26
s6
26
26
z6
26
26
l-.^
9« 42
9' 75
92 08
92 41
»2 74
93 07
93 4*
93 76
94 «2
94 47
94 82
95 «7
95 53
95 89
96 25
96 61
96 98
97 36
97 73
98 10
Bat
Br
20 1* N E U ^^ A T I C S.
"By TC^Sonoi tYitSpnng of lSr/Sr\'\t%Vzs%ir^
muft be always different in different Altitudes
from the Earth's Surface; for the lower Parts of
t!ie Air, being preffed by the Weight of die
fuperior Parts, will be niacfe to accede ^iearcr to!
each other, and the niore fo as the Weight of the
i i i
^LXXXVIII.) K Ti)at we may here dduhk a,plam and:
. clear Idea of the Force with urluch the Partidet of Air re-.
pel one another, 'twill be nece^ to proceed in the follow-.
P1.XXIX. lAg Manner. If in any DiAnce AB, theve are placed any*
Fie. z. Number of Pkrtjclcs ^t equal Intervals firon^ one another; ancS
in any other e^nal M<adcc CD, there are placed twice as
many Particles at equal latbivals aUb; 'tis plain the Intervals)
between the Pirtides in CD will be but half fo great as thofe
between the Patticles in thfe tine AB. Hence the Number
of Particles in any ecjual Parts of A B, C D, will be inverfe-
ly as their Di(bm^es from each other. Or, if we put N =r
Number of Parddes, anU 1= to the Inters between eadi ;•
dien will N be always a& -j, for Liftes.
2. But for Snperfides, Inee they are a» the Square of their|
like Sides, we ihall have H*' ai j^s and in like Manner, fince'^
Solids are as die Cubes 4f tlleb like Sides, we fhall have N^ i
^ Ti' .But N* is as the Denfity of the SupCTfides ; and N ^ !
99 the Denfity of the Solid ; confeqnently the Denfity D, of a ,
Superfidesofthis Sort,isjas|-^iand*ofaS<flidas^. Audi
to fadlitate the Idea, let'A BC be a^Superfi^es of fuch Par-
tides^ eqtial' to a fquare Inch; and 'D F a Solid of a oibtc *
Inch.
3. Nexl; let itjbe fuppofed that e^ch of thefe Partides se- .
pels thofe, ahd thofe only, which ar^ next to iC; and jet this \
xcpulfivc F6fcd(F) be ii^verfcly as the h Powcf' of the In- *
terval I, between tfie Centres of two! adjacent Parades; that 1
f ?
is, let F be as =^.. Hence 'tis manifeft fuch an Alftmldage
of Partides mud <on(litul|p an elafiic ^luU^ or fudi aa one as»
iKheo i?ftiflt*rcft'd, »»• «^=^ upoa- by - any -^external Ar-
gent, will, by Virtue of its itinace repdlent Power, re-ad or
incumbent
fig. 3-
Pneumatics. 21
incumbent Air is greater; aqd hence we fee tbe
Bpffity of the Air is greateft at the Earth's Sur-
£)CC9 and decreaies upwards in geometrical Pra^
portion tp the Altitudes taken in arithmetical Pro-
greffiou. Now it i3 fouod that the Air Is four
Times more rare at the Height of feren Miles
aiske Rcfilfauice wfehan eqidl I>Pgrec tiTForqe.
4. llow'tl^ Pprqe of the fopB^dal Fiam is as the Dea-'
fitjf D, and the nepeOent Potce P between two Panklet. oon*
jointly, or as DxF; but D b asT-, and Pis as >L; where-
^ I* !•
fbreDxPisas — X |^=;:|-^^;77^,wh]di therefore wiUexptefi
Che elaftic Force of the Fluid. Now the Oenfity D of the
Flaid in die cubic Ittdh is as j-^» whcn^ Vp ^ i^ i^ |*
1 , _ I
f* 5»*n**«»T7:^; which foMitatcd for { in the Eipref.
Son of the elaftic Force ^, pvcs D — 7— j that i^ the
elaftic or compreffive Force b as the Cube Root of thst Power
of the Denfity, whofe Index is «-f~ 2*
5» Hence if £ the elaftic Force be as the Deofity D, jb
imjr Fluid; then the general Ejjijnre^Qn D--^ becomes
H '^ 2 ■ it J 2
E -r7—^whcBoeinthftCA*-|— =r I, and ib«^ 2 = 3
andnzri. Cen%uently infuch aFluidP is as-i,orth^
Partides repel each other with Forces that are ledprocallv
•proportional to the Diftance of their Centres. Such then u
the Propeity of th^ Air, whofe Denfity is always propor-
tional to the Force which compreffes i^, as is proved by t^
following Experiment. ^ • ^ / '^
6.
ping the <
furc the Length of confined Air DC vety nicely, and pour
Mercury into |he other Leg AB, till its Height abovethe
Surface of that in C D be equal to the Height at Which k
li 3 riwq
i .-t
2:^ Pneumatics.
tb^n at the Earth's Surface j and therefore at the
Altitudes ©f 7. 14. 21, 28. 35. 42. 49. Gfr.
the Rarity of the Air will be 4. 16, 64. 256.
1204. 4096. 16384. i^c.
If the Air were of gn equal Denfity throughout^
the Height of the Atmofphere might be detcit-
fiands in the ^^roin^ter. Then it is plain the Air' in the
fhoiter Leg vfiW be comprefs'^ with a Force twice as great
as at firft when it pc^efs d the whole Space C D ; for then it
was comprcfs'd only with the Weight of the Atmofphere i
but now it is comprefs'd by that Weight, and the additional
f qaal Weight of a Column of Quickiilver. Let £ be now the
^ ^urfjce of the Mercury in the Leg C D^ and upon meafuring
t> E, the Space into which the Air is now coniprefs*d» it will
\)t found to be jut half the fbroaer Spac^ C D, that is,
PE = 4DC.
7. Hence it appfan that the Spaces S= DC, and /=DE,
• which a given ^antity of Air pofTefles, under diferent Pref-
fures p and P, are as thofe PrclTdrcs reciprocally; that is;
S:s::?:f. And becaufe the Denfities J, D, where the
Quantity of Matter is given (jittmiat. LVL 9.) are pcci-
procally as the Magnitudes of Bodies, vi«. ^:D::/:S;
therefore the Denfities of the Air are as the Comprefling
Forces diredtly, tnx. JiDiif:?. This Property of the
Air is the Principle to which we owe the Invention and Con-
trivance of ieveral very ufeful {nftrumenrs and Machines, fome
pf which I will exhibit here, and othen in the Sequel of (hit
Work.
8. Wc have (hewn in the laft jinnotation that the Prefliiie
of the Air, in its State of Mean Gravity, will fupport a Co-
lumn of Q^ickfilver to the Altitude of 29I Inches; and in
(Anmt.L^l\l.) it was (hewn that the fpecific Gravity of Mei^
cury was to that of Wa^cr, as 14 to i nearly; therefore die
faid Mean PrelTure of Air will fuflain a Column of Water to
the Height of 14 x ?9,5 =413 {nchess: 34 Feet 5 Inches.
But fincc Mercury is not quite 14 Tim^ as heavy at Witer,
ive may take 400 In^ches for the Meafure of the Moan Gra-
vity of jhe Air on Water, and 29,^5 for ^ercury ;; and then
we (hall J^ave D*C : D E ;: P : 29.5 in Mercury; or DCcDfis
• t* : 400, in Water; confequently 400 D C = D Ex P.
9. Again, let the Standard Altitude of Mfcrcury or Water
'%t |i^29,5 or 400, ai;d let the Altitude ^Gz^bi then
mined 5
Pn eumatics.
mined ; for by Experiment we find die Length
of a'Colurrn of Air 72 Feet high is equai in
Weight to one Inch of Water of the fame Bafe :
Hence the Denfity of Air is to that of Water as
I to 864. It is alfo found by Experiment, that
the Weight of a Column of Air the Height of
wHl P=i H4- ^» and then the above Equation wiH give this
Analogy; As S:/ :: H + it:H, whence S:S — /:: H:.^,
or DE:EC::H:i&; confequcntly, by having DE or CB
given, you know the Altitade i&cz F G. Thns for Exam-
ple: Let DCz:: i o Inches, U is r^mreJ f^ fotdwhai Altitudt
•f Water F G twill ly its Prefure raife the Surface mt C one
Imh? Here CE=:i, DE = 9, and H=: 400: Then DE:
CE::H:/&, tl^t is, 9:11:400:44,4; or F G =: 44^ In-
ches nearly, or 3 Feet 8^ Inches. Thus again, Qoeiy the
Altitude F G that ihall raife the Sarfiu:e C 9 Inches, or -f^
of the Whole? Say, As 1:9:: 400 : 3600 = F G, or 300
Feet. Thus the Altitudes are found for every tenth Fart of
tlie whole Space DC, as in the following Table.
23
het.
Incbts.
Tttt. hcbtt.
I 3
8
2 8
3 H
4 r »*
5 .33
4
2
I
4
7 77 9
8 <33 4
9 300 0
9i 633 4
10. Hence i^ deduced the Nature and StroAure of the
SjfeA-GAGE, invented by Dr. Hales^, and Dr. DeJaguHersi
whofe Defcription thereof I (hall here give. A B is the Gage- PI. XXIX.
Bdttle, in which is cemented the Gage-Tube ?i in the firsts-
Gap at G. The upper End of the Tube F is hermetically
feal*d or dofed; the open lower End f i»immerfed in Mer-
cury C, on which fwiras a finall Thidcneis or Sur^Kre of
Treatle. On the Top of the fiottk is Icrew'd on a Tube
of firafs H G, pierced with feveral Holes to admit the Wa.
ttt into the Bottle A B. The Body K is a Weight hanging
by it^ Shank L. in a Socket N, with a Notch on one Side
at M, in which is forced the Catch / of the Spring S, and
pafling thro* the Hole h in the Shank of tlie Weight K, pre**
vents its filling out when once hang on. On the Top, in
the upper Part of the Br^fs Tub^ at H, is fix'd a large empty
BiiU, or fulKblowo Bidder ?^ which mud not be fo large.
a4 . thf
^4 Pneumatic?.
the Attoofphere will be equal to the Weight of^
Column of Water of the fame 6afe, and 32 Feet, oc
384lnchc$high: Whercfore864ntiultiplied by 384
will produce 331776 Inches, or a little above 5-
Milf S| for $he Height of ^e A^mofphere, were
the Dcnfity erery where the lame as at the Earth.
Vut that the Weight K nay be t^t (o Dak tbf Wh^Ie uadet
Water.' ' " '
MI. The Inilraiqent, thus conftnided, is ofed IQ the fol-
lowing Manner. The Weight K being hung on, the Gagfe;
is let fall intq' deep Water, and faaks to the Bottom 1 tke
Socket N is ibmewhat longer than the Shank L, anfd there-
fore, after thq Weight K ^c^nes to ^he Bottom, the Gage
will continue to dei<^nd» till th? lower Part of the Socket
firikes againil the Weight; (his gives Liberty to the C tch to
fly out of the Ho'e L, and let go the Weight K 1 when this
If done, the Ball or Bladder I i^aatly buoys up the Gage ta
the Top of the Water.
12. While the Gage is under Water, the Water haviM
free AcceA to the Treacle and Mcrctiry in the Bottle, wilJ
by its Preifure force it up into the Tube Ff, and the Height
to which it has been forced by the greateft P/efTure, inx. that
^t the Bottom, will be ftiewn by the Mark in the Tube which
the Treade leaves Befimd it, and which is the only Ufe of
the Treacle. This (hews into what Space the whole Air m
the Tube F f is compre&'d ; and confequently, by the Rule
(in Jrtif/e 9.) the Height or Depth of thq Water, w^kk
by its Weight produced that Compreffion, which is the ThiB|f
required. . • * -.
13. If the Gage-Tubte F{;be ofGlafi, a Scale might
b^ drawn on it with the Poin^ of a' Diai^ond, (hewing; b^
Infpe^ion, what Height the Water fiaad^ above the Boctomi
wiiieh Scale is made frcmi the Numbers in the foregoing T^'
Ue, where the Diviiion may be made ^ J^nndredth nuts,
at well u Tenths. But the Length of 10 Inches is not fuf-*
^ient for fatlibming Depths at Sea, fmce it appears by the
Table that when all the Air in fuch a Lengibh of Tobe i|
^mprefs^d into' half an Inch, the Depth of Water b not
triore than 634 Feet, which is not half a Qoarterof a Mile.*
^ 14. If to remedy this We make ufe of a Tube 50 Inches
lomg; which for Strength may be a Mufket-Barrel, and fnp-
Pneumatic'^ 2g
But fince the Denfity of the Air decreafes witb
fJie Prefiure, it wiH be more rarefied and ejcpand*
ed the higher we gO} aad by this ineaii$ the
Altitude of the Atmofpheic becomes indefinite^
and terminates in pu^e jEiber. But though we
cannot aflign the real Altitude of the Atniofphere^
Dofe the Air ixniipre&*() intq 911 |oo4th Fart, or ^ an Inch \
then by ikying* At i : 99 :: 490 : 39600 Inches, or 3306
Feet s even this is bat litde more |han half a Mile» or 2640
Feet. But fince *tis reaibnaUe tp (bppofe the Cavities of the
Sea beaf ibme Proportion to the fnoontainous Parti of Land;
iome of which are more than thre^ Miles above the Earth's
Surface 1 therefore to explore fuc)) great Depths, the Dodor
contrived t n^w Form for his 'Sea»Gage, or rather for the
Ciage-Tube ih St, a| f>Dows* BCDlg is a hollow metalline pt.XXIZ:
d<N)e, communicatmg on the 7^p with a long Tube AB, pjl 5,^
whoie Capacity is ^ Rart of that erf* the Globe. On the lower .
Part, at D, it has alio a (hort Tube DE, to (land in the Mer-
cury and Treacle. The Aif confaifiM in this compound Gage-
Tube i»comprefsMby the Water, u l^efbre ; bat the Degree
of Compreffion^ or Heteht to whK;h the Trecde has beeq
forced, cannot here be^leen through the Tube: Therefore
to anfwer that End, a flender ^ofi of Metal or Wood, w!tl|
a Knob on the Top, mufl be'thruft np to the Top of the
Tube AB, wliich will re^ve the M^jc of the Treacle, and
fliew it when taken put.
15. If the Tube i^B be jo Inphfs long, and of fuch a
Bore as that every Inch in Lei^th ihould be a Cubic Inch of
Air, and the Concents of the Globe and Tube together 506
Cubic Inches ; then, when the Air is comprefsM within a
loodth Part of the Whole, it is evident the Treacle wDl noi;
approach nearer than 5 Inches of the Top of the Tabej|
which will agree to the Depth of 3300 Feet of Water, as
ibove. Twice this Depth will comprefi the Air into half
that Space nearly, vix, zi Indies, which correfponds to 6600;
t^eet, which Is a-N^ile luid a (Quarter. Again, half that ^pocej
Or i:^ Inch, will, i^ew doMble tihe foro^er Depth, vm* 13200
t^eet, or two Miles and a half ^ wl^c^ is probably very neariy
the greateft Depth of the Sea. *
' 16. A Gage of this Kind may be of very great Ufe in
. many other Cafes: Thus the prodigious Force of Compref*
Aqn arifing from Freezing may be accurately tried 2 Let a Boml^
?6 . PWEUMHITICS. i
it b cett^dn froih OUbvation ihcf Experiment,
d\at 45 dr 50 Miles is the utmoft Height ^vhere
Ae BiHjity isfltgUienf to refrail a Ray of Light ;
and dierefof e that may be eftcem*d the Altitude
of caft lK>n fix or eight Inches Diimetery and aboat ooe luck
thick, ^e fiird with Water ; then if a (inall Gage of this Sort
be made and fix*d to a Stick, which is to be fet upright in the
Middle of the Bomb, fo thbt th6 <jage«fiotde maj be in the
central Part; and if then the Hole of the Bbmb be faft fcrew*<l
dp, and the Bomb cover*d 6vet with %frttKiHg Mxture (whidk
is made of equal Quantities off Salt and Snow, or f>oandedlce)
in a little Time the Water will begin to freeze all round the
Infide of the Bomb, and hf its Bxpanfion will produce a
greater Force upon the Water, aYid a greater Degree of Com-
prcffion of the Air of courfe, than by any other Means yet
known: And this may be cetotinoed till it fliaU borfl the Boaib.
whm the Gage taken out of the globular Shell of Ice {for
the Water will be frozen only oh the Outfidc) will (hew the
exaft Qdairtity of this Fdrte of Compreffion.
17. Dr, HnUs (the AutJibr Of this Contrivance] afliTally
made the Experiment, but not having well feanred the Gage,
it was broken to pieces ; hot fi^m computing the Force ne*
ceifary to barft an Iron Bomb an Inch thick, it appeared that
this Force Was about equal to 1 340 Atmofphei^, or the Fref-
fure of 1 340 tnnes the Weight of 33 Feet of Water. But
this Computation was made upon Suppo6tfOii that the Cohe-
fionr of cai^ Iron is the fame with that of Iron- Wire ; bat as
it muft be conliderably lefs, fo the Number 1 340 may be di-
minished to T 660 ; and thefi the Air moft be compref%*d into
1 000 times lefs Space than it had in its natural State, and muft
Sn that Cafe have been more denfe than Water : Forits Den-
fity then to th^t of conomon ASf was as toco to t s whereas
the Deniity of Water and Air are but as 860 to 1 .
18. After the fame tnaiinei* itia^ be tried the Foree wit^
which dried Peafe, Beans, &r. expand with Moifture, when
confinid in a Bomb ; for it muft be a very ftrong Veffel indeed,
fince it has been found by Experiment they will borft a Guii«
Banrf in fwelling. In like manner alfo the ebftic Force of
fedhfoos Air generated from Bodies by Fermematioa may be
eftima^ed in a very nice and entertaining Manner : With many
other Things 6f this Sort, which the ingenious Kcada wi^
readily exc^gita^c of himrdfl
of
.Pneumatics. 27
of the Air to the leaft fenfiblc Degree of Denfity.
(LXXXIX;.
Since the Gravity of the Air is lb various^
that at x)ne time it will fuftain a Pillar of Mercury
(LXXXIX) I. The Dcnfity of the Air on one hand, and
the Rarity on the other, are both limited : No Condenfatioa
can reach fo far as to caufe a Penetration of Parts ; the utmoft
Limit, tlierefore, of Deniity, muft be a perfeA Plenum^ or a
given Quantity of Air reduced into a Space abfolutely fully
or without ^ny Pore ; which is a Degree of Dendty that hat
not been, and probably never will &, in the Power of Art
toeflFca.
2. On the other hand, the Rarity of the Air cannot pio-
ceed ad inJUiium^ but has its Limit from its Gravity : for
though the Rarefaction of the Air be (UU greater as the Difianoe
from the Surface of the Eaxth mcreafeth, its Spring at leag^
will be fo weaken*d, that the Force by which the Farticlet
tend upwards from thofe next below them, will be lefi than
the Force of Gravity by which they tend downwards. The
Rare^Clion of the Air muft therefore be bdunded^ where
thefe two oppdfite Forces come to balance each other.
3; Now though we cannot poflibly define the Limits of the
Atmbrjrfiere, yet we may ftill inveftigate how much the Air is
rarefied at any propofecl Altitude above. the Earth's Sorfiice:
For doing which, feveral Methods jhave beenpropofed i Ibme
of which are very tedious, and difficult to be underftood. I
(hall here illuflrate Sir Ifaac^i Theorem for that Purpi:^ which
is very concife and plain. It requires only two different Den*
fities of the Air, at two given Altitudes above the £arth*a
Surface, to be known, and which we cafily obtain by Experi-
ment as follows.
4. Take a Vial AEFfi, iUl*d two Thirds foUof Water to
CD; in which let a long Tube IG (open at both Ends) be
immerfed, and clofely cemented to tlie Vial at AB, fo that
none of the included Air may efcape. This done, blow a
little Air through the Tube into the Vial, which increafing
the Spring of the contained Aur, will caufe it to raife and fup-
port a Column of Water in the Tube, to fuch a Height H,
that its Weight, together with that of a Column of Air pref-
iing on its Surface H, is equivalent to the increafed Spring of
the confined Air.
5. The Vial and Tube thus prepared are to be carried up
to the Top of a Tower, Mountain, or fome high Phcd ; and
31
f
T^Tn^FT
S8
Pneumatics.
3^ Inches high, when at another it will raifc it
but to the Height of 28 Inches, in the Baro-
peieri it follow^, that we may take 29vlnches of
in the Aftent, fince the Qrfamn of Air preffing on the Water
^t H is confb^ntly fhortenM, {b its JPorce of Piefiiire wiU be
diminifhed . ' The ^priog of the Air in the V ttl will therefor^
keep the Column of Water conftantly rifing m the Tube ; (b
that when yon have afcended the Heieht ot at>oa^ 72 Feet^
the Water in the Tube will have rifen n<m H to L, through
the Space of one Inch ; and fo in Proportion for any otheir
Altitude^ as I have fevend times found |py tr^in^ the £xperi-
inent.
6. From henc^ it appear^, that the Akjtode of <ne
Indi of Water is equivalent to the Altf^e of 72 Feet, of
^4 IiuJies of Air ; and therefore the fp^cpc Gravity of
Air is to that of Water as i tg 864* or, as Sir (faac has
Hated it, 860. Now fince the fp^ific (Jrayity of Water vf
kothat of Mercury as 1 to 14* therefore the ipfxi^c Gravity
pf Air to that of Mercury will be as i to 860 x 14=::? 12040$
and fince the Height (xT Mercury fupported by the ^ir in the
Barometer is 2,5 feet; if we lay. As 1 : 12040 :: i,^ : 2,5 x
12040= }oioo Feet, which would be the Height of the
JMr were it every where as den|e as aj; the £aJtfl^ or about
5I Miles. »>'•.♦
7. But fince the Aif is not miiformly denle, we muft (eek
Jts Height by another Method to he taught by and by. In the
mean time, as the Air's I)enfity conflandy decreafes, we ihal|
ihew how to find the Ratio of its Denfity at any Altitude to
that at the Earth's Surface. Thus, fince the Denfities are af
the compreiliiig Force, which is as the Altitude of the incum-
l>ent Column of Air, and fince the Weight of Mercury is t^
Water as i to 14, it is plain that the Air which fupports i|
Column of Mercury 2,33 Feet, will fuflain a Column of War
ter to the Height of 33 Feet. The Denfity on the Earth's
Burpee then is as 33.
8. Again; it is evident, fince 860 Feet Altitude of Air is
equal in Weight t6 i of Water, therefi^re at the Height of 86a
Feet above tne Earth, the Air (continuing in the ume Statei
would fuftain only 3? feet of Waiter. At the Height there^
fore of 860 Feet, the Denfity of the Air is as 32. •
.9. Hence the iDenfity at any other Altitude is eafily finmd
by the Hyperbola /«//&, and its Afymptotes SF and S/, S be-
iiig t)ie Center of the Ear^^ and A its Sur&ce : Then thf
' ' ' * * . ' Mercury
PriEtJMATids.
Mcrciiry for the mean Altitude^ and conftqueritly
its Weight for the mean Weigbi of a PUkr of Air
of the fame Bale. But a Column of Mercuiy
EartK*s Semidiameter S A =: 4000 lifiles nearly, or f i f iobod
Feet. Take AB = 860 Feet, and let die l^aAtf of tke Air
be reqaired. for any other Height, as AC = 7 MHA, or
^6960 Feet. In the Points A, §, C, treEt the Perpendkolars
AH, fi J, C K, which let be made propoftional to the Den*
ftiesof the Air in the Points A, fi,C; that is, let AH: BI::
33 : 32, and AH : CK :: 33 : at ; and from the Points H, I,
let fall the Ferpendicohrs Ht, In.
10. Then patting S A = A« = r» SB :;;r a^ SC = h^
«ndSB:SA:: A«:B«s — ; tkiaCrs^; then A «
^lib^^LlllZ.uAhm'^Qcz^t:^. And pot
ite : « r: 33 : 32 :: AH : Bh Their; by the Nature of the
Hyperbola, we have the Area iiim as the Lo«rithm ^
St at
r-, aod the Area ^kiw u tke Logfurithm of »-; or tht
Am thin ithkw :: L. J : L.^- But (by CaroIL toPrtf^
XXII. Lib. 2. of the Priwdfia) it is, tbim : tbkw :; An —
— — : * •• -— I * •
a , b a b
11. Now, becanfe «-— r := AB = 860, and b'^r zs
860. 36060
^
ii; Atf~Cr::
AC s£ 36960, .we have «
t: L. -r- •
21120000 21 156960
L. ^ % whence we have L. — = 0,57319b > thefkfore L. m
X X
•^L.jp = 0,573190; whenceL.w — 0,573190 =lt.^ =
^,045324, the Nomber anfwering to which is 8,8 1 7 = ;r =:
ek, the 0^n4^ re^nirtd. Or, the Oenfity at A is to the
Denfity at C as AH to CK, or as 33 to 8,817, which it
nearly fti 4 to I, . .
12. Since the Denfities s», «, Xf acre defined Logarithms, it
is t vident they Qiuft be in a ^amOric ffgreffiin. ^ But tb Ihew
Aefe Things more geneialiy: Let SC =r jr Be a variable
Diftancf,. ami it» Floxion CE= x; let the Denfity CKr^jr,
the coMveffiilg Force in the AJfitude C as c^, and the Power
tf Gravicy as ^. Then will the fyect^ Gifinrity of the Air
• . .' i whofc
m
M'
30
. Pnbum atics* ^
whole Bafc is cne Square Incb^ and Altitude 29!,
Weighs f&KXxt 1 5 lb. which is equal to the Preflure
of Air on every Square hcb \ and therefore upon
be tlieie as|jr; for it wiO be a^ the Denfitjr jr when tb^ Gfi-
wkf g'n giiren. and as the Gravity when die Deoficy is ^iven,
9iiii wfaen neither is given* it wpl be conjointly as bodi.
13. Since the w£>le V^eight or Preflure of a CQluma ef
any bomogeoeousFhiid, of a uniform Denfity, b ai its fpecifc
Gnvity mukiplied by iu Mj^nitude, (by Atmt. I. VI, iq.) aa4
if tbe fiafe be the iaine as t^e (aid Gravity paultiplied by the
Aldtude, and therefore its i^Iu^an fu the fpecific Gravity ipol-
dplied 1^ the YhxMaoa, of-th* Altitude^ therefore we i^ve
iyx=. — ii^ becade the I^Sty of the Air through the ve-
ff imall Space C£ may b# looked opon as unilbnn ; aadfinct
the Preflure diccreafcs as the Altitude x increaies, therefore it
is that ^s niake the Flmdoil of i( iegpaivf^ vix. — te»
14. If the Gravity 1: be aa. — , Ittul the Denfity.y at aiy
P6wer ji of the compreffing Force v, w», \£j : 'i^^ and there*
fore V : j" , by taking ihe Fluxions we have — y * j tiz
n/. In the Place, of ^ and <£» in the Equation gyx =: -^«^
let their Valuet be iubftifiuted» and we have — 1 '^ x sl
n ' -
x^
M
15. If .we put «= I, that is, if the Dcn&y b(e as the
CQpprefline Force, we have — zr . Now^ fince any
Quantities x^x^a^ x^za^ J^ + 3«i "» arithmetical Fro-
greflion, liave alt their Flcmons e^ual and the fiune, yri.x ;
t^efore if any Quantkieai ^ bo taken in fiicb a ?«ogrtf-
fion, their Fluxions -
x^
lor-— will be all dieftM
or conftant ; therefore i =: i— — = 1 1^ confcquehtly _^ :},
that \&i ^t Fluxions^ bf the Denfities are at the Denfities
tl^em^ves ; w^ich therefore are in Gvometricti P«)grtfoa»
as is manfibil from the Do^ine-of Flwcions. '
every
u
PNEU^ATICS.i 31
' every. Square Fool it le^iU \K,2i6o3.y wdallow-
ing Ki ^Si«^^^-P^'.Xwbfi Surface of ^ ^ody of
a rni^d^^-fized JV^^jt SBHft fuftAip a jPisJTurc of
16. If ia tke femr HTfOliiefii yoo pat. sto.?,. cii (upfofe
tlie Gravity to be every where uniform, or given ; then
— =s ^^^. If nowwinke'-^^'coiiftot, or make * :x,
J X X
Uien will 4ie Diftaoces x* be in Geometric^ Progreffios ; and
in that Caf^ alfo we have — r= i, or y : y » whence i)ib the
y
Oen^^s jr aie ip peonncttiqU Progreflipn.
17^ TheFhicntof ikeaboveEquicion ^— ^ • jr =t
;v«
— I
x^"^'+^ i^coi|fc«Q9i»*
tity. Heft; *tis plain, it eannoc be irrr^, for dienj^* := In-
finite; .nor can «r=: i, bepuife.then it would be x^ — ^x<» :db
I, land fo the Denfity y would b^ every where the £une, or
conftant; heither can »=i, fpr thenjF * r=y* ==•. To
determine the Value of (^. wc muft firft define the Altitude
S P, where the Denfity vaniihes, or jp = 0^ and call it
ii=:SFj then we havei Qj=: ^^ «'— «i and hence
, . .. • . . ■ «i-*"l ■
1 — a
, » ;^I - ; where *tis phun -ought
to be a pofitlve Number, and leik than Unity, that whde the
Diflancep f increafe, th^ penfitipsy may docpWe.
iS.'ijT.the AUitnde at which the Denfity y vanifhes
be fuppofi^d infinite, then Q^= 9, and the Eqnatioa is
m — I
jt::^Of iad x = Infinite, then
fore
^'TT* fpr if in the £qaa|ion (drt, 1 7.)
a^-^m 4fi-
ai**l
• =9; there-
JttppofitiOQ*
— ^= , afldfe«s;:jr=Infinitr; contrary tv
3132©
■p
Pn E tj MA TIC S.
I1320 Pbunds, or 14 Tons^ when the Air is of
k mcaii Gravity. THls prodigious Force would
tfufh us into a very fihtfl Compais^ were it no€
PI, XXX.
hg. 2,
i
ihc JXttix^e, or « = 2, we have the EqaatSon -«^— ' j «
^ ■" , *•« — w become r j» " =: — ; wfience j will
be redorocally as ap*~;S which is a general FmmJa firt*. wsf
Hypotfiefis of the Ratio of the comprefling Power and Den-
tty. . Thus, if you fdppoft the Obmprdffiiig Fmdl id the <la.
plicate Ratio of the Deniit^r, that it, j*:*u; then jzzz^l,
and n s=4/ tftid therc^fore ''!' '= i| whence jr will be rc-
1— IT
ciproodly as x. Hence all thofe Cafes of Sch^&m to
i^M^. XXIL Li^. I. of the Prindfia are defived» and anf
others at Pleafuie.
20. The Denfity of the Air decreaJOne indefinitelf ^ it a
evident there is no certain Limit or Boundary of the Atmb-
fphere^ wHieh gradually rareM into pure JEtber^ or ^0^
as it is often catlM. But fincc one principal Efted of the! Air
!s the Refraiflioii of Light, and fince the Particles 6f Light
are the finalleft Bodies we know of ih Nature,' ^tii reafbnabiS
there to fix tl^e Boiwdary of jvhat .^ft^aiay properly q^ Mr^
in the Altitude where it bfgins to have the Power of produ-
cing this leaft £ffeA in Nature tnz. the refradihg a Ray of
Light. • .
2Z. To difcover this Altitude of the Air we have th^ fol-
lowing Mithod. Let A DP l^e the Surface of the Earth,;
Sth^ Sun below the Horizon, SB a Ray of Light touching
the Earth, which is reflefted by }iPartide of Afr, iathe High-
eft Part at B, In th6 horliibnt^l Line B A to a Spefbtor at A*.
The Angle SBN is the Depreffionof the Sun below d^ Ho-
rizon in this Ca(e, which, oecaufe ids at the M9m^t.Twi«
light ends, is known from Obfetvation to be abodt t8 De-
grees. . But b«€au(e BA is alfo aTfmgent,' th^ Angle ACX)
z=z SBN=: ^8^ Degrees'; andtheAngle ACB =:4AC D =
QDeg)6fes;v which would bc|roc, cHdthe Kay SB pats thfougti
the Atmofphere without Rcfra^ioni but becaufe it does not,
but is refracted or bcpt tcvvards H, the Ar.^lc ACB^ibuft.bd
^ thar
I^NEUMAtlCS. ^^
tliat it is equal on every Part, and courfter-
balanccd by the equal Re-adion of the Spring off
the Air within us. (XC.)
dufaiiiifhed iyy the horizontal Refiiaion, w]»ich isabodthalf a
Degree; whence the Angle ACB =r 8^ ^o^
22. Therefore io the right-angled Triangle ACB we have
all the Angles given^ and one Side, (inx: A C =z 4000 Miles;
or the, Semidiameter of the EarthJ to find the Side fi C;
thosy
As the Sine ABC=:8i° 30^^ -9*99S203
Is to the Side A C := 4000 2= 5.602060
So' is Radius qo^ =r 10.000000
To the Side BG= 4044^ 2= 3*606857
i^hereFore BC— HC=HB=44i Miles, the Height of th^
Acmofphere required.
(XC. J I . Since a cubic Inch of Mercury weighs yery nicely
8, 1 osi. Averdupnt; a Pilhur Of M^my, whofe Bafe is one
fquare Inch, and
Altitude
Inches, will weii
C15 t« N
firi.
2. So that the Air, at a Mean Gravity, is equivalent tc)
the PreiTure of 15/^. upon every Jfnare Incbi and therefore
upon tvety fquare Feoi it will be equal to zi(>Qlh. and 2i6ox
14,5= 3 1320 ZJ. or 14 Tons nearly, the Weight or Prcf-
fure fudain^d by a middle-fized Matf. When the Air H
lighten,, this PreflUre is 13^ Tons) and when, heavieft, it i^
14 A Tons, the Difference i% 1,1 Tcfas, ==^464/^. the
Weight \^ith which we are comprcfi'd mote at one Time
than another.
3. This great Difference of PrdEure mnft gieflltly aflFed us
in regard to the animal Fonftions, and confequently in re^
fped to our Health. If st Perfon,* for infiance, be aflhma-
tical, he will find hci Diforder increafe with the Levity of the
Air; for fin-e a pure, denfe,- ehftfc Air, which n very heavy;
is only capable to diilend his Lung9 in Refpiration, when the
Air is le(s compr^(s*d by its dimimfh'd Weight, it will have
le^ £laflicity, and fo be leis capable of expanding the Lungs j^
the Valetudmarian will therefore find his Difikulty of Breath-
ing hKreale in Proporticm.
Voi;. U.
TRi
3+
Pneumatics.
The Weight of the Air is proved by a great
Variety of curious Experiments, the principal of
which here follow.
P1.XXX.
4. Again, the Reaibn wliy we tltmjc iht Ak lighted in fine
Weather, when it is really heavieft, is becaufe the greater
Preffurc conftringes and braces the Fibres a^d Nerves, and
brings them to a due Tone, by which Means all the Blood-
VeiTels a£l with their full Power and natoral Vigour ; hence
a proper Velocity is given to the Fluids, and a greater ilfa-
mentum to oyercome Obibodions in the Capillaries ; thus by
a bride Circulation of the Fluids, and a due Compreilion of
the Solids, we find ourfelves firm and well, alert and light^
and therefore fancy the Air is fo. »
5. Whereas, on the contrary, when this Preffu e is Icf-
fen*d by near 2^00 lb. the Fibres are relaxed, the contra£Ule
Force of the VeiTels diminifh'd, a languid Cuxulation enfaes^
Obftrudtions, Vifcidities, l^c. happen, and produce Agues,
Fevers, Aches, Cff c. in fome ; and in all, a Sort of Indolence
or gloomy Inadivity, and Heavinefs ; and therefore we iroa'^
oine that it refults from the Heav^& of the Air, when it is
|uft the contrary.
6. If it be required to find the Weight of the whole At*
laofphere on the Earth's Surface, we may proceed thus : Sup<r
pofe the Earth's Diameter in round Numbers 8000 Miles, the
Area of a great Circle will be 8000 x 8000 x 0,7854 =:
,50266400 fquare Miles, which multiplied by 4, gives
201065600 fquare Miles for the Surface of the Earth; but
becaufe we took the Diameter a little too large, we may take
200,000,000 for the Number of fquare Miles in the Earth's
Surface; in one fquare Mile are (5280 x 5280=1)27878400
fquare Feet^ therefore on the Earth's SurBtce we have.
55756 80000000000 fquare Feet, which multiplied by 2 1 60
(the PreiTure on each fquare Foot, Article 2.) gives
12043468800000000000/^x. for the- whole PrefTure. N.B.
Since 2240/^. make a Ton, the PreiTure a 160/^. upon a
fquare Foot, is very near a Ton Weight,
7. I fhall now prefent the Reader with a Solution of a very-
curious Problem, viz. To find the fhicknefs ¥H of an hoUvut
Ball or Globe FDME, made of an^ gi'ven Metal, &c. nubofit
fpecific Granjity is kno^fty fucb that it Jball f'wim immerfed i«
fart or twholly in any homogemous Fluid, nubofe fpecific Grannty
is alfo knonvn. Let AB be the Surface of the Fluid, and let
the Globp FDE fwim th^reln^ untnerfed .to tk^ Depth LM;
(I.) Br
Pneumatic s#
(i.) By aftually weighing it in a nice Balance ;
>Vhere we ftiall fee that one Gallon of Air will
weigh a Dtam vtrf nearly/ (2.) By filling a
Glafs Tube with Mercury, and inverting it in a
Bafon of the fame Fluid, where it will appear
that a Column will be fupported in the Tube by
the fole Weight or Preffure of the Air, to up*
wards the Height of 28 Inches, (j.) By taking
the Air off from the Surface of the Quickfilver
in the Gage of the Air-Pump, which then im-
mediately rifes by the Preffure of the external Air.
(4.) By exhaufting a Receiver placed over the
Hole of the Brafs Plate on the Pump, which will
then be kept faft on by the Preffure of the in*,
cumbent Air. Or, (5.) More •demonllrativeJjr
by exhaufting a fmall Receiver under one larger,
and letting in the Air at once upon it -, which will
then be faftcnM to the Plate, as before, though no«
35
aad let the fpecific Gravity Of the Metal be to that of the
Liquor as i to iz.
g. Then putting the Diameter FM=D, HN=r^<
LM =:x; we have the fpherical Shell equal to thd Spher«
FDE— Sphere HI K, that is,^- t^i ilfo the Seg-
ment of the Liquor DME, "•"JS^^'Tq' and, in Cafe
of an Equilibrium between thefe Quantities, we hay«
(> 2D 3D ^
D' — </*D = 3 D**« — 2W*' J and thence D* — 3 D**«
-f 2»;t'=^D; orD* — 3**«+.—^=^; whence
y ' "2*1?T m. r ^
atlafti/=2^D* — 3;r*;» — --g-. Therefore-^
the Thickneft of the Shell required.
C a
'd
placed
36 Pneumatics.
pfaced over the Hole. (6.) By placing the Hancf
on the open Receiver, and exhaufting, the Weighft
of the Air on the Hand will be extremely fenfible.
(7.) By placing a plain Piece of Glafs on the faid
open Receiver, which, when the Air is a little
exhaofted, will be broke into Pieces by the Weight
of the Air. (8.) A Bladder tied over the fame
Glafs will be broke in the fame manner. (9.)
The Air exhaufted from a thin Bottfc under a
Receiver, and then fuddcnly let in, will, by its
Weight, inftantly reduce it fo very fmall Pieces.
(10.) A Bottle broke by the &me means another
way. (i i.^ By putting a Piece of Wood under
Quickfilver in the Receiver, and then exhaufting
the Air, and letting it in again, it will by its
Weight force the Quickfilver into the Pores of the
Wood, and very fenfibly increafe its Weight.
(12.) The exhaufted Brafe Hcmifpheres prove not
9. If we fuppofe the Body to fwim hi the Fluid whoUy im*
merfed, then jt = D, and ^ = •D* x \—n = D V^i— rf.
Now admit FD£ be a Sphere of Copper 10 Feet in Dia-
meter, and that the fluid Medium be Air, whofe fpecific
Weight to that of Copper is as 1 to 860 x 9 = 7640; hence
764»'
and becaufe
atid therefore i — n = i
120
D = 10 Feet,
V-^7^=:^= 1 19*992 i
7640
— 7^39.
7640 7640
120 Inches, therefore
and 10'- ^c 0,004 =^
or
FH, the Thickneis of the Metal' re^^uifke for the Globe to
fwim in Air.
* JO. But in order to this, one Thing more is neceflaiy,
wix, that the Cona^ty of the Globe be a pure ^6/V^ Vacuum j
for if it be fill'd with Air only, the Globe will fink in the
Air, be it ever fo thin ; becaule in that Cafe it muft fale hea*
vier than an equal Bulk oj? Globe of Air. Hence we fee how
only
Pneumatics.
only the prodigious Weight of the Air, but aMb
the Quantity thereof very exaftly. (13.) By
CKhaufting Glafs Bubbles fwimming in Water,
and letting the Air in again, it will force ihe
Water, into the Bubbles, and make them link.
(14.) The Syringe with its Weight deftrendingi*
FacuOy and afcending again upon the Adrtiiflion
of Air, does very prettily prove the Prejfure of
the Air^ and the Rationale of Syringes in general.
(XCI),
soapoilible a Thing is that AeriaJ Navigation^ which Tranaf-
cut de Lanis and other MiracIe*Mongers have amafed as with«
before true Philofophy appeared to deliver us from thofe vain
Speculations, and fruitlefs Attempts tliat may be gronnded
Xhereon.
(XCI) I . I ihall here give the Itaiionaii of the feveral Pbie*
fiomena of th^ Experiments on the Air- Pump, as they are
fhewn in the Order of my Lef^ures on this Subje^. The
Firfi of which is, to fieiv the Mfolute IVeighi tf the Air iy
^weighing it in a Balance i of which we have akeady given aa
Account in Annot. LXXXVil. 2.
?. The Second Vi, fixing fl. fiftflU JUceivtr om the Plate of
fhe Air-Pump^ by exhaufiing the Air out of it. The Reafoil
of which is, that the rrel&re of the Air a^ now alone on
the Outiide of the Glafs, and perpendicukily on its Top, and
preiTes it down with a Force equal to fo many times i^lb, as
there are Square Inches in thp Top of the Glafs, or in the
largeft horizontal Sedion of it. The Spting of the Air,
(which is always equipollent to the PreSure) bemg now taken
away from y/ithin the faid Receiver, wiHtoveit to fuftain the
tentire Force of PreiTure, which wi^ therefore fix it M down
to the Plate.
3. The 7^;W Experiment/*^/ the Glafs firmly on tb( Plate,
notf as heforey wer the Hole^ but o^ one Side of it* This is to
undeceive People in regard to the con^i^on errgneous Nodoh
of a Su^ion^ which they fuppofe is foniething withm-fide of
the Glafs that draws it down as the Air pailes out through the
Hole. But when they fee the Glafs placed on one fide the
|iole under a {Receiver, and that as the ^ is drawn out 9f
C3 That
37
38 Pneumatics*'
IThat Water rifes ia Pumps ^ Syphon s^ and all
Kinds of JVater- Engines^ by t\\t Prejfure of the
Air only, is made evident by taking off the faid
Prcffure (m the exhaufted Receiver) from a Ba-
fon of Mercury, which then will not rife in the
Pipe of the Syringe on drawing uptlie Pifton, as
it will in the open Air.
the Receiver it will by its Spring all cfc^pe from under the
(jiafs at the fame time, and then when the Air is let into the
Receiver all at once, it falls on the little Glafs, and fixes it
down in fuch manner that it is plainly ktn to fmk into the
Leather upon thfi Pfete ; I fay, when all this is fcen and con-
fider'd, it entirely eradicates tjiat vulgar Error, and fcta the
Truth in a clc^r Light.
4. The Fourth Y^igtrimtnt fixes a Tafon's Hand on the ^op
£/* an open Recei*ver. This is done by the Preffure of t]ic Air
on the Top or Back of the Hand, when the Spring of the
Air is wanting within the Receiver to counter- ad it. This
great Preffure is very fenfible to the Hand, though not hurt-
ful ; and the Skin and Flelh is yifi})]y prcfs'd down between
%ht Metacarpal Bones. The Spring of the Air in tji^ Han4
fX the fame time exerts itfjslf, by extending the Skin and Flefh
of the Part of the Hand on the Qlafs fis fjir dpwn as poffible^
by which means the Blood flows thither in great Quantity, as
jn Cupping, and makes the Part look very red. U the Area
pf the Top of the Receiver be 4 Square Inches, the.Hand
' will be prefs'd or kept on by a Weight equal to 60 lb,
c. The Fifth Experiment h fixing the Bra/s flm/fberes to*
^etier hy the Freffure of the external Air^ in fiich manner as to
fequire ^iv^firorig Men to pull them afimder. This is done b/y
exhaufting the Air from their Cavity, and thereby taking away
|he Spring, l^viixg the Preffufe to aft alone. If the Dia-
.metcr of the Hemifpheres be 4 Inches, the Area will be
'12,556 Square Inches, which multiplied by 15 gives 188,3/*.
by which they are comprefsM together.
6. The Sixth ExperimentyZ'^«u'j the Spring of the Air throw*
i^gJ^^ -^'^ ^^^ ^/ ^ Qlafi'Bubhle through the Water in 'which it
i's plact*", in Form of large round Bubbles of Air, This is done
)y taking the PreiTure of the Air oiF the Surfacf of the Ws^-
tcr in the Jar under the Receiver; and by that means the
fepring of the Air, having nothing to counter-adt <^r confine
\\^ will e^ert itfeff| and c?uife the ^ir tq efcape put of the
P N EUMATICS.
The Spring of the Air is demonftrable by va-
rious Experiments: As, (i.) By the great Ex-
panfion of a imall Quantity of Air in an emptied
Bladder, when the Air is taken off from the ex-
ternal Parts in the Receiver. (2.) By the Ex-
trufion of a Fluid out of a Glais Bubble, by the
Expanfion of the Bubble of Air contain'd therein,
fiubblc, and from all Parts of the Water, inveiy fmall Glo-
bules rifing op to the Top ; whence, by the way, ic will ap.
pear, that Water is a veiy porous Body, and all its Interilicet
poflefs'd by Air« which is now expanded into v^e Volumes
or Qloboles, and feen to make its fifcapc.
7. The Senjtntb Experiment is bat a Part of the former^
imd (hews, thai tifom Utihg the Air again into ibi Receiver, it
falls 9n the Sur/aee tf the IVaier, and hy thai means cemfrej/is
ibe nsMe Bedy of IVater, and drives Fart ef it into tbe eva*
.enated Glafi'BmoUey li/bicb tben hetomes beavier ibnn Water ^
emd Jinks to tbe Bottom. As there is but ytry little Air left in
.the fiubble,^ its Spring will be very weak, and fo will yield to
the Forae of the external Air compreffing the Water, and
therefore will' give the Water Admittance till it becomes (b
far compreisM as to have a Spring equal to that of the outward
Air, or to that wich was in the Babble at firft. Its Denfity
will then be the iamealfo ; and its Bulk, compared with the
whole Bulk of the Bubble, will ihew what P^rt of the whole
Quantity of Air remamed after Exhauftion.
8. The Bigbtb Experiment Jtews tbat th fame BnbUe^
flac^ viitb' i(s Ned nfon a bolhw Glajs over a finall Bafin,
under $be fie^nver, ppon e^baufiing tbe Air tbe fataU ^^nantity
of Air in the Bubble vjill again expand it f elf, and drive ont eUl
fbe JVater. The Pr^ure of the Air, whjch before kept the
Water in the Bubble, being now taken away, the Spring o^
the Air in the Crown 1^ the Bubble gn^ually exerts itfelf, and
s^ laft txi^h ^11 the Water. . From this Experiment it plain->
ly appears, that the Spring of the Air is equ^ to the PrdSure,
. pecaiife the Spring drives out all. tbe Water which the Pref-
fure forced into the Bubble.
9 . The Nintb Experimmit is tbe Exfnlfion of tbe Contents of
an Egg tbrougb a finall Hole in tbe little End by tbe Spring of tbe
Air contain d in tbe great End of tbe Egg, While the. Egg i|
new and good, t)iere is always a fmall Quantity pf Air con-
.t^*d in the g^eat End beOY^epi the Sh^ U imd Ae Skin orP«*
. C 4 " (3) B/
39
4Q
Pn euma tics,.
(3.) By the Expulfion of the White and Yolk of
an Egg through a fmall Hole in the little End,
by the Expanfion of the Air contained in the gre^t
End-, andalfo, (4.) By raifing up the Skin of the
Egg (after the Yolk is taken away, and one half
of the Shell) by the Expanfion of the faid inclu-
fded Bubble of AiF, fo as alnaoft to fill the Half-
tamen^ which, upon taking off the Prcffurc of the Air from
the Hole, will expand idelf, and drive out the White mid YoU'
through the Taid Hole in the little End.
10. The Henth Experiment^j&fw/, that nuhenbalf the SbeU
of the Egg thus emptied is taken off, the faid Bubble of Air 'wiii,
ttpon Exbauftim^ fo expand iff elf by its Spring eu to raife up the
Siin of the Egg, and tbrvw it fofar out ms to make the /?f/^«»-
hlance of the entire Egg, This will happen only when the Egg
IS quite new ; for as ttie Egg gcbws flale, the Air will lofe Its
Spring by degrees, and the £gg will become putrid or addlo.
lit is obferved by Nataraliil% that this included Bubble of Air
is abfolutely neceifary for the Produ^on und Maturation of
the Chick^ whic|i is effeded by the Warmth and Fermenta-
tion occafion'd by the conftant Incubation of the Hen.
11. The Eleventh Experiment it tojh^ the great ^uatoity
pf Air contain' d in all f Aid Bodies^. Fot when a Piece of Brafe,
Iron, Stone, i^c, is put into the Water of a Jar under the Re^
peivcr, and the Air drawn out, the Spring of the Air con-
tained in the Pores of thofe folid Bodies, will, by ejcpanding
the Particles, eaufe them to apoear on the Surface in number-
lefs Globules, and exhibit a conous Spefbicle to the Eye, like
the peady Drops of Dew on the Pile^ of Grais ; all which
fuddenly difappearby letting the Air in again.
12. The Tivelftb Experiment Jhi^s, that a Pint of CoKk
with a Weight added to it^ to make it juft fink in^ the Water,
luill be raifed to the Top^ or made to fwi>n^ by exbaufting the
Air, For the Bubbles of Air which are fxpuided from Its
Pores, and adhering to its Surface, render it lighter than Wa-
ter, in which Cafe- it mult neceffarily " rife tp the Top, pr
fwim.
13. Thp ThirUffith Experiment y^^ty/, that Glafi'Images^
and Bubbles, nuhichfnk in Water ^ <wiU^ on, exbaufting the Re-
eeiwr, rfe /« the ^op and ftA^im. For the Bodies of thefe
^mages, bfc. being hollow, are fill-d fo fax with Water as to
jn^ke th^m juft fidc| an4 the reil of the Cavity Ixeing ppf-
*; / ' ' ' '^ ' ' Shell,
Pneumatics. 41
Shell. (5.) Glafe Bubbles and Images Bird witli
Water, fo as to make tliem juft fink in Watcr^
•will, upon exhaufting the Air from the Surface,
rife to the Top of the Veffel. (6.) Alfo a Blad,
der fiird widi Air, and juft made to fink with a
Weight, wilJ, upon Exhauftion, foon rife by the
Expanfion of the contained Au-. (7O The Spring
fetML of Air» this Air will, upon taking off tlie Preflbre of
the external Air, exert its Spring, and drive oat the Watef
from the Images and Bubbles ; they then become lighter than
the Water, and rife, to the Top. When the Air is let in
again, the Water re-enters their Bodies, and they fink dovm
again.
1 4. The Fourteenfb Ej^perimenty&Mv/, thmi a BUdder aMsrw
iy emptiid tf Ait^ and Junk nvith a Weight to the Bottom of a
?'ar of Wittr^ nmll, npon Exbanfium^ rife to the Tof and/wintm
'he Reafon of which is, that when the Preflure of the ex-
ternal Air is taken off, the Spring of the little indoied Air
will dilate and expand the Bhuider to i^ fall Balk ; and then
the Quantity of Water equal to its Bulk will be heavier thai^
the Weight and Bladder, and fo Will buoy them up to the Top,
according to the Laws of Hydroftatics^ which iee.
1 5. The Fifteenth Experiment raifis Seer or AU into a large
Hvhite Head or Froth to the Tef of the Jar. This happent on
account of the great Tenacity of the Floid i for when the
Preffure of the Air is taken off, the Air in the Beer expands
jtfelf into large Globules, to which the Particles of Beer ad-
hering on every Side render them too heavy to rife firom the
Surface, an4 4y away in the Air. The Bobbles of Air being
thus raifed are, as it were, conglutinated or ftuck together bgr
. the Adheiive Qiiality of the Liquor ,; and thus rife in great
Quantities, t)ie upper Part being raifed and fuftain*d by the
Pxpanfion of that below. When the Air is let m, the Air-
3ii^bl6s contrad, fubfide, and retire within the Pores of this
Fluki. In ^^ (ame Maniyr Soap- Water, YqO^ (^c v^ rifii
|n a Head.
16. The Sipft^eiftk Experiment is fxhihitp^ ih^ Pkenomena
ff Boiling Water in the ej^haufted R^cei'ver. To this End the
Water muil he a^ hot as the Finger can w^ll bear when pot
under the Receiver. Upon ej^haulling, th^ Air-Bubbles will
)>e feen to rife very foon, an4 at firft very fmall ; they foon
appe^ bigger, an4 at l^ft ^c (o la^. and n(c withfinh H«-
4-2
11
1
1
Pneumatic s<
of the Air will Ihew itfclf alfo by raifing hea*
vy Weights laid on a Bladder, half fill'd with
Air, in a proper Veffd under the Receiver.
(8.) Beer, Cyder, Water, and porous Bodies^ da
emit great Quantities of Air under the exhaufted
Receiver. (9.) Fifhcs are made fo light or
buoyant by increafing the Spnng of the Air Iq
'pidity, as Mitly to agitsce the Water, and cauie it to appear
m all the QrcuififfamceB of Boilmgi whkh Agitation tof the
Water wilt continue till die Air be let in again, and then it
miR ceafe, and all will be qaiet and ftill as at fiHL Some Peo*
iple imagine the Water gpows hotter by4>oiliiig under the Re-
ceiver, as it does over the Fire } not confidering that Wato'
hoik only by the great Expanfibn and Rare^iAiba of the Air
it contains, from whatever Caufe it proceeds, asftom theHe^
jof Fire, fk-om taking off the Prefiiuv of the Atnofphere by
^he Air-Purop, dt^.
1 7. The Sfv§Mte$ittb Experiment ^invx, that a/krivetd A^
^le ifAlihs flumped dut, tmdwadi t9 lonkfmr^ undtr tbt exbauft*
^d Rtciifvir. TheReafon of whkh is the Expanfion of die
,Air in the SubAancepf the Apple,- when the PrefTure is taken
' off from its Suit&ce ; Ibr though fome Parts of the Skin be
perviotts to theinchided Air, (a» appears by the Iktle Streams
irkkig from tbe Pores if the Apple be placed in Water) yet
^the greateft Part of the Sm^oe is not, and will not therefore
rfufier the Air topafs out, but will yield and expand to its ut-
•moft Dinwi^ons, (and fomctimes burft) on which all tho
Wrinkles disappear, and the Apple puts on a youthful Face,
.till the Air be again let in, when it inftantly retuins to its Ibr-
Qier State of I^oay and (hriverd Countenance.
18. 1^ Eightsinth Experiment fxfniits the hea^lfitl Af^
fehranc* of Air rifing frrni, mil Parts of a nf^getahU Sifhftaiti
'n}try lofioujl^ thrpugh tbeWater in Vtuuo, For when the Pref-
-fure of the incumbent Air is taken off, the Spring oP the
Air, contained in the Air-Ve^lsof Pl«^, will, bv expand-
ing the Particles, caufe them to rife from the Orinces <A all
' the VeiTels^ and that for a long time together, by which i$
fhewn what a great Quantity of Air is cont^in'd in all vege-
table Sabflances ; and iince it is feen to come out of the Sides
or all over the Surface of a Piece of Stick, as well as fron^
its tranfveife Se£lions, it is a convincing Proof, that the TeXt
t^re of the Stems of Plants 1^14 T^efs ^oi^fts of Ve^ek in ^
their
Pneumatics^
their Bladders, upon Exhauftion, that they rife to
the Top of the Water, and cannot again defcend
to the Bottom. ^(lo.) Siirivei'd Apples are made
to look fair and fmooth by the Spring of the con-
tained Air filling out the Wrinkles,, (ii.) The
Spring of the Air in a fquare Botde, cemented
clofe^ will immediacely burft it in pieces^ upon
longieadinal and alfo in an horizontsd'Pofition.
1 9. The Ninettmtb fi9q>eriiiient Jhtnvs tin Mithodof hjeB^
tng n 'Vegetable Subfiana nvith ^mckfihier. Tims if a Pieoa
of Stidc be cut even at each End with a Penknife, and im-
mer&d in Mercaty, npon pomping out the Air from the Re-
ceiver it will at the ikme time come oat of the Pores of the
, Wood through the Mercwy, as will be vifibie at each End*
When the Air is let in again, it falb on the Snrfiwe of the
Mercury, and forces \X into the Pores of the Wood to pofleis
the Place of Air. Whei) the Wood is taken oot and weighed,
it will be found feveral times heavier than before ; it will have
changed its Oolonr, being now of a bhieiih Hoe all over;
and, if fplit or cut tranfverfely, the Quickfilver wilT be fcea
Jglittering in all its Pores, ami through every Part.
20. The 7wyM//r/!& Experiment fV tbt hrealdmg of u Bladder
fy the Wpigbt of tbi Air. For if the Bkdder be tied over one
End of an open Receiver, as the Airuexhadfting the ^)ring
will be weakened, and give way to the Prefliire<? the Air on
the Bladder, in which Cafe the Bladder will pot en a ooncave
Figure, i^ich will be nicely fpherical ; and this wU conti-
nue increafing, till the Strength of the Bladder be overcome
by the FrefTure^ when it will break with a very great Report.
Z I . The Twenty-frft Experunent u tbe btwhmg n Glafs^
Bottle by tbe Prejkre of tbe Air. For this Paq)ofe the pottle
ought to be of a ^uare Form, and not qrltndrical or globu-
}ar ; it (hould alfp be not very thick, if fmall. Then the
Bottfe is fcrew*d on to the Hole in the Plate of the Pomp,
and tlie Air drawn oot ;' by this means the Botdc (iiftuns the
PrefTure ffom without, io long as its Strength will permit;
then the Parts yield, and the Bottlp is infiandy leducod into
very froali Piepcs.
22. The 'T^snty-fecofid Experiment hreah a Sottk by thi
Spring of tbf Air, For the Month of the Bottle bemg fe-
purely feal'd up, fo that no Air from within can efcape, it b
Pill andef tlic Rc^eiyifr i and ^s the >^ is d^awn off firom k%
fjtjiaufting
4J
rfinrm-
Mil
4'
44 Pneumatics.
cxhaufting the incumbent Air. (i 2.) But that
curious EKperiment which fhcws the Force of the
Spring of the Air to be equal to its Weight
or Prefllire, is by raifmg the Mercury, by the
Expanfion of a fmall Quantity of confined Air^
to the ianfie Height in an exhaufted Tube above
the Pump, as that .which it is raifed to in the
Surface, the Spring of the Air included will take place, and
a£i more and more forcibly againft the Sides of the Glafs,
which having now nothing but its own Strength to defend it,
as foon as that is overcome the Parts give way, and the dais
is burft in pieces.
23* The rtf^/sr/yr/^r/ Experiment h tojhenu^ tba$ a Blad^
dfr hting ifnftied of its Air^ ail to € *very little^ aad thet^fuf-
funded in the Recevver^ the httU Portion of Jir woill expand itfelf
infuch manner upon Exbaufiion^ thai at lafi it nj^ill difiend and
fill out the> Bladder to its utmofi Bulk^ and make it appear m oM$
full-blown. The Reafon of which is apparent from what has
been fo often repeated abov« ; as al^, of its contra&ing
again when the Air is let in.
24. The 7nveniyf(mnh Experiment >j&€<w/, that the Syringe
Weill defcend from the fufpended Pifton in Vacuo, ^henthe Hole
at bottom is floppy d^ and a fmall Weight added to G*vercome the
Frisian. If the Hole be ftopp'd in the open Air, and th^
X Pifton drawn up, it will be refifted by the PreiTure of the in-
cumbent Column of Air ; but in Vacuo, where this Air is
taken away, the Pifton may freely rife ; or, which is all one,
the Syringe may defcend ; as it will, if a fmall Weight be
added to overcome the Friction of the Pifton. When ihp
Air is let in again, it will be feen to pufti up the Syringe upon
the Pj/lon again.
25. The 7w/«/y7^i& Experiment ^^w/, that Water rifes
in Pumps, and ^irkjiher in the Barometer, hy the Prfffure ^
the Jir only. For a GJafi Tube being fcrewM on to the above-r
mentioned Syringe, and inunerfed in th^ Mercury in the open
Air, if the Pifton be then lifted up, it wiU attenuate the Air
contained in the GlafsTube, by giving it a greater Space tp
expand in, and by this means leften its Spring, The Preflli^e
then of the external Air wtli raife fo much Mercury into the
Tube, a< its Weight added to that of the Spring of the iq-
Vlnded Air is an equipollent Force, and then an Equilibrium
WiU enfue: fiat if th^^^CT^i}!;^ ^ phi9e4 midcf the exhauft-
\ ■ ' }■ ' J4ercuri4
Pneum Af leg.
Mercurial Gagp by the Prcflure of. the Atmo-
Ij^ere below it.
The great Aft ion of animal Life, viz. Breath-
ingj by Injpiration and Expiration of Air, is ow-
ing to the Preffure and Spriiig of the Air conjoint-
ly, as is evident by the ContraSion and Expan--
fion of a Bladder in a fmall Receiver, widi a Blad<»
ed Receiver, and the Piftoo lifted op, no Mercmy will thch
be feen to rife ; which plainly (hews the CauTe, vix, the Air's
Preffure is in that Cafe taken away.
26. The Twmtyfixth Experiment fihtws^ that the Sfring
•f the Air hat a Fora eqmil i9 the Pnjfitre •/ the Air^ hy raifing
th§ ^tuckfilvir to tbi fam Height. For if a Tube open at
both Ends be cemented into a Glafs Vial, nearly fiU'd with
Qoickfilver, and placed under the exhaofted Receiver, as the
Air is gradually exhaufted you will lee the Mereuiy r^e from
the y& into the Tube above the Pump, by the Spring of
the included Air, to the (ame Height as it is in the Gage-Tube
bdow by the Preffure, and that during the whole Time of
the ^xhauiUon. And Uu<will always happen, let the Quan-
tity of Air in the Vial be ever ib fmaU, or what it will ; the
Phsnomenon depending not npoA the Quantity, but die
Strength of the Spring.
27. The T'wenty'fevtnth Experiment >&nvi tht Method of
making an artificial Foaattain in Vacuo,- hy the Air's Prefftire.
For this Purpofe a very tall Glafs Tube is hennetically cloftd
on the Top, and at Bottom by means.of a Brais Cap fcrew*d
on to a Stop- Cock, and that to the Plate of the Pump ; then;
when all th<^ Air is exhaufled, the Cock is turned, and taken
olf the Plate, and immerfed in Mercury or Water: Then,
upon turning the Cock again, the Fluki by the Preffure of the
Air will be feen ytvf beautifully to play up in the Tube in the
Form of a Fountain^
28. The Twenty-eighth Experiment Jhews^ that thi Mag-
mtic Virtue frtm the Stone^ or a touched Piece of Iron^ affMt
the Needle in Vacuo, in the fame manner as in <fpen Air.
29. The Twenty-nimth Experiment Jhtws^ that the Attra^
SHon of Cobefinn is the fame in Vacuo as in the open J6r, For
this Purpofe a hurge Gkds Tube, drawn out into a very fine
Capillary at Top, when £ll*d with Water wiU fuftain it to'a
certain Height in the Air: If the fame be placed under the
Receiver, and the ^ drawn out, the Water will reasin fuf^
der
45
46
P N E tJ M A T I C g.
dcf tied on at Bottom to reprcfcnt the Dia-
phragm.
tiENCE the NeceQity of Air for Refpirationznd
animal Life in moft Sorts of Creatures, which die
very foon in the exbaujied Receiver: Though
fome Animals will not be killM in this manner ;
as Flies J Frogs j Toads ^ fomc fort oi Fijhes^ &c.
pended as before ; which fhews k to be wholly owing to tbtf
Force of Attradion. • *
30. The l^kirdetb Experiment Jhenvs, that Bodies^ fwitcb
g^uiiihrat^ each other in the Air^ lofe their Equilibrium in Vacuo.
Thus if a Piece of jLead at one End of a fine Balance, and
a Piece of Cork at the other, are in Equilihrio in the Air, and
thus placed under the Receiver, as foon as the Air begins to
be exhauded, fo foon the Equilibrium will begin to be de-
flroy'd, till at M, when all the Air is taken away, the Cork
will defcend, and (hew itfelf really heavier than the Lead.
The Reafon of which is evident from ^ydroflatiq Laws ; for
both Bodies being weighed in Air, each would lofe the Weight
of an equal Bulk of Air, confequently the Cork will lofe a
greater Weight than the Lead in the Air j and therefore when
the Air is .taken away, the Weight that is reftored to it being
greater than what the Lead has retrieved, will cauie it to pre-
ponderate, or weigh down the Lead in Vacuo. And hence
we fee, that a Pound of Feathers is really heawer than a Found
ef Lead^ if weighed in the Air.
3 1 . The Thirty-frft Experiment ^wv/ the Air to he the Me*
dium of Sounds, For if a Bell be fcrew'd on to the Air-Pump^
It will ring in the i\ir, and be heard under a thin Receiver:
But whfn the Air isexhauHed, the Sound is not heard, which
plainly proves it to be propagated by means of the Air , and
this i^ farther evinced by letting the Air gradually into the Re-
ceiver, becaufe if, in the mean time, you keep (baking the
£e]], the Sound will increafe in proportion as the Gkfs is
fiird with Air.
32. The Th'irtyfecondExpttimcTitJhews, that thi Air isne^
€ij/hry for the Exijience of Fire and Flame, Thus if Charcoal
thoroughly lighted, and a Candle burning, be placed under
the Receiver, as the Air is exhaufted the Coals will begin to
decline and die away, and the Candle will go out by degrees.
J3, The Thirty 'third Experiment ^^wi the Rife of Vapours
mnd Smoke to hi o^ing to the Air -, becaufe when the Air is ta*
That
Pneumatics. 47
That Air paflSng through the Fire, and heat-
ed Brafs Tube, is unfit for animal Refpiration, -
Is Ihewn by the fudden Death of any Animal put
into a. Receiver fiU'd therewith. Alfo Candles
ftnd living Coals, put into this aduft Air, im«
ttiediacely go out. Hence the noxious and pefti*
lential Qualities of Damps and fuffocating Ex-
ken away, the Vapours, which at firfi rife very plentifully
from the wet Leathers of the Plate fo as to obfcure the Re-
ceiver, begin to fall when the Air becomes greatly attenuated %
and the Smoke, which at £rfl rofe from the Candle extinA,
now begins to defcend ; and when the Air is all exhaufied^
the Receiver becomes quite clear, and free from all Appear-
ance of Smoke or Vapour. Hence, by the way, we fee the '
Reafon why, when the Air grows lighter, it lets fall the Va-
pours, and the Weather becomes mifly, hazy, and wet or
rainy.
34. The thirty- foierth Experiment fifews the Explo/ion tf
Gunpotvder u owing t9 the Air. For if it be kindled im Vacmo^
the Air, that fo fuddenly expands itfelf from the Powder,
and gives fuch a Shock to the common Air, now finds none
to encounter, and fo makes no fenfible Appearance, other -
wife than by the finking of the Mercury a little in the Gage
by its Spring.
3 5 . The thirty 'fifth Experiment fl>ews bow Halo's are fro^
iuced hy refraBed Light, Thus if a Candle be held on one
Side of the Receiver, and the Eye placed at feme Diibnce
on the other, 'as foon as the Air begins to be exhanftcd, and
isecomes attenuated and repleted with Vapours to a proper De-
£ree, the Light of the Candle will be refracted through that
Medium in Circles of various Colours, very much refembling
thofe feen about the Moon in a hazy Air at Night.
36. The Thirty-fixtb Experiment Jbews bvw the Lungs of
an Animal are affeiied in Vacuo ; in 'what Manner it dies^ and
is re^i^ed again. For this Purpofe a fmall Bladder is tied to
a Pipe, and fcrew?d into a fiottle, which then reprefents the
Lungs in the Thorax. This Pipe is perforated quite through
to the Bladder, and is therefore analogous to the trachea or
Wind-pipe. . The Air coniinM in the Bottle about the Blad-
der is in the fame Circumftances with that in the Breafl about
the Lungs. When this Apparatus is placed under the Re-
€f iver» one or two Exfuilions will attenuate the Air in the Re-
halations^
48 PuttjU AlriCs.
bdtaiions^ fo frequent and . fatally experienced ifl
Mines, and other fubterranean Places.
That Air in \t% natural State is neceflary fot
Fire and Flamey is obviotis from the ftiddin Eoi-
tiriilion of a Candli^ a live Coal^ &c. in the ex-
haujied Riceinjer. Alfo Gunpowddt fired therc'^
ceiv^r and Bladder^ upon which the Spring of included Air kt
the Bottle will cooiprefs the Bladder, as that in the 'Vhoxzk
does the Lungs ; and a few more Turns will cauie the Bladder
to be coQiprefsM together. The Lungs Being thus comprefs*d,
. the Animal is fenfible of a prodigious Weight, the Circula-
tion of the Blood through the Lungs is ftoppM, the Creaturt
Is all over convuUed,. and at laft expires in the greateft Ago-
iiles of a moft cruel Death. When the Air is let in again,
the Bladder gradually expands, as do the L6ngs of the Ani-
nnal ; and if it has not lain tod long, the Blood will again
pafs through them^ and the Animal will recover its fufpended
37. The TtnrtyfeHfeitth tx^mmtoX fitnus Air to te abfi-
lately nectffary to mbft Sorts of AnitnaU, This we do by ex-
haufting the Air from a Cat, a Rat, a Moufe, a Bird, lie.
which foon die in the Manner above defcribed. It is not al-
ways, indeed, that Gentlemen can thus fuffer their Curiofity
to get the Afcendant fo far over their Humanity, as to defire
fo (hocking a 3pedlacle. The Ladies (greatly to their Ho-
liour) (hew more Confideration, in generally voting agaiufl if.
38. The Thirty-eighth Experiment Jhen»s Air is not ahfo-
iutehf necejury to the Lift: of/cftu Animals : For it is well khowii
that pumping the Air from a Toad, an Eel, a Viper,- and all
Sorts of Infedls, feems not immediarely to aiFeft them. In-
deed, the winged Infers cannot fly, but they will crawl and
run ab^jit very briflcly. Some fay Fi(h will die for want of
Air; l^cphfefs t never could kill any. They appear greatly
difturb'^,;fwoln, and fickifli ^t £rit; but Mr. Htpiukcfiy fays
he has Ugpt them a Week in f^acuo^ and they recovered theif
firfl Illne^» and were at the Week^s End as lively and alert
as thofe which had been kept as long in th6 Air.
39. The Thirty-ninth Expefim^t Jht^s ito WingeJ Animal
can fiy without Air. For this Purpofe a large Butter fly is a
proper Subjedl, for as foon as it is put under, tha Glafs it wirf
£y and flutter abbut,< but when the Air h taken aiway, no-
-ih-*-^
P N E U M A T I C S4 4^'
'in will not take Flame, .or be explo/he^ but melt
and die away. ......
Th a t- the different Velocities with which heavy
and light Boc^ies defcep4 in the Air, is owiog to
tj)c Ai?*3 Refiflance only, is manifeft from the
equal Velocity or Swiftncfs with which all Bodici
thing more of that kind is feeil. If a fine Silk be tied aboQ)
one of the Horns of this Animil, and it be thos fufpended ia
t!ie Middle of the Receiver, it wilt at tirft fly towaxds erery
^^9 .of t2i« Olafsy bu^ wh^n the Air .is exjiaufled. it CMim4
get out of the perjpendicular Pofition into which it is brought
by its Gravity^ though it will be conftantly endeavouring to
flo it.
40.^ The Foftuth Experiment is that ef JIdMft.or Bumi Jirj
this Air is bfoagh't into the Received thro* the Fire; and if u^
Candle be put down into it» it infbiiitljr goes out^ aind will do
fb foi many timej together/ buf every time the Candle boms
longer than before; which feems to (hew, that this Air is
feme what of the fame Nature with that in Mines, commonly
cfallM Damply and is, like that^ purified again By Fire.
41. The Forty-fir fi Experiment j^/ac/ that Adufi Air is in-
ftant Veath to moft Sorts of Animals. Thus a Sparrow put
into this Air tumbles down with a kind of Vertigo, is con-
vul/ldy' and dies diredly.; much after the fame Manner aat
Men fait down d&d In the Contaminate Ait of Mines, deep
Wells, fafc.
42. The Torfy ficond'tx^yimtrit Jhtws ^hat all B§£es de-.
fccad equally Jhii/} in Vacuo. Thus a Guinea and Feather
liet fall from the Top of a tall exhaufted Receiver, come
down to the Bottom in the fame time, or both together. Buf
when let M from thence in the Air, the Feather will defcen<i
much' (lower than the Guinea, anfl with an oblique or indiredt'
Motion. . ^ . ^ , • i •
43; The Torty^'tiird EiperimcntyJ/wj tul Tertntntatton and
Putrffaaion depend on JUf. Thus Apples, Pears, Plums,
Cherries, £«ff. which vd the Air foon grow mellow,
p\itriid ahd rotten, will, if kept in an exhaufted Receiver,'
placed under Water, . be prefcrv'd a Idng time untainted, ap-
^ear frefh and in their native Bloom. Thus Eggs aMb, which'
in the Air foon grow ftale, putrid, ahd addle, will in Vacu9
xetain their Goodnefi, and be lit for ufe after a great while.
. Vol. \i JS 4efcchd'
50
P H E U M A T I C S#
defcend in the exbaufted Receiver^ as is Itiewn in
the Experiment with a Guinea and a Feather.
Air is likewife nedcffary for the Exiftence
and Propagation of Sounds; for a Bell placed
under the Receiver, and ruhg, will not l?c heard
when the Air is drawn out ; but in condenfed Air,
the Sound will be augmented in proportion to the
Condenfation,
^ That Fermentation^ PutrefaBion^ Set. depend
On the Air, and arc promoted by it, is Ihewh
Which is tlie Redfbn Why tnany People kee)) them in Pot)
of Butter^ Lard^ feV. tojprcfcrve than from the Air.
44. The Ferty-fiurth Experim^tt /be^ws bn^ necejary JUr
is for the Germination and Growth, of Plants and FeretahUs*
' For if the fiime Seed be planted in two different Pou of
Earth at the fame time, and one of them be kept in an ex-
haufted Receiver, the Difference between the Appearance
aftd Growth of each will b» fuficiently fenfible to any that
ihall try the Experiment.
45. The Forty-fffh Experiment Jhcws^ that the Writing
made ivith Pho/phcrus upon Paper ^ laid on the Plate of the Pump^
njoill in Vacuo afptar btmhioust and not be extinguilb'd like
common Fire. It will alfa fend up lucid Fumes or Clouds to
the Top of the Receiver.
46. If the Paper be nvetted iy Patches, on which the Lines
home been drawn with Phojphorus^ infiead of a Cloud it will
give Fla/beM in Vacuo. For thefe Experiments with Pho^ho-
rus thq Room fhould be made very dark.
47. The Forty feventb Experiment y^^nv/, that upon fomt
Chemcai Mixture a ftrong Efferwe/cency, Ebullition , and Ac^
ienfion will happen in vacuo. Thus if to an equal (but finall)
Quantity of Oil of Vitriol, Oil of Tartar per Deliquium, and
Oil of Cloves, you put two or three fmall Pieces of Phof-
phorus, the Mixture will take Fire in the open Air, and i^
put out by the Addition of a little Water. It will not only
ihine^ but boil up into a Flame in V^cuo.
48. Melted Lead, and other Metals^ fet to cool m Vacuo,
haa;e their Surfaces concave ; whereas they ajre convex in the
open Air. The Reaibn of which Is the fame as of the Ex-
panfion of Water when it congeab into Ice. Thus Ice be-
PfitVlAAtlCS^ 51
by prdferving Fruk in their natural BIdom and
Perfe&ion through the Winter in ^ tpchau^ed
The Ufe of the i)ivi$ig'BeU deitendi oh th6
Preffwre and Sprii^ of the Air: For fincc thp
^pace which Air takes up is reciprocally as the
Power conipreffit^ xt» 'ds evident that at the
Depth of 33 Feet of Water, where die Preflurt
of the Atthofphere is doubled, the Bell will be
half fUl'd with Water, at die Etepdi of 66 Feec
^omesfptdfioltylMttrdiahWittr, tUdMtakmkt mmj
fttUd Metal ii fpedficilly lighitr than when melted: Thus a
lisaden Bulkt fwimii in oeked Lead. Whit Agent Natuie
tmplbfi in the Aim at Cdngdation, is perhaps ai yet on*
kaomu to Iddrtda j but whtterer it be, 'tis cattasn that ond
Ban o£ its Opesatioii is td fever the Pftrttdes^ and ix them at
k gieaser IMteiOB fiom each cither in the ix'i, than they are
ia the fiaid State.
49. Tife Cttmicai Pracfjs 9f Cf^^fidHui^mt mil wH Jkectei
in VaeAo. U Salts be BBx*d with WaSer and evaporated to i
Fell]cle» and then placed under an tarhaaiM Rcceivtr, and
fet in a cool Race as nfiial, it will not ihoot into CtylUs^ aa
ip tii&open Air it readily will.
90. The Ftftitib £9^Kriment ftewa, that if a Reoe of
Wood becenuniced m the lower Fut <lf the Neck of the open
kecdircr, and Meccory be poor'd upon it, after two or tltfee
EahatdBonS the Prcfiore of the Air wiU be ii> great on the
Metoiry, as to canfe it to defcend thrott^ the Pocte of the
Wopd ia Form of a biiaotiful Shower 1 which «HU ihine (if
h he wdH deanfed and the. Weather dry) in a daik lUmn.
The AirdfoSirafoUowtheQnicfcfilverthsoagh thePoKsof
the Wood, and caafe the Gage to fink.
51. To thefe Experiments ofal^^rcftM, I flnJi add the fol-
lowing Partkidars rebting to the Condimsatiom of Air :
A«, <i.) That the VefiU dligfat to be very firongto bear the
Force of the Air*s Spring thos uoeaftd s for v^h Iteafon
fliey ai« generally made of Brafi. (2.} H Gbft be nfed for
a CoMeder» it nttl not indeed fidfer Ui yfcat a Degree of
Condensation, bat the Exfierioient will be pleafanter, by view^
ing the SobjeA pheed in the cendenftd Air. (3 ] The Spring
Pa it
52
P IJ E U M A T 1 C Sf.
it will be two Thirds fill'd ; at the Depth of gg
Feet it will be three Fourths fill'd •, and fo on.
Whence appears the NeccfTity of having the
Veflfel in the Form of a Bell^ that the perpen-
dicular Height of the Water may be as little as
polfible. Hence alio we fee how neceflary it is
to have a very gentle Defqcnt of the Bell, that
the Divers may have Time to admit the Air, {o
greatly condenfed, by proper Degrees^ left it»
Ihould burft th? fine Veffcisof then: Bodies, arid^
of the Air will be greater in proportion to its Condenfationjr^
SLtid therefore (4.) The Sound of the Bell will be twice and'
thrice as loud as in the common Air, if the Air be made twice
orthriteas denfe by Injedion. (5.) A round Vial will be
broke! by condenfed Air, that could* not be broke by tkc
Freflkre of the common Air. ^6.) Hiought Animak foom
die by not haying the natural requifite Quantity of Air, yet
they will not be eafily kilPd by having that Quantity increafed.
by Condeniation. (7.) If Air be condenfed upon Water in a
Bottle, it will caofe it to fpout through the Tube of Com-
munication to^ very groat Height, vsk. to 30 Feet, if only
one Atmofphere be injeded i to 60 Feet, if two ; and £0^ on*
(8.) A Bladder, that will fuftam the Spring of comnoiLAir,
wHl be broke by the Spring of eondenled Air. In ibort, the
Force of condenfed Air may be fb far increafed, as to coun-
tervail or antagonife the ^reateft Power of Nature that we.
ean apply. ' (9) Water with Air condenfed upon it. will con-^
^ive a much greater Degree of Heat than in the common Air/
where it will boil nroch fooner than in condenfed Air. ^lo^) So
great may the Degree of Heat acquired in Water this way^
be, as to melt fofc Solder; and chere£6re Veflels ihoirld' have'
their Parts put together with hard Solder, that are ufed about
thefe Experiments.
52. From this vaft Power of confined and elaiHc Air andf
Steam it is that we account for the prodigious ESe&s 'of Paf-^
fhiit Digester in diflblving Bones and reducing them to
a Jelly^ fo as to becopie a wholfome and favoury Diet^ for
which Purpofe they are put into a metalline Vefie), with a
Cover, which is &ft and ifarongly fcrew'd down, and
Air-tight. Jhe Digefler nearly fill d with Water and Bones
kill
Pneumatic $• ^3
Hill them : Together with fevcral other Particu-
lars relating to the Nature and Manner of udng
this Machine, which will be more fully explain'4
in the Note below (XCII).
is fet over a gentle Fire, which by degrees rarefies the Water
into Steam, which with the included Air in a fhort Space of
7ifne ^£^9 upqn the Bones with fo great an Energy, as to ef-
fe& their utter Di^qlution, and caufe them to mu and incor-
porate fo intimately with the Water, or Broth, as to make a
perfedl (kagultt^ or JelJy lyhen all i^ coI4. which may be then
flic^ out with 9 Knife. They who woa(d fee more of the
wonderful Effedi of this Infirumenc may confuit tlie AHt}ior*9
own Sook upon the Subje^
(XCII) I. That the Reader may have a juft Idea of th^
Cavfana Urinatoria Of Di vii|g-Be ll, according to the lateft
Improvements by Dr. lUilfey and Mr. Trie^ald. of Stockholm^
I h^ve here exhibited tivQ Figures of tlie fame. The ^xd la
that of Dr. HaUty^ Fonq, wmch was 3 F^ wide at Top^
5 Feet at Bottom, and 8 Feet high ; and contained about 63
Cubic Feet, or near 8 Hogflieads, in its Concavity.
2. This was coa,ted wit^ Lead, fo ^eavy that ^^ wonld fink pf, XXX.
^mpty ; and the Weight was ^iftributed about the Bottom I K, p|^, m
that it would go dowii in a perpendicular Fqfition and no
other. In the Top was fix'd a ftrpng but <^ear Qlais D, to
let in the Light from above ; and likewife a Cock, as at B,
to let oat the hot Air that had been bipeathM ^ and below, as
LM, was fix*d' a drcnlar Seat for the Dive^ to fit on ; and
jaflly, from the Bottom was hung,^ l^y tl\ree Ropes, a Stage
for the Divers to fland upon to do their Bufinefs. This Ma-
chine was fttfpended from the Maft of a Ship by a Sfrii^
whid^ was fuiiiciently fecored by ^tays to the Maft head, and
yfOA direded by Bractx to carry it over-board dear of the Side
of the Siyp, and to bring it in again.
3. To fttpply the Bell with Air under Wa^r with two
Barrels, fuch as C, of about 63 Gallons each, were made
and caf^ with Lead, fo that they might fink empty, ead^
having a Ho)e in its lowpft Part to let in the Water, as the
Air in them is condenTed in their Defcent, and to let it out
again when they were drawn up fall from below. And to a
liole, m the Top of the Barrels, was fix'd a Hofe or hoU
low Pipe, well 4)repar*d with Bees- Wax and Oil, which wa}
Ipng enough to fa^ below the Hole at the Bpttom, being
P 3 t«»
54 Pneumatics.
The Spring of the Air is ipoft cYicfently con-
cernM in that Chirurgical Operation we call Cup^
fingi for when z Vacuum is njade by a Syringe in
|he Ciipping-Glafs applied to any Part, the Spring
of the Air in the FIclh under the Glafs doe^
funk with a Weight appended, fo that thf; Air in the oppez
Part of the Barrels could not efcape, unlefs the lower £iid|
pf thefc Pipes were firft lifted up.
4. Thefe Air-Barrels we^rc fitted witji Tackle, proper tQ
make them rife ^nd ff^U alternately, like two Buckets in a
Well J in their Defcent. they were diredtcd by Lines 6ften*4
^ to the under Edge of the Bell to the Kfan ftanding on the
Stage to receive ^hem, who by taking up the Ends of the'
Pipes above the Surface of the Water in the BcH, gave Oc-
cafion for the Ipl^ater in the Barrels to force all tl^ Air iii
the upper Parts into the Bell, while it entered below, aii4
fiird the Bf^T^ls. 'And as foon as one was difchsu'ged^ by 1^
Signal given, it was drawn up, and the other de(cended; M
be ready for Ufe*
5.* As the cold Air rufh-d into the Bell from the Barrel below,
}t expeird the hot Ai|r (which was iightei*] t^ro* the Cock B,
at the Top of the Bell, which was then openM for that
purpofe. By tUs Method, Air is comtotmicated fo quick^
and in fuch Plenty, that the Dodor tells us, he himfelf waa
one of five who were together at the Bottom, in nine or tet^
- Fathoms Water for above an Hour and an half at a Time»
^ithout any Sort of ill Confeqnence; and he might have con*
tinued there, as long as lie pleafed^ for any thing that ap-
peared to the cipntrary.
' 6. In going down, *tis necefiOiry it fitouM be very gently
at firft, that the denfe Air may be infpired to keep up, }^f
Its Spring, a Balance tq the Pte^ure of thtf Air in the BeH. '
Upon each 1 2 Feet Defcent, the BeP is ftopoM, and the Wal-
ter that enters is driven out by letting in tlifee or four Bar-
rels of frefh Air. By this Means, the Do6tor fays, he couM
fby takih|; off (he Stage) lay the Bottonv of the Sea, juft with-
in the Compais of the Bell, fo far dry, as not' to be over
^hocs thereon. ' )
7. By the Glafi s^bove fo mudi Light was tranfmitted when
i he Sun Ihbne, and the S^ ms clear and even, that he could
ee perfectly well to write and read, and mtiek mose to take!
¥? y y Thittg under the Bell i and by the Return of tl^e AJr-
ftroi}gly
P N R U M A T I C 8. 55
ftrongly a£t, and by that means cauies the Flclb
to diftend and fwell into the GlaTs, while the
Preflure of the Air on the Parts without the Glafs
accelerates the Motion of the Blood and Fluids,
towards the Part where it is dioiinilh'd or uken
Bttreb, 1|8 could iend up' Orders, written with in Iron Pen.
on finall Pieces of Lead, dire^ng they were to be moveci '
from Place to Place.
8. Bat in dark Weather* when the Sea was /tough and
troubled. It would be as dark as Night in tlie Bell ; but then
the Doctor found he could keep a Candle burning in the Bell,
as long as he pleafed; it being found by Experiment, that
one Candle confumes much about the fiune Quantity of con-
fined Air ^$ one Msn does, d^, about a Gallon fir Minute.
9. The only Inconvenience the Do&or complained of was,
that upon firft going down they felt a fmall Plain in their
gars, as if the End of a Quill were forcibly thruft into the
Hole of the Ear. This may proceed from its being foijie
Time before the Air can get from the Mouth, thro* the' fmalt
Canal of the Euftmcbian Tuh^ which leads to the inner Ca-
Tity of the Ear; where, when it comes, it makes an M^U^
brium with the outward Air, pre^ng on the Tyw^Mmm^ ,txA
thus tl^e Pain, for a (hort Time, ceafes; then defcend*
log lower, the Pain of the Sars returns, and is again abated i
9^ fo on till you come down to the Bottom, where the A^
is of the fame Denftty continually.
10. One of thofe Divers (who thought to out- wit Damt
Nature for once) put a Pjf ce of chew'd Paper in his £ars« '
which, as the Bell defcended, was fo forcibly prefled into hi^
Ears, that it was with great Difficulty the Suigeon could ex*
daft it. Thus a Bottle with only common Air in it^ an4
eork*d down tight, if it be let dowi^ to ^ coniiderable Deptl^
of Water, will be found, upon drawing ft up agun, to have
had the Cork forced in by t^e Prefiure of ^e Water at tfa;^
Pepth.
1 1 . This Bell was fo fa^ improved by the Dodor, thnt he
CQuki det!(ch one qf his Divers to the Difbmce of 80 or ioq
Yards from it, by a Contrivance of a C^p or Head-piece,
fomewhat like an inverted ^a^id-Baiket, as at F, with a Giafs
in the fore Part, for him to fee his way thrp*. This Cap.
was of Lead, and made to fit quite clofe about his Shoulders ;
31^ th^ Top of i^ was ^*d a flexible Pipe communics^ting witl^
P 4 PS"
56
Pneumatics.
t
t
I off by the Glafs.
I SiNcrf^wc know that Heat augments the re*
I pelient Power in the Particles of a Fluid, and by
j that means increalcs its Elafticity, and thereby
cau&s it to expand itfclf into a large Space i and
t|ie Ben, and by which he had Air when he wanted, bf
; tttining the Scop Cock near his Head-piece. There was alfo
another Cock at the End in the Bell to prevent any Acci-
dent happening from the Perfon without.
* 12. 1 his Perfon was always well clothed with thick Flao«
nels, which were warm*d upon him before he left the Bell,
and would not fuffer the cold Water to penetrate to hurt him.
His Cap contained Air enough to ferve him a Minute or two s
then by raifiiig himfelf above the Bell, and turning the Cock
F, he could replenifh it with freih Air. Th'is Pipe he coil'd
^und hi& Arm, Which ferved him as d Clue to £ad his Way
to the Bell again. • • *'
I J. This jbiving'Bell received its latt Improvement from
Mr. Martin Triewa/d, F.R.*S. Captain of Mechanics zt^ Aft-
hfary ArchiuOure; Xxi his Snxjedijh Majeffy ; the Manner and
W- XXX. Formwhereof is fliewn ilia FigufiB of his bwn drawing. A,B,
i^ig. ;: i the Bell, whidi, as appears by the Sca?e of Feet under it;
.1 .. y \% much' le(s than Dt. Halley^s^ ifnd therefore will come
cheaper. It is funk with leaden Weights D, D, appended
at the Bottom; the Subitance of the Bell b Copper, and
tinn'd within all over ; and as in the Rivers and Coaib of the
Baliic Sea, the Water is very clear, fo he has illuminated '
the* Bell with three ilrong convex Lenfcs G, G, G, ' with'
^ Copper- LMs H, H, H, to defend theto. ^
i^. The Iron Bing, or Plate E, ferves the Diver to fiand
upon when he is at Work; and it i& fufpended at fucha Di-
fiance from the Bottom oif the Bdl, that when the Diver
n^nds upright'; his Head is juft abov^ the Water in the Bell,
and it is much better there than higher up in the Bcfl, be*
caufe the Ajr is colder^ and confequently more frelh and fit
for Refpiration n4»ar the Surface of the Water, than towaids
the Tbp of thfc Bclb • . • ^ «
15. Bae when^there is Occafion for the Diver to be wholly
in the Bdl, and his^'Head bf Courfe in the upper Part, Mr:
TVtV'wii/dfhas fcontriVed, that'even there, when he has breathed
the hdt -AiV as long as he well can, by means of a fpirai
Gbpppj T^be hi 0 placed clofe to th^ Infida of tjie BeiijJri
Pneumatic?. 57
' that Cbldh2S a quite contrary EfFcd; we learn
?j the Ufe of the Thermpmeter in indicatfl% fhc
i: various Degrees of Heat and Cold in ibe Air^ by
T tlje different Altitudes of the Spirit of Wine in
a that Inftrumcnt (XCI|I).
.„ may then draw the cooler and ftefher Air from the lower*
1^ mofl Parts ; to which End, a flexible Leather Tube, about
two Foot Ion?, is ^'d to the upper End of t|ie Tube at b^
^ to the other End of which u a tam*d Ivory Month-fMCce^
^ for the Diver to hold in his Mouth, to refpire the Air from
^ below by s and this he may do in an/ Pofture of ibuidjiig»
fitting, bowing his Body, &<.
(XCIII.) I. A Thermometer being defignM toi
the various DeMis oflhai aaii CM by tbe elaftio or enan-
five Power of Bodies of the Fbid ibrc, lb many Ways^ Me*
thods, and Forms of conftruding foch an ufeful Indiument
have been thought of, and invimted at feveial Timet for thia
Purpofe; at fiiit Ain then O//, then Spirits §f Wime^ and
laflly ^iekfilvtr have been every Way attempted and tor^
tur'd in this Experioicnit. i
2. The Spring of Air being fooner alFedled by Htat and
€j)!d than that of any other Flaid, was firft chou^t apon as
the befi Expedient to anfwer this End; and fo it itaUy would
be, were it tiot that the Weight or Prcfliue of the Atmo-
fphere affects it alfo at the fame time; and by afiing fomc*
times with, fomecimes againil it, renders the Efed by Heat
or* Cold very uncertain, and therefore the Inftrument (i(<de6.
For Example: The Air in the Bottle AF will, by its Bx* p| XXX*
panfidn, when the Air grows wanper, taifethe Water higher pj^ |^
In the Tube than the Point H, and if the Air be lighter at ^'
this time it will prefs lef^ on the Surfiice of the Water at H»
and fo will faffer it to rife ftill higher. Bat if the Air be
iieavier it ' will a6t againfl the Spring, and not peiBiit it to
raife the'Wkter fo high. The fame vAj be obGmred with
refped to its' Contra^ion by Cojd i wherefore foch an Inftm-
ment, for tonlmon or conltant Ufe, will not do at all, tho*
perhaps none is better calculated for fome eztempoiancoQS
Ufes, as mcafuring the" Degree of Coldneft in diSerent CeU
lars, or of ' Warmfh in divers Rooms upon the fiune Floor.
3. It vtzi upon this Account found aeceflaiy to have re*
Kf)yxx(p to i'&mt oU^cr fluid, which^ ftcurc4 ftom (h^ PVef*
M
c8 P N 5*U M ATI C S.
fure of the Air in a Tube iieiiii/stiadlx leal*d, mig^t expaad^
and coi]lra£l fplcly by the Heat and Qoldnefs of the Air a-
boat it. And becaufe mod Fluids are fubjedl to freeze 6r'
thicken in great Degrees of Cold, it was foon confiderM thftt-
Spirits of Wine, a Sttle tinged wi^ Cochineal, woold beft
anfwer the PurpoCe, and nccordingly Thermometers were gc-
fierally made therewith, ^nd bequne of common Ufe.
4. Tho' the Spirit of Wine Thermometers would do verjr
* well to ihew the comparative Heat of the Air, yet this was
£u: ihort of the Vhtnofo's Views, who wanted to explore th^
various and vafUy different Degrees of Heat in other Bodies,
^ bnUng Wa^Ty huiltng Otis^ mdttd iStt^^ and even Firf
ififelf, and Degrees of Cdd too, beyond what the Spiric
Thermometer can ihew. For Spirit in a modemte Degree
of Heat will burft the Tubei and in an intenfe Degree of
Cold will freeze, as the French Fhilofophers found, who went
to meafure a Dt^tt upon the Surface of the Earth under the
North Polar Circle.
5. It having been found by Experiment, that I4piee4
Oil required four tunes the Degree of* Heat to make it boi)
as Water did, it was qqickly fubftituted inftead of Spirits
for Philofophic Ufes. This Sir ]^(tat Niwt^tr always ufed^
and l(y it difcover'd the ccmparative Degree of Heat whicl^
makes Water bail,> which me^ts Wax, which m^es Spirit of
Wine boil, and melts Tin and Lead i beyond which^ we dq
liot fmd the Oil-Thf rmomecer has been applied ; for wbicl^
feafim (as alfo for its fullying the Tube) it has httn leis uied
^ late, and given w^y to
6. The Mercurial Th^rmpmet^r wjikh w^l fuilaiii
any Degree of H^t or Cold, as &r as any Inilrument of
this ELind can be expelled to ip. Mr. Farenbiit^ of Jmfiet^
dam, was the Contriver of thtt Thermom^er, and tho* fcr
vend Artificers made them as well a? he, ^et they ihll ga
\y his Name. I>r. BoerbflOFog ofed only this Thermometer.
As the Mercury yery^ freely and un^ormly expands itfelf
from hani Froft fO th^ Heat of S\^^mer, fq one Sort of thoff
Thermometers are contrived with a S^e, to ipidade thof<;
Extremes only, ^nd the Beginning of the Divifions,^ or o,
is ix'd to that Altitude of the Qui^^iilver, as is obferv^d w^en
Water joft begins to freeze, or Snow to thaw; for whicjti
reafon that is calVd the Fritzhg Point in the Scale. Th^
Thermometer is fmall, il^ort, ptt^ in a neat Frame, and. carried,
in the Pocket any where.
7. Bat the Grand ThermwHeter of Farbnheit is graduated
afier a diferent Mlinner, as deftin'd to a more critical and
extcnfive Ufe. |n this the Bulb, oJ: la^e fart a\ the Bot-
- ' toip^
Pneumatic 8» 59
DOBiy is tak^^herical (at in rnwwilB ooct) Wt fyMneJ^ to
the Eiid» that the Heat ney penetote tad reach thtimnoft
Pftfts as fix>ii as poffibk, i^ that the whole aiajr expand mi* ^
fbrmly loeedicr. Hence it i% that in the cyloKbic Balb» the
Fictid wiacxpaad and rife inniMdiately, wheites m the t^*
rkal Bdb, k is ften firft to M (by the (nddca Expanfion of
Ae Ball, befefc the Vhid is )icate4) aad then to rife» by
the Expanfion of the Fhiid when heated. I have here pvcn
a Figore, both of Fmrtmhek^t Mntmud Vhermmmter^ and
alio qH Sir Ifmac NiwHm'i made with Linfeed Oil.
8. I take diis k/ Sir Jfaa€** to be the beft fitted of any
foi a Shuukrd Wmher TJkermmetir; and even for any De*
gree of Heat which the various States of the haaun Body
exhibit; and aUb for thofe di^erent Dmees whic|i Vegeta*
tion requires in the Green-Hoafe, Hot-Bed, 'bTr. In all
^hich Cafes 'tis neoeflaiy there fliooU be one common* an-
erring, and univerial Meafore, or Standard, which at all tones,
and in every Place, will fliew the fiune Dmee of Hea^ by
the ftme Expanfion of the Fluid, according to which the
Scale fiiottld be made in every Standard Thennoeneter.
9. In or^ to this, the Tube propofed fiiOQhl be very
nicely weighed wh^n empty, and 4lien the Bolb, and aboof
a tenth Part of the Length of the Tube above it, is tO/be
^U*d with Quickfilveri then it is to be weighed agah^ and
the Excefs of 'this, above th^ former Weight, will give the
Weight of the Quickfilver ponr'd ins this will give the
Weight of loodth PM. Let a Mark be made with a File
u^Qn the Tul^ at the Surface of the inctofed Qoicfcfihrcr.
10. Then w^igh out 9 or lo Ppuxels of Qiiickfiiver,eod|
equal to loodth nut of ^ firft put in theTube.aadhambig
poorM the feveral Parcels m one after another upon the in«
clofed Quickfilver, and marked the^Tube fifccrffively at the
Surfafre of eac|i Parcel, you'll have the Tube divided mt0
proper Intervals, which, if the Bore of the Tube be every
where the fame, will be equal to each others if not, they
will be unequal^ and each of thefe Intervals is to be divklea
into 10 otherB, mcreafing or dccreafinr as the Intervals do.
11. When this is done, the Capaaty of the Tube is di*
vided into7Aa^/tfiidSr^?4rr'of thatof theBaU, andthec^^
tjguous Part of the Tulie reachh^g up to the firft Matfc. The
Tube is now to be pat Into a Frame, and by the Side of
it is to be phcpd a Scale, divided into Tbamjkndtb Pmrts^
txaiE&j conttpoDding to thofe on the Tubei and writing
1000 pver-againft the firft Mark» ypu write loio over-
againfl the fecond, loao a^gjunfi the third, aod fo on» as yoa
fee in d}0 Figure
|S. Th|.
^O Pm E JJ M A T I G S.
|2/TJicStiuidardThcirmo»et«r-Tubc, anditsSfolp, be^
ing thqa conilruded, b then to be fill'd with Tome pn>per
JFluid, as Umi/etiiOi/, where great Degrees of He^t are not
propofed ; and Mercury is to be ufed, when they are. Whei^
the FIi}j4 13 pour*d in, it is to be tfdjufted. in fitch $ Quantity,
that it may (land juft at tlie principal Point, mark'd ipoo,
ip footer juft freezing. And liere great Pre^u(ion is ^o be
lifed; for many Trials mail determine this Point to which
%1^ Fluid muil always rife by flow Degrees, apd with 2J\ uni-
form Motion.
1 3. When this Ppint i9 well fecured, all the Trouble is
over the Ball, being then immerfed in beiUng Water, Sfmits^
Or//, milted Metals, Sx.. in. S»9W, Freezing Mixtures, Sec. the
Expanfions, by all the various Degrees of Heat and Cold,
^ill be fhewn by the Numbers againft the Heights to which
the Fiuid rifes in the Tube in each Cafe, thefe are to be
^rote on the Side of the Scale ; and fince the £ime Deg^ie^
of Heat will caufe the fame Expanfion of the fame Fluid at
all Timet, 'tis evident, if Thermometers were every where
conftru^ked in this Manner, the Obfervations made by then%
in any Part of the Worl4, n^y be compared together, which
cannot otherwife be dQne. i whence (his Par( of Fhilofophy
would xfic^v^ its final Perf^6lion.
14. ByiQDe of thofe Standard Thermometers well made^
many more might foon be cqnto^ed w^th any expanding
fluid, without the Trouble of graduating their Tubes by
equal Quantities of Quickfilver. For having fiil'd the Balls,
and a convenient Part of the Tube, with the propofed Fluids
place them all together ii) a VeiTel of cold Water ; and while
, it is warming as gently as po^Jble, when the Oil in the Stao*
dard Thermometer fhall arrive fuccefiively at the feveral D^-*
yiiions of its Scale, at the fame Indant of Time nurk the
|iew Tubes at the feveral Hoghts of their Fluids, and forn^
a Scale for every Tube, that fhall correfpond to thofe M^ks.
Then, while the Liquors fubfide by cooling gently, examine
whether they nicely agree at the feveral Marks. To deter-
xmne the Freezing Point in all, they are to ftand togetheir la
the Water till it ju^ begins to freeze : Or, having all the other
Points duly, thai; may be 4educed very exa&ly by the Role
of Proportion*
1 5. A Thcrmon;ietcr that (hall va^y very fenfibly by ^ycry
fmaU Variation of Heat and Cold, as thofe of the ^tmo-
^here^ muil have a large Ball iq Proportion to the Qore of
the Tube ; and that the Heat or Co)d may fooner penetiate
the innermqft P^^rts of the Liqpoi:, the Ball ihould not be
fpherical, but oblong and flatted like a Fren(ihFIfJk ^.and di^
- • s * ' 'Lengtha
Pneumatics* 6i
Lenfftlo of the Tabei ihoiild be propoitioii'd to the Degrees
of Heat they are intended to dtfcover.
1 6. Sir Ijaii Ve^ta^ graduated fais Sttod^ ThernKMBetfer
6n botl\ Sides, as (hewn in the Figare. ThoTe on the R^ht
Hand meafuivd the Heat of the Dili as thoTe on the Left
xneafurM the Bulk thereof: But finte t£e latter, as well as the
former, begins from a Cypher at the Fieeaiiig Pointy and it
regalariy continued upwards by the common Divifiona lo, ao,
46, 40, t^c. it will equally ferve both Forpofes; fince die
^gree of Heat will always be proportioned td the Expan-
iion of the Bulk of the Fluid above or below the Freezing
Point.
. 1 7. By this Divifion therefore on the Left Hand, I (hall
exprefs'ibme of the principal Articles of Sir Jfaac NrwtuTs
^ale of the various Degsees of Heat, as in the Tablet below.
D.ofHiii.
o 'Water juft free^g, and Snow joft diawing.
^ ' ^ The Heats of the Air in Winter.
£^ . I \Tht Heats of the Air in Spring and Aotonm.
> The Heau of the Air in Summer.
8
to 1*2
i$ The greateft Summer-Heat«
26 The gieateft Heat of the eiitemal Ftes of the Hu-
man Body.
3 1 ' Water juft tolerable to the Hand at Reft.
^6i Water hardly tolerable to the Hand in Motion.
43 Melted Wax juft growing Riff and opabe.
5 1 i Melted Wax ju^ before it bubbles or boils.
54 Spirit of Wine juft begins to boil.
.72. Water begins to boil.
75 Water boils vehemently.
86 A Mixture of ^^ of ^^^9 r 0^ '^'^f «^ i ^-
muth, melts.
103 A Mixture of equal Parts of Tin and Bifinuth melts.
122 A Mixture of f of Tin and | of Lead melts.
^54 i The ^eat which melts Tin.
174 , The Heat which meks fiifmuth,
. 206 The I'eaii Heat which melts Lead.
1^96 The Heat with which bunuDg Bodies ftune in a
dark Night.
410 The Heat of a finaU Coal-Fire.
450 The Heat of a imall Wood Fire,
I The
6i PniuMAtics.
TtiE Moifture and Drynifs of the Aif are Ihewri
by the Hygrometer, which is mode leverat
ways, but that with a Cord is iriott Common and
ufeful ; for that by Ihrinking with NIoifture will
turn an Index one way, and extending with Dry-
rtefi will turn it the contrary way, over the gra-
duated Limb of a Qrcle (XCIV) (XCV).
1 8. Dr. Hales confiders the Freezme Point as one Bonndiii
jy to Vegetadon, nnt, on the Side of Cdld ; and die other
Boundary he fixes td that Degree of Heat viVtL which Wtok
will begm to ifielt, becaufe a greater Degree of Heat wffl,
infteady of colleding and affimilating the natritive Firticlcitf
diffipate them, even thofe which are moft vifcid and glutinoos;
and therefore die Plant will rather fade than vegetate in fuch
Degrees of Heat. .
19. This Space the Dodot divided into lop equal Rms in
his TfaexmonieQKst Bot hb Nomben* eatpiHB^d hi th6fe of
the Standard Thermometer, are for feveial Particukrs men-
tion'd by the Dodlor asfoilows. Fo# fifyiU, \i t Ormigis^ 6|;
Ficoidts, 7I; Indian -E-^,^ 8i ; jiloe, 10; CereuSy 11 ; Eufbor-
btutn^ 12 j FiamentOy 15; AhanaSy 14I5 Mekn-ThiJUe^ 'Si *
AirundtrtheQhfstf aH0i'Bedy 17; thtJioi-Bed it/elf, 28.
If the Hot-Bed exceed the Heat of 40 or thereabouts^ it will
fcorch the P!«its and kill them. The Heat of Milk from the
Cowis'r8« that of Urine 29, and of Blood m a Fever ncariy 40.
20. As Fannbeit^s Thermometer is come into fuch gcnc-
tal VCe, i have here placed it by the Standard Thermometer^
that the Divifions on each may foe rednced to the other's re-
fpedtively by bare Inipeaion, and the Ufe of both be ftiil pr^-
ferved.. If the Reader woald fee 'all the diCertnt Sorts of
iThennOHieters, or rather all the different Methods df gra-
duating them, he may be fully iatisfied by tonfidting Dr. GHrgii
Martine^t Treatife on this Subjed.
(XCIV) I. An HtCROMtTSR, fometimcs ciird aNof-
tioMETEKy is any Inftrument oi^ -ContntanCe, by whidi wif
can eftimate the Quantity of Moifhire or Vapours in the Airi '
or by which we ean compiirv the vihrious' Degrees of its Hu«
midity and Siccity at difterent Times. For this Purpofe dif-
ferent Subjects have been at times ^ffiiy'd; but npne as yet
have been found fatisfii6lory or iafHng.
2. Thus Cotton^ SpuDge, i^c. hmig at the End of a nic^
I %Hkhli
nxxiit
P rt E U M A T I C S. 63
t SHALL finifli this LeAure with giving you
An AccountvOf the Strudurc and Ufe ot the com-
tnon Air-Pomp, and of one of a new bfventim
of my own. The common or large Air*Fump
Is rcprelented where aa^ ^a^ are the two Brafs pjj^-^
fearrels, ih whicfi the Piftons rr, €c^ move by
Chains faltenM to each of them, and to a Wheel
moving on the Aide /^ when the Engine is put
into Morion by the Winch l^k. ggy gg^ are two
Balance^ In ap exajl EqwiSart, will by costtadling Moifture
from the Air become heavier, which will therefore be (hewn
by its defcending ; and when the Air becomes dH6f . it ought
to part with the Moidure and become lighter ; but this it will
not readily do^ and is therefore of little Ufe. Salts iiave
been Jikewife ufed this Way, but to no purpofe.
3. It would be endlefs to take notice of all the Methods
that have been attemptei by Philofophers, and all without
Sttcceis. However, as fome are better than others, and wilt
endure for a confiderable Time very well, I fliall here give an
Account of one which is the beil of any I have hitherto
thpught of. It is made of a String either of Hemp or CatV
Gut, (as all th.e beft Sort are) and fiiews the increafing
Moijiun of the Air by its Tixfijiing and Sbortining, and the
Dryneff by Unthvifting and Lenphemng,
4. Thus, Let ABC be the lower Part of a twifted Line ^^ XXX.
or Cord, hanging from the Height of the Room againfl one y\o 5
Sid« thereof on the Wall or Wainfcot 1 let there be defcribed
a large Circle, graduated into an 100 equal Parts, fuch as
KLMN ; in the Center of which is a Pin, with a /mall Pul-
ley I B, carrying an Index OP. If now a Cord be pft round
(he Pulley, and a fmall Weight or Ball D be fufpended at the
. lower End to keep it Urait, then as the Cord gathers MoKlure
from the Air, it will twift and become (hotter; the Confe-
quence of which will bQ, that in contracting it will turn the
Pulley I B, and this by its Index will point to the Nambers on
the graduated Circle, which will (hew the Degree of Moifture
or Drynefs by the Contraftion or Relaxation of the Cord.
5. Again: If the Ball D hang over the Center E of ano^
ther graduated Circle CFG^ placed horizontally, carrying
an Index £F upon its Divifions> it will (hew the fame Thing
Pillars
64
7» ♦- • » *
Pneumatics.
Pillars or Pieces of Wodd fupporting the Fr^tnc
of the Pump-Wheel, which is fcieW'^ upon them
by Nuts under the little Pieces , of Wood Cj. ee:
The Tube or Pipe mkrk'd bb is called the S^wan^
' Neck, made of Brafs : By this the Air pafles horn
under the Receiver oo^ throt>gfi a foi^U HoJe.it
in the Middle of the Brafs Plate Hi on ?he Top
of the Pumpj to a Braf^ Pitsce in the Box dJ^
'iji
Phxxxr,
by the twifling and untwidine of the Cord BC, as in the Cir*
cJc above -, (a that this may be lookM upon as a Double Ify^
gro^eifr^ and fo fimple in its StruAure, that any Pcrfoh may
make It I and that it will anfwer veiy well for a con^derable
Time, I am fully fatis^ed by Experience : And I believe i
better than this was never made.
(XCV) 1 , There remains vet one more Pneumatic Machine
to be defcribed, whidh has made a confiderable Noife in the
Philofophic World, but hias never been of any Ufe in Civil
Life; I mean, th^ fadibus Invention of the Air-Gun, of
which there are two Sorts; one the Common j^trGun^ the
other the Magazine j^ir^Giin : Of both which I fhall give the
foUowjng fhort Account.
2. The Comffon AiK'(jU}i Is made of Brafs, and has two
Barrels; the Infide Bao-el KA of a fmall Bore, from which
the BuJleEs are (hot ; and a larger Barrel ECDR on the Out-
fide of it. There is a Syringe Sl^ NP fix'd in the Stock of
the Gun, by which the Air is inje^ed into the Cavity between
the two Barrels through the Valv^ EP. The Ball K is p\ii
down into its Place in the fmall Barrel with the Ran>mcr, as
in another Gun. At SL is another Valve, which Being drawn
open by the Trigger O, permits the Air to come behind thd
Bullet, fo as to drive it out with great Force.
5, If this Valve be openM and (hut fuddenly, one Charge
of condcnfcd Air may make fever^I DiTcharges of Bullets;
but if the whole Air be di(charged on one fingle Bullet, it
will drii^e it out more forcibly. This Difcharge is efFc£led
by means of a Lock i/ placed here, as ufual in other Guns ;
for the Trigger being pulPd^ the Cock A will go down, and
drive a Lever 0, that will open the Valve, and let in the Aii
upon the Bullet K.
4. TteMi7g^i^ine Air-Gun is the Invention of an ingenious
/.^cfft, who^e Name* is I. G/3/. By his Coritrivah& fen BuK
P N p U M A t I C.S. 6^
^hich being perforated length-ways to the Middle
Point under each Barrel, docs there, through i ^
imall Holei by a Bladder- Valve, tranihiit the
Air from the Receiver into each Barrel to be
punipM out by piafling through the Hole in the
defcendlng Pifton. Thcfc Hdles in the Piftohs
and Bottorns of thiii Barrels are coverM with
ValveSj to prevent the Return of the Air intd
. the Receiver, ///is the Mercurial G^e> or
common Barometer, immerfed in a Bafbn of
1 Mercury f» m fix'd in the Bottom of the Frame>
' and at top communicates with the Receiver^
-Which therefore Ihews how much the Reccilrer is
exhaufted by the Rifing of the Mercury in the
: Tube, by a graduated Scale affixed thereto. The
[ lets ar^ fo iodeed in a Cavlt jr near the Place of Difcharge;
that they may be drawn into the (hooting Barrel, and fuccef-
lively fhot (6 M a^ to be nearly of the &at Ufe as fo man^
feveral Guns, in the Figure you have a Sedion of the Gan»
L as big in every Part as the Gun itfelf; and (6 inuch ot the
I Length as is necefTaiy to fbrm a coinpleat Idea of the
I Whole^
! 5. AEE is Part of the Stock; G is the End of the injcS-
) ing Syringe, with its Valve H opening into the Cavity be* .
tween the Barrels, as before. KK is the fmall (hooting Bar- P1.3tXXl.
I re!-, which receives the Bullets from the Magazine E D; which
Is of a Terpentine Form, and clofed on the End p when the
Ballets ^, X K^i F^ lodged m it. The circular Part slsiMi
i h the Key of a Cock^ having a cylindric Hole through it IK,
t which is equal to the Bote of the frnaU Batreli and makes a
s Part of it in the preftnt Situation,
6. When the Lock is taken off, the feveral Parts Qj R^
{ ^, S, W, £ffr. come into View, by which means the Difcharge
i is made by puihing u|> the Pin P^, which raifes tod opens a
'i Valve V, to let in the Air againft the Bullet I from thfe Ca-
vity F, F; F i which Valve is immediately fliut down again by
i ineans of a long Spring NN of Brafs. This Valve V being
i> i conical Piece of Brafs, ground very true in the Part whkh
i Vot. II.' E Stop-cock
)66 !PNfiUMATlCg.
Stop-cock »», alfo, communicates with the fee"-
ceiver, and confcquently with the Swan-Neck
and Mercurial Tube : Its Ufe is, by turning the
Cock, to re-admit the Air, when there is Occa-
fion. The Receiver is groimd trte on the Bot-
tom, and is fix'd on the Pump a£ firft bjr means'
of wetted Leathers, to exchide the Air, inftead
oir Cement formerly ufed for that purpofe.
But with how much more Conveniency, and
Jefs Expeitce, Pneumatic^l Experiments of all
^ Kinds may be performed, by a New^ Elegant^
and Portable Air-Pufnp^ which I, have lately con-
trived and made, will be eafy to apprehend from
i bare View of the Figure thereof: In which A B
is the Head or Part containing the Wheel^
receives it, will of itfelf be fufljjcient^to confine the Air.
7* To make a Difcharge /oii' puff the Trigger zi^ Mich
throws up the Sttxyx, and difen^ges it from the Notch x^
upon which the flrong Spring WW moves the Turiiblcr T,
to which the Cock is fix'd. This b^ its End u bears down the
End v of the tumbling Lever R, which by its othei' End m
raifes ^t the fame time the flat End / of the horizontal Le-
ver Qj and by this means, of courfe, the Pin P/ is pulh*d
up, which ftands upon it, and thus opens the Valve V, and
difcharges the Bullet. This is all evident from a bare View
Of the Cut.
S". To bring in another Bullet to fucceed I inflantaneoufly,
• flicre is a Part call'd the Hammer H, which by a fquare Hole
goes on upon the fquare End of the Key of the Cock, and
turns it about fo as to place the cylindric Bore of the Key IK
m any Situation requh'ed. Thus when the Bullet is in the
iMate Gun, the Hanmier ftands as in the Figure, where the Bore of the
XXXI. Ifey coincides with that of this Barrel KK; but when the
Ball is drfcharged, the Hammer H is inllantly brought ^down
to fliut the Pan of the Gun, by which Motion the Bore of the
Key is tum'd into the Situation ik^ fo as^ to coincide now with
the Orifice of the Magazine ; and upon lifting the Gun up-
right, the Ball next the Key tumbles into ics Cavity, and falb
behind twoimall Ends f,s, of two tender Springs which like
which
Pneumatics: ^"j
which alternately raifes and deprefles the PiftoHs
C D in the Barrels E F, which are ftrongly
prefs'd down by the faid Part AB, fupported
on the two Pillars G H, fix'd into the Bed or
Bottom of the Machine I K L. . On this Bottom
ftands the Receiver MN on a large fmooth Brals
Plate, in the Middle whereof \% a Hole, by
which the Air {iafles out of the Receiver into a
finall Tiibe on the under P^rt of the Frame,
and goes to the Piece O, which communicates
with the perforated Brafs I^ece on which the
Barrels ftand^ and from which they receive th4
Air to be exhaufted. On the middle Parf of thii
Brafs Piete is a Perforation, over which is placed
a fmall Receiver PQ^, and under it a Bafon of
Fingers Ends detain it. The Key in, this Pofition is feen in
the Fi|;are. Then opening. the Hammer again the Bnllet Plate ^ '
18 brought into its proper Place near the dikharging Valve, XXXI^
tad the Bore of the Kejr makes again a Pan of that of the
(hooting Barrel.
9. It evidently appears how expeditious a Method thu it
of charging and difcharging a Gun ; and were the Force of
cbndenied ;Air as srett.as that of Gunpowder, fuch an. Aires*
Gun would ^dualfy imfwer the End of many Guns, ai^d prove
the beft Defence againft Highwaymen or Robbers that Peor
pie are aware of ^ becaufe when they have Reafon ao fufpeA
them/ the^ might then make five or fix Difcharges before the
Thief can come within Piibl-ihoti ....
10. in the Air-Gun, and in all other Cafes where the Air
18 required 40 be condenfed to a ytpf great Degree, it will he
requiftte to have the Syringe of a ^udl Bore, nnx. not ex*
ceeding \ an Inch in Diameter ; becaufe^ ,as haul ^een ihewn»
the Prefiure againft every y^ttore Inch is about 1 5 W. and agaioft
every circular Inch it is therefore about xzlb. li therefore
the Syringe be one Inch in Diameter, when one Atmofphere
is injeded, there will be a Refifiamce of 1 2 lb. againft the.
Pifton; when 2, of 24/^.; and when 10 are injedbed, ther^
will be a Force of xzolh. to overcome ; whereas io.Atmo-«
/j^beres aa againft the circular Half- Inch Pifton (whofe Ar^
E 2 Mercury
68^ Pneumatics.
Mercury R, in which a fmall Tube RS (her-
metically fcaled at one End, and fill'd with
* Qiuckfilver) is inverted; and therefore as the
foi^U Receiver PQ^is exhaufted, (at the fame
time with the large one MN) the Approach of
the Vacuum will be Ihewn by the Befcent of the
^iekftlver in the Tube RS. By the Stop-cock
T the Air is again let into the Receiver. I take
this to be the lafi ImprG^emeni this Machine is
Capable of, as to its Fornnr; for it confifts of only
fuch Parts as are Eflential. And thus conftruft-
. cd, it may, together with its Receivers, be con-
tained in a Box of a fmall Size, and comes to but
a fmall Price in comparifon of the other Forms.
(XCVL)
is but ~ Part fo big) with a Force but a -j Part fo great, s^
30 16. i or 40 Atmofpheres may berii^e^^ed with fuch a Syringe^
as welt as 10 with the other. In aV^ord, the Fa<^ty of
working will be (cateris paribus) inverfely as the Squares of
the Diameters of the Syringe,
(XCVI) I . I fhall conclude this Subjcd with a few Articles
•relating to the Rarefa£lipn of the Air in the Recipient in
working the Machine ; for the Reader muft not fuppofe that
all the Air can be exhaufted, if the Pump be ever fo good> 01?
work'd ever fe long. The Reafon is evident when we con*
fider, that the Air which is exhaufled is only pufh'd out by
the Spring of that which remains behind : If therefore every
Particle were fuppofed to be exhaufted, the laft would be ex-
peird without an Agent, or there would be an Effed without
•a Caufe, which is abfurd.
2. Let the Capacity of any Receiver be to that of the
Barrel as C to i. Alfolet the Rarefadicm of the Air which
remains in the Receiver be to the common Air as R to i, af*
terany Number of Turns or Exfu6Uons N. Then, upon
raifmg the Pifton, the Air will rufh into the Barrel, and fo
will now be rarified in the Ratio of C to C -4- i, or of i to
C+i
" ^ ' i and fince this is the Ratio of the Rarefadlion by every
' ' Exfuftion,
Pneumatics.
Exfoakm/ds evident it will be the common Ratio of a Geo.
metrical Series of Rairefadions produced by the feveral
Tumsof the Winch, wk. TTie Series i : SdLl : Si+jj*
Series, which th^r^ie as it exprefies the laft Rare&Aioo will
be equal to R, that is R
_C+^
5. Hence from the known Property of Logarithms we hare
69
whence.
L. R
-= N. Wherefore if C = i.
L. C+i— L.C
that is, if the C^p^ty of the Receiver be equal to that of the
L R
Barrel, we fhall have N = -^ — . . Confequemly, if R ex-
L. 2
preis any Degree of Rarity propofed, as i , !:, 3, 4, 5, 6, &c.
we have N the Number of Turns or £xfu£lion$ to eSe^ it.
4. And from hence the following Table is conftrufled ;* in
which the fird Column expreflfes the Rarity of the Air in the Re-
ceiver, ajad the fecond the Number of Turns to produce it.
Rarity.
Numier tj
Rarity.
Nmnhir rf
Turns.
Rarity.
Ntmbtrtf
Tun:!.
I
•
0.
60
5.907
90Q
9.a«4
2
1.
64
6.
1000
9.966
3
1.585
70
6.129
1024
10.
' 4
2.
80
6,322
2000
10,966
S
2,322
90
6,4^2
2048
II.
6
M85
100,
6,644
3000
".55>
7
2,807
128
7-
4000
1 1,966
8
}•
200
7.644
4096
12.
9
3,170
256
8,
5000
12.288
10
3.3"
300
8,229
6000
»2.5S«
16
4-
400
8.644
7000
".773
20
4.32*
500
8.966
8000
12,966
30
4.907
512
9-
8192
'3-
32
5-
600
9.229
9000
13,136
40
5.32«
700
9.*5«
1 0000
13,288
50
S.644
800
9.644
16384
14.
P3
S' fwn
7Q Pneumatics.
5. From this Table we may obferve, that if any Numiien'
|n tlie hrUt Colamn be taken in Geometrical Progreilion, tLe
correfpdnding Nambers of the fecond will be in Arithlnetical
Progreffion. Thus againft i» 4, 9; 16 intheficft, you fee
i; 2, 3, 4 in the fecond Column.
6. When the Capacity of the Recehrer exceeds that of the
Barrel, tneh the Number of Turns N to produce a giyen \Rarc-
fiidUon R will be greater than before. Therefore if the Num-
ber of Turns in this particular Cafe, which let us call n, be
jnultiplied by fome Number m, it will produce a Number o£
Turns N that ihall afFed the Rarefaction R in any Receiver
*» 'i • » t, , \i. L R ^ " *' ' .
propofed. Now fince « = y— r , we Ihall have n x m z:^
L.R
L. 2^
:N=-
L. 2'
L.R
L. 2
L.C + i— L C
whence we have
m =
L.C+i— L.C
7 From hence a T^ible of Multipliers exprefJing the Value
of m,' when the I^eceiver h in' any given Proportion larger
tlian the Barrel, is eafy to be conftrufted. Of which the fol-
lowing is a Specimen. ^ * '' '"
Capacity
Capacity
Capacity
0/ Re:
Multiplier
of Re^
Multiplier.
of Re
Multiplier.
cet'ver.
cetver.
cet<ver.
I
I.
20
14,207
300
208,291
2
^7?o
30
21,139
400 •
277,605
3
2,499
40
28,071
500
346,920
4
3,106
^f
35.003
600
416,235
5
3.802
66
4«.934
700
485,549
6
4.497
70
48,866
800
554,864
7
KV
80
55.798
900
6h,I79
8
5.835
90
62,729
loodf
693^4^4
9
6,579
100.
69,661
'
10
7.273
200
138,976
' 8. By means of thefe two Tables, thofe who know no-
thing of Algebra may find how many Turns are neceflary to
rarify the Air '^ the Receiyer to any given Degree, when
thp Ra^io of x\^ {leceiv^r'.s Capacity to that of the Barrel is
known. • For fxample:- Let the Receiver be ip times as big
•as the Barrel,- and let it be requir^to fin^how many T^irnl
of the Winch w^ tarify the Air 100 times/ Firft feek th<i
' ' ' . « ' ... Number
Pn eum atics. 71
Number that will do it when the Receiver is equal to the Bar-
rel ; which I find by the firft Table is 6 Tarns, and 644 Parts
of 1 000 of another. Then, againft 10 in the fecond Table,
I 'find the Multiplier 7>273, by which if I moltiply 6,644^
I (hail have a ProduA 48,322, which will exprcis the Num-
ber of Turns requhred.
9. The Afcent of tb^ Qjiipkfilyer ip th^ Gage of the Com*
inon Pump is proportional to the Quantity of Air drawn otit,
eith^ upon the \yhole, or upon ^ any fiogle Tur^ of thp
Winch : And the lieficiency from the Standard Altitude of
29I Inches is always proportional to the Quantity of Air re-
ipaining in the Receiver; as may be eaiily deduced from
what has been (aid of the Denfity^ Springs and Preffitre of the
Air.
10. Tfa^ Gagp of a Coitdenfir will have the Spaces unpof-
fefs'd of Quickfiiver at the End decreaiing in Harmonical Pro-
portion: For fince equal Quantities of Air are injeded by the
Syringe at each St^ke of the Pifton, the Quantity of Ai^r in
the Condenfer will increaie in Arithmetical Proereffion, and
* fo will its Denfity, and of courfe the Deniity of that in the
End of the Gage, becajiii; the Quickfiiver is pre(s*d on each
Side equally ; but the Spaces diminifh as the Oenfides incrcsafe»
as we have elfewhere ihewni ^Therefore the Spaces are in-
n>erfely as a Series 0/ Terms in Ariskmetical Progreffion^ and con-
feqoently are in Mufical Proportion ; for that this is a Property
of Mufical Terms will be (hewn in Annot. CIX.
E 4 LECTURE
7^
' LECTURE VII.
V^he PoBrineofyfmm and Sounds^
P/ Wind in general. Tb^ Theory of Winds
'By Dr. Halley. Of the'^Confiant^ or General
Trade Wih^dsj ?/ /i&^ Monsoons ; tbeCaufa
^Variabx-e Winds. 0/ Aerial Tid^S;.
Of the VELOCITY ^/ Wind. Of the Momen-
tum or Force of Wind; -/f Calculation
thereof^ and its Application ta the Saics of
a Wind-Mill. The b^ Form and Position'
^f the Sails. A Calculation of the Forcr
^/ Bellows in impelling Wind, yi New In-
vention of Water-Bellows. The Nature of
Sound in general. The Sensation of Sound.
The Organ "of Hearing defcribed. Of the
Waves or Pulses of Air. Their Various
Propertied: eo^plain^d. The Newtonian
Doctrine of Vibrations and Tremors
it/" Sounding Bodies explained. The Waves
pf Water accounted for. Of the Velocity
ff Sounds. The Distance to which they
may be heard. Of Echo's. Of the Speaking
Trumpet of thebeji Form. Of Or acoustic
Instr^uments. Of the Hot z^ Tone, otr.
Tune ^/Sounds.* 0/ Concords and Dis-
cord^ i ' /isp RatJ^owale of tk? Diatonic
•Scale
Of Winds md Sounds. 7^
Scale <?/ Music, 7'i&^ Mathematical Theory
0f Musical Chords, and cf Harmohic
pROpaRTioHs. 0/ the Sympathetic Vibra-
tionIs of Musical Strjnos, (md other
Bodies.
IN this Lefture I fhall confider the Nature of
Wind and Sound in general ; and of the
Vibrations of Mufical Strings and Sonorous
Bodies^ with regard to the Science of
MUSIC.
WIND is a Stream or Current of Air: As the
Air is a Fluid, its natural State is that of Refi^
which it endeavours always to keeper retrieve by
?fn univerfal Equilibriunf oi all its Parts. When,
therefore, this natural Equilibrium of the Atmo-
fphere happens by any means to be deftroy'd in
any Part, there neceflarily follows a* Motion of
all the circumjapent Air towards that Part, to
reftore it ; and this Motion of the Air is what we
caUr^W. (XCVII.)
(XCVII) I. I Ihall here give the pfiocipd Phaenomeaa of
the Whidy as the^r are deduced from Dr. Haileft admirable
HHlory thereof in the Pbikftpbical l^rmfaBlsHs^ and iUufirate
the fame by his Map of th^ World 4fawii up for diat Pur*
ppfe.
2, TheFirftjs, TJiat in flic great /*««)& or ^F?5^«w Ortwr,
the Atlantic and Ethiofic Seas, there is a general EaAerlf Wind
allthe Vear long, \(nthout any oonfiderable Variation; ex-
cepting that it is fttbjedl to be defledled therefironi fomefew
t'oints of the Compafi towards the North or Sooth, aoooiding
to tlie^ituation of the Place. The Reafen is, becanfe the ^
i'arts under the Eqaator are nv)re heated and rarified than wuf
pthers, ^s above mentioned.
, 3. Th? Sefoud is, Th?t on wjl} 8jd|c '^ Equatpr, t<»
JIencE|
74-' (y Winds and Sounds.
Hence^ wirib refped to that PUce jyhere the
Equilibrium of the Air 15 difturh'd, ve fee the
Wind may blow from eyery Point of the Com-
pa& at the fame time ; and thofe whqjive Norjb-
wards of that Point have a North ff^indy tljpfe
who live Southwards J a South Wind \ and fo of
the reft: But thofe who live on the Spot, where
all thefe Wind? n^eet and ipterfere^ are ppprefs'd
about 27 or 30 Degrees, the Wind doe^ more and more-d«-
dlne fjoiri'the^Eaft to tKc North-Eaft oh one Side, andSoutK-
Ead on the other; occafion'd by the, two contrary Motion^
of the Air, arifing from Heat and Cold, as above explained.
Thefc Wmdb are indicated by thePofition of the Arrows 4n
thie Jiflaiiitic anad PJicific Ocean in the Map.
4. Towards the Caribbee Iflands, on the American Side of
the Atlantic Ocean, the dforefeid North-Eaft Wind becomes
ilill more and more Eafteriy, fo as fometimes to be £aft»
fometimes £aft by South, but moftly Northward of the Eaft
a Point or two, feldom more.' It is like wife obferved that
the Strength of thefeWii^s does gradually 4ecreafe as yo«
fail to the Weftward. - ^
5. All along upon the Coaft of Africa on the W^flern Side,
the Wind fets in lupoti'the Land froAi various Pointd of the
Comjpafe, North- W^a, W^eft, South by Weft, Squt^-Wcft,
and almoft South, efpecially toward the Cafe of Good Hope ;
all which is eafily feen in the Map. '
6. In the Atlantic Ocean, towards the North of the Line,
between 4 and "lo Degrees of Latitude, and 20 and 30 of
Weft Longitude, there is a Trad of Sea where the Wind^
are not properly fdid to be conftant or ^uariable ; for it feems
to be coii4emn!d to perpetual Calpn* attended with terrible
Thunder and Lightning, and Rains, fo Ifrequent that our Na-
vigators^from hence call this Pnrtof th^ S^ t)i^ Rains, as
by others they are'caU'd the Calms and Tornadoes, as
. in moft of our conimon Maps. The Reafon of Uiis feems to
be, that this being the Place where t^e ^'afterly and Wefterly
Winds commence, the Air is divided find held as it were in
Equilibrio bet^eei) both ; by which means it is renderVl more
fUre than the reft, and too Light -to fuftam the Vapours raifed
into it, fo that it lets them defcen4 in continual Rajns. Sgs
^^PartingoOhe Air jytthej^ap. ' ' , /^
with
Of Winds and Soundb. 75
with turbulent and boifteroua Weather, Whirl-
winds and Hurricanes; with Rain^ Tempeft^
X.igbtning^ Thunder^ &c. For fulpbureous £x-
balations from the Souths Torrents df Nitre from
the Norths and aqueous Vapours from every Part;
are there confufedly hqddled and violently blend-
ed together ; and rarely fail to produce the Pb^g^
nqmena aboveniention'd.
7. |n the In^an Ocean the Winds are ptitly Qmfral^ as ii|
the Atlantu and Etbiopic Oceans ; and partly PerUidica/, diat
ii, fach as blow one Half of the Year one Way, and the
other Half ^f the Year near upon the oppofite Points : And
' thefe Points and Times of (hifting are different in different
Parts of this Ocean. Thefe Winds ase. call*d by Seamei^
Mxmffms or Monfo9ns.
9; Between i6 and 30 Dmees^ from Madagajcar to M«iu
Etliand^ the general Thide- Winds about South-Eaft by Eaft
are ftfuiid to bloi;^ all the Year long in the (ame Manner, and
lor t&le fame Reafoils as in the other Oceans above- mention*di
9. During the Months Of May^ June, July, Auguft, Sfp^
tmberj OSlober, the aforefaid Soath-Eaff Winds extend to
Within two Uegrees of the Equator; after this, for the other
fix Months, the contrary Winds fet in, and blow from thfe
North-Weft fmmthe Latitude of "3 to ip Degrees South.
10. From about! three 'Degrees' South Latitude, orer all
the" ArahiaH and ItuBan Seas^'and Gulf of Bengal, from ^«-
ikatra' to the Coaft of Africa, there is anothex'Monfbon, blow-
ing from Oaoher to April on the North-Eafl Points ; but in
the other Half- Year, from April to O Sober, from the oppofite
Points of South-Weft and Weft-South- Weft, and that with ra-
ther more Force than the other, accompanied with dark rainy
Weather; whereas the Noith-Eaft blows 'dear. '
11. The Sea between Madefgafcar and Africa, and South-
wards to the Equator, is fubjedt to the fame Change of Wind,
Or Monibons, whofe Courfe from Afril to 05ober is South-
South- Weft; wl^ich, as you go more Northerly, becomes
more and more WefterJy, till at laft they faJl m with the Weft-
Soutli- Weft Winds mention'd iii the laft Articles. What Winds
blow the other Half- Year in thofe Parts, the Doctor couldf
not^obtain any fttisfaftory Account of; only that they were
Eafterly, nn^zi often to the* North as to tho Southward
^erfeof. ' '^^ • • * Many
76 Of Winds and Sounds.
Many are the particular Caufes which produce
Wind by interrupting the Equipoife of the At-
mofphere ; but the moft general Caufes are twa^
viz. Heat, which, by ratifying the Air, makes
it lighter ;n fome Places than it is in others ; and
Cold, which, by cgndenjing it, niakes it heavier.
Hence it is, that in all Parts over the Torrid Zone^
the Air being more rarified by a greater Quanti-
ty of the Solar Rays, is much lighter than in the
Other Parts of the Atmofphere, and moft of all
over the Equatorial Parts .of the Earth. And
12. 1^0 the Eallward of Sumatra and Malacca, on th^
Korth Side of the Equator along the Coaft of Capihoia and
CbiiM, the Monfoons blow* and irhange at the fame Times
as before ; only their Dire^ions are much moi'e Nbrtherlf
and Southerly than t|ie others, as is eafy to ol>ferve in the
Map, Thcfc Winds reach to the Philipfine Iflands Eaflward,
and to Japan Northwards ; and are not fo cofiflant to their
Points as the others above-mentioned.
\ 13. Between the fame Meridians, on the Sooth Side the
Equator, from Sumatra to Nnv Gmnea Eadward, the £une
Northerly and Southerly Monfoons are obferv'd; only the
Northerly are here North- weflerly, and the Southerly blo\y
fromi the South-Eall. They are not mo|-e conflant than the
others; and beiides, they keep not the fame Times, bu( ^
fhange a Month or fuc Weeks later*
14. The Shifting of thefe contrary Winds, or Monfoons,
}s |lot all at once ; and in fome Places the Time of the Change
is attended with Cairns, in others with variable Winds^ an4
particularly thpfe of China, at ceafmg to be Weflerly, are
very fobjedt to be tempeftuous ; aod fuch is their Violence, :
that they ftem to {>e of the Nature of the Wefi-lndia Hur-^
I'icanes, and render the Navigation of thofe farts very uniafe
at xhat Time of the Year. Thefe Tempefts the Seamen cal^
the Breaking up of the MiJifions,
15. The Cagfe of the Monjbons^ or Periodical Winds, 14
owing to the Courfe of the Sun Northward of the Equator.
one Half of the Year, and Southward the other. While h^
paffes through the fix Noifttern 5i^8 of the Eclif ^c, the v^-
fine?
iucc •
At.
Of Winds a/ui Sounds. 77
(ince the Parts at the Equator are moft fanned
which are near the Sun : and thofe Parts are, by
two '
' [ the Earth's diurnal Rotation Eaftward^ continual-
^^ I ' \y fliifting to the JVeft \ it follows, that the Parts
^"^' of the Air which lie on the Weft S^idc of the
f^^' t Point cfgreateft RarefaStion^ and, by flowing to-
wards it, meet it, have lefs Morion than thofe
Parts on the Eaft of the (aid Point, which follow
it ; and therefore the Morioa of the Eaftem Air
would prevail againfl: that of the Weftem Air^
and fo generate a continual Eaft Windy if this were
mti-
the
Fall
ISO
tlie rions Coundies of AraUa^ Perfia^ Indioy and China are hcAt-
^ ed, and r^iedt great Qoanticies of the Solar Rays into the
jBO ^ Regions of the ambient Atmofphere, by which means it be-
erlf comes greatly rarified, and has its Equilibrium ki^ colirfe de-
tiie fh-oy'd; to reflore which^ the Air, as well from the Equatorial
^ Parts Southwards, Where it is colder, as from the colder
^ Northern Climbs, muft neceilarily have Tendency or Modon
towards thofe Parts, and fo produces the Monfoons for the
^ firft foe Months, during which Time the Heat of thofe Conn-
ie tries is created:.
{JK 16. Then for the other fix Months, the Sun traverfing the
^ Ocean and Countries towards the Southern Tropic, while in
^ the fix Southern Signs, caufes the Air over thofe Parts to be
1^ now moil heated and rarified ; and confequently the Equato-
rial Air to alter its Courfe, or the Winds to veer quite aboot^
^ and blow upon the oppofite Points of the Compafs.
^ 17. Thefe are the general Affections of conftant and regn-
^ lar Winds ; none of which are found not fubjeCl to fome Va*
^ nation and Exception, on account of the different Circum-
ilances of Heat, Cold, Land, Water, Situation, i^c. concern-
^^ ing all which I (hall refer the Reader to ahe Dodtor^s own
j^ large hiflorical Recount of the Winds, publiihM in the ^ranf'
ji uSioMy or MifceiJanea Curio/a, Vol. I.
18. From what has been faid, 'tis eafy to underfland, that
j^ £nce fo large a Portion of the Atmofphere as is over the
J Torrid Zone, and Parts about it, is in fuch continual Agita^
V tioa and alternate Motion, thofe Agitations in an elaftic Fluid
muft extend every way to a great Dillance, and produce Ef-
fedts of the fame Kind in a various Manner; by which means
all
cc,
:f
Of Winds and 8dUNps.
all thc'EfFedt of thai Ranfaliion. But we ^re ta
confider, that as all the Parts of the Atmofphere
are fo' greatly rarified over the Equator, and all
about the Poles greatly condenfed by extreme Cold^
this heavier Ait from either Pole is conftantiy
^he Air in all other Latitudes and Climes will fuffer a Pcrtur-
■fcation more or lefs, and have a perpetual Tendency to Mo^
tion in various Dircdions, depending on the Situation of
Country, the Degrees of Heat and Cold in the Climate, the
Pofition of Hills, Vales, &f r. befides what may be owing to
the Accenfion and Explofion of Meteors, the Eruption of
fubtcrrancan Air, and a hundred other Caufes : I (ay, from
all this it is eafy to infer, thai our Climate y ^wherever <we /i<ve,
muft mcejfarily be attended iJoith variable Winds, almofi perpe*
tualh* ^ ,1
19. I fliall only add farther; that fince the Atmofphere is i
gravitating }uid Suhfiance'i it muft b^ fubjed to the atttaahig
Power of the Sun and Moon, as well as of the Earth; ana
therefore when the Influence of thofe Luminaries, either fmgly
or conjointly, is oppofite to that of the Earth, the fame Ef-
fefts muft follow in the Body of fluid Air, as we have fhewn
were produced in the ambient Fluid of Water, inx^ that the
Atmofphere ftiall be of an oblong Figure, or of different aU
titudes in difff rent Parts ; and that thefe Tides of Air have
nearly all the fame AfFeaions with thofe of the Ocean before
explain'd, excepting only in this, that they muft be as mucli
greater as the Denfaty of Water exceeds that of Air, <viz, in
the Ratio of 860 to I. . , .^ ^
' 20. Nowbecaufe of an Equality of PtefTufe of Weight
in the Atmofphere in unequal Altitudes of Air, we can
iiever be fenfible of an Aerial Tide, cither of Ebb or Flood^
fcy the Barometer; and can only know it by the Pofition
of the Heavenly Bodies. However, as this prodigious
Protuberance of the Atmofphere is conftantly following the
Moon, it muft of courfe product a Motion in all Parts, and
to produce a Wind more or lefs to ^very Place/ which as it
confpires with, or is oppofedt6 the Winds arifing ffom other
Caufes, makes them greater or lefs. And 1 believe fome-
thing of this may be deduced from Obfervations made of the
State cf the Air at the Times of the Neno and Full Moons.
And that this was the Cafe in refpeft to the two laft great
Storms, 0r. Mead has obfervcd in his Traift De Imperio S9IU
is Vunieci
4
Of Winds and Sounds. 79
flowing towards the Ecpiator, to reftore the Ba-
lance deftroy'd by the RarefaHion and Levity of
the Air over thofc Regions: Hence, in this re-
ipeft alone, a conftant North and South IVind
would be generated (XCVIII),
.' : .... 4
(XCVIII) I . I find by Experience, that People fa^ve in ge-
neral biit an obfcare Idea or confufed Notion of the Caufe of
•this .peipeti^ . Current of Ave from Eaft to . Weft» or. of a
Qonilant Eaft Wmd under the Equator s therefore in order to
elucidate this Matter, I fhall reprefent it in, and ex|)]i(in it by,
a Figure. lit CBADE be Part of a SeAion of th€ Atmo- p]atc
fphcre oyer the Equator^ C the Eaft, E the Weft, A the Point XXXlII,
to which the Sun S is vertical, and K the Point of greateft i^'^„ ,^
Rarefa^ion, of that where the Air is moft of all heated, and
confequently lightefl. ...
2. That this Point R is on the Eaftem Sic{e of the Point A
is not difficult to be conceived, when what is faid concerning
the Tide in Annnt. LXXXIV. is well confider*d. And becaofe
the'Air at R is by Suppo£tion lighter than where it is colder at
C and D, it is plain that, in order to maintain an Equilibrium*
{which is neceOkry in a fluid Body) the Air by its greater
Weight will have a Tendency from C and D towards R, and
rife to a Height there greater than at C or D, in jproportioa
as its Deniity is lefs.
3. Now this being the Cafe, it is evident, the Sun being
always between the Points R and D, will be heating the Air
on that Part J and thofe Regions between R andC^ having
been deferted by the Sun, wiU grow cold : Confequently, the
Air between C and R, as it is colder, will likewife be hea-
vier than that between R and D which is hotter, and {o will
have a g^tST Momnttum* or Quantity of Motion,- towards
the Point R; and fince this Point R is conftantly moving after
the Point A Weftward, the Motion of the Weftern Air to-
wards it will be in part diminiih*d by that means; and being
^fo inferior in Quantity to the Motion of the Eaftem Air, the
latter will prevail over it, and be .conftantly following the
faid Point R from Eaft to Weft, and thus produce a continual
Eaft Wind. . .
4. It may perhaps be here faid, that though the Motion
of the Air be lefs from D to R, yet it is fomething, and fo
there ought lo.be a WeHem Wind, at leaft in fome Degree,
and to fome Diftance WcftwarJ of the Point R. To which
I anfwer. That the Nature of a Fluid will rot permit two
, Now
8o Of Wmbs and Sounds.
Now it is eafy to undcrftand, that by a Corti-
pofition of thefe two Direftions of the. Air from
the Eaft and Norih^ a conflant Nortb-Eaft Wind
Will be generated in the Northern Hemifphere,
and a confiatlt Soutb-Eaft Wind in the Southern
Hemifphere, to a certain Diftahce on each Side
the Equator^ all round the Earth. And this
Cafe we find to be verified in the General ^rad^
WindSj which conftantly blow from the North-
Eaft and Soutb-Enfti to about 30 Degrees on
each Side the Equator, where thofe Parts are
over the open Ocean, and not affeded with thel
Refledion of the Sun-Beams from the heated
Surface of the Land i for in this Cafe the Wind
will always fet in upon the Land j as on theCoaft
contrary Motions to re((ore or fufiain an Equilibriam, (t mean*,
in regard of the whole Body of it) for wherever one Part of
the Fluid is detentiined to move, all the refl mufl neceiTaril]^
follow it i otherwife th^e Equilibre of the Air woald be de-
ibroy*d in one Part, to make it good in another; a Defe£t
>vhich Nature cannot be guilty o^ Thus we fee the Tidea
of the Ocean always follow the Coorfe of the Moon from
Eaft CO Weft, without any Motion of the Waters ^om the
Weft towards the Moon, in the open Oceans : And the Point
R caUxOnly be coniider'd as the Aerial ^ide^ or Flood of High
Mr I and has nearly the fame Phaenomena with Aqueous
Tides.
5. This being clearly nnderftood, all the reft is ealy; M
no one can find it difficult to conceive how the cold Air from
each Pole muft necefiarily fet in towards the Equator diredUy/
where meeting, and interfering with the Eaftem Current, %
does with that compound a new Dire^ion for the moving Air^
which lies between both the former, «i;/«. a North- Eaft Cur-
rent on the North Side, and a South-Eaft one on the South
Side : All which naturally rcfults from the Dc^irine of tbe^
Cttmfojitkn of oblique Forcps. {See Annot. XXIV.)
of
/
of Wikns and Sounds^ 8i
oF Guinea^ and other Parts of the ^irrid Zone^
we know it does (XCIX).
:As the Motion of the Air has a greater or
leffer Velocity4 the Wind is fironger or weaker ; .
and it is found from Obfervation, that the Ve-
locity of the Wind is various, fit>m the rate of
t tb go of 66 Miles jp^ Hour (C).
^ (XCIX) Mr. C/are, io his M$tsaM ofFtuiJs, has i vtrj ^i
tioent Experiment for niuftradng this Matter. It is thus : Let
there be a very wide Di(h or VefTel of Water^ in the Middle
of which is to be pbced a Watei--Ilatd ^'d with warm Wa-
ter; the fir^ will r^prefent tHe .ddean, the other an Ifland
lirifying the Aii-aSove it Then holding a Candle over the
cold Water, blow it oat, and the Smoke will be feen to move
towards the warm Plate, and rifing over it will point ont the
Courfe of the Air from Sea to Land. And if the ambient
Water be warm*d^ and the Plate filled with cold Water, xtA
the fmoaking Wick of a Candle held over \ht Plate; the con-^
trary will hiip|^h.
(C) I. "fixe Experiment to prove this, is to chafe a ftti
bpen Place, where tiie Current of Air, or Wind, is not ac •
all interrupted, bat flows uniformly, or as much ib as the
undulatory State of the Atmofphere will admit; in fuch a
Tlace, a Feather^ or (bme very light Body, is to be let go in thd
Wind^ and then by a Half-Second W^tch, or Penddam, yod
oliferve nicely to what Diftaoce li is carried in any Numbec
o^ Half-Seconds ; or in how man^ Half Seconds it has.pais*ct;
over a ^ven or meafured Space; this will give the Rate of
Velocity in the Wind //r Second, and of courfe per Hour.
2. The late R^v. Dr. Derbam^ who was moft ad&irate hi,
making Experifotats ol"th]s Sort, approves cfif tUis Method
l^efore that of thfe Mold talata or fnfumatica ifiveated by DrI.
Hook (of which f^e 'tSl Account m the PBlofopbiial Thanfa^ioni
I)^ 24.) And h^ tells us (in N""* 3 13. J that )k thus mea^
fired the Vcldcitjr of" tAe Wind io that very greA Storm of
1705, Augufi \\\ and by many &periments he foand,' thaf
It was at the Rate 0/33 Feet /«r Half-Second; or of 4s Miles*
jer Hour; whence he concludes,' that the mdft vehement
Wind (as that of 1703 in Novkmberl do^es not rfy it th^
iK^it of Aio^e iobt 60 Mifo ^er RlM; ^iHUtAi fS/ld^
Of Winds a„a <j
Th<,s mud, „ f „ i«3t/J»i>s,
»«VWeM?of f '""^Cone nS? ,°^f^* ^^ l«'
Of Winds And Sounds. 83
how to the Do&rine of Sounds. We know by
the Experiment of the Bell in the exhauiled Re*
Line or Scale tif 28 equal Pans be dx^wn dn the Sid« of tlul
Cone, and the Strength of the Wind will be bdicaied hf
that Number therein firom which the String fhall at any time
hang.
7. Furthermore^ the String may be of foch a Size, anl
ijie Cone of fach a Length, that there^ fhall be 16 Revoln-
tions of the String between each Divifion of the Scale dn thd
Cone i fo will the Strength of the Wind be expre&M in Poimdi
and Ounces. And if greater ExaAnefs be required, let the
P^riphezy df the Cone^ £a(e be divided into 16 eqitti F^utf^
then whenever the EfltUiiriMm happens, the String will leavt
the Conic Surface againft one of thofe Divifions^ and thoa
ihe w the Force of the Wind, to a Dram A^Qgrdnpois Weight. .
8. Having premi&d. thus much relating to the Strudorft
and Natmt or the Inflrument, I fhall now proceed to a more
particular Examination of the Theory of Wind-Mills^ by re*
afliiming what we have formerly faid on that Head (^m
Anmtat. XI^VJ Therefore let Im (parallel to the Azia.
QJiJ) =:«, reprefent the, whole Force of the Wind on the
^i I this Force is reduced to / n^ and this aeain to « «, which
a6ls normally to the Axis, and, turns the Sail. Alfo we have
ihewn, that, patting m 9 =; a*, this Force which turns the
aax* — *■'
Sail ises^refi^d by -i and tint whea it wia a
Mdxbmm^ x-zz ^ ^ =:ai/-^ » ^^ the Ang^ Imn'X.
3 3
9. Hence we obferve, that when the Mill ism its greateil
Perfeaion, /«= Vaa—x9czs.V « *— ~ = « V^!l.
3 3
hence the whde Force in the Direction /^ is to the fame
i^oced^. in the Direction in, as Im^ to In^^ or as a* to
fc-it*, or as I to — , nnk. as 3 to 2.
3 ' 3
10. Again, the whole Force in the Diredion /ijn is td
the fanie a fecond Tim:e reduced hi the Direction no^ as a*
to ^ ,f '^^.'■■. that is, asii^ t04tf V^— t eras i to •'-I*
tf * * 27 27
S2c£^::::i. nearly; ox"^ the Force thus reduced u to th#
519 ij
Fa ceiver.
6^
criv^r, rhrt Soutid has ^ nee. / ^^^^^ ^^
^ the Air. and if ^^ '^^^^
^bol^ Fo^ .3 s to 15, ^^-y^'^ arepofiteJ rntte
^n"" Now'in or6er to ieterrt.^^ jfte abfolute Fon:e of the
^ind, wc m^acompai^ it jvith.that C^ Water, as follows.
Jincc Air and Water Vre both Fluids, if they move with e-
^ual Velocfties, their EffeGt^ in a given Time will be as the
Quantities of Matter, that is, (pattipg the Roman Letters for'
ihSfc Particulars in Water, and Italics for the fame ih AirJ
jf V =r f, then E : i" :: M : M. Butjn equal Quantities, of
J^atter, inx, Mz=:M, their Effeftsrwill be as the Squares of .
rhe Velocities, *w«. E : i? :: V * iV (See J/wwV. XLIX. 1 7.)
I'herefoi'e, when neither the Velodty,^ noir Maffcs of Mat-
ter ai*e knoWn, the EflFedls will tfe in a given Timfe ih a Raticf
compounded of both ; that iS, E : £ :: M V * : iff Z'^*.. .
12. Bbft w6 have IhfcwnMt: M:: jyB : f>5, (See ^»«7/l
LVI. 9.) th^rtfore E : £ :^ D B V * : Z> ^ /^* in apvenTiih^;
Let us now fuppofe B = 5; then B^caufe D:D:: 860 : i,
(See Jfmot. LXXXIX. 6.) we have E :E ::,86o V* = : T*^;
and laftly, if we fuppofe the EfFeds to be equal, viz. E zz E^
then wc have 860 V * = F\ Therefore if we put V= i,
we have 860 =: F^; and fo F;zz 1^860 =: 29,326 ; .that
is, 7)&^ Velocity of Air ought to he fotnenMhat more than 29
^inas griater than that of Water /p ftrike a ghven Sitrface
ivith the fame Force, *' .
13. In4eed .Mr. Belidor makes ^=: 25^, becaufe he has-
ftrangely miilaken the fpecifie Gravity of Air to be -L., iih
640 '
dead of rr— , Oft which Account all his Calculations on this
860 ^
Head are very faulty. If V denotes any equable Velocity
of Water, the Height H of a Fall neceflary to produce that
Velocity h thus found. As 32 : V^ i6(=:4) - V : S/'Hi
i6V^ V*
cr thus. As 1024: 16 :; V*:Hs:z— — zr-r^- J or put-
1024 64
ting V=ri, we have H =t-« Now a pibic Foot of Wa- ,
ter, whofe Height is i, ftrikes with a Force =i62^5/(J;
therefore the Force of a Column, whofe Height is H, ftriking
agau^^ Surface of one Square Foot is 62,5 H zz;,
when |h£ Vdw'ty i not given.
62, <;
m-ssn
th^
J.
• Of Winds and Sounds^ 85
thf Partjcles of a fonprous Body find thol^ of *
Air, we fhall find that Sound is nothing but thi5
y% y%
14. But (by Art. 12.) V* = — — , therefore — — ^
o90 860
-~i= 62,5 H = 0,976/^. the Pofce of a Stroke of a Co-
lumn of Water whofe Velocity is V=z i and of Air, whofe
Velocity^ is ^=s: 29,3, and Heighc H z^ V? o^ * Yoo^i
therefore ~7-x 0,976 1= 0,001 13 r* will be a conftant
Multiplier to reduce the Force of Wind blowing with any
Yelodty Vy on any given Number of fquare Feet or Area A,
to Pounds Averdufois Weight. For Example, fuppofe the Ve-
locity of the Wind at the Rate of 20 Feet fer Second ; here
Vziz 20, and V^ = 400, and 0,001 13 ^* = 0,001 13 x
400 z=: 0^452 of a Found on a fquare Foot; and therefore
on 10 fquare Feet it will be 4,52 lb.\ on 100 fquare Feet i(
win be 45,2/^.; on 1000, \^zlh. ; and foon.
15. Hence, to compute the Force of Wind on the Saib
of a Mill we proceed as follows : Admit the Length of a
Sail be 30 Feet, and Breadth -6 Feet, the Area or Surfece
will be 180 fquare Feet, and 4 x 180 ;= 720 fquare Feet,
the Area of the 4 Sails ; then admitting the Velocity of the
Wind the fame as before, «vr». 20 Feet fer SeoHid, the Force
on each fquare Foot is 0,452, and therefore 0,452 ^ 720 =
325,44 /i^. This is the abfolute or whole Force of the
Wind blowing dire£tiy on the Saib : But iince when the Sails
are fet right, this Force is diminiih*d in the Ratio of 13 to 5^
therefore — x 325,44 = 125,17/J.
1 6. Suppofe the Diflance from the Axis Qjto each Sail he
5 Fei*, then will the Diftance of the Center of Gravity PQ^
be 20 Feet I therefore 20 k 125,17 = 2503,4/^. the me-
chanical Force of the Wind qn the Sails pir Second to produce
the Effeds within the Mill, which may be computed as in the
Example of the WaterrMiU, Amoi. XLIV.
17. Toreprefent thefe Things more generally, let A ==
Area of all the Sails, Y^z=l Velocity of the Wind ; then
0,001 1 3 V^h = abfolute Force, which multiplied by — |s
0,000435 r* A =; Force reduced bv the oblique Pofition of
the Sails. Now fuppofe a Weight W hanging from an lini-
F 3 Propa?
8^ Of Winds and Sounds,
Propagation of the Tremors and Vibrations of
the former imprefs'd on the latter, to the 3>i»-
forni Axle, whofc Semidiamcter is 4^ keep the Saik in I,quu
fibrio with the Force of the Wind; then D being the Di-
ftancc of the Center of Gravity of the S^s, we have D 2
i/:2W:o,ooo43sr»A = F=^.
18. Bat becaqfe, ^hen tht Machine is in it? greateft Per-
leftion, the Weight it is charged with is but | of W, (Sec
jhmt. XL.) therefore $Wx^— |F = 0,000193 T* A
:^Pj then putting f^ 0,000193, we have rr*A = P, the
p
Induced Foxye for the greateft Effeft; and— r;:^ =: A, the
Area or Surface of the Saib j and lafUy, i/— - =:r, the Vc-
1* A
locity of the Wind, which thf refpre noay be found by having^
A and P given.
19. Let I W = w, the Velocity of which Weight let bo
Ui then \ /^= Velocity of the Center of Gravity of th^
Sails ; then -^j x P = .« x w, whence any one of the fomr
• • • • 3 .
Terms may bf found, the reft bemg given. Alfp P =
"f--^ = rV^A^ or 3 ftfu; == r V^A 1 w^ience again any od<i
of the four Quantities A, V, <u', u^ may be found, the othe^
being known.
20. Since the Force of the Mactune i$ ^ A x V^ x, J>, it
will be a Maximum when A x D is greateft, the Velocity or
the Wind' F remaining the fame j W if A be given, the
Maximum will be* whfn O is greateft of iall. 'Hence it ap-
pears, that if we are iiot ponfij^efl to a given iHftance froa^
^e Axis Q^for adjufting the Sails, we may diipofe the given
|H^^^ Surface A Into the Form of an 1/o/celis Tfiangie iii each' Sail,
XXXIII ^^' ^^^^ as A B C D, inftead of the equal Paralldogram-Saij
^* ' abed m common Ufe ; for in the Triangular Sail the Cente^f
^ r • ?' ' of Gravity is at P, and its l)iflance is QP ; whereas in the
keflangular Sail ah^d the Center of Gravity is' in the midl
(^e Point /^ ajid its Diftance is Q/, much le^ than l)efore»
^iV For Jlxapple,^ let ah =p^Feet, and ^r 5= 30 1 thei^
the Area A ''z^ 30 Feet fquare. Let Xxp equal 5, then i^
1^ •=; fo ^ P^ and A >^ P 5f; 69$, " ^ut ^n the Triangu-
panum
Of Winds and Sounds. 87
panum or Drum of the Ear, by the Aftion of
"whofe Membrane they are communicated to the
larSail the Ditonce QP=r 35 =? D,aiid thAefere A x D:;:
1 050. The Force therefore of the fame Wind apon the iaine
Quantity of Sail, at the fame Diftance QJ> fxx>m the Axis^
in the Triangular Sail A B C D, is to that on the common
Sail ahcd as 1050' to 600, that is; QJ* = 35 tQ Q/ = 20,
or as 7 to 4, which therefore is nearly twice as great. The
Truth of all is evident by Infpe6UoQ of the Figure, and ^n-
not, XXXV. 8, 9.
22.1 fup|>ofe it was fome Coniideration of this Kind which
led Mr. Parent to propofc Sails in Fortn of EHiptic SeSorst
for the Centers of Gravity in them alfo arc removed to aboat
two Thirds qf their Length, and are moreover better adapce4
%o £11 a circular Space when placed oblique to the Wind, fo
that no Wind be loft when you would take in all that Msoa
a given Space or Area. But for what Reafon he fhould declare
th9 tranfverfe Pofition of the common Sail to be more advan*
tageous than the longitudinal one, I am at » Lofs to goefi.
However, as I have not feen any thitig he has wrote on the
8abjed, I (hall fay no more of the Matter.
23. As it would be endleG to recount 3II the varioiis Ufcg
which are or may be made of th^s moft ufeful univerial Ele-
ment of Air, both for Natural and MechaniqU Purpo(e»; I
fhall content myfelf with fetting before the Reader the The-
ory of that moil ufeful domeflfic Infbumenc the Bellows,
by whofe means tlie Adion of Fire, or Intenfity of its Heat,
may be increafed to a prodigious Degree. And for this For*
pofe I (hall h^ye rfxrquHe to the Example of that curious Na-
turalift Dr. Hale$^ in his Statical EJfays^ Vol. II. Pag. 329,
which is as follows.
24. Thjs Do^or meafure^ the upper Surface of a Pair of
Smith's Bellows, and alfo the Space th^ defcended through
In a Second of Time ; by which he found the Quantity of
Air expeird in th&t Time was 495 Cubic Inches in its com**
prefsM State. Now to find what Degree of Compreifion it
fufFcr'd, he fixM ^ Mercurial Gage to the Nofe of the Bel-
lows, and found the Force of the comprefsM Air fufficient to.
I'aife the Mercury one Inch high, at a Mean. Hence it ap-
pear'^d, that the Force with which the BeUows impeird Ai^
into the Fire was -3^ of the Weight of the Atmofphere.
"^ 25;. Hence alfo it follows, th^t the Air driren through th^
Nofe of the Bellows in one Second was more than 495 Inches^
tuy ^ :^ Part of <h^t Quantity, mm, by 16,5 Inches, vtfhic^
^ ^ - F 4 Air
?? Cj/. Winds anji Sounds.
f^\x in the internal Cavities of the Ear, where ^h^
Auditory Nerve receives the: Impreffion^ and cx-
(dded to the former make 5 1 \\ Inches of common .^\x. Tc|
$nd the Velocity with w^idi this Air was iiapeird, he ^ea-
fitr'd the Area of the Ori^ce of the Nof^, s(nd by that di-
vided the 495 Inches^ which* gave fof the Quotient 825
Jnches, or 68,73 F^etj for the Lehgth of the Cylinder of
Air which ruih'd per Second through the Nofe of the Bellows ;
whicfh prodigiouj^ Velocity of Air adling conftantly on the
elaftic re-aCling Particles of Fire muft immenfely incrcafe thei^
i(ite(tin]p Motion, atid proportionably augment the Heat, which
coniifls therein, and from which all our Senfations of this
Kind are derived.
26. The Doctor concludes with a Query, Whether if the
Force with which the Air is impeU'd by the Bellows i^tp the
Organ- Pipes were taken in this' Mann^, >ve ^ig)it 'no( elli-
mate the Velocities <>f ^he. Undulations of Air required' tq
d^orm the yarieUs Notes or Sounds? Th^ Velocity of undu-
lating Air to that i^ ^ater beinjg as their Deniities inverfely*
nearly^ <vi2:. a^ 36a to i, as will be i^ewn f^irtl^er on.
27. Mr. Martin Trirvtiald oi Swed(^ has htely exhibited ^
new Invention for produpng a continual' Streap ojf* Air, to
blow the Fire of great FQfgr8,'Faunderies, (fc. and whicti
inay properly be caJl'd Watbr-Bellows j for t^e Contri-
. vance i^ two hollow Setl>form Veflels, fufpend^d from the
Ends of a LfVer, w)|ich is pot intor Motion by a Stream o^
Water rubnxng into (wp Troqgh^, \toth uniting tor joining ra-
ther at the Stream, fo th^only one ara time can receive the
Water ; which running to the larger and wider ^nd,. laid over
lie End of the Lever, does by its Weight carry the Lever
down on that Part, till by defcending the Water all runs out ^
^nd then the other Trough (which was filling in the meait
time) preponderates, and forces down the *other End of the;
Lever i and thus r^e Mac))ine is con(lantly kept in Motion.
28. When one Ann of ^^ Lever is raifed, the Bell or
Bellows hanging frpm it w^l be raifed above, the Surface of
Water (in which the Machine is placed) that it may be fiird
fvith Air. Upon the Dcfcent of the > Lever, the Bell (by
Weight affix'd to it) defcends into the Water, by which meanij
the included Air is greatly corhprefs*d, and thereby forced! tQ
pafs through a* long fmall leathern Tube, going from the 'l^op
^f the Bell to other metalline Tubes, which convey it to the
i?ire. Thus, by means of thefe two librating Bells, a conHanf
Blaf^.of Wind is fapplicd^ whofe Vclpcity ma]f be increafe4
cites
Of Winds anJ SouNSts. 89
Cites the Senfation in the Common Sensory m
theBRAjN (CI).
or dimSnifliM by proper Contrivances, which the Reader may
fee in ^e Pbihfofbical TrMnfaSiufs, together with a l^finc Kit
. the Engine.
(CI) I. The StniQureof the Ear, with its admirable Ap^
faraius to conftitute an Organ of Hearings is well worth th^
Attention of t\txy Man. The external Part is adapted for
taking in a large Portion of the tremulous Air» which is re-
£eded ftrpngly by a fine, elaftic, tremulous Cs^tikge, and by
this means it is conveyed more denfe and elaflic to the interior
Oivity, 'or Concha of the outward Ear.
2: The free, hollow, elaiUc Apertqre of this Cavity, coii«
ibnded with proi)er Mufdes, i| by that means capable of be-
ing expanded; contr^ted, and eveiy way adapted to receive
the vWiQUS rf reniors of the Air : And moreover it is fo dif-
poTed, that it is able more firmly to unite and condenfe, or
more laxly to difperfe or rarify, the (ame aerial Rays, ia a$
to acconmiodate itfelf for attempecating a Sound too flrong,
and auCTienting it when too weak, as occafion requires.
3. T\x^ Meatus AuditoriuSf confiding partly of a cartikgi-
noii^ and partly of a bony Pipe, conveys the Sound towards
the inietidr Parts, and the Obliquity of the Canal increafes
the Superficies, and confeq«iently multiplies the Poinu of Re*
fledion. Moreover, the triangular cartilaginous Tongue, by
its elaHic tremulous Texture, and ere6t Poudon in the Hollov^
of the Ccncba, juft over the Orifice of the Auditor^ Fsilagjey
caufes, l^ an egregious Mechanifin, that all the Rays of
Sound which arrive at the Ear (hall enter the faki Pafiage i
and preVen6 their flying out again by any Reflefiions what*
foevdr.* ' Its tubulous cylindro-elliptical Figure, by a Terpen-
tine Progrefs firft afcending, then defcend'uig, and thenmfeend-
ing agaih till it terminates in the Membrane of the Tya^amimp
increafes the Refie6Uon and Sound, and caufes that all the fo-
norific Bay^ fhall at laft fall united upon the central Point of
its End ; hindering at the fame time all Senfation of a con*
fhfai and clangorous Sound.
' 4. The Memhyana fjmpam^ or fine Membrane at the End
of the Mtatus Auditorm^ is fo obliquely extended acro& the
Pafifage, as above to make an Obtufe Angle, and below an
Ac\ice one with the faid Mtatus, Hence the Surfiice b In-
cfeafed, and rendered more capable of tremulous ConcufiionSj^
and of concentring the Rays upon ^ts middle Pointy
go Of Winds and Sounds.
For the Parts of a fonorous Body, being puc^
into Morion by Percuffion, do vibrate forwards
juid backwards through very fmall Spaces, by
their elaftic Quality. In this Adion, they affefl:
the Particles of Air contiguous to them, and
compel them upon the firft Impulfe to move
forwards alfo; and thofe propel the next, and fo
g. This Membrane being expanded, npon and conne6le4
with the bony Margin of the Mtatus^ is on the fore ?2X!C
(towards the Meatus) concave, and convex behind or on tho
internal Part, where it is applied to the Handle-Part of a lit-
tle 3one call'd the Malleus or Hammer, whofe Head is move*
^ble in a bony Sinus on one Part, and on the other it is arti^
culated with another little Bone calPd Utit Incus or Anvil^
which freely moyes in t)iat Articulation; and on the other
End it is again articulated with a little orbicular Bone, and
with the Stipes or Stirrop, w^iich on its Bafe-Part is^coxined-»
^ to a Membrane fpread over the Foraaun 0<vaU or elliptiq
Hole of another bony Cavity call'd the Vefiibulum.
6. But as it will be impoifible to giv^ an Idea of this won«
derful Confb-uftipn without a Print, therefore let AB be the
Plate external E^; C its Concha^ or Cavity i BE the Meatus Au^^
XXXIV. £ tortus t which in Length is ji Tenths of an Inch, in Breadth
Fig. I* 3) and in J^epth 4. G is the Membrana Tympanic h the Han-»
die of the m^ileus ; k the Incus, an(] i the orbicular Bone 1^
n the Stapes, and r the Veftibulum hoUow'd out of the Os P<-
trofum, ia the Cavity of the Labyrinth.
' '%, In the Veftibule we obferve the following particular
Conft'ru6lion of Parts. On the larger Part are three fcmi-
drcular Cailials or Conduits O, P, CJU which communicate by
five Orifices with the Cavity of thcv eftibule ; they are of a
bony Subftance, and of an elliptic Cavity. The leffer Parf^
of the Veftibule comoiunicates with the Cochlea, or fpiral Fa^ '
bricS. ,^ *
8. This wonderful Part merits particular Notice, and U
j«g. 2 3. therefore reprefented .by itfelf in two Figures 5 wherein ia -
* ihewn the bony cpni^ Canal ^T, making 2^ Revolutions
round a bonjr Cone from the Baft to the Apex T. This fpi-
lal Cavity is, from the Bafe S to the Top T, divi4ed by s^
tranfverfe Septum, or Partition, of a triangular Figure, repre-
fented by ZX. This on its Bafc-Part adhering to the Cone;
is bony, (wh^ch is ft?v^n ty a.%a,ai\ ancl is o( an el^idic trc-
Of Winds and Sounds. ^r
on, to a vtry confiderable Diftance^ according to
phe Intenfity of the pcrfuffive Force. By this
means the Particles of Air are comprcfs'd nearer
together, than in their natural State.
But when the Particles of the fonorous Body
niake the fecond Part of the Vibration, by re-
turning baclf again, fhe Particles of Air alfo, by
indbus Texture, a^d exceeding finootli or polite. The escr
terior Fart h^h^hy is oJF a membranaceous nervous Teztoie^
whofe Chords or Fibre^ lie as reprefented in the -Cut : It i$
connected with the bony Safe on one Part, smd lyith the Ca«
iial on the other*, fo that the Spiral Dud of the Cochlea is dir
vided into two equal Cavities without any Conmranicatioa
with each other ; though the Orifice of the fuperior Cavity
^ opens into the Vefiibuiumy and the pt|ier is fhut dofe by the
Membrane of the Foramen 0*i>aU.
9. The Auditory Nerve V enters the VefKbule by feveral
little Holes as at S, and forms a cu|rious Lining or Tapis all
pver the infide Surface both of the Veftibule and its femi-
circular Canfds O, P, Q^ Thefe Nerves alfo pid& into tho
Cochlea, and entering between the two Membranes of the
triangular Zone^ or Septum, Z X» do there divide, and brandif
themfelv^ out into an exqiiifite membranous Expanfion on
each Side the fame^ which thus become the more immediato
prgan of Hearing.
10. "this Cavity of the Vpftibule is :dways fiird with. as
^lailic Air, though there appear^ no vifible Way by which it
pan enter. Alfo the Labyrinth or Cavity of the Drum is fill*d
ynxYi common Air, by means of th^ Eu/achian Dua or Tahe,
^ M N ; the Orifice M opening into the Mouth, and N intQ
the Cavity of thp Labyrinth.
1 1 . Having thus premifed a Delcription of the iev^ral
Parts, we (hall the be^er apprehend how Sounds are excite4
in the Mind. Thus the Pulfes of Air entering the Mtat^
Auditorii^s D£ are condenfed by various Refledions through
fhe Paf{age,to their Incidence on the Memhrana Tympam at G,
which |s r^nder'd more or lefs concave, or lax and tenfe, by
f he Handle & of the Malleus ^ aduated by its proper Mufde.
fiy this means the Air containe4 in the Labyrinth is admitted^^
expeird^ comprefsM or rarified. according as the Eujtachian
7"^^^ is opened or fliut. '
1 1. f he Mefo^rapa ^J^^ G being ^us adapted for re*
their
9^ Of Winds and Sounm.
their repulfive Power, repel each other towar4$
4|eif proper . Places, and thus agiin expand
thcmfclvcs.
Now fince Motion onfe generated in elaftic
Bodies continvies {qa\e time before it can be de.
ft|r9y-'4 by the Refiftance and Counteraftion of
contiguous Bodies, it follows, that the Particles of
<;piviBg the Sounds of tremulous harmonic Bodies, and mor
dulating the internal ^\x of the Labyrinth, can eafily commu-
nicate the Jmpreiiions to the Incui k, which tranlinits them to
the Os Oriiiqiiare i, this to the Stapes n, and that to the Mem-
l^rane of ^hp Foramen Ovale of the Feftibulum r.
13. This Membrane, by fuch an Afpetratus of Parts, may
1^ intended or remitted in infinitely di^erent Degrees, fo as
Ip become adapted for the Tremors of every Sort of Degree
of Sound ; and for communicating the^i to the internal Air,
which affefls the Nerves ^'^tx^ yrher^ ^anded over its in*
temal Surface, but more efpecially th^ nervous Expanfion of
the Cochlea.
14. For here, as we have ihewn, the Fibrps pf thp S^-^
turn *TranfverfaUy b, b^ b, are contrived like fo mapy Strings
of an Harpfichord, of various decre^ne Lengtl^, and dif-
ferent O^ves, that fo fome or other of them may be of a
proper Lqigth to be in Ccnconl with th^ founding Body, or
to tremble with the fame Vibrations, which by means of tbq
Nenrgs ai^ cqnv^'d to the Coi^mon Senfory in the Brain,
, where the Mind perceives and diflinguiihes the infinite Dif-
ferences of harmonious and difcording Tones.
15. Thus, though we are admitted to view the amazing
Mechanifm of the Organ of Hearing, yet can we get but 3^
genera] Notion of the Manner in which thefe Senfations are
produced, or of the particular Functions perform'd by every
Part, 4nfl t)\f (peclal Ufes to which they are fubfervient, in
the general Execution pf ^his Senfe ; with refped to whic]^
there remain many Things yet to be enquired after, even hy
the Leanied Boerba^f, as we find in Page 250 of his In-
fiitutes, which fee.
1 6. From this Account of the Ear, we hive a Soj^^tion of
fome Difficulties ; as. Why the Ear is affeded with giieat Pain
in going down into the Sea in a Diving- Bell: Why People
generally open their Mouths when they lifien with great Atr
t^tipn : Why Deafnefs epfuce on a |lupture of the Membra*.
the
Of Winds and SoOndj. 93,
the fonorous Body, and confequently.thofe of the
adjacent Aif, have for foriie tinie a reciprocal
Vibratory Motion, by gomg forwards and ba^k-
"Wards through very fmall Spaces in an'irt'de'finiteljr
fniall Particle of .Time; which Motion gradually
Idecreafes, till it be totally deftroy^d (CU).
Ha Wjtf^ainy bt ftora an Obftra£lion of the luftachian Tube:
Wiiy we hear Irut <mk S<ytmd with two Ears, fiat how foMe
People. taHing SmQkf; into the Moath can emit it by their
Ears, is hot fo eafy to anfwery there being as yet no Perfo-
ration of the Merhbrdnii Tymfani difcovered ; though this Teems
ii pldn DemOiiflration th!at theife is one or more^ though not
perceptible to the Eye;
■ (CIIJ 1. The Doarihc of Sounds is the inoft intricate and
perplex'd of any thing, we. find in Fhiloibphy; and perhaps
this is the only Subjedt which the greatdft 6f Men has (in his
Principia) treated in a Manner not quita (d phyfical and ma-
thematioal as the Nature of the Thing re^uirra. I ihall re-
fer the ReaJder to the Conuninfafies of Meff. Le SeJr and -Jac-
quier on the Principia^ where they will find Sir tfaac tf^wtont
JEJypothefis relating to the Motion of thfe Particles of an ela-
foQ. Medium to be fallacious ; and other Methods propofed, by;
il^hieh the Ninxjtonian Dodlrine of Sound is feftored. I (haB
Ber^ add an E^tplication of fuch Phanomni only, as are of
princifial Concernment, and at the fame ^e pretty e^afy to
be underftood.
2. Let ABC be an claffic String or ChAfrd, &'d m the pj^^^
Rnnts A and C, and drawn out of its natural right-lined Si- vyvrrr
tuation ABC. Such a Chord, in its State of Tenfion, will, C:^^*"*
when let go, return by its natural Refort, not only to its na-' *S' ^*
tural Situation ADC, but with the Motion it there has will
gooAtoE, fo that DEiii nearly equal toBD; and iron/
Sience 2? will return again nearljr to B; which Motion from
B towards E, and from E towanis B, will be iredprocated af,
grbat Number of Times befbre the Chord will come to a State
of Reft: And esich Motion' through the Space BE i^ callM a
/9fc'<i/iw»^f the Chord.
3. Wh^n the Chord bfegras its Motioh at firft froni B, it
ilrikes the Particle of Air cc^tiguous to it in B, and that will
by its Approach towards the nact affeft it, by means of the
>cpulfive Power, which keeps them-all at equal Diffcante^ from
From
94 ^f ^-^^^ ^^^ Sounds.
, Frojw the I»Jature of a Fluid, whatever Motiofi
h generated iaany one Particle^ it is by that
Particle com^iunicated equally to all around it^
as from r a Center; confequently the Treniors of
each other J anifo'bh through fuch fttfaxnter of Particlei
as can recjeive >he Amotion iVHile the String moves from B td
D. Let A, B, C, D^ E, F, G, &fr. r^prdfent fuch a Scries of
Partide$ o^Air ftt an. equal Diftanqe^ ^d the £rfl Partidie A
^ontjjgpQii? tQ. the Middle i^oilit.fi of. fuch a Strings aodagi*
t?(tcd!i)y it m its ]\^otion. . . . i.
' 4, The Siring beginpiijg to ttioV«?, alj. the Particles A,B,'C|
^ill begin to move forwards, alfo 2 and iince this Motion is
j^ropf^gatcd in Tigi^^lfct E be the remoteft Partidc movei
whilethe Chord Ts moving from B to D; during whicliTime
the Chord, having an accelerated Motion^ will cauf<^ the Par-
tides to approach ^f:h other within accelerated Motion like*
f^fcf and DecauTe thofe. accelerated Ajiproaches beghi at A
therefore 1
thahCD*
begin to he leHe'n^d When th^ String is arrived to ^he Sitq
AD Ci andi the Particles A, B> C, t), E, F, &fc. will Mve th<
Airangemeht reprefented in the fecond Line.
5. But now the Chord, havinff acquired the Situation A DCgi
yrill be no farther accderated, out on the contrary retarded,
asjt .will ^ow Z9 oft from D to E ; the Eflfbd of which upoi^
the Particles oT Air before it will be> as follows. They wfll
all,go on forwards till the Chord comes to E, and ihePartidd
A to ib Sitvatioii in.the third Line: But. fmce the Force upon
A begins to abat^,. as the String begins to move from D, /^
elai^c ^Qice now.jbetween A and B will, by adihg both vv^Sji
continue to accderjite the Motion of B^ and retard tha^qf Jji,,
Thus the. Difiance^ B C will flill diminifh till B come.to be^^
nearly equi$fiaAt,betiwe(;4 A W ^; and C will he.aq^li^-^
rated till it be ^qu^^ti. betweei^ ^ and D $ and fo <9u SdT
chatas.theAcceleratiQnis continued forwards, the I^ift^t^i^ev
^ill d^jn^ towards F i and by the.Tinis the Chord isar^^
lived at £9 the Particles E £ will be at their neareit Di^ce^*
And lince the Motion of A is continually retarded, . it wi}},loM^
what before it had .g^'d m the iame Time } and.wijti there-
fore now be at the lan^e^DiilanG^ from $ as at firft^ej^ly > .S(^:
that the Parti$;Ies ^om A to G wiUhftve the Situatt9fs.as re^
prefenied in the third Line, . . . , :t
the
Of WiKDs and Sounds^ 9^
the founding Body will be propagated all around
from the Point of Percuflion, as a Center, in cm-
centric hollow Superficies or Shells of Air^ which
are not improperly call'd aerial Pulfes^ or JVave^
6. The Chord pqw returning from E to D, gives Libertf
to the repuIiiiHe Power between A and B to feparate thenx to
a greater D^hce than in their natural Stated and which they
at prefent have. By this means all the other Intervals BC^
C I>, D £, E f^ will atfo inaeafe; and become foCcefiivelf
grater than the natural 'Diftance ; but that ExcefrtiriU be
lefler in each, tiH jrou conietoF^, which wiK be equal to
the natural. JDiftance, at .prefent between. A and B. The
Motion at the {ame Tinie continuing in all the Partidfdi fttnsk
H to N, they will all move fbrwi^s,' and* the prefent con-
traded Interval between H and I will fncceed. between all
the refty till it Arrives to the Partlde N, when (he Intoval
M N will be the &me as at prefent is H I. And thofe Par-* '
tides beyond N to S, wSly by the preceding ones^ be pat
into the fame refpeflive Diftahces, bat in an mverfe Qrder^
as'diofe have between G and N. And the whole Series
(now the String is at D) will have the Intervals of the Par-
ticles refembling thofe in the 4th Line.
7. The Chord not Hopping at the Situation ADC» bat
going on towards ABC with a retarded Motion^ the Velo-
dty of the contiguous Particle A will alfo be retarded and
become lefs than that of B; upon which the Diftance be-
tween them will be leflen'd, and the mofi fo as the Strins
approaches to B. Hence all the Intervals, now dilated beyond
their natural State, will, by degrees, contract; but gradually
flower, till you come to F, where the prefent largeft Inter-
val* between A and B will be found between F and G,
and that between A and B will have aajuired its'natural Ex-
tent when the Chord is arrived at B. Then like^ifp the ^
Particles from G to N will acquire the iame Situation as
thofe DOW have between A and G; and from' N to S, the
£mie as now is feen between G and N; and from S for-
wards, die fame as is now before the Particle N, the Point
S being now the middle Point of Conden&tion i al} which
is cleatly feen in die 5th Line of the Figure. '
8. Thus the Condeniation which beean at A, by the firft
Part of the Vibradon, was propagated to G by the fecond»
from thence to H by the third, and lalUy to S by the fourth
Part of the whole Motion of the String in going and return-
of
^6 Of Winds and Sounds^
cf Air: Analogous to which are the circular
Waves generated on the Surface of Water all
around the Point where any Impreffibn is madei
in any Manner or Diredfcion whatfoeVer (CIII).
ing;, aod this E^cint of Air^ thus agitated by
going and retumpig, is calPd by ^.Ifaac AV
the Chord in
^,_^j^ ^, , ,^ ^.: Nenvton a Jfave .
^r PulJiqjtJir. In which Wave the Particles from A to N
are in- a dilated State, and from N to Jt in a cbncraaed or
cpndenied Sute; which two Parts of tJLe Wave anfwer to
tjie concave and convex, or low. and iiigh Part of a ivatry
Wow.
. or.As the Chord goes on to make another Vibration, it
'wiU not only continue to Agitate the Air at prefent in MotioUj^ .
but will fpread the Pul&cion of the Air a;^ much £irther, and
by the fanpie Degrees as before; an4 the like will happen afte^
«vexy compl^t Vibration of the String. Thus the Air be-,
ing a fluid j^ody, and the Impreflion. mad^ on any one Part
affedting aU the Particle^ alike around it,, 'tis, plain, thofe
*^ j^ulfes will ))e propagated in every Diredlion all around ini
• . cdncentric Aerial Shells or fphcrical Waves of Air.
io. That the Motion of the Pulfes in an elaftic Medium,
is analogous to that of Waves generated in the Surface of
ibgnant Water, is evident, when we confider that the Con-
denfation.of the P^rts of the elaftic Medium is in lieu of the
Elevation of the Water ; the elaftic Force effe^b the fame in
the Medium ais Gravity does in the Water, and the denfefl
Parts of the Pulfes correfpond to the higheft Parts of the
Waves. Wherefore as there is fo great an Affinity between
thefe two Phxnomena, it will be requifite, before we go hx»
ther, to explain the Nature and Properties of aqueous Waves,
which will therefore be ihewn in the next Annotation; '
* (CIII) I. Sir Ifaac Niovtofi exp/ains the Nature, of Waves
Plate i^ Water after the following Manner. Let A fi and C D be.
XXXIII. *he Surface of Water quiefcent in the upright Legs KL,
Pig. 6^ 7, M N, of a recurv'd Tube. And if the Water be put ipto*
Motion, and afcends In the Leg KL, to £F, it will de-
fcend in the Leg, M N to G Hj fo that E F == pH. A-
jjain. Let P V be a Pendulum vibrating in the Cycloid RPS/
its Length V P, from the Ppint of Sufpenfion to the^ Centre oi^
Ofcillation, . is equal to half the Length of the Water in the
Tube; let P be the lowcll Point, and P<i.an /frch of tli^'
Cycloid equd to the Altitude AE;
fktii
Vj Winds and Sounds. 97
These Pulfes or Waves of Air are affeAcd
with the following Properties, viz.
I. itey ah propagated all around^ iH afpberlcal
nniulatory Maniiir (as I faid but now;) and that
tiot bnly from the tremuloui Body., bui from the
H6les in any Obftacles they nieet With : Whence
It comes to pals, that one and the fame Sound may
be beard by feverdl Peffohs^ in any different Sitiia-
i. Tht Force by which the Water is alternately accele*
rated and retarded in its Motion in the Tube, is the Excefs
<^ the Weight of Water in either Leg above the Weight in
the other; and therefore when the Water in the Leg KL
afcends to £F, and in the other Leg defcends to GH» tha;
Force is equal to the Weight of th^ two eqqai Qjiantities of
Water AEFB + CGliDzzzAEFB; and therefore is
to the \V^eight of the whole Water as £ A to VP, or as
PQ^tdPk, becaofe the Semi-cycloid PR. is equal to th^ .«
Lengtk of the Pendulum which dcfcribes it, from die Nature
.of the Curve.
3. Alfo the Power by which the Weight P is .in any Point
Q accelerated or retarded in the Cycloid, is to its whole
.Weight ^s the DiHance. PQ^froqi the lowefl Point P to the
Length of ihe &emi-cydoid PR. Wherefore the moving Forces
of the Water and Fenduluni, defcribing equal Spaces AE,
T Q^, are as^the Weights to be moved ; and therefore, if the
Water and Pendujum are at firll quiefcent, thofe Powers will
move them equally in equal Times, and caufe that they go
forwards and backwards together, with a reciprocal Motion.
All which is eaiily deduced from what haa b^en fiud of the
Natore of the Cycloid, the Motion oi heavy Bodies, toA thr
.Forces of Bodies in Motion.^ « . >
4. Hence it follows^ thaf whether tbe l)ifbuice A£ be
creat of JQnall^ the Jkeciprocations of the Water will be all per-
7orm*d in, equal Tifnes. « Alfo It follows, that if the whole
Length of the Water be 78,4 inches, each Reciprocation, or
Afcent ^ndDefcoit of the Water, will be performed in om
,Secopdo(T'vnnci oecaufe a Penddum of half that Length vi-
Brates in that Time. LaAly, if the Length of the l^[ueoa8
Canal be increafed or dimini(hed, the Time of each, Recipro-
cation will be increafed or dimtniih*^ in the fubduj^ioite Ri-
tioofth'e Length.
Ytfii. II; Q ttoftS
98 Of Winds and Sounds.
tions with refpeft to the founding Body, if not at
too great a Diftance.
. II. The Denfity of tbefe aerial Pulfes decreafes^
as the Squares of the Dijlances from the founding
Body increafe: For fince the Force or Motion in
each Shell is the fame, it muft decreafe as the
Number of Particles increafes in each Shell : But
this Number of Particles is as the Superficies of
5. When the Nature of Wjaves in Water is confiderM, it
^^\ be found to agree very nearly with the Motion of the
Water in the Tube above-mention'd ; and confequently their
Plate Motion will be fimilar to that of a Pendulum. For let EF G
XXXIII. reprefent the level Surfece of Water when it is not agitated
Fig 8 fo as to produce Waves ; when it is thus agitated, let A, B»
^' ' C, D, reprefent the wavy Surface ; A, C, the higheft Parts
ef the Waves; and B, D, the loweft or concave Part. Then
'tis evident the Weight of the Water at A above E G will
caufe it to defcend as far below the Level to B; and with
the Motion acquired by that Defcent, it will again afcend to
the fame Height C, and fo produce a conflant Sncceffion of
of Waves in the watry Surface, after the fame Manner as
was fhewn in the Tube.
6. Hence it follows, that, becaufe the Length of the
whole Water to be moved is froni the higheft Point A to
the loweft Point B, if the Length of a Pendulum be J A B,
it will ofcillate once while the Water defcends from A ta B ;
and in another Ofcillation, it will afcend from B to C, and
fo on. So that a Wave will pafs thfo* its whole Length in
the Time of two Ofcillations ; and therefore in the Time of
one Ofcillation of a Pendulum four times as long, or equ^l
to ABC.
7. Whence becaufe A B C jn very large and wide Waves
ie nearly equal to the Breadth AC; therefore when the
Waves are 39,2 Inches broad, they will undulate in one Se-
cond of Time ; and confequently iince the Times of all the
Undulations are equal, there will be 39,2 x 60 = 23 J 2 In-
ches, or 196 Feet run thro' by a Wave in one Minute, which
is 1 1 760 Feet fer Hour. Hence! alfo the Velocity of greater
or leffer Waves will be increafcd or diminilh*d in the fubdu-
plicate Proportion of their Breadth; that is, if Vzi: Velo-
city of the greater Waves A B C D, and «v =: Velocity of the
the
Of Winds /zW Sounds. 99
t\it SheJI, which is as the Squares of the Diameter
or Semidiameter of the Sphere, that is, as the
Diftance from the founding Body. Hence the
Diftinftion* of Sounds into loud and hrjo^ firong
and weaky according as we are nearer to, oc
farther from, the founding Body. The utmoft
Limits of audible Sounds are about 180 or 2oa
Miles. (CIVO
leffer Waves_g, b^ c, d, r,/, &c. then it will be V : v ::
i^ACiV^ac. Bccaufe the Velocities and Times of Bo-
dies moved in Bay manner by Gravity^ are proporrional to
the Square Roots of the perpendicular Altitudes; and thofe
Altitudes are as the Lengths of Pendoloms* and therefore as
the Breadth of Wums.
(CIV.) I. Let A B C rcprefent the fonorous Body ; by the Plate
twhnalous Modon of its Parts, it will agitate the Air cxm- XXXIV^
tiguDus to evciy Pohjt as A, wheae it will be condenfed to Fig. 4.
acerteinfmall Diftance, and make a Pulfe or Wave of Air
in the Manner as has been large y (hewn (Annotai. CII),
The firft Wave or Pnlfe will by its elaftic Power in expand-
ing itfelf produce a Second, that a Third, and fo on i till
the imprefs'd Motion be .diffufed thro' too large a Qaastity
of Air to be any longer feniible.
2. Tjie Quantity of Motion produced by each Tremor of
the fonorous Body, being communicated fucceffively to larger
Portions of Air, the Part thereof which each Particle will ac-
quire will conilantly decreafe. This Decrement of the Mo-
tion will be as the Increment of the Number of Particles,
which is as the Superficies of the fpherical Shell ; and iincc
all Superficies are as the Squares of their Diameters or Semi-
diameters, therefore the Force in the Particles of the Wave
or Shell at D is to tktt in the Particles of the Shell at F as
AF^ to AD^; that is, the Force of Sound deaeafes as the
Squares of the Diilances inaeafe.
3. It is plain, the Diftance to which Sounds may be heard
lyili be proportional to the Magnitude or Intenfity of the
Stroke made on the tremulous Body emitting the Sound 2 for
the greater that Stroke is, the greater will be the Agitation
of the Parts of the fonorous Body, and of courTe the greater
will be the Force with which they will ftrike the Particles of
G 2 in. ^i
lOo Of Winds dnd Sounds.
Ill; All. the Pulfes^ whether denfer *or rarefy
move with equal Velocities: This Sir Ifaac Newton
has dcmonftrated a priori^ and alfo that this
"Velocity is at the rate of 1 142 Feet in one Second
of Time; which moft exactly agrees with the
repeated and moft accurate Experiments of the
late Reverend Mr. Derlfam. The Velocity of
Sound is therefore near thirteen times as great as
that of the ftrongcft Wind : And fince it muft
neceffarily increafe with the Air's Elafticity, it
will be greateft in Summer when the Air is moft
heated, and vice verfa in Winter: Alfo, as the
Motion of the Wind confpircs with, or is con-
trary to that of Sound, the Velocity of Sound
will be in fome fmall Degree augmented or di^*
miniftied thereby, though not difcernible in Ex'-
periments.
IV. The Interval or Biftance of the Pulfes from
each ether is the fame among all that are excited by
the fame Stroke: For fince each Pulfe is caufed by
a ifinglc Vibration of the founding Body, and
fince they all move with equal and uniform Ve-
Air. LafUy, the greater the Force is upon the Air, the moxt
flrongly will it be condenfed and expanded ; hence the greater
will be the Stroke at any given Difbnce on the Drum of the
]kar, and confequently the greater will be the Difbnce at
which the Agitation of the Air will be fenfible.
4. The l^cperiments are numerous by which it has been
found, that Sound is audible to the Dx^ance of 50, 60, or
80 Miles : But Dr. Hearn^ Phyfician to the King of S^weden,
tells us, that at the Bombardment at Holmia^ A, D. 1658, the
Sound was heard to the Diilance of 30 S^vcJ/Jb Miles* which
make 18^0 of ours. And in the Fight between England juid
Holland A. D. 1 672, the Noife of the Guns was heard evert
in fTfllfs^ which* cannot b^ lefs than 3co Mile^
_ • .:* : ^ locities.
0/* Winds qnd Sounds, ioi
JocitleSy 'tis plain they mwft fuccced each other
at Intervals proportiqn'd p the Times of the
Vibrations : But the Tinaes of the Vibrations of
the fsjune Body are all equal ; confequen^ly, tl^e
Intgvals of the Pulfcs will be fo too. (CV.)
(CV) I. Sir Ifaac Newion and other Mathematicians have
. ihewn {in a Method too prolix and intricate to be here re-
peated) that if a Pendolam were conftra6led whofe Length
was equal to the Height of an homogeneal Atmofphere, whofe
I>.enfitx is ever)^ where the fame with that of the Air upoi^
the Surface of the Earth, in the fame Time that fuch a Pen-
dulum makes one whole Ofcillation in goii^g forwards and
backwards, the Wave or Pulfe of Air ij^ill pafs through ^
Space equal to the Circumference Qf iTCircle described witl|
a Radius equal to the fai^d Pendulum.
2. Therefore while the Pendulum makes half an O/cflla-
tion, or one fingle Vibration, the PuHe will move through a. .
Space equa} tQ half the Ciicmiference : Whence the Space
defcribed by the Pulfe in the Time of a Vibration b to the
Length q^ the Pendulum as the Semi-circumference to the
Radius, or as tl^e Cirpumference to the Diameter, that is, as
3^14159 to |. Now the Leneth of fuch a Pendulum b
30100 Feet/ (as we have clfcwhere fliewn) but Sir Ifr^
makes it 297x5 Fe^, whofe Meafore we (hall here fellow.
The Circumference of a Circle whofe Radius b 29725 i^
186768^ the Half whereof b 93384 =: Space a Pulfe pdles
through in one fingle Vibration : Bat fince a Pendolam 39,9
ofcill^tes in the Time of one Second, and the Times of Ofcil-
lation in different Pendulums are in the Subduplicate Ratio of
thcif Lengths; therefore, fincc in 29725 Feet we have.
356700 Inches, we muft fa^. As ^39.^ : V356700 :: i :
95 1 Seconds. But in that Time the Pdfe paffes over 93384
F^eti cqnfequently, 95^ : 93384 :: i :''979 Feet = SpacQ
pafs*d through by a Pulfe in one Second of Time.
3. This then wo^ld b^ the Velocity of the Pulfes« were
the Ps^rticles of Air fo y^ry fmall as that their Magnitude
ibould bear no fenftble Proportion to tbci Intervab between
them ; and 9,\(o if the Medium had no Admixture of any
other Particles but thofe of pure Aic: Neither of which is
the Cafe ; for the Particles of Air are fo gro(s that they will
not pafs through the Pores of Glafs any more than Water ^
a^d Sir I/cntf Nevjta^ fuppofes them to ^ of th^ laii^c Mag-
G ^ V. r6#
I02 Of Winds and Sounds.
V. ^he aerial Pulfes are propagated together in
great Numbers from different Bodies without Bif-
turbance or Confufton \ as' is evident from Con-
certs of Mufical Inftruments, where divers
Sounds, of different Intervals and various Coin-
cidences, ftrike the Ear at once, yet with Di-
liitade with the Particles qT Water or Salt. If this be fo, let
'Dz=. Diameter of the Particles, S = Space or Inteival be-
tween them J then will S -f^ = Diftance of the Cefiters of
the Pa^ticlea. Let N = Number of Particles in the Side of
a Cube of Air, then will N S -j- N D = Side of the Cube.
^ 4. Again, let M = Number of Particles of Water in the
Side pf an equal Cube, and M D = Side of the Cube of
Water; whence NS + NDz^MD. Then if the Den-
fity of Air be to that of Winter as i to A, we Ihall have i :
A :: N^ : M' ; whence i : A^ :: N : M ; confcquently, M.n:
N A^. Wherefore, fmce it is N S + N D == M D = N D A^,
it will be S + D = D A^, and S = D x A^ — i j there-
fore D : S :: i : A^— i ; whence D : S + D :: i : AX
5. If therefore A = 860, (as we have Ihewn) then
A"^z= 9 nearly; if we put A =1000, then A^= 10,
Whence D : S-J-D :: i -9, or as 1 : 10 ; whence the Di-
ameter of a Particl^ of Air will in fuch a Cafe be to the In-
terval between the Particles as i to 8 or 9. And fmce the
Motion is indan^neous through the folid Particles of Air, and
they make up -J or ^ Part oi the whole Space 979 Feet pafs!d
tlirough inronc Second by a Pulfe, therefore to a*low for thia
we muff add — ' or 109 Feet to the former Sum ; that is
9 . ,
979-}- 109 ==: 1088 Feet, for the Velocity of Sound per
Second. ^ -
6. Butfincethe Atmofphere confifts not of pure Air, but
feis an Admijrtdre of Vapours of a different Elaflicity and
Tone ; thefc Vapours will not participate of the Motion of
pure i^ir, by which Sound is propagated; in like manner as
ah elaflic Suing, if flruck, will not move another very near
at, unlcfs it be under the fame Degiee of Ten/ion, and of the
fame Tone. Therefore the Quantity of Air producing Sound
jmufl be dimiriifti*d in proportion tb the Quantity of Vapout,
* ftindnefs
Of Winds and Sounds. 103
ftinftnefs aiid agreeable Confonance.
VL The Particles of Air^ and confequentfy the
PulfeSj ftriking againji an Obftade^ will be refleSled
back Tinder an Angle equal to that of Incidence ; in
the fame manner as will be ftiewn in regard to
the Rays of Light. Hence a Repetition of the
in a given Spa^ce ; in which Sir Ifaac fuppoTes the Air is to
the Vapour as i o to i . Whence the Air and Vapour together
in a given Space is to the pure Air as 1 1 to lo.
7. But the Velocity of the Pulfes will increafe in the Sub-
duplicate Ratio of the diminiih*d Quantity of Matter, that is,
in the Subduplicate Ratio of ii to lo, or in the entire Ratio
of 21 to 20, (as he has (hewn, Piincip, Prop. 48. Lib. IL)
Therefore, if we fay, As 20 : 21 :: 1088 : 1 142 ; whence
the real Velocity of Sound (thus inveftigated from the Nature
of elaftic Air by our great Author) is at length found to.be at
the Race of p 42 Feet per Second.
8. The Truth and Accuracy of this noble Theory have
been fu$ciently confirmed by Experiments, particularly thofe
inade by the lace Rev. Dr. Derham^ of which I ihall give fome
Accoant by and by ; but will firft lay before the Reader a
View of the diiferent Eftimates made of the Velocity of
Sound by feveral eminent Philofophers^ as in the T^Ue foU
lowing.
Fief per Second.
The flonourable Mr. Rqberts^ 1 300
The Honourable Mr. BtyU, 1 200
yiv.lValkir, ' 1338
Merfennus^ , '474
The Academy at Florence^ 1 148
Royal Academy at ?arU^ 1 1 TZ
. Sir Ifaac Nenuten^ Flamfiead^ '7
Hal/e^, Sind Dirbam^ ' S '^
9. As no Man ever had a better Opportunity, fo none could
improve it with greater Diligence, Afliduity, and Accuracy,
in determining and fettling the various Phenomena of Sounds,
than the fo often celebrated Philofopher laft mentioned. He
proved by Experiments made with the Strokes of a Hammer«,
and the Explofion of a Gun at the fame time, at the Diftance
of a Mile, that the Velocity of Sounds produced from dif.
ferent Bodies was the fame, or came to his £ar in the fame
Time.
G 4 Sound^
^P4. Of Winds ^7id Sound^.
^ouni, heand by the dijr.ift Pulfes, will bp mad§
by thofe which are refleaed ; which is whaf we
c^I an Echo.
?^i6(? LOcirs, cr audible Place of Sonnd^ will be
there where the Particles of Air firft begin to
diffufe tl)efnfcl^es in J^orii) of Waves, Thus, a
|o. That the P/Iotion of Sound was equable and uniform
Of that it pafs'd through Spaces proportioparto the Times, he
found by various Experiments made by 'the Exp!ofion orGuhi
^t different Diftances, as appears by tr.c following liable which
he has given us: Where the firll Column (hews the Places
at which the Guns were fired ; the fecond theNumber of Vi-
l^rations of an Half^Sccctnd Pendulum; the thira theDillahce
of the Places in Mila ^nd decimal Parts, as meafiircd by Trf-
gonprnctryj tjipfounh the Dillanteb meatUred by the* Vclo.
city (?f Sound, admitting it to be at the Rate of one MU'e
every 9^ Half Seconds.
y.W*C«.»^ Church. ,|. _ ^^^
J:<veim\, 1^* _ 3.58 -• 3.S9
D^^hammW, {\ _ \i. _ I'll
1 1. Til? great Exaftnefs of meafuring Diftances by Soands
liruHJT ?^ '^'^v« Tabl«.a, -well.a, the EqmlbUity of
the Motion 5 bat to render this Matter ftill moreceitain and
Ihl ??„ ?''f t/r^°^" '°°'*"» J°^'y '«> ^'"Vi Sands on
S^Uo^^v^^' :*'"•''' ^°™ * fi»°«'?> (W Plain fo?
Miles. On this Plain he meafured 6 M^le in alright Line!
Slfl »»« former Obfervations were very joft and ^e.
Sis n^g" r'^lr'-^^^" Milein'9iH2lf-Seconds. twd
Ihc "x '? " ^''*' *" '7f. |nd fr on jo the End of
!?•' "^-^ "^f!*"'? ^f^Cimt^fo jna^e E3q)f^pnts of dii*
Of WiNps and Sounds. 1Q5:
Berfon fpeaking in one End of a Tube, or Tnim-
pepy will be heard ^ fpeaking from the other.
Serty from whence they concluded, that the Velocity of Somidt
was fo far equable, as not' to be accelerated or retarded by
confpiring or ad verfe Winds; but in this they led themfelvet
and many others into a great Mifiake, which ' was owing to
tHeir firing Guns at too near a Difbincc ; for in great Diftancos
tKe Difference is fenfible, as will appear by the ibUowii^Tai-
l?ie of many Experiments which the Doflor made on the Qunt
fired at Blkckbeatb^ at the Diihnce of' twelve Miles 6om hit
Houie at Upminfter.
JQ: H. Fihrat. Whd.
1704. ft*. 13. 6toi2N.— ^J^^]^— N.E.byB. I
21. iiJM. — 119 — E. 2
S. W. 7
S.byW. f
S. 4
S.W.byW.7
N.byE. 2
S.W.byV)^. Q
W. 2 ^
W.byN. 2\
S.S.W. 6
E. S.E. 1,2
S.S.W. 4
S.byW. I
/: V .^y"iM. — 116 — S.W. o
^7^6.iV^.29-^Noon' - ii8 ^ S.W.l^yS. i
Feb. 7, ' Noqn -^ 113 — S.W.by W. 4
1 3 . In the firft Column of thi< Table M denotes the Morn-
ing, pM the Afternoon, and N Night : Alfo the Figures ij,
2, 3, 4, 5, 6, 7, ^ffix*d to the Points of the Wind in the third
Colunm, denote the feyeral Degrees of Strength with which
the Wind ble^ at the Time when the Experiments weie
IDad^. Fr<^ this Tj|l)le it is tafj tQ obferve, that in this
large Diilance (of near 1 3 Miles) the Velocity of. Sound is
fenfibly afFedcd with the Current of the Air or Wind; for
lince Blackheatb lay near S. W. by W. from Ufminfter^ we fee
that on j^lnil 5. 1705, when there was a fbdng Wind con-
fpiri|>g With the Sound, it came in 1 1 1 Half-Seconds; where-
as in Feb, 13. 1704, when the Wind was diredlly contrary,
Ibeugh but a gentle onc« the Sound took up nolefithan lao
1705. Jl*w. 30. 10 M.
—
113 —
Jfr. 2. 8ipM.
—
ii4i-
3. 10 M.
—
ii6i —
J. I pM.
-^
III —
13. 8|M.
— '
I20 —
24. SP^-
—
,,6 -
S.^.,..{6ipM.
•~"
11$ —
115J —
29. lol M.
— •
iiz —
oa. 6. 10 M.
—
"7 —
Nov, 30. Noon
—.
115 —
Feb. 15. II M.
—
116 —
Xo6 Of Winds and Sounds.
And as in the Cafe of Light, we fee the Image
of an Objeft always in the Direftion of the re-
9nd 122, Half-Seconds in pa/Hng the £une Diflance. The fame
18 confirmed alfo by the Experiment on April 1 3, 1 705. .
14. And it is farther obfervable, that the Acceleration of
Sound depends on the Strength of the Wind ; for on April 24,
1705, a S. W. by W. Wind in the lowed Degree permitted
the Sound to arrive in 1 1 6 Half-Seconds ; the fame Wind on
, Feb. 4, 1 706, blowing with 4 Degrees of Strength, brought
the Sound in 113 Half Seconds ; and on April 5, 1705, the
fame Wind with 7 Degrees of Strength brought the Sound in
1 1 1 Half- Seconds. The Winds which blow tranfverfcly (as
on^/r//3, February 15, 1765.) feem not to afFedl the Velo-
city of Sound, it paffing then in 116 Half-Seconds, which
^ is the 9iean Velocity, as appears by the former Table in Ar-
tide 10.
15. Thegreateft Difference we here obferve in the Velo-
city of Sound, with or againll the Wind, is 10 or n Half-
Seconds, or 54, Seconds; whence 1142 x 5,5 = 6281 Feet,
which Js foniewhat more than a Mile = 5280 Feet; and
therefore for every 10 Miles we may allow Half a Mile,^ or
2^40 Feet, when the Wind blows ftrongly againft the Sound,
and deduft the fame when it fets with it ; and fo in Propor-
tion for any other Diftance.
16. The Velocity of Sound being determined, the Inter-
vals of the Pulfes are known by finding how many Vibrations
the founding Body performs in one Second. Thus D. Sau-
veur found by Experiments, that an ojpen Pipe, whofe Length
\va5 about 5 Paris Feet, had the fame Tone with a String that
vibrates forwards and backwards 1 00 times in a Second ; con-
fequently, of the Pulfes made by founding fuch a Pipe, there
are about 100 in the Space of 1 142 Feet, or 1070 of Paris ;
and therefore a fingle Pulfe occupies the Space of i i-j^% Feet
Englijh^ or io-,% Feet of Paris-, fa that the Length of the
Pulfe was about twice the Length of the Pipe. Whence it
is probable, that the Lengths of the Pulfes excited by the
founding of open Pipes are in all Gafes equal to twice the
Length of the Pipes. '•
• 17. This was farther confirmed by the fame GentJeman by
another Experiment he made afterwards, in which he found
that an open Pipe, of about two Paris Feet in Length, was
in Unifon with a String which vibrated forwards and back-
1070
wards 243 times in a Second; wherefore — ^ =: 4I neady ;
flcfled
Of Winds and Sounds. 107
fkAed Ray •, fo in Echoes^ we hear a Perfon fpeak
at the Place from whence the refleded Wave
comes to the Ear (CVI.)
that is, the Length of a PuUe was aboat 4^ Feet of Ftitis^ or
nearly twice the Length of the Pipe.
(CVI) In order to account for the Nature of Echoes, we
mufl confider, that Sound is perceived as coming from that
Place, from which, as a Center, the Pulfes are propagated.
This is well known by Experience : But to illufbate this Mat-
ter, let A be the Center from whence any Sound is diredly ^Ig^xt
propagated, and ftrikes againil any plain Obftacle CB, fuffi- XXKllL
ciently large; draw AF perpendicular to BC, and produce ^i^ q
it to H, fo that it may be A F = F H ; - the Sound reflcfted
will be perceived as coming from thq Point H.
2. For let AB be the incident Ray, impinging agaiofl the
Obftade BC in the Point E ; fr6m £ draw the Ray K D, in
fuch a manner that the Angle C£D may be equal to the hn^
gle £ FA, or that the Angle of Incidence may be equal to the
Angle of Reflection; then will ED be the receded Ray of
Sound, and, if produced, will pafs through the Point H ; for
the Angle FEH = CED = FE A. Therefore in the Tri-
angles AFE and EFH, fmce the Angles of one are re-
fpedively equal to the Angles of thex>ther, and the Side F£
common to both, the Sides of one Triangle will be refpedive-
ly equal to the Sides of the other, and therefore HF =: AP ;
wherefore the reflex Sound will be heard by a Perfon at D,
as coming from the Point H.
3. As the Place of the Auditor or Point D approaches to-
wards A, the Cafe will conftantly be the fame with refpedi to
the Center of Sotund H ; the Triangles will dill be equal, and
all their Angles and Sides re(pedively ; therefore when Deo*
incides with A, the reflex Sound, or Echo, will be heard from
the Point H; which was to be demonfbated.
.4. The fame Sound therefore is heard twice by an Auditor
at D ; firfl by the dure£l Ray A D, and fecondly by the reflex
Ray AED ; provided the Difference between AD and AED
be fufliciently great, that the dire^ and reflex Sound do not
in the fame fenfible Moment of Time affed the Ear : For if
the reflex Sound arrives at the Ear before the Impreflion of
the diredl Sound ceafes*, the Sound will not be double, only
rendered more intenfe.
5.* We know hy^ Experience, if more than 9 or io Sylla-
Becaitse
ip8 Of Winds and Sounds.
Because tte Sound is ftronger in proportion
as the Air is dcnfer, it muft follow, that the
Voice pafllng through a Tube or Trumpet muft
be greatly augmented by the conftant Refleftion
an4 Agitation of the Air through the Length of
the Tube, by which it is condenfed, and its Afti-
bl^ are pronounced in a Second, the Sounds will not be ^'
iiin^ and articulate ; therefore, that the ref]ex Sound may not
be confounded with the diredt Sound, there ought to be at
lead the 9th Part of a Second between the Times of their
Appulfe to the £ar. But in the 9th Part of a Second Sound
1 1 ^2
runs through the Spaceof — — =127 Feet ; theBiffercnpc
9
therefore between A D and AED muft not be lefs than 127
Feet, for the Echo to be diftindly heard in D.
6.' Hence alfo it follows, that a Perfon ipeaking or utter-
ing a Sentence in A aloud, in order to obferve the Echo by
ReHedtion from the Obflacle BC, ought to ftand at k9(l 73
or 74 Feet from it, that is, AF=: 74. And iince, a t the
common Rate of Speaking, yft pronounce not above i \ Syl-
lables ftr Second (or read more than 20 Lines of Engiip Poe-
try per Minute) therefore that the Echo may return juH as
(con as the 3 Syllables are exprefs'd, we muft have twice A F
equal to about 1 000 Feet ; or the Speaker muft ftand about
500 Feet from the Obftacle C C ; and fo in Proportion foe any
Qther Number of Syllables.
7. In all the Experiments which Dr. Btrham made with the*
Gtfns at Btackheath^ there was always a Reduplication of the
Sound, particularly the £cft in the foregoing Tabl^*, on Fehru-
ary 13, \ 704; where the di|ed Sound came iirft in 120 Half-
Seconds, and the reflex Sound or Echo in 122 Half-Seconds.
TheDifterence in Time, being a whole Second, {hews the Echo
pafs'd over 1 142 Feet more than the diredt Sound ; and that
therefore the Phonoc4tmpt$c Ohji^^ or Obftade which reflcfted
the Sound, was very probably near the Guns ; fmce after the
Fnlies had pafsM a great way, they would hzv^ been too
iveak, when refle£led, to have made an Echo as ftrong oc
ftronger than the diredt Sound, as the Docior^dways^ found
it was.
8. By fome Experiments which he made on Guns fired on
the River Jbames^ between Drptford and Cuckold's- Point, ho
^bfery'd the Sound wa^ not only dou|pled, but tripk(l,'qua-
on
Of Winds and fiouNiis. 16^
oii on the external Air greatly inereafed at its
Exit from the Tube ; which from hence is calPd
the Sttntorophonic Tube^ or SpeMn^-Trumpet.
For the fame Reafon, thofe Funncl-likc In-
ilmments, which gather the larger and more
languid Waves of Air, do greatly condenfc them,
drapledy and fometi/n^^ rej^eated man^ mor^ iimd, Ind each
fucceediog £cho was louder and louder; aAd ofti^ wben He
Iieard thofe Fragors of great Guns» he obferved a Murmur
aloft ifi the Air, efpecially if the Heavens were ^uiet ifnd fb-
rene : And thofe Pulfes of Air he has obferved to ftrike againft
a thin Cloud, and produce in it a Murmiir for the Space of
1 5^^ From hence he judged, that thofe Murmurs in the Air
proceed from the vaporous Partkies fufpendcd in the Atmo*
sphere which refill the Undulations of Sound, and reverbe^'
rate them to the Ear of the Obferver, in the Manner of in*
definite Echoes.
9. Among the many pleafan^ aiid ludicrous Phaenomena of
Echoes^ thofe which are Poijpbomus^ or repeat divers Syllables
or Sounds diflin£Uy, and are therefore ^'d TauHlt^cal or
Prattiiug Echeitf affi>rd the moft curious AAMifement. Of
thefe there are feveral remarkable in dilFefent Farts of the
'World, and particularly here in Englamdi concerning which I
refer the Reader to Harris'^ or Cbamhirs*% Dictionary un-
der the Word £r^y or to my PHrLOsoPHiCAL Grammar.
10. Nor is this merry Phsenomenon of Sound withoat its
Ufe ; for by means of an Echo you may meafureinacceffibte
Difbnces, the Width of large Rivers, faTf . Thus Dr. Drr-
ham (Unding upon the Bank of the names ^ oppofite to W^oi*
nuicb, obferved that the Echo of a fingle Sound was reflected
back from the Houfes iki 6 Half-Seconds, or % Seconds ; cqn-
ftquently, 1142 x 3 = 3426 Feet; the Half of which,
nrix. 1 71 3 Feet, is the Breadth of the River there; which ii
iBore tha n a Quarter of a MDe^ or) 1320 Feet.
1 1 . After this fame Manner we find the Meafure of any
Ucpth, as tliat of a Well for Inftance. To do this, let « .=5
Space an heavy Body falls freely in one Second of Time, b =^
Space through which Sound moves in the £ime Time, and
c zz. Time given in Seconds from the firft Defcent of the Stone
to the hearing of the Sound, and ;r = Depth of the Well
icquh-ed, * ,
and
no Of Winds and Sounds.
and heighten their Power and Aftion on the
Drum of the Ear ; by which means Voices and
Sounds are rendered ftrong^ loud^ and audible^
which were net fo befofe to a deafened Ear; and
hence thefe Inftruments come to be' call'd Ota^
coujiics. . ,
12. Then to find how long the Stone is in defcending to
the Bottom oi the Well, fay, A& a.x :: i"^ :t«* = ^=:
a
Square of the. Time / in which the Deicent is made, becaufe
the* Spaces d^fcribed by falling Bodies are as the Squares of the
Times, [Annot. XXVI.) wherefore /=V— .
r j; Again, to find the Time t in which the Sound afcends,
fay, As h'.xii i" : t^ ;=; -p ;:z the Timefou^t in Seconds;
b
''XX % 'X
but/-l-t = c = i/ J--7-; therefore ;^ + ^l/—=Ar.
Bnt h V — =B77=- V oc ; and fince x is.the Square of V^;«',
a V a V . .
the foregoing is a Quadratic Equation ; and, by compleating
1. *. ' 1. .. h ^^ ^ bh bh , ,
the Square, we have x + — rrii v x A =i |-^f=z
bb+^abc _ s^ . ,j^i,b + ^abc): Whence
extrafUng the Roots on each Side we have v ;r* + ,- =^
=!= — 7=, that is, vT*:^ — — ~— But x cannot be
a negative Quantity; and therefore it cannot be V^at ;;=
*— ^ — f . ^ — ^ + j
>— , 1t)ut muftbe V^ ;r = ^— • Therefore x =
1. ■■ =: die Depth of the Well required..
4^
14. Now a = 16,122 Feet, and 3=1142; whence ^a
. = 64,488, and ^3= 1304164s alfo 44^=173646; aiod
t I SHALL
Of Winds and Sounds. hi
I SHALL only obfervc, in regard of thofc In-
ftruments which magnify Sounds, and aflift the
Hearing, that the longer they au^ the greater is
their Effect \ and that of all the Forms or Shapes,
none is fo good as that derived from the Revolu-
tion of the Loo A Ri THYMIC CuRV£ nhout its Axis
(CVII.)
if we fuppofe r= lo^, then j^ahc z=. 736460, and hb-^
j^ahc =: x/-=z 2040614. Wkence / =: 142^,5 ; and / — b
1*
±=286,5 J aadx — ^*=: 82082,25. Confeqaently =
1 273 = 4f ; or the Depth of the Well is 1 273 Feet.
ic. Since jr=i ill- , w« Audi have V^jr ==: — 7=5
^ 4tf 2t/a
^ X s h i^'jr
and therefore — ^^ = z=, divided by 4/ ^ , that i«, Z^
\^ a iV" a y/ a
=:im- = ^i^ = %M Seconds, the Time of the Stone's
^a 32,24
Defccnt to the Bottom of the Well. (See Art. 1 2.)
* 1 6. The Time of the Sot^nd's Afcent is •-► sx sa
o /^ab
?^^l^'/^ = I ,M of a Second, But 8,''89 +1/11 = Io^
73646
the whole Time, as it ought to be.
(CVir.) I. The Stenforophomc Tu^, cr SpeaiiMg^Trumfee, pj^^^
IS ufed for magnifying of Sound, particularly that of Speech, y v vjy
and thus cauung it to be heard at a great Diftance, how it p- ,
docs this will be eafy to underHand from the Stmdive there* ®* ^'
of. Let ABC be the Tube, BD the Axis, and B the
Mouth-Piece for conveying the Voice to the Tube.
2. Then *tis evident when a Perfon fpeaks at B in die
Trumpet the whole Force of his Voice is fpcnt upon the Air
contained in the Tube, which will be agitated thro* the whole
Length of the Tube; and by various Reflexions from the
Side of the Tube to the Axis, the Air along the middle Part
of the Tube will be greatly condenfed, and its Momenium
f roportionabfy increafed, Co that when it comes to agitate the
From
iii t)/" Winds ancl Sounds.
From the fourth Property of the aerial Ptilfes
^e have the Origin of the various Degrees of
what we call the Not e; To ne, or T une of
Sounds, in regard of Whidh they are diftinguifh'd
into Icliv and higby or grave and acute^ by Mtifi-
cians call'd Flats and Sharps. Now the Tone
of a Sound depends on the Time or Duration of
the Stroke made on the Dhim of the Ear, by a
Wave or Pulfe of Air ; for as that is longer or
fliorter, the Tone will be move graive or acute :
And fince all the Pulfes move equally fwift, the
Duration of a Stroke will be proportional to the
Interval between two fucceffive Pulfes ; and con-
fequentlyi a Sound is mort or lefs Gripve or Acute
in proportion to tbi Length of that Interval.
Air at the Orifice tit the Tube AC, its Forte will be H
much greater than what it would have been without the
Tube; as the Sur^ce of a Sphere, whdfe R^ius is equal to
the Length of t&e Tube, is greater than the Surface of the
S^finnent of fuch a Sphere whofe Bafe is the Orifice of the
' Tube.
3. For a Perfon fpeaking at B, witKdut the Tube, will harfe
the Force of his Voice fpent in exciting concentric Super-
ficies of Air all around the Point B ; and when thofe Super-
ficies or Pulfes of Air are diffufed as far as D every way^ *tis
plain the Force of the Voice will there be diffufed thro' th«
whole Superficies of a Sphere whofe Radius is B D^ but in
the Trumpet it will be fo confined, that at iu Exit it will be
difiFufed thro* fo much of chat fpherical Surface of Air as cor-
refponds to the Orifice of the Tube. But finee the Force is
t^ven, ks Intenfity will be always inverfely as the Number
of Partides it has to move; and therefore in tiie Tube it wiU
:be to that without, as the Superficies of fuch a Sphere to the
: Area of the large End of the Tube nearly.
4. To make this Matter yet plainer by Calculation i Let
B D = 5.Feet, then will the Diameter of the Sphere D£zr lo
Feet, the Square of which is 100, which multiplied by 0,7854,
gives 78,54 fquarc Feet for the Ajrea of ^ great Cirelt
Of Winds and Sounds^ 113
Hence ic follows,* that all the Sounds from the
ioudefi to the loweftj which arc excited by the Vi-
brations of the fame Body, are of (Ate Tone. Jc
likewlfe follows, that all thdfe Bbdie^ whofe Parts
perform their Vibratiohs ih the fame or equal
Times, have the faille Tone : Alfo, thofe Bbdies
which v\hx2X& Jloweft have the graveft or deepefi
Tone ; as thofe which vibrate qtlickift have the
Jharp^ of Jhrilkft Tone.
The Times of die Vibrations df Muficai
Strings-^ arid confequcntly the ToneSj vary in rc-
fpt&, of the LeHgtbj the MdgnUude^ and die Ten-
Jon of thofe Strings. For if two Strings A B, pj^^^^
CD, are of the fame Magnitude, and ftretch'd XXXV.
by equal Weights E, F, have their Lengths as ^* '•
AHE FC; And tWfoit 4 dmte that Area. vi£ ^nyS,;4,zs:
^14,16 =: fquare Feet in the Superficies of the Aerial Sphere;
If now the Diameter A C of the End of a Trumpet be ond
Foot, its Area will be 0,7854; but, 7854: 314,16:: 1:4009
therefore the Air at the DiAnnoe of B D Will be agiuted by
means of the Trompet, With a Force 400 times greater thaa
by the bare Voice aldnd.
. 5. Again, *tis farther evident how Infboments df thb Form
affift the Hearing greatly; for the Weak and buigaid Pdfes of
Air being received by the large End of the Tabc, and greatly
maltij^iM and condenfed by the tremulous Modon of the
Parts cff the Tube and Air agitated by them, are conveyed to
the Ear by the fmall End, and flfike it With an Impetus a^
^ttch greater than they would have done without it, as th«
Area of the fmall End at fi is leTs than the Area oi the large
End AC.
6. From what has been Aid, *tis evident the Effed of the
Tube in magnifying Soiind, either for Speaking or Hear*
ing> depends principally upon the Length of the Tube.
But yet fome Advanuge may be derived from the particular
Form or Shape thereof. Some very eminent Philofophers
have propofed the Figiire which is nuide by the Revolution
of %ftiraiQla about Itt Axis at the belt of any; where the
Vol.. 11. H 2 to
ri4 Of Winds tind Sounds*
2 to I, the Times of their Vibrations will be in
the fame Ratio. Hence the Number of Vibra-
tions of the two Strings. A B, CD, performed in
the fame Time, will be imrerfely as their Lengths ;
ot C D will make two Vibracion^, while A B per- .
forms one. The Vibrations of two fuch Strings will
. therefore co-infcide at every fccqnd of the leffer.
Fkr. i. Again : If two Strings of the 6me kind A B,
C D, have their Diameters a$ 2 to i , and are of
eqiial Length, and tended by equal Weights
E, Fi the Tims of the Vibrations will be as their
Diameters i viz. as 2 to 1 3 and fo the Vibrations
in a given Time,- and the Co-incidences, as bc^
fore*
Lastly: If the Diameters ^id Lengths of
Mouth-Piece is placed in the Focus of the Parabola, and con^
fequently thQ fonorous Rays will be refleQed parallel to ^ the'
Axis of the Tube, See the Figure of fuch a Tube in Jku/^
tbinbroek'% Effai de Piyjique.
7. But this, parallel Refiedlion &ems no way eflential to the-
magnifying of Sound ; on the coatrary, it appears rather to.
hinder fuch an £iFe£l, by preventing the infinite Number of
Reflections and ReciprocaticMU of Sounds in which^ according
to Sir Ifaac Nitvion^ its Augmentation does principal^ ^odift. .
For all reciprocal Motion, in every Return, is augmented by^
its generating Caufe^ which is hers the tremulous Motion of
the Parts of the Tube. Therefore in every Repercuifion
from the Sides of the Tube, the Agitations and Pulies of the*
confined Air muft neceffarily be increafed; and cohfeqaently
this Aug^ientation of the Imfituj of the Pulfes muft be pro*
portional to the Number of fuch Repercuffions, and therefbror
to the Length of the Tube, and to fuch a Figure as is moft
produdlive of them. Whence it appears, that thg ParmhoUt
trumpet is tf all others the tnofi unfit for this Purpefe, indead-
of being the beft.
8. But there is one Thing more which contributes to th«
Augmentation of thofe Agitations of {i\x in the Tube, and
that 18 the Proportion which the f^veral Por^iojii of Air beai uy
the
Of Winds and Sounds. t i ^
the Strings be equal, tht Times of the Vibtatiohs
^ill he inverfily as the Square Rootis of the Weights
which Jlretcb tbfffi. If the Weights E and F be
as I to 4 (the Square Root$ of which are i and
2) then the TinnLCS of Vibration in A B and C D Fig. ji
will be as 2 to I. Hence in conJlruHing firing^ d
i^ruments^ as Spinets, Hari^sichords, &fr. a
Ikilful Attift will compound thcfe Proportions of
the Letigihy Diametefy and Tenfion of the Strings
10 very great Advantage.
In Wind'IfiftrUmentSy as the Flute, ORCA^i
fe?r. where the SoUnd is made by the Vihration of
a Column bf elafiic Ait contained in the Tube, the
Time of Vibration or Tone of the Inftrument
Will alfo vary with the Length and Diameter of
Jbach other when divided by banfVeHe Se£Eions, at very fmali
but equal Dilhtnccs, ftoin one End of the Tube to the other.
Thus let thofe feveral Divifions be made at the Points a^ h, c^ P^^te . .
1/, r, &c. in which let tlie Right Lines ak^hl, cm, dn^ &c. be XXXIV.
taken iif Geometrical Proportion. Then will the Portions of ^^g- 6;
Air contidned between B and h, i» and ^, ^ and r» r and d. Sec.
be very nearly in the fame Proportion, as being in the fame
Ratio with their fiafes when the Points of Divifion are inde-
finitely near together. '
9. Bat ft has beeil ttievm already, that wiieli any Qoan*
tity df MMi<m is comtnanicated to a Sfeties of eiafUc fio-
^eaf, It will deceive the greateil Acrgmeatadon when thofe
Bodies Bre in GedJM^idai Proportion. Therefore fince the.
Forte of theVok^^ is impreft*d upon and gndoally propa*.
gated throQgh a Series of elafiic Portions of Air in a Geome*
^ tricai Ratio to each othef ^ it ihall tecelve the greateft Aag«
ixfentation pefflble.
to. N^w finc« by CO|iftm£lion it it Ba = tf^ = 3r=^
tdt ^t. and ^fo at : hi :: Bi : cm :: cfm : dn, and fo on ;
tha-efore the P<nnti k, I, m^ »» '» /t i^ f, ', A, will ih this Cafe
^orm that Cur^ Ihe Which is call'd the Log^bitbmitic Curvi :
Confecjuently, i, Trumpet formM by the Revolution of this
Curve about its Axis wUl augment tht Sound In a grefttcr De .
H 2 the
ii6 Of Winds and Sounds*
the faid Column of Air, and Force of fbe Voice,
which comprcffes itj as will be eafy to obfervr
from Experiments.
If one Body be made to found with another,
their Vibrations will co-incide after a certain In^
Cerral \ and the iRorter the Interval of the Co-
incidence, the more agreeable is the EfFcft or
Confonance to the Ear; confequently, thofe
which are molt frequent produce the mod per-
feft Confonance or Concord, as it is commonly
calPd. When the Times cf Vibration, there-
fore, are equal, the Concord is moft perfeft and!
more agreeable than any other, and thi^ is calfd
Unison'.
If the Times of Vibration are as i to 2, the'
^o-incidencc will be at every fccond Vibration of
the quickeft, and fo this is the next perfect Cort-
cord, and is what we commonly call as Diapa-
son, or Octave.
If the Time^ of the Vibration be as 2 to^ 3,
grce than any other figured TuBe whatfoever.
II. But to^ftiiew the Reason of die JV^^/ttT^^WATaMv of this
Curve, fuppofe the folbwing Series of Quantities ifl Geome-*
trical Progrcflion, viz a? : «' :•«* : «' : «* : «*, &c. then \^
is plain the Ratio of ^2' to a^ is i, the Ratio of i^* to a^ 18^2^
the Ratio of a^ to A^ is 3, andib-on; whence it appears, thac
the Indices of the feveral Terms exprefs the Ratios of thofe
Terms feverally to the firft, and are therefore their Logarithm$,
Now if in the above-mention'd Figure we put the Ordinate*
akz=i a? '=^19 i/=;«* = tf, cmz±a*:zzaa^ Sec, then
will the intercepted Parts of the Abfciffa be B ^ 1= i , B^ = 2^
B< =: 3» C^^f And therefore the Logarithms or Expomnts of
the Ratios of thofe feveral Ordinates to the firJl or Unity.
Hence the Curve which connedls thofe Ordinates is call'd the
Logarithmitical or Logifiic^ Qw'Vi,
th?
Of Winds and Sounds. 117
tke Co iiKideace will be at every third Vibradon
of the quickcft -, which therefore is in the next
Degree of Perfeftion, and this v^ callM a Dia-
FEWTE, or Fifth. If the Times of Vibration
are as 3 to 4, the Co-incidence will be at every
4di of the lefier; and this is call'd the Diates-
SARQN, orFouRTa. But this, and the next
which follow in Order, are not fo agreeable and
plealant to the judicious Ear, and are therefore
caird Imptrfea Concords. Nor are there above
ft^en Notes in all the infinite Variety of Tones, ,
which can merit a Place in Mufical Compo(itions«
and they are exhibited in Fig. IV. which repre- flatc
fcnts the Strings in an Oftave of a Harpfichord, XXXV.
with the Semitones or Half-Notes^ call'd Flats and
SharpSy by which the natural Notes are made half
lEi Note lower or higher, as the Air of the Song
or Mufick requires. And this is eallM the Pia-
TONic Scale of Mulic.
In this Scale, the feven natural Notes are
mark'd on the Keys by the feven Letters C, D,
E, F, G, A, B. The firft of which is caird the
Fundamentai or Kevj the reft in Order are the
Second GreatiTy fhe fbird Greater^ the Fomrtb
Greater^ the Ftftb^ the Sixth Greater ^ the Seventh
Greater^ and then the Eighth^ which begins the
next Oftave. Between thefe are interpofed the
five Semitones^ viz. the Second Lejfer^ the Third
Lejfer, the F^urtk Lejfer^ the Sixth Lejfer^ the
gfuentb Leffer. Thefe fcveral Tones and Sdni-
tones have the Lengths of the Strings adjufted
from the Divifion of the Monochord^ ar Lii*
H 5 divided
Ji8 Of Winds and Sounds*
divided into lop or looo equal Parts, as is very
eafy to apprehend fronfi the Figure.
The Number of thofe Divifions are alfo (hewn
for each String, by the firft Series of Numbers
pn the Strings \ the next Series fliew the Propor-
tion of the Length of each String to that of thp
Key^ or Monocbard*^ and confequcntly the Num^
bcr of Vibrations of the Fundamental and each
String refpcftively, pcrform-d in the feme Time.
Of thefe twehe Intervals or Ratios of Mufical
Sounds, the O&aves and Fifths are f erf eSt Con-
cords \ the third Greater, third Lefler, the Grea-
ter and Lefler Sixth are imperfeSl Concords ; the
Greater Fourth, the two Seconds^ and two Seventh^
lire Difcords ; the Fourth is in its own Nature a
perfedt Concord^ but lying between the Third and
Fifth, it cannot be ufcd as fuch, but when join 'd
with the Sixth, to which it ftand$ in the Rela-
tion of a Third. All Melody and Harmony
are compost of thefe twelve Notes-, fojf the
Oftaves above or belo\y are but the Replications^
pf the fanie Sounds in ,a higher or Jower Tone,
MELODY is the agreeable Siiccelfion of feveral
Mufical Sounds |n any fingle Piece of Mufic ;
as Harmony is the EfFed of feveral of thofe
J^ieces or P^rts of Mufic played together (CVIII).
Plate ^ (CVIII) I . In order to account for the Motion and Tone
XXXIV. of an elalHc String, or Miijlcal Chord K% iX, will be proper
Fig. 7. to confider it as tended or ftretch'd by a Weight, as F, accord-
ing to its Length, and drawn out of its right-Jmed Pofition A B,
into an oblique Pofition A D B, by another Weight, as E. The
former may be callM the Tending Force, and the latter the In-
Jteduig Force,
I . . ' Harmot
Of Winds /?W Sounds. ii^
Harmonical Proportion is that which is
between thofe Numbers which afTign the Lengths
of Mufical Intervals, or the Lengths of Strings
founding Mufical Notes ; and of three Numbers
it is, when the Firft is to the Thirds as the Dif-
ference between the Firft and Second is to the Dif-
ference between the Second and Thirds as the Num-
2. Now iince the Tending Forc^ F adls upon the String In
the Diredion DB, it may be reprefented* by the Line CD,
^yhich Line or Force may be reiblved into two others, inic. CB
and C D ; of which the former draws the String horizontally
from D to B, and the other a& in drawing the String dircdly
upwards from D to C. Therefore the Part of the Force which
ads in drawing the String perpendicularly* upwards is to the
whok Force as CD to DB; or, by fuppofing DC to be inde-
finitely fmall, as CD to CB$ becaufe in that Cafe DB =;:
CB nearly. But the Force which ads in drawing the String
upwards is equal to the Inflecting Force, becaufe they balance
^ch other. Therefore the Infleding Force £ is to the Tend-
ing ForceFas CD 0CB, or^^^^ = E.
CB
3, Therefore, putting CD = S, and 2 CB = L :;= th«
Fx S
Length of the String, we (hall have — =-t : E ; hence it fd-
lows, that if F and L are given, that is, if the Tending
Force and Length of the String remain the fame, the Idled-
ing Force £ will be always as the Line C D = S. This is coo*
firm'd by Experiment : For if A B be a Brafs Wire 3 Feet
Ipng, ftretch'd over the Pulley at B by a Weight F z= 3
Pounds ; if then £ be firft i an Ounce, it will draw the Wire
throwgh C D = f of an Inch ; if E be an Ounce, it will draw
it through CD =: f of an Inch j and fo on.
4. The String beiog drawn into the Pofition A DB has an
Endeavour to return, which is callM the Refiitutpue Forces an4
which re-ads againft the Infteding Force; it muft therefore
be equal to it, and confequently proportional to the Line CD.
Wherefore the Point D is carried towards C with a Force eve*
ry where proportional to the Diilance or Space pafs*d over.
But we have fhewn, that the Spaces pafsM by Bodies in Mo.
fion a;:e %9 thf Tiine§ and Velocities conjointly, that i? S : T Y j
H 4 bera
i20 Of Winds and Sounds.
bcrs 3, 4, d. Thus if the Lengths of Stringi be
as thefc Numbers, they will found an O&avSy 3
to 6 ; a Fifiby 2 to 3 ; and a Fourth^ 3 tp 4.
A<3AIn: Harmonical Proportion between fpur
Numbers is, when the Firji is to the Fourth as
the Difference between thefirji andSfiCon4 is to the
Difference between the Third and Fourth^ as in the
(S^e jHnotathu XXII.) s^lfo thgt the Force of moving Bodies
i? a« the Quantity of Matter and Velocity copjointTy, w^.
U^Oyi therefore 1 = V = M or TM=:SQ^ Bat
in the prefcnt Cafe Q^is a given Quantity, therefore TM is
as S ; and bepaufe it ha» alfo been ih^wn that M is as S in the
prefent Cafe of the String, therefore T, or the Time in which
the Vibrations are made, whether through greater or finallfr
Spaces, is ever the fame, or a given Quantity.
$. The Reftituent Force of the String, as it a£ls through
very fmall Spaces, may be look'd upon as uniform ; and then
the Motion generated in the String will be as the (aid Force and
Time of its adling, that is, M : £T. Now in all Cafes it is
M : QV; but here it is Q^* D*L, (fuppofing D = Diameter
and L = Length of the String) therefore M : ET : D^LY^
D* LV FS
and confcguently T : — - — j but J)eforc wf? had E : -r-*,
ii* Is
^hich fubftituted in the above Ratio gives T : "^ ■ '.Bpt
(iincc S : T V) ^e have j : ^, therefore T : ^H ; thft
is, F J* ; D?L% therefore F^ T : DL ; fpnfeqiiently, T a
i-7-. That is, the Time of a Vibratiqk is ms tl^e Diameter and
F-5 ■ • ' ■•.'.. . . '
Length of the String dire^ij^^ and as the Square Root of the
Tending Force inver/efy,
6. liehcc if D>nd F be given, T is as L ; that is, if eke
Diameter of the String and its Tending Force continue ike
fame, the Time of a Vibration at/// 'vary lixjith the Length of the
(Siring, cr be alnvajs proportional to it. Thus \ of the Mono-
chord vibrates in i of the Time that it docs, which is calFd
fih O^avei 4 of thq Mbnpchord Vibrates in \ of the Tinic,
* Ntmhrs
Of
Winds and Sounds* 121
Nufnbers 5, 6, 8, 10 : For Strings of fuch
Lengths will found an OSave^ 5 to 10 1 a Sixth
Greater, ,6 to 10 ; a Third Greater, 8 to lOj a
TThird Leffer, 5 to 6 i a Sixth Lefler, 5 to 8 ; 4
Fourth, 6 to 8,
It may be here obferved, thai a Series of
Numbers in Harmmcal Proportitm are reciprocally
and is caird a Ftfihi i vibtatti in | of the Time, and is
caird a Fourth i and fo on.
7. If F and L be given, T is as D; that is, if the Tend-
ifi2 Fo^e and Length of the String remain the (ame, tbg Tinu
tffa Vibration nutU vary 'witbi ondht proforttGnal to tbe Dia*
meter of the String.
I
S. If D an^ L be given, then T is invericly as F^; that is,
if the Diameter and Leneth of the String be given, then the
T'ime of a Yihration wjU fe as the Sfuare Roots of the Tending
9. Now as the Tope of a String depends entirely upon th^
Time of a Vibration, it is eafy to onderfhind, that whatever
th|e founding Body be, or how maqy foever there be together,
if when they emit a Sound the Vibrations in each are of th^
^me Duration, they will all be pf the fame Note, Tone, or
Tune, which is called Unrfin. ,
10, In |i Drinking-Glai'% If a Perfon paifes his wetted Fin-
ger bri(kly round the Brim of the Glais, prefling it at the iamc
|ime, he will by degrees raife Tremors ex Vibrations in the
Parts of the Glafs, which will produce a Tone or Sound, which
will be conilant fo long as the Adion of the Finger is conti«
Dued, and more and more intended or heightened : So that if
the A£Uon be continued long enough, the Agitation will be (b
. great as tq djfengage the Particles, or break their Contimiity,
^ thus reduce the Glafs to pieces, if not too ftrong.
1 1 . The ^und excited in the Gbfs feems one entire YS^^
whereas it is in reality an Aggregati^ or Affemblage of an in-
definite Number of Sounds, each effeded by each fingle Vi-
bration of the Glafs; but as the Times of the Vibrations are
fo quick and ihqct, their Intervals will be imperceptible, and
cbnfequently the Diftindion of the particular Sounds, which
will therefore be loft, and the Whole will appear but one en-
tire Sound. After the fame manner a red-hot Coal whirled
: ^ou^ makes the Apptaia^nce of a fiery Cir^c; be^ufi; the
122 Of Winds and Sounds.
as another Series in Aritbmitical Progreffiofiy
CHarmonical lo : i2 : 15 : 20 : 30 : 60 : ?
^Arithmetical 6 : 5 : 4 : 3 : 2 : i : 5
for here 10 : 12 : : 5 : 6; and 12 : 15 :•: 4 : 5 ; and
fo of all the reft. Whence thofe Series have an
obvious Relation to, and Dependence on, each
other; which in fome Problems of fpeculative
philofophy will be very ufeful to know (CIX).
Coal focceeds to every particular Point of the Circle fo quick»
that a new Impreffion is made upon the Raina before the £f»
fed of the M is obliterateid^ aud fo the Coal appears in every
Paft of the Circle.
1 2. The Tremors of the Glafs are made extremely fenfible
by potting a little Waier into'the Glafs ; for the Agitations gf
the Glafs will by degrees give Motion to the Water, which
Motion will continually be increafed till it be thrown up from
the Surface in Form of a Mid all over the Glafs, and to a
confiderable Height above it every way. It is remarkable
that the Motion'of the Water is in Form of a Vortex^ circu-
lating round by the Sides of the Glafs, and raging with impe-
tuous Waves like the Sea after a prodigious Terapeft.
13. Orotherwife thefe Vibrations of the Giafs are made
fenfible by adjofting a Screw very near the Rim of the Glafs ;
then upon ftriking the Glafs, it will immediately be heard to
ifarike againft the End of the Screw ; which will (hew not only
the Vibration of the Giafs, but a]fo that in vibrating the Forih
IS altered from circular to elliptical.
(CIX) I. Let A, B, C, be three Numbers in Mufical Pro-
£>rtion ; then becaufe we have A : C :; A— B : B— iC, there-
re AB-r-AC = AC — BC; whence if any two of th/»
three be given, the other i6 immediately found by the follow*
ing Canons, *viz»
Canon L If A and B be given^ then C ;;;;: — r — -5.
« 2AC
Canon II. If A and C be given, then B =: ^ , ^*
, * CB
Canon III. If B and C be given, then A = J^J^*
2. Thus, for ExampFe, fappofe you would find a Mulip4
I?
Of Winds and Sounds. 123
If the three Lines AD, BG, CH, be taken Plate
in Mupcal Proportion, or as the Numbers 6, 4, 3 ; p.^^^*
and in the Line A D we take A E equal to B G,
A F equal to C H, then will the Line A D ^^ di-
'vided in Harmonical Proportion^ in the Points
A,F,E,D;w2;. AD:AF::DE:EF. And
in this manner is the Axis of a convex and con*
cave Mirrour divided by the Objeffy the Image^
the Vertex of the Mirrour ^ and the Centre^ as may
be cafily fhewn by Experiment.
mean Proportional betyreen the Monocbord loo = A, and the
2AC
OStave CO = C ; then .by Canon II. we have B = =;
A-|rC
i^ = 66.6, which is the Length of that Chord which ii
ufually caird the Fifth.
3. Again, If .there be four Nafnbers in Mufia4 Proportioiiy
as A, B» C, D ; then, fincc it is A : D :: A— B : C — D, we
have AC — AD=: AD — DB. From which Equation wc
have the following Canons.
Cakom I. A == . , y ■ '
zD — C
Canon IL B=2D — Cx^-
_ _-- ^ 2AD — DB
Canon III. C = : •
A
Canon IV. D =
2A— B
4. Hence, when any three of thqfe Numbers are given,
the fourth may be found by the above Canons. Thus to the
three Numbers lo, 8, 6, we find a fourth Harmonical Pro-
portion, which is 5, the Odiave ; for thus the Theorem will
AxC 10x6 60'
5. But to carry this Harmmcal ^bwj farther^ and render
It more general : /
J 24 Of Winds and Sounds,
Also the Limits of the Colours of Light, as
feparated by the Prifm, fall upon the [even Muft-
cal Divijions of the Monoehord ; as will be far-
ther taken notice of, and exemplified in the next
Ledure.
I sHALi, conclude this with taking notice of
one fingular Property of a Mufical Chord, viz.
that it will be put into a vibratory Motion by the
Palfes of the Air proceeding from the Vibra-
tions of another very near it, and in Concord
Let the Terms of an Harmonic*? . n n t\ ts \^ s^
Serifs be denoted by i ^' ^' ^' D,E,F.£^r.
And let the Difference between 1 xm \x n -o r\ e^
each two be dtpoted by I ^' ^' ^' ^' Q' ^'-
6. Then will the Produdl of the two firft Terms, wn;.
A X B, be to the Product of ^ny other two Terms immedi-
ately fucceeding each other as C x D, in the fame Ratio with
their refpedive Differences M and O. For by the Definir
c A • C •• 1^ • NT
tion of Mufical Ratio we have < g ." ^ W JJ '. q
Therefore AxB : Cx D :: M x N : NxO :: M : O,
fA:C::M:N
Alfo<
fA:C::M:N
)<B:D::N :0
Therefore A x B x C : C x D x E (:: A x B : D x E) ;:
M X N X O : N X O X P :: M : P. T|iat is, AB : I? E ::
M : P i and fo on univcrfally .
7. Ag^in ; the Difference between the two firft Terms M
IS to the Difference between any other two, as O, In the Ra-
tio of B— ^M to D; orM:P:: B— 3M:Ej orM:Q.::
B-rr4M : F ; and fo on continually. For, by the Nature of
the Progreffion, it is A : C :': M : N ; and it is alfo A=B'^r9-
M/(becaufe B— A = M) therefore it is B— M : Q :: M : N ;
or, to put it in Form, we have M ; N :: B — i M : C. A-
gain; B — M : M :: (^ : N, and by Divifion B— rzM : M y
C — N : N :: B : N 5 but (by the Defoiitioo, jirt. 1.) it is
?: N :: D : O. therefore M ! O :: B—zM S P. Again ;
— 3 M : M :: D— O ! O :: C : O :: E : P j therefore M I
P;« B — 3M : E. And univcrfally, Icr n = Number of
Of Winds and Sounds. 125
%Uh It: if the Vibrating String be IJnipni with
it, the other will tremble thro' its tvhole Length \
if an Offai;ei it will vibrate by the Half-Lengths
only ) if the String which communicates the Mo-
tiort be a DouMe-Offave abirve^ of one Fourth of
the Length of the other, the Modpn will be
ftill corrcfpondent in that other String, for it will
vibrate only by the Fourths of its Length from
one End to the oth^r. Thus if A B be a String pjg, g;
four Feet long, and CD another of one Foot; if
Terns in the Series between the firfl and the laft, aiid let the
hA Tenn be Z, and let the Difference between it and the
oext preceding Tenn be S; then wiU it be M : S :: B— irM
:z.
8. Becaafe (by Art. 6.) it is M : S :: AxB ! YxZ, fup-
pofine Y, Z, the two kft Terms of the Series; theiefoM
AxB: YxZ;:B—»M:Z.
A X B
9. BecaufethefirftTermoftheSeriesisAs— ^^,aixl
Jd
A X F
the fecond Term Bs= — ^~» andAszB-^M; therefore
A
A X B
Ihe fecond Term isBae ^ ■ ^y. ^n cbe ftme manner it ia
B — ?M
A xB
fliewn, that the third Term is C zz -— — --, the fourth
B-^ 2M
A X B
^*"^ ^ ti » ^^ univcrfally, fince A x B ! Y x Z ::
B— -«M : Z, or, c^yiding the Confeqnents by Z, AxB :
V::B~8M: i j therefore V :=z -^iilJL ; apdikice» =
B — II nd
Number of Terms between A and Z, it will exprefs the Num-
ber or Hacc n^hich the Term Y holds in the Series. There-
fore ofy Term Y is equal to the Pr$du£t of the firfi and fecond
Term B ^ the Series £*tnded hy the Difference Ifetween that fi-
condTerm B, diffiimjhed hyfo many timet its Difference from the
frji^ as is equal to the Number of the Terms from the frft to the
f^iven Term Y. 1
10. Jll the Termt in a Mufical Frogrejpon are among tbem-
the
126 Of Winds and Sounds.
the- latter be ftruck with a Qulll^ the Vibrations
will be communicated to the former in fuch a
manner that k will vibrate only by a Foot-Length
at the fame time thro* the whole String ; which
will be evident by the fmail Piecei of Paper b^d^
/, b^ hung upon the Middle of ei/^cry Foot-Lengths
fuddenly leaping off 5 while the other Pieces a^ ci
t^ g^ /, reitiain unmoved upon the String at the
End of every Foot, where the Vibrations fevc-^
rally begin and end, and confcquently where .did
Line has no Motion at all (CXl);
fihei as ^lUrtUitUs tvhpfi Ri(fiffoeah cnfiituti a Serus in Ariith
mtkal Pr$ff^^. Thus the Terms of die frft Shaa A, B^
^ -r^ -ms t^ - ^ * AxB AxB AxB
C,D,B,^c,;ire(by^r/.9.Ja8.«|p, 5—^, fiZTISi'
-, l^c. to ^ — -j-^ ; whieh Scries divided by: A x B^
B_3M_. B — «M'
pines
die Scfitfi '4^> ~-^^»
B ' B— M' B — 2M* B— 3M'
to
■■•' ■-■'■'"J';. ' ifiif the Sedpkycals of ttilsMdil^i Series are B^
B — »M
B-^^M) Btr^^M» 8-4.31^/^0 6 «-irMj w%iGh l^rinif
are all in Aritbmeiical Progrejfltin. If the Hannonic Series had
been decmafing, inx, A-^B=z;M, B-^CssaN^ &fr. wa
fhould have had A 3: M — B, inz, the Signs of M and B
changed, but every thing elfe the.faine«
(CX) I. Whai II here b^ xdatiiig tdf Mirrotirs;, and the*
Colours of Light, will be explain'^d and demonftrated in it^
proper PMc^. That one SSbig A dxotild b^ put itito Vibra-
tion l^ anothel- B, by^eans of 4che.Ait» is no^(fa^a^ngey be*
cauie the Air will afie^ the String A with the fame Iinpulfe»
it receives itfelf from the Striug B. If thereferc the Stringi
A be nnder th^ fame Circnmftances with the String B ether-
wife, (1. /. if it be of equal Magnitude, and equally tended)
it mufl neceffarily movt in a ilmilar Manner^ or vibrate in an
equal I'ime.
2. If the String A be t^e the Ltogth of B, ttien (caUrii
farihus) the Air by its Impulfe received from 6 cannot fo af-
feaf
Of Winds and Sounds^ 137
fe& A as to caufe it to vibrate through its whole Length ; bat
it will fo alFedt each Half of A as to produce a fimilar £ffed»
or equal Vibrations. Hence the String A will become divided
in the middle Point, which will be at Reft.
3. And if the String A were three times as long as B, it
would be for the fame Reafoit div^ed mto three Parts, whofe
Vibrations W tyifchroihms to thofe of B, With tWO Points of
Reft between ; and fo on for any other Length. Alfo, if the
Lengths of A aid B are a» 3 to 2^ then if they txt CoNftcoi^^
and one be ftruck^ the other will be put into Motion by de-
grees, and in fuch a Manner that wn! alter the Vibrations of
^ firft String 1, and edch will vibrate by ihetr ali^t Parts^
and tlieidbre in equal Times.
LECTURE
128
LECTURE VIII.
Qf the Niiture and Properties of Light ; the
Ve Loc I T Y thereof bow- difcover^d and computed.
Of the Nature of Heat^ Fire, Flame and
Burning. Of the Ignes Fatui, Noct'i-
LuciS, natural and artificial Phos?hoki. The
Theory of Heat and Cold. Of Asbestos.
Of the Nature and EfFcft of Burning-Glas*^
SES, whether Mirrours or Lenfes. A Calcula-
tion of the Light and Heat of the MpoN.
Of the Caufe of Transparency and Opacity
in Bodies. Of the Reflection of Light ;
0/ //J Inflection ; 0/ /^^ Refraction of
light, The Fundamental Laws thereof demon-
ftrated. The different Refractive Power of
various Subjlances. The Ratio of the Sines of
IsciDBitcE and RzYRACt ION Jiated, Of the
.True ^»i Apparent Places of Ohje£ls. Of
the Analysis of the Solar Raysj /i&^ feveral
KisDS. thereof y their different Refranoibi;
hirvftatedi Experiments relating^ereto by
the Prism. Of the Various Colours of Light
hy the Prifm; the Harmonic Ratio of their
Linear Extent in the Sun's Image. The Co-
lours of Natural Bodies thence explained. Of
the different Reflexibility of the Solar Rays,
and Experiments relating thereto. The Manner
and
S/" Light and CdLbuRS. ia^
iifid Caufe thereof enquired into. 0/ Rings of
fcOL0UR*D Light between Glass Planes, and
Bubbles of Water. Th^ different Orders
nHd Degrees c/ tbe felieral Colours explained.
The Fits of EASY Reflection aid Trans-
mission explained. iTAtf Artificial Composi-
tion ^Colours. Of /i^ Rainbow j its
Caufe eicplain^d\ Cdlculations relating thereto.
The Phenomena of HXlo's cbnjider'd and ac-
counted for:
THAT Light is not a mere S^uatity of
fomc Bodies, but is itlclf a real Body;
or diftind: Species of Matter, and en-
dued with all the natural Propef ties thereof, will,
i prefume; be fufficiehtly riianifeft frorri the fol-
lowing ExpeHnients relating thereto: We fhall
therefore,' at prefent, take it for granted, that
Light eonjijls of inconceivably fmall Particles of
Matter of different Magnitudes, which are emitted
ior refieSed from every Point in the Surface of a
luminous Bd(fy in Right Lines ^ aridik all DireSions^
with an unparalleVd Velocity^ and whofe Power or
Ihtenjity deireafes as the Squares of the Diftances
increap.
Th A t the Particles of Light arfe refrdfted thrcr
the Humours of the Eye to the Retina^ or fine
Expfanfidrt of the Optic Nerve over alj the in-
terior hinder Part of the Eye ; arid therei bjr
painting the Images of external ObjeS^, become
the immediate Means of Sight, will be fully
ihewn in the next Lefttire.
tot.IL 1 iVE
*3^ 0/ Light and Colourst.
We (hall now confider'd Light under the va-
rious Charadcrs and Qualities of a natural Body,
and point out thofe remarkable AfFeftions and ^
Properties fo peculiar to itfelf, and the Caufes of ^
fo many very curious and extraordinary Phaeno- jj
mena in Nature. ji
That the Particles of Light are inconceivably
fmallj li evident from hence, that the greateft r
Quantity of Light, in the State of greateft Den- «
fity, or Flame, is found to have fcarce any fen- ,,
fible Gravity or Weight, which, we have Ihewn, k
is always proportional to the Quantity of Msttter . A
in all- Bodies i Alfo, becaufe thofe Particles per- . ,
Vade the Pores' of all tranfparent Bodies, how-
ever hard ou heavy, a& Glafs and Adamant. But (cx
we know it more efpecially from hence, that the j[^
Stroke we receive by a Particle of Light has no ^,^
fenfible Force or Momentum j which, on account ^l(rf
of its prodigious Velocity, would be very great, j^^
and infufferable,. we j€ it of any affignable or con- ^^
fiderable Magnitude. ^^^
Yet fmall as they are, we find the Rays con- 2. yj
fift of different Sorts of Patticles in Light emit- ^1^
ted from all Bodies; and that this Difference of ^^
the Rays of Light arifes from the different Mag- *»<iCha,
nitade of the Particles, feems moft evident from
the different Directions the feveral Sorts of Rajts
move in, after they have pafs'cl thro' a Body of J^«er, ,
Glafs, Water, (^c. of fome fpecial Figure,, as J^JJ
that of a Prifm efpecially. 4c moft.
That the Particles of Light are emitted ftoift /^Jy
every Point in the Sutfacis of a Body, is evident w
fronx
1
r
Of LiGHt and Colours; 131
Irom hciice; that any given Pdint in that Sqt-
fape is vifible to the Eye in any Situation, from
whence a Right line can be drawn from the
Eye to tliat Point; which could not be, if the
Light were not propagated from tint Point in
all Direftions.
That they proceed from thfe Body in Right
Dnes, is clearly feen by Experiments on the Sun-
Beams, Candle-LigHt, i^c. In a darkened Room \
alfo from the Shadows which Bodies of every
J^igure caft, being fuch as woUld be determined
by Right lines drawn from the luminous Poiht
tbuching the Extremities of thofe Bbdies (CXI) :
(CXI) f . Befoft, Sir Ifaac NenvUn's Time, fcarce any thbig
bf the Nature or Properties of Light was known. It faa4
been efteeni*d a n^ere Qoality or Modification of Matter, and
was prop^ga^ii. by Premoii» and I know not what of fuch
Kind of dtuff^and renieleis jargoq ; jhan which nothing cai^
be more Urefonie to read » orukfon^^e to^ repeat. . Leaving. |
therefore th^ idle < Reveries of tht Carisfians^ we (hall con-
template this glorious Phaenohienon in. thfc Nie^wtonian M^^ *
lier, which difftti{es tjxAit over the whole Face of Nature, ^d
iAd& new Splendor even to Light itfeif..
2. That Light IS 4 material S^bfhLace, aiyl wha( we pro-
perly call Boifyt is i^c^^tq be doubted ^ becaufe we find it 1$
{i>m%thm% tiisUL has Motion, or is propagated in Tipe ; ibme*
tiung that afis Upon Bodies, and produces great Alteration
and Chailges in their Natures and Forms. , It is fomething
that Bodies ad upon, by refle^ng, inflefting, and refradin^
It on their^urkces, and in theur rats : ^Atid it would Appear
to have Weight, and all other fenfible Qualities of comquon
Slatcef, were it not that the Smallncfs of \ii Quantity rendcri*.
rlieni entirely imperceptible by us,
3. Nor are we to confider Light dnly ^s a Body, fciit as
lie thofl aftivfe Principle or mofS gen^l Agent in Nature.
[ greatly queflion if it be not the true Frimum MoUle in Na-
iire, or the Spring of Motion and A^ion in alt other Bodies.,
Were the Particles of Light to be ahnihilated, we (hould fee'
rd Mai-ks 6r Footileps of Fife of Meat remaining, ixA there*
•I 2 tui
1^2* Of LiGHt and CoLotJRs, *
Thi: Velocity of the Rays of Light furpaffcS
th&t of all other Bodies we know of. By ob-
ferving the Times of the Eclipfes ofjupiter^s Sd-
telUtes when the Earth is neareft, arid again when
it'is fartheft diftant- from that Planet, we fliall
fdti'no '?Ofkti ofMotSoii in Bodies, but all Things would
putpn thfsjyippear^^eof lifelefs ii&ert Matter^ rigid and in*
nexiBle, as' it. would be abfohitely cold and dark.
.4.' The Divine Wifdoiti and Providence appears perhaps
in i^odftyig.ib remarfeab))r.'ai in the ^reme SubtUcy of (hci 1
PaVticies of If.ight,; ^jthout this Qgsdification it, could not 1
have pervaded" thi r6'rei of Bodies, and T<J wfe could have ]
h3d:n6he of thafe which ire call MMpbutms ot tranf^arent
SnbAances, and tvm tlwg but the* Surface of a Bod/ would. in
haviii been concealeff frbni the Sight of Mankind. Again 1 ' g
the Velocity of a Body is always as the^Quantity of Matter ^
ittf^rfelyr and Acfef&re the fraallcr tH^MIy, the gfcafter jj
V*!6cl4y it is fufceptible of frohi the-lahieFbl-cc ; whence it\ ^
ciftfesild pafs, that Light is thus quali^ed t6 be'trahfimi^teil' jj,
thrbttgh' ihimenfe'Diftance in a fmall dtid "inftnfible Tiift of ^
Times whiA TMW^ wks« quite neccffafry itfcording to the- ^
pfeefent Frame and Slate bf Natui'e.- ' ' *, ' }^
'5.- But laftjy,; it w^ abfolotdy rfeccflary that* the Partidies ' j^
ofli^t Ihould l5c fb^e^ceeding fmafl,' tha^'*jMbi,C0tnp6iittd-:' ^
eb wiehr its Vctedty it ibould produce no fenlRfjle Potce, as/it ^
linuft otherwife have done, and winch di^itfere xobltf uot^ ^
have.bfet?n' bohi ^by the tendfer and tielicate T^xttore of the Te-
^ra! Parto of Vegetable aiid Atoirfial' Btf^Jies, ' T6 give airi' T
E«airtple : The- Vclociry of • a P^i-titte; of Li^t is found «>' 7,
hi'WxYit kate of 897606000' Fci^//?r Second; fdppofe iti^ ^
Matter . to be but one Millionth Part of a Grain, then iii ^
iPqrce to ftrikc an Objcfft would be as 'n?7^° ^?.^ = 897,6 fe
I 000000
to
I^eet '^er Second for one Craini or it would ftrike with the
£line Force that one' Grain Weight would do falling from C
halfthatHeighj^ <;^'s;. through 448,8 Feet; which we fhould' ]^^
find to be yery great, were the Experiment to be made on the, ^p^
rehiibTe Coats of the Eye,' p^jj,
^ 6*. Since the Weight of Bodies is proportional to the Q^^n-* j.^
tity of Matter, ic follows, that where the latter is diminiflied '^
rndefiriitely, the former wit} be fo too; therefore the Weight ^j
of Light xnnft be ihfehfible iq ever fo great a Quantity of it. j
^ -^ find, ■
r
Of Light and Colours. 133
find, that in the former Cafe thofe Eclipfcs hap*
pen too foouy and in the latter too late^ by the
Space of 8 Minutes and 13 Seconds; which
Ihews, that in fhat Tirpe die ^.ight paffes over
the Semidiameter of the Earth's Orbit, which is
Pr. BoirbaoFVi caufed a Globe of fron 1 2 Inches iQ Dijune*
ter to bp heated red-hot, and fufpended at the End of a very
^xad Balance, and counterpoifed by Weights at the other End
very nicely, and thus let \i hang till all the Particles of Heat
or Light were efc^ped, when 1^ found the Equilibre of th^
Balance no w^ys altered ; which plainly proves the above
Theiis.
7. That the Particles of Light have not only Magnitude^
but that in Sffirent Degrees alfo, is another and perhaps the
moft fubtle Difcovery of the Neivtoman Philofophy. The
comparative Terms of Greater and Lejfer are now as applicable
to the Particles of l^ight, as to any other Bodies. This is
abfolutefy proved by the different Refrangibility they are
found, to have in paffing through a Priim^tic figore of Gla^
or Water ; for the Power of the Priiin detains the ifTuing Par-
ticle, and draws it a little towards the Surface; and fince this
Power is the fame, it woufd have the fame Effe^ on all th^
Particles of Light, if they were all of an equal Magnitude,
becaufe they have all an equal Velocity. But iince this £f-
fed is dififerent among the Particles, fome being de(ainM ao4
drawn afide to a greater Dilbmce than others, it fqllows, they
rottH {)e lefi in Magnitude, to become more fubjedl to the In*
fluence of the attrading Surface ; in like manner as the
eleflric Effluvia will adl upon and agitate very finidl and light
Bodies, q^uch fooner and more ealily than they can move
thofe which are larger. But of this more when we come tq
ipeak of the Manner in vyhich this Power ads refrading thq
Rays of Light.
9. If Light were not refieded from everv Point in th^
Suiface of a Body in all I)iredions every Way, there might
be affign'd a Point of Space where a Ray of Light from fuch
a Point in the Surface 40^ i^Pt come ; and there the {ai4
Point of the Surface could not be vifible, but becaufe the
^ye can find no Point of Space in all the viiible Hemifphere
refpeding that Point, but where it is vifible, therefore a Ray
of Light is refleded from that Point to everv Part of Space,
frpm wljence a Righ(, I^ne tQ that Point can be drawn.
I 3 about
134 0/ Light and Colours.
^bout 82,000,000 Miles-, which is at the rate of
1 70,000 Miles in a Second of Time, and which
is therefore nearly 680,000 times greater than
the Velocity of Sound (CXII).
g. That tbe Rays of Light proceed in Right-lined Di-
re£Uons» is evident from hence, that whatever the Figure of
tRe'Bb(}y be', if it Wheld perpe'n^iculaf tq the Says of Light,
It will always caft a Shadow of the' faxh^ Figure againil a
Parallel Plane. Thus a Circle will produce* a circular Sha-
dow, a Triangle a triangular one, and fo on. Whicl\ plain-
ly (hews, that the Rays of Light pafs by the Extremities of
thoie Bodies in Right-lined Directions, excepting thofe only
which pafs contiguous to the Edges of the Body, for t^ey
will be a little infleded, which will caufe the Extremity ojf
ihfi Shadow to be not fo dillindl and well defined as it othei:-
wifc would be ; of which we ihall take farther Notice here-
after. ' ' V
(CXIL) As all the other Af&aions of Light, fo that of
Velocity, was utterly unknown' to air the ancient, and ^moft
of the modern Philofophers, whi, before the Time of Mr.
Reaumur , v/tx'e of Opmion that the Motion q( Light was
inflantaneoiis, or that it was propagated ihra" im^menfe Spaces
in an InHanti But Mr. Reaumur and other Philofophen a-
boat thi^ time, making frequent Obfervations on the Eclipfes
of Jufiter\ Moons,' found that the Time of thofe ' Eclipfes
did not corr^fpond to the Calculations foui(ided ypo/i' the
aftronomical Tables ; where the Times are all calculated for
the Difbnce of the Centre of the Sun, and confequently,
where the Eye of the' Spedator muft be fuppofed to be in
viewing the faid Eclipfes, Occultations, ^c. of Jupitt/%
Moons.
Platfe 2. To illuftrate this Matter; let S be the Centre of the
XXXVL Sun^ A B the Orbit of Mircwy^ C D the Orbit of Finus, E JF
Fig. I . ^^^^ <^^ t^« EartUfy and G H a Part of the Orbit of Jupiter,
Let I be the Body of yufiter, and K L its Shadow, OM N
the Orbit of one of Jupiter s Moons M juft entring the Sha-
dow of Jupiter, Now a Spectator at S would obferve the
Moon M to eater the Shadow juft at the Time which is cal-
culated from the Tables; but a Speftator at the Earti^ at T
' always obfefves it to happen foqner, and when the Ear^ih h
in the oppofite Part of its Orbit R; he will always obferve it
to happen later, by tl&6 Space of abourj MiAiiites m both
AoALf:
Of Light and Colours. 135
Again: Since Ijght is propagate^ in Right
Lines, its Powex or Intenfity will decreafe as the
Squares of f he Diftances increafe ; and therefore
the Light and Hc^at of the Sun at the Diftances
of the fix Planets, Mercury ^ VenuSy Earthy Mars^
Jupiter and Saturn^ will lie nearly a$ 700, 200,
100, 43, 3, 1. fuppofing their JDiftances as the
Oafes. This Obfervation gave tke firfl Froof <hat Light was
progreflive, and took up about 14 Mmuces to pafi over the
Diameter of the Earth's Orbit from T to R, or 7 Miaucrs
to pafs from the Sun S to the Earth T.
3. But this, tho' a fuificient Difcovery or Proof of the
jprogreffive Motion of Light, was yet but an Experiment in
the Grofs, and not accurate enoogh to determine or define
the true Rate of Velocity which did really belong to Lightl
The Method by which it has been more nicely determined
.was hit upon in the following Manner : Tho* Sir I/aac Newtom
had dembnftrated the Motion df the Earth from the Laws of
Gravity, yet as his Book was underftood by few, thofe who
could not comprehend his Method were witling to be fatisfied
of the Truth thereof otherwife, and rightly judged, that if
llhe Earth did move about the Sup, it moft neceilarily caufe
an apparent Motion in any fix*d Obje^ at a Difhmcefrom it.
4. Thus if A B C D reprefent the Orbit of the Earth, and ^
A and C the Place of the Earth at two oppofite Times of **
die Year; then a fixM Objedl at E will be feen from the
Earth at A in the Line A E, which will point out its apparent
Place at G in the Concave Expanfe of the Sky Hi. B«t ac
the oppofite Time of the Year, it will be feen from the
Earth at C m the Line CE, wj;^ch wiU projed its Place in
the Heavens at F. So that w4iiie the Earth has.pa(s*d from
4 by D to G, the Objea -(tho' in reality fix'd) has appeared
to move thro' the Space GF; and the Angle which meafures
thb apparent Motion of the Object, 'viz. the Angle A EC, is
caird the FarallaSk Angle^ or Parallax of the Jhm»at Orbit, •
l»ecaufe it meafures the vifible Appearance of the Diameter
A C of the Earth's Orbit at the Objeft E.
5. This being the Cafe, it was applied to the &c'd Stars,
which they concluded would certainly have an apparent Mo-
tion, or Parallax, provided an In^rument could be made fuf-
exa6^ to obferve it, and this would be a fatisfa^tory
I 4 Numbers
Jciently (
4
136 Of hlG^T cind Colours.
Numbers 4, 7, 10, 15, 52, ^5.
. From the ftnpendous Velocity of luminovis
Particles arife thgir prodigious EfFedts in regard
of Heat J Flame J BurniiHi^y Melting, &c. Thus
when they are confiderably denfe, they aft very
forcibly on the Parts of an animal Body, an4
raife the Senfation of Heat^ by the great intcftinq
Dcmonftration of the Earth's Motion. Accordingly feyeral
Pcrfons addrcfs'd thcmfelvcs to difcovcr a Parallax of the foc'i
Stars ; and in the Year 1725, the late Hon. Samuel Molyneux^
iEfq; with an Inftrument made by the accurate Mr, GraJbam,
{)egan to obferve the bright Star in the Head of Draco as \i
^aS'd near the Zenith. Profeffor Br^ley alfo obfery*d it a-
long with him; and fjrbm many Obfervatiops made with great
CarCy it appeatr'd that the Scar wa^ more Northerly y) ^^-
conds of a Degree in September thaii in March^ juft the con-
trary Way to what it ought to appear by the annual Parallax
of the Stars. That is, the Obfervers, who in Seftcmier faw
the Star at F, did in the Marck following obferve it at K, in
ihe Right Lin(? A K parallel td C ¥, and not at Q where i(
bught tp have appeared by the parallaflic Motion. '
6. This unexpected Phaenomenph perplexed the Obferver^
very much, and Mr. Molyneux died before the true Caufq
of it was difcover'd. After this, Dr.'^r^<&y,with another
Inflrument more exaA and ac<^urately adapted fof this Pur-
pofe, obferved the fame Appearances, not only in that, but
jnany other Stars; and being by many TqaU fully airure4
that the Phjenomcnon wais not owing tp any Errpr in the In-
flrument or Obfervation, applied himielf to confider whac
might be the Caufe thereof, and after fevcral Refiedions and
Hypothefes, which he ftfll found infuflicient to account for it,
he at laft found, that it was really owing to the progrcflive
Motion of Light, and the fe: Jible Proportion which the Ve-
locity thereof bore to the Velocity of the annual Motion oif
the Earth. '
7. This he was fully affured was the true Reafon, not
only becaufe nothing elif could be thought of thait would ac-
count for it, but becaufe fuch an Appearance muft ne^effarily
refult from the above- mentioned j^y^othefis, as jiiay be thus
pj(y, 3. ihewn. Let A6 reprefent'a P^t oiF the Earth's ainhual Or^
fait, a:nd let C be a Star obferv'd by a gpedator at the Earth
4t Aj wh^n the Eartjj iirriyps ^t 9 th^ Stir wili'npt be pb-
Of Light and Colours. 137
Motion which they produce in every Part. Hence
all other Bodies are hotter or colder^ as they con-
tain a greater and lejQTer Quantity of ignitious Par-
tijcles, and fo have a greater or leffcr Degree of
inteftine Motion of the Parts.
If thefe lucific Particles are fufficiently imbibed
or generated in any opake Body, they caufe it to
ferv'd at C, as before, but at D in the Linf B D pandlel to
AC; for let AB be divided into the equal Parts Ka^ ah^
hc^ cJ and ^B, then thro* thofe Points draw the Lines ag^
t'ff ^g* ^^f parallel to A C and D B. Uow let the Velo*
city of the E^rth be to that of Light as A B to CB. When
the Earth fets oat from the Point A, fopqpoie the Ray of
Light commences its Motion from the Star at C in the Di-
re^on C B perpendicular to A B ; then 'tis plain when the
Earth is arrived at a, the Particle of Ught will be got to /,
the Point where ae cats BC, and the Star will be feen in
the Diredion «/, and appeaf at #. In like manner, whea
the Earth is at 6, the* Particle of Light will be come to i,
and will appear at/, and fo on; when the Earth is at c,d, B*
^he Particle ^ill be' at /, nt^ and B, and the Star will appear
at g, b^ and D.
8. If therefore the Line C A reprefents the Axis of a Te-
lefcope, making the Angle* BAG with the Diredion of the
Earth's Motion A B; when he. comes to B he will fee the
Star at D^ which he could not do if the Telefcope was di-
rected in the perpendicul^ Line BC; bot the Difference of
the Pofitions of the Lines D B and B C, or (he Angle DBC, .
19 fo very fmall, as to amount to no more than 20^ 1 5^^^,
which gives the Proportion of the Sides BC to C D or A'B«
' as 1 02 10 to I ; which ihews that the Vtl^c\t y of Ught u ten
TJbou/a/id two Hundred and ten Times greater than the Velocity
qftbe Earth in her Orbit.
9. But the Velocity of the Earth is knowp, which is abpu^
500,000,000 Miles in 365 Days, or aboat 56,000 Mil^
per Hoar, whence the Velocity of Light will be found to l>e
fach as carries it tliro* (he Space of 170^000 Miles, bf
897,600,000 Feet in one Second; and therefore it will pafs
from the Sun to us in 8^ and 1 3^'.
10. If a Cannon will throw a Ball i Mile perpendicular
Height, or 5iz8o F^t, the Velocity with which it goes from
the Mouth of the Capnoh is the uniform .Velocity of 10,560
' ^ fhine.
138 <y LiCSHT /zW COJLOPRS.
Ihine, or glow, or become red-hot ; and by their
prodigious Activity will in Time difunite, dif-
fplye, and dertroy' its natural Texture, and thus
change its Form, and reduce it to anotlier Spe-
' cies of Matter ; even the AJbefios not excepted
(CXIII).
Feet per 18 J'' (which is the Time of the perpendicular Afcent
or Defcent,) and therefore the Velocity of the Cannon- Ball
U 57S Feet fgr Second, Whence tbe Vdocity of Light is
to xhat of the Cannon-Ball, as 897,600,000 to 578, or as
1,550,000 to 1 nearly.
1 1 . The D9aor found that the Parallax of the fix'd Stars,
inftead pf amounting to many Seconds, as many have deduced
from their Qbfervations, does not make one Second; and from
thence it follows that the above- mention *d Star, in Drato, is
^bove 400,000 Times farther from us than the Sun; sind
Gonfequently, that the Light takes up above 493^x400,000:=
197,200,000''' Seconds, (which is more than iix Years,) in
^mtng from that Star to us. In the mean Time we may
tefled how different are the Places of the Sun, Moon, and
Planets in the Heavens from thofe in which they appear.
Thus, fctting afide the Refradtion of the Atmofphere, when
the Centre of the Sun is really afcending in the Horizon, it
will be 8' I}'' after, that we obferve it there; in \yhicji
Time the Sun will be far advanced in the Heavens.
1 2. The Motion of the Earth is by this Method abfolutely
demonllrated, and therefore put beyond all Doubt and Ob-
jection ; they who deny it now muft confcfs themfelves wholly
ignorant Qf one of the £nefl and moft important Difcoveries
\ial was ever made in Jjiroifomy^ and which was finiih-d in
the Year 1728; concerning which, fee Dr. Bradley ^ own
Account in Phil. Tranf. N°. 406. which we fhall farther ex-
plain in a future Part of this Work.
(CXIII) I. That Bat, Fire, Flame, See. arc only the
different Effects and Modifications of the Particles of Light,
is, I think, very evident; and the Particles of Light them-
felves depend entirely on Kelocity fow their ludjic polity ; fince
by many Experiments we know that the Particles of Bodies
^become lucid, or Particles of Light, by only producing in
them a requifite Degree of Velocity ; thus the Particles in a
Rod of Irqn, being hammered xery nijpbly, ihinc and fee'-
If
Of Light and Colours. 139
If the ignific Particles of Light arc fufficiently
eondenfed, as the Rays of the Sun by a Ltm or
Buming'Glafsj they become ardent y and bum with
^oipe red-hot; thus alfo the viofent Stroke of the Flint ag^inS
|he Steel, in ilriking Fire, puts the Particles of the Steel
which it takes off into fuch a Motion as caufes them to melt*
and Wome red-hot, which makes the Sparks of Fire pro^
duced by each Stroke. The fame Thmg you may obfervc ia
many other Ca|es.
2. As Fire cpnfifls in the great Velocity of the Particles, fq
it may be communicated from one Body in which it is to an*
other in which it is not, after the fame Manner that one
Body in Motion will communicate Motion to another Body
phat ha^'none. Fire difers frqm Hfat only in this, that Heat
|s a Motiqn jn the Particles of a Body with a lelTer Degreo
of Velocity; and Fire a Motion with a greater Degree of
Velocity, *viz. fuch as is fufficient to make the Particles
|hine, tho' we often call fuch a Degree of Heat as will bum.
Fire, tho' it does not adually (hine; and we feldom call
thofelucid Bodies Fires which only (hine and do not bum.
Thcfe are a Sort of Ph-fphoH^ which tho' they have no Heat,
yet feem to owe their Lucidity to the Motion of tjie Par^.
3. This I think will appear for the followhg Reafons ;
(i.) We obferve feveral of thofe Phofphori aw owing tf\ Pu-
trefadlion, 4is rotten Wood, xtry ftale Meat, efpccially Veal,
fome Sort of Fifll long kept, as Oyflers^ LobJIers^ Flounders^
Whitings f &c. which Putrefadion is the EiFed of a flow and
gentle Fermentation, and that confifts in the intefHne Mo-
tion of tjie Parts as we have formerly (hewn. (2.) Moft of
thofe Pb^fpbori have their Light fo very weak as to fliine
only in the Dark, w|iich feems to indicate a leiTer Degree of
Velocity in the Parts thj^n what i? neceflary to produce Heat ;
for fuch^ a Degree of Velocity will caufe Bodies to ihine in ^
ppen Day.Light. (3.)Som9 of thofe 'NoMuca^ or Bodies
which ihine in the D^rk, are the Parts of animated Bodies,
as in the Gloiu Worm^ a fmal^ Sort of Centipede^ &c. but all
the Parts of an Animal are undoubtedly in Motion. (4.) O-
ther Phofphori pot on the Appearance of Flame, as the Igid^
Fatum^ the Writing of common Phcfihorui made from Urine,
Flafhes of Lightning, 6fr. but all Flame is nothing but a kindled
Vapour, whofe Parts are all in Motion, but may be too weak
to caufe Burning. (5.) Several of thofe innocent lambent
Flames may have their Matter ^q agitated, or the Velocity
an ,
140 (y Light and Colours,
an Intenfity propqrtiohal to the Denfity of the
Ray^ in the Focus^ or Burning-Point of the Glafs \
which Denfity of Rays in the Focus is always
of the!]: Motion fo increaTcd, as to produce Heat and bum \
thus, the Writing of Phojhhorus on blue Paper, fufficiently
rubbM, will immediately kindle into an ardent Flame, and
bum the Paper. (6.) Thofe Pbofphori feem to have th^
^ffentiai Nature of Fire, becaufe they are fo eafily fufcep-
tible of a burning Quality from Fire; thus common Phop
fborus is immediately kindled into a moll ardent and inex-
tingujfliable Flame by common Fire. (7.) In ftroking th^
Back of a black Horfe, or Cat, in the Dark, we produce in-
numerous Scintilla^ or lucid Sparks ; in the fame Manner aif
rubbing a black Piece of Olpth, which has hung in the Sun
CO dry, will cade it to throw out the Particles pf Light
whkh it had inibibed from the Sun; whereas a \vrhite Piec^
C|f bioth, which refledb mpft of th^ Sun*s Rays, emits no fuch
]uci4 Sparks in thie D^rk. Many other Reafons might be
urged to Ihew that Light of every Kind is owing to one
anq the fame Caufe in a greater or leiTer Degree, viz. to the
Velocity of the Parts of the hfcid Bo^.
4. It has been juflly obferved by fome of our n[iodeni
Philofpphers, that a^ual ox ahfolute Heat is to fenfiUe or
relati've Heat the fame as Mqtion is to Velocity i for ahfolute
JHea^ is nothing but the whole Motion of all the Parts of the
ignited Body, and fenfihle or relati've Heat refpefts only the
compar^i<jje Velocity of the Parts. Thus equal Bulks of Mer-
cury and Water fet in a Sand-Heat, where the Heat of the
Fire may be uniformly communicated to both, will acquire
in equal times equal Degrees of abfolute Heat, but the rela-
tive Heat of the Water, or that which is fenfire ^o the Fin-
ger, will be near 14 times as great as that of the Mercury ;
becaufe the Water having ; 4 times a lefs Quantity of Matter,
will sidjpi'it of Velocity fo muc^ in Proportion greater.
5. Again, if Mercury and Water have the fame relative
or feniible Heat, that is, if both are heated in fuch a Man-
ner as to caufe aQ equal Afcent in the Thermometer; then 2^
Quantity of Mercury will heat 14 times as much Water as
the fame Quantity pf Water v^ill do ; or it will make the fame
Quantity of cold Water 14 times hotter than the fame Quan-
tity of hot Water can. All y^hich is cafy to be fhewn by
Experiment, and abundantly proves the Tr\^th of the fore^
going Theory, vi?. That Heal and Fire are wholly (Fkvivg^ ta
as
(y Light »W Colours. 14!
Us tbi Area of the Burrting-Glafs dtreSfy^ and the
Square of the Focal Diftdnce inverfefy. Thus (bp-
pofe the Surface or Area of one Glafs contain'd 12
tke VtUtiiy of the Tarts of the heated or ardent Body,
6. The v^ious Phaenomena of Heat and Cold, Tin, Burn*
ing. Sec, are rationalfy accouiHed for on this Theory. For
fiitt, we are to confider that Cold and Heat are only compa-
rative Terms, or that the fame Thing may be cither hot or
Cold According to the Relative Idesl, or Standard Degree ;
thus Ice or SnoW is (aid to be cold with refped to the Fin-
ger» but Ice or Snow is warm if compared with 1 freezing
Mixture. So that if (as w^ commonly do} we ihake the
Haiid or ^ny Part of the Body the Standard bfHeat or Cold«
or the Term of Comparifonjlhen *t!s evident, (i.j If the
I^arts of any Body applied to the Hand have thb fame Ye-
looi^ as the Parts of the Hand/futh ^Bodjr wenatntaliy
phMiounce is neither hot nor cold/ (£} If the Particles of
the Body have a greafer Velocity ihan thofe of theHtod^
we pronounce jt nvarm. If the Excels be Cnall; hni bot^ if it
be great. (3 .J IT the Veloci^ of the Par6 of'thc Body applifcd
be lefs thaii that in the Haiuli t&e'Senfation then is what we
call Cold^ whidi alfo may be. iii vandus Degrees. (4.) Hence
it is plain tjiere can be no foch Thing as ahfolute Cold, but
where the Piurticles of Matter are abftiTutely ouiefc^nt or at
reft. {5.) Hence alfo there can be nd fuch Thing as abfo-
lute Hea,t, beqkafe no Degree of Velocity can be a£gn*d,'
but a greater is ' aiCgnable; till we come to Infinity; where
we are qiiice loft^ as having no Idea of infinite Velocity 6r
Heat.
7. From thii Theory of Heat and C(dd,' we may conclude
that there is nb Body in Natui'e who(e Parts are not in Mo-
tion in fbnie Degree, fince we havd yet been able to difcover
no nltimate Degree or Limit of Cold ; and if any^fuch Thing
were to be found in Nature, I believe it would be as im-
poflible to bear or endure die Teft sts any extr^ifie Degree
of Heat; both Heat and Cold naturklly tending to deftroy the
animated Part, or Teft, in the extreme Degrees ; Cold, by
deftroying th^ vital Motion, and fixing the Part rigid and in-
flexible i. but Heat, by putting the Parts into too great an
Agitation, caufihg a greater Velocity in the Fluids and Dif-
iipation,. ^nd ji Force of Tension in the Solids beyond what
the natur^ State of the Body can bear; and therefore it will
fiievitkbly dcfb-oy it.
iquare
142 Of Light ^;i^ Colours;
Iquare Inches, and its focal Diftance were 8 In-
ches ; and the Area of another Glafs were 9
fqtiarc Inches, and its focal Diftance 4 Inches {
8. Whatevei: be the ailing Principle in Fnexiag or Coj^e-
lotion^ 'tis certain, the Modui Agendiy or Manner of OperdtioHi
miift be to diminifli the Velocity of the Parts of the congeal-
able Subflance tp a proper Degree, hy which means the
Fluidity will be 16ft, and the Parts become rigid and fix'd.
Thus if the inteftine Motion o/the aqiieotis Particles be abated
by the Admixture of any extraneous Body, the Parts will be
xio longer fiuid> but remain to Appearance fixM in a Congela*^
tlon, and become a Body of ltt\ Whatever this Principle of*
Freezing be, it is cehainly of i faline Nature, becaufe 'tit
well known Salt will gready increafe the Coldnefs of Water,
Ice, or S^dw ; and freexing Mixtures are always made there-
with, by equal tjuantities pf each. \
. 9. On the qther Hand, fix*d Bodies are render'd fluid by
Heat, .only ^y increafmg |che Velocity of the Parts; thus Ice'
liecomies 'Water, thus Metals, are put into Fuflon, and a
greater t>egree of Heat, gives, a ftill greater. Degree of Ve-
locity to the Parts, and throws them off m the Form of i.
Steam or Vapour. This Steam of Vapour, if it conMs of fuch"
Particles as will admit -of a proper Increafe of Velocity, will
concejve it very readily, and kmdle into a Flarhe,*at the Ap-'
proacji Qf a Body whofe Paris afe thus in Motion; fhfit is,
of Fire or Flame.
icr,, There <^ems tp bfe n6 other Difierencfe bi^tWecn F/V<?
einJFlarki than thi*, that Fhe conMs In a glowing Degree of
Velocity in the Parts of a Body while yet fubfiftihg together
in the Mafs ; but FUme is the iame Degree of Velocity '\ti
the Particles diflipated and flying off in Vapour; or to life Sir^
Ifaac Nt^ton^ Exprefllon, Flame is nothing elfe hut a red hJ
Vapour.
1 1. The Efledl of Fire in burning co'nfifts in this, th^t the
Velocity of the Particles of tif6 fd far inCreales the Velo-
city of the Parts of the Body to which it is applied, as to'
caufe a Separation beyond the S|)hefe of c6r|>urcular Attrac-
tion, by which means the Body will b6 diffolVed, and the
Particles which are volatile will fly off in th^ Form of Steam,
Smoak, Fume, i^c, while that which remains appears In' thcf*
form of CoaU Calxy ^Jhesj Caput Moriuum, Sit,
12. The Parts of foroe Bodies are extremely volatile, and
win moft of them be diflipated by fhe A^ioh of Fire ;' but
{here
(y Light ^W Colour*. 143
then the Efiefts or Intcnfity of Burning would
be as li to V'tr, or as 12 x i6 to 9 x 64, viz. as
197 to 576 (CXIV).
others again are to be foand whole Raits ate of (iich a Na-
ture» or fo fixM, as not to yield to the Force of Fire, or the
Velocity conuntinicated to them will not be able to diffolve
the corpufcular Attradion ; but when this glowing Velocity o£
the Parts is abated, or, in other Words, when the I^ire in the
Body is extind» the Parts (and of f ourfe the whole Body)' ap«
pea^ nnalterM. Of which Sort of Subftance we have a no-
t^le Inftance in that Foffil caird the Jfiefies or JmiantBui^
Stone. This Stone is found in divers Parts of the World ; par-
ticularly in ff\Ua a great deal may, be kea adhsring to, and
growhig up with the Stone of many of their Quarries.
(CXIV.) I. In order to account fo^ the Nature of Burn-
lAc-GtASSBs, whether MirrMirs or LenfetjVr^ mud coniider
the Ar^ of their Surfaces, and tlie focal Diftance; becaufe
both thefe Quantities enter into the Expreifion of their Powei^
of Burning. Let A B, and I K, be two Mirroun expofed Plate '
diredly to the Rays of the Sun CD, E F, and L M, NO;. XXXVl.
then win all the Rays, falling on the Surface of thefe Mir- Fig. 4» 5:
TOUTS, be reile<6ted t6 the Focus of the Glaffes, where they
will be cbncenter'd, not in a' Point of Space, but into a ihiall
round cm:uhr Arca^Q H; ^nd P Q^
. 2. Now this cttculBr Spot ts the Image of the Sun in-
verted, in both Glafles;* and the Angle under which the I-
jnage of an Objedt appears from the Centre of the Glafi R
and S, is equal to the An^Ie under whidi the Objedt ap-
pears ; all which will be ihewn here^te^. Therefore the An-
;le G R H = P S Q, and confeqnently ^t Qmti OR H and
^SQ^are fimilar, and the Areas of theii^ Bafer GH and PQ^
will be as the Squares of their Heights R H and* S Q]^ that
is, as the Squares of their focal Biibncesdireftly.
5. Let A =r Area ox Surface of the large Gla(^, a= t!hat
of the lefTer, F and f die focal Dittahces, and P and / th^
Power of Burning in each, Then^ fince while the focal Di-
ilance remains, the Power of Bummg (P) will be as the Den*
ficy oi the Rays in the folar Spot HG, and this Denfity
ef the Rays will be as the Number of Rays refleded thi-
fher by the Glafs, which Number of Rays will be » the
Surface of the Mirrour (A); therefore P will be as^ A di*
redly in a Mirrour of the fiune Concavity, liut ir^ P : p ;:
A:a.
I
144 ^f LiGiit and CdLotjRs.
Whek Rays of light fall on the Surface of
an opake Body, pirt thereof are refleded to the
Eye, which render it vifible*, the other Part is
tranfmhtcdi and tTirioufly refleded thro* the
, 4. AgSfn, if the Afea 6f each Glafs Jke the fame; the fam6
^antitjr 6f Rays will be colte^^ed, ind converged to th^
Focus's GH and PQ^ and iponfequendy the Denfity ofthof<^
Rays will be grfeitef, the lefs the Spot is in Which they arc
contalnMV confe^uently the Powfer of Burning (P) in this
Cafe is invejrfely as the Area of the folar Spot, or the focal
B^laQce, that is; P will be as ^\ or P :^ :: -^ : ~ •'
f»:F*/ ' ' .
5. Confeqtiently when neither ^ Area of the Glafs not
focal DKiance is.given, we. have the Power of Burnu^ com^
pounded of thedireft Ratio of the Area and ihverfe Ratio ot
;he Square of the focal Diiltance of the Glafs; or we have
_ P:/::Af*:aP^^ Whrch is the' Rule above laid down,
6. It has been ihewn if ^«f/. XClII.) that the Heat of a
* * "/ , wood Fire is about 35 tim^s greater than that of the Sum-
' ^ tner.Sun (becaufe it raifes the Fluid in the thermometer
^5 times higher nearly); therefore that a Glafs inay beable
to condehfe the Rajrs fu^cieiitiy to burn, or to have the
Heajt of cof^mon Fire^ the Sun's iniage^ ox fyhx %ot in the
f'ocus, Gfught to be at nioft but^^j rart of^ the Area of the
Glafs ^ and as much as it is le6 than a 7^ Part pf the Glafs^
fo much the ftronger will it.biirn. In this Cafe, if it be def
£red.to know in what Part of the Pencil of Rays the. Den-
fity is \ 5 times, greater than the eommon Denfity, and where
Ihe Power of Bunung i^^e^ual to that of common Fire, it
is found as ini t&e foflowu^ Example. Admit a. Gla6 be 9
Inched in Diameter; and lel^ the Dimeter of the required
Cirple be (a)i then iince circular Areas are as the Squares of
jtheif Diameters, we have 3^ : i :: 9* : «» j confequently
8 1 •*' /o I
— = «*, and fo tf =r t/--^;=;;i,j nearly j wheitce that
Vi ^ . 35 ■ ■ '
Part of the Cone or Pencil of Ra^, whofe Diameter is i|
Inches, has the Denfity and Power of Burning required; and
that -this is Faa, and that the Dinf^y of the Rays- but a little
lefs than that will not bum, J know from repeated Trials
^ith fttch a Glaf$i or cohcft\^e Mirrour.
Pore^
Of Light and Colours* 145
tores of the Body, till it becomes totally fufib-
Cftted and loft therein ; and fmce none of thoie
Rays come from the interior Parts to the Eye^
we can fee nothing of the internal Sqbftance.of
7. Of Bttrmng-GUffls we have feme extraordinary. Iq-
flf^nces and furprizing Accounts of tiieir prodigious Effe^.
Thofe made of refleding Mirroars are more powerful than
thofe made with Lenfes, (ceteris paribus) becaufe the Rays
from a Mirrour are refleded all to one Point nearly, whereas
by a Lens they are rtfraded to different Points and arc
therefore not fo denfe or ardent. Alfo the whiter the Me-
tal or Subflance is, of which the Mirrour is made, the fhong-
er will be the Effed; and it is obfervable, that the great
Mr. Boyle having m-^de a very large Mirrour of blaclc Mar-
ble, it would not fo much as fet.Wood on Fire, tho* ex-
poTed a long Time in the Focus, fo fmall a Qjuanttty of Rays
are refledled from black Surfaces, the Reafon of which we
(hall hereafter explam.
8. Among a great Number of Mirrours made for humtng^
meittMgi caldfting, and ^vitrifying Bodies, that of Mr. FiUette
is worth our Notice j it was 3 Feet 1 1 Inches in Diameter^
and its focal Diftance was 3 Feet 2 Inches. The follow-
ing Experiments were made ^ith it by Dr. H^ris and Drw
Defagulien.
1 . A red Piece of Ronum Patna began to melt in 3"^
and was ready to drop in 100''.
2. Another black Piece melted at 4^, and was ready to
drop at 64^.
3. Ghalk taken out of an Echinus Sfartagus, fled away
in 33*.
4. A FoflH^-Shell calcinM ki 7^.
5. A Piece of Pompef^ Pillar at Alexandria vitri£ed in the
black Part in 50'', and in the white Part in 54*.
6. Copper-Ore vitri&d in 8*^.
7. Slag,. or cinder of ancient Iron- Work, ready tarun in '
8. Iron-pre fled at flrft, but melted in 24^.
9. Talc began to calcine at 40^, and held in the Focus
64^ ., ,
10. Calculus bumanus was calcined in i!^,. and only dropped
off in 60^.
< 1. A great Fifti's Tooth melted in 32 J^.
12. Tht Jfiejios feem*d a little condeafed in 28^, andf
Vol. IL K fuch
146 Of Light and Colours.
fuch-a Body, which tjherefore is laid to be ofoke.
But when Rays of Light fall on tranjparm
Bodies^ part is reflefted at the firft. Surface, and
part is trar/mitted into the Body, which is re-
Mr. Vilhtte fays, the Glafs ufiially calcines' it.
13. Marcafite of Gold broke to Pieces and began to mek
in about 30".
14. A Silver Six-pence melted in 7 i-^.
15. A Copper Halfpenny (of King ftH/ia^s) melted 'm
20", and ran with a Hole in 30^.
16. A King Georgt*£y ditto>^ melte4 io 16^, snd ran \m
34'. . '
17. Tin melted in 3^.
18. Call Iron melted in \(^.
19. Slate melted in 3^, and had a Role in 6^.
20. Thin Tile melted in 4^, had a Hole and was vitrified
in 80^.
%i, £one calcined in 4^, and was vitrified in 33'.
Z2. A DiariTond weighing 4 Grains loft | of it» Weight.
9. The Power of Burning, in Villettf% Mirrour, may be
computed, and compared with the Heat of Wood- Fire, as
follows: Since the focal Diftance R X is 38 Inches, and the
Angle under which the Sun's Image in the Focus appears at
R, is equal always to 32^ of a Degree; therefore if we
fey.
As Radius — — — — 90*00'== 10,000000
^* A^gte-^ -''''^^^''1"*^ '^' = 7*667849
Se is the focal Diftance RX=: 38'=: 1,585461
To the Semidiameter of 7 tTY--«i^«/— ,^,^^^,^
rhefolarSpot J HX=:o.i79'=: 9,2533io
Whence 2HX=;o,.358 of an Inch, the Diameter of the
folar Focus; but the Diameter of the Mirrour was 47 In-
ches; now 47x47=2209, and 0,358 x ,358 = 0,1 28.
^c. wherefore 2209 is to o, i 28, as the Denfity of the Rays in
the Focus to their common Dcnfity^; but 7o,i28J:f209t=
17^57; which ftiews that the Mirrour condenfed the Ray»
Sev:cnteen Thoufand Two Hundred and Fifty-feven times.
10. Since Rays but 3; times denfer than in their natu^
rtil State with us, 'haije a Power of Burning equal to Wood-
J^ire, if we divide 17257 by 35, the Quotient will be 493 »
therefore fuch a Mirrour will burn with an Intenfity of Heat
493 times greajcer than common Fir^. No wonder then that
'^ fraded
Of laiGwv and Colours. 147
frafted in Right Lirtes to the fecond or lower
Surface,\ where it is again partly rcflefted ano! in
part refra£led into the Air, and coming to the
Bodies which remain iinaherM hy the Force of our greateft
common Fires (as chat of a Glafs-Hoofe, whefe Gold has been
found to lie feveral Days in Fuiion, without any feniibla
Lofs of Weight) ihoold inunediacely become foied, fume a- /
way in {MUt^ part be diffipated and driven away in large Par-
tides, and part remain in the Form of a Ctxfui Martmrni
all which Phenomena have been obferved of Gold in the
Focus of a large Buming'Ghds. And how rudely fuch a
GlaTs would treat the Principles of the Cbymtfts^ and what
Copfufion it would induce in their Arithmetic of Elements^
they will be better certi£ed of^ when they (hall attempt to
analyfe Nature, and reduce Subftances to their original Prin- "
ciples, by more a£tive and elFe^hial Means than Laboratories
at prefenc afford.
11. Notwithfianding the prodigious Denfity of the Rays
.jn the Focus of thofe large Burning-Glaflfes, yet it has been
always obferved, that the Rays relieved to us by the Moon
when at Full, and concentered la the Focus of thofe GMes^
produce no Heat that is fenfible in the leaft Degree, as is
demonilFatcd by holding a Thermometer in the Focus of
lunar Rays, which always remains without the leaft Ap^
pearance of Motion. The Reafon of this will appear by the
following Calculation.
12. htt ABD be the Earth, C its Ceptre, MO the
Moon, N the Centre, N / the Semidiameter of the Moon,
which is equal, to 1087,$ Engltjh Miles; the Semidiameter *
Qf the Earth D C =3 4000 Miles; the Diliances of the Cen*
tres of the Earth and Moon N C xr 240000 Miles. Then Fig. 6^
fmce the Rays of the Sun's Light at the Moon are of the iame
Deofity as with us (as being parallel}; and fmcc the lunar Rays
are only the folar Rays' reflected to us by the convex Sur-
face of the Moon ; and lafUy, fmce parallel Rays are re-
lieved by a iphencal Convex Surface, in fuch a Manner as to
go after Reiledlion diverging from a Point which is ^ the
Semidiameter of the Sphere diilant from the Vertex (as will
be (hewn hereafter) ; therefore fuppoiing the Sur^e of the
Moon to be perfedly i^herical and poiilhed, we may com-
pute the Denlity of the folar R^ys reHeded from the Moon
10 the Earth as follows. ,
13. Let ai^ cd, be two parallel folar Rays falling on
K 2 Eye,
-1*48 Of Light and Colours.
Eye, renders the internal Parts of thpfe Bodies
yifible, which for that Reaibn are faid to be dia-
phanous or tranffarent (CXV),
the Surface of the Full Moon, thefe Rays will be refieded CO
the Earth in the Diredions hg and db diverging from a
Point /in the Radius N f, half way between N and e. Now
the Denfity of the Rays falling on the Moon will be to thoie
refledled at the Earth's Surface, as the Square o£gb to the
Square of 6 d, or as the Square of / D to the Square of
fe; but/^= 544 Miles, and/D (=r NC— CD— N/z=:
240000 — 4544=:)z35456; and theSquare of 2^5456 is
•to the Square of 544, as 187400 to 1 nearly; confeqaently
. the Denficy of the lunar Rays is to that of the folar Rays at
the £arth*s Surface as i to 187400 nearly; therefore a
Burning-Glafs mufb condenfe the lunar Rays 187400 times
to make them have the Heat of the common Sun-Beams. But
this is 10 times more than Fillette^^ Mirrour can effcft.
14. 'Now this is all upon Suppolition that the Moon is a
Sphere, and its Sur&ce a perfect PoLfh, whereas neither of
thefe Things have Place in Nature; for the Moon is not a
Sphere bctt a Spheroid, and her Surface \txy unequal or un-
even, on both which Accounts the Reflection of Light muft
be many times weaker than we have fuppoied it; and ac-
cordingly Mr. Bouguer^ by Experiments, has found that it Is
about 1 7 times leis, or that the Denfity of the lunar Rays is
to that of the folar as 3000000 to i ;. wherefore a Burning-
G\siS& mufl condenfe the Rays of the Moon neav 3000000, /. r.
three Millions of times, to make them warm enough to raife
the Liquor of the Common Thermometer; which is an £f.
fedl almofl 200 times greater than FilUtti^ Mirvour cm pro*
ducc.
Plate (CXV.) I . The Opacity and Tranfparency of Bodies in ge-
XXXV II. neral is thus occafionM: Lee A B be the Surface of an opake
Fig. I. Body A B C D, a Ray of Light G H falling thereon in the
Point H will m part be refleded into the Ray H I, and by
this refledUd Ray the Point H becomes vifible to the Eye at
I; and thus all the Points, and coniequently the whole Sur-
face, is made vifible by that Part of the Light which it re-
ficds.
2. Bat the other Part of the Ray entring into the Body
being irregularly refradted and reflected thro' its internal Sub!
fiance oi Particles and Pores^ bcc^mps divided, dilTipaced^
Whex
Of Light and Colours. 149
When a Ray of Light HC faJls on any Pl«c
plain, convex, or concave Surface, as A B, D E,
FG, in the Point Q tl>e Angle HCK, madfe
by the incident Ray HC and the Perpen-
dicular K C, is always equal to the Angle K C I,
made by the faid Perpendicular and the reflefted
Ray C I : Or the Angle of Incidence is equal to
abforbM and loft therein ; and therefore as none of the Rays
can come from the internal Parts to the Eye, fo none of
thofe Parts can be viiible, and the Body is in that cafe faid
to be opake,
3. In order to this we mud confider, that tho* the whole
Body be opake, yet the Particles of fuch a Body are nor
iingly opake, but freely tranfmit the Light without refle£ling
any Part between the Surfaces, and are therefore in them-
felves transparent ; and were thofe Particles contiguous to
each other, the Light would pafs from one to another (and
fo thro' the whole) without Refledion, as we find by Expe-
riment it will pafs thro' feveral contiguous Pieces of poli(h*d
Glafi, and thus produce Tranfpacency.
4* But if the Particles do not touch in fuch manner as to
leave the Interftices or Pores exceeding fmall, there will be a
RefledUon of Light at every Pore from the Air which it ther«
meets with, as being a iViediam of different Denfity. For
it is known by Experiment, that tho' a Ray of Light will pafs
from one Piece of Glafs to another, that is contiguous with,
out RefledroQ, yet will it not p^s from the Gla& thro* the
contiguous Air without being in part reflected ; confequently
where the Pores are large apd very numerous, there the Re*
fledion of the Light will be To great upon the whole, as to
caufe a total DifQpation and Lofs of the Light that enter'4
the Body, and fo render it opake.
5. This is coniirmM by uking ten Pieces of cleaf Glafi, .
and laying them one upon another over a Leaf of Print, quite
dry, and having only Air between them i then taking tea
other Pieces of the fame Glafs, and putting them into Water,
fo that it may fill all their Interdices, and then laying them
on the fame printed Paper by the other, a Perfon looking
thro' each will fee the Print or ^Reading much more di(lin£^,
clear, and bright, thro' the latter Pieces than thro' the for*
nier ; the Rays being more regHlarly tranfmitted thro' them
where the Denfity of the Parts is not fo unequal, and alfo
K 3 the
150 Of Light and Colours.
the Angle of Refledlion in every Inclination of
the Ray of l.ight. This is evidently Ihewn by
Experiment; and it is very well worth our Ob-
• fervation, that in this Cafe only, the faid Ray
with much Icfs Reflexion, than thro' the other, where the ,
Light undergoera confiderable Reflexion at every. Interftice
or Flaic of Air between the Glaffcs.
6. 'Tis hence alfo that tranfparent Bodies are render'd Or
pake by feparating their Parts and rendering them more po-
rous ; thus Beer before it is raifed into Froth is tranfparent,
but the Froth, by reafon of its Pores, becomes opake; thus
dry Paper is more opake than that which is wetted with Wa-
ter or Oil, becaufe more porous. Thus the Oculus Mundi
Stone is more opake when dry than when fteep*d in Water ;
and Glafs reduced to Powder is noionger tranfparent.
7. Hence it follows, that the Parts of Bodies and their
Pores muil not be lefs than a certain definite Bignefs to render
them opake. For the opakeft Bodies, if their Parts be fub-
tilly divided, become perfectly tranfparent. Thus Copper dif-
folved in Aqua-fortis has all its Particles pellucid, and the
whole Solution is tranfparent. Thus a Bubble blown of Soapr
Water may become fo thin on the Top as to reflect bq
Light, but will tranfmit the whole. Thus Water, Salts, Glafs,
Stones, 6fr. tho' they ar^ as porous as other Bodies, yet their
Parts and Interflices are too fniaU to caufc Refleftions in their
common Surfaces.
a. Therefore in all tranfparent Bodies, as B E F C, a Ray
of Light, as KL, fallina on its Surface in the Point L, will
Fig. 2^ ^^^'"^ ^^ ''^ P^*"^ reflected (as before) into the Ray L M ; tha
^* ^ other Part will go regularly on in a redlilinpal DirefVion from
the upper to the lower Surface at N, where meeting with
the Air (a Medium of a different Denfity) it will be in part
reflected again into the Ray NO; th^ other Part gops out to
the Eye at P, by which means all the internal Parts from
whence that Ray comes will be rendered vifible to the Eye \
and fince this may be conceived of every Point in the Body,
it is cafy to underftand hpw tjie Whole becomes tranfpa-
rent.
9, I have often found Gentlemen rcfleft with great Sar-
fwize on the exceeding great Porofity of Bodies neceffarily
required for tlie TranfmiflidH of Light, and yet at the fam0
time on the Hardncfs and Firmncfs of the Parts of fuch bor.
dies, as Glafs, for Inftance, and others. But 5ir ifaac hW^tt^n
takc$
Of Light ami Colours. 151
takes the Jhorteft Way fofflhle from any Point H,
to any other Point I, if it muft, in its PaflfagCy
touch any of thofe Surfaces (CXYI).
has put us into a Method by which we may conceive this
with as much Eafe as it produces Surprize; and it is this : Sup-
pofe a Body be compoTed of fuch Particles, and of fuch a Fi-
gure, that when laid together, the Pores or Interllices may
be equal to the Particles themfelves ; how this may be done,
and the Body hard and firm, is not difHcalt to conceive; fuch
^ Body then will be half foHd and half porous.
10. Now if each of thefe conflituent Particles, inftead of
being foHd, fhould be fuppofed to confift of other Particles,
£qua! in Bulk to their Pores between them, then woald the
folid Part of the whole Body be but half what it was before
fippoftd to be, that is, it will be but \ Part of the whole
Bjolk. In like manner if thefe Parts are fupjMed not (blid^ b^
to confiil of other Paru with equal Pores between them^ "gs
then manifefl the folid Matter will be but 7 of the whole
^ulk of ^e Body. And thus by continuing this Subdhrifioi^
of the Parts, you diminifh the Quantity of the folid Parts, and
increafe that of the Pores, till it (hall be m any Proportion
greater than that of the folid Matter, and yet the Parts, and
confequently the whole Body» (hall be every where comp^^
and hard.
1 1 . Hence it follows that the leaf! affignable Partick of
Matter may be conceived to be fo minutely dividq^, £hat t(
(hall be difFufed thro' any afHgnable Space, how great foever,
in fuch a manner, as to be in Conta6l, and to confdtute a-haM
and compa6t Body, whofe Pores (hall be lefs in Diameter
^han any aflignable Length ; or, in other Words inverfely,
•Che fblid Matter in the Globe of our Earth, yea of all Bo-
dies In the Univerfe, may be no more than what may be re-
Viuced within the Compad of a cubic Inch, or be contain*d
.In a Ladfs fhifnhU, They who wouli fee a Mathematical
^Demooilration of this, m^y confult Dr, iSr/7/*s Introdudlion
to Natural Philofiphy. ^ ' . ,
, I z. Hence we fee the Poffibiltty of Bodies being fo ex«
cee^ing porous, as to be rare enough, to tranfmit Light wick
all that freedom pellucid Bodies are found to do. Tho* what
their real Stradlure or inward Frame may be» is yet unknown
to us.
(CXX^L) I. 'The Demonftration oftliis is as follows: Let Fig. 3.
AC be the incident Ray, aiidCB the rcflcdcd one; from
K 4 The
155 0/" Light tww/ CoLoyRs.
The Rays of Light rcflefted from the firft
Surface of a Glafs are in 4 much lefs Quantity
than thofe reflcfted from the fecond Surface, as
\& evident from hence, that the Image form'd in
ihe firft Cafe is lefs bright and fplendid ;han that
of the latter 5 and if the fecond Surface be eontir
guous to any tranfparent Medium^ as Air, Water,
. (ffc. the Rays will be reflefted from thence in
greater Plenty, as the Medium is more rare ;
whence the Image by Refleftion from the fecond
Surface is brighter when that Surface is conti-
guous to Air, than whpn it touches Water; and
moft bright when it is contiguous to a Vacuum.
If the ftcorid Surface of Glafs be covered with
an opake Body impervious to the Rays of Light,
A and B let fall the Perpendiculars A £ , B D, 9nd let A£ =: q^
BD=r^, ED = f, andEC=:;r; then CD=:c^— jr, anj
ACz=z\^ aa + xx, and alfo CB = l/^^-f-rf — 2fjr-fjf«.
dThcn fincc AC-^-CB is to be a Mhimum, we muft make the
Fluxion of its Expreffion %^ aa-^-xx-^V^ lfb'\' cc — zcx -f xx
, ^v ' • XX , XX — ex
^qual to notmngi ovz — + t
sro; whence dividing by A-, and multiplying crofs-wife, we
have xv.V bbAr^f: — 2f ;t-|-Ar.v -J- Jf-^f ^ ^ «« + **» ^^'*"
fequcntly xv.^ 1}b-\'cc — zcx'^xx:=:c — xy.\^ aaJ^xx^
thatis, £CxCB = tDxAC,- and fo we haveEC:AC::
CDiCB. Confequently (by Euclid, 6 and 7.) the Triangles
A EC andBDC arc equiaF.guiar, and therefore the Angle
of Incidence ACE=BCD the Angle of Refleaion.
2. Since the concave Plane P C G,' ?.nd convpx Plane D C E,
do both touch the Plane AB in the fame fingie Point C on
which the Ray of Light is fuppofcd to fall; the fame Law
pf Refl^dlion muft4iold with refpedl to all the Planes equally;
bccaufe the Situation of any other Particles have northing to
dp in the Caufe of Reflexion of Light, ^ut that on whici^
jhc R^y immediately impinges, " -
they
Of
Light and GoLouits. 153
they will dien be reflected in 'much grciter abun-
dance from the fccond than from the firft Sur-
face, and the Image will be proportionally more
bright than that formM by Refle6tion from the
firft Surface ; which is- the Cafe of all Glai&s for
liated or quickfilycrM. ,Whence it appears^ that
the l;i^ht reflei^ed fnom the iirfl: Surface bears a
yeryjfmall Proportion to that which ]& cramitted
into the Subilance of the Qiafs. .
Wh£n a Ray of Light, as H C, paflTes out of piate
Air into a denfcr Medium^ a* ABFO, it will "xvm.
be ilrongly attracted by the Particles of the Sur*
face of the Medium A B, a little way on each
Side \ the Confequepce; wh^i^f 1^9 that its Mo-
tion will be accckrated at the Entrance of the
Medium, and its Dire&ion fomewhat altier'd; for
fince the Attraftion of the Medium is pcrpendi^
cular to its Surface, it will defleft or bend the
Ray out of its firft Dii-edlion H F, into a new
one CE, (tliro* \k)& Medium) which lies nearer to
.the Perpendicular KJD, drawn, thro* the Point of
Incidence C: And this. is cst^il'd the R'efractiow
^/ a Ray pf Light ; H C K; iS the Angle of Inci.-
dence, and P C E the Angle of Refradion.
If cm the Poitit C be defcribed a :Cirde
PHKG, a^id from, the Points H and G (where
jhe Circle cuts the incident and refradlcd Ray) be
drawn the Lines H L, G I, at Right Angles to
the Perpendicular KD, they will be the Sines cf
the Angles of Incidence and RefraSlion. And it
isfeveral ways demQnftrabJe, that in every Incli-
p^llon of the R^y gf Light HC to the Surfeoe
pf
.11
'J34 ^f Light and Colours.
of the* Medi\3iii AB, diofe two Sines HL and
Q I wKI always have one certain or conftant Ra-
tio or Proportion to each other: And that HL:
GI :::'4 ij, if the Refraflion be out of Air into
Wctetfi'^ but HL:GI:: 17:11, or 3:2 nearly,
if our of Air into Glafs-^ and in general, the den-
ier th^ Medium, the greater its refradive Power,
fer'li)tf{)rbpoiHiiGnQf the Sines j alf which Parti-
culars will be very evident by Exf)eriments.
? . ; ij?'a^Ray; of lights as EQ pafs om of a den-
• " '^ fep Medium inlfo t rarer, as a Water or Glafs in-
«fS%V ift'^1), uf)0n dnterirtg the rarer Medium
dit>€,f5betc*raaledi ftoai' its «rft Direaioh EN
«M «InftW?OFm CH, ^hich will be^ either off
dFrom the PerpehdictiUr KCD; and'fi*i this Caf^,
•IG will be the Sine of the Angle of Incidence,
•and HI^ that of the Angle df Refraftion ; and
•^11 otfaflBi Barticulafas jiift theffeverfe of w4iatthey
were ibcfioiic ,imder the fame Nam^s.
He»cb it follows, that if ahy 6bjea be placed
at E, and dover'd witti -Water to the Height
C D,- It will be feen by an Eye placed any where
above the Sutface- AB, in a{ Situation *]6w<?r iSiah
would-be otherwife pdffiMel .'and' thus- Objeds
which are invifible may be rfehder'd vifiBIg by the
Interj)oriti6n of « denfer* Medium,*- as is well
ldiij>wni by a common Experiment. On this Ac*
icoonCit is that wg fee the Siin, and other ^Lumf-
' '(iari«5>- Millie they are yet below t!hc Horizon, in
a M&ning before they rife, and -in jthe Evening
t^ltt tfeey are fet, by the Refraction 'oJT the At.
mofphdre* ' Hence alfp the Difference in^he Dia-
meters.
Of Light and Colours; 155
meters of the horizontal Sun and Moon^ and their
elliptic Figurcy by t^le greater Refraftion of the
Rays coming from the lower limb.
Again; it follows, that if an Objeft be vfew'd
which is part in one Medium and part in another,
as a Staff reprefented by NE, it will not appear
Jhaity but crooked 'y for if rfie Eye be in the rarer
Medium, the Part of the Staff in the denfer^
CE, will be rcfrafted into the Line CF, and
the whole Staff will appear- in the crooked Form
NCF.
Hence alfo all Objefts in a denfcr Mediuni
appear raifed or elevated above their real Si*
tuations : Thus ,the Part of the Staff C E is raifed
into the Situation C F ; and the Bottom of all
Veffels, if cover'd with Water, appear raifed, or
higher by a fourth Part of the Depth of the
Water, than what they really are (CXVII),
(CXVII.) 1. If Bodies, o|i which Light fidls, were fupW
pofed to aflfeA it no other ways than by giving Admtffion to
the Ra;ysy or pennitdng them to pais thro* their Subftance^
they would then perfevere in the hmt Right Line after their
Immerfion, as before ; and of courfe there couki be no ftich
thing as the Refra£lion above defined. Bat Bodies are not
paiTive to the Rays of Light, but a6l upon them with a rea(
and determinate Force, as is evidently proved by £}q>eri«>
ments. Thus if a very fmall round<Hole be made in a thim
Piece of Metal^ and the Light oft the Sun tranfmitted thro*
it into a dark Room; if the Mebd aded not on the Ray
.JpaiTing thro' the Hole, the Spot of Light would always be
of the fame Size with the Hole at all Diibnces from it; but
becaufe we always obferve the lummous Spot is larger than
the Hole, and the more fo as it is farther diflant, is a plaia
Proof that the P^uticles of the Metal in the Periphery of the
Hole a6t with an atcradting Force on the Rays of Light, and
inAof^ ^m in facb a manner as to caufe them to proceed
The
?5^ 0/* Light V2^W Colovrs.
. Th£ Sun's Ra,ys, as I have faid, are not ho-
mogenepus, but of different Kinds; and each
Sort has a different Degree of Refrangibility j
riiat is, inpafling through a d?nfe Medium, .they
diverging from eiach other,
' 2. Jti likc'manher» if the'Raya oi Light are made to pafi
between t)ie paraUel Edges ^f two Knives placed at the Dir
riance of t^ of an Inch, we (hall obferve on each Side tlie
tranfnMtted Beani a Glare of -Light like that of the Tail of a
Comet, if the Beam be received <>n a Sheet of Paper, at the
Diftance of about 4 or 5 Foot from the Knives. And if the
Knives are placed withthcfr Edges about ts 3 of an Inch
apart, inftead of the Light above mentioned, yoa'U <^ferve
0n each Side the Beam of Light, three Fringes of coloured
Light parallel to the Edges of the Knives, which are more
diitin& as die 'Hole of the. Window or Beam of Light it
kfs.
* 3. If the Edges of the Knives be brought within ^o of
txi Inch, 'no Light will appear on the Paper between the faid
Fringes, fo that all the Light which paiTes between the Edges
is innefted. on either Side, which plainly (hews that Steel
afts at the Dillance of-^^-Q Part of an Inch upon the Rays of
Light, by an attra^'ve Force which is increafed as the Di^
fiance of the Knives is diininifh'd.
4. On the other Hand, the Shadows of all Bodies placed
it\ the Beam of Light in th& dark ^obm are larger than they
ought to be, were the Rays of Light to pafsby them on*
;#eded. by: any Power from xhem ; for then the Shadow
would be at all Diftances of one ^ and the fame 'Bijgnefs, n)ix.
equal to that of *the Body ; but fmce. we obferve the Shadow
always' larger' thasi the Body, 'it follows, that the: Rays mufl
)>roceed dKerging from the Surface, of the Body, which they
could not da but by virtue Qizrepeihnt Pvwtr^ which canfes
Chcm to feparate to a greater Diiiance after they have pafs'd
by the Surface of the Bxi^y ; thus the Shadow of a Hair has
l^n obferved' 3 5 times bigger thanl the Hair itfelf.
5. This actrafting and repelling Power in- the' Panicles of
Bodies, -by which tliey iniledl the Rays of Light, is the Caufe
of all RelbSaon and.Refraflion.of Light, of which we fhaU
now treat more particularly^ Let there be two Mediums
Fig- 4' (fup^ofe of Air and Ji^ater) and a Ray of Light H G in the
i-arer. Medium fJir) tend towards a Point K in the Surf2i,cc
of the denier Medium (JVater^) A B ; Ac attrading Power
^re
Of Light and' CbLouRS. 137
are differently dilppfed to be reffaAed, being
bent or turnM out of their firft Courfe to dif-
ferent Diftances from the Perpendicular: And
thefe feveral Sorts of Rayii.have each a peculiar
of the Pacticles io rhe Surftcf of the denftr Mediam extends to
a certain finall Dillance> as to the Line £ F; as foon then as
the Ray is arrived at the Line £ F, it gets into the Attni£Uon
of the Medium, which a6b perpendicular to the.Surfa^.
6. The Particle of Light in the Point G, begins to be
a£led upon by two Forces j one derived from i^ natural Ve-
locity in the Direction GK, tUe other derived from the at-
tracting Medium in the Direction G I ; let then the Paral-
lelogram G'KMI be compleaced, and *tis'manifeft (from
what we have fhewn already) that the Ray will move in
the Diagonal of this Parallelogram, in%, in the Diredioft
G M, and impinge on the Surface at L.
7. Now fince the Ray of Light, after it comes to G, Ik
influenced by the attraCling Virtue of a Number of Particles
continually increaiing till it comes to L, the Force therefore
by which it is urged in the Direction G I; is a Force raii*
formly increaiing, like that of Gravity; its Motion there
fore will be conftantly accelerated, and its Diredion G L not
a Right Line, but a Curve. But lince the Diftance G I is in-
definitely fmall, the Curvature of its Path for fo fhorc a Space
is not fenfible, and may therefore be repreientcd by a Right
Line.
8. Let N O be drawn 'parallel to the Surface A B, at the
fame Depth below, as £F is above it; and then it is evi-
dent, that fince the Particle of Light is attradled every way
equally within the Diftance of IG all round, the Attraction
will be greater towards the Line N O as it approaches nearer
to it; confequently its Motion will ftill be accelerated from
L to the faid Line, and will alfo be a Curve; therefore the
Particle will not go on to M io the Diagonal G M, but will
go to a Point P in the Curve L P, nearer to the Peipendi-
cular Line L (^
9. After it is arrived to the Line N O in the Point P, the
Attradion will be on all Sides equal, itt Motion or Velocity
uniform, and its Direction a Right Line, till it comes witluii
the fame Diftance G 1 of the under Surface of the Medium
C D, where its Path will again begin to be incurvated into
R S, and every thing will be the Reverfe of what we have
flow obferved at its Iixmierfion, that is, R S wiH be fimilar
Colour,
1^8 Of Light and Colovils.
Colour^ viz. thofe which are leafl: refrangible ure •
i?:^;:the fecond Sort, Orangey the third Sort»
Tellowytiit fourth Sort Greeny the fifth' Sort^
Sluci thcifixth Sort,. Indigo-, and the feventh
Sort, Fiolefj which are moft refrangible, or re-
frafted to the greateft Diftancc from the Per-
pendicular.
To illuftrate this Matter, let G F reprefent a
to G L, and S V parallel to HO, or the Angle HOXzs
VSY.
^ lo. The denfer any Medium i», the greater will be the
Number of attr^ing Pxrticks in a given Space, and (b the
greater will be the Force G I, or the refractive Power of
the Medium; thus Water is lefs dtnfe^ and therefore ht6 9l
lefs refradUve Power than Glafs, and Glafs lefs than Diamonds
But OiJj, though lefs denfe than Water, have yet a greater
refraflive Power, as containing a greater Proportion of Sul-
pbur than other Bodies ; for fince A6lion and Re-adion are
mutual and equal between all Bodies, and fmce we fee that
Hays of Light congregated by a Burning Glafs ad moft upon
fulphureous Bodies in turning them into Fire and Flame, to
on the contrary, Sulphurs, Oils, Spirits, 4ffr. ot^ht to ziSt
moll upon Light, as we conftantly lind they do ; and Sir Jfaac
Keixtort thought it reafonable to attribute the refradlive Power
of Bodies chiefly, if not wholly, to the fulphureous Parts with
which they abound.
]>|j^^ II. Since the Velocity of Light in different Mediums is
xxxvitt* ^^^^^U let its Velocity in the rarer Medium from H to C
* be to that in the denfer Medium from C to £, as m to « ; and
fmce the Spaces defcribed are as the Redlangles under the
Times and Velocities, the Times will be as the Spaces di-
rectly, arid the Velocities inverfcly ; whence the Time of de-
icribing the Line HC will be to the Time of defcribing the
LineCG, as » x HC to /» x CG. LetCI=:tf, CL = i^,
HL + IG = /, and IG =;r; then will HL==:r— x,
^nd confequemly C G = V^tf-j- x:c, and H C zs:
^ bb^cc^^zcx-^xx I whence theTiroe in which HC^- CG
is moved through is mi^aa-^xx-^-nS^ bb^cc — icx-^-xx,
12. Now admitting that Nature does t\try thing i« the
fijQTtejl H^ay^ wc have the foregoing ExprefRon of the Time
Paicd
0/* Light and Colours. 159
Parcel of the folar Rays entering through the
Hole H of a Window-Shutter, into a darkened Plttc L.
Room ; and there let them fall on the Prifm ^*' '*
ABC, in the Point F: In paffing through the
a Mmmtmf »d fo-iu Fluadon equal to Notbing, viz^
o ; WJiettcc \Ve have
'"■'^ IG
:) that is.
Vaa-\^xx V^bh'\'cc---2cx^xx ^^
^■^— -. Hence, makibgHCsCG, we have mxIG =
nxUhi an j conrequently, nr : « :: HL : IG.
13. But the Ratio of m to n^ that it, of the Velocity be-
fore and during the R^fradlion, is confiant, or always the
fame in the fame MeMa i therefore the Lines HL and I G are
in a given or conftant Ratio. Hence we have this fimdanxen-
tal I^w of Refradion, That th$ Sim of the AngU of IncidencM
is al<ways in a confiant Ratio to the Sim of the Angle of Ri*
fraSion^ in all Inclinations of the incident Ray whatfoever.
14. Since the Proportion of thefe Sines is confbmt, it re*
mains that we determine what that Ratio is in different Me-
dia ; and for that Purpofe there are various Methods, one of
the bed of which I ihall here defcribe, but mud fird premife
the following Lemma. Let GHD be an equilateral Trian- »•
gle, dnd let the Angle D be bifefted by the Right Line DO ; ^^^
let A KM C be drawn paiallel to the Side GH, and through p?^^'
the Point K draw I KN cutting OD in N; then is the Angle *• 5
AKIzrNKB, as being vertical to each other. Alfo the
Triangle NKD is divided into two fimilar and equiangular
Triangles N KB and BKD, by the Perpendicular KB; and
therefore the Angle N K B is equal to the Angle K DB. All
which is evident from Euclid" % Elements.
1 5. Suppofe now that GHD be the Se£lion of a Prifm of
Water or Glafs, or any pellucid Medium, and KM a Ray of
Light paiUng through it parallel to the Side GH ; and let it
go out of the Prifm and be refradled into the Air on each Side
into the Diredlions KF and ME ; upon the Point K defcribe
the Semicircle PIQj then is NKB (= KDB) = AKI, the
Angle of Incidence out of the Prifm into Air, and FKI is
the Angle of Refra^ion; confcquently, AR andFS are the '
Priiin
r6o O/LiGU't and Colours.
Prifm they will be feverally refraAed in a dif»
' fercnt Degree, and thus fcparated from each o-
'- ther, fo that at their Exit on the other Side at
Sines of the Angles of Incidence and Refradion out of the
Prifm into Air..
\(i. On the contrary^ we may confidet PK as the inci-
dent R^X falling upon the Prifm in the Point K, and refradted
in the Diredion KM parallel to the Side GH, which at the
Point M emerges again into the Air in the Diredion ME,
making the Angle £ ML with the Perpendicular ML equal
to the Angle FKI. In this Cafe the Angle FKI is the /^n-
gle of Incidence, and N KB is the Angl6 oi'Refraftion in the
Prifm, which Angle of Refiadion isther^OTe given, or con-t
fiant, as it is always equal to the Angle KDB, or half the
Angle of the Prifm.
Plate '7' '^^^ Angle of incidence FKI confifts of two Parts,
'i)m, of the given Angle AKI (= KDB) and the additional
Fie^6 ^^^ ^^^* ^^^ ^^^ ^'^S^^ ^^^ " known, as being
** * equal to half the Angle of the Prifm ; and the Angle FK A
is known by placing the Prifm by the Center of a graduated
Semicircle, as ABC, carrying an Index, whofe two hrax%
F K ?ind K E iare equally elevated above the horizontal Line
' AC, and corrcfpond to the incident and emergent Ray FK
and M E in the other Figure. For here 'tis evident, if aa
Objc6t be placed on the End of the Arm F, it will be fecn
by an Eye looking through the Sights at the other End of
the Index E ; and when the Objed is thus fcen, the Angle
AK F is known by the Number of Degrees which each hxvok
cuts upoi^ the Limb of the Semicircle.
1 8. This Number of Degrees, added to the conftant Num-
ber 30**, which is equal to half the Angle of the Prifm, gives
the whole Angle of Incidence FKI; and thus the Angles oiT
Incidence and Refradion being found, the Proportion of the
Sines FS and AR will be difcover'd, which Ratio is always
the fame while the Matter of the Prifm remains the fame, aa
was before fhewn from the Theory, and may by this Inftru-
ment be proved by Experiment. For Example, Let the Prifnt
be of Water ^ it will be neceflary to elevate each .Arm 1 2 De-
grees upon the Limb, before the Image of the Objeft at P
can be fecn by the Eye at E ; then 1 2 -f* 30 =: 42** =
F K A + A K I = F K I, the Angle of Incidence, But thd
Sine FS of 42** is to the Sine AR of 30*^ as 4 te 3 vei^
ftcarly.
Of Light and Colours* i6i
fe^ they will proceed at different Diftances from
the Perpendicular E P to the dther Side of the
Room, where they will make a long and varioua*
19. Now it is plain, if tbe Ratio of the Sides AR and FS
Were not fix*dy fince FS might be in any Ratio greater or.leia
than AR« the incident Ray FK nay make an Angle FKI
greater or Idi Chan 42''^ and yet the ObjeA at F be feen by
the Eye at £ ; but this we find by Experiment to be impoffi-
ble^ becaufe there is no other Elevation of the Arms of tiie
Indiex that will exhibit the Appearance of the Objed» but
the one above-ndentioned.
20. If GiiD were; a Prifm of Glals, as ihat Is a denfer
Body than Water, fo its refradive Power will be greater, and
confequently it will ad more (liongly upon the Ray KM at it
Exit into the Air, and caofe it to be retraced farther from the
Perpendicular IK or ML. Therefore the Angle of Inci-
dence out of Air into Clafs, <ivx. the Angle FKI, ought to
be greater, and fo to require a greater Elevation of the Legs
of the Index than before in the Prifm of Water : And this
we find by Experixnent is the Cafe ; for then the Eletation^
infiead of 12% niuft be about 22® or 23°.
II. H«nce *tis plain, the Sine of Incidence FS muft be in
a conftant Ratio to the Sine of Refra&ion A R ; becaufe, fince
the Angle A KL is invariable, (being always equal to GDO)
and in the fame Medium G DH, the Angle FKI mud always
be the fame, becaufe the refradive Power is every where foj
therefore, the Angles being conilant, the Sines will be fo toOj
Or their R^tio to each other always the (ame.
22. As by this Inflrument the Angles of Incidence and Re-
fradion aredifcoverM, the Ratio of their Sines will be knowd
of coorfe, for each refpedive Medium. Thu& in Water the
Sine of 42^ is to the Sine of 30^ as 4 to 3 very nearly ; and
in Glafs the Sine of 46^ is to the Sine of 36^ as 3 to 2, or
more nearly as 17 to i i . ^^ fome Experiments it has beed
found, that the Sine of Inddence is to th^ Sine df Refiradioa
in Diamofui tL^ 5 to 2,
23. But iince in Phyfical Matters we have no Authority
comparable to Sir J/aac Ifrwioni I Hiall here give a Tabid
(from his Optics) of the Proportion of the Sines of Inddencd
and Refradion of Yellow Light (that being nearly a Mean be«
tween the greateft and leaft refrangible Rays, as vire ihall fee
farther on}. This will be contain d in the firfl Column ; the
fecond exprefles the Denfities of the Bodies eftimated by theif
Vol. IL I* ' coloured
l62
Of Light and Colours.
colour'd Image of the Sun XY, which is, per-
haps, one of the tnoft iurprizing and agreeable
Spedbacles of Nature.
Specific Gravities \ and the third the refraftive Powtf of each
Body 10 refpeft of its Denfity.
24.
"The Rifraaing Bodf.
Frofortien of
tbi Sings,
fDtnfUy,
Hif.
Power
Air
3201 to 3200
0^0012
5208
♦
Glais of Antimony
17 to 9
5,2800
4864
A Pfeudo-Topaai
23 to 14
4,2700
S979
A Sclcnites
6t to 41
2,2520
5386
Common Gkfs
31 to 20
2,5800
5436
Cryftal of the Rock
25 to 16
2,6500
5450
IflandCryibil
Sto 3
2,7200
6536
Sal Gemmae — —
IJtO 11
2,1430
6477
35 to 24
1,7140
6570
22 to 15
1,7140
6716
Nitre
32 to 21
1,9000
7079
Dantdck Vitriol
303 to 200
1,7150
75S»
Oil of Vitriol
xo to 7
1,7000
6124.
Rain- Water — —
529 to 396
1,000
7854
Gum Arabic
31 to 21
^37S<5
8574
Spirit of Wine reaified
Camphire —
io« to 73
0,8660
10121
3 to 2
0,9960
12551
on Olive
22 to 15
0,9130
12607
Linfeed Oil
40 to 27
0,9320
12819
[Spirit of Turpentine
25 to 17
0.874©
13222
14 to .9
1,0400
13654
100 to 41
3.4000
.4jfj6
25. The Refiafiion of the Air in this Table is determined
by that of the Atmofphcre obferved by Aihonomers; for if
Light paTs thro* many refra£Ung Subftances, or Mediama,
gradually denfer and denfer, and terminated with parallel Sur-
faceh, the Sam of all the Refradlions will be equal to the
iingle Refhi£lion it wocdd have fuSer^d in pacing immediately-
cut of the firft Medium into the laft; becaufe the emergent
Ray will be purallel to the incident one in. every Meduin^
fingly (by Art, 9 ) if they were feparated; and their being
contiguous can make no Alteration. Hence, if A A be the
XXX VL Medium of Air interceding two different Media, as 6B of
Fig. 7. Water, and CC of Glafs; then the cmcrgeat Ray ei oat
The
Plate
Of LiGttt dnd CoLouks; 163
P^* The fevcral Sorts of Rays, after they are re-
^ ' fr»5ted^ appear in their own proper Colours in
Order as follows, 'oix. Thofe which are Icaft rc-
^^ ^ the Water is paniiiel td the incideiit Kaf a r, and the e-
inersetit Ray U <Nit of Ghfa is piialkl to the inddent Rajr
.. »» i Whence 'tis plain^ the Refindioii of the Ray il is the
lante «s if the two Media B B and € C were coatlg;iioas» the
Ray it in (hat cafe beii^ loil» which makes no DiCerence.
26. Hence^ if the Sine of Incidence oni df Air into Wa«>
ter be as (tih \ii)l\ R, ind that of {nddenob to the Sine
of Refraaion out of Ait into Qlais .as (%• \ik) l\Ki then
n9z=L^^^z=LalzJ^i Whcntc Rx/)t/i = ^xlx
i/fl bttt when the two Medift BB and CC are tontigaoo^;
i/^=:4/ will be the Sine 6f Incidence oat bf Water into
Glafs, and ^ ism/ the Sine of RefhK^idn; therefore cf\
iitlziKxiiRyt III the Sine df Incidence dnt of Witer: td
tiie Sine of Refiadion in Glafs.
27. I cannot here omit to mention the accdrate Method
which was made ufe of by Mr. Hcpwfihee^ at the Appoint-
inent of the Rdyal Society; to determine the refradi^e Pbwer
of the Air, which was thus: He made choice of a diflin£t
erea Objea P» at the Diftance of 2588 Peet j a Prifin ABC Fig. 8^
Was exhaufted of its Ahr, and applied to the End of a 10
Foot Telefcope with a Hair in its Focus. The Objea wa^
then view'd thro' the Vacuam by the Ray PES; then ad-
mitting the Air into the Piifm, the Obje^ was feen to rife
above the Hair gradually, as the Air entered j in the End,
the Hair was found to hide a Mark in the Objefdt 10 1 Feet
below the Markj as at P, fo that PM =: 10^ Feel.
28. This done, the Condenfer was applied, and One At*
mofphiire inje^ed into the Prifm, whic^ was applied to the
TelefcOpe^ as before, and letting oat the Air, the Objed was
feen to defdsnd thro* thib fame Space of io| Feet. Now
fince the Radios PI=: 2588, and PM=: 10,25, we fhall find
the Angle P I M := 68^ the half of which gli^s 34^ for thii
Angle op I, which taken from the QJ) K or QB D (=
32'' =; half the Angle of the Pri&i) gives the Angfe KDt.
or LDS;=: 31^ 5^ 26^^ and fd the Sine of the Angle of
Incidence in VkKuo{ii^) is to the Sine of the Angle of Re*
iraaioh into Aif (31^ ^^ 26^] as ioo<5ooo to ^99736:
(See Mr. Hawkfiei^ own Figures in flau 36. ttg. 7, 8, 91)
29. In order to ludtrfiand the KSbenoe between the trni
& 2 ItHB&Ai
,164 Of^LlG^T and Colours;;
frafted, or fall neareft the Perpendicular PEy-are
Redy and make the red Part of the SpSlrtm a|:
R; the next are the Orange at O, the Tellpw at
and api^arent .Placed of Objeds, feieiitlm>*7a Medium ofiWi-
^fcrent Dcn&ty from the Air, let tke ScheiAe be cdiliibtt^ed as
in. the Figure, where the Sinies of Incidence and Refntdiion
Plate are ]Hl L and G I; and thefe are in a given Ratii) of A to B» .
xxxviii. thatii, HL:GI:*A:B).bat bccaufe of paralW Lines n6
KC, we have HL = N Kj therefore NK:JG :: A: B::
^C:IC=HC; hutNCiHCriCErCM, becaufePEis
paaUel to K D, ^herefo» CE.: C M :: A ::B.
. 30, Now fmce the Ray EC coming from an Obje6^ at E
is Tcffra6ted in the Air into the Ray H C; if HC be con-
tinued ta F, the apparent- Place of the Ofajedl will be in the
refracted Ray at M in the Perpendicular £ P, aqd proje^kd
10 F on t;he horizontal Plane O R, but the Point M will al*
ways be the viiible Place of the Image; therefore when the
Angle CEO is indefinitely fmall, or the Point C coincides
iwitliO, the LinesCE andCM will becomeOEandOM;
and in that cafe, OE:OM::A:B::4:3, in Water. Whence
."'tis evident that the apparent Place of an Object immerfed in
Water, and view'd in the Perpendicular, will be at | of the
Depth of the Water.
3 1 . But if the Medium be Glafs, then O E : O M :: 3 : 3,
^r more nearly as 1 7 to 1 1 ; fo that 47.O E = O M, or the
apparent Place of an Objed feen thro' a Medium of Gla6^
will be at the Dillance of 44 of the Thicknefi of the Glais
OEv In Diamond, it would be at the Depth of | of the
Thicknefs, and fo on for all the other Bodies mentioned in the
foregoing Table., . , .
.32. On the other Hand, as the Point C recedes from the
J'oiQt O, the Angle CEO which is equal to the Angle of Itt»
'cidence E C D, becomes greater, and therefore alio the An-
^le of RefraOion tlC K, or the refraded Ray HC will
•have a greater Inclination tp the horizontal Line A B, and
^therefore alio CF; on which Account 'tis evid^t the Di*
fiance of the apparent Place of the Obj.e£t« inz, the Line
ti M, will decreafe, and of Courfe the Obje^ will feem to
-rife in the Perpendicular. And when the Angle CEO is fo
jgreat, that the Ray CH is refraded parallel to the Horizon,
or becomes coincident with A C, thenC M will become CO,
and the Objed at the Bottopi at E will appear OQ the Sur-
^cof flicMedij^aiO.*^; '4 , ,/ /. . ,. ...
Of Light and Colours^ 165
Y, thft Gm« at'G, the Blue at B/ the Indigo zi
I, knd the yiclet at V: And thcfe Seven arc all
the original fimpk. Colours in Nature \ and of
. '. r . . •, • . ' J '^/
' 33; In' this Cafe, if the Medltnn be Water, we Kav«
CE:CO::4:3, whence' we (hall find Q E z= 2,65 nearly ;
therefore iq any Ytfk\ whofc Width i» 2CQ;p6, an4
bepth OElrr2,6'J,*when fillM.with Water, any Qbje^
placed at the Bottom, when view'd in the Perpendicular, will
appear raifed frOm E to M, \ of the Depth; and as the Qy.c
Recedes from the Perpen^icuhr to the horizontal Line A C,
the Objecl will Appear to rife from M to the Surface of th«
Fluid at Oj all which may be cqnfirm'd ^>y poaring Watv
into a common Tea-pi(hjj or Baibn, and viewing tfee f Iqw^r,
tfr. painted at ^the Bottofrt.
'34, Hence appears tlie Reafon why a ^it Stjck^'as NCE,
when placed with one Part QE in Water, will always ap-
pear crooked, wiic, in the Form N C M, the Part C E being
raifed by Refr^ftiqn into the apparent Situation CM; and the
Part under Water will always appear fhorter, for £ C wiU
be contrafled into CM. All which is known by commoa
E:tpcrience*
35. Alfo, fince EM the Difference between the true and
apparent Place of Objects, feen thro* a Medium, is always
greater in Proportion to the Depth O E, and the Obliquit]f
of the Rays rpfr^Aed to the Eye, it will follow, that any dr*
cular Body immerfed in Water, in a Pofition perpendicular
Or inclining ta the Horizon, will fuffer a ^eat^ R^fi:ai^oa
of Rays from the tower Parts, than frQm thofe above 1 and.
eonfeqaently the lowermoft Semicircle will put oi( the Ap-
Jsearance of a Semi-ellipfis; and alfo the upper one, but not
9 mqch fo, the Refn^flipn bein^ lefs than below. The
Confequeilce of which is, that the Circle thus view'd m the
Medium wiir appear elliptical, as having its vertical Diameter
fhorten*d by the Kefra^Uon ; whereas the horizontal Diameter ^
will jemain of the fame Length, bbing only raifed apparent-,
ly abotve its real Situation, whence the Reafon of the Figurq
of the horizontal Sun and Moon above -mention'd. .
36. From what has been ftid^ 'tis cafy to underftand,.tj^at
when the Ray EC in the Medium is refiafled into the Aii;
tiearly parallel or coincident with the Hbrizon A C« in which,
Cafe (if the Medium be Water) the Line CEzzAQfeeipg
Radios, we have the following Analogy; As 4 is to .3,, fo k
Radios A C <yf CE to the Sinii of the Angle of Refia£iao«
L 3 which,
f^§ !^LiG|fT ^</ Colours.
lyluch, ^by v^iipu^ Mixnjres^ ^U Qthcy» arc com-
pounded, in the commcm R(^fra(5lions and R^r
fleftions froip natural Bodies. (CXV III).
CQor Dg, whjch Angiitis tjicrclbre. nearly 48'' i Lfiy,
^tis e^fy to'onderftaLQcl, that if the Ray of Light £C rail oi|
the Surface of the I^edium wi()i a greater Obliquity thaa
)vhat (s here fpedfied, that is, fo as to make ^e Angle ECO
greater than 48**', "the Ray will j>e wholly rpflcfted^ back a^
pin to t^e lower Surface, and no|^e ^ill go out ipto the Aif
at either Surface of ft e Medium. '
37. Again, if th^ jMedium be Glafs, fmcf? th^ Sines of
Incidence! and |^efra£lion in that Cafe are as 1 1 to 1 7, the
Angle EC'D^viU be about 41% when tlie reffaac^ Ray CJJ
becomes coincident withi the horizontal Line A C 1 and there*
jTore when thf Apgl^ is greater^ the Light will be wholly rei-
fiedefd jfrom one ^ur^ure of the Glafs to the other; and neve(
let out into the Air^ whence it follows, that tho* the Par-
ticles of Matter in Bodies' be in themfelves tranfparent» ye^
^f they are fo ^i^pofed one aniong another as to reflet the
Light veiy obliquely, 'tis plain, the Light in fuch a Cafe
|vill be loft by various Reflexions' within the Body, and thuf
iprove a Caufe of t)ie Bodj^'s Opacity.
(CXyilL) 1. This, diffcr^t Refrangibility of the Sun'^
JLlght proceeds frofli hence, that the Partidcj of Light are
of different Degrees of Magnitude i for \f any Ppwf r aft, m»
ph a Body, fo as to give i^ a particular De^i^nnination or pi*
^eftion of Motion, that Determ^tion 9rJPire6lion of the
Bofjy's Motion will always be the fam?, while the Energy of
fhe Powe^ and the Quantity of Matter remain the fame, and
iviil.be variable in Proportion as either of thefe'is fo.
2. JBlut the refracting Power of the Me;^ium will be al«
ways the fame while it is homo|;eneous or all of one Sprt of
Matter, therefore when a Ray of Light paffcs thro' a Sub-
ftance of Water. Glafs, Cryftal, ifc. and a different Di-
reftio^i of Motion is thereby communicated to different
Parts of th^ BLay, it follows, thiat the Particles which con-
ftitute thofe Rays, Vhich hav^ a different Direftion, muff be
pmong themfelves une(]^aal in Quantity of fatter, and con<p
fcquexitly in Bulkj and fince the 'Quantity of Motion is in
the Ratio of the Bulk arid Velocity, (in this Cafe) 'tis plaip,
the greatfltr th^ Velocity is, the Ids will be the Bulk; an^
therefore thofe Rays ot Light which fuffier the greateft Re-
^aftion are lefs in Bulk or Magnitude than others which
Since
0/" Light a?td Colours. 167
Since a Lens does, in the manner of aPrifm,
more or lefs (eparace the Rays of Light pafling
through it, it follows, that all the feveral Sorts of
Rays will have their proper Facu^Sy or be con-
vened to £0 many different Points in the Axis of
tjft, not fo noch refraAed/ the greater P^klet beiM; not Ib^
mach Tabjed to the Power of the Glafs ; as a large medk ir
not fo eafily moved by a Loaditone, nor at (b great a Diftaoce.
3. This beiiig the Cafe, *tis eafy to be anderftood, that
when a Beam of Light, as H F, k let into a dark Room,
thro* % Hole in the Window-Shatter, and is made to fall on a
Prifni A C B at F, it will be attraded by the Sorftce of the'
Q\A at F in a perpendicular Dire^ion, and caufe the fe?e-
fal P^cks to deviate from their Tight-lined Coorfe to T,.
(which they before had) and decline towards the Pependico-
lar ah^ that is, towards the Part F a within the Glaiss which
Deviation or Refradtion will be greater in i^portien as the*
Particles of Light are fmaller.
4% Hence the feveral Particles of Light will proceed fitmi
the Side A C to the Side D C hi different Direftionsi where,
when they arrive, and go out again into the Air, they will
be aeain afeaed by th^ fame attnftinc Power of the Glafi,
whl<£ will here prodi^ce the fame Effed as befbre, that fa, it
wiU caafe each S(»t of Ray to inclme towaids the $ide of
the Glafs, and conieqoently to be refimfted from the Di-
re6Uons they feverally had in tl^e Qlafi. and fimm the Per*
pendicttlar P £.
5. Thus thofe Rays, whofe Particles are brgeftf will de-
viate leail from the Perpendicular, and will thermre go to R,
and make the lowed Part of the colottr*4 SfeOnm^ and thefe
will appear K^f zRed Colour. The Pkrtjcles next le(s (n Mag.
nitude will be fomewhat more refiafied. and will go to O,
and be of an Orange Coiosr; the next Siae left will be fUU
more refiraded, and appear TeiUw at Y, and thns the Refrac-
tion will proceed in the Green at G, the Bike at B, the Indigo
at I, and' the Fiolet^col^mr'd Raj^s at V; which as they are
ipoft refraded, are thereby proved to be the leaft of all u^
Magnitude.
6. I (hall now proceed to ihew, fince the Sun*s Light it
varionfly refrangible, what the particukr Degree of Refra«
^ion is which every Spedes of Rays undergoes, and the Sinetf
qf thofe Angles refpe^threly . In order to this it mnft be con-
L 4 the
r€S . 0/* Light and Colours,
the Lens, ^nd not all tp one Point only, as is he-
cf^ffary-for a perfeft gnd uniform Reprtfentation
of th^ Iniage of any Objedl 2 For th^ Red Rays
proceeding frpm the Qbj^ft will be converged to
a, Focus at a: greater Diftance from the Lens, than
fider'dy that.th^ Sine of Incidence i^'the fame id ali; land that.
I^late wjhpn the Inpd^qce is fuch as that the Ray F K, upon the firft
XXXVII. Befraftioji, ft^U pdfs^ in the Direftion paraUel lo the uppe»»
Fig. 5. Side of the Prifm G H, the Refrad^jons ma^eat each Side of
tjie Prifm: aw e<qual, and «qQal to the refr^tting Angle .of the
'BxKmlGQH.i aU which 19 evident from.whftt waa demonHra*
$cd in Jm/ot, CXVI.
7. Alfoit is.kpoyvp \>j Experience^ th^t wheft tlie Pfiifad
ABC is held wM i^ Axis perpendicular to the- Sun* Beam,
and thei^ iorn'd round upon its Axis, the Imag^ or co]ojir'4
Spe£irum wili firft defcend to a certain Limits where i( will
become fiationary» and then af^ead to the fame Place as at
iiril ; whence it appears plain, that, fince the Altitude of the
boage above the PlaCe where the San-Beam would fall, were
the Priih) away, is owing to the Sum of the Refra^ons made
at each Sdp of the Prifm* while the Image defcends the Sum
of thefe Ro&actions d^crefife., and V^h^A t|)e Image a&enda
the (aid Su^ muft increafe.
8. Cpiifeqoently> iinee the Image falls twice upeiv the fame
Place in one Rotation of the Brifm, there are two Portions of
the Prifm whei^in the Sum of ihe Refra&ions at its Sides are
equal ; and thefe happen when the Angles of the incident
Fig. n. Beam HI^ and OX) L are fuch 4u wiS caufe the rcfradled
- '' ?aits DGand DF to be equally indined to the Sides of the
Prifiti, but <xmtraiy Ways ; that is, fo ^s to make the Angle
DGB ?? BEIF* ajid G.DB =: DFB, and therefore the Tri^
angles I)]^G4md D^F equi anguIaiE. .for ini the Poiition
of the Ray HDG the Refra^ionsatthe Angles D and G are
xefpedtively equal to (he Angles £ and P in the Other Situa*
tion of the Ray QD£ ; ajid therefore the Sum of the Re-
fradlions on e^ph Side in «aqh Cafe muft be equal, and caufe
the Image to appear twice in the fame Place,
9. While the unequal Refra(5lions at each Side the Prifm^
at D^and G, or IX and F, ate approaching towards Equality,
the refrained Ray DG or DJ^ is continually approximating to
the Situation D £ ; where when it arrives, the Angles at D
f^nd £ being>ti^en eqqai^ t\^€ llcfra^i^s z,\ e^^^^ Sjdcw^l be
Of Light nnd Colours. 169
the Indigo or Violet Rays •, and fo the Imi^e will
be coloured and porifufcd in every Point between
thofe Extremes, except juft in tKe middle Pointt
where the feveral Sorts of Rays all interlcft each
other, and exhibit the Image tolerably diftindt
eqi^al fiUb^ and tbe Image in that Cafe he hrooght to its Lir
mit Qr.loveft Site. Then R D will be the incident Ray, and
£ P thi^ .^ergent^ one.
10. Produce RD and. £P till they bterfedl each at I, and
any l^oriatont^l Line in ,M and N \ then let the ngle R M N
l>e the Altitude of the Sun, and PNM thgt of the Speamm
atP; which Angles are.eaiUy meafur^ with a Qoadranc * -
Their Sum is equal to the external Angle PIM, which is
again equal to the two intern^ Angles of Refra^on IDQ^
and lEQj and, \>y vvh^t has been now (hewn, IDQ^=:
IEC^= QJOKi wherefore QDK =; DBK = iN + NT.
Jlen^e i N+'M + I D(i= IDK or R D L, the Angle of
Incidence.
I r. We (hall give Sir Ifaac NtnutM"^ Example in this Af-
fair. The refrading Angle of his Prifm ^ as ABC = 62^
30^ the Half of which is 31^ 15^, whofe Sine is 5188, the
Radius being lOOOOt When the Sfe^ntrnvf^ in its Limit,
or fUtionary, he obferved with a Quadrant the Angle PNM
of a mean refrangible Ray EP, that is, of one that went to
the Middle of the coloured Image at P; and by adding this
(o the Angle RMN of the Sun's Altitude taken at the fame
•Time, he obtained the Angle PIM to be 44** 40'; whofe *
Half 2a° 2o\ added to Half the Angle of RefracUon 31*15',
makes the Angle of Incidence RDL = 53° 35^ whofe Sine
is 8047. The Sine of Incidence, therefore, is to the Sine of
j^efra^on of a mean refrangible Ray. or that of Yellow
Eighty as 8047 to 51^88^ which fs as 31 to 20. (See the
T^ble, Jnnot. C5(Vir. 24)
12. If there were but one Sor( of Light, it then would
be equally refrafted, and the (mage of the SUn would not
then be long, but round ; and if the Rays were firft received
by a Cpnve?^ Lens, they would all p^is tp its Focus, and
there reprefent the Sun's Image very diftinftly in a drculax
Spot;, which Image would fubtend the fame Angle at the
h^m as the Sun i^fe^ does, or half a Degree, at a Mean.
Ali thia wil} be ^ep^onftiat^d hfr^aftcn
and
170 Of Light and. Colours.
^nd cQlpjurlefs. To this different Rcfrangibility
of the Hays is owing the ImperfoEkion of .the*
commoii rtfra^ng Telcfcope, as will be but too
cafy to experiment.
13. If tlicfe Rays, after having pafs'd through the Leiw,
were received by a; Prifm, fince the Sum of Refrgdtions at
the Sides of the Prifm are equal, (as we'have {hewn they am
when the Image- is ftationary, j^t, 8.) the Rays wtMhave the'
fame Inclination to each other after Refraftion thrOiugh th«
Prifm as before ; whence the Angle is not changed, but ghresi
the Image of the Sun M\ eqaal to 30^ But to illuftratethis,
Plate l^t MN be the Se^ion of the Window-Shutter in' a dkrk
XXXIX. Room, in which, through a Hole O, a Pencil of ftkys
Fig. I. KOL is tranfoiitted to tJie Lens KL ; which would conli^ge
them to a Focus at H, were they not intercepted by the In^
terpofition of the Prifm A BC, by which means they are re-
fra^ed to I. •_ And fince the Sum of the Refractions at £ jucl '
i) is' equal to that at F and G, the Angle FIG will be equal
tb the Angle FHGr and if the, Sim were but a Point, its
Jmage at H and I would be a Point alfo.
. 14. But fince the Sun has the apparent Magnitude of Jo',
8- ^' let the Angle MQN be the Angle under which the Sun ap-
pears ; that is, let MQJ)e a Ray coming from the upper Limtn
of the Suni arrd NQ^another froui th§ lower Limb. Thefe
croffing each other in the Center of the Lens K L, at Q^,
make the Angle DQE =: MQN j nqr is this Angle alter'd
by th? RefraSions through the Prifn;i, as being e^ual on eacK
Side ; therefore the Ip:\age at I will be fubtended under ad
Angle of 30 Minuter
15. And fince thi? will be the Cafe 6f every Sort of Rayi
ContainM in the Sun's Light, if that which we have been con-
fidering be a mean refrangible Ray, then the leaft refrangib^^
Rays will form an |mage in like manner at R, the moft re-
frangible Rays another at P, and the intermediate Rays their
feveral Images refpe^ively. So that the coloured SpeSruin^
PR confids of as many circular Areas as there ar^ dif&i^nt
Sorts of Rays ; and is every where 0/ an equal Br^th^ nnz^
half a Degree,
\6, Now 'tis evident, that if the Sun be fuppofed a Point,
each of thofe Circles, being th^ Images of the Sun and fimi-
lar to it, mnft alfo be contrafted into a Point, and -fo the co-
loar^d Sfe^rum PIR would in that Cafe have no Breadth i^
and its Length vyould d^ci;eafe at each End by the Semidia*''
Hence
0/" Light and Colours, 171
HiMC£ alfb Objeds of anf of the fimple
Colours, though cpntiguous to each other, yet,
if view'd through a Prifm, appear fcparated, and
at a diftapcc from one another : And thofe Objefts
meter of t]ie Circles P and R, and therefoi^ would fubtend
an AjQ^le of 30' lefs than it lyiw.doei.
1 7. in order to determine the Angles of Refradion of the
leaftand moil refrangible Rays, we muft firft determine the
Angle PIR, whi^ the Image PR fiibiends at the DiHaoce
it is formM from the frifm ABC. The Son being fuppofed ™^^
a Point, let SD be the incident Ray, which continoe p$|t to xxxvif.
V; and let LDK be perpendicular to the Side AB inthe ^*S* ^^*
Point of Incidei^ce D. The Ray S D at its firft Refni^on la
difiufed through t^e Space GDP within ,the Prifiv; I>G is
the leaft refrangible Ray > D P the greatei^ and D E (paralld
to AC) the. mean refrangible Ray. The Sine of the Angle
of mean Refraflion EDK to that of Incidence ID K has
been already (hewn to be as 5 1 88 to 8047, or as zo to 3 1.
1 8. We are now to find the Quantity of the Angles G D£
and FDK. Since each Ray will fuffer the fame Degree of
Refra£Uon at the fecond Surface as at the firil, very nearly ;
let the refra6led Rays FP, ET, GR. be produced, and they
will interfed each other in the Point I, making IF, IE, I G
federally very nearly equal to D I. and therefore the Aagles
IFD = IDF, and IGnz=IDG; therefore P I V =5
2FDV, and RIV=:aGDV. Hence PIV — RIV =
PIR=2FDV— 2GDV; confequenily,^PIR = FDV
— GDVsrFDG.
19. The Angle PIR is difcover'd by roeafuring the Length
pf the Image PR, and its Diftance from the Priim ABC,
This Sir Ifaac Newton has done with great Exadneis. The
refrading Angle of his Prifm was ABC =62° 30^, the
Difbnce of the' SpeSirum 18^ Feet, the Length 9 J or 10
Inches, tiie Breadth 27 Inches. This fubdu^ed from the
Length leaves 7^ for the Length of the Image were the Sun
but a Point, and therefore fubtends the Angle which the moft
and leaft refrangible Rays PF ^d RG do contain with one
another after their Emergence from the Prifin.
20. But at the Diftancc of 18,5 Feet, the Length 7J
Inches is the Chord of an Arch equal to 2® o' 7^ = PIR j
therefore i PIR = FDG =r i** o' 34^; whence EDG
(= I FDG) == o'' 30' I'f = F DE. But the Angle EDK
s= DBK = 31** I c^ CO*. Wherefore EDK + EDG =
J72 Of Light ancl .Colours'.
will, have their Images forni'd by a Lens at very
• different Diftances in its Axis, efpecially in Ex-
31*^ 45' 2^ se: GDK, the Angle of Rcfraaion of the lead
refrangible Rays ; and ED K — E DF = 30^ 44' 58" =
£ D |C« the Angle of Refra^on of the mpft refrangible
Rays.
21. The natural Sine 0f 31*' 45' 2''^ is 5262, (as perTsL-
- We, Jfinot. XLYL) alfo the Sine of 30** 44' 58" is 5x12,
The common Sine of IncidcnCt being IDK or SDL i^
53* 35^ ^^^ Sine 8047 ; thi? compai'ed with the' Sines of
Refradionof the moft, meap, and leaft refrangible' Rays will
ftand\as;follows. \ • . -
' • * /"The moii refrangible Rays FD,
•'*"'-'^"' '■ • ■ V as'8047 to 5112. '
rfhe Sine of Incidence ) The mean refrangible Rays ED,
iVitotbe^ine of A a^ 8047 to ^i58.
/The leaft refrangible Rays GD,
X. as 8047 *to 5262.
. 22. I have hitherto confider'd the Refraftion made out of
Air into Glafs, after the common Way. But as Sir Ifaac Neiv-
/d/f!Tias proceeded in a contrary Method, and flated'the PrQ-
portions of the Sines of Refradlion (as they are out of Qlaft
mto Air) to the common Sine of Incidence in Glafs, I (hall
for the fixture follow his Steps 5 and therefore fuppofing ^
Plate Beam of compion Light within the Prifnpjj as Dfi, Ihall cw-
XVII ^^^^^ ^^^ Refraftion'into the^Air at the Side BC in the Point E.
ft A ' '^^^ common Sine of the Angle of Incidence I^£ D or IE L,
^^'^' =31^ 15', was found to be 5188; and the Angle PER, =
I** o^ 3^'', the fame as before. Alfo the Angle of th,e mean
refrangible Rays TEL being 53** 35', we have the Angle
of the leaft refrangible Rays R£L = 53^4' S^^t and the
Angle of the moft refrangible Rays PEL = 54** j' 2'. The
Sines of thefe Angles are 7995 and 8099 ; the Sine of Inci-
dence, therefore, and of Retradlion into Air, in the lead ancj
moft refrangible Rays, ar? \n tjie leaft round Numbers as 50
^0 y/ and 78.
23. Now if you fubdu^ the common Sine of Incidence
50 from the Sines of Refraftion yy and 78, the Remainders
?7 and 28 (hew, that in fmall Refradions, the Refra^ion of
the Icaft refrangible Rays is to that of the moft refrangible as
27 to 28 very nearly; and that the Difference of the Re-
fraftions of the leaft and moft refrangible Rays is about the
?7l P^t of the Refriftion of the ipcan refrangible Rays.
periments
Of Light {ind Colours. 173
periments of die deepeft Reiy and VtoUty or Blut
Colours \ as aCard.paintedhalf withCanw/zr/, and
24. Now in order to define the Refrangibility of the fe-
veral intermediate Rays of Light, Sir Ifaac took the follow-
ing Method. He caufed the Spedrum to be well defined, and
delineated upon Pap^r its Perimeter, as F A PGMT ; this he
held in fuch a Manner that the Spi&mm might fall upon and
exadly agree with the delineated Figure ; this done, an Af-
iiikot drew the Lines ab^ cd^ ef, &t. actofs the Fignre very p^
nicely upon %he Confines of the feveral Coloort, that is, o£ xXXtX
the Red MabF, of the Oiange aicJ, of the Yellow ^de/,'^i„ ^^
and fo of the reft $ which Operation being divers times re- ^' '
f«ated, he found the Obfervations agreed very well, and that
the Divifions made by the crofs Lines were diofe of a Mmfi*
C0I Chord,
25. That is, if CM be produced to X, fo that it be GM
= MX, then the Line XM = ^ XG will be the i}aavg. '
The Line aX : XG :: 9 : 16; therefore aX will be die
Lefer Seventh. The Line rX will be | of XG, and there-
fore the Sixth Greater. eX will be -f of X G, which is the
Sifih. gX is iof XG, a Fourth. iX a i of XG, a Third
Lejfer. /X is | of XG, the Second. Greater. So nicely has
Nature obferv'd an harmonical Diftribution of Colours in the
Soiar Spectrum.
26. U then the Difference between the Sines of 77 and
.78 be in like manner divided, that is, as the Line MG is di-
vided, we fhali have the Sines of Refraction in the feveral
Red Rays extend from M to a, or from 77 to 77I ; thofe of
.the Orange Colour from a to r,. or from 77^ to J7\ ; thofe
of the Yellow from 77^ at f , to 77^ at ^ ; thofe of the Green
from yj^ to 77I zig; thofe of the Blue from 774 to 774
at ii thofe of the Indigo from jy^ to 77^ at /; and from
thence the Violet to 78 at G.
zy. This Difcovery of the Harmonic Proportiotk of Cdoun
in the San*s Light has fuggefled the curious Hint or Idea of a
Fi/ual Mujic by means of an Ocular Harpfichord^ which ihaU
entertain the Eye with the Succefiion of harmonic Coloun, aa
the common Harpfichord does the Ear with mnfical Sounds.
Yea, fome have carried this Matter fo far, as adually to at-
^ tempt the making of fuch a Harpfichord, with full AfiTurance
of being able to play Tunes to the Eyes. It were greatly to
be wiih*d this Chromatic Mufic could be made as effeCkual to
give Pleafure to our Eyes^ as. common Mufic does to the
£ars. We fiiould (hen have Harmony the Subjedk of two of
half
1^4 . ^f Light dfid CoL6ijViS.
half widi VltramdrtJKi made deeper with a litflcf
Indigo. (CXIX). ,
ooi* Senftfs : And who can tell bat we iaif liiive mufical Eyes^
as well as nakjicdl Ears^ could they be exercifed by proper
Objeds ? Nay, wbo can tell what may be the Confeqaence
of this Difcovery in regard of our other Senfes in the Aged
to come ?
Plate (CXIX) t. Let DEKI be a doable Convex Lens^ N its
XXXiX/ Center, and ND the Radius of Convexity at D; FV its
Fie A-i ^^* ^^^ H£ a Seam of the Sun's Li^t incident on the
**^* Lens parallel to ib Axis in the Point F. Let ABC be a Prifm
touching the Lens in the Points £ and D, and it is evident th«
Law and Manner of Refradion of the Beam at £ will be the
iame, whether we confider it a^ made through the folid Glafe
iPrifm ABQ 6r through the Lens D £Ki becade the Point of
Incidence £ is the fame in br common tothem both.
2. The Beam being refracted to^ D,^ it is plain the Refra-
ction will be there alfo made into the Air m the ikme Manner
from the Lens as from the Prifm, fup^fing them to touch in
the Point D. Let ND be continued to L, then will LD \ki
perpendicular to the Lens in D; and the RefradUon being
made into the Air, (a rarer Medium) the reddled Rays wiU
tend towards the Axis, and meet it fooner or latet as they are*
more or lefs refrangible. Thus the mofl refrangible Rays
D W will cut the Axis in G, the Icaft ref togible Rays DT in
Q^ and the mean refrangible Ra^s in O ; and the others in the
intermediate Space between O and G, and O and Q^ The
fame is to be underilood of the Beam IK on the other Side
the Axis.
3. Hence we fee, that in the Axis of the Lens the Images
of an Objeft will be formed in feveral Parts from G to O ; by
which means the Objed will appear Red at G, Violet 'Cotonr'd
at <^, and of other Hues in the Parts between. Nor are
we to underftand that feVen Images only are form'd by th£
feven Sorts of Rays ; but each particular Sort of Ray, accord-
ing to the Intenfity of the Colour, from the ffarongeft to the
famteft Pa^, confifts of an indefinite Number of differently
refrangible Rays, each of which will form an Image of the
Obje^ in its proper Focus : And therefore we may conceive
atm^ny Images form'd in the Space from G to Q^, as there
arc Points in the Line GQ^
4. The Objea fcen by fuch a Refraftie*! of Rays, in fuck
asi Infinity of Images, xDxSi neceffariiy appear yzxy indHlin^ly'
Sir
Of Light and Colours* 175
Sir Ifaac Newton founds by a very curious and
convincing Experiment, that the Rays of Light
were as varioufly reflexible as refrangible j and
that thofe which were moft or leaft refrangible
were alfo moft or leaft reflexible: And farther^
that Rays of light were not rcflefted by imping-
ing on the folid Parts or Corpufdes of Bodies,
con&fedy coloured » and obfcorei and the Objed-Glafi of
every tommon Dioptric Telefcope being of this Sort, is the
Occ^OB why they will not bear an Eye-Glafs of fo deep a
Charge^ or fo ihort a focal DiffamCe as is requilite for great
Degrees of magnifying. This pat Sir Ifaac upon inventing
another Sort of Tdefcope by Rcfledion, of which we (hall
fpeak largely hereafter.
5. Suppofe DE parallel to the Axis of the L«is, and pro-
duced to Z ; then is ZDL = £DN the Angle of Incidence,
andPDL, ODL, MDL, the Angles of Refraaion in the
leaft, mean, and moft refrangible Rays; and confequently
the Angles ZDP, ZDO, and ZDM will ihew the Quantity
of Deviation or refpedivc Refiadioii of thofe Rays ftom the
£rft Diredion £Z. Whence ZP : ZN :: 27 : 28 ; and
ZP:ZO:: 27:274. Alfo PM = -i- ZO, the whole
. 27^
Refia6Uon of the mean refnUigiUe Rays.
6. But the Angle ZDP = DQX, and ZDO = DOX,
and ZDM = J^GX. Now the Sines of the Angles DQX»
and DOX or DOQ^ are as their ofppoiite Skies OD and
Qp, that is, nearly as XO and XQ. For the fame Reafon
the Sines of the Angles DOX and DGX are nearly as GX
and OX. Wherefore ZP, ZO, ZM. ait as GX, OX, and
QX; whence PM : ZM :: QG : QXj therefore GQjs
,V QX* Bat OP is nearly equal to 06, when 6x is very
gieati andQp:qX:2PM:DY:: i : 56, beca^ QX s
i8 0Q^or56Qp.
7. Or thus more atCarately^ withoat regard to the fbca!
tKftance QX or OX. Let I, L, 6, be as the Sintt of Inci*
dence, and of the leaft and greatdl RefiadUon, or as thue
Numbers $0, 77, 78 ; (S^ Jmioiat. CXVII. 22.) then will
ZP=:L—^I,ZM±;G — I,amlPM = G— Li whence .
PM :ZP:: G— >L: L— I; and doubling the Confeqnents,
we have PM i 2 ZP (s DY-^PM) :; 0--L : 2L— 2L
and
176 Of Light and Colours*
and rebounding from thence like a Dennis-Ball^
but from fome other Principle depending on the
Size of the Particles of Light, and the Thicknefs
or Denfity of the Particles of the Body refledbing
it, which are all of them, in the moft opake
Bodies, tranfparent in themfelves, asiseafytobe
fhewn in the thin LamelLe or Plates, of which an
Then conjointly, PM : DY :: G — L : G-|- L — 2I ::
1^ — 77 ' 784-77—100 :: I : 55; or PM= ^V^^^,
the Aperture 01 the Glafs.
9. FroiB henfce it appeal^, that the Riitio between PM aUd
D Y is conftant, or always the fame, whatever be the focal
Difbmce of the Lens. It is alfo very evident, that PM is the
Diameter of a Circle, in which will be a Mixture of every
Sort of Rays, from the lead to the moil refrangible. Thh
Circle therefore is that in which the Light is ivhtu, or not
dnftur'd with the Colour of afiy particular Sph of Rays ;
for the Rays being here promifcuoufly thrown together, tht
Light compounded of them mud be nearly the fama with
that of the Beani before Refradibh.
Q. By the fame Rule we may iind.|he Diameter of the
leaft Circle that receives the Rays of any finglc Colour, or of
any contiguous Colours. Thus all the 7>/W is contained in
a Circle whofe Diameter is a 409th Part of the Breadth of
the Aperture of the Glafs, (which we fuppofe a P/atnCam/ex^
becaufe of D£ parallel to the Axis) for in this Cafe G = y';}^
L = 77i, and 1=50. {See Jnmt, CXVIL z6.) Whence
by the Analogy we have PM : DY::G*-L: G+L — ^I
:: 0,133 : 54*533 :: i : 409. Thus for two contiguous Gd-
lourSy the Orange and I*el/(nv ^ the Sines on each Sid6 behig
f7if 77i^ g^^^ ^^ Diameter of the Circle in which both
thefe coloured Rays are contain*d, a 260th Part of D Y.
. lo. From hence it is plain, that when the Sun's Rays are
received upon a large and very convex Lens, the conic Super-
fides of the converging Rays DPM Y will confiA of the Red-
colour'd Rays ; and if received on a white Paper, held per-
pendicular to the Axis, the Circumference of the circular Sec-
tion or Area will be remarkably tinged with a rcddilh Colour
inclining to Orange, by the leaft refrangible Rays DP and
Y M. On the contrary, the diverging Rays will, in the conie
Surface RPMW, have all the Violet and Indigo Rays NPR
and D M W, and will therefore exiiibit fuch a colour'd Circl*
L Oyfter-
Of Light and GoLduRSi t^^
Oyfter-Shell doth confift.
It \«^ilJ be thought very ftrange to aflcrt, that
a rare Medium is more impervious to the Rays of
Light than a denfer one ; and yet nothing is more
certain, or, eafier proved by Experiment: For
Example^ a Beam of Light is much more copi-
oufly reflefted from the fecond Surface of a Piece
of Glafs when contiguous to the Air^ than wheii
about the Light received on the Paper held any where in that
Cone of Rays.
11. Since G is the Focus of Violet Rays, that is the
Place whetc any Body of a Violet Colour will be fcen di-
ilin6lly, becaufe the Rays of that Kind» palling from that
Point to the Lens, will . after Refradion pais parallel to the
Eye ; which is a Condition abfolutely neceflary to diftindl Vi^
iion, as will appear hereafter. For the fame Reafon Q^vwill
be. the Focus or Place where Objcds of a red Colour will be
jnoft diftmftly feen. Whence it appears, that in viewing Ob-
jedls through GlaiTes (as SpeQacUs for Inftance) the D:llancc
of the Glafs from the Object will be variable according to its
different Colour,
12. Hence a various-colour'dObjcS ABEF will have its pj^^g
Image form'd in Parts by the Lens' H I. Thus fuppofe xXXfX
ABCD be a Red Part, and DCEF a deep Blue i if this 05* pjg -^ *
jeft be well illumined, and black Threads or Silks laid acrofs
thofe Colours, they will appear didindly in their reipedive
Focus's, <viz tbe red Part ABCD will have its Image di-
ilinftly form'd at K, and the blu.e Part at L ; the former will
be reprefented by abed, the latter by dcef\ and thcfe Images
Will be at very different Diftances from the Lens. Thus if
the Lens H I be of 3 Feet focal Diftance, and the Objed be
placed at the Diftance of 6 Feet from it, the Images on the
other Side, at the Diftance of 6 Feet, will be form'd one Inch
ond a half from each oth^r ; that isj the Red at K will be
1 1 Inch beyond the Blue at L.
13 Another Confcquence of this different Refracgibility
of the Rays of Light is, tliat if two Objects of different Co-
lours, as Red and Blue, be view'd through a Prifm, they will
be refraded to different Heights ; and though they were con-
tiguous before, or Parts of one and the fame OhjeSl, yet will
they appear feparate> or as two dijiinci and dijlant OhjeSs,
. Vol. 11. M- it
178 0/* Light and Colours.
k touches /?^/^; and ftill more, if contiguous to
Water ^ than when it is contiguous to Glafs ; in
which Cafe the Rays are totally trahfmitted ^
Hence, wonderful as it may fcem, 'tis necef*
fary, in order that a Body may be tranfparent,
that its Subftance fhould be very denfe, and its
Pores very fmall ; and that Opacity refults chiefly
from the Largencfs of the Pores of a Body, oc-
Plate Thus fuppofc DHEI be an Objea whofe Part DG is m*
XXXIX. tenfely blue^ and the other Part FE intcnfcly tei\ if this be
Fig. 6. view'd by a Prifra BAC^^^r, with the refrading Angle or
Edge A a upwards and parallel to the Horizonand the Sides
DI and HE of the Objet^, the Image of this Objedi will ap-
pear at de, with the ^/tf^ Part dg refracted higher thian the
red f e. On the contrary, if the refra^Hng Angle of the Prifm
be turnM downwards, the Image will be refracted downwards
to de^ the blue Part lower to dg^ and the red higher at/<p.
14. We alfo fee the Reafon why Objedis appear differently
coloured when the Eye is held near the Prifm, as at D, to view
them ; inx. becaufe the Rays of every Colour are there fo
very near together, that they can be all received by the Pu-
pil of the Eye, and will therefore paint the Image in all its
proper Colours on the Retina. Whereas if the Eye be re-
moved to a greater Difbnce from the Prifm, as to a, b, c;
there, becaufe the Rays fpread through fo wide a Space, but
few can enter the Pupil, perhaps only one particular Sort,
and then the Objed will appear of that particular Colour on-
ly J as Fiolet'Colour^d at a^ Green or Teilouu at ^, and Red at r.
?^8' 7- I J. The Rays of the Sun's Light, once refradled, undergo
no farther Refradlion by a fecond Prifm, and of courfe exhi*
bit no other Colours : For let an Hole be made at g in the
Board de^ on which the colourM Spe^rum is made in the dark
Room, by Rays which come through a Hole G in a Board
DE placed juft before the Prifm ABC ; by turning the Prifm
ABC flowly about its Axis, the Image will be made to move
up and down on the Board de^ by which means each coloured
Ray will pafs iingly through the Hole g fucceflively ; and if
thefe Rays be refraded a fecond time through the Prifm « Re-
placed jufl behind the Hole g, they will go from thence to
the oppofite Wall at M or N, and there appear juH as before
in their proper fimple ColQur 2 the Blue will appear Bbttt the
cafion'd
Of Light and CoLouliSi i'j^
fcifion*d by its Particles touching in but very few
Points : Becaufe; if the' Pores of fuch a Body be
fiird with a Subftance hearly of the fame Den-
fity, it becomes in fome Degree tranfparent, as
Paper wetted with Water or Oil: And on the con-
trary, fFdter blcwH up into finall Bubbles has iti
Denfity diminifhedi and its Porofity increafedj
and thus becomes opake (CXX).
^ed will be ftill 'tUi^ and the Vi(dit the faine rioUt as be^
fore.
i6. But though the Rays are not any farther refrangible
b)f tlie fecond Prifm ahc\ yet it appears that thoTe Rays which
were lealt and tnoil refrangible by <he firil Prifm are likewife
fo by the fecond % for the Boards D£ and i/« being fix*d« caufe
the Incidence of Light on the fecond Prifm to be always the
fkme : Yet by moving the ^rft Prifm ABC abtmt its Axis, the
Rtd Ljght would go by a fecond Refra^ion to M, but th^
Violet Light would go higher to N. Which plainly and un-
dehiably fllews that fome Sort of Rays will always be mor^e
refraded, and are therefore more refrangible than others^
And hence this decidve Experimtot has gain'd the Tide df
ExperimentAm CnuiL
(CXXJ I. The fiiiie great Author of the DodHnc of the
different Rifrungihility of the Sun's Rays» (as deliverM in the
laft AnnotaHon) found alfo by other Experiments, that the)r
tirere in the fame manner differently rejlexibUi or that thofe
kays which were leall and molt refrangible were alfo leaft and
ihofl reflexible. This he proved in the following Manner.
2. From a Hole F in the Window-Shuttef EG, a Beam bf Plate .
the Sun's Light FM pafs'd to the Bafc BC of a Prifm ABC, XXXIX;
whpfe Angles B and C were equal and h^f right dn&s, and the Fig* ^«
Angle A a right one. The Light was firft refraded at M
into the diverging Beaih MGH, of which MG was the leaft
i-efrangible Part, and MH that i^hich wasmoftfo. MN is
ihe Light refledled from the Bafe through the other Side to a
fecond Prifm VX Y, by which th6 refledlcd Beam is refraded
io / and/; N/ being the lefsj and N/ the more refradled
i. Wh^n the fird Prifni ABC is tiimM about its Axis zt-
^Cfrding to the Order of the Letters ABC, the Rays MH
Mi I#
l8.o Of Light and Colours/
If the Obje6l-Glafs of a large Telefcope be'
laid with its convex^urface on a plain Glafs, the
Light falling on the thin Portion or Plate of Air
contained between the GlaiFcs will be, at feveral
emerge xnofte and more bbliquely out of the Prifm, till at
length they become re^e^ed towards N. And it was evi-
dently obfcrved, that as the Prifm ABC was flowly moved
about its Axis, all the Rays from MH *to MG became fuo
ceffively reflected towards N'.
4. The Coufequence of this was, that the Violet Colour p
received an Addition to its Strength and Brightnefs upon the
firil Refleftion of the Rays M H, beyond any of the other
Colours towards / ; but as the Prifm ABC continued its Mo-
tion, and the other Ray between H and G became refleded,
fo the other Colours from ^ to / became more intenfe and vi-
vid', one after another, by the new Acceffion of Light to the
Beam MN.
5. In this Experiment no Notice has been taken of any
Rjefradion made at the Sides of the hrH Prifm ABC, becaufe
the Experiment was made in fuck Circumllances that the
Beam FM enters it perpendicularly at the firft Side AC, and
goes out fo at the fecond A B ; and therefore can fuffer no
Refradtion, or fo little that the Angles of Incidence at the
Bafe are not fenfibly altered by it. In order to this, the An-
gle FMC ihould be about 45 Degrees; and then a fmall Mo-
tion of the Prifm, to make the Angle FMC= 49°, will
caufe the Beam FM to begin its Refraftion. Or if the Ait-
gles B and C were each of them 41°, the Sun-Beam FM
making an Angle FMC = 49** will begin to be refleded at
the fame Time that it contains a Right Angle with the Side
AC(by^«w/. CXVII. 37.).
6 The Reafon of the different Reflexibility of the Rays
df Light is the fame as was before aflign'd for theiF different
Refrangibility, ^oi%. the different Sizes or Magnitudes of the
feveral Rays; for when the refrafted Beam MGH ap-
proaches very near the Bafe of the Prifm BC, the attrafting
Power of the faid Bafe will fooner affedt the Particles of a
lefTer Size than thofe of a larger, even though they were at
an equal Diftance from it ; and therefore the moft refrangible
Rays M H will be iirfl within the reflexive Power of the Sur-
face B C, on account of the greater Tenuity of its Particles,
as well as on account of its greater Pl^oximity than the other
Rays MG ; on both which Agcoun$s therefore the Ray HM
Diftances
Of Light and Colours. i 8 i
piftances from iht Centre, alternately tranfipitted
^nd refledled. In the Centre of the Lens, where
it touches the Glafs, it will be tranftnitted, and
fo caufe 2idark Spot to appear: At a fmall Di*
will be firft and raoft eafily refra^led.
7. Now though in Refraflion the Sine of the Angle of lut
cidence is different from the Sine o( the Angle of Refradionl
on account of a fmallef Particle being attradlfd mo^ out of
its Way towards the Perpendicular than a larger one, whereby
a Separation of the Rays is produced ; yet becaufe in Re-
flexions every Particle whether great or finajl muft neceilarily
be reHcAed under an Angle equal to that of Incidence, it
follows, that all the Rays after Rcfleftion will have the fanM
Inclination to each other as before, and fo no Separation can
bl; made among them, and confequently no different coloured
Light will be produced by a total Refledion of the Sun*$
Rays. , , ,
8. What has been faid of the Manner in which Light k
relieved is in the gro(s only, and true but in part ; for though
in Refleiiions the Angle. of Incidence be ever equal .to the
Angle of Refledion, yet the Refledion of the Panicles of
Light is not made by their impinging on the folid or iroper-
.vious Parts of Bodies, as is commonly believed. This our
great .Author proves by the following Reafons.
9. //•;/, That in the Paflage of Light out of Glafs into
Air, tnere is a Refledion as ilrong as in its PaiTage out of Air
into Glafs, or rather a little ftronger, and by many Degrees
ftronger than in its PaiTage out of Glafs into Water. And ic
feems not probable that Air fhould have more ftfc-ngly refled-
ing Parts than Water or Glafs : But if that fhould be fcppofed^
it will avail nothing ; for the Refledion is as flroag or flrpnger
when the Air is drawn away from the Qlafs by an Air- Pump,
as when it is adjacent to it.
10. Secondly, If Light in its PafTage out of Glafs into Air
be incident more obliquely than at an Angle of 40 or 41 De-
grees, it is wholly refleded ; if lefs obliquely, it is in a great
meafure tranfmhted. Now it is not to be imagined that Ligi)t
at one Degree of Obliquity fhould meet with Pores enough ip
the Air to tranfmit the greater Part of it, and at another Dc-^
free of Obliquity fhould meet with nothing but Parts, to re-
ed it wholly ; efpecially confidering, that in its PaiTage out
of Air into Glafs, how oblique foever be its Incidence, it
f nds Pores enough in the Glafs to tranfmit a great Part of it.
M 3 ft^ncc
|8^ 0/ Light ar^d Colovjus.
fiance from thence, all around, the Light will be
reflefted in various- colour'd Rings: In the next
Diftance it will be tranfmitted, and in the next
to that reflefted i and fo qn alternately to a. con-
1 1 . If any Man fuppofe th^t it is not reijefled by the Air,
but by the outmoft fupcrficial Parts of the Glafs, there is flill
the fame Difficulty ; befides that fuch a Suppofition is unintel-
ligible, and will alfo appear to be falfe by applying Water
^ehind fome Part of the Glafs inftead of Air : For fo in a
convenient Obliquity of the Rays, as of 45 or 46 Degrees,
(at which they are all refledcd where the Ajr is adjacent to
the Glafs) they Ihall be in great meafure tranfmitted where the
Water is adjacent ^0 it 5 whiph argues that their Refie6Uon or
Tranfmiflion depends on th^' Conftitution of the Air and Wa-
ter behjnd the Glafs, pd not ^n the ftriking of the Rays 01^
the P?^rt8 oif the GJafsl'
12'. thirdly y If tjie Cqlours made by aPdfm placed atth^
Entrance pf a Beana of Light into a darkened Rooni be fuc-
ceffively call upon a fecond Prifm placed at a greater piftance
froin the former, in fpch a manner that they are all alike in-
cident upon it, {as they will be when trajcftcd tbrobgji the
Holes G and ^'in the two Boards mentipn'd ^n Jrt. 15. o(=
the laft Note) the fecond PrIfm m^y be fo inclined to the in-
cident Rays, tb^t thofe which are of a Blue Colour Jhall be
all refleded by it, and yet thofe of a RedCoioviX pretty co-
pioufly tranfmitted. Now if the Rcfledlion be icaufed by the
Farts of Air or Glafs, I would aflc why, at the fame Obliqui-
ty of Incidence, the Blue fhould wholly impinge on thofe
i^arti fo as to be all refledled, and yet t}ie Red&xxA Fores enough
^o be in a great ineafure tranfmitted ? ,
13/ Fourthly,' Where two Glafles touch one another, there;
IS no fenfible Reflection, (as will be fticwn Annot. CXXI. 7.)
yet I fee no Reaion why thf Rays fiiould not impinge on the
Parts of Glafs as much when cantig^oua to other Glafs, a$
when contiguous to Air.
14. Fifthly, When the Top of a Water- Bubble, (as will
be (hewn Jmot. CXXI. 24.) by the continual fu'bfiding and
exhaling of the Watpr, grows very thin, tliere is fuch a little
and almofl infenfible Quantity of Light refleded back from it,
khat it appears intenfcly black; whereas roiind about the
black Spot, where' the Water is thicker, the Reflexion is fo
Jlrong as to make the Water feem very white'! Npr is it
— ^jr ^t the jeaft Thi^kn^fs of thin Pfe|^$ qr bubbles th^t t^verla
' ' * fiderftble
0/* Light tfW Colours. 183
fiderable Diftance from the central Spot. If we
take the Diftances as the Numbers Ot i, 2, 3, 4,
5> 6, 7, 8, 9- 10, yc. then at the Diftances o, 2,,
>t no manifefl Refledlion, bat ^t many other Thicknefles con-
tinually greater and greater. And yet ia the Superficies of
the thinned Body, where it is of any one Thickneis, aad
the Rays are tranfmitted, there are as many Parts for theth
to impinge on, as where it is of any other Thickneis where
the Rays are refle£^ed.
15. Sixthly, If RcfleAion were caufedby the Ptots of re-
flefiing Bodies it would be impoffible for thin Plates or Bub-
bles at one and the (ame Place to reflet the Rays of one Co-
lour, and tranfmit thofe of another, as is known by £xperi«
ment they do : For it is not to be imag^ed, that at one Place ,
the Rays, which, for Inftance, exhibit a Bl^e Colour, fhouI4
have the Fortune to da(h upon the Parts, an4 thqfe which
exhibit a lUd to hit upon the Pores of the Body ; and then
at another Place, where the Body is a little thicker or a little
thinner, that (on the contrary) the Blui (hould hit upon its
Pores, and the Red upon its Parts,
1 6. Seventhly, and laflly. Were the Rays of Light refleQ-
ed by impinging on the folid Parts of Bodies, their Refle-
^ons from poliih'd Bodies could not be fo regular as they are:
For in poliflung Glafs with Sand, Putty, or Tripoli, it is not
to be imagined that thofe Subftances can, by grating and fret-
ting the Glafs, bring all its lead Particles to an accurate Poliib^
fo that all their Surfaces (hall be truly plain or truly fpherica],
and look all the fame Way, fo as together to compofe one
even Surface. The fmaller the Particles of thofe Subftances
are, the fmaller will be the Scratches by which they conti-
nually fret and wear a^i^ay the Glafs until it be poliihed ; bat
be they never fo fmall, they can wear away the Glais noi.
otherwife than by grating and fcratching it, and breaking the
Protuberances, and therefore polifli it no otherwife than by
bringing its Roughnefs to a very fine Grain, fo that the Scratches
and Frettings of the Surface become too fmall to be vifible ;
And therefore if Light were re^ledled by impinging on the
folid Parts of Glafs, it woul4 be fcatter'd a$ much by the
moft polifhM Glafs as by the rougheft. So then it remains a
problem. How Glafs fdified hy ^ettpig Suhjfancis can refliB
Light fo regularly as it does f
1 7. And this Problem is fcarce otherwife to be folved than
\j facing, i:ba{ thf Refkaim rf the R/y is e^eSedj^ ^. h ^
M 4 4f
i34 0/ Light and Colours.
4, 6, 8, 10, 6?f. the Light will be tranfmittcd •,
and at the Diftances i, 3, 5, 7, 9, fc?^. it will be
rcfleaed in coloured Rings: And this alternate
Jlngk Point of the refieSing Sabf hut by fime Power of the.
Body *which is efvenly diffufed o^er all its Surface, and by *wh;ch,
it ^^s upon the Ray^ ^without immediate ContaSl. For that the
P^rts of Bodies do a£l upon Light at a diftance, has been al-
ready obferved, and may be feeh more at large in the Third
Part of our Author's admirable Treatife of Optics.
18. Now (continues Sir Jfaac) if Light be rcflefted, not by
impinging on the folid Parts of Bodies, but by fome other.
Principle, it is probable that as many of its Rays as impinge
OJQ the folid Parts of Bodies are not rcfleftcd, but (lifled and
loft in the Bodies i for qtherwife we muft allow two Sorts of
BeiJedUons. Should j^ll the Rays be reflefted which impinge
QD the internal Parts of clear Y^at^r or Cryftal, thpfe Sub-
ftances would rather have a clpudy Colour than a clear Tianf*-
parency.
19. Conceniing this Power, by which Light is reflefted
and refradled. Sir Jfaac underftands it to be of an attradlivo
and repujfive Nature ; for he reafons thus : Since Metals dif-
folyed in Acids attradt but a fmall Quantity of the Ac}d, their
attradive Force can reach to but a fmall Diftance from them,
i^nd as in Algebra, where Affirmative Quantities vanifh and
ceafe, there Negative ones begin | fo in Mechanics, where
Attradlion ceafes, there a repulfive Virtu^ ought to takq
place. '
20. And th^t there is fuch a Virtue feems to follow,
(i.) From the Refleciions and Inflexions of Light, as before
pbferyed. (2.) From the ^miflion of Light ^ the Ray, {o^
ibon as it is ihaken ofF from the fhining Body by the vibrating
Motion qf tjie I*arts of the Body, andgets beyond the Reacl^
of Attraftion, b^ing driven away with exceeding great Velo-
city. For thaj Force which is fufficient to turn it back in Re-
Jedlion may be fcCicient to emit it. (3.) It feems alfo to fol-
low from thf PrpJuXion of Air and Vapours j the Particle|
when they are Ihalcen o|F from Bodies by Heat or Fermen-
tation, (o foon'as they arc J)eyohd the Reach of the Attrac-
tion of the Body, receding frpm it,' and from one another,
• with great Strength^ and keeping at a diftance, fo as fome-
times tD take up a Million of times more Space than they di4
^fforc in the Form of adenfe Body.
21. To this rcpuliive Power he afcribes the Pefe5lion of
Dirpofition
Of Light and Colours. 185
Difpofition of Light to be reflefted and cranfinitted.
Sir Ifaac calls the Fits of eafy RefieEtion^ and Fits
of eafy rranfmiffton (CXXI.)
Rays, and to 4he attraflive Power the lUfraSion ; as has been
before defcribed. But how the Light is partly refleacd and
partly refrafted Vit the Sarfaccs of Bodies, and what Phacno-
jnena do thence arife, we (hall (hew fron| th^ lame illaftnous
Author in the following Annotation.
(CXXI.) I. Concerning the particular Manner in whxcl|
Light is reflefled from natural Bodies, whether it be by a re-
pulfive Power before it arrives at the Surface, or by an un-
dulating Virtue every where difFufed over the Surface, and
caufing a Refle£^ion by the rifmg Wave, and a Tranfmi^on
hy the fubfiding Wave ; or laflly, whether the Refledion be
occaiion'd by the Vibrations of the Parts of Bodies, or the
Mediums next the refle^ing or refra^ling Surfaces, it will not
be worth while here to fpend Time in examining, fince Sir
Ifaac Ntwton has confefs'd himfelf unable to determine the
Modus agendiy which Nature makes ufe of in this Affair.
2. Nor is his Do6lrine of the Fits of eafy Reflexion and
eafy TranfmiJ/ton to be eftecm'd a meer Hypothefis, or {o
much clogged imtb Suppojitions, as to be dilTonant from that
Simplicity, Uniformity, and Regularity with whidi Nature
is every \yhere obferved to aft ; fince nothing can be more
.certain than that Light is at one Diftance reflected, at another
refra^ed, and that this is by a continual Alternation at ex-
ceeding fmall Intervals thro* the Subftance of various Media
or Bodies; and ihe Experiments ^ich he made weremany^
and moil convincing Proofs of the Thing,
3. And his Vibratiqns in the Parts of Bodies, and the e-
laftic* Mcdiuna ^hich every where furrounds them, ariiing
from tliepcc, is very cpnfo<^ant to the Procefs of Nature, in
propagating' Sounds by the Undulations of the Air arifing
from the Vibration of the Parts of Bodies agitated by Pcr-
jcuffion. Nature in each Cafe fcems very conMent with her
felf, and to aft with a wonderful tFuiformity, and equal Sim-
plicity. Nor can I fee any reafon to hope for (much lefe to
promife) a Solution of this Phsnoraenon from the ambige-
neous Principle of Attraftion, whpfe Adion is well known to
be always the fame to a certain Diftance qr Limit one way,
and beyond that as conftantly the reverfe ; fuch a Circum-
ftance little favours the Prediction of an eafy and fimple So-
lution. . See Ronvning's CompenduiusSyftefn^ P»rt III. pag. 1 67.
As.
1 86 0/ Light and Colours.
As Light, falJing upon this thin Plate of Air
between the Glaffes, is varioufly difpofed to be
refleSled or tranfmittedy according to the fcveral
4. I (hall therefore proceed to give an Idea of one of the
SDoil beautiful, delicate, and importing DifcoTcries that was
ever made; and that as nearly as may be after the Manner,
and in the Words of the Author, by the Experiments which
he made, and his Obfervations and Reafbnings thereupon.
5. The firft Experiment he mentions is the Compreffion of
two Prifins hard together, whofc Sides were a little convex,
by which means they touched by a fmall Part of their Sur-
ges, and contained every where elfe a thin Plate of Air, at
it may be properly caird, whofe Thicknels did every where
mdiLaliy mcreafe from the touching Parts. He obferved the
Place where they touched became abfolutely tranfparent, aa
if they had there been one continued Piece of Glafs.
6. For when the Light fell fo obliquely on the Plate of
Air between the Prifms as to be all refledled, it feem'd in
that Place of Contad to be wholly tranfmitted, infomuch, that
when look'd upon it appeared like a black or dark Spot, by
reafon that little or no feniible Light was refleded from thence.
$is from other Places.
7. When he looked through the Prifms, this Place of Con-
tad feem*d (as it were) a Hole in the Plate of Air, and
through this Hole Qbjeds that were beyond might be feea
# diftindly, which could not be feen through other Parts of
the GlaiTes .wh^re the Air. was interjacent. By harder Com-
preflion, the Spot was dilated by the yielding inwards of tho
Parts of the Glaffes.
8. When the Plate of Air, by turning the Prifms about
their common Axis, became fo little inclined to the incident
Rays, that fqme of them began to be tranfmitted, tl*ere a-i
rofe in it many flender coloured Arches, which at firfl were
Plate XL. neaped almoftlike the Conchoid, as in Fig. i. and by con-
tinuing the Motion of the Prifms, thefe Arches increased and
bended more and more about the faid tranfparent Spot, till
they were compleated into Circles or Rings encompafiing it i
and afterwards continually grew more and more contraded.
yQ. Thefe Arches and Rings became tinged with various
Colours, as the Motion of the Prifms was continued, being;
at hx&of a Violet and Bl»ei afterwards of a White. Bim^
Violet i Black,, Red, Orange, Yelk^, White, Blue, Violet, &c.
After this, the coloured Rings contraded, and became only
hhck and avtoir: The Prifms being farther inoved about, tha
Degrees
0/* Light ^«^ Colours • 187
Degrees of Thicknefs; fo-when it faKs on the
Surface of natural Bodies, it is as variopfly re-
fledled from the Pores of Air of different Thick-
Coloars all began to emerge out of the Whltenefs^ and in a
contrary Order to \yhat they had before. *
10. But to obfcrve more nicely the Ordeir 6f the Colours
^hich arofe Out of the white Circles, as the Rays became left
and lefs inclined to the Plate qf Air, Sir Ifaac Nrwtom made
vfe of two Objedt-GlafTes, one a Piano-Convex, and the o-
ther a t)oubIe -Convex, of the lame Sphericity on both Sides,
pf 51 Foot focal DiHance; and upon this he laid the pkne
Side of the other, preffing them flowly together to make the
Colours fuccef&vely emerge in the Middle of die Circles, and
then ilowly lifted t^e upper Gbfs from the lower to maka
tiiem fucceflively yanifh again in the fitme Place.
11. Upon Compreffion of the Giafles, various Colours
^ould emerge and fpread into concentric Circles or Riogt of
different Breadths and Tints encompaffing the central Spot.
Their Form, when the Glafles were moft comprefied, is d4«
lioeated in the ad Figure, where a is the central blade Spot, Plate XL*
)uid the Circuits of Colours from chenoe outwards as fol*
jows.
Ch Blue C^' ^^'^'^' C'' *^^-
) f ' White V' ^^"^- j"*' *^-
'• S J Yellow *• \^» ^^f^tm. 3.<ir, Grccn.
w. Yellow, ^^^ YeUow. >#, Yellow*
K.i^\^ca. C^,Rcd. C/,Red.
^ Ttf, Green. ^ c i, Greenifh Blue.
+ lr,Red. S'l/, Red.
^ r i«, Grecnifh BluCf ^ Cj, Greenifh Blue.
^' \ X, Pale Red. ^* 1 «. Reddiih White.
12. To determine the Thickxiefs of the Plate of Air,
Vvhiei-e eaph of the Colours was produced^ htmeafured ch«
Diameter of the firft fix Rings at the moft lucid Part of their
Orbits, and fquaring them found thole Squares to be in the
Arithmetical Progre^on of the odd Numben W 3» S> 7* 9*
1 1 ; and Aucf one of thofe GlaiTes was pl^ne, and the other
fpherical, their Intervals at thofe Rings muft be in the fame
^rogreffion. Alfo h^ meafured the Diameters of the dark or
faint Rings between the more lucid Colours, and found their
Squares to faf in the Arithmeti^a} Pro0:ei|q9 ^ the even
lumbers a, 4» 6, 8, 1 c, 12*
' %i. AU this follow ftom the Na^ut^ of ^^e C^rde ; fof
*^ '*' " ncUc»
1 88 Of l/iGHT dnd Colours.
ncffes in thofe: Bodies -, and according to the dif-
ferent Texture of Bodies, and Magnitude of the
Particles of Light, it will be either tranfmitted
Plate XL. let the Circle EFG be the SedUon of the Sphere whofe Con-
Fig. 3. vexity is equal to that of the Double-Convex above-mention 'd,
^d the I^ine AB a Sedion of the plane Surface of the Plano-
convex pouching the other in the Point D \ then fuppofing
P^f P/> ^^® Semidiameters of two Rings, the Thicknefs of
the Air between th^ Glafles af thpfe Rings will be ^r and //,
which are equal to Da and D^ refpeftively. If therefore,
as ufual, we put DG=:«, T>a-zzx^ I)^ = X, ^c =r
(D^=)>, and J^zr (D/=:) Y; then by the Property of-
the Cirde we have jj^ -^ZLax-i— xx^ and Y V =: aX — XX ;
and therefore t* : Y* :: ax-^xx xa'^ — XX*:: x : »
X X. But when a or 'Dg is very great with refped to x and
X, or D/2, D^, then n: i nearly 5 confequently^ iii
the prefcnt Cafe y* : Y* :: x.\ X ; or the Square3 of the Se-
midiameteiis of the Rings D^, D/, are as the Intervals ec^
fd; or Xhickiie&s of the Plates of Aii^ in thofe Places j and
therefore the Squares of the Whole Diameters are in the
fame Rad6. * •
14. Sir i^tff meafured the Diameter of the 5th dark Cir-
cle, (fuppoi'cL 2 "Df) and found it eqoal to ^ of an Inch ; but
thea viewing itvthrough a Giafs \ of an Inch thick, and near-
ly in the Perpendicular, it mnfl by Refradion appear dimi-
nifh'd nearly in the Proportion of 79.10 80; fo tliat, Afr 78 :
8a :: T : — = 2 D/ the real Diameter between the Glaffes.
- 79 '/
g
Whence D/n—, and in this Experiment DG = i8i
Inches, we have, DG : hf (:;^ J>f) ;: S/: Dl =fdi or,
in Numbers, As 182: — :: — : -^ — or : ^f^i
79 79 5^793* >7747H
and iince the» Thicknefs of the Air at the 5 th Ring is .to that
at thefifftas I© to 2, or 5 to i, (by Jrt, 12.) tha-efote.| of
5- = ^^ Part of an Inch, for the Thicknef? of
1774784 88739 ^* ■
the Air at the firft dark Ring.
1 5. By another Objeft-GIaft of a Sphere whoft Dmimcter
D G =; 1 84 Inches, he found t^e Dimf nflon or Thicknefs of Ai^
wholly^
0/* Light and Colovk^: iBg
wholly, or ih part; and that which is reflcfted
will be all df one Sort of Rays^ or of fsveral Sorts
promifcuoujlj and unequally^ or of all Soris equally.
mt the fame dark Circle to be Part of an Inch : Bat the
88850
Eye in both thcfe Obfcrvations was not quite perpendicularly
over the Glafs, and the Rays were inclined to the Glafs in an
Angle of 4 Degrees ; therefore (as per next Article) had the
Rays been perpendicular to the Glaflfes, the Thicknefs of the
Air at thefe Rings would have been le^, and that in Propor-
tion of the Radius loooo to the Secant of 4 Degrees 10024.
The ThicknefTes found diminifhed in this Ratio will be ■■ ^ • ■■*-
8895Z
and , or in the neareft round Numbers Part of
89063 89000
an Inch. Now half of this, w-c. — , is the Thicknefs
178000
«f the firft colonr'd Ring ; and of the reft as follows, — -f —
® I 78ooo»
178000 178000' ' 178000 178000/ 178000*
&r. are the Thickneffes at the feveral dark Rings.
1 6. The Rings were obferved to be leaft when the Eye
was held perpendicularly over the Glafles in the Axis of the
Rings ; and when they were view'd obliquely, they became
bigger continually, fwelling as the Eye was removed farther
from the Axis. And by meafuring the Diameters of the fame
Circle at feveral Obliquities of the Eye, and by fome other
Methods, Sir Ifaac found its Diameter, and confequently the
Thicknefs of the Air at its Periphery in all thofe Obliquities,
to be ycry nearly in the Proportions exprefled in the following
Table ; where the firft Column exprelTes the Angles of Inci-
dence which the Rays of Light make with the Perpendicular
in the Glafs ; the fec<Hid Column exprefles the Angle of Re-
fradion into the Plate of Air ; the third Column (hews the
Diameter of any coloured Ring at thoie Obliquities exprefled
in Parts, of which ten conftitute the Diameter when the Rayt
are perpendicular ; and the fourth Column (hews the Thick-
nefs of the Air at the Periphery of that Ring exprefled in
Parts, of which the Diamf ter confifts of ten sdfi> when the
Rays are perpendicular*
Whence
190
Of LiGHt d«i/ Colour^.
Whence it will follow, (i.) If the Lighf bd
ivhoUy tranfmitted, the Body will appear blacki
*7-
Angle ef Inci-
Angle if Re-
DieUnter
nicknefi
dence en the
froQitn into
of the
of the
? late »f Air
ibePl.pfAir.
Rit.
Air. .,
Deg. Min.
Deg. Min.
oo oo
00 60
16
10
06 36
10 00
10^
IOj\
12 45
20 00
loi
lol
18 49
30 00
.o|
>Ii
24 30
40 00
"1
•3
29 37
50 00
I2i
>5i
3J 58
60 00
'4
20
35 47
65 00
•li
23i
37 >9
70 00
16^
28i
38 33
75 00
'9t
37.
39 *7
80 00
22«
S*i
4* 00
8$ 00
2g
84T?
40 II
90 00
3$
t22i
18. ^5^ I(5oking thrdirgh the two contiguous Objeft-GIaiTej^
or Prifms, it was obferved thatthe Rings of Colours appeared
as well by tnmfmitted as by refleded Light. The centra!
Spot now becape white and tranfparent. The Order of the
Colours was Tellonvi/b RiJ; Black, Fiotit, Blue, White, YeU
low. Red', Violet, Blue, Green; Tellono, RiJ, Sec. as they are
Plate XLt written in the 4th Figure below, thofe above being the Co-
lours by Reflexion ; AB and CD being the Surfiiees of the
GlafTes contiguous at £, with Lin^ between fhewing the In-
tervab or ThickneiTes of Air in Aiithmetical PrO^^ffion.
Where comparing the Colours, you obferve that White is op-
poiite to Black, Red to Blue, Yellow to Violet, Green td
' Red, bfc, in tepefied and refracted Light : But the Colours
by refracted light were very faint and diluted, except when
view'd very dbliquely, for then t^ey became pretty vivid.
19. By wetting the Glafles round th^ir Edges, the Water
crept in uowly between them, and the Circles thereby became
lefs, and the Colours more faint. Their DiaAneters beio^
meafured were found in Proportion to thofe of the Rings
made in Air as 7 to 8, and therefore the Thicknefs of Air at
like Circles as 7 x 7 = 49 to 8 x 8 = 64, or as 3 to 4 very
nearly, which is the Ratio of the Shies of Incidence and Re-«'
fraAion out of Water into Air, And thi« perhaps (fays Sir /-
Of Light and Colours, 191
v?hich is the Abfence of all colourM Light- (2.)
If the Light reflefted from Bodies be all of one
fiiac\ may be a general Rule for any other Mediom interce-
ding the GlaiTes more or kfs denfe than Water.
20. The coloured Rings made in Air became much more
diftindt, and vifible to a far greai;er Number, when viewM in
a dark Room by the ReHedtion of the coloured Light of tht
Prifm. The Rings made by Refle^on of Red Light were
manifieilly bigger than thofe made by the Blui zxAVi9Ut\ and
it was very pleafant to fee them gradually fwell and contraA
according as the Colour of the Light was changed. The
Motion was quickeft in the Rtd^ and floweft in the VitUt ;
and by an Eftimation made of the Diameten of the Rings^
the ThickneiTes of Air in the Plakes where the Rings are
made by the Limits of the feven Colours, Rtd^ Oramge^ Tel-
iow, Greeti^ Biue^ ^^gOj Violet ^ fucceffively in Order, were
to one another as the Cube Roots of the Squares of the 3
' Lengths <^ a Chord which ibund the Notes of an OSave,
that is, of the Numbers i, |, |, |, |, |, t^, J.
2 1 . Thefe Rings were not of various Colours, as thofe
made in the open Air, but appear*d all over of that Priiina-
tic Colour only with which it was illumin*d ; and by throw-
ing the coloured Light dire^y on the GlaiTes, that which fell
on- the dark Spaces between the Rings was tranfmitted through
the Glafles without any Variation of Colour. This appeared
by placing a white Paper behind, on which the Rings were
painted of iht lame Colour a> thofe by refleded Lij^t^ and
of the Bignefs of their immediate Spaces.
312. Hence the Origin of thefe Rings is manifeil; namely,
that the Air between the GlaiTes, according to its various
Thickneis, is difpofed in fome Places to refle^l, in others tcf
tranfmit the Light of any one Colour s and in the iame Place
to refle£l that of one Colour* where it tran&nits that of an-
other; in the Manner'^ you fee reprefented in the 5 th Fi-
gure : Where A 6, CD, are the GlafTes, as before ; and a, r, pjate XL.
'» g* h h ^i p% the Parts of the Beam tranfmitted ; and ^, d^
/, h^ k^ iff, 0, the Parts of the Beam reEedled, making the co-
lour'd Rings.
23. The Squares of the Diameters of thefe Rings made
by any Prifmatic Colour, and coniequently the Thickneifes of
the Air at each, were in Arithmetical Progreflion, as in. the
£ings of common Light » and the Qimenfion of the Rings
made by Yellow Light the fame as fpecified hi ArUch 14.
Sort
192 Of Light and Colours;
Sort, that Body will appear all of one Colour;
which will be moft fimple and intenfely deep;
Thcfe Obfcrvations were made with a rarer thin Medium ter-
minated by a denfer, n)i%. Air and Walter between Glafft^.
In thofe which follow are fet down the Phenomena of a
denfer Medium thinn'd within a rarer, as Plates of Mufco^
Glafs^ Bubbles of Water, £«ff. bounded on all Sides witk
Air.
24. In the Experiment made with a Bubble of Soap- Water
coverM bjr clear Glais, and expofed to the white Light of the
Sky, it was obferved, that as the Bubble grew thinner by the
continual fubfiding of the Water, it exhibited Rings of Co-
lours flowly dilating, till they overfpread the whole Bubble;
and vanifh*d at the Bottom fuccefiively. The Bubble was
black at Top, and this central Spot waLs furrounded with
Rings of the fame Colours, and in the fame Order as thofe
of Air in Art, 1 1, but much mofe extended and lively.
25. As the Thicknefs of thfe aqueous Shell diminished, the
Colours of the feveral Rings by Dilatation were fucceeded
by others in Order from the Red to the Purple. Thus the
Red of the fecond Ring from the Top (or fixth from the Bot-
tom) was at iirft a fair and lively Scarlet, then became of a
brighter Colour, being very pure and brilk, and the bcft of
all the Reds. Then after followed a lively Orange, which
tvas fucceeded by the beft of Yellows, which foon changed
into a greenifti Yellow, and then into a greeniih Blue. After-
wards a very good Blue, of an azure Tint, appeared \ which
was fucceeded by an intenfe and deep Violet. And fo it
happened in all the other Orders of Colours, only not in fb
regular and perfedl a Manner, the Colours in them being
more compounded and lefs dillind.
26. Thefe Rings of Colours, view'd in various Pofitions
of the Eye, were found to dilate according as the Obliquity
of the Eye increafed, but not fo much as thofe of Air in
Art. 1 6. For by the Table, Art» 1 7, it appears they expanded
to a Part where the Thicknefs of the Air was to that where
they appeared when viewed perpendicularly as \zz\ to 10, or
more than 1 2 to 1 ; whereas Sir Ifaac found, by meafuring
the Thicknefs of the Bubble at the feveral Rings, as they
appeared at the , feveral Degreed of Obliquity mentioned in
the Table below, that the greatc!ft was to the leail only as 1 54
to 10 ; which Increafe is bat abcfut a 24th Part of the for-
mer in Air.
(20 If
Of Light and Colours;
^3.) If tKe Rays are promifcuouily rcflefted^ but
one Sort liiore (han the reft, the Body will ap-
. • <
' , 27. The Aogles of Incidience on the Water, and the Re-
fra^on into the V^ater, are f^ewn in, the. twp firft,Cplomiu^
tnd in the thifd the Thickneffes of the aqueous Sh^l corre«
ijpoiiding thereto . .
i5»3.
InciJUnte qH
tbi Water. .
Rifraahmin
t9 tbe Watir
fbkknefsof
tbe Shell.
Deg. Min.
00 00
Deg. Min.
00 00
10
15 00
II II
toj
30 00
45 00-
60 00
75 00
90 00
22 01
32 02
40 30
46 25
48 35
iol
"^
Hi
154
« 2$.. The Sine3 of theie Angles out of Water into Air are
afluined a^ 3 to 4 ; and Sir ijfauc has cblleftedy (with a pro-;
digious Sagacity) that the ni'cknefs of tbe Plaifof^^r or SbeU
^ W^ter^ lequifite to exhibit, ome duid the fame Cojokr at federal
Obliquities of tbe Eye, is frofortional to tbe Secinti of an AngU
Aubofe Sine it tbe Jkft.of 106 fnean ProfortionaH bet^-oen tbg
Sines of Incidence and Rtfra&ion... .
29. As in Art. 1 8^ fo here the Bubble by tranfmitted LighC
appear*d of a contrary Colour to that which it. exhibited by
}(efleaion : Thus that Part which looked. tUd by refleae4
Light looked Blue bj^ reffafted, and the Part whldi was BIia
hy refleded Liglft was JHed by Rays tranfmitted. Thefe Ringa
f ppear much more numerojus, and piore" dilated, when view'd
^ottgh a Prifm than to the naked Eye;. and by means of
^he Prilm fcveral Rings may £e djlfcpv^r'd bee ween the GkfTes
or in the Bubble, when none appear to the bare Eye*
30. The coloured Rings now described appe^ alfo in tbia
Sieces pf Mufcovy Glafs \ which when they were wetted oi|
\t Side oppoiite to the Eye.exhilbited.ftill the fame Colour s»
t>ut.ippre languid and flaunt. Whence, and by Art. 19, it
evidently appprs, th^t th,e T hKknefs of a Plate requiiite to
produce any Colour depends only on the Density of the Plate^
ai^d not on that of the ambient Medium. . And upon th^
yirholej if the Plate be denfer than the ambient Medium, it
^^hib.its m^re briik and lively Colours than that which is (o
muf^h rarcr;^
V6l.ii; n
194 Of Light and Colours.
pear of the Colour proper to that Sort of "Ray,
but it will be rtor fo pure and ftrong as before,
.31, The Colours which arife on polifh'd Steel being heat-
ed are of the fame Kind with thofe in the Rings of the Bub-^
ble, emerging one after another from Rtd to Blue or Purplcr
fucceffively j and like the others will change iri bemg.view'd
at different Obliquities of the Eye, but not in fo great a De-
gree.
32. That we may be able to fhew. how. the Colours in the
feveral Rings are produced, we fhall a little illuftrate Sir /-
faac"^ Invention fq^ that Purpofe. Iji order to this, Let there
PlateXLI. betJCken, in any Right Line YH, the Lengths ^A, YB,
Fig. I. YC, YD, YE, YF, YG, YH, in Proportion to each other
as the Cube Roots of the Squares of the Numbers i, ^, y, f,
ii -6> |f ^ » that IS, in the Proportion of the Numbers 6300,
6814, 7114, 7631, 8^55, 8855, 9243, loooo. See Jrti-
£le 20.
33 . In the Points A, B, C, D, E, F, G, H, ereft the Per-
pendiculars A/?, B^, Cf, tff. by whofe Intervals the Extent
of the Colours wrought by them will be rcprefented. For if
at the Thickncfs Y A the Violet Colour begins, and the In- .
digo at B, the Extent A B will reprefent the Breadth of the
Violet ; and fo of the reft. ?
34. Then let the Line A^? be divided into equal Parts, and
number'd as in the Figure to 43 ; and through thofe Divi-
fions from Y draw the Lines 1 1, 2 K, 3 L, 5 M, 6 N, 7 O, ^c.
Then will the Parts A 2, A 6, A 10, A 14, ^c. be in Propor-
tion to the odd Numbers i, 3, 5, 7, g, 11, t^c. or as the
Thickneffes of the Air at the feveral Rings. See Art. 1 2.
35. Therefore fmce A 2 reprefents the Thicknefs of any
ihin tranfparent Body, at which the Violet of the firftOrdei
• or Ring is mofl copioufly refleded ; then will HK reprefent
its Thicknefs where the Red of that Order is moll copioufly
reflefted : Becaufe, in the fmiilar Triangles A Y 2 and H YK,
we have Y A : YH :: A 2 : HK. But Y A and YH are as
the Thickneffes of the Plate of Air at thcfe Colours, an4
therefore alfo A 2 and HK. See Art, 32.
36. Again; becaufe (by Art. 12.) A 6 is the Thicknefs
where the Violet of the 2d Ring is moft copioufly reflected,
and (by Art. 20.) the Ratio of the Thicknefs of the Air where
Violet and Red are refleded is the fame as of YA to YH ;
therefore fmce YA : YH :: A6 : HN, the Line HN will
reprefent the Thicknefs bf the Plate where the Red of th«
i€(ond Older h reflected moft copioufly. Thu$ alfo A to
/ • '- • (40 If
Of LiGkT and Colours. 195
(4.) If three or four Sorts of Rays are promif.
cubufly refleded more than the reft, the Colour
and HQ^will reprefent the fame for the Violet and Red of
* the third Order, and fp on.
37. And the Thicknefles at which the intermediate Co-
lours will be refle&ed moll copiouily will be defined by the
Diflance of .the Line AH from the intermediate Parts of the
Line 2K, 6N, loQ^ (^c. againft which the Names of the
Colours are written ; which is eafy to underftand.
38. Bat farther to define the Latitude or Sreadth of thd
Colours in each Ring, let A i denote the leaft ThickneG, and
A 5 the greatefl, at which the extreme Violet in thefirft Se-
ries or Ring ii reflededj then fhall HI and HL be the like
Limits for the extreme Red, and the intermediate Colours
will be limited by the intermediate Parts of the Lines 1 1 and
3 L, againit which the Names of thofe Colours fland ; and
fo on. l^oie. The fame Latitude is affign^d to every Series
of Colours^ AHL3i 5M07> 9PR11, k^c, becaufe the
Difference of the Breadths of the Rings in the Plates of Air
and Water were infenfible to the Eye in the Experiment.
39. From hence it is eafy to obferve, that the Spaces
A I IH. 3 5 ML, 79PO, fcff. are thofe at which the Rays
are trannnitted, and the dark Circles appear. And therefore
we may know from this Scheme what Colour muft be exhi-
bited (in the open Air) at any Thicknefs of a traniparent thin
Body : For if a Ruler be applied parallel to AH, at the Di-
* fiance from it by which the Thicknefs of th^ Body is repre-
fented, ahe alternate Spaces 1IL3, 5MO7, {s^c which it
croiTes, will denote the reflefled original Colours, of whick
the Colour exhibited in the open Air is compounded.
40. Thus, for Examp!e, if it be required to find what ii
the Conilit;ution or component Colours of the Green of the '
third Order or Series, apply the Ruler as you fee at rstuw^
(parallel to A H) and by its PafTage through fome of the Blue
at s, and Yellow at u, as well as through the Green at /, yoa
may conclude that the Green exhibited at that Thicknefs of
the Body is principally conflituted of original Green, with 2
Mixture of fome Blue and Yellow.
41. By this rnean^ alfo you may know how the Colours
from the Center of the Rings outward ought to fucceed iit
the Order as they have been defcribed in jirt. 11. -For if yoa .
move the Ruler gradually from AH through all the Diibmces^
liaving pafs'd over the firit Space A i, which denotes little <>if
no Reiiedion to be made by thinned Subibuu:es^ it will firfil
N 2 of "
196 Of Light and Colours.
of the Body will be a Mix'd or Compoiand, in-
clining to the Tint of thfc naoft: predominant Co-
arrive at I the Violet, and then quickly at the Blue and Green,?
which together with the Violet compound Blue; and then at
the Yellow and Red, by whofe farther Addition that Blue is
converted into Whitenefs, which continues during the Tranfit
of the Ruler from I to 3 j and after that, by the fucceffiVe
Deficience of its component Colours, turns firft t6 compound
Yellow, and that to Red, which ceafes at L. Thus are ihe^
CoioliTS of the £rft Series generated.
42. Then begin the Colours of the fecond Series, whick
fucce^ in Order during the Tranilt of the Edge of the Ruler
from 5 to O, and are more lively than before, becaufe more
expanded and fevered : And here, becaufe the Ruler arrives
to and paiTes over the Point 7 before it comes to M, there
cannot be a RefiedUon of all the Colours at the fame Time, and
therefore no Whitenefs between the Blue and Yellow, as be«
fore % but there will be a Reflexion of original Green, with
Ydlow and Orange on one Side, and Blue and Indigo on the
other, which together make a compound Green.. The Vio-
let will here firft appear at 5, before it comes to be refleded
with Indigo and Blue.
43. So the Colours of the third Scries happen in^Order;
fiHl the Violet at 9, which as it interferes with the Red of
the fecond Order, i^ thereby inclined to a reddifh Purple,^
Then the Blue and Green, which here are lefs mixM with
other Colours, and confequently are more lively than before,
efpecially the Green. Then follows the Yellow, fome of
which towards the Green is diflindl and good, but that Part
towards the fucceeding Red, as alfo that Red, is mix*d with
the Violet and Blue of the fourth Order ; whereby various
Degrees of Red, very much inclining to Purple, are com-
pounded.
44. Hence the Violet and Blue, which fhould fiicceed and
begin the fourth Series, being mix'd with and hidden in the
Red of the third Order, there fucceeds a Green, which at
iirft is much inclined to Blue, but foon becomes a good Greeff,
being the only unmixM and lively Colour of this fourth Or-
der : For as it verges towards the Yellow, it begins to inter-
fere with the Colours of the fifth Series, by whofe Mixture •
the fucceeding Yellow and Red are very much diluted and
made dirty, efpecially the Yellow, which being the weaker
Colour is fcarce able to fhew itfelf ; fo that this Order con.,
fifb of Gre^n and Red only.
• lour.
Of Light and Colours. 197
Ipun (5.) When all Sorts of Rays arc equally
i;efle6ted from Bodies, thofe Bodies appear whiUy
45. After this, hy paffing the Edge of the Ruler along pa«
railel to AH, it jvill cat the Colours of the fecond, chMy
and fourth Series at once; which will ihew thofe Colours be-
come more and more intermixed, till after three er four more
Bievolotions ^in which the Red and Blue predominate by turns,
making the fifth, fixth, and feventh Rings) all Sorts of Colours
^re in all Places pretty equally mix'd, and compound an even
Whitenefs. Thus the Line xy paffing through the Red of
the 7th Series, the Yellow and Green of the 8th, the Blue
of the 9th, and the Purple of the loth. (hews Whitenefs at
the Thicknefs hx or H4 muft neceflariiy refult from the
Mi?fture of fo many original Colours.
46. Since (by Art. 20, 21.) the Ray€ of ov^ Colour are
jtranfmittecl where thofe of another Colpur are refle^d, the
Reafon of the coloured Rings mjide by tranfmitted Light is
jfrom hence roanifeft; becauie wh^t has been faid with reijped
to the Colours made by Refledlion from the Spaces i L, 5O.
9 R, {ff r. is equally applicable to account for the Colours msbdc
by Refradlion through the Spaces AT, 3 M, 7P, 1 1 S, fcfr.
47. Not only the Order and Species, f)ut alfo the precife
Thicknjefs of the Plate at which any of thofe Colours are ex-
hibited in Parts of an Inch, ma^ be obtam*d as follows. Since
(by Art» 14, 15, and 23.) we have the Thicknefs of the Plate
where Yellow Light is reflcfted already meafurcd, inx, F/rz Pl. XLI,
TTiW^j F«» = T7 Ap^» F« = Tri^'s^* Foz=. Tii^d&f bfc^ Fig. 2.
and fii;ice ttV^^^ = 0,000005$, or 56 Parts of Ten MiUiQi|
of an Inch } if the Scale of equal Parts be conftrudied fuch
of which F/pi 56, it is plain any other Thicknefs of Air
may be immediately meafured thereon by means of a Pair of
Compaffes, or by a parallel Ruler. Thus Goo :^ 0,00002 54 ;
A 2 = 0,0000040 ; HK=: 0,0000065; A6 = 0,00001 19}
H N p: 0,0000 1 94. And thus any other Thicknefs fpr any
propofed Colour or Series is evident almoft by Infpeftipn, to
the Ten Millwnth Part of an Inch.
48. Since by Art, 19. it appears, that the ThicknefTes of
Air and Water, exhibiting the faipe Colour, are as 4 to 3 ; if
the Thickncffes in Air are known for the feveral Rings, you'll
have the Thicknefs of the Bubble of courfe where the feve-
ral Colours appear ; and thq# the Table in Art. 27. was n^^^.
Alfo hence the Thickneifes of thin Plates of Glafs producing
the Rings of Colours will be known, being to'thofe of Air as
i 6 to 31, 'v/x. in the Proportion of the Sineg of Incidence
* ' * ' N 3 or
198 Of Light and Colours.
or of the Colour of the Sun*s Light. (6.) Where
there is no Light at all incident on Bodies, thofc
to Retra£tion out of GlaTs into Air for YeHow Light ; and
the Difference of the Proportion of the Sines for the other
Rays is not confiderable.
49. Thefe arc the Meafures nearly, which Sir Ifaac has
cxprefs'd in the following Table, where the Numbers are {<^
inany Millionth Parts of an Inch for the ThickneiTes of the
Plates of Air, Water, and Glafs, which exhibit the variooa
polours of the feveral Orders.
Mr, Water, Clafi.
f Very BUck, 4 . i
Colours of the
Firft Order.
:i
Black, > '4
Blue, 2f If
White, si 3i 3f
Yellow, . 7i 5^ 4
Orange, S 6 5^
LRcd, 9 6| jf
f Violet,
I Indigo,
j Blue,
Of the Second OrderX ^"^^^^^
I Orange,
I Bright Red,
L Scarlet,
J Purple, 21 15 J III
Indigo, 22tV 16-j 14J
Blue, 23I 1 7 J- t5T'«
Green, 25} 18^ 165
j Yellow, 27f 20^ \ji
Red, 29 2i| iSf
I^BlueiftiRed, 52 24 2o|
26
ui
H
74
izf
9i
8t\
H
•oi.
9
•Si
u4
9^
.6^
"i
10^
'7f
•3
?'i
>H
•3i
I "4
•91
Hi
I2.|
prtheFourthOrder.^g-, 35| ^6|
Of the Fifth Order. I ^If "^ ^''^*' '^'^. 54f ^9^ '
' !;''^ 39I 34-
Df the Sixth Ofder. j ^'^''"^^ 2'''^> f -^ 44 38
tRed, 65 484 42
©fthe^«,^nf»,rvj-,5"Grecni(hBIae, 71 S3i 45?
*^^'^'^*"*^*^"iRuddy White, 77 571 49l
Bodies
O/* Light /z;^^ Colours. 199
Bodies can have no Colour, which .is a Property
of the Rays of Light only (CXXII).
50. Thcfc are the principal Phaenoi^cna of thin Plates of
Bubbles, which follow from the Properties of Light by a
mathematical Way of Reafoning; whence it follows, that
the colorific Difpodtion of Rays is connate with them, and
immutable, there being always a conHant Relation between
Colours and the Refrangibility and Reflexibility of the Rays.
In this refpedl the Science of Colours becomes a Speculation
as truly Mathematical as any other Part of Optics i and con-
fifts of two Parts, one Theoreticaly which delivers the Proper-
ties of . Light,, and the Principles on which the various Phae-
nomena of Colours depend. This Part we have hitherto been
treating of: The other is Pra^ical, and confifts in applying
thefe Principles to account for the permanent Colours of Na-
tural Bodies i to which we fhall now proceed in the following
Note.
(CXXII) I. As I here intend to deliver the whole Ng-wta-
man Doftrine of Colours, it will be neceffary to begin and
proceed with the Definitions and Precautions which Sir Ifaac
Nenvton himfelf has niade ufe of, and which are as follows.
2. His general Pofition is. That if the Suns Light confiftid
hut of one Sort of Rays, there nxjould hi hut one Colour in the
ijuhole World i nor nxould it he pojjihle to produce atr^ uenv Colour
hy Reflexions and RefraSions ; and hy Confequence that the Vor
riety of Colours depends upon the Compofition of Light. All which
is evident from the Subjedt of the foregoing Annotations on
the Properties and Phenomena of Light by Reflexion and
Jlefradlion.
3. His Definition of Light is as follows: The Light whole
Rays are all alike refrangible he calls Simple, Homogeneai^ and
Similar ; and that whofe Rays are fome more refrangible than
others he calls Compound, Heterogcneal, and D'jJJimilar.
4. The Colours of Eomogeneat lights hp calls Primary, Ho'
mogeneal, and Simple ; and thofe of Heterogeueal lights he calls
Heterogeneal and Compound, becaufe thefe are all compouaded
©f the Colours of Homogeneal Lights j as hath been in part
already, and will be farther ihewn in the Sequel of this Anno^
tat ion,
5. The Homogeneal Light and Ray? which appear Ked^
or rather make ObjeAs appear fo, he calls Ruhrific or Red-
making Rays ; thofe which give Obje<5U a Yellow, Green, Blue,
9f Violet Colour, he calls Yellow-makings Grefs^maJUng, Blue-!
N 4 LE.t .
20O Of Light and Golqurs.
Plate L. Let BNFG be a fpherical Drop of falling
^* ^ Rain, and AN a Ray of the Sun falling upop
it in the Point N, which Ray luppofe re-.
jfrafted to F, from thence reflected to G, and
there again refr^fted in the Dircftion G R to ^q
faking, Violet ptaking Rays ; and |q of the reft. And therC;
fore whenever he fpeaks of Light and Rays as coloured, 6t
endaed with Colours, he would be underftood to fpeak not
philofophically and properly, but grofsly, and according tO
^c vulgar Notion of Comilion People." '
■' 6. For thcf Rays, to fpeak properly, jire not coloured; in
them (Wc is notliing but a certain Difpofition and Power to
exdt^'a^^nfatidn of this or that Cblour. For as Sound in a
^eli or miuical String is nothing but a tremulous Motion, and
in the Air nothing but that Motion propagated from the Ob-
je£l in aerial Undulations ; and in the Sen/orium *tis a Senfe
of Motion under the Notion of Sound; So Colovurs in the
P)>}e£l are nothing but a Drfpoiltion to reQe6l this or that
Sort of Rays more copioqfly than the reft ; in th6 Rays thej"
are nothing but ^h^ir Difpbricioii to propagate this or that
Motion to the Senjorium'hy the Optic Nerve ; and in the
Sen/erium they are Senfations or Ideas of thofe Motions under
the Forms or Notions cf Colours. ' • '
7. Every Ray of Light in its Paflage through any refraft-
ing Surface is put into a certain tra'niicnt Conftjtution or State;
^Jiiph in the Progrefs of the Riy returns at equal Intervals,
anddifpofes 'the Ray at evelV Return to be eafily tranfmitted
through the next refradting Surface, and bet\Ceen theReturni
to be eafily rcfledled by it. This is ma^ifeft frbpi Art* 21,22,
of the laft Note. Thefe Return? of the Difpofition x>f any
Ray to be reflefted he caUs iti Fits of eafy Rifieaidh, and
thofe of its Difpofition to be tranfmitted its Fits ofeafy iLtanf-
mjpon I and the Space it paffes between twtry Return he Cialls
Xhtlftter^valof tbeFits,
'8. This Alternation of its Fits depends op both the Sur-
faces of every "thiri Plate or Particle, becaufp it depends on its
"T^ickncfs ; and alfo becaufe, if either Surface be wetted, the
Ctiours caufed both By Refljftion and Refraftioh grow faint,
which fliews it to be ^e<ited at'bpt^. • It is therefore per-
form'd at the fecond Surface, for if it'wer?) perform'd at the
iSrft, it could n6t depend on the fecond \ and" it i^ inflaence4
by fome Adion or Dirpofition propagated from the firlt to the
Of Light and Colours. %o\
Eye of a Speftator \ and let I G be perpendiculai:
to the Point G : Then will the Beam, by its Re-
fraftion at G, be fcparated into its fcveral Sorts
pf RayS) which will paint their refpedive Co-
lours \\i that Part of the Drop; of which that
feoQn^^ becaofe pthen^ife ^t the fecond it p^old not depend
dnthefirft. ''
9. Tfab Adlion or Difpofition, in its Propagation, inter*
mits and returns at dif&rent Intervab in different Sorts of
Rays, emerging in equ^l Angles out of any refrading Sur-
face into the fame Median). Thus in the Experiment of
Art* 20. and 2 1 . of the laft AnnQtation^ 'tis plain, the Violet
Ray being in a Fie of eaiy Tran&nii^'on at its Incidence on
the Plate of P^y^ was again in that Fit at the fartheft Surface,
in paffing through a lefs Space than that which the Red pafs'd
through in the Interval of its Fits ; for thofc; Spaces were as
the ThtckneiTes of the Gltfes, and confequgntly the Inter-
vab of thefe Fits were as the Numbers 63, 68, 71, 76, 824,
881^, 92^, 100, for theRaysrefpediteJyfropiyiqlcttoRed.
See Art. 32. of the laft Annotation. * ' '
IQ. Hence when a Ray of Light falls upon the Surface
of a Bqdy, if it be in a Fit of ^y Reflection, it fhall be
reflected ; if' in 4 Fit of eafy Tranfmiflion, it ihall be tranf-
niitted ; an^ thus all thick tranfparent Subftances are found to '
refled one Part of the Light which is incident upon them,
fmd to refrad the reft,
" 1 1 . ^he leafl Parts of alnaoft all Natural Bodies are in fome
meauip traniparent. This is well known to thofe who are
cpnverfant in Fxperiments wit^ the Common and Sohr Mj*
crofcopes: As alfo by the Solution of denfe and pp^e 60-
djes in Menftruums ; for then their Particles being fo minute-
ly divided become tranfparent. And therefore, coniidering
the inconceivable Smallnefs of the Particles of Light, evea
in comparifon of the fma]left Parts of Natural B^es, we
may conceive them as always incident on the Surface of tranf-
parent Subftances.
12. I haTe obferved (briefly] before, that thofe Superfidca
pf tranfparent Bodies refled^ the greateft Qp^tity of Li^ht,
which have the greateft refrading Power. Thus Glais pro-
duces a total Reflediion of Light at a leis Angle of Incidence
on the Air than Water ; for in Glais that Angle is but 40*^ 10^,
l^qt in Watfr it is 48*^ 35'. '^h»i8 alfo Diamond, whofe r^.
i
-2<>2 0/ Light and Colours.
next the Perpendicular IG will be red^ as being
leaft refriaAed, and the reft in Order above it-
Now it is found by Computation, that the greateft
Angle S<fO, or EOP, (drawing O P paralld to
S E) under which the moft refrangible Rays can
fraftive Power to that of Glafs is as 34 to 26 nearly, is found
to rcfledl a much greater Quantity of Light than GhXi, .
13. Hence 'tis obvious, there can be no Refledlion at the
PlateXLL Cionfines of equally refrafting Mediums. For let Hi be a
Fig. 3. fingle Ray of Light palling out of a dcnfer Medium AC into
a rarer D£ ; in tbis Cafe there will be a certain Limit or An-
gle of Incidence HIK, in which the Ray will be reflefted
mto IG, If the Medium AC be fappofed to have its Den-
sity dccreafing, then the Lmiit or Angle HIK will Be con-
tinually increafing; or, which is all one, the Ray HI riiuft
have a greater Obliquity than HIK that it may be reflefted.
Therefore when the Dcnfity oP-the Medium A C becomes
equal to that of DE, the Angle HIK will become equal to
DIK; and fo no Ray*inclined to the Perpendicular K I can
in that Cafe poffibly be refledled.
14. Hence the Reafon why uniform pellucid Mediums, as
Water, Glafs, Cryftal, l^c. have no fcnfible Refleilion but in
their external Snperficits, where they are adjacent to other
Mediums of different Denfities, is becaufe all their continuous
Parts have one and the fame Degree of Denfity.
1 5. Hence alfo it is, that iince .in common Subftances there
are many Spaces, Pores, or Interftices, either empty or re-
plenifh'd with Mediums of other Denfuies, various Refle£Uotts
mud be made in the Confines of thefe differently refracting
Mediums j lind thus the Bodies become varioufly coloured and
opake in different Degrees. As for Example, Water between
the tinging Corpufdes wherewith Liquor is impregnated j
Air between the aqueous Globules which conllitute the Clouds
or Mift ; and Water, Air, and perhaps other fubtil Media be-
tween the Parts of folid Bodies, give them their proper Co*
lours and Degrees of Opacity, by a confufed and promif-
tuous Reflcflion an*d Refraction of Light,
16. The Parts of Bodies and their Interfaces muft not be
Jefs than of fome definite Bigi^eA to render them opake an4
'coloured: For, as was faid before, the opakefl Bodies, if
their "''^rts be fofEciently attenuated by Solution, become tranf-
parent. I'hus ^he Top of th^ Water-Bubble being \tr^ thii^
4.
come
0/ Light and Colovas. 203
come to the Eye of a Speftator at O, is 40 Deg. Rate L,
17 Minutes; and that the greateft Angle FOP, '^' ^*
under which the leaft refrangible Rays conre M
the Eye at O, is 42 Deg. 2 Minutes, And fo
a]l the Particles of Water within the DifFerehce
inadenofenfiWcRefledUon, and therefore exhibited no Co-
Jours ; bift, tranfmitting the Light, appeared black. Henee
it is that Water, Salt, Glafs, Stones, £«fr. having their, Paru
and Interilices too fmall to caufe Refledions, become .tranf-
parent and colourlefs.
17. The tranfparent Parts of Bodies, according to their
feveral Sizes, re£ed Rays of one Colour, and tranlmit thofe
of another, on the fame Grounds that thin Plates or Bubbles
did the fame; and this is undoubtedly the Ground and Reafoa
of all their Colour. For if fuch a thin Plate fhould be broke
into feveral Fragments, or (lit into Threads of the iame Thick*
nefs, they would all appear of the fame Colour; and by con-
feqaence, an Heap of thofe Threads or Fragments would
ponilitute a Mafs or Powder of the fame Colour the Plate ex«
hibited before it was broken ; and the Parts of all Natural
Bodies, being like fo many Fragments of a Plate, muft on
the* fame Grounds exhibit the fame Colours.
18. And that they do fo will appear by the AfHoity of
their Properties. The finely-colour'd Feathers of fomc Birds,
as of Peacocks Tails, do in the very fame Part of the Fea-
ther appear of feveral Colours in feveral Pohtions of the £ye,
in the fame manner that thin Plates were found to do in Jr-
tides i^. and 26. of the lail Annotation ; and therefore their
Colours arife from the thin tranfparent Parts of the Feathers^
^ that is, from the Tenuity of the very fine Hairs or Cafilla'
iuenta, which grow out of the Sides of the groifer Parts or
lateral Branches of thofe Feathers.
19. And hence it is, that the Webs of fome Spiders being
fpun very fine have appeared colour^ ; and that the coloured
Pibres of fome Silks, by varying the Pofition of the Eye.
do vary their Colours.
20. Another Circumftance in which they agree is, that the
Colours of Silks, Clbaths, and other Subdances, which Wa^
ter or Oil can intimately penetrate, become more ^nt and
obfcure by being immerfed into thofe Liqu<»'s, and recover
theu" Vigour and Vivacity again by being dried, in the fame
jnanner dfi was obferved of thin Bodies in 4^/. 19. 9nd 30.
of
?P4 Of Light and Colours*
of thofe two Angles E F will exhibit fcverally
the various Colours of the Prifm, and conftitute
jhe interior Bow in the Cloud.
If the Beam go not out of the Drop at G, bu^
js reflefted (a fcconfi fime) to H, and is there
of the lad Annotation,
* £il A third CircumfUnce, in which Natural Bodies agre^
in their colorific Quality with thin Plates, is, that tney refle^
one Colour and tranfmit another. Thus Leaf-Gold looks
Yelled by rcflefted Light, and of a blueifh Green by the
tranfmitted Light. Alfo an Infufion of Lignum Ncphriticum
reflet the Blue and Indigo Rays, and therefore by Refle£tioa
appears of a deep Mazarine Blue ; whereas by refradled
Light it appears of a deep Red. And the fame Thing is
obfervable in feveral Sorts of p?iinted Glaffes.
*^ -2 2. Again; as thin Plates and Bubbles exhibit different
Colours in different Thicknefles, (q the Parts of Natural Bo-
dies are obferved to undergo a Change of Colour in fome De-
jgree from Trituration, and a Comminution of their Parts,
Thus fome Powders which Painters ufe, by being elaborately
^and finely g^und, have their Colours a little changed. Thus
Mercury by feveral Chymical Operations has its Parts fo al-
• ter'd as to look Red in one Cafe, Yellow in another, and
White in a third. Thus Copper in the Mafs appears Red-
but having its Parts attenuated by Solution in acid Mediums
a]f)pears intenfely Blue. Hence the Production and Changes
of' Colours by the various JWlixture of traufparcnt Liquors.
'Thus Clouds receive their different compound and beautiful
Hues and Tints from the different Sizes of the aqueoas Glo-
bules of which they cohfift.
23. The Sizes of the Particles of Bodies, pn which their
Colours depend, arc indicated by thofe Colours : Thus the
leaft Particles of Light exhibit the Fiolet-Colour^ and the leaft
Thicknefs of the Plate of Air or Water exhibited the fame
Colour in the feveral Rings. Again : The largeft Particles of
Light exhibit a Red Colour ^ and Red is produced by Ref!e6lioi|
and Refra6lion in the thickell Part of the Plate in each Ring';
Arid the intermediate Colours, Blue, Green, Yellow, are pr<^-
duced' from Particles of a larger Size in Order.
• 24. The Magnitude of the Particles of coloured Bodies
may be pretty nearly conjeftur'dby the Colours they exhibit:
For 'tis pretty certain they exhibit the fame Colours with the
refracted
Of Light and CoLduR^'s* 205
i-efrafted in the Direftion HS, making- the An-
gle S Y A with the incident Ray A N, it will
paint on the Part H the feveral Colours of Light;
but in an .inverfe Order to the former, and more
faint, by reafon of the Rays loft by the ficoni
Flate of ^aal Thickncfs, provided tliey have die fame re^ • "
iradive Denficy i md iince their Parts feemi for the moft p^K
tp have much the fame Deniity with Water ot Glafi, as by
many Circumdances is obvious to collect, we need only have
Recoarfe to the Table or Scale (in Art, 47* 48, 49. of the
laft Amft^ation) by which the Thickneis of Water or Glafi
exhibiting the fame Colour is fhewn.
25-. Thus if it be defired to know the Diameter of a Cor-
pofcle; which being of equal Denfity with Glais fhall refled^
Green of the third Order ; then in the (aid Table you fee
under Glafs^ and oppofite to Green of that Order, the Nimi-
ber i6i, which (hews the Corpufde to be — -2E— Parts of
* I 000000
an Inch. But her^ the Difficulty is to know of what Order
the Colour of any Body is : But for this Purpose we may b^
aUxiled by viewing the Scheme of the feversd Orders of C6-
lours ; and by laying the parallel Ruler acrofs them (everally,
|rou will obferve thofe whidi atd leaft compounded with
others in every Order, and confeqnently are moft vivid and
intenfe.
26. Thus ScfirhtSy and other Udi^ OrangeSf and Telkws^
if they appear pure and intenfe^ you may conclude they are
of the Second Order. Good Greens ihay be ef the Fourth
Order, but the beil are of the Third. Bines a^ PurfUs may
be of the Second or Third Order, but the beft and leaft
compounded are of the Third. Whitenefs^ if moft ihtenfe and
lominous, is that of the Firft Order ; if leis ftrong and bright,
it is that arifes from the Mncture of the Colours of feveral
Orders.
27. The Reds therefore of Carmine, Cinnabar, Vermi««
Con, of fome Rofes, Pinks, Peonies, f5fr. are of the Second
Order. The Green of ^1 Vegetables is of the Third Order ;
Ultramarine is a Blue of the Third Order, Bife a Blue of the
Second Order, and the Azure Colour of the Sky feems to
be of the Firft Order. Goldf is a Yellow of the Second Or«
Att, The Whitenefs of Paper, Linen, Froth, Snow» Sil-
ver, &r. is of the Firft Order. Conoeming all which fee
Refieaion.
5o6 Of Light z?;^^ Colours.
RefieEtim. It has been found alfo, that the leaffe
Angle S G O, or GOP, under which the leaft
refrangible Rays can come to the Eye at O, after
two Refledlions and two Rcfraftions, is 50 Deg*
HK)fC in Sir Ifaac Newton* s Optics^ p. 230—237.
28. It has been obferved, (See Art. 41. of the laft Jrmoia-
tion) that Whifmefs arifcs from a promifcuoiis Rcfle6Uon of
all the Colours together ; and this is proved by feveral Expe-
riments. Thus the Colour of the Sun's Light is White in-
dining a h'ttle to Yellow, as being a Compofition of all the
different coloured Rays, among which the Yellow being the
brighteil: is mod predominant. Tims alfb the Rays when fe-
parated by a Prifm, if received by a broad convex Lens of a
large focal Diilaoce, will all be thrown together in a fmall
round Spot in the Focus, and appear of a white Colour.
Thus alfo a Powder compounded of Orpiment, Purple, Biftf
and Verdigreafe, in proper Proportion, appeared of a per-
fcdl Whitenefs in the Beams of the Sun.
29. But the moft curious Experiment for Proof of this is
. as follows. Xet any circular Area Be divided on its Periphc-
n. XLI. ^y into fuch Parts AB, BC, CD, DE, EF, FG, and GA,
J^^g« 4- as arc proportional to the Differences of the Lengths of the
Muiical Strings in an OAave, or the Numbers |, /j, |, |/
i» |» l» * 5 then (Iriking a Circle ahcdefg at a fmalj Diftancc
from the Pciiphery, the feveral Divifions of this Atmulm or
Ring are to be laid over with the primary Colours proper to
each, that is, Red from A to B, Orange from B to C, and
the reft in Order as they are wrote in the Figure. Then
making all the internal Space very black, let this Area with
its painted Ring be whirPd or fpun round in the manner of a
Top, and the Ring will appear very white, efpecially in thef
Sun-Beams : For in this Cafe aH the Colours are blended to-
gether in the View, and muft therefore exhibit Whitenefs.
30. On the other hand, Blacknefs the Abfence of all Co-
lours ; for it was obferved, that in the Middle or Center of
the Rings of Colours, both in the Plates of Air and Watery
there was a black Spot, which was occafion'd by a Tranfmif-
fion of all the Light in that Parr> and confequently by a to<<
tal Deficiency of Colour.
3 1 . But this happened in that Part of the Plate of Air^
and Water Bubble, where it was thinneft ; and hence we arc
taught that the Corpufdes of black Bodies are lefs than any
of \hfik which exhibit Coloim^ Hcnee wc fte the Reafon
.57 Mi^
r^
Of Light and Colours. . 207
57 Minutes-, and the Jeaft Angle HOP, under
which the moft refrangible Rays can come to the .
Eye in this Cafe, is 54 Deg. 7 Minutes. Whence
all the Colours of the exterior Bow .will be form'd
why Fire, and the more fubtil Dlflblter PutrefaAioriy by irt-
tenuating the Particles of Bodies turn them black . Why a
Razor, while fetcing, turns the Oil ypon the Hone black :
Why a fmall Quantity of a black Sub(bince will tinge fo great
a Quantity of any other fo intenfely : Why black Subftances
fooneft of all others do become hot in the Sun*9 Light and
burn : Why being foft, and ftroked hard with the Hand, they
fcintillate, or emit Sparks of Light in the dark : Why a
black Cloth will, if wet, dry fooner than a white one : Why
moft Blacks are a little inclined to a blueiih Colour : With
various other Phenomena of this Kind.
32. From what has been faid, the Newtonian Method of
compounding and decon;poimding Colours may be eafily on-
derflood, if we only firft premife, that the Colour refuhing
from a Mbcture of any primary Colours is an Eflfedt in whkh
each primary Colour has a Share in Proportion to it$ Quanti*
ty ; therefore this compound Colour is analo^bs to the Com"
mon Center cf Gravity between two Powers aSing againft each
other : For as this Center of Gravity will always be neareft
to the greateft Power, fo the Hue of the compound Colour
will always approach neareft the Complexion of that primary
Colour which was largeft in the Mixture.
33. Therefore to know what Colour willrefuk from a
Mixture of two Parts Yellow, and three Parts Blue ; from
the Middle of the Yellow Arch at H to the Middle of the
Blue at I draw the Line H I, and divide it into five equal
Parts, three of which fet from the Point H, pr two from the
Point I, will give the Point K, through which if you draw
the Line N L, it will point out the Colour of the Mixture at
L, which is Green ; but becaufe the Point L is ib much nearer
the Blue than the Yellow, it will be a blueiih Green.
34. Again : If it be required to know what Coloor the
Mature fhall be of that has two Parts Yellow, three of Blue,
and ^ve of Red ; then fmce we have already determined the
Point £ for the two firft Quantities, which are five Parts ; al-
fo fmce there are five Parts of Red, if we draw the Line M K,
and divide it into two equal Parts in P, and through P draw
the Line N O, this, as it falls upon the Orange, but near
, 9he Rcd^ fh^^s th^ QQmfOmi will b^ 0^ an Orange Colour
in
1
^b8 Of LiGH^ and Colours.
in the Drops from G to H, which is the Breadth
of this Bow, viz. 3 Degv ip Mihutes; whereas
the Breadth of the other, viz. E F, is but i Dcg.
45 Minutes, and the Diftance between the Bows^
inclining to Red; And tbiis 70a proceed in other Cafes.
35. Itinuftbe fardaer obferv^d, that the Colour will be
lefs or jnoi^t broken or imperfet^ as the Point, of Interfedion
K or P. falls nearer to or ^her from the Cirounferen^ to-
vrards the Center N, where White ,18 reprefeoted: Tluit is,^
the Euther the Point K is fituaced from 1 towards N; the lefs
pure and i^itenfe^ or the ^ore broken and mottley, the Green
Colour will be.
36. Hence^ if it be required to find (on the other hand)
what Colours .<n^ft. be taken, and in what Quantity, tQ exhi-.
, bit by their Mixture the bfoken blueifh Green at K, let the;
Line HI be any how. dra^rn through K* and it will fhew
that if you take fuch Quantities of Yellow and Blue as are
in Proportion to IK and K]L, they will when mixed produce
th6 given Green at K.. , Alfa the Line LN; pafling through
the fame Point K, fhews that. a Quantity of pure Green and
tVhite, in the^Proportion of N.K, LK, will in the Mixture
produce the fame Green Tint a( K.as required.
37. What .has been faid relates to Xheory,.and to.the Co^
lours of the Sun*s Light; and therefore .in ]Pra£lice we nufl:
not exped fo greaf. Accuracy pn feveral Af:copnts ; as, (i.) Be-
caufe the Powders made uf(b of in artificial Mixtures h&ve
different Powers of refieding Light : Thqs lighter Materials
refleA more, and darker ones kfs ; .and. therefore their Quaur
tides mufl.be in Projportion. (2.) Different Bodies, being
inix*d,. operate upon each other ;. and thereby, .either by at-
tenuating, the Pat-ts; of by incraflkting them» produce Cplours
quite different from what y/k mfghtexped front a.Mi^ure of
bodies or Particles which do. not affed or ad on^ upon anov
\ ^er. (3.) Becaufe all artific^d Colours ar^e ip themfdves
more or lefs compounded, and therefore cannot produce the
^ffeds of pure, unmixed, and primary Colours. Yet not-
withftanding thefe Exceptipns, this Theory, when w^U.conr
fider'd and underftood; will be of the grcat^ft Service to
Painters. ^> ,
38. LafUy, I fliali apply this llieory to explain and aci»
^ount for feveral other Pha&nomena of Colours, Thus in exr
amining Mineral Waters, it is ufual, in order to difcover wher
ther the Salts contained in them are of an Acid, Alcaline, ik
vi^.
6f i>iOHT and CoLouM. ;hq9
'^iz. FG, is 8 Deg. SS Minutes* And liidi
would be the Meafurcs of the BoWs, were the
Sun but a PoiM\ but fincc Kis Body fubtends ail
Angle of half a Degree, it is evident, by fd
keutral Sort; to ihut Syri^ of Violas with thbn ; bf duife then;
if there be an AciJ^ it will change the Syrap Red hy atte-
nuating its Parts ; fo that if the Syrup be a Purple of the
.Third Order, the Acid will cbfnge it to a Redpf the Second
Order, the Particles which rttLtS. that Colour being of ti^e
Size next lefs.
39 Again : If an AlcaR abofind in the Water, the Mix-
ture will turn Green ; for the Alcali by incraflating the Par-
ticles will increafe their Size to thofe of the Green of the
Third Order ; therefore the Syrup, and confcquently the Mix-
tore, will appear of that Coloiir. But if there be neither
kn Acid not an' Alcalt in the Water; It will neither turn Green
lior Red.
40. Hence klfo it is, that when even the l^ume or fubtit
Vapour of a flrong Acid, as Aquafortis, reaches a Greed
^lotb, it changes to a Blue, becaufe that in the fame Order
i-efuits.from the next lefs Size of Particles. ^.If the Acid be
droppM on thb Cloth in Jubilance, .it adls more violently iii
attenuating the Particles, and thereby produces a Yellow of
the next preceding Order, whofe Particles are lefs than the
kforefaid Blue. And after a like Manner may this Theorjf
be extended, to atcoiint for other Ph^enomena of the famd
Kind.
41. To conclude: Since any Obje£l becomes vifible whed
It fubtends an Atigld o^ ome MinJkte^ and alfo becaufe Obje^
Are difltn£lly viewed in the Focus of a Lens ; therefore fup-
{)ofing the Focus of a Lens were ^ of an Inch, (as they
have been made thus fmalij it will be Ibund by Calculation,
that an Ol)jc£l in the Fotus of fucH a Lens, fubtending a4
^ngle of one Minute; will be equal to 0,0000007 Parts of
sin Inch in Length. Therefore the Diameter or a Panicle
lefs than the Diameter of any coloured Particle (except thofe
of the Firfl Order} will be vifible in th^ Focus of fuch a Lens:
And therefore the Particles; of all coloured Bodies would be-
tome vifible by fuch a Lens, wefe it n6i that Partides equall]^
thick appear of the &ine Colour, and all fo very fmail are
tranfparenti whence, though th^y ar^ big enough to be vifi-
ble, yet we may want a Difference of Colour, and fome
ilther Means, to tender them diftind, and capable of b^ing
YoiiiH. . O ^ xtwcH
9Y0 0/ LiGrtT and' CotouKS.
much each Bow will :be increafed, and their Di-
ftance dimimftxM (CXXIII).
viewM rqparateiy frgm qach other. Sir I/aac Nekton thifti^
the Difcovery of thofe Corpufcles by the Microfcope will be
the utmoft Improvement of tnis Scieoce: For it feems im-
poffible to fee the more fecret and noble Works of Nature
within the Corpufcles, by reafon of their Tranfparency.
(CXXIII) I. Having cxplain'd the Do£trinc of the dif-
ferent Refrangibility of the Rays of Light, and the T^htwy
of CJ<mrs confequent thereupon, it will now be eafy to ex-
plain and underitand the natural Caufe of the Raintonv, which
is wholly owing to the al)ove-mention'd Property of Light.
For though it was, by long Obfervation, known to proceed
from the Sun's fhining upon the falling Drops of Rain ; and
even before Sir Jfaac Ne<wton'B Time it was difcovef 'd to be
the Effed of the Sun's Light feveral times refraded and re-
fle&ed in the aqueous Globules ; firft of all by Antonius de Do-
minis f Archbiftiop of Spaiato^ in a Book publilhM in the Year
i6ii, and after him by D ef cartes i Yet no one could ever
account for the Diverfity of Colours, and their inverfe Order
in the two Bows, or give a diredl Method of Calculation, be-
fore Sir tfaac Nenufon.
2, To afjprehend rfghtly the different Affeftions of this
remarkable Fhaenomenon, we muft attend to the following
Particulars. Firfi, That though each Bow be occafion'd by
the refrafied and refledled Light of the Sun falling on the
Drops of Rain, yet neither of them is produced by any Rays
falling on any Part of the Drop indifferently, but by thcMfe
Plate L. °^^y which fall on the Surface of the Drop BLQG in or
Fie 2. * *bout the Point N, as the Ray AN ; thofe which fall nearer
^* * to B, or farther towards L, being unconcern'd ia this Pr^
' duftion.
3. Secondly, The internal Bow is produced by two Refisf-
flions and one Refledlion. The firil Refradion is of the in^
cident Rays extremely near A N, by which they proceed from
N to one common Point or Focus at F, from whence they
are reffedted to G, and are there a fecond time rcfradled to-
wards R, and produce the various Colours of the faid Bow.
PI XLII ^' ^^^^^fy* There is a Neceffity that feveral Rays (hould
«.' J ' be refraded together to the Point F, that being refledted
** ' tpgether from thence to G they may there go out parallel,
and fo come in Quantity fufficicnt to excite the Senfation of
Halo's^
Of Light and Colours. tii
Halo's are form'd by Rays of Light coming
to the JEye after two Rcfraftions through Drops
Cblodrs . in a (bfong and lively Manner. Now thofe Rays^
add thple only* whi^h arfc. incident on the Globule about the
Point N, can do this, as will appear froni what follows : For,
5. Ffmtthlyy The Point F makes tlie Arch Qif a Maximum ^
Or the Difbnci* QF from the Axis of the Drop SQ^is greater
than any other Diilance froth whence any other Rays nearer
to the Axis» as S D, SS, or £uther from it, as Sk, SI, are
refieded ; btcaufe thofe which arjc nearer aifter the firft Re-
fraftion tend to Joints in :he Axis produced more remote
than. that td which the Ray SN tends; and therefore as their
Diiiance from the Axij^ increa^s, fo likewif^ will the Diflances
of their Points of Refledion QP, QO, till the Ray becomes
SNi after which the Rays more remote from the Axis, as
SH, Sly are refraded towards the Points XY, which are
nearer and nearer to the Axis ; and this^ occafions the Points
bf Reflexion on the farthed Side of the Drop to decreafe
again from F towards Q^
6. Fifthly^ Hence it will neceflarily happen, that fomc
Rays above and below the Ray SN will fall upon the fame
Point, as O or P,, on the fartheft Side ; and for that Reafota
|hey will be fo renewed from thence as to go out of the Dropi
by Refradion parallel to each other. Thus let SE below;
and S H above the Ray S N, be rcfrafted both to one Point O i
from hence they will be refleded to M and L^ and will there
emerge parallel, 'tis true, but alone ; being diyefted of their
intermediate Rays S N,^ which going to a different Point F
will be r^Heded in a different Direction to G, and emerge on
49ne Side, and not between thofe Rays, as when they were
incident on the Drop. All which is evideiit from the Figure.
7; Sixth^, As this will be the Cafe of all the Rays whicU
are not indefinitely near to SN, it is plain, that being de-
prived of the intermediate Riiys, their Denfity will be fo far
diminifhM, as to render them ineffedlual for exciting the Sen*
ration of Colours ; and they are therefore calPd Intjjkeicious
Rays, . ii> Contra- diflindtion. to thofe which enter the Drop
near S N^ and whieh, having the fame Point F of Refiedion,
are not fcatter'd like the others, but emerge together at G,
(9 as to conftitute a Beam GR ot the fame penfity with the
Incident Beam SN, and therefore capable of exhibiting a Vi-
>id Appiearance of Colours^ and for this Reafon are called
iiii Of LiGpT and Colours.^
of Rain, or fpberical Hail-jiones ; which Lifehc
. ought to be ftrongeft at the Diftance of about
^ 8. Thcfe Things premifed, we (h^U now fhew the Mathc-
inatical Principles on which the Cakuiandns relating to t\A
iPhaenomenon depend, according to Dr. HalleyH iftoft eiegatit
and eafy Conftrudions, a little explained and' facilitated hy
©r. Morgan y late Bilhop of Efy. -LetSN, /«, be two of
the efficacious Rays incident upoh a Drop Of Rain ; theA
when refrafied to, the fame Point F, and .thence, refle£kcd t^
G,^, will have the Parts withirt the Drop on 6ne Side, NF;
i»F, equal to thofe on the othc¥ Side, FO,^g^ from the Na*
lure of ^Ac Circle, and the Ai^lesof Incidence CFN, CF».
Tbeing equal to the Angles of Rcfle6iph CFG, CF^. Sincd
the Parts withm the Drop are equal and alike fitaated^ they
will alfo be fo with it ; and therefore as the incident Rayl
SN, Sn, are fuppofed parallel, the emergent R^ysGK, gr,
will be fo too.
PI. XLII. ' 5- From C the Center draw the Ridii CN, Cn, OF ; then
fig. 2. Is CNF = CFN the Angle of Refradion, and the (VnaA
Arch Nff is the nafcent Increment of the Angle of Incidence
%CN ; and as it meafnres the Angle at the Center NCdt, it
is double of the Angle at the Circumference NF^, which h
the nafcent Increment of the Angle of Refraction NF,C.
Fig. 3. 10. Again : . Let the Ray SN enter the lower Part of th*
Drop, and be twice refleded within the Drop at F and G ;
then is the Ray N F = the Ray FG, and the Arch NF =
to the Arch FG. ^ Drzw/g parallel to FG^ and it will be
the refkdled Part of ibme Ray sn, whofe Obliquity to the
Drop is fuch as obliges it to crofs the Ray NF in its Re»
frad^ion, as it mull do if it be a little more oblique than SN,
(by Jrt, 6.) Then alfo will the Part nfz=:/g, and the Ardh
7f/z=/g, and the fmall Arch F/=: Gg, *
' II. Therefore, 2F/=i (F/4-G^=rthe Arfch FG —
the Arch/^ = the Arch N F — the Aith »/=] N «— Ffi
confcqucnt!y'N» = 3 F/. That 'is, the nafcent Increment
of the Angle of Incidence is equal to three times that of the
'Angle of Refraftion. After a like Mannfer you proceed t<>
"ihew, that after 3, 4, s,'^e^ Reflexions, the Increment of
the Angle of Incidence will be 4, 5, 6, (^c, times greatur
than that of rhe Angle of Refra£lion.
12. Hence, in order to find the Angle of Inddenoe of an
efficacious Ray, after any given -l^nmber of Refledions, we
'are to find an Angle whofe mScvnt Increment has the fam^
Ratio to the Increment of iu coxrefpondini^ Angle of &d-
Of LipnT'xind CoLouFts*!^ zi^
^6 Degree? from the Sun or Moon, or fom^what
lefs, if the iaid Hailftones be a little flatted, as
fra£Hon,* generated in the fame Time, as the eivcn Number
of Re&e&iortr (ff| in^aCtd 4>)r Unky lias tx> Unity ; that is^
in the Ratio of « 4" ^ ^ ^ * ^^^ ^^^ Incremenu are ^'
the Tangents of the refpedive Angles dire^Uy j as is thus de-^
montlrated.
13. Let A C D, A B D, be the Andes of Inciden(;eattd Re- PI. XLH.
fiadion propofed ; and if we fuppote the Line AC to move. Fig. 4.
about the Point A in the Plane, of thofe Angles, the Extre-.
mity rhereqf C will deicrlbe the circnlar Arch Cc ; and when
AC i$ arrived to the Situation Ao the Line BD will be there-,
by^iemoved into the Situation BJ, DrawcD; then^is the
Angle ACD = ABC+CAB, and the Angle AWzr;
AB^+rAB. Wherefore the Exeefs of Af^ above ACD;
or the Jncrement of ACD^ is eqiv^I to both the Angles CBf.
atidCAc. But fince the Angle ArC differs infinitely little
irom a Right one, a Circle deicribed on the Diameter AC
ihall pafs through the Points D and c ; and tlzerefore the An*
fles CAr, CDr, (infilling on the fame Arch.Cr of the faid
^ird^) will be equal. WherSforc the Increment of the An-
gle ACD is equal toCBr'+CD<- = Dri/. Butthenafcent
Angles DcJ and OBc areas their Sines, that is, as their op-
pofite Sides BD and Dr = DC, becaufe of ifie Angle CDir
ipftiitely^fraall. But BD : CD :: DE : DA (the Line BE
beingparallel to AC) .:: Tangent of the Angle (EBD=:)
ACD : Tangent of the Angl<? ABD. Ttoefore the In-
crement Dr^of the Angle ACD is to the Inciement CBr
pf the Angle ABD (generated in the fame Timel as the
Tangent of the former to the Tangent of the latter diredlly.
14. Hence, taving given the Ratio of the Sine of Inci- Fig. 5.
dence I to the Sine of Refradlion R, we may fmd the Angles
of Incidence and Refradlion of an efficadoos Ray, aft^ any
given Number {n] of Refledions, thus : In any Right LiAf
AC, let there be taken AC : AD :: I : R; and ^;ain, AC:
AE iin-^-i : |. Upqn the Di^uneter EC defcribe the S^-
n^icirde EBC; and on tl^e Center A with the Radius AP
.defcribe the Arch DB, interfering the Circle in B. Draw
. AB and BC I then let fall the Perpendicular AF on CBl con-
tinued out to F. So fhall ABF a^4 ACF be the Angles of
Incidence and. Refradion required.
/ 15. For drawing BE parallel tjo AF, the Triangles ACF
^and £CB are fimilar. Now the Sine of the Angle ABC or
^B^ is to th^ Sin? of ACB as AC to A B == A D^ that is, ^
O 3 pft^n
2i4 0/ Light and Col6vks\
qften they are. Thefe Halo's^ if the Hajl be
duly figured, wilj be cpIourM, and rnuft then ap-
as I to ]^ ; therefore if ABF be the Angle of Incidence,
A C F will be the ^"8^^ °^ Refrad!ion. Moreover, the
llalcent Increment of ABF is to that pf ACB (generated iri
. . fhe fame Time) as CF to BF, (b]^ Art. 13 ) that is, as CA.
• • toAE, (by fimilar Triangles) that'i$> asw-f-^ ^^ ' byCon-
- ftruftfon.' The Ratio therefore of ' the nafcent Increment of
the Angle of Incidence ABF,- to that of the Angle pfjRe-
fraftion ACB, is that which is reqnirecj in the Angles pf In-
cidence tind'Rcfra^libn of ^n efficacious Ray, after a givefi
Number of Refie6^ions, (In^r/. 12.) Conlcquently the An-
gles ABF and ACF are thofe required. J^ £. p.
' 1 6. From this Conftruftion we eaiily deduce Sir Ifaa^ Ntw.-
ten*s Rule for finding the Angle of Incidence ABF in /. 148,
149. of his Oftits^ thus. \Ve had AC : AB :: I : R, whence
AC == ^ :k AB- Alio C F : BF i: j?+ I : ^ therefore CF
;=«4.i X BF, or ( putting « -f. 1 =»i) CF = «y BF|
and becaufe of the Right Angle at. f^, it is AC* — CF* r=:
AB*— BF», thatis,i4*AB^ — w*FB*=:AB*— BF?|
ind therefore m^ FB* — FB* == il A ^* — A B*^ i and
' , FB > II — RR
, confcquently-^=: 1/-
AB i«*RR — R"
1 7. Hence, becaufe in the firft Jpw the Ray emerges aftty
one Reflexion, we have nzizi^m ~ 2, «* == 4, ;w* — 1= J ;
therefore v^aRR : t^lI-r-Rft v AB : BF :: Radius : Cq-
Sine of the Angle of Incidence. In the fecond Bow, wher^
there are two Reflexion?, ;f«*-r- 1 =r 8; whence ^ 8RR :
Vll — RR : AB : BF. In the third Sow, after three Rg.-
fleaions, w* — 1 5= 15 ; and ^ 1 5 RR : l/'Il — RR :
. AB : BF ; and fo on fpr any ^iven Number of Reflexions.
18. To find the Values of I and R, it niuft be remerober'd,
that the Ratio of the Sipes of Incidence anci Refradipn was'
Ihewn to be conftant, (in Jnnot. CXVII. 13.) and therefore
their Excefies in divers Sorts of Mediums are alfo in a given
. ilatio. Thus it was fhewn, that in the leaft refrangible Rays
I : R :: 50 : 77, out of Glafs into Air ; the Excefs of R abo^
i is here 27. If the RefrafUon be m^de out of Rain- Water
pear
Of Lk3ht and Colours* 215
pear red within by the leaft refrangible Rajrs, and
blue without by the moft refrangible ones.
Into Air, then it is I : R :: 3 : 4 very nearly for the leaft re*
frangible Rays ; the Excefs here is 4 — 3 = 1. Wherefore
fay. As 1 : 27 :: 3 : 81 e: 4 : 108. Whenoe it appears, that
the Sines Tand R out of Water into Air are as 81 to 108, in
the leaft refmngible Rays : And' if to the lefter Sine you add
the giVen Differences between thoie Sines out of Glafs IntQ
Air for all the othet Sorts of Rays, ^i«. 27I, 27^, 274, 27^,
2^7f, 27!^, 28; we fiiail hav« the ieveral Values of R fot.
thdisRays, «OT%. 4084, io8j, io8§^, 10^, io8|, lo&J, 109.'
'19. But iince the Refra6\ion here is not out of Water into
Ah*, but the contrary, we (ball have the Values of I and- R.
interchanged ; or they will ftand for the feveral Sorts of Rayf;
1^5 below. . :
9^t the Red, I : R :: ic8 : 81 Extreme.
For the Orange, I:R::io8|:8i Beginning. . .
For the Yellpw, I : R :: io8f : 81 Beg.
For the Green, I : R :: 1084 : 8 1 jBeg.
For the Blue, I : R :: io8i : %\ Beg.
For the Indigo, I : R :: .1 o8f : 8 1 Beg.
For the Violet,, I:R:: io4:8i Beg.
For Violet, I : R :; 109 : 81 Extreme,
20. Wherefore in the leaft refrangible Rayj, j^nce I r=: 1 08,
11=116641 alfoR=:gi,andRR = 6s6i,andI* — R*
==5103} 1/3 RR zs; 140,3, and V'X^ — R*.= 71,4;
Therefore (ay^ (^y Art, 17)
As i/3'RR g= 140,3 = 2.14704J
Is to . l/FZnF= 7'.4 = i.8539'3
So is Radi^s. == 90"" 00^ = 10,000000
22. Hence the Angle of Ipcidence ABF is 59^ 23', 19
jhe Red or leaft refrangible Rays. Wherefore in the Drop
pf Rain whofe Axis is SQ^ if we make the Arch BN =±
59° 23', we ftis^l have SN the leaft refrangible Ray. Ha-
ving ^iven. the Angle of Incidence, and the Ratio of I to R,
we have alfo given' the Angle qf &efradUon : Fof fay,
'As *^ I =: 108 z=: 2,033424
♦Is to R=: 81 = 1,9084^5
So is the Sine of Incident 59** 23' = 9,934798
To the Sine of the Angle of Ref. 40** 12' =9.809859
O 4 Thb
2^6: Of LiGur ami Colour^.^
The Reafon why thete is^way^a detvitnirraie '
^ngle for exhibiting the Bows^ or HaU*s^ i» be-
PJ. XLJI. «?. Therefore, soaking the Angje CNF = 4<^'* l*^ N?
JFig. 6. will be the refra£lcd Ray ; which At F is rcfie^ed into FG,
and at G emerges in GR. Produce the inciklellt ^d ^met-x
gent Rajs SN and RG till they imerfe^ each other at X|
and as CF bifeds tb^ Angle NFG, &y ^hen pfpdocod it will,
bjfea the Angle SXR. Then GFN =;? CXN + FNX^
butFNX=:CNX — CNForCFN; tbcr^fbreCFWrs
CXN + gNX\:- CFNi that is,. :?CFN — CN,X =3:
CXN; Pr 8o" 2j^f—^(f 25'=2i**o.i';xCXN; there*
fot^c 2CiN2=SXR==42'* 02', which '}$ the Meftfure oi
lih^An^e tb^t the incKipnt ^ind emergent R^iy^, whicb ani.
the leait refrangible, 'co|itain with each other. . • • ' ^
23. If inlteid of the Ratio loBto 8i» we taltethatof
109 to 3i, wcfJiaJl find the Values <Jf \^jK9i arid i/l^-i-R*
fuch as will givfe the Angle of Incidence BCN, 0* thcf'Arch
BN =: 58** 40'; ^nd the Artgle 8XR i=.4C* 17^ which will
%t the Cafe for the moll refrtingil^e, or exti'enic Violift Rays.
' 24. If the Ray be twice rejle{\ed, «r^«. at F abd G, as
in the Prodn^on bf the exterior Bow.-'dnd 'eiy^rgeis'at H(
in thie Dirtttfon HA interftfting the? incident Rjiy SNin Y j
ilytri lyre bay ind the Angle AYS, which thofe Rays coftfeiri
\vith ^aA othei*, - thus. Produce A H, ' till it meets G Of- pri)Z
djwn^ in R ; t]»€n In'th^ Triapgle HGR, the extemml jVid«
HGX=:HRG + GHR. But. becaafe of eqtiri Angles of
Refleaioq at .F ?nd G, it is GjiRrzrFGX; therefore
HGX — FG"Xi±H'GFi=:HRG=:2CGF or 2CNF.
fetKi <In •^/^.' ?2^.) we --had '6XR =z:> CN F — ? CNX j
therefore ih the Triah^c-Y XR we have the t«^o ifcterhal An-
gles R 4- X = 6 CN F — 2 CN X =: the external Angl^ z%
. 2^5. lii thii Cafe to find the Angled of Incidence and Re-
fedlion, we*have yf S RR : V^i^— ;** :; Railius ': the; Co-
pine of the Angle of Incidence ; whence' the fyj^ Angle oif
Incidence * win be found 71*^ 56'==: Ct^^X.. . Arid ^s 108 \
8j ;: Sine of 71^** '56' : Sine of 45^ 27^'== CNFjRc.Angte
of Refraction ; therefor^ 45° 27^x 6 — 2 x 7jit**. 50^ =;;
j-29° 02^ =1 A Y N, and therefore its Coipplement A Y S iiS
.50® 53' the Angle Required, for the le^ft i'efrangible R|iyf. '
26. But for the raoft refi angibl^ ^^)[K where I '• R :: ij^<) :
Bi^ we have the Angle of Incidence 71** 26', and the Angle of
Rrfraai^ 44° 47' i and tliei«fbre the Angle AY S'=?-54«iio';
^- ■ ' •• ' ••'■•• ■•■ ■'•• ■• »*^ ■ "'■" ■ ^
1
\
%
\
Of Light and Ck>LouR3.? 2iy
caufe theit is but one particalar Point N in al)
After this Mannqr yod proceed to cakdlate tbe ftme Anglei
after three, four^ orniore ReftedicMis i bat beeanle the Beani
jin being ib olten refledUd lofes fo inaiiy of its Riyi, that tho
remah&g refra^ledPart is in general too fiiint to excite the
Uea of Coioun, we p^fi it by, and proceed to apply what
hu been .faid to account ibr the Pb^tnofketm of the fiows,.
which fo ftrongly ftiiloB tke £ye s the principal whereof hero'
fbliow;
427. ThcF/V/?i«, Tb^ iatb it ^HUifgitteJ^tb ail tbe Pri/*
matic Oioi^s. This is a aeccffiiry -Cdnfeciaenpe of the dif.
ferent Refrangibility of the Rays reffa£(cMi and r^titGted iir
Drops of failing Rain. Let A be^ fuch a Drop, SN> a Ray
entering it at N, which is refrsM^d to F, ftbm thenee re-
flected to G, where, as it emcrgef; it is re^aded into aif
theieveral Sorts of Rays of which it* is compofed, nne. GR
the leaft refrangible or RiJmakiHg M^y^ GO tbe Of-attn,
GY th^ re/Uw, GG the Gr^n, G^'^eSbe^ 0t the In-
£g9,' and GV the FioUt or nioft refrangible Ray.
ad. Now we have (hew& {Art, 22, 23.) that the Angle
SFR is to the Angle SF V as 42* 02' to 40" 17^- the Dif-
feence-iH^hcredf is the Angle VGR sr i* 45'. Through PI.XLIII.
this Angle all the original Rays are diffiifed ; and thoogh ^e Fig. i.
Anglete fmall, yet at a great Diftaifce k fpreads fo a confi-
derable Width ; and therefore by coming from the Drop A
to rhe^Eye.of a Spe6buor at A, ^y will be fufiiciently fe-
parated, and fall upon the Eye finffy, each Sort of Rays by
thctnielves alone.
29. Hence, were there only one Drop Ay the Eye at A
woald fee only one Colour in. that Drop, 'vix, the ReJ^ by
^ leaft refrangible Ray GK^ the others, G O, G Y, ^c, be-
ing refracted above it, as is tevidem e!lx)ugh in the Figure.
if now we fuppofe this Drop to deicend fo the Situation S^
theh womld the Orange'makmg Ray GO^ftfll upon the Eye
continuing in A, and then the Drop would exhibit an Orange
Colour, if after this it ihould fink down to C, the Yellow-
inakia^Ray G Y would enter the Bye at A, and excite thelde^
of Yellow in the Drop at G. And fo continually, if we fup-
pofe the Drop tofucceed to tbe feveral Situations D, E^ F^ G,
the o^her more refrangible Raya GG^ G6, CF, GV, will
&11 upon the Eye fucce^ively, and raife the Senfation of their
-propefCeloursy Green, Blae* Indigo* and Violet when the
;Pr0p n^G, . ' .
' 30. The Tffqth of. t^iis nu^j be eafily piored by Expeiv
the
ai8 0/ LiguV ^«/ Colours)
the Part of the Drop between :B and L, where
mektf* 'ty fyfytaimg a Gbfs Globe BVd with Water in tlio
Sonihin^, aqd viewing it is &cB; a Pofition that the ^ys SN
which f^l.upoD it ipay cmei^e to. the Eye at A^ linder the
feveral Angles from SFKito SF V; winch may be eafiiy efi-
fe^M ty letting th^ Glebe defcetid from ^ to G by a &tnng
going over a Pal)ey. And this iwas the famous Expenmeiic
of j4^Uf0us de DonfintP and /)// Caries^ who by this means
confirmed the Truth of their Dodrine of the Rainbow, which
had been d^moodra^ flwtlh^matically. The .Tame Thing
may be aUb ihewn, if .tbe Globe, be at Reft at 2^, and the-
£ye;^be raifcd from R to.V. : \ . . .
57 . If now, inftead of depcteffing the Drop from ^ to G,
we^ fuppofe a Drop placed in cach.Point J, B, C, 2>, £, F, G ;
^en tljefe^^ill feverallvfi»nd an original Ray to the Eye, ac-
cording to their Si|oacioq9 in refpeA of itl Thosthe Drop
in ]^ wiii^rad theRjAd-makingRay^GR; the Drop B will
refra<5l th^ Orange G0i; thp Drop C the YellowGy s and
fo the other Drop9iZ>, £yj^ G, .»vUl by the Rays Gg. Gb,
Gif, Gv, excite the i^ral Co^rs, Green, Blue, indigo,
Violet,, .all at the fame Time ; and therefore . all that Part of
the Rain from ^ to ^ wiU appear varioufly colour'dy as is re^
prefentedAn the Schenfeij •. ^
31. Now let SP.baa.Ling drawn through, the Spe£btor\
Eye at A, parallel to the Sgii'sifi^ys Sil^, ard conceive thb
feveral Rays Gjl tUroinff about the Line A P as an Axis^.and
always nnder> thp ftme invariable Angle GKP.; 'tis evident,
the Extremity of each Ray wou!d in the Cloud or Rain dcf
fcribe aCirde whicjk^ 'would be* tlie Safe of a Cone whofe
Axis is^VP,. and its V.ertec A ;, ^nd for the fanie Reafon that
the Drop ^ excites the Scn&tion.of ;Red, every Drop in the
Circle defcrib^d b^ (he>£xtremity of the Ray GK will excite
the fame Senjpitioii ; thus will a. red circular Arch JH be
^orm'd asi far 1^ the Rain extends. Next to that the Ray BA;
by revolving^ defcribes the ^rch of an Orange Colour, as
Bli the R^y CA wiU jn like -^manner trace out the Yellow
Circumference, ^ CKt aad fatQf '^U t^ reft, as reprffent^
in the Figure, ^ Y
3^. HQVice the Secett^ P^aenominffn^ *vix, the cireular Form.,
TTT " accounted for ;. gnd gjfo iheTJdJrd, which is Mr Breadth 9/
flXLUi' ^^^ ^^^ . £qj. jJj^j ^m be.c;qtial to the Angle JAG =
Fig' 2. KGV = 1° 45^ wjiere the Ray ^^s, here, emerges after o;a^
Refieflion. Thefe Particulars are reprefented more com-
pleatly in; the Ji^r#' ty^ere'BGD is the red Circumference
the
Of Light and CoLouRSr 2:19
theRayis AN can enter, fo that •after a fecond
formM by t)ie Rotation of the Ray AG, that can firH come
to the Eye at A } and C^E is the Violet Arch form'd by the
leaft refrangible Ray ^A; after wl^ich the Rays are all re-
frafled below the Eye. And thus by Hxe intermediate Ray^
and Colours the whole interior Bow is piodac^.
33. The Fourth Phenomenon is the appearance of Ttvo
Bows. This follows from hence, that after an efficacious
Ray of Light SN, entering a Drop of Rain, has been twice
4-cfle^ed on the fartheft Side at F and H, it will emerge re-
fracted into all its fimple or conflituent Rays at G upon the
upper Side of the Drop, fo as to make with the incident R^y
the Angle GYN or SY^ = 54** lo', if that Ray be the
Violet Sort, or ipoft ^-pfrangible, (by 4rt^ 26.) but if it be
of th^ red or Ipaft refrangible Sort, then the faid Angle is
but 50**. 58' = Sj^ A, (by /frt.z^.)
34. Therefore all thofe Drops which are fo fituated arornid
the Eye, that t}ieir moft refrangible Rays (hall fall upon it,
mull with thofe Rays make an Angle with the Line AP pafling
|:hrough the Eye parallel to the Sun's Rays, ^vix. the Angle
GAP, equal to the Anele SYA, or GAP = 54"* 10'.
Thefe Rays the^-efpre will every where exhibit a Violet Co-
Ip^ir in the Arch PGL. For the fanie Reafon thofe Drops
^hoie leaft refrangible Rays fall upon the Eye at A, make th^
Angle ^AP == 50° 58'; and fo the Ray A^, revolving a-
bout the Axis AQ^, will dcfcribe the circqlar Arch M^K^
which wi|l exhibit the deeped Red ; and ^U the Drops be-
tween G ^nd g will paint the feveral otjier colqur'd Periphe-
|-ips, all which together will coinpleat the exterior Bow.
35. T|\e Fifth Pb^nomtm^ is the greater Bxeadth of the ex*
terior Bow, Thus, if. from 54*" 10^ we fubduft 50** 58', we
(hall have 3** 12' = G^ = the Width of the outer Bow;
which therefore is almoft twice as y^ide as the interior Bow.
36. The Sixth Phanopienon is the t)iftance bet<ween the tnu^
fonvs^ which is thus determined ; From the Angle which the
leaft refrangible Ray in the upper Bow makes with the Axis
y^P, «v/«. 50® 58^ fabftrad the Angle 42° 02' which the moft
refrangible Rays make (herewith in the lower Bow, and the
Rem^'udcr 8"* 56' z= ^ AF is the Arch of Diftance betweeii
the Bows.
37. The Seventh Phanomenon is the iwerfe Order of the
Colours in the two Bows This follows from the contrary
|*arts of the ' rop on which the Ray is incident, and from
^hence it epi^rges and is refracted. Thus becaufb the Rays
Rcfradlion
3(20: Of Lioii> and CowIjrs^^
JUfrad^iop at F for H^ii?V, .of Rc^cftipn qt F.
SN enter the upper Pact of the Drop and emerge from, the
lower, 'tis evident the Rays refracted in this Cafe (<i;f». in the
interior Bow) will have a Situation quite the reverie of thofc.
which enter on the lower Part of the Drop^ find are refraded
from the upper, as in the exterior Bow, whofe Colours are'
VioUty Indigo, Bluf, Green, Tellow, Orange, and Redi whilft*
thofe of the other are Red, Orangey Yelltyw^ Gnen, Blue, Iht
Sgo, and Fioht i counting from the upper Parts downward^
in both.
}8. The Eighth Phtenomenon is the Faintnefs pf the exUriot
$o*w in Cotnfarifon of the interior one. This is the Confequence
pf the Rays being twice reflecled, within the* Drops vyhicl\
form the oqtey Bow. . They who make the Experiment in a
dark Chamber may wonder when they obferve how ikrge a
Part of the Beam (that enters the Globule at N) goes Out at
p, that there- fhould be enough in the remaining Par^ FG td
exhibit the Colours fo ftrong and vivid in the ,firft Bow as they
appear ; but then confidering how much of this refidual Ray
is refrafted at G, 'tis rather a Wonder how the very fmall
Part refledled to H fhould there when refradled be in (^antity
fufficient to excite any diflinft Ideas of Colours at all.
39. The Kintb Fbammcnon is, that fometimes more than tnv^
*^onx}s appear | as in a very black Cloud I have my felf ob-
fcrvedyt^r, and a faint Appearance of 2i fifth: But this hap-
pens rarely. Now thefe fpurious Bows, as I may call them,
cannot be fprm'd in the Manner as the two principal Bowt
are, that is, by RefraSiQn after a thitd^feurthy fiflh, &c. Re^
'feSHon\ for the Beam is by much too weak to exhibit Co-
Jours by Rcfradion, even after the third RefleAion only^
inuch lefs would it after a fiurth or fifth, Befides, though
after a third and fourth Reiledlion of the Rays they (hould
te fuppofed capable 0/ fhewing their Colours, yet the Bows
made thereby woi\ld not appear at the fame Time with the
othectwo, nor in the fame Part of the Heavens, buC in the
Rain betwegi us and the Sun, and mad be viewed by the
Spectator's Face ti^rn'd towards the Sun, and not from it, as
jn the other Cafe. .
40, To account for the Appearance of thefe coIourM.
'Rings within the interior primary Bow, we (hall here tran-
.fcribe what the learned Dr. Pemberton has wrote upon the
Subjedl. He obferves, that Sir Ifaac Nekton take's notioe^
,that in Glafs which is polifti'd and quickfilver*d there is an ir-
regular Refraction made, whereby fome iffoXL Quantity of
aiwj
•O/" Light avd CoLovKi, zzt
and Q for the ^owsj there can enough ga out to-
' Light 19 fcateer*d from the principal refleOed Beam. If we
'allow the fame Thing to happen in the Reflexion by whkh
the Rainbow is caafed, it feems fuffident to produoe the Ap-
pearance now mentioned*
41. Let AB reprefent a Globale of Water, B the Point
from whence the Rays of any determinate Species beiog re-
- flexed ^o C, and afterwards emerging in Che Line C D, would
proceed to the £ye, and caufe the Appearance of that Co-
lour ki the Bow which appertains to this Species. Here fup-
poCe^ that befides what is refleded regv^i4y-, fbme faiaUPart
of the Light is irrcgularfy fcatter'd every Way ; ib thatfioai PI.XLIV*
the Point B^ beiides the Rays that are regolarly reflected hota ^L i,
B to C^ fbme fcatter^d Rays will /etoni in edier Lines, as ki
BE, BF, BG, BH; on each Side of the Line BC.
42. Now it has been obferved, {Jmtoiat. CXXI.) that the
Rays of Light in thek PaiTage from one > Superficies to ano-
ther, in any refracting Body, undergo -alternate Fits of iofy
^ran/mifftonand Rijb^iotty facceeding each other at equal In-
tervals^ infomuch that if they readh the faitber Saper£d^
in one of thofe Fits, they (hall be tnmfmitced s if in tbe
other, they Ihall be refleded back. Whence the Rays that
proceed from B to C, and emerge in the Line CD, being in
a Fit of eafy TranfmiJUtti the fcatter'd Rays that £dl at a
fmall Diilahce without thefe on either Side (fuppofe the Rays
BE and BG) (hall fall on the Surface in a Fit of ea^ Refits ...
JStitm^ and fo will not emerge ; but the Rays next to thefe,
n)i%. BF and BH, (hall arrive at F and H in a Fit of 4afy
'Tranfmiffion, and fo be refraded in the Rays FI and HK»
43. Now thefe Rays will emerge, fo as to contain a lefs
Angle with the incident Beam SN than the Ray C D, which
was (hewn to make the greateft Angle therewith of all others
whatfoever: (See j^rt. 5, 22, 23.) The Colours therefore
which they exhibit muft appear within thofe of the primary
Bow. And ii we fuppofe other fcatter'd Rays without thefe
to emerge {having the intermediate Rays intercepted by Re-
fiedUon) they will contam Angles flill lefs with the incident
Ray SN, ahd will therefore form coloured Arches flill within
the former: And this may be conceived for divers Saccei£ons.
44. Now as the fcatterM Rays by various Refl^£tiom and
RtJraSions form Arches varioufly mixM together, fome of
thefe made by the lighter Colours may be loft in the inferior
Part of the primary Bow, and may contribute to the red
Tinware which the Purple. of that 3aw ufually has. . Tkef
*^ -^ gether
222 0/ Light £?W CoLbuRi. \
gcther at G or H, to form a llrong and di(Hn^
darker Colours of thofe refra^ed fcatter'd Rayi ^rm the
Arches which reach below the Bow, and are feen diftinfi | qt
which the iirft has a /igJbf Greeni dark Green, and Purple ; the
fecond has a Gr^f« and Pttrp/e ; the third a /^/x/ Gr^^iv and
nfanifiing Purple,
45. The Diftances between the Bow and thefe fecondary^
Arches depend on the Size of the Drops ; to make them in
- any degree feparate, 'tis requisite the Drops ihould be exceed-
ing fmall. It is therefor^ moil likel/i that they are formed
in the Vapour of the Cloud, which the Air, being agitated
by the Rain, may carry down with the larger Drops ; and
this may be the Reafon why they never appear but und^r the
upper Part of the Bow only, this Vapour not defcendiqg very-
low. As a Confirmation of this, thefe Arches are (een
firongeft when the Rain falls from very black Clouds, which
caufe the fierceft Rains, and therefore produce the greatefl
Agitation of Air. Thus far Dr. Pemherton.
j^6. But to return: The Tenth Pbtemmenm is, the ^-
fear once of the Bows in that Part of the Hea*vens opfofite to
the Sun* This necei&riiy happens from the incident and e-
inergent Ray being both on one Side of the Drop, for 'tis
evident, that in order to fee the Colours, we xxiull look to
that Part againfi: which the Sun fliines.
47. The Eleventh Phenomenon is, that they never afpeat^
hut nvhen anywhere it rains. This is becaufe Rain affords sL
fufficient Plenty of Drops, or aqueous Spherules, proper to^
Tefle£t and refradt the Light fit for this Purpofe, which can-
not be done without a reqaifite Size, Figure, and Difpofitioif
of the Particles, which the Vapour of the Cloud does not ad-
mit, and therefore Clouds alone exhibit no fuch Appearance.
48. The Twelfth Phenomenon is, the Dimenfion of tke
Bows, This is determined eafily^ for continuing the Axis
Pl.XLIII. A P to Qjthe Centre of the Bows, we have the Semidkmeter
Fig. 2. of each Bow in the Angle QJigt or QAG ; the double of
which gives the Angles which the whole Diameters of the Bows
fubtend, and are therefore the Meafure of their Magnitude.
49. The Thirteenth Phttnomenon is, the Altitude of the Bo<tv
aho*ve the Horizon, or Surface of the Earth, This is equal tO
the Angle GAT, which may be taken by a Quadrant, or it
may be known for any Time by having given the Sun's Al-
titude, which is equal to the Angle T A Q; which theiefote
fubdufted from the conflant Angles QAF, orQ^AY, will
always leave th« Angle of the apparent Height of the Bow/
Imag0'
0/* Light »W Colours. 223
Image of the Sun -, which Rays, therefore, en-
50. Hence it foUowSy that when the San b in the HorizoOy
the Lines Q^ and T A will coincide« and therefore the Points
Qjmd T ; whence, in this Cafe, the Bows will appear com-
pleat Semicitcles ; as on the other hand, when the Altitude
of the Sun is equal to the Angl^ Q3F=:42* 02', or to
QJi y=: ^4** 10', the Summits of the Bows will be dc-
preis*d below the Horizon, and therefore within a certain la*
terval in many Days, in Summer-Time, no Rainbow can ap-
pear.
51. We have hitherto eonfidcr'd the Bows, and given their
Dimenfidns, fuch as they would have* were the Sun bat a
Point ; but becaufe the Sun fubtends an Angle of half a De-
gree, or 30 Minutes at a Mean, therefore the Breadths of the
Bows will be increafed, and their Diftance decreafed by half
a Degree, and fo the Breadth of the interior Bow will be
2° 15^ and that of the exterior one 3"" 42'^ and their Di-
ftance 8° 26^; alfo the greateft Semidiameter of the interior
Bow 42^ 1 7^, and the lead of the exterior Bow 50'' 43^.
52. For let SPA be the Angle of any one particular co- PL XLIL
lour'd Ray coming from the Centre of the San^ and refledcd Fig. 7.
from the Drop to the at Eye A. In the Ray S F take any Point
S at Plealure, and make the Angles F S N, F S M, each equal
to 1 5^ as alio the Angles F AM, and F A N ; then will S N
be Fart of a Ray n N coming from the lower Limb of the
Sun^ SM a Part of a Ray ^M coming from the upper Limb;
and fo the whole Angle NSM=:fflS/i^ 30', the Sun's ap-
parent Magnitude.
53. Join SA ; and (ince the Sums of the Angles at the
Safe S A of the feveral Triangles ASN, ASF, ASM, are
equal among themfelves, their vertical Angles at N, F. Mp
are alfo equal to each other. Wherefore the Angle S M A
will be that whkh the emergent Ray makes with the incident
Rays S M of the fame Colour, as before, coming from the
higheft Point m of the Sun^ and S N A of that which comes
from the loweft Point of the Sun n. Therefore, if all the
Rays of the Sun were of one Sort^ the apparent Breadth of
the Bow, meafured by the Angle MAN, would be but 30'
or half.a Degree.
54. But fmce the Rays of the Sun are diiferently refrangi-
ble^ conceive the Drop F to be placed any where in the in-
ward or outward Verges of the Bows (above defcribed) and
then it is manifeil that the Angle F A M muft be added to
the Infide, and FAN to theOutfideofthe Angles, which
tering
?224 O/' Light a^d Col^xjks.
tcring ac the Point N, are caird Efficmws Ra^i;
, jlkt Breadths of th()fe BoWs fubteiid it A ^ to db^ .their api
. Jmrent Breadths; which therefore will be focih as are defined
in Jrtie/e $ i .
55. I deiigiiM here to have added Dr. Hai/^'i Method of
dKcoveriog the Ratio of the Sine of Incidence to that of Re-
fradion, 1^ having given the Angle which an effieaciofis Ray,
as SNy contains Moth its emergent Part GA; but as this
■ Angle ie detennined only by Experiment, and the Caleula.
tion brings as to a Cubic Eqoatton, I think It a Matter of tod
mach Intricacy to trouble the Reader with in this Place,
. «fpeciaUy as it if (6 eafy to determine the refra£iive Power of
aoy tnnfparent Bodies, by the experimental Methods before
ileUver'd. {See Jnmt0t. CXVII.)
56. i have often taken Notice (with Mr. Whifton) of the
Silence of Authors cOQcenui^ the Reafoo why the Iris, or
rather a ftrong and deeply cdour'd Ceraia does not appear a-
bottt the Sob in the felling Drop of Rain, ^t the Diibmcei
tvtry way of about 25 D^ees; oecaufe at that Diihnce from
flXlXV* the Axis j the efficadoos Rays SN^ i«, /«• after Refradion
Fi^ z. 1^^ ^^c T>tQ^ are refiaOed a fecond Time at F towards the
Eye at I. For if S BCLbe the Axis of the Drop, we have
ihiewn tj^ Angle BN=:59'' 23' fArt. zi,) and the Arch
NF=99**36^ therefore the Arch FQ==:2i% wherefore
in a Glafs Globe of Water, held in the San*5 Light in a dark
. Room, we fee a colour^ Circle or Corona A D F of about
42 Degrees in Diameter, and tfa6 Superficies within it ex-
tremely luminous, as containing all the Sun Beams that fall
on the fore Part within 60 Degrees all round the Axis.
57. But becaufe the Rays are there promifcuouOy blended
. together, they produce onJy a white Light ; whereas, on the
Circumference F D A, where the eiEcacious Rays fall, there
^1 the Colours of the Bow appear; and fropi thence many
have wonder'd why we fee not a Circle c6lour'd with fh-onger
Tints than even the primary Bow itfelf, from this Refradion
hi the efficacious Rays in all the Drops of Rain between nJ
and the Sun from the Circle FDA. But we are to obferve,
With Mt. Whiftofi^ that the efficacious Rays SN; /», p9i
which are parallel when incident on the Drop, are not fd
when refraded at their Emergence at F; for being there tt-
framed to one Point, they are not parallel within the Drpp,
and therefore cannot be fo after their Emergeno^^ but yn&
proceed diverging 6 the Eye at i in the fev^ral JDire^ions
fig ^ri. Fp and thcie&fe wilt not be. iufici^ndy.deslev
W
6f LiGHf ancl^ CoLduitS. i±i
to diftinguifli them from the reft which are in-
find at the fame time too much blended with others to exdte
any Seniktion of Colours. . • *.
5S. Bat why it ihoi^.be (aid, this variegated Circle ought
to appear at the Diflance of about 26 Degrees from the Sun.
I do not fee ; fol- the rfefraded Ra^ F I contains an Angle
FMG with the Ihcidcnt Ray SN (produced to G) of 3^^ ™te
22' ; for 'tis plain that NMriMF, and therefore the Angle J^^V-
MNF = MFN = C N M — C N F = 59« 2}^— 40^ vzl % 5.
=i9« II'; bat the external Angle IMd=MNF+MFN
zr 38^ 22', and confequently this is the Angle of Di^ance
At which foch a Bow muii appear all around the Sun,
&CHoi i u M.
59. In Artide $. it is aflerted, that the efficacious Ra|j
SN makes the Arch QF a Maximum by its rcfra^ed Part
JJ D. To prove this, let Radius CN=CB=ii. the vcrfed Plate y
Sine B A = ;r, and C D = «, and by the Nature of the Cir- XLIII.
cle C^BtAN:: AN:AB; thercforeAN = v^ 2*^. Again. ^'%*i-
UtazzL Ratio of the Inddence and Refra£Uon i then becauf^ft
i:R::ND:CD, we have ND = ^CD = tf«; likewifc
from the fimilar Triangles B N D and F QJ), we have N D :
NB::QJ):QFj that is, a« : ./Tx:: »— i : \/2Ar
frQF. . , ,
60. This Value of QP w to hi dctcfmincdjto a Maxmumt
in order to ihis we neglea the given Part ^, and take thd
variable Part ^=1^=^-::^==: V^^-^=?
x^ r~; then making its Fhixiontjp"!**.^-.^* ^ ^ * x-U
z. ^x^i=Oi or(multiplying by 2«***J«*x— jKjr^2;rK
; ..." 2J;C— JS*X
±z o. Whence 2 * 55 = « * — z^x. and k ^- .-^_.
2*
61. We muft now find another Value of « in order to ex-.
terminate it, which we find from the right-angled Triangle*
N A D,, where N D* = A N* + AD* ; that is, a* «* =s«*
4- 2«— 2*a+ I* which in Fluxions is 2«*«x:;=:2zk-J**
tOL.lf. P effedittf
226' Of LiQHT and Cplou r».
efFedual (CXXIV.)
zk^^zxx'-^zxxi theieforeg ;;?•■' ■>■■;■■■ =;;
r'^*^^ ^; whence **—«*«**•**+«* «+3*-*-i5=oi
now by means of this and the preceding Equation^* v?" zz
%*'^2»^^2xz'\'i^ if we throw out ;r, we (hall get this
cubic Equation z^ — «*«' — g*g*4'«* + S^^j =o;
whofe Roots will be found a^—i. s = -— a/ — —i
«=• ^3~i of which the ty/iy fiift Mug tt?gative>,are
of no Ufe; therefore .the Arch QF is a Maximum when
62. By inferdag this Value of a ktto die Equackm «^ )s^ s
t
lefrangihle Rays^ we have « = -^^ therdfore t^ \ ■ :?t
1,964 = 00; and A B=: 0,4008 the verfed Sine of the
Angle BCN=: 59*" 2%', the Ume aswas found before in
Jrtiete 2 1 . Alfa if we put a = — ? (See Art. 1 9.) we fliall
have the Angle B C N = 5 J^ 40^ ibr the mod refrangible
Rays, as in Jktkk 23.
63. Alfo we get the Value of QF =: ~r" v^ 2 jf /=i
o,3€48, whidi i$ the Chord of 2 1* 02' s= QC P; as was be-
Ibre (hewn, Jrticie 56. Hence all the Particulars relating to
ihe^hcipal Bow are- eafy to be underilood;. and this is an
egregious Inftance of the extreme Ufefulnefs of the Fluxienofy
Calfit/us in Natural Philofophy. This noble Theorem wa»
firft given us by Mr. Stefwart in his Comment on Sir If, Niw
ioit^s Qgadratures.
64. If BNQ^were a Globe of Glafs^ then uss -|-,
CD
Of LiOH* and CoLobi^d. i 27
iDDa»= t,549a» juid the Arch B N~ 49"" 48"^ } alfo th^
Arch QjP sz 1 1 "* 2 2^ Soriie oth^r cooMnaUe Ufcs, whiek
may be made of thu Tilebrem, wiH be conflier'i In the tfSIK
Ledare of OfHa.
.'(exXIV.)i. Gonovtniifg die ProAiaioti 6^ Hk to% oof
illuftriotts Author has teft'm to diabe the b^ft Shift we tiOi hi
aotowitiiig fci^ it; faavh^ fiiM nothing of this Phaenomenoyi
that tan )£ of any Service to help us in thjn ]>ifqaifition He
Intinlaiesr indeed, tUat HMs are fomCd hj the U^i nvhicB
ipmit thfiggh' ike Dnfi tf RMn fy Aio« Rtfruai^ni {rit.- di
N omS F) nmthwt atty Refie3i9H\ but hOiV' this can be if not pi ^I^ry
t9£i to tonoeive« We have fliew*d thtt a Rakib^W or deepljr pj' *
cohMir'd Ring mijghc have been e^kpeded at the Diftadce ili ^' ^*
about 38 Degrees from the Son, and alfo wh/ k cannot hapi^
pen.
2. For the ftme Rttdbn We fbdnlidfd not expea an HaW
to be formed by the fame refracted Rays, owz. on accoont ^
their not behig rtefiaditdi panlld to the Byt^ and tonfeqaent-
ly not entering it denfe enou^ to render that Part of chir
Heavfens more luminous than the r^fl, (Mr to produce the Indid^
Ring we odi by this Name. Again, Sir yiuie fays, it ougti
to Appear frtmgtfi at the Diftance 9/ aina 26 Dlsgrttt front
tbi Sum (tnx. when the Angle IM6s=26*y dnd ta djcaf
gradually both nvays. But though our Authot* did not un*
doubtedly affert any Thmg without very great!' Reafon, yec
this does not appear to os.
3. For that the Angle IMG may 'be 26 I^grees, the
Angle of Incidence BCN muft be about 46, and then th^
Angle of Refraaion CN P will be near 33 Degrees 1 but why
iuch an Incidence and Refradion flioukl caufe the Rays to be
refraded in grater Plenty to the Eye than any Other, does not
appear to me^ nor can I find it by any Experiment. On thd
contrary, as the Angle IM G increafes with the Angle of In*
cidence^ and confequently with the Angle of RefndUon, it ia
evident that with refped to heterogeneal Light, the greater
the Angle IM'G isj the mdre will it be r^fraded and feat-
ter'd ; and confequently, the £irther the Drops are fituatd
from the Sun^ the lefs denfe will be the Light tranfmitted hf
Ref)a£Uon to the Eye, which therefore ought to decreafe i$
the DifUnce from the Sun increafes.
4. As Sir Ijiuu Netoton has faid but little, fo his Expofi*
tors. Dr. PembertM and Dr. fOra^efoMt^ have thought fit
to be abfolately fiient out this Head. Mr. Huygtns £» ad-
vanced an jEiypotbefis by which the Phammtnon may be
folved, if we grant him sdl.his Petitions. And fincc n|ane of
P 2 eolf
228 0/ LigAt and GoLauks;
our great PhOofophers^' not even .Sir Ifme himiclf, have *tttfi».
dertookto difproveit, but on the contrary feem r^er><Q
approve of it, a$. Sir IfiMc in his Oftici^ and Dr. Smthm
his Optics has adopted the fame entirely $ I think upon thefil
Accounts, and confidering the Charader of the great Ab-»
thor, the Reader will.be pleafed to have the iam^ iii a'v^ry
coBcife Manner reprefented tO'liim. >. . « . >'t
5. His Foftulatum is, Ihat thtre urt- tertmu GloMetm the;.
Jktnofpbere confifiing of,a:Coat or ^beilrf transparent*' lUimn
Wattr, containing an opake Nucltiu or Kenulivithia ; aind.that
thefe are made from l^article^.of Sii0w> (which *ii in it£^€
opake) attracting the aqueous Particles in, the Vapour or.£x-
hala^on by w.hich it^ is. fudain^d, wlueh. gathering togedwii
form the pellucid Shell of Wat^j» or are frozen into a ciy-
flalline Shejl qf Ic^ }^.a.pd.ihi8 he.thinki is proved to be Mat-^
ter of Fad by the Hail-ilooes which fall to the Earth, fos
^efe. (fays, he) when broken 'do difcover fome Snow at the
Center.
Plate 6. Thefe Things . premifed, he addrefies himfelf to the
XLIV. Solution as follows: LetABCD reprcfcnt fuch a Globnle^i
Pig. 4. with the opake Nucleus £F in the Middle of it ;> and let us
ibppofe the Rays coming from G, H, to fall on the Side A D..
Xt is manifeft they will be refcaded inwards from the Surface.
AD i from whence it follows, that a great Number of them
mu!^ ftrike upon the Kernel £ F.
r 7. Let GA and HD be the Rays which after Refra6Uo»>
touch the Sides of the Kernel EF, and let them be refraded
again at B and C, emerging in the Lines BK, CK, crofling
e^ck other in the Point K, whofe Difbnce frotn the Globule,
is. fomewhat lefs than its Seniidiameten
8. Wherefore/ if BK and DK be produced towards M^
and L, it foUows, that no Light x:QmiRg from the Sun througlv
the Globule can proceed «o the Eye any where placed with- .
in the Angle LKM, or rather in the Cone which that re- ■.
p^cf^ts,. fuppofing that the ©bliqiiity of the incident Rays.
HD and GA is fuch as Ihall make the Arch QC and Q.B.
the greateit ppffible ; (fee the laft Note, Jrt, 5.) for- then all
the Rays exterior to FID, GA, will, be refradled nearer ta
Q^. and after Emergence crofs each. other in a Point k nearer
th.^ Globule than the former^ and therefore cannot come at
the Eye placed within the faid Cone LKM.
Fig. 5. . 9. Supppfe now the Eye placed at N ; and let NR, NQ.
be- drawn parallel to LK. and MK ; then 'tis plain, notte of
the Globules (the fame as A BCD) within the Cone RNQ^
can. come to the Eye at N. Thus the Globules at O and P
htve th^ir refjra^^ Rays akf^mi cid- iachiding the Eye in
V - " . the.
Of Light and CoLovts. 229
Ae Cone of Obfcoii^: Bat other Globoles, which lie with-
out the Cone QN R, as S and T, do not involve the Eye N
by^heir fhsdy Cones /ke wcA/km\ and therefore fome of tlioii;
Ray's, which are more refraded- than ir or i/, will fall upon
the Eye, and produce a luminous circular Ring or Corona^
iBchxiing a'^rk Area wfrhin, and whoTe Light ontwardly
decreafes ab It is more remote from the Center.
10. Much after a liice Manner this great Man undertook
to account for the Appearances of Mock-^um and Mock*M$mis,
called Parhelia and Farafden^ ; which I (hall not here detam *
the Reader with, beca^ I cannot help^ thinking the Whole
is bat too much like a mere (though ingenious) Hypothefis ;
having never dbferved in any Hail^nes any fuch opake Ker*
nplsy fo reguUirly formed, and furrounded by fuch reg\dar
^lls of pellupid Ipe as is here fuppofed.
?3
LEC-
a3P
t.^
,...■.. ^^..>... 4;''.,' j-'i, ■;
■"> .
Optics.
0/ the Science of Optica in 'general. Of Catop-
trics And. Dioptrics, Of diverging^ con*
verging^ an J parallel Rays. Of the ffveral
Kinds of Mirrours and Lenses. Of the Yo-
cusEse?/Rays; //&^ Calculations thereof^ani
Theorems for evpry Cafe. Of Objects and
fheir Images, with Theorems relating thereto
for every Kind of Glafs. The Theory of
Vision explairtd. The feveral Parts of the
Eye defcribed. Of the Defects' ^Vision,
and bow remedied by Spectacles of fever-al
§orts. Cy Reading-Glasses. Of Single-
MicRG^copES of every Sort hy Reflexion and
Jlefraftion. Of Double-Microscopes by
Refiellion and RefraSiion, Their Strudure and
yfc fxpkin^d. ^Ncw Pocket-Microscope
defcribed, furnijh*d with ^Micrometer. The
Nature, Structure, ai^d magnifying Ppwcr of
a refraEting Telescope of every Sort\ the
Reafon of their Imperfcftion explained. Of
Reflecting Telescopes, with their Theory
at large explained. Of the Camera Obsc u r a,
^nd its various Ufes. Of the Scioptric Ball
4nd Socket. Of the Sqlar Telescope ; and
Sx)LAKMicROScoi'2Sof feveral Sorts. Of the
»^:c?- I
.J
Optics. 231
new-invented Heliostata of s'Gravefande,
' with Us Theory, and Manner of Vfe exflai$Cd.
WE are now arrived to that Part of
Natural I*hilofophy Which treats of
Vifion^ and the various Phaenomena
of vifiblc Objefts, by Rays of Light
reflefted from Mirrours, and tranfmitted through
Lenfco, which conftitute the Subjc6t of the moft
delightful Scier.ce of Optics. (CXXV.)
(CXXV) I. Optics is divided into Two Parts, Catop*
TRics and Diqptrics; the former treats of Yi^on by
Light refleded from Mirronrs or polifliM Surfaces, and tKe
latter of Vifion effedled by Light tranfinittod ,tim>iigh Leoies^ -
Of thefe Lenfes the feveral Sorts in Ufe are the Plano-Convex ^^
A, the Doi^e ComrqcB, the Plano-Coocavc C« theDonUcf ^ Y'
Concave D, the Madfcut E, (whicji is convex on one Side, ^%* ^'
and concave on the odier) and the Hemiiphere F. The Line
GH9 that is perpeodicnlar to and pafies through the Middle
of each Lens, is call'd the Axis of the Lens, and that Mid<^
die Point the Vtrtix of the Lens.
2. As Rays of Light fall on tfade Glaffes, they are va*
rioufly refleded and refraded, as above defcribed in th^
Leaure. The Theorems which ihew the different Effeds of
all thefe Glafles in refledting and refrading the Rays of Light,
and forming the Images of OI]jeds, are ihveftigated feveral
Ways ; one of which is by jtlgthra. "By dus oceans Dr. Hal^
ley has raifed a general Theorem extending to all the partkn*
lar Cafes of every Kind of Optic-Glaifes of a fpherical Form,
and which I have largely appUed and exemplified in my 7>ta-
: %,: Another Method of doing this is by Fliiximts, which it -
cafy 9fod univer^, p^mprehen^g aU the Cafics of MimHDH
and Lenfes of every Form. Th^ I propofc to exhibit and
illuilrate here for Variety, and for the Genninenefs and £x<*
cellency of this Method above all others, it depending on
Pnnc^[^ths|frare8iere of a Philofophical than of a M^he*
matical Nature. I6 is as follows.
4. Let VBG be the Seaion of any curved Saperfides of F^. 'f*
a Medium VGH!I^ V the Vertex, and AI the Axis of the
^i)rve y Q. 'Trom any ?om in the Axis A 1^ a Ray of
?4 The
232 . Op T I C^,
TiJB priftctpal Things here to be ccHifider'd
jare, Firil,.;/^ Rajt .cf Light \ Secondly, the
Glafffis by.whkh theyh ^r^ refleUed and refra5ied\
thirdly V thi TJbmr.Qm^or Laws relaimg- i^ -ijft
pprpifitim ^f-^f Jm^^s i^fObje^s thexehy \ Fourth-
ly, /|fe^. M^^W? ^f ^ifi^^^ ^^ StruSiure of tpe Bpe ;
^d Fifthly, the Stnuilure and Ufe of. the principal
Qptii^Jnpmcm.
-, TǤ K^y^ ^f Light are diftinguifhed into three
Sorts^ vm; Pi^rallely Converging^ _ and Diverging
Ray Si Parallel Rays art fuch as in their Progrcfs
kpfep;41w?ys &n ecj'ual Djitance from eaeh other,
Plate U gs. A BD Ci iuplj as are the Sun's Ray?, in theii:
f*S' 4- natural State, with refped to Senfe. Converging
" tight AB be ineideht on the Medium in B, which fuppofc
- tefradted tdna 96m ¥ in the Axis.' Then, by having giverf
ttic.DiftanccePthe-ra'diating Poin^AD, and the Sine of In-
cidcnfc BD, w^arc'to find the focal Djftance VF after Re-
fraftrom -- ■ t " * -' '
5. To do thfsj . from ^hc Point 9 let ftll the Perpendicular
B'D to th^ Axis ;' and pdttmg A V =: </, A B == «, BF =: <v^
y D =? ^, B Dp ; , andVP—/, then wift D F =/— x;
At) = i-f-V, 'z =: ^y^^^^J^2^;^^x^, and v =:
*^ J''^ +/* -^^/x 4* ^* ^ *^ therafofc in Fluxions we have
6- Btrt« and «v being the Fluxions of the incident aind
refradlcd Rays, will rcprefent their Vdocitles before and afte«
Refteftion, which Vdlockics we have (hewn {;/«««/. .CXVll.) -
an^os the'6in€5 of incidence and Reijadion /sand a rwhenott
fc.:.^ :; « : «;, And frpn} the Nature of Refra6lion (above
e;cpja|n*d) tt ismanifeflihat-whiie the/ incident' Ray inGreafes,
^e refradled Rax deaealfes; therefore their Fluxions muft
liave co«traty Sigoa; .^,^%; zxA'^^'v, Wherefore ■£:
yy-^dX'i' XX ' f^^^yy XX
O p T I C S^ 2?3 J
Ri^s are fuch as in their Progrefe approach nearer
apd nearer to each other, all of them tending to-
wards a certain Point F, where they all unite } as
the Rays of the Sun colledcd by a Glafs, as C D F.
Diverging Rays arc thofc which proceed from a
Point, as F, and in their Progrcfs recede from
one another towards the Parts G E.
The Point F, where the Rays are coUefted,
iS'Caird the Focus^ or Purning-Point, becaufe
there the Sun's Rays, being united within a very
fnjall Compafs or Circle, arc greatly conftipated
and condenfed, by which means their Aftion or
Heat is proportionably increafed, and therefore
Objeds pofited in tliat Point will be greatly heat-
7, Now becanfe ia thofe Mirroun and Leafes wUch aie
of common Ufe in Ofti€s we regpu-d only the Focus of thofe
Rays which fall very near the ^s, in which Cafe the Arck
B V is very (mall, and therefore V D = 4^ = 0 nearly ; there-
&)re XX and xx i|iay be rejeded, without fenfibly affedhig
the Value of the Expre^ons ; therefore m\nii ^-^ ' •
^^*+/* ^y'+r ^y^+d-
8. From which Equation we fhall find /=: F V, in any
Carve VG from the Equation expreffing its Nature. Thus if
VG be a Circle, its Equation iayj = zrx — xx, (where
C B z= r :;=: the Radius) the Floxion of which is^iry = r x -r-
XX ; and fmcc x:zzo, we have_y> z=:o,yy^rxi and, fub*-
^ituting thefe Values in the general Equation above, we have
fx — rx ^^ rx-^dx .
^^V/^ "" y^ir" *" ' ^ ^ ""' ^ ""
ed.
"i^^ Optic s. '
cd, bunit, ormcked
•i Or G^A*srs there are two Kinds, viz. Mir-
rmrs^ and Lenfes.- A Mirrour or Speculum is that,
which froro one polifli'd. Surface refleds the Rays
of Light 5 and thcfe are either ConviXy Concave^
or Plane^ as will be fliewn. A Lens is any tranf-
parent or diaphanous Body, as Glafs^ Cryjlat^
Water J &c. through which the Rays of Lr^tdo
fireely p^fs^ and is of a proper Form to colleft or
difperfe them. Of thefe there are feveral Species^
/ . as a Plane Lens^ a Plano-ConveXy Piano-Concave ,
DouMe-Convexy Double-Concavcy and Memfius.
I SHALL now confider the difFerent Properties
todEffeds of thefe Glaffes in reflefting and re-
' 9. ffi; the Mediam he Glafs, then ;»:»;: 3 : 2 ; therefore
.JL, — ^/. And for parallel Rays JB, where ii is isfi*
/— zr
Bite, m have ■ mmT,. 3= LS ;s: 3^ :5=/= VF. But m
d — zr d ^ ^
A,dr
Ws^r, where m : « :: 4:3, we have/= ^ , and 4r
«— 3''
=/=! VF, for parallel Rays AB.
I o. This Theorem (fh Jfr/. 7.) may be alfo adapted to the
Ellipsis', ,the Equation of "whrch Curve is jj^si/*" — •
ir^j, w^i^iftPliaioBs is tjisr ^ -^^ ^^ j and, potdnS'
a '^'^ z a. , \ .
X 5^^» we- hate /jr :s:;a,yjz=i ^, which Vahrcs feWHtuted
Wthegeitefal Equation give ^2^ =/} and when d k in-
d'-^p
finite, or the Rays parallel, then X. 5= VF, the focal Di%
§tfnce tof the ElHpfiB V^Gc, a fourth Part of the Utus neOmm
from the Vertex, for the Son-Beams. TheExprcffion is aifo
(he fame for an HyPEMOLJjf V(^^ l?cc%jifo only ^^ is a£,
i. J framing;
Optics. 235
framing the Sun's Li^ht, and fomring the Images
of Objeas : And this ail tlcpcnds (m ReJUffm of
Ugbt) on that fundamental Law, fbai the yinglc
of Incidtnce is equal to the Angle of Refle0m. .
LEt E H be a concave Mirrour, V its Vertex, j^i„ j^
and C the Center of its Concavity. Let A be a
Ray of the Sun's Light incident on the Point E,
and draw E C, which will be perpendicular to the
Mirrour in the Point E; make the Angle CEF
equal to the Angle A E C, then (hall E F be the
rcfleacd Ray. Thus alio HF will be the re-
flefted Ray of the incident one DH, at an equal
Diftance on the other Side of the Axis B V.
If iiow the Points E and H be taken very near
fjtBbti with a difFerent Sign^ and vaniflies la chat Eqvaiioa
alio.
11. If VG be a Parabola, its Equation isj^jizsfx^
and m Fluxions zy^ = px ; whence, (u^ot:f^:iap we. hkvm
yy z^0.,yyz^ v^, which fubftituted as before «ve f * =/j
and in cafe of patallel Rays, or the Sun-Beaxns, -£« zs VF^
4
the Focus or Buming-Poine of the Parabola.
1 2. Hence we ob6rve« iJiat in the Circle VG, whole IU«.
dius CB is equal to half the Latm lUBum of the Ellipfis or
>i!^ai>da^ ^k. r =: ^^ the Focus will be at the (ame Di*
il^e from the Vertex V, or VF will be the fame itt all j for
then It is 4-^ = v ' *^ =/in all the Curves, and con-
fequently the Qnck^ ElUpJu^ and Parabola^ have all the fane
Pegree of Curvatare at the Vertex V in this Cafe.
13. When^ssar^ or ^=;:^ then tike fiicalI>iftance/=
i^;=i^=yF|>fC0ine8 infinite; thatii, if the Radiant
^oint A be at the Dtfiance of the Diameter of the Ciidt,
or the^ Parameter of the Conic Se^on from the Vertex V of
^e Medium of G]a% then the I^ inttbe nfinaed paral«
the
^^
O P- T I C S.»
tl^c Vertex V, we fhaU have EFi or HF, yerjr
nearly equal to f V ; but E F = F C v therefore
FV =.FC' ^V Cy./ That is, the F^cal J^ifr.
tance F V af paralkl Rays will be at ibe JDiJiancs
A of half the Radius CV qJ the Concavity jff tke
Mirr our y from the Vertex V^ in the Axis B V.
After the .fame manner, zxonvex Minr^r i%
Plate U fhewn to refleft the Rays A E, D H^ into E F,^.
Fig. 6. H[F, as if they came diverging from a Point
F in the Axis C V, which is half the Radius C V •
diftant fron> the Vertex V. But fince tlj? Rays da/
liffX adlually come at, or from the Focus. /^ic; '^ -.
caird the Imaginary or Virtual Focus.
Parallel Rays falling diredly qa a ^ane
lei to the Axis. And, ince ^^f/^, parallel itn^s will be m-
ffaftcdfrorti a Jabilance of Glafs by a fpherical Surface tQ
the Diflance of the Diameter of the Sphere ; or from an el-
liptical or parabolical Surface to the Difiance of the Latu$
Re&wHi from the Vertex V.
I4» After the fame Mamierwe expreia th^ feveral Cafes of
'*'PIate a Spherical, Elliptical, or Farahdical reflcdUng Surface V B G,
XLIV. that is, fuch a one wheie the incident Ray AB is refle6:ed
Fig. 8. from the Point B inftead of being refraded ; and then fince
the Angle of Incidence ABL is equal to the Anj|le of Re«v
fieaion LBJ!^, the Ray KB will be fo refleAed from the
Point B as if it came from a Point F in che Axil, aiid there-
fgre that Poipt F we mail confidcras the Focus tX rHte^ed'^
Rays. In this Cafe the Velocities of the incident and re-
flexed Rays are the faine, viz. » =: nj, and both affinpa-
tiv^ ; alfo « = «. Whence — "^^ ^ ' ^^^-^-r =^
' ' ' ttVQ^ putting /r c=Ltf, rjr =rtf, and
yyz^^Lrx, or^n^px, (as above) then thb general Thiebreml'
bcciWies -^Lj: =/=: VF, in'thc GrcU ; and -^L- ;=;
f^ y F, jn tte EW^$ Hjperhala^ and P^ab^: ' - •
Speculum
Optic s/ 2^7
fyicUlum are feflefted back upon rfrem(e!ves j if
they fall obliquely', they are reflcaed in the fanje.
Angle, and parallel as tbey felf. Hence there is
no fuch thing, properly fpeaking, as a F^cuj be^
longing, to a plane Speculum^ neither real nor
'Virtual. ^ ' \ . .
Ttit f^ocus F^ or/, of parallel Ray^, is eaU'd .
tbe'5^r Focus y becaufe fn that the tniage of the .
Sun is form'd, and of all Objefts viery remote.
But the Focus of an^ Objeft fituated near the
Mirrour will have its Diftance from the Vertex
more or lefs than half the Radius: The Rule m .
all Cafes being as follows :
Multipfy tbeDifiance of the OhjeH inio the Radius
ii^.'UJ, or AV,. be in&ute, as in paialld Rays,.ortke
Siih-Beami, then f"" ■,= — , = Jr =/= VF. in the
ipherical convex Mirrour VG ; but if the iaid Mirrour be EU
lipiUal, HyfirMkaly or Paraholical, then — j — 3= \p =
/:==:. VF. But becaufe the Rays BK do not aftually proceed
from the Point F, that Point is in this Kind of Mirrours call'd
the Fhrtual Focms,
16. If the Radius BC =: r of the convex Miirour be in-
finite, the fpherical Surface VBG will become a Plane, <i;/2. a pj^^
plane Speculw or. LpQiung-4Sla6» as VBG in the following XLIV.
Figure; and the Theorem --^,== — ==^=/=VF, Fig. 9-
r-^zar
that k,' AN k^ equal toVF, or the incident Ray A B is To re-
medied at B;iitto BK as if it came from a Point F, juft as far
behind the Glafs as (he Radiant A is before it.
f 7. Furthermore, if r ssr BC be fuppofed greater than In-
finite, or from affirmathe to become negative, the Center C
iVlIl then lie on the cont^ry Side, the Specolum VBG wOl Fig. 10.
become concave, )ind in the Theorem above r muft have a
•egativc Sign, which then will be ~ ^. =: / z^ V^ F ^
fffajch ihcwi that in concave Mirix>urs, when d is lefs than
0/
33.8 Optica.
^ ike MS/mwr^ Mi di^id« thai PradkS hy the Stm
^ the Ra^Ms end twice tie Diftante of the, ObyeS \
the S^uotient Htfill he tbi Feed Dijiame ef a Cemjex
Mirreur.
Again; fojr a Concmn Mtrrour^ the fame Tr^^
dua 6f the Radius into the Diftance of the. OiyeS^
divided bj the Difference of Radius and twice, the
B^ance of the ObfeHs ^iUgiVfi the Focal Difiance
V F ^ V/. And hem We ire to 6bfcrve, that
M twice the Diftance of the Object i« loSer or
greater than the Radius, fi> the Focus will be
pofitivf or iv^atir^ fhac is, behind the Glafr or
befoit it.
The Im^e of every Objcft is form*d in the
ir, Aaeis, when AV is leTs tlum jCV, the Fboos /wfll be
^fimativf » or on the ikiiie Side as before s or the Ray AB
Ivill be fo reflected at B into BK as if it came from a Point P
behind the Specttlum.
i8. When /=ir, or AV = JC V, thea is the Focus P
at an infinite Difiance, the Theorem then being * ==/#
0
lb that in diis Cafe mU thei Rays AB will be refleaed parallel
to the AxiSf as BiT. But when d is greater than ir, theh
the Focus/ will be ncgative| or it will be ~m^ i= — /.
Wherefore in this Cafe the Focus F will be on the fitine Side
With the Radiant A.
19. laSHLyf when dzzir, then alfo/s= r ; that is, if the
Kadknt A be phcsd in the Center C, the Focas. F will be
there too j or« in other Woids^ Rays proceeding from the
Center will be refleAed back upon themfelves.
20. On the contrary* (in all thefe Caie() c^^iverging Rajs
- KB are reflected to a Point in die Axis iefs diftant than i C V#
or half the R^ios. f.aralUlRttf$ iTB are refleded to that
Point F of the Axb Where F V = 4 CV. This will there-
fore be the Bmndng Pcini of the Sun's Rttft^ and is the S^lat
tocus above mention'd. Dkfirring Rays have tiktir Focus a#
% JDifiancc &09 the Yerttx V^ .|;rcafirf thiMi half the R«*
Focus 3
O P T 1 C5# .^39
Focus proper to its Diftance : And fince t^
Writers on Of ties demooftrate, that $b$ 4t^gUs
under which the ObjeB O B and its Inu^e llAare K»« I-
fern from the Center or Vertex of the Mirnmr Care ^* ^*
always equal ; it follows, chat the Image I M will
be always in Propordo^ to the Object OB^ »thc
Focal Diftance V F to the Objea's Diftance G V. :
The Pofition of the Objcft will be always c- ,
u& at; a fqfitive Focus j or behind the dpecuhmi
diniinilhed'by a convex, and oiagpi&od by a c<nl-
cave one. Hence, fince a comvdlx ha& but one^
viz. an affirmative Focus \ fo it can never osignify
any Objcft, howfoever pofited before it.
T01 Pofition pf Ae Image in a negt^ive Focus^
4ia8,CV.
21. If VBO be an ElHpb, Hsrpetboh, or Patabola^ the
Theorem is found in the lame Manner to be ^ ^ = A
m coDCafe Specnhims of tbit Sort; and all that has been (aid
withrefped to ^and \r in the f{^rical Speculoms, is true of
V and i/ in thefe. Thua when ^= \f^ the Rays will be re-
newed parallci to the Axis ; and on the other hand, parallel
Rajs will be refleded to a Point in the Axis whofe Diftanc^
from the Vertex V is \f, Thas the Son's Rays aie collected
at the Diftance of wm Fourth Part of the Faranutir (in each
SedUon) from the Vertex^ and as this is the Burmmg Pmtit^
we iee the Propriety of its being called the Aow of Aoto
Curves.
^^. As within the Curve of an BUipfis V G^vH efaeieaie pi. XLV«
two of thofe Focus's, 'tis obifervablev that if the Radiaat A p|l |^
be in one Focos, the Rays will be refleded.to the other at P,
wherever the Point B be taken in the Perimeter of the EUipfe.
For -in this Cafe Vv=:«, Av=«, AP=:jr=s4/^ (for
PP=/) AV = ^=« — *, and FV=A«=/=— «
therefore writing a — x^ and — jp for / and — /, in the E-
cniation above, weftallhaye ^^~cf — =r — ;^, and (9
4^ ;r-« 4«^ =SK/«« tf ^^^r-'Xi* ss t/«> whidililhe'knovril
'^iO Optics.
of that before the Glafs, witt be cvfer inverted' j
and if nearer the Vettcr than the Center C, it will
be lefs ; if fanher from it, it will be greater thaft
thcGBjea; butintheCdn^er, it will be equal to
the Objeft, and feem to touch it
ThE Image forinM by biplane Specutim is txt^ ;
large as the life ; at die fame apparent Diftancfe
behind the Glaft, as the Objeft is before it ; and
on the feme Side of the Glafe with the Objeflf.
Thefe Properties render this Sort of Mirrour of
moft common Ufe, iHz. as a L<^king-Gl ass.
It the Rays fell diredly, ot nearly io; oh i
plane Mirrotir^ and the Objeft be opiake, therfc
will be but oAe Jingle Image firh^d, or at leaft be
Property of the EUipfis. ^
25.. And the (amc thing holds with fcfpcft to the Fott ot
two oppoike Hype Aola's V B and a; hi for if the RadiMt be
n XLV. in the Focus A of one, any Ray A BT wffl be fo rcflea^ into
Fie 2 B K, as if it came from the Focus F of the oppofitc «ypcr-
** ' tola a; ^, as is evident in the Figure. In the ^a«*^»J ^^'
if the Radiant be placed in the Focus A, thei-cfleaca Raya
Fig. 3. B K, tending to the other Fbcus at an infinite Biftance^ wiD
be all parallejl to the Axb V C; agreeable to what is fiid
above, Articlt 21.
24. If we refbfve the Equation -il-5=/, intp an Ana.:
i»y, we ftaH difcover that the Axis of the Miiroui', is divi-
ved hannonically in the Points V, F, C, and A; or that it li
A V : A C :: VF : F C. For fuppofing it to be fo, we have
i^:iz±=.r::/:r=±=/, which gives us the above Theorem^
— ^=/, in the amveic Speculum; and —3; — -^=s/,iii
2^+r •'' "^ ^ ^^~^, . tJKi
the Concave. This citriabs Pfeptfrt;^ of Spcculums was firtt
difcoverM by the late Mr. Diiton. .
.25. We now proceed to apply thts Method to Dioptnc
Prohlemsy that is, to find the Focus of Rays reiraaed ;hio'
any Sort of Lenfw. To this Bnd we muft recolka, that m
JtikUZ. wt had md/'^mdr:ssnr/^ndfy^htidic9 deduc*
vjfiblc i
Oi^ftds. 241
vifible ; and that by the fecond Surface c^ thd
Speculum^ and not by the firft» through which the
Rays do mpft of them pafi.
But if the Objeft be lumiROUs, and the Rays
fall i^ery obliquely on the Sfeculum^ there will be
iilore than one Image forni'd, to an Eye placed
in d proper Pofition to view them. The firft
Image being forni*d by the firft Surface will not
be fb bright as the iecbnd^ which is form'd by thd
fecond Surface. The third, fourth, fc?r. Images
are prodiJced by feverai Refledions of the Rayd
between the two Surfaces of the Speculum -^ and
fince fome Light is loft by each Refledion, the
Iniages from the fecond will appear ftill more
this oflier Eqiiati<m — = t-^— x -^=7^77 ^ TTt» ^^^ "
n d—r 4. ^^ ^^
W««dsi9thtt»eypre(3'd: The Raiio rf tbt Sine of Incidenei
i9 iht Siiti^ 0/ RtfraSiom ft cdmp9»i2ed of the Raiio of thi
DifiM^m of the Fdci A aad F from the Cenfn C, Mid of thi
M0ti^ y thmr JHfigntei from the Vertex V.
26. If then we confider B^ (in the double convex Lens Plate
VD^t;) as a converging Ray rcfraded from Glafs into Air; XLV.
we fhall find the Diftance a;f, at which the refraded Ray ^f Fig. 4.
ihall interfed the Axis of the Lens, by the Rale in ^r//V/f 25.
dniy here we mu/l confider, that the Point A will he nega-
tive, or. on the fame Side with the Focus f, nn%. at A. And
as the Refradlioii is out of Glafs into Air, we mull ufe the
"■*•«. ^ 1 ^ » , n Ac fv
Ratio — mftead of — ; then -r-^:;-^— x -y- .
27. Let the Thidmeiii of the Lens be Y o^zr ^, and 'ufzzft
elfo let the Radios oJF the iecond Sorfiice be chznr; then
!Lz=:-[+Lzl^ J—, nrhcntcf^ ^r^'^nft—fitt
«w f^-r /— '* mf—mt-^-rnX'^ftf
=:<i;fthe focal Diftance required. But if the Thicknefs /
be inconfiderable, as it cbmmonly is« it may be negleded, and
ftenf = —^Il—i ^eiK»/= ^ ^\\ .=;
«i/-J-«r — nj _ - . at -J- «»—«».»
- Voir. n. (^ faint
242 O P T I C Si
faipt and obfcure^ to ihe eighth, nlmh^ or|eBt!i^
which can fcarcely he,<^ife^ncd gt all .
We proceed now \^t4nfes\ and hejce, fince all
Vifion by theni is e£fe|fted by the JRefradion of
Rays through their Subftanjce, it will be top in-»
tjic^te an Affair to fhew the particular Manner
how Rays are collefted by them to their feveral
focus's : It muft fuffice only to iay^ Tbatpurallet
Ra^s are refra£lei through a flam-convex Lens to
mdr
— ^-r — y — r- , wludi Equation rediiced giirct f =
ndrx t . «
mrd^^nrd'\'m4t — ndt — nrt ^ * « — n ^
wc have f =: ^ , .^, ^'^ . Bat ia Glaft, q=: 2 ; and if
rd+dx-^grx ^
We foppofe the Lens equally convex, or rz=::T, we have/ =;:
df
'r-— ssvf, the foeal IXftinct of the Ray A B after pai&ng
through the Lensy asrequiited.
n. XLV. 28. lEd be infinite^ then r=/} thtvefore patallel Raya»
Fig. 5. or the Sun-Beams, will be colleAed iA a Point f, whofe Di-*
fiances from the Lens is equal to the Radios of Q<Kivexity.
Fig. 6. . ^9- 1^^ one of the Radii r, r^ be infinite, the 1js» wiU ^
a Phifro-Conveft, and f n -"— — ; and for p^aUd Rays where
^ is infinite, f^sizr.
(is* 7* ^^* ^^ ^^ ^^ ^^" '^ infinite, the Speeulom then is nor
' other than a //ai» Glafi terminated by two parallel i^es ; and
the Fpcas f will be at an infinite. Di^nce for pandlet Rays^^
or they will be parallel after Refra^kion as they wele be«
fore.
Fig. S. 3 1 . If one Radius r be infinite, and the other r. negative^
then will the Lens be a PlM9»Cmcavei then wiil the Tbea*
^^zdr
rem be •--- = f, which is therefore negatiyej or the Ray^
"+ ^r . .
pfoceed diverging after Refra£Uon. When d is infinite, the
2dr
Theorem is — j — ='— 2 r = i^ or parallel Rays £veige
. from a Point F, at the Difiance of twice the Radius of Con«^
cavity.
. a Point
Optics. 243
ft Pmt 6^ Pocusj which is the Dimeter of the
Sphere of its Convexity diftant from it :
That the fame Reys att coUeSed h) a deuhU
Iknd equally convex Lens in a Point which is the
Center of the Sphere of its Cemexity :
ThaIp parcel Rays are refraSled thros^h d
fiano-concdve Lens in fuch a mann&j as though they
c^dme from a Point diftant frm it by the Diameter of
ih Concavity :
J2. If both of the Radii be aegaciyey iht Letts becomei t PI. XLT*
boktti OMcavit mi if d\kt hBnite, and (he Radu equal. Pig. 9.
nfSz. r=^, the Theorem thtoit--— — --=::^^r=: — r
= «-*/» fo that paiaitel BMf9, or the Son-Biiaint; are fc ft-
fei£Ud through a doubk and equally concave Ltnt^ ai tf thet
proceeded from a Point f at the Diftaaoe of the Ridina or
Coacafi^r fmn Uie Verubc cif the tkm.
33. If one of the Radii, at r, be affirmativ^» and the other . F^. loj
t negative, the Lens becomes a Menifctts» and the Theoreqi
ihen is=li^=:nili = f; which iiicws that whtt
t =r r, and 1/ is infinite, the Fbcus f is itt an in&ute Diftanok,
br the Riys are parallel after Refinftion as before; as in the
cafe of a fTafch GJap> If r be greater than t, or the Coih
divity \A than the Convexity* the Focus f will be affrmative;
or parallel Ra^s will be Converged to a ital Fodosi bot if r
to left than r, the Focus f will be negative, or {famllel Rifa
#ill proceed diverging after Reftnftidn.
34. We now proceed to desermine the Pofitkm, Magnt
tnde; Form, ^c. of the Imilget of OH|eai Ibrm'd ty Mir^
rows and Lenfes, lutvmg lirft premifed, that the laoages ol"
to Objeft always imears in (he Place fiom whence the Rays
diverge after Aefleaion or Refinaion; or, hi other WoidK
the Image vg^eut m tfait Place, wl^di we .have hitherta
ddrd the Fofctts of the Ra)^s. Thiil Sir Ifiuu tUwim has de^
firer'd as an Axiom, as being ytrf evident, beoiufe the %^»
ties, or fliveral Pomts of the Imaige of ain Objea, aro bhwghi
td the Rye by M refleaed or refoasd Rav9.
35. Let A VGbe a refleamg Speculum, C its Centre, p:, ,; .i
VB its Axis, P the (blar Focus; and let OB bean Objea ''
ct theDifiaixce YB| thro' the Centre C drawOA, #hioh«i
:244 O P T I C S#
. And that the fame Rays are r^fraSlei through m
double and equdify concave Lens^ in fucb manner as
though th^ proceeded from a Point which is ths Cen-
ter of the Concavity.
And. in cafe of a double and equally convex
'Lens, we have this general Rule for finding the
Focus of Rays univerfally, be the Diftance of the
'Objeft and Radius of Convexity what it will,
viz.
!t is perpendicular to the Speculum will be refleded back
upon itfelf, and therefore the proper Pbcus of the Point O
will.be in the Line AO, and that of the Pbint B in the Line
or Axis B V. Thofe focal Points are eafily found, thus :
Traw O V and VD making equal Angles with the AxirVB;
'alfo draw B A, and A£, making equal Angles with the Axis
O A; then (hall thofe two refraaed Rays VD and A£ in*
terfed the Perpendiculars O A and B V m the Points M atid I,
which will therefore be the focal Points where the Repre-
fentation of th^ extreme Pbints O and B will be made; and
^confeqnently all the Points between O and B will be repre-
lented between M and I, and therefore the Line I M will be
the true Reprefentation or Image of the Obje£b O B«
Plate * 36. Hence alfo *tls eafy to obferve, that the Pofition of
XLV. the Objed O B is inverted in the Image I M, and confc-
Fig. 1 1, quently. the fame Parts of the Obje^i and Image are on con-
trary Sides of the Axis in a concA*ue JMtrrour, where the Rays
Jiave a real Focus, or form a real Image : But in a coirvex
Fie. 12. S^irrouTf where the Rays have no real bat an imaginary Fo*
01s, or forAi not a teal but an apparent Image, no fuch In-
verfion can happen, but the Obje^ and Image bothappeat
in an ere6l Pofition, as is eafy to underftand from the Figure.
' 37* Again ; the Objed and Image are conuanutable, 01-
may be taken the one for the other in the Schemes. Thus if
OB be the Objedl, then IM will be its Image; but fuppofing
IM the Objeft, thei> will OB be its Image,
38. Hence alfo it appears, that if IM reprefent an ObjeiS
placed before a convex Mirrour nearer to the Vertex V than
the Solar Focus F, the Rays will be fo refkdkd as to foim
an apparent Image O B behind the Speculum ; and this Cafe
will be tveTf way the fame with that of the convex Specu-
Multiply
Optics. 2+5
. Mildffy the Diftance of the OhjeSl by the Radius
^f Convexity^ and divide that ProduH by the Differ-
ence of the faid pifiante and Radius ; the ^otient
iJoill be the Pijtqnce' of the Focus required.
Hence, if the Diftance of the Objeft be greatrt*
than the Radius, the Focus -will be 4J5mig//T;#, or
behind the Lens ; the taage will be inverted^
and diminilh'd in Proportion of itsDillance to the
Diftapce of the Objeft. . . . : v
, 1%M 18 farther obviou8> tliftt.die Objed OB .aod Jmagf
IM fubtend equal Angloiy both at. the Vertex V and Center
X^ of the Mirrour» whether concave or convex ; for at the
^yertextheObjedlOB fubtends the A^g^c OVB = BVD
or I VM, which the Image fubteods, (by Art. 55O And a(
the .Ccnt<?r C, . the. Angles OCB and ICM, uadcr which tlic
Objc^ 4pd lQ)agp.appear» a^e e^ual, a^ J5. evident bjT Jn**
^edbqn, they being vertical to each otther.
* .46/Thereforc the Triaxiglea OVB andlVM, aTfo the
Triangles OC^. and ICM, .are fimilary at having. all their
Angles refpcdively equal; therefore we have OB : IM ::
VB ; VI I alfo OB ; IM i: BC : IC. That if, the Lengthi
of the Objedt and {mage are proportional to the Diilancef
from the Vertex or Center of the Speculum.
^ 41. HeDce in Symbols, (potting O zsl Objed, and I =z
Id dr
Imag^ we hfive O : I :: ^:/} whence — =/= 1
therefore Q : I ;: 2<^— r ;r. Wherefore, by having given the
Radius of the Speculum, you may place the Objed at fuc^
a Diilance, that it fhall bear' any given Proportion to its
Image, as that of «i to »; for then, fincc m\n\\ zd^^r : r,
we have mrz:^ zdn-^m^ and mr'\'rn'Z=,zdn\ code-
-Quently, dz:;rx T **■?? for a concave ^eculam, nnddzzrx
Ztt
-7 H>r a convex one.
2ff
"' 42. From hence it is manifeft, no Objed can be magnified
^ a convex Speculu^a | for, becaufe in tha^ Cafe n is greater
(han m, r X ^ ". ^ould be a negative Quj^tity, an4 fo d
Zfl
WoqU have a n^acive Value^ ,whickis impofible* And when
.0^3 Again:
«44 O F T I C «•
Aoain; if the IXftaiice of die Objeft beJpfs
tthan the Radius, the Focus wiH be negaif&$i ^
on the fame Side of the Lens as the Objcft ; and
the Itnagp wiU be magnified, and in an <xtd^
Pofition.
If the Diftance be equal to the Radius, 1:he Fo-
cus will be at an infinite Diftance ; that is, the
|lays, ^ffcr Re&a£tion, will proceed parallel,
and wlU therefore enlighten Bodies at a vaft Di-
' m:zt9f tbea 4f=r oi oxthf Objeft and Image arf theft oo^
equal, whp they coincide at the Vertex of wt poncayjs Ifir*
jour. ' ' ■ .
' 43. In a concave Mirrour, while p h greatef dnm «» it ^
fUin the Diftance ^ of the Objed is greater than the Radios «:
6f the Mirrour. $ut wh^ni flirr «, then ^ z=: r | or the CX>«
jed and Image a^e etjoal in the Center of the Mifrolir. ' When
m tt Icis t^n «• or t|i0 Ofaje6t is magnified, then i/ is left
ihan r, Now this may be done two different Wf ys^ b a con*
cave Spe<fulQm ;' for » may be a;9rmatiye, or the InHage re^
and ibnn!d before the Glafs, then dz:;:^r x SLju! i or « may*
zn
be negative, or the Image oply apparent and reprefptcd be*
\mA the IV^our, then /=;s r u ■ "^ ; in which pife, 'tis
zn
plain, the Obje6^ cannot be dimini(h*d. ^ut laMy, if n be
infinite in refpo^lf of mr, then ru z:;: idn^ or r x: zd^ that is,
^=: ir. Or when the pbj^d is placed in the S6}ar Foca$;
the Ima^e i« fprm'd at an infinite DiftancCi and ififinitel^
large.
' 44. Sqch ar|^ the Theorems for Specula \ thofe for Xm^
*re raifed after a like Manner. For let G V A be a double
p.XLy . j^j,^ equally convex Lens j C its Center, or C V the Radiu)
"^g* 'S- pf Convejdiy ?=r; OB an Objca, EV its Diflj^nce {in the
^* Axis of the Lens) ^^, IM* the Image, and FV ;=/, 4e
focal Diftanc^ at which it is form*d. Then a^ the Point E'in
the Objea is fdrmM in the Point F in the Axis of the dired
double Pencil of 'Ij^ays EGF A, fo the Point O will be formed
jit M in the Axis of the Pencil OG]^ A ; and fince. thcfe tw<f
Axes crofs eacfi other in the Middle of the Lens at V» there-
^ Ihe rpi9t9 p«u| M^ and (for ihe bme {U^fcw) 9 ani i;
ftancc.
Optics. 247
itatnce. Hence the Contrivance of the BarkLant-
born for this Purpofe.
Lastly: If ths Dlftahce of the Objeft tic
equal to twice' the Radius, then will the Diftancc
of the Focus and Image be equal to the Diftaiice
of the Objeft ; and confequehtlf die Inwge will
be equal in Magnitude to the Objeft, but invert-
ed. Hence the Ufe of thefe Lenfes to Painters,
and Draught Men in general, who fa^cve often Oc-
1K^ be on contrtry ^et of tfie Axis £F, mi conleqiiendy
tSie lAftge in rcfpcd of the Objeft is inverted.
45. Bec^ufcthc Angles OVBandlVMai* equal, as be-
ing vertical, die Ql^ed and Image have the fame apparent
Ma^ude if view'd from the Vertex of the Lem V ; and
zft m Proportion to each other tt their Difbmces from the
LetJi, that is, OB : IM :: VE : VP.
* 46. flence, if (as before) wo make OB : IM :: m : « ::
diA wehavc,r5r=r/=:-7-^; whence as; «:: ^/--rrcri
;ind fomrt:?;/^ — rn^ or mr-^.rnizzdmi wherefore dzz,
r X ^IjLf, If asr s: a, then zr:=zd% and if « he infinite
u
, in ceQ>ea tosir»r == d. And if #beneg^ve» oron theiame
Side, of the Lens with the Objeft^ then iif = r x *"**» whic|i
fliews Ae Obje^ in that Q$k is alvyajrs magnified.
47. If the Lens be a iingle or doable Concave, the Rays
eannbt be converged to a Focus, (as is manifeft from Art, 32.)
and confe^aently no real Image can be formed, but only wcl
imaginary one ; smd b^omfe it is in this Cafe d:s:r x
*^ "* *tis plain when mz^M^ then dx:^rx ^— =sa.
n ' »
that is, the Image can Only be egual to the Objed when thef
coincide at the Lens.
48. The Form' of the Image IFM is not a right or ftra^
^iiic, but a Curv«| for let VEzs^, VF=:/, and VO
wd,f VMasfj t&enfittce — l*t3/;andT-^ =f, wo
l^ypf: f :: j£L- ; ^^ but if IFM were aRightLine.
0,4 «fion
«4? QPT. I C Si.;
cafion fQ6 tbalmages^.ofObitSs as large as.tfce
Life, to delineate or draw from.
A&,:to PZtf»^rff»r4J^#f, .they^ having na real
FoctB, fpcm noTma^s of Obje^s ; . fo that we
Ihall pp^ theni.to prpqeed to the Stru6lurc of .the
Bycy^ih^' M.anner,,oP performing Vifion thereia^
the ftKyaJ>Defefts thereof, aQdhQwreff)';died by
Glaflefti^;^^hkhrWiH,be!liuftj^te^ by.t|ie PiffedH-
k »fo^ btf /': f :: J A d. Neither Is the- Imige df A circu-
lar Form, unlefs the Objedl be fo ; becaufe in that Cafe/=: f ,
which pruMV be but whfin^</=::.d,.or VE;=; VQj, fo tisac if
the Objelft be the Arch of a Circle, the Image will^ th^:
•^rch of a Circle concentric with the Objcft, or elfc of a Co-
iuc ^e^^t fa before obfcrved of Images form'd by Mir^
ifpurs, Jrt. 36. •
! 49. If the Objed |)e a Surface^ the Image will b^ a Suiw
face iimilar thereto : and iince Surfaces are in duplicate Pro-
portion of their like Sides, (^«»<^. II. ^r/. 3.) therefore m :
n :: OB* : IM*, in this Cafe. And if the ObjeA be a So-
lid^ the Image will be a fimilar Solid, and they vrtll be in the
triplicate Proportion of their homologous Sides; whence
I, 50. Though Specuimi and Lenfes arc of moft general Ufe
in C^//Vi, yet it will be neceiTary to confider the Property of
a Glohe 0/ Sphere, as alfo of- an Hitnif^here^ wit J rwpcato
their Power of converging the Rays of Light to a Fociu^. ,If
TJatc ■ theref(^e in the Theorem of Art, 27. we put / =1 2r z=: Dia-
XLV. meter of the Globe, and becaufe r 2!= ^, we ihaH have
«►• -I- _JII — !; -- yr j|jg Focus of diverging Rays j and when d
il infinite^ the Theorem is — ,=; -1 =;;/=;; Yfc - Thwefore
id z
^ Globe of Glafs will conyerge the Rays of the Sun to a Fo-
cus, at the Dift^nce of hajf the Radius.
51. But in cafe the Globe be Water, then in the afore-
faid Theorem we have j« = 4, » = 3, and the reft as bc-
fbr^^ tj»en Jjy Rediidtio© it will become ^~m s: /; foi
diverging Rays ; and for parallel Rays^.wher^ d is infiBite^ we
)iave -^ ;i; ir.=:/, jaft twice as larg^ as in Qlafs.
pa
Opt^1'C«. 249
on of a natuMi Eys, and eMmplifted by m mifi-
cial 0ne.
Th« Eye is die noble OrgM of Sigbt or V^n:
Ijtcooiilb of vmous Coats aad Humours, of
which there are Thtee remarkable^ viz. (r.) Ihe
Jqueo¥s orWatvy Humoury which lies immediate-
ly unider the Cornea^ and makes the Eye globular
before, (a,) The Vitrtous Humour y which: i» by
much the greateft Quantity, filling the Carity of
52. IiKiia JKriw^iinr of 'dsfs, vriwn the cttbvex Side is Hafg
lvro'4^witfdstiiCLRadtaqt,- having rmfintte, and/ = r, the XLV.
Thcpam will become l^i^=/, th« fbcal Diflanoe of J'ig- »S-
4iverg|ng Rayj; but fpr.parMi4 Rays it bedomes ^-j=c
3 '
53.^If the p}ane,Side of the Hemifphere be tuni'd to-
i^rards the Radiant, the Theorem for diverging Rays will be
—.i—S— :^ /. and for poralW Rays, — - = -^r =;= a r
5^/"; wl^h i^ — r greater than before.
54. In an Hemifphere of Water, the conrex Part bein|{
(Qwaxxls the Radianti we have 9 /*. 9^ . z^fi and for pa-
4^ — iir
»llelRay8itiai^=:-ir=/. Bat if the Radiant be op-
4« 4
dcd to the plane Side, then lrzs,f, greater by |r than
ore.
55. We have hitherto confider'd the Property oi Jpkerkal
P^odies onlj.^ with refpe^ to their Power of refratUng a Ri^^
9f Light ; let us now confider the ^atare of Refradion m
Bqdie^ whofe Figures are derived ffom the Carves of the C#«
nic Seaims, In order to this, let DBKC be an £llipfi», DK fig. 16.
its tranfverfe Axis, H, I, its two Foci, and A B a Ray of Light
parallel to the Axis be incident on the Point B. Let BE be
a Tangent in the &id Point, and LG drawn perpendicolar to
the Tangent through tl^e P9int B; jom (IB f^d IB» make
^' "''*"'"'■ ' the
55© 0*-T I c's; '
thei^^i dnd 'giv30g; k die Fomi of tgr Gbbc^ or'
Sphere, (3}. The CryftalUne HunuuTj (kuate<l
between lbs pthct tiws riexr ihe f^'ore-pat't of the
£]re». anitistheiistmediacb Ittftniment of Sl^v
Cor being of a lenticuhr Form, it converges the
R^ysy .^ich pafs tfirougli the PupU, 'to a FocuHs
on tbe Bottom of the Eye, where xkt Images of
actexnal Ofajeftsiare by thi^t means formM ai^d re*
prefentcd (CXXVI). c • • ^ •
A'B £S^ IB^ and ftdDit)ie,F(km€B Aitadr r tet M
V ' .dicolars AIi» IG, oftthe.LiML&rprodyie^iBttf 0| and^
' 4niw HO panllel to LG.
$6. Tketi 1ft die AnifBr Kight angled Triangles AXB,
JNG,.we have AL:IG::AB:NI:;IB:NI» becaufe
ABszIB. BlllIB:Nt::IO^IH, becaiife ^f thii'iimfliu^
Triangles BNI and OHI. Ag^in, the Ang!e HBG =s:
G B I from the Nature of the Curve s whence G B I = H<>B
(=HBG) = BHO; therefoxethe Triangle H?0 is Ift-
foie«; orBH=BO. But IB + BH — D^ fet Gmesi
. therefdre IBXBOssIOrrDK. OM^fetfUeiltly, A t :
JG(::IB:Nl::IO:IHl«D.K:IH. ^
57/ ^iQce LG is perpendicular to the Tangent or Carte
|n the Point B, 'tis evident that A L is the Sine of Itttidence»
and I G Uie Sine of Rt^radion to the Radiu» A B == B 1 1?
^therefore a Solid be generated by the Revolqtioii' of an Itl-
fipfis about its Axb, which EUipfis has iu tran^erfe Axis DK
to tfaie ttftaaee between thr Foci in the Ratio- of the Sincf 'bf
Incidence to that of Refradion; then parallel Rays AB, M-
tfig.Qn every Point B of lis Sttrfaee, wil^ ^ rtfraaed td m
remote Focus I.
58. After !^ fame Manner we proceed fbt the ffjferidSd
ComiJ't but as Lenfes oiada of the^ Forms are extremely dif-
iiHilt to wOrb, and are filcely never to be of tjfi>, (fin^ thf
f^eat Defe^ of thefe Glafles is owing to quite a diileivnt
Gaufe^' aa we^ Adl ih^w in the next A$m0tatiini\ IftOXi iky na
mora df them here, but refer the fnquffitive Rieader \b fhe
V : \l Woftrks^ M. Dtf €afitf, vAiO trcsLpi largely of this Sdjk-
'^' •.'. ' '.. " '.' ' -.V v^
^ (CXXV«J f .1 Iir ord^ to exhibit a jdft ftfea of the /5^
fit^f^ tf^ Vijhk^ I fla£ hm g^ a i^rf axaO; isA pa^ticnla^
'.. ^ Over
^ OrsK tU die Bottom of the Eye is fpicad a
ycry fine and curious Membrane, cajf d the 1th
ima^ which is an Exptnfion of the Optic Nervti
upoa whicli the Images of Objeds being panted
Itfid impneis'd, they are by that means convty'd
to the C$mm^ Senfary in the BraiA, where the
Mind views ^nd conteipplates their Ideas \ but chi<
in a Manner too myftenous and abftrufe for us to
underftand.
Defcr^tion of the B ri and of in fevenl PartSt wMi an Aa^ ^
jCQuat or Calculatioa of tbe varioot Refindiofis of the lUya
pf Light through tl|e federal Hiunonn, lor ferming the
Imagesf of Objedt oa thf Rakuk at the Botton of the Eye.
^\ Jo thisEnd I have here lepccfeDtcd a Scdautk of the
^imarn Eyi initi true or nataral MligBttndQ whkh coafiflsof
?'ro Sq^^isnts of two fiifoent Spheres, fw.otie huger, at PI. XLy.
NB» and a \tgbs Bit. The hunger Sd^moit oonfias tifig. ly.
ihree Tunki qr CoatL of whack the oetanoft is of a hard« '
thick, w)utc» op^e St4)femiB« caU*d Ae Sdemiea, as BN B*
Withm this U another thin. ibft« and Uackttb Tonic, caH*d
^ Chroidea which jervet at it weve for a Lining to the
.iodtor, or rather a$ a delkate Strmm ler the third Tnnk
^rd the KttitHit which it acnriooi fine Ripanfion cS the Op«.
tic Nerve YZ over all thefaugerSegment of theBye, every
WajftoBB.
. i. The lefler Scgmenjt jpenfiCt df one Coat or Tm^
plrd the Coma, as refemUing a Piece of tranfparent Homf
thbii more convex ch^ the o&er, and it denoted by BIB.
Within this Coni^ at a fmall Diftaoce, is placed a drcniar Di«
nphragm, as B«, B«, caird the (/««», or Jhv, bccade of the
4ifieient Q4ottn it has in dilRprent Eyes. In this is a mend
liole in the Middle caird the Pepil, as et, which in fone
Creatores is of a diflcient Figpue, «rak oUong,- as in Co«fs,
; 4* Ab the Genua by its Tfao^aiency admits the Light td
enter the Eye, fo the Pnpil is ddtined to regohMe the Qnaa-^
tity of the Rays that oi^t 10 enKr the intctior Fiut of the
£ye for rendering Vifion d^ft» and (he Images of Oiijefts
properly illiiminM. To this Parpofe it is eompofed of twi^
Sets of muicuhr Fibres, we. one of a drcoUv Ponbt whioh^
|>ycQi7ug^g» coiurnftordiauo^
. "• ' " * *' Th«
TiiB €r^4illine Humur isi of fuch a Convejcity,
that in a« found State .of:, riie I^ye ^its Eocvis falls
^twifely i)n the.R^//»^^ there paints the (;X>-
j»Ss» aiid:thewfofe yifipn.l^.-fiot diftiodt, wJqfs
jjyv^^ys jwhkh are par^Ufly pr. neirly fo:; ^car
tbofe only wijl have their JF<xm$ at^the Bottozji of
tiic-Eye; Now* Rays proceeding f/:orn any f Qint
mow thaa 6 foc^eji diflant ffpm tlie Eyej^-wilJ,
is an Amulus of radial Fibres, tending every where from the
Circumference B B of the Uvea to the Center of tlje .PupiJ.
wbltb, ixy. coirtiaSSig;, JilAte ani cnfargc nthe ^Pupil bF Ac
Eye. ; : :; V .':: r. ■ . -s. -■•t ^ ...;..>:-.
.5. linmeldialdy -within tJie &^^ is'anotW>fiinriy?k'i>o^ ra.«.
dial- Fibres, Whis^^joft th»* #ltt«0ni6 Pare is e very ^"wWtf. com j-
ncftcd with the Cor»B^ w|jere*it jotes- the '"^cierotica^t BB ;
«nd on thetoth«r Circumference' It is'^dnn^&^d 'vHth thd an^
<r.»,; •■ tcrior Partt)f 'the Crt-j^A/tf including' the er^ilolK^^^
^,> , > . ) und i&.ca21M.the Ugam^tum CUiare^* atid foinctfenclr t^ Prff*
f£^^ G/irtr«i ''ami is denotecl by- JB», B*; J ■ "",■,,
6. TheBidfcorBadjLof^eEyeis ihadijtrp of threeSubr
fboMs^'cominddiy calPd HumburSf ktiic, th& J^aeous, the G^ .
jfiai/w, and dityJ^itftffks:" Th^ -r^ifc^Sifij Humour m properly
, jfo.caB'd, beingevcry WSiyUk«Wat^,in'fefpe6l of itsConV
M^nce* LimpKiity, fpec^fic (Siavicy, and refraftlvc Power,
It- jacqataifi'd Between <heGy^^A*ahd ihe LigamentumGHare^
as BIBtf/zB. This Humour gives the protuberant Figure to
fhe Gr;!r»r,iwiikh^aiakes the firft Kefradtion of the Kays of
l^ight. . :;.. ' > . ■ . . .. •
7^ The Iccond Humour (impopetly fo call'd) is t\it Cry^
fimtlmit having its Name from refembHng Cryllal in Cleari^efs
and Tranfparency; It is denoted by GKHL, aiid'*is/in
Fonn of a thick Lens unequally convex, Whofe ahtbrior ^r«
fitce GKH iy/tbe Segment df a larger Sphere, and its poile»
jior Sur&cfl;CrLH the Segment of a leffer. This Huxnour
is of a folid Confiftence, and very little exceeds the Ifp^ific
Crrayity^.^iiier, «c;x».ift^e' Proportion «f ii to lo nter-
lyj asf lihamioften found>l)y' Ex^ei>im^nt. • It ia ^ontliih^S
within a molt .deiicate Tunie ^i^ Qttpftdhy oXCA^AirmJmtiiAii^
ev^lt whore feMcid. as the Ctyiblline itfelf. This ^nktiint
JLeiis Qondiiofamoil to the Bcfraaionaiid donvergency of ih^
|lftys pf liight: . • • ) .^t. , . .<
whea
1
Optics.
y^hm they enter the Pupil, be Very, nearly cchii*^
cident wich parallel Rays; and therefore to a ibuad
Eye diftindt Vifioa cannot be c&&€d aciefs than
6 or 8 Inches Diftance, a$ is evideot £o any .who
cries the Experiment.. .
Since dien there is a certain and detdrxt^lnadb
Degree of Convexity in the Canea and Ctyfial-^
line Humour J for forming the Images of Objeds
3. The diird Hrnnonr is the Vitreous^ (being clear as OiaJ})
and. is largeil of all in Quantity, filling the whole Orb of the
Eye BMB, and giving it a globular shape. This Humour
is cxadlly like the White of an Egg, ^nd bat a little exceeds
the fpecific Gravity and refraftive Power of Water.
9. We proceed now to give the Dimeniions of Ac | Eye
and its feverah Parts, (in orc^r for Calculation] as they havj^
been detemrined by adual Meafurement in a great Number
of human Eyes with the greateft Care and Exadnefs. Thefc
Meafures are exprefs'd in Tenths of an Inch, as follows.
The Diameter of the Eye from Outfide*!
to Outfide, taken at a Mean horn fix > IN z= 914
adult Eyes, 1 ■ ■ — — — j
The Radhis of Convexity of the Conua,, BIB = 5,3294
The Radius of Convexity of the- anterior p
" Surface of the Cryftalline, frgm twenty- > C KH =: 3,3081
fix Eyes, — ^ — 3
The Radius of Convexity of the hinder ')
Surface, frow the fa^e Eyes, at a >GLH=;x2,5056
The Thicknefs of the Cryftalline, from,? w-t - o-
the fame Eyes, -^r— 1 KL= 1,8525
The Thicknefs of the Cornea and Aque- ? 1 »- . «
ous Humour together, ' - — I IK _ 1,0355
4o. Moreover, it is found by E^qperiment, that the Ratio
of ReiradiQa at th^ Cornea I is as 4 to 3, being th^ fame
with that of Air into Water ; the Ratk> of Refra£tion.at K as
13 to tz; and at 'L as 12 to i). Thefe Thipgs prtmifed,
let A X be the Axis of the Eye, and ED a Ray parallel there-
to, and injcident on the Cornea very near it at D ; we are to
determine the Foci of the feveral Refractions of this Ray ac
the ftveral Surfaces I, K, ind L/
': on
^53
a54 O F T I c s^
CO the i^/iM; if it happens that the Cbtird&if
4>f tbofe Parta ihoiUd be more or lefi than jufty
the Focas of R^ wiU,fa!l ihort of, or beyond
^e Reiinoj and in either Cafe wiD caufe indiftinft
Vifion. The fiift is the C^ of ihott-fighted «r
fmrBlhul Pe<^^ the latter of the J^ed.
A twrbtifdPirfin^ having the Convexity of the
Eye and CryftaUhie Humour too greats vdll have
m. CXXV, Jrt. zy.l , *^ . i for fuppofog aU W*
kind the Cv^tf BIB were the Aquecint Honour comisee^;
then fince m this Cftfe m =5 4> « = ;; r s: 3,32$4» and d/ ii
inHnite, we have /= 4r = 1 3,3 176 szlQ^ the food IM«
fiance from I by the £ril Refraftton.
12. The Ray tending by this meaaifiom D to QftUa eo»-
verging on the anterior Surftce cf the CfyfigUhie Homcnr
at S. We mnft now find the Focus of the conv^sjfmg Ra^
BS refraded through a Medium evdry where the 6me wMi
tht Ciyftalline Huoaonr. This we do by the &me Theoitaa^
for at K we hav6 # : sr :: 13 ;.i2, and r =s 3»3q8» and IQr^
IKs;: 12,2818 z^ KQj±s<^ the Diftaaco of the Radiaik
Q/rom the Fokt K; but ^ is in this Cafe negadye^ cnt.^^^.
and the Theorto is '^'^^/ — =/= 10,06' =
— md^dn'^nr ''■
KP, the new focal Difiance from K, by the fecond Vit^
fia£lion.
13. The Ray ci^nvcrgiagfi'dmS to Pis intercepted by tinf
hmder Snrftce of the Cryfbdlhie at T, and meeting tbeie
Mth a Medium of difoent Denfity, and a; cwicave Sttftse^
IS again refraded by it » and here we have ss3»n 12: 13;
(by Jf4. Ko.) alfo the Radios r n negttive, as wdii as Mi and
hereitis-— r=:2^$056» and~.i/ssKPi— ^KLsLPstt
i,3i I therefore the Theorem is -^ — ^ 7 ^j .^ ^ »
^'^ ;;;:/sL«&s6»iiai the kS focal Diffantei*.
Quired.
14. The Point M therefore is that in which parallel R^.
ED are coliefted withini the Bye« and where oe Imafes <k
the
the Rays united in a Poix)Z before ttey reach the
Bottm[i of the Eye, and confequently the Images
of Objeds will be formed, not upon the Reiinal
(a$ they fliould be) but above it in the GlaflV
Humoor, and therefore will apptat indiftcn^b or
Confufed. "
Th I s Defed of die Eye is remedied two Ways,
Vii. (I.) By dimini&ing the Diftance between
f^ote bbjeas art fonxiM. The Diflance of this Police frffOL
thi|anri^9lM:=sIK + KL+LM32i,056+Mc2 42
6^1 1 2 =: o. Then IN -— IM = 9,4 — - 9 :r: 0,4 ::;= NM,
lioir th* Tkickftefii of the Scfentfca h by the Micrometer
IbuAd to be veiy nmslf 0,25; then 0,4 — 0,25=0415 ;
whidi it much about tqaal to the Thkknefs of the Choroidet
and Ritina together. Henee nve fti the Forms and refl-affi've
Fimer •/ tUfi ft.*vkrai Hsimtn^s an fmch as mctlj aneverp fa*
fmUsi Rays f9 a FocMs 1^ tHk RpHna in thi Bot/m of thi lyt^ •
'I5. VWUL hence k foUowf, that fihce parallel Rays onljr
haf« their Pocut updn the Retina, they alone can paint aa
JbMfB there diftiaftly, or produce a diftinft Vifion of an Ob«
jcft^ If theffifbr^ the Ob}eA be fo dear, that the Rays front
ny {NWlicaUr Point come di^rging to the Pu|m1, they will
Qtcd&tily require a greater focal XXflance than I Nf, and
therefore, as the Rays are not united upon the Retina, that
Point cannot be there diftin&ly vefntflent^, but will appear
i6* Thus if A B, AB, are two parallel Rays fidlihgopon pi^j^
thd Bapil of Che Bye, then any other two Rays, as CB» CB, xLVL
ih^ithmUy €U?efging» yet as the Point C, whence they pi^. 1*
Smeiri* ii reaftoift froai the Eye, they will at the £ntranc<i
^ the Eye be lb aearly coioddent with the parallel Rays,
, ajs to havaneaHy the iiune focal Point on the Retina; whence
the PoUit C will there be tti^ndiy reprefented by r. But if
any other Poiai £ belriew*d very near the Eye, fo thitt th6
ARgl<^C;9 A which they contain with the parallel Rays be
very coafiderable, they will after Refra^on tend towards a
Point/ ia the %ai% Df the -Eye producedl, and upon the Re-
tina wUl reprefent only a circular indiftinft Area like that at /^
whofe Breadth^ eqdal to^i, the Diftaoce of .the Rays upon
<krRe(ina. The fame* Poiat at D will not be ^uite fo much -
. w the
I
fiS6
Of 1 1 ci.
the Objeft aiid the Eye ; for by leffcning the Di*
fiance of the Objcft, the Diftance of the Focui
and Image will be increafcd, till it falls on the
Retina, and appears diftinft; (2.) By applying
a concave Glafs to the Eye i for fuch a Ghi&
makes the Ray3 pafs more diverging to the Eye^
in which Cafe thfe Diftance of the Focus will be
alfo enlarged, and thrown upon the RetimsYfhtr^
diftinft Vifion will enfue.
cyiated and iodiib'na; the Rayf DB^ DB^ liavi&g a ie^ De^
gree of Divergence.
1 7. It is found by Experience, that the neareft Limit of
diftinA Vifion is about fix Inches froni the Eye; for if a Book
he held nearer to the Eye than that, the L^ttecs^ and Lines
will immediately become confufed amd indiiHo^. Now th»
Caufe of indiHindl Vifion n&ay be in fome meafure remedied
by leflening the Pupils, which we' natuially do in looking at
near ObjeSs, by contriving the annular Fibres of the Uvea;
and artificially, by looking thro' a (mall Hole made with a
Pin in a Card, btc. for then a fmall Print may be read mudt -
nearer than otherwife ; the Reafon is phun, for thelefs the Dir
ameter of the Aperture or Pupil B B, the lefs will the Raya
diverge in coming from D or £, or the more nearly, will they
coincide with parallel Rays.
18. Befides the Contradlion of the Pupil, Nature has fur^'
nifli'd the Eye with a Faculty of adapting the ConformatioD
of the feveral Parts to the refpe^ve Pofitions of Objedb as
they are nigh or more remote ; for this Fufofe, die Comea
IS of an elaiiic yielding Subflance, and. the Cryiialline is in-i
clofed with a litde Water in its C^nk; that by tht Con-
tradion and Relaxation of the Ciliary Ligpuaent, the Con*
vexity of both the Surfaces of the Ct^ula may be a little
altered, and perhaps the Pofition of the CryMUne, by which
means the Diftance from the Retina flM^ ke irtM and adjufled
to nigh Objeds, fo as to have their Iniaget very diibn^y
form'd upon the Retina.
19. I have mentioned mgh Obj^ffily, (b^ which I mean
fuch as are near the Limit of dii^a^ Vifioss^ as between fix
and a hundred Inches Diftance) bMaufe Objelb more remote
require fcarce any Change of the Coafonnati<llft of the Eye^
the foeal Diftance in them varyiiig fo veiy Mb. Thus fup-
Henc»
optics; 257^
tikiJcB the Ufe of Concave SpeSiacks: Arid
the M^s or purblind Pcrfon, who ufes them;
lias the three following Peculiarities, viz. (i.) To
him Objcds appe^ir nearer than ihey really are, or
do appear to a found Eye. (2.) The Objefts ap-
pear lefs bright, or niore obfcQre, to them than
to otHcr Pedple, becaufe ^ lels Quantity 6i Ra^s
of Light enter the Pupil. (3.) Their Eyes grow
pofe all the Refraffions of the Ejt were eqaivaknc to that
pf a double and equally convex Lens, whofe Radius r =1 i
inch; if then the Otyed were 10 inches diflant^ or dz=: 10;
wc fhould have the focal Uiftance /= rj '■ z= ^=:
^— r ^
0,1 1 1 1 X ; and if another Obje6l be difbuit 100 Inches, then
i/=s ICO, aBd/= -; = = 0,10101. The Dif-
d—r 99
ference between thefe two focal Diftances is but 0,0101, <viz.
the hundredth Part of an Inch, which the Eye can eafily pro-
vide fb'r. If we go beyond this, fuppofe to an Objed 1600
J
Ilich6diftant, wehavc/=- ^^i= 6,i6dtodi,' which is
d-^r
only a thoc^ddi Part of an loch k(s than the former, and
is therefore inconfiderable.
20. We have feen the nattural Limit of diftin^ Vifion for
idgh Ohjeas\ we fhall now coniider what th€; Linut on the
oUier hsuid may be fof remu Oljt&s% for Objedb may ap-
p«ir indiftidd and confuied by being removed too far fromi
the Eye, at well as when they are too near.it. And in thi^
Cafe we £nd Objects will aj^pear diftintS^fo long as their Parts,
arc feparate and d tiling in the Image formed on the Retina.
'jThofe Parts will be feparate {q lopg as the Axes of the Pen-;
cilsof fbiys which paint them are fo at their Incidence on
tiie Rctiinai^ that is, fo long as tJie Angle they contain \& not
leis than «M 7V«#i' rf a Degree i for it is foui|d by Experience
that Objeds and their Parts become indillinft when ^e Angle
they fubtend at the Pupil of ^e Eye is lefs thad that Quan-
tity.
ai. Tfios fapppfe OB be a Circle -rg of an Inch Diam^ r ; ,»
ter» it will appear diftindl with its central Spot till you recedo ^^^
^fthe Dillancieof 6, Feet from it, and then it becomes cc^i- XLVl.
fufed } an4 If it be t of an Inch, it will begin to be confuTed ^'g* ^•
VeL.lI. R belter
258 Optics^
better v?'ith Age j for whereas the Fatilt is too
great a Convexity of the Eye, the Jqueous Hu-
mour^ and alfo the Crjiftallmi wafting with Age?
will grow flatter, and therefore more fit to view
diftant Objeds.
The other Defeft of the Eyes arifcs from a
quite contrary Caufe, viz. jthe Cornea and Cry/laU
linf Humour being too flar^ as is generally the
&t 1 2 Feet Diflance, and fe on ; in which Cafes the Angle
fubtended at the Eye, *vi%. O AB, is a^oot jV of a Degree,*
or 6 Minutes. And thus all Obje^, at they are bigger, ap-^
pear diftindl at a greater Diltance ; a fmi^U Print will become
confufed at a lefi Dtftance than a larger; and in a Map of
England the Names of Places in fmall Letters become firft in-^
diitin£t, where thofe in Capitals are Ytry plain and legible ;
at a bigger Difiance thefe become coafuied, while the ieveral
Counties appear well defined to a mueh gifeater Diftance.
Thefe alfo at laft become fo indiilind as not to be known oner
from another, when at the fame Time the whole Bland pre-
ierve^ its Form very diftindlly to a very great Diilance; which
qiay be fo far increafed, that \i alfo at kft will appear but a
eonfiifed and unmeaning Spot.
22. We have feen the Caufes of indiftin6l Vifion in Ah
ObjeSs^ and fhall now enquire what may produce the fame in
the Eye itfclf. And firfl it is to be obferved, that there is a
Pl.XLVL proper Degree of Convexity in the Cornea K?L^ and Cryftai-
¥\%* 3. line S't, for converging^ parallel Rays to a Focus on the Bot-
t6m of the Eye in a fcmnd State; hence eveiy diftant Object
OB will have its Image IM accurately depided on the Re*^
fha^ and by that means produce dillind Viiion.
2 J. But if the Cornea KPL, or Cryftalline ST, orboth,^
ihould chance to be a little more convex than juft, it will
caufe the Pencil of Rays oQo, which comes to the Pupil 009
from any Point C in the Object OB, to unite in a Focus be-
f ^2* 4* fore they arrive at the Retina in the Bottom of the Eye ; the
Image IM of the Objea OB will be form'd in the Body of
the Vitreous Humour, and. will therefore be vtry confufed
and indiftind on the Retina at im, A Perfon having fuch an
Eye is call'd a Myops^ in Allufion to the Eyi of a Moufe^ by
tcafon of its great Convexity.
24. To remedy tbis Defeft of the Eye, a concave Leni
: , , Cafe'
d f-T 1 c J: 259
tsSc df ^n did Eye. This Defcft is reihedied hf
Convex Lenfes^ fuch as are the 'common SpeSaclet^
and Reading Glaffes. For fince the Rays, in thefc
Eyes, go beyond the Bottom of the Eyc^ before
they come to a Focus, or form' the Image j a con-
Vex Glafs will make the Rays fall more converging
to the Pupil, and ori the Humours, by which
hieans the focal Diftance 'Will be fhorten'd, and
£ F is applied before it } for hy this means the Rays Ca^Ctt
Which fall diverging on the Lens, will, after Refraflioii
through it, be made to proceed ftill more divergmg, inx, hi
ihe Dirediion ar^ br^ (inftead ofa9,iop as before) as if they
came froni the Point C inftead of C. All which u plain from
the Nature of a concave Lens above defcribed.
25. HenAe i| follows^ that finoe the Rajs are made to fall
with greater Diveigfsnce upon' the Eye» they v/iil require a
- greater focal Diftance to be united in the Axis, and confe-
quently the Focus may be made to fall very nicely on. the Re*
tina, by uGngaLens £F of ai proper Degree of Concavity ;
and therefore diitind Vifior^ will be efFedled in the (ame Man-
P^r as in an Eye of a juH Conformation, by painting the
Image on the Retina:
... 26. Since the P6iat C 19 nearer to the Eye than the Point
C, the apparent Place of Objects feeil through a concave Leasi
IS nearer than the true Place ; or the Object will i^ppear at
Ofig inilead of OB. And alfo fince converging Rays Oai
B^, proceed leis converging after Re^£lion dian before* the
bbjeft appears under a lefs Angle, and therefore the apparent
Magnitude of Ol^eds feen by a tenoave Lens is leis thaii
^ V^' . • • . ^ , ... , ■ •
, aj. The Objpd is U5 laminotis or bnght feen througii
fu^h a Lens than without it ; becaufe the Rays b^ing rendered
inore divergent* a lefs Quantity enters the Pupil of the Eyt
than ptherwife would do. But the Pidlure is always more or
iefs bright or enlighten'dj according as it is made by a greate^
br lefs Quantity of Rays.
.28. LafUy, it appears froni whai has bein iaidy thatwheii
a, cQacave Lens £F /cannot be applied, we may ilill efFe^
diitinA Vifion by leiTening the DiiUnce between the Obje£t
kni the Eye; for it is plam, if OB be fituated at OB, the
Iiiifage at IM will recede to /m.upon the Retina, and be di.
R 2 adjuftcd
i
26o O p T i,e 6»
adjuftcd'to the RetiHa% where diftinta Vifion elf
Objects will then be dFedted.
Bir (Jonvcf Spcftacles Obje6ts appear morS
bright^ becaufe they c6lle6t a greater Quantity erf
Rayi bn the Pupil. And they appear at a greater
Diftance than they are; for the nearer the Rays
approach to parallel ones^ the more diftant the
Point will be to which they tend.
9an€tf in the fame Manner as when made to by the Lens £P.
PI. XL VI. '29. On the other hand, when the Cornea ot CrylWline b
Fig. 5. * too flat, (as often happens by Age) ^n Objcft OB, placed at
the fain« Diftance from the Eye PC as before, will have the
Rays Co, Co, after KefraTftion in the Eye proceed to K FoctiS
fteyofad the Bottom of the Eye, in whkh if a Hoi* were
made (in an Eye taken out of the Head)'- fhe Rays woold
a:£lually go on, and form the Image im; whiell * image muft
thcrefoie be very confufed and indilHnA on the Retina.
30. To remedy this Dtft€k, a convex Lens GH i* ap^
plied, which eaufes the diverging Rays Ca, Ch, to faHl left
diverging upon the Eye, or as if they came frbm a Poinl
ft!ore remote, as C; by which means the focal DIfiance is
fhortcn'd, and the Image duly form'd on the Retma at 11^^
by which diftinCl Vifion is produced.
-; • 31 . Hence the apparent Place of the Obje^l is at C, more
dilbnt than the true Place at C ^ and itk apparent Magnitude
OB if greater than the true, becaufe the converging Rays
Oa, Bh', are by this Lens after Refra^ion made to unit*
fooner than before, and fo to contain an Angle 0Pi? greater
than the true OPB. The Objedl appeal^ through a' conves^
Lens brighter than without, becaufe by this means a greater
Quantity of Rays enter the Pupil ; for the Rays ao, bo^ are
by the Lens made to enter in the Dire^ions ar^ Sr, which
are nearer together, and leave Room for more to eiittr Cb^
Pupil all aroimd between 9 and r.
' j2. As the Image of the Obje6l painted on the Retina Is
frreater or lefs, fo will' the apparent Magtiieude of the Objefi
f\^. 6. be likewife ; or^ in other Words, the Angle IPM fubtended
by the Image is always c((ml t6 the Angle OPB fubtended by
the Objed at the Eye, and therefore the Image IM will ht
always proportional to the Obje^l OB. Hence it foHows»
that Che Angle OPB under which an Object appears is tho
— Meafure of its apparent Magnitude.
I HAVR
OlfTICfi^ 261
j. I«AV£ already obierved, that if the Objcft be
placed nigher to the convex Glafs than its Focus*
if. will appear ereft and nxagnified ; which makes
them pf fuch general Ufe as Readifig Glafes. .
Jf an Object be placed in the Focus of a con^.
vex'Lens, the Rays which proceed from it, after
they have pa&'d through the Glafs, will proceed
parallel; and therefore an Eye placed any where
15. Tiierefore Objeds of difiereat Magnkiides, as OB»
4C« D£, which fubtend the fame Angle at the Eye, have
^e fame apparent Magnitude, or form an equal Image in the
^ttom of the Eye. Hence it is that Obje£b at a great DU
fiance have their Magnitude diminiih'd proportional]/ : Thos
the Objc^ D£ removed to DE appears under a lefs Angle
DFEf and makes a lefs Image oa the Retina, as is fhewn by
the dotted Lines.
34. The Angles of apparent Magnitude OAB, OCB,
when very fmall, are as their Sines, and tberefore a? the Sides
QC and OA, or BC and fiA; that is, the apparent Mag.
nitude of the Objea OB, at the Diibnces BC and BA, is inJ
verfely as thofe DiHances ; or its Magnitude at C is to xhskt^
AasAB^CB.
35. The more dire£Uy any Objed is fitoated before the
£ye» themor&diitiadly it will aj^ari becaufe thofe Rays
only which &11 upon the Eye near its Axis can be convened
to a Point in the Bottom of the Eye on the Retina^ and there-
fore that Par( of the Image only which is formed by the di*
teSi Pencil of Rftys can be clear and diftindl ; and we arc (aid
tQ/ee an Obje£l by fuch a Pencil of Rays, but only to Uoi ai
u by the others which are oblique.
•. 36. Suppofe A, B, C, reprefent three Pieces of Paper Plate
fli^Ic up.againfl the Wainfcot of a Room at the Height of the XL VI.
Eye; if then a Peribn places himfelf fo before them, and Fig, S
ihutting his Right Eye views them, with his Left, it is very ^
lemarkable that the Paper B, whofe Pencil of Rays falls upoii
Hhe liifertion X) of the Optic Nerve DE, will immediately
vaniih or di&ppear, while the two extreme Papers C and A
are viiible 1 and by altering the Pofition of the Eye« and its
I>iflance, any of the Papers may be made to vaniih^ by
caufmg the Pcn9il of Rays to fall on the Ppint D.
37. Why the {lays of Light (hoold not e}(cite the Seala«
H 3 l;»
I
a6? G p T I c 5.
in the Axis will have the mod dtftipft View of
the Objcdk poflible; and if it be a Lens, of a fm^ll
focal Diilance, then will the Object appear as
much larger as it is nearer, than when you view:
it with the naked Eye. And hence their Ufe as
Single. Micro/copes^ To give an Jnftance of which^^
fuppofe the focal Djftance of a Lens were one*
X enth of an Inch, then will the: Diameter or^
tion of Vifion in that Pqint D yvhtxe th^ F&res 0f the Nervci
begin to feparate and expand every way to form the Retina^
I cannot tell. Bat *tis highly worth oaf Notice, that'thi
Nerve D£ is for that Reafon placed ss one Side of the Eye^
where only the oblique Kays come, the Lois of which is not
confiderable, and nq way aiFeds or hinders the Perfedion d(»
Sight* Whereas had it entered in the Middle of the Bottont
of the Eye, it had rendered ufelefs all the dircd Rays, by-
which the jnoft perfedl and diftindl Vifion is cffeded j and we
could have had only a confuifed and imperfeA Perception of
ObjcAs by oblique collateral Rays. HoVv glaring an fniiance
is this of Contrivance and Defign in the Conftrudiion of this
admirable Organ ! ' :
' 38. I ihall conclude this Head with obferving, th;it the
Nature of a Reading-Giafs is the fame with that of common
SpeGacks \ on)y in the latter Cafe we u/e a Lens to each £ye^
but in the former one Lens is made large enough for both.
Alfo in the Ufe of them we have different Ends to anfwer j
for by Spedtaclcs we only propofe to render Objedb dillindt
iit a given Diilance, but the Reading Qlafs is applied to |nag*
nify the Objeft, or to render the reading of a fmall Print ve-
ry eafy, which othcrwife would be apt to ftrain the Eye too
inuch. Therefore the Size of a Lens for Spedlacles is not
required larger than the Eye; but that of a Reading-Glafi
ought to he big enough to take in as large a Part of the Ob-
ject, at leail, as is equal to the Diilance between both thci'
gycs. ; ' ' "
plate ' 39. In the Jleadine-Glafs ECD the Objeft or Print AB is
XLVJ. always nearer to the Glafs than its Focus F ; becaufe in this
Fig. 9. Cafe it is necelTary the Image or magnified Print GH fhoiild
be eredi, and on the fame Side of the Glafs with the 0(>j^ ;
that is, tjic Dif^nc^ d is negative jn thji Equation ^j— ^/
Length
Optics, 263
Length of an Objeft appear 60 times larger than
to the naked Eye at 6 Inches Diftance : Alfb the
Superficies of an Objeft will be 3600 times lar-
ger; and the whole Magnitude or Bulk will be
216000 times larger than to the naked Eye it
will appear at the abovefaid Diftance (CXXVII.)
Hence the Pendl of Rays AED» proceeding from, any Point ^
A, will after RefradUon through the Lens be divergent, but
lefs fo than )>efore, and therefore will ieem to come from a
Point G. Thus alfo the Point B will be referr'd' to |I, and
the Print at GH will be magnified in Proportion of GC to
AC. All which is evident from the latter Part of fki 1^
Annotatian.
(CXXVII) I . I fliall here giye a fuccinft Account of evciy
Sort of Microfcope, with refped to their Nature and Theo-
ry. Microscopes are diflinguiihable into two Kinds, <v/«.
Dioftric by Refra6lion, and Catoptric by RefledlioB j and each
of thefe is either Single^ as confiiting of one Glafs only, or
Compounded of two or more.
2. A Single MiCROscoPE,of the Dioptric or RefradUng ^b^
Sort, is either a I^w or a Spherule, Thus if any Objedt ab XLVII.
)3e placed in the Focus r of a fmall Lens ACB, the Rays F%* !•
proceeding from thence will ^ter Refraction go parallel to
the Eye at I, and produce diftind Yifion i and the Objeft
will be magnified in the Proportion of 6 Inches to the focal
Dillance Cr, according to the Example above.
3. Again ; if an Object abht applied to tlje Focus r of a pu^ 2.
Spherule AB, it will produce diftindt Vifion thereof by means
of parallel Rays, (by Anmt. CXXVI. Art. 15.) and it will
appear under an Angle equal to DCE, and be magnified in
proportion of 6 Inches to the focal Diftance Qc from the
Center. And here it is remarkable, that if the focal Diftance
of the Lens and Spherule be the fame, the Object will be «
three times farther diftant from the Lens than from the Sphe-
rule, becaufe CD the Semidiameter of the Sphere is -f of Cr, Fig. 3.
the Diftance of the Lens ABj confequently an C5bje^ is
Vie wM by a Lens to a much greater Advantage than by a
Sphere; in regard to the Light, ^c.
4. A Single Microfcope of the Catoptric Kind is a fmall
concave Mirroor, as ADB, having the Objed ab placed be-
fore i^, nearer to the Vertex than its Focus F. In that Cafe
Jl 4 Compound
^H
Plate
' XLVIII.
Fig. 1,2.
Plate
JCLVIL
FJg-4-
fig- S-
fig. 6.
O E,T I c s;.
GoH?ov*?D Mictofcopes, efpcotUy the oom-y
monSortj are cofifhrq^iied with three. Glares, ^^t
the Obj^-Letis //a imd two Eyc-»Gbfles D®
and Q^. Tl>e Objcft. a-^ c bei*g pkced $t ^
little iipOfe thap tkt Eqc^l Diftanoe- frojp thf
Len^i^jtf, wiii hare its Image fcrmM at ^
the Image /M will be forxnM f>ehind the Speculum, veqr
large, -wft, drtddiftihdt, as has becnalrpady fhewn. Such a
' " ' ^eing
bugtneciy witn the f ne
l^^iteatiiOins of the Btood-Vcfiels, and Bait of (he GlanJuU
Lachrymdlisy are all by thi& means greatly magoified, aodren*}
der'd; curious Subjeds of onr Sight.
5 . Alfo if the Obje^^^ be placed ai>y where between the
Center C and Focus F of the faid fmall Speculum A B,- tbefi*
will its Im^ge IM \ft formM at a great Difiitic^ from iS^t
Claf^ ^i^mBij be made to bear any aiSgn'd Proportiofi ^o
the Qbjed/. by pladtug the<3bj^6fc nearer to or fanher koas '
IheSecuftF: But for comnion Objeds thf Room ought t^'
be dark^ or the Objed exmtmely lucid, as f^ Candle^ l^i.
But mox0rdf this wiben i cdme to fpeak of the ^dat jidl/frt-
ffope.^. 1,'. • : • '\
6. The next Sqrt of Single Microfcopc is a Cata-dioptric
pne^ ^nkh*" performs its Effed by Reflcdlion and Reff^j^ion ;
the Theory of which belne curious, I fhall give the Res^ler
as fol|o\^^, D B L H is a Gbbule of Water ; ^nd it was ibewp
that ^ Obje^ A A, placed in its Focus A» would be feen di-
ftind and magnified by |efra^d Rays ^BDE. (See Jrt. 3.}
f^Tow !'tis Evident we lii^y confider the Ray B D cither as the
refraAed Ray of ^B* ^ the reileacd Ray of FB, the Angle?
CBF, beipg. equal to the Angle ClBD; aiid firtce in each
Cafe ihejR^y "pD is'at,P refraflecf iptq EJE parallel^ to thp
Axis 6 K» it fQllQws, that diftindl Vifioh will be prQ^iif^d of
an OBjeft F/ placed in the Focus by Refledlion F withih the
Drop, as. the Q^cd ha in ^ts Focus 4 ^V Refradloii with-
out it^ * ' '■ ' '\ ' ' ' " '' ' \ ■ "^."
' 7. Jn order to dftermine the focal Diflance IV \^ ^^9^'
dUon from the Concdve Bli. for converging Rays' D^^ we
vhaveHKf;z:4HC, or 4IC, (by Jnnotat. CXXV.) whence
=: 2IC, that is, ^fc^ 2r, in the Theorem
W'
zd—r
grcatef
Optics.' 265
grestter . Diftanor' oa the- other' Side^ and pTopbt-
tionabiy brgiey as at M N ; which large Image is
contriaQed into. one ABC fomewhat lefs, by d&
lower £ye>(j3ai3 D E ; and diis Image is viewed
by the Eye through the upper EyerGlafs G H }
where it alio diftih£tly views the Micromever
f^ (in the fame Am9taii6n.\ Alfo btouife the xefleAiag Sar*
face IS here concave^ and ^e Rays converging, the Theorem
will become — r-^ — ^ ^/= — ^ =s !/» = IF; whence
CF=:ir. Alfb k]|as)3een (hewn that AI = IC, or CA
^ 2r J and therefore CF : CA :: \ : 2 :: 3 : ip :: t : 34.' * '
8. And iince the fame Objed will appear as much larger
at F than at A, as the Angle FC/ is greater than ACir, or
^ Dfftance C A greater t£m CF, it follows, that an Oljeft
in a Gbbak of Water feen by Refle&ion is magnified 3^
times more than k would be in the Focus A by Refira6Hoai '
Suppofe then C A =z: | of an Inch, then will Ql^ z^z-^Al
an Inch; and theifefqre, fince v6 : -^'5 :; loo : i^ it nppean '
that the Diameter of an Objed at the Focus F is feen^ 100
times larger than at the Difiance of 6 Inches from the Eye. •
9. In a Glafs Globule. H K ;= 3r, IK = \^y = /; -
and the Theorem ——^ — =: :^^^ =:; \pz=lIVv whehce
CF=i:|r, Andbccaqfe IA=:|r, we have QKz^\r%
Cpnfcqaentljr, C A : CF :: J : | :: 2J : 1 ; th^t is,, an Objea
is ma^fied z\ times more at the Focas F within, than at the
Focus A wkhout a Glafs Globe : And hence it appean, that'
equal Globes of Glafs and Water magnify by Refledion in
Propottwn of z\ to 3 j. Alfo becaufe CF =r 4 in Water,
and C A =: I when the fame Globe is Glafs, it appears that
Objef^s are magriified in the Water Globule more than whe^
fcen through the Glafs Glol^ule in t}ie Proportion of 4 to |,
Or 2i to |.
10. A DocBtE Mic^q^cpPE is compofed of two convex
Lenfes, a;<«. an Ohjeel and an Qcular Lens. The ObjeA piatc
Lens is df,' placed a little farther diftant from the Obje^l ab. XLVII.
than itar fcKral-Difiaticd e/; becaufe thcii its Image A B will Fig. 7,
be formed at the required Diftance cC; and as ec : eC ::
ab : AB. li thi^ In>age A B be view'd by a Lens DF placed
^ its fopal I>i^ce fro^ i(, it will appear difUndt^ bcca^9
1
Q P TI G 8.
1^68
. Ti^^,TEL«s?Qpjt is. ^ two. 5<wts,, Wa;. Dtpfix
n«tcL. triCf^^^ pr Cata-Dioptric, by JS^M,
^' ^* £!fon ancj. ^^yrtf^/^» cppjointly., Jir^ra^ing .ST^-b
/W^^^V^confifts c>f an ObJ€;fft-GUft ;i;;5, by vyhicfr.
tl)e, image /^ of ^n Object O B, ata 4iftancC|» ti^
the Radius Hr defcribe ^he Arch ca, and draw all; this wjll
Ibtite Axis of alf'the Rays which go from rtic Pojnt « tp t}«?
LeikSiGK f confequently, the Ray aK will «fter Refraaiori
lie pardlel to tlie Axis, i. e. die Ray KO is paallel to «rH i
therefore the Image of the Objcft beirig in the Focus c of th^'
!befisGK, will be feen under the Angle KOH, wUithii'
cqoal^o the Angle a^c\ but it is feen frmn the Len^s df nilr'
4with^ Angle ate. But the Angle aJAc : «er v,'ti'\ cl^)
WiMiefore this fecond Part of the Ratio for magnifying is Ukt
tc ' '^
of cc to^H, or-j-*
1 ^. Laftly ; let C be the Focus of the Lens DF, and witif j
th^ Radius EC defcribe the Arch Qe\ then will,/E be thcjf
Axis of the Pencil of Rays proceedihg from the Point § to
the Lene DF, of which «F being one, it will be refra6bed>
into Flparallci ta^E ; and {o the Angle FIE = CE^. But
FIE is the Angle under which the Image is view'd througj^,
the Lens DF. which is to the Angle COA ^s CO to C£.
Therefore the third sod iaft Piart of the Ratio for magnifyiitg^-
.CO
•^cl-
19. If now we compound the feveral Parts of th^ Ratio
i^Qw iasxA into qne^ it will make the Ratio of ^^^ ^ tf7 ><
-r^ fo I. For Example, let cc = ^ an Inc|^^ c}\=. 3^, f^.
=22, CE =
haverCO: , , .
wiilbe T.. X : — X — r- =: 40,87. Thci^fore the- DtaJ'
meter of any Object \% magnified near 41 times by fudi, i:
VpnjpQund Microfcope.
'?o. If this Calculation be enquired into, we ftiall find th^t
.the' GlaTs GK diminifhes the magnifying Power, which, i*^
•gf^atcr'by the Eye-GIafs D F alone, and more diHindt. Thus;
ii^ Fi^. II. of (he large Pla^f. XLVHI,^ if the lower Ghii.
E =r 1 J ; then HE being 2, and HO:=r 1 1,66, W^]
>ni 10,665 whence the above Ratio in Numbert'
O p T I chi 269
hm'd m the Focus e of the Aid Giafi, and in sm
if^tefied Pqfition, This Image itsay be i^jewMtiy ,/ •
a linglc Lens a *, placed at its Focal Dfftance, ^is
is ufuaJly done for viewing the heavenly Bodie^
becaufe in them we regard not the Pofidon .'But
p^ were taken away, the Rays would go. oa and ^inited
in a Focus at the Poipts M, P» N« aud there form an Iimgo
of the tengjth MN ; but by replacing the Glaft DE we ftaft
have .the large Im^ MN contracted into alefler ««• Noi^
tius larger ^g^ M N may be confider'd as formed b^r the
Ic^ns.DEac an^tiv^ Focus from an Objed^ir, whofe-
Itiftance FB is le^ than the focal Diftance of the (aid Lena^
AU which istpafy .to uoderftand from the foivgoing Theory
of Dioptrics.
21. Nowtff :MN:: A/: /P; and drawing MF and NI^,
we have MN : mn :: FP : FB, becaufe the Obje^ and lU
tiiiigc do in ewery Cafe fubtend the fame Angle fronv tjj^
Vertei of the Lens, as was fhewn before. Since FP h given^
foafifo is FB, ftsom die commow Theorem y^ zsiK for a'
QinAik and equally convex Lens; or ^ rr /! fgr a*
|)laiio-convex onje« For fince ^ Fooot / it: negative; tr
j-£- = — /= FP, therefore i/r = — ^/-f. r/, and/Jr*
^r + </•= r/; therefore -^^=: ^ = FB ; and -^^ —
4J^, ili< a Planb-Conve:^.
22. It is evident from th6 Scheme, that no more of th6*
large imagcf M N, dr of the contracted one ;»», can be view'iSK
tbtpugh the Eye-piafs HG, th^n what is cpntain'd ^etweeit
th'5L.perpend^ular Lines HC and G A ; and that thef^fbre^i'^
inucn greater Part of the ObjeC^ can be feen in the Imi^e mtf
thaa in the image MN, which is wholly owing to its being
contracted by the large Lens D£ ; and this is all the Reafon
^fitsUfe. ; ^
23. The next Sort of Microfcope I (hall take notice of is «
^ daaiRoptric one, i. e. fuch an one as performs its Effeas fiy yrvrr
XifeSim and Ref ration JMnily i for it h conftrufted with a «.
tmall ObjeCt-Speculum fed, whofe Focus is at F ; and it has *^* ^*
been ihewn^ that if a finall ObjeCl ab be placed a little fkr-
for
2^0 Optics'.'
for viewing Objedls near us, whofe Itnag^ we
would have ereft, we muft for that PWrpbfe add
a fecond Lens ^ y, at doable its Focal Dlftance
from the other,' that the Rays which come frotri
a h may crofseach other in the Focus O^ in brder
ther from the Spectilum than the Fofcus/; there will be foVm*d
a large Image Uiereof AB ; which Imiige will be inverted;
jind in Proportion to the Obje£! as the Diftance Ce to the
Diftance /e, as when an Obje£t-Lens was ofed.
24. Part of this Image is view'd by an Eye-Glafs FD;
which is or ought to be a Menifcus^ as here repreftoted ; be-
caufe the Image b^ing formed by^Refledion, it will be more
perf^dty and admit of a deeper Charge in the Eye-Glafs DP;
and thofe of thb Menifius Form are beft for this Purpofe, be- ,
caufe the Errors of the Rays, and confequently the Confu-
iion caufed thereby^ in the Refradion made at the convex
Surface,' ar^ in a great meafufe redified by the contrary Re.^^
fraction at the concave Surface, as is eafy to underhand from
>hat has heca faid of refraded Light, Jnnot, CXVIL
Plate 25. Another Sort of Catoptric or Refle^ing Microfcope is
XLVIL c6nibu6led with tw6 Speculums, abed and ABCD» with a
^lo iQ, central Hole in each. The larg^ Spedilum is toncave, tKe'
other oonvesS, and both of equal Sf^eridty. They have
their Focus at One Inch Diftance, and placed at the Diftance
of 1 1 Inch from each other, that fo an Objeft OPQ^ being
placed a little beforb the fmall Specdum, might be nearer t6
the large one than its Center E. ,
26. This being the Cafe, the Rays PA; PD, wjiich flow
from the Point P td the SpeCulupi AD, will be reflected to^-^
wards a FoC:us /^, where an Image op^ would be formed, if
the Rays were not intercepted by the convex Speculum ab^
and the Point/ being nearer than its Focus f, the Rays A a;
Dd, which tend t6wards, it, will be reflefted to a'^bcus P^
, where the laft Image OjPj^ will be form'd, to be view'd by
the Eye-Glafs G, tranfmitfting parallel Rays to the Eye at I. ^
27. The Power of magnifying in this "Microfcope is thus,
eftiinated. (i.]f The Objcft OP feen from the Vertex V of
the Speculum AD is to the fame feen at the Diftance of 6
inches from the naked Eye as 6 t6 V P; 6r afe ----. (2.} The^
nrft Image opq^ (to be coniiderM now as a nnrtual bhjtSJ
feto from the Vertex V of the MirtoW A B, is to the fame
0*tlcs4 271
to erefit the Image f», which it will forth in its
own Focu5 w, becaufc the Rays come parallel
from the firft Lens ab. Laftly, a third L^ns i c
is added^ to view that fecondary Image^ ». Thcfe
three Lenfes, or Eye-Glaflfes^ are ufually of the -
fcen from the Vertex *v of the Minoar ad as «;/ to Vp, <ir m
^. (3.) Laftly, the Image OPj^, ften fomthe V«tex^
of the Speculum a<i« 1$ to the iame (een through Che Eye^
Glafs G, as GP to P'v, of as ^. Where the whole nu^;-
iiifying Power is as —-- x — x 7^? to i. This Contrivaiioe
V " If p \j P
we owe to Dr. Sikith of Cambridgt,
28. But a better Form and e^er Method of coniftrading
a Catoptric Microfcope, with twjo reJleSiing Mirrottn^ is that p.^^
which follows. ABCDEF is a Cafe or Tube, in one End XLJKL
bf which is placed a concave Speculum GH, with a Hole p.
IK in the Middle ; the Center of this Speculum is at c, and **' ^^'
and its Focus at O, fo that VO = Oc. At the open End of
the Tube is placed a fmall cohvex Speculum def, on a Foot
fefy by which it is moveable nearer to or farther from the-
larger Speculum G H, as Occafion requires.
29. If now an Obje6l ab be pofited in the Centre c of the
large Speculum, the Image thereof a b will be form'd in the
fame Place, as has been (hewn already) and this Confi-
deration is all the R^afon 6£ this Form of a Microfcope %
for, if now we look upon the Image ^i^ as an Objedl nearer
to the convex Specuiuiii d f than its Focus /^ 'tis phud a larger
Image AB mVL be formed thereby at the Focus Cj or that
Rays cG, J: 11, proceeding frOm any Point c ift the Obje^
ib, will be refledled back upon themfelves, as being perpen-
dicular to the Speculum ; bat the tefra£led Rays meeting with,-
or itlipinguig on, the cbnvex Surface of the Speculum d f,
will (as they tend to a Point c nearer than the Focus/) be
i-cfledlcd to a Focus C, whicfi is found by the Theorem
.-^=//^^«^. CXXV.)
30. For in this Cafe /=:e<c^ and dzzzeC; and fince
rf
drAr/+ 2 df, we have — =r^= ^- Thus if we put the
fame
270
O P T I C S',
fame Size and Fecal Lwigth ; and the Power ot
magnifying is always as the Focal Length of the
OkjiSi-Glafs e w divided by the Focai Length of the
Eye-Gkfs 1 m ^r h c. For inftance : Soppofe eixf
= 10 Feet or 120 Jfa^hes, and he or Im =f
Badios of the fiaill Specalttm r±i 2 Inches^ then e/= 1}
and let ef=/=sio,8; then > ^{"'j=i V ,=±-^^-.=4:
•^ * r — 2/ 2 — 1,6 0,4 ^
Jadws3:eCi and nh: JBiOfSi^zi 1:^9 or the Imag^
ji will be 5 times longer than the Obje£l a b. This Image.
JB isYiew'd by' the Menifius Eye-Gkfs LM» whence 'tis
cafy to obferve that this Form of a Microfcope is the fanae
with that in ji^ticle 23^ 24. only there is bat one Reflexion;
and here b two; and there a fmaU Concave was ofed, but
here a Convex; faecaufe by this means the Inflrmnent is
ihorter by twice the focal Diflance e/nearly, which is veryi.
eoniiderable^ as being a ^ Part of the whole.
31. I fhall fhew in the next Annotation how both thefe
Microfcoptef may be ha^ very conveniently in the reileding
Telefcope, and conclude this with an Aoebunt of the Na-.
tttre and Ufe of the Micrometer ibr meafuring the fmalleft.
Parts 6f natural Bodies; and here I fhall not t^e Notice of,
the feveral uncertain conjeflural Methods defcribed by others^^
but only fuch as I ufe in my own MicroTcopes, which i^ ilridly
Mechanical, and gives the Meafurement abfolutely.
32. The Micrometer confiils of a graduated cncular.
Plate Xy of a Screw q e, and its Index f r. The Threads of
die Screw are fuch, that 50 make the Length of one Inch,
^xaaiy. When it is td be uled, the Point « is fet to the Side
6f the Part to be m^afured, and then the Index is timiM about
widi the Finger, till the Eye perceives the Point has juil .
pi^Sed over the Diameter of the P^t; then the Number of.
Turns, and Parts of a Turn, fhewn by the graduated Cirde» .
will give the Dimenfions in Parts of an Inch, as I ihall fhew .
by the following Example.
3). Suppofe it require to meafure the Diameter of an hn-
flMm Hair, and I obferve the Index is tnni'd juft once round
while the Point o pafTes over it. Then 'tis plain the Diame-;
Cer of the Hair in the Image is 3*^ of an Inch. Now if the^
Micrefdope magnifies 6 times, or makes the Image 6 times
kiger in Diameter than the Ob]e^, then i» the Diameter . of ^
the Hsrif itfelf but 4 of ^V, tbat is but j^ Part of an Inch.
3 Inches If
Optics. ^ 273
5 Inches ; thefi wi?I the Length of the Objeft ap-
pear to the Eye through fuch a Telefcope 40 times
larger than to the naked Eye ; and its Surface will
be magmfied 1 600 times, and its Bulk or SoKdity
64000 times. (CXXVIII).
' ^4. Al(o it is to be obTervedy that as there are ten Huge
TXy'mlas, and twenty fmall ones, on the Mktometcrfbxeyio
each of thofe fmall DiviiioQs are the ^^ of ^V» or the 7^^
Part of to Inch. Therefore, if in meafurlng any But pf an
Ohjeft, you obferve Kow many of thefe fmaller Divisions are
pafs'd oyer by the Icdex^ you will have fo many looodth
nm of an Inch for the Meafuie required. All whicih ii (9
plain, that ifothing can be faid to illufbate the Matter, ^
35. In PJafe XL VIII. I have. given a Print of the Form
id my Nkw Focket-Microscofe foroifhM with Che Mi-
^no M B T ^ R above defcribed . - This Microfcope is of the moft
fimple Strudore, moft eafy and expeditions for Ufe, aiid comet
at the IwA Piice of ahy hTtherto invented of the compound
Sort But for a particular Account of its Theory, and al£b
«f another, in a large Form, mounted on a Ba l l and, Sock e t^
ibr tmlveflal Ufei as* alio a large Account of ail' Kinds of .
Mitreftopic OhpSs^ and' the Manner of applying fhtfm; I re-
far the Reader to my Tr<atife on that Subjek, endtoled Mi^
CROGRAFHiA Nova.
- (CXXVIII.) I. The Nature and Scmaurc of a comfflcw
. refrading Telefcope. is above defcribed, and is fo evident from
the Figure^ that I fhall fay nothing farther relating to its Com-
?' ofition, but (hall proceed to (hew th^ Imperfedton of this
'^lefcope, and that it arifes from the diftrent Refrangibility
of common Light, and not from the fpberical Figure of the
Glafs, as the Opticians before Sir I/aac Newton's Time ima-
pmd, anid therefore propofed to bring them to greater Per-
fedion by introdudng the Method of grinding and polifliing
Glafies of the Figure of one or j:>ther of die Come SeSiom^
2. But this great Pkilofopher foon (hewM them their Mif-
! - take, by proving that the Error arising from* the F%ore of
I the Glafs was many hcwdred times left than that which pro-
I ceeded from the unequal Refrangibility of the Rays, and was
fo fmall as to be altogether inco£d&derable ; and this he did by
I an degint Mietkod in his ieatatas Opttt^^ idnch I SbAhau
trandate fiom that admirable Book.
VouU. S If
274 Optica
^ , Lf.. ipftcad of zcpnvex Eye-Qlafi wc (hoaldule
, z concave ont of thclame Focsd^r^gfh^ itwdttld
rcprefeijt the Objeft, ex^^ equally jnagnificd,
at^jd more diftin£t ai\4 bright ; but, the Di&dvan-
Pt.XLIX. 3. Let NBM be a fpherical Sar&oe, C the Center, CB
Fig. I. the Seaiidiainecer or Aidt pacaUel to the Inctdent lUys^ AN
an incident Ray, and NK the Tame refra^d, cutting the
Axb CB produced, in the Point K ; and let P be the Solar
or prindpal Focus, where the RsLy% meet th^ibdi which are
infinitely near to the Axis. The Error KF is now to be de-
tennined.
' 4. Let Ikll the Petpendicalare CE upon NIL, and NG upon
CK, and callCBn^^, GB=i;r, andCK=r«s and from
the Nature of the Circle we have NG* = 2«ir -r* xx^ to
whfeh add GK* = {^—a + x*) k* + 2 jr« — 2«» + *»
'^zax^a*, and the Son willbe NK*s=s^«|^3xff»^ .
Zas^^4ia.
5. Now fince NG : CE 1: 1 : R, viz. as the Sine pf In-
cidence to the Sine of Refradion i and becaufe of fimilar
Triangles CEK and NGK, it is NG : CE :: NK : CK::
I : Ri theidbre I* : R» :: (NK* : CK*) «* + ix% — •
20Z -]-«*:«*; and I* »* = «* -f a;r« — zaz + a^x
R», ami by Redaftion xz =^ »^«R'--^*«R;~''*R'.
R*ji R*j;
apd (putting n^^^wW .= '* we have,** ;=: 2«/ —
' R^/f* ' R*A*
~— — , and«*~2/« = — ~_p, and oomplcating
R* **
file Square, «*«—«/« 4-// ssj/— i n ...m} aadaemAi*
R* — . 1*
iDgtheRoot,!E = /-f~v'^'~^Tr: 77« whence by Sabfiita-
tK«wehave)«= R* — i' • ^^
6. And, redqcing the radical Part to an infinite Series, we
R« R^* R»*» ;R
»»»
have«=:g~-. j^— P- jP^-'^p-,{:f.. Now
w^,=... = S^ = CP,w.«ceCP-CK.
O ? T 1 C S. 375
tage ofthis Glafs is, that it admits of but aTmall
Areh^, or flftW of VieWy and therefore ttot to be
ufed >frhcn we would' fee much of an Objefl, or
take in a greatScope ; but it is ufed to great Ad*
.K:f = .-.^^+^^. 6fr. which is the Value or the
Error required.
^. Meribe when BO or 4: is exceedhig fin^II, -, ., =
KF nearly, becaofe in that Cafe the other Tenns, where the
,a£:eiiduig Powers of. h are foun^ becoipe caRrnudy {ball,
. and nothing in regord to the fiift Term where x is finale.
e. Again, potting NGrcjr, we haire --^^1_ =
KF nearly; fo NG^sesBGx BC + CGcs BG x 2BG
nearly, (from the EUmims) that is^ j>* s= a^jr nearly, or
r- = .*. .If then for * in the Equation of the kft ^i^
«*
. we fi^ilimte it^ Valqe — » it gives the Equation above hi
thisv
; 9. ikntt al(b it follows, that the Error ICF is always «t
the Sagitta or Verfed Sine GB, or the Square of the Semi-^
chord NG,
~ 10. If the Ray ANK be given in Pofitbn, and* an b6
any other parallel Ray nearer to the Axis, and on the other
Side ; of which let n> be the refraded Fart cutting the Axis
in i, and the refraded Ray NK in Q^ ahd from C^draw Q«
perpendicular to the Axis : Then will the Line tic become
greatell of all, or a Maximum^ when the Ray a n is about
hfdf the Diftance of the Ray AN froni the Axis.
i\. For dr^w hg perpencUcular to the Axis, and put ng z:*
nr, Ko = I, GK rsy; aAd KF :;=: ^ ; and fiiice, by Art. 9,
we have NG* : ng* :iKP : iF, or y*:^*:ih: — =
^F, therefore KF-iF = K^ = i&-i2::==k^i:^
y^ yy *
12. Moreover, GK : GN :: K0 ; Qf 1 wherefore Qf ss
•^. Alfo gn:GK(=:g4 neatly) i:Q4:«i=i-?jJ; there-
- - S 2 vant^e
?76 O FT I a.'
vantage m viewing the Planets and their SaielH-
tes^ Saturn's Ring^ Jupiter's SelH^&cc. This is
cairdthe Galilean Tek/cop^i: from Galileo^ the In-
ventor, and is the firft Sort of Telefcc^e ever
made.
fore i. + K.=JLf + . = ^^ + ^^r=ki=^^""^^^
and dmdiiig by. v-^-jf, and reducing; the. E^oation^ wc have
hvy — Jb'w /
• szaz ■ *
' yy
. 13. Now to detcrttiae /a Mz;»riimMr,' we mnft make its.
Fluxion = 09 that is, j = /^-^"^ ^ =: e ; whence wc
. yy^
get b'vy^zknf'D^zo^ that is, /rj> = 2i&v, Or 2<u srj^, or
2ng =: NG, when / 01: K« ii gresieft of aU.
14. Tb^rffo^e K<^, when greateft, is e<|a^ to about ^ of
KF ; for if in the Equation expreffing the Value of f (in Ar*
tide 12.) you write 2 v for jr, there will arife ^h s= x.
15. Alfo becaufe CF — CB = RF = GK nearly, there-
fbreGK= -^ — a= -i^. Whence fincc GK
R — I R— I.
16. If the Arch BM be taken equal to the Aich BN, and
B^ z^ Bn, and Rays iucident on M and m are refraded in-
tcrfpfting each other in the Point,?, then 'tis evident P(>=r
2Q£ z: / ^ ; ^ and it is ^fa plain, that all the Rays which
fall on the Curve between N and M are fo refraded as to
pafs through the Space PQ^ and that the faid circular S{«ce
F^'QJs the leaftpoi&ble in which all the Rays can be congre-
gated ; and therelbre that this Space is.the Focus or Bkoe of
the Image of an Object, which fends parallel Rays upon the
wiole Surface of the Lens NBM._
1 7. For no Rays can be refracted without this Space, be-
caufe iinfCe Q^ ^^ ^ & g^^^ Ratio to R^, it .will be at the
fame time a Maximum with it; and therrfoure the Point Q^k
tiie moil cpijiQte from the A^, h»^ which' any of ^ofe re^
J
0»TIC^ 277
Tnt Cdtadi^pirSc or Ri^EHt^S^tUfcopt is the
maflnoble and ufefulof all othora ; the Mecbmijm
whereof isas foltows : A EE H is.thc large Tube Jj^^^'
or Body of the Inftrument, in which BE is a large
fraaed towaidf Fo^ttipodibly lattriea tbe external Ray NK.
Neither can they berefraded into a.lefs SfMoe, becaafecfae
lUytMK, NK, aitthe external Say» nk aad «ii in the
Points. P and Q. by which the Space PQJa tenninated.
1 8. li the Aperture of the Circle (or Lens) NBM be in-
ereaied or diminiihed, the lateral Error F(^willbeas^^» or
as the Cube of the Breadth of the Apertare NM. AMb, if
the Aperture of the Lens reinain the faine, the (aid Error
PO will be reciprocally a» aa^ or asCB*« and therefbrc ai
BF^, fince CB and B P are in a given Ratio. Bat if neither
^e Magnitude of the Ciicle nor of the^Ap^^tture be conftant,
(he JSrrqr PQjviU'be.aa ^, or a^ -mr» )a9. ji eviUnt from
•R*f' R*
Its Value ■%/ ■, whefcin the Part — ?^ is cbnRtnt, anddierc-
+i*«* ' .4i* .. * * •
fore omitttd.' Thte<ferr$ir^r. /
19. In all that has been fiiid in the pivceding ArHeks^ wt
. «re to underftand Sir lfaa£\% Defign is to ihew what the Qoan-
Xity of the Error is, and in what Proportion it varies, that
arifes from the cicccdar Figure of the Giaft only lin refraAins
the fame Ray as it is nearer to or farthf r froBLthe Axis. And
jtherefore we are to underlbnd that the' Raya here meant are
homogeneal, or all of the fame Sort, and which admit of no
£iror from a diflbrent R«frangibility.' ' -> '
20. Hence we are able to compare the Errors arifing from
4Khe different Refrangibility of the Rays, suul from the ^ph^
ricai Figure of the Glafs, (fuppofing it a Phan-Cmiveffp as it
commonly is) in a Telefcope of any given Length. Fbr Ex-
ample: In a refrading Telefcope of too Feet Length, that
is, where BF rs 2BC = 20 z;; D := I^ameter of the
%h«re ::=: 1206 foches, jr= NG = 2 Infches, and kt I :
R :: 20 : 3 1 out of Gla^ into Air, Then will the Expreffion
R*v*
for the lateral ^rror from the Figure of the Glafs be ,/
* 4P41.*
3=-^ i — ..^. M I . ■<= — 2—^ — Parts of an India ,
4 X 20 X zo 'ii 600 X 600 7£000000
ttue Diameter of tjhe circular Space FQ^
S3 refleding
n
278 Ot tics;
reReAing Mirroof , with a Hole in the MidHte'
CD. This Mirrour receives the Rkystfr;, id,
coming from the Objed at sdifti^nce, and reflefts
them convergfeg tD'its Focus'^, where they crofs
ai. Bikthe Diameter of the 'littfe Circle through which
the Rays are fcattef^^ bv unequal Refranglbility is about th^
^^^ Part of ^hc Breadth of the Apertua-a of thd Objea7
Glafs, (as we have already ihewn) that is, in the! prefent Cafe;
^ 55th Pa^t of 4 Inf:h^s^ or J^. Whfrefore the Error arifing
from the fpherical Figiirfe of theplafs is* to 4at arifing' froii
Ac different Refranglbility of the Rays as ■ ^ ^ ■ ■ to
. , ** . » 72SD0000O'
x^, that is, «s I to 5449 ; and therefore' beinj; in sompari-
Ion fo very fmall* deferves not to be coniiderM in theTteoiy
of Telefcopes. -
Pl.XLIX, 22.. X-ct us now fee, according to Sir Jfitac's Method»/whait
Fig. 2. ' *^ Value of this lateral Error PQ^is in Rays rcflefted from
^' ' a fpherical Surface, where evdry Part is denoted by tii€ fame
jifttexs as |t)efQre ; Only now the refradted Ray NK is the
rcflcjaed. Ray : And' here alio NG^ = lax-^xx, and
GK^=:(fl — a — x^ r=) a* — lax — 7.tf«-4-Af*+ 2«*
+^»«; • as- htftfr&, 'i:Artich 4.) thcreft*« NG* rf G'K* ==
CK, ffom'lhe Law of Refteaionl Whence /i* = 2«« —
\xx, and therefore «= — 2— == CKj but CF = ii,
za — 2x
therefore CK r^ OF = FK =r — uf^ j^ it
i 9$. .(lenpe, .v^hen.^. 13 io^&iitely .fiaall, FKs=:..*^s±
lAfsr iGB nearly ; And becaufe yyzzi Z4ix nearly, (fee -<*•-
^kA?, 8.) therefore ■=— = |;r = FK ; and hence it appears,
\a •
that the Error K F is always as ;r or the verfed Sine G B, or
as^*, or Square of the Sine or Semi- Aperture NG.
24. Again; every tfciug VkArt. 10, n, 12, 13, and 14,
each
O p^T rcis; * 279
each ddier^' and form the inverted Iirtage I M.
xyh a fimll concave Mirrour^. whofe Fotus is at
/, ^ at a . 6nil Diftance from the Image; By this
ijfe^s: the Rays coming from the Image are re*
isth^fam^licrearthcper; andfo fctf = jKF = -~-. ^And
becaaf^ GK is nearly equal BF == ia, thetfefarr GK :
V* f* ^
GN::Ko:*Q§i thatk, i«:y:: -4- = Tr— = Q£» ~»*
-1
fcqoently zQ^ c^ PQj=: -^. ^£. /.
2$. Hence if we put a =: BG =: Radios of the re&^g
Sphfire^ NBM, we (hall have PQin the refraaing Surface or
t<ens, to PQ^itt the refleaing Siahu <»r Minour, «i -—^
IP JL.^ or (if Y> =3 a) as -^ to j» that is, as 2,4 to i s fo
that the Error ly JRe/raffiom, it near twin and a half greater
thoA ibat ty S^e^tQH^ when the Radius of the Sphere is the
laxne in both.
■ 26. l£ the Medium be given, or the Ratio of I to^R, and
alfo the Aperture NM = 2^; then the Error bjr Befle£Uoa
is to that by Refra^ioa as JL to -L. Hence, fince if the lb«
aa ^a ,
cal Diftance of a refledUog Telefcope and a refradidg one be
equal, we have a :^ 4a, therefore — to — as— ^toi, it
appeM that the Error PQjn the R<0Jrador is to that of th«
Refle^oras 16 to t.
27. Again ; it appears, that In the Refledor, as well af
the RcfeStor, the Error is (ceteris paribus) proportion^ tq
^% or the Cube of the Aperture of the Ofajea-M^t^^ NBM.
28. Laftly, we obferve in the refrading Telefcope, if the
Radios CB z£ tf, and Semi^Ajpertnre NG ;;=j:, be givca^ ]^
R*
Error PQjNrillbeas ^s* Hence, if the Lens be Gkfi. ^
_3^'<3» _
:«,4J
9
and if the Lens l>e Wa|er,
= 1,7. Therefore th? Enw
S 4 fleded
Wfthave
20 X 20
i» 3x3
Zj8q Ort, ic.Si) •
fkf^^d back thrpugb the c^ntjr^l jtlole, C D^C tb«
large Mirrour, where they fall ^,pn the plancH
cony.e^'Lcns W X, and arp hy itxonycrg^idito^
Focus, and tljere fpftri a fecond IiiMgp R S» ig^
by Refra6lIon in a Glafs-Lens is to that in a Water-Lem
(caferis paribus) as 2,4 to 1,77, px stf 4:tQ 3^«farly» - * ":
29. Before Six Ifaac Ne^ton^ all Opticians imagioedjhf
Injdifthidnefs or Imperfection of Tclefoopes^yao owliig Wholl^
to the Figure of the Glafs or Lens; wfiic^^p^tth^ apod
intrbductng the Figures of the Gmic Se^ioHs^ bfeaitfe^ bciif
acquainted with the Ratios of Incidence ao4 R^ft^^fUpn* tl^
could find by Geometry that aii Aberration of Rays from the
prii^cipal Focuf F.wQidd be occaiion'd by tht Ctwature of
the Glafiy and. that was always lefs of ppiirliB ,ai thd Cnci«^
ture was lefi ; and that therefore if NBD, EBF, QBP, and
Plate QBR reprefentthe cunred Surface of a Ctrclei^-wt'EHiflfs, i
XLIX. ParaMa^ and an Hyperbola, whofis comnftOD focus is C,. 'tis
TTja j/ r{ain^ if a paraliti Ray AK be indd^nt .on eqcb) of - ^cA
Curves in the Points N , « , /, r, the Aberration or Erior caid<^
in the MyVby Kefra£iion in each will be as the Ctirvature it
lef$f cr #s ,ike Radius cf Curvature in the PoiMits N^ a\ ^l c^
increafes; and it has been ihewn to be as the Squarr of that
Radius iRVeriHy.(^y//-/, 18 and 26.}' Confequentfy, fincQ
th« ApStfsui^i^nd principal Focns is the fame m all thofe^
Leiifej, the Errors of; the Rava will be kiS^iat'd in «ad^.of
them itefpedliVely.
30. 9iit if the Jmperfeaion of the n^frailmg Tdttoopef
had beetr owing only to the fphjerical Figure of the Glaft^
$ir J^Mtt Neii^ton'^TO^okd a Remedy without Recourfe to tfc
Coftic Se^ionu which w^by coippoitilg,th« Qfeq^Q^CUb jof
two Menlftfns-GlaiTes, with Water betweei^ tlitm. Thus'ldi
Fig. 4. A DFC rept-efent the 6l:^'e£\.Glafs ^n^pcifed ofriwo- GlaiTet
ABBD and BEFC, alike convey on the Ootfidea'tAGD
and CHF, and alike concave on tjue In&des .BME^' BNE^
with Water in the Cavity BMEN-^ . : . — •-
31. Now let the Sines of .'J'pci^^pi^ and. ^efiiftioii oattif-
Glafs into Air be as I to R, and out of >Vater into A^ ^ ]^
%o R ; tfewi i>ut of Glafs into Water they will be at I to K,
{Jttnot.QXYlI.} Ax^d let the Diameter. of the Sphere to
which the convex Sides arc ground bfi D, and the Diameter
of the Sphere to which the concave Sides are ground be to D
as the Cabe Root of K — I x K io the Cube Root of K-^^t*
ic R. Then the Refra^ions pp. the conoaye Sides of the
/ '* \ ^ ]?r§9
O P T 1 C $• 281
Vnge and txt&j . -whkh is i^xwM by a AMfius
Rjtdafs YZ by the Eye di P, rfnough a very
iinall Hofe in the End of the Eye-Piece Y CDZ;-
" I^TAjthe fitft'ljei^s W'X were taken away, the
0affiss'willi$e ra^ niuch comded by the Enon of Re.
fnS&oof rni^th^^onvejr Sides, lb ftr v ^ey arife horn the
Sphencakeft of^ the F^re.
- 3i.^Ait fiACe dK^fe compoend Lenies ^ dais and Water
are MriditTrotoble and Diffi^lty made. Opticians have applied
tlk>miita»4a4aveAttlle %l!ftF%iire of Lenfes for this For-'
pofe, that is, loch that the Refradtion at the iecond Sui&ce
wi^HtKxinifdL the Brrors of Refraaion at the firft Surface
(arifiag ^<MH the'Figurfe of tbe daft only) a^ nrach as poffi.
Me: And tke^ ftmbus Hugens has given at a Theorem hy
which he proves die following Pardoilars.
' : jj. Firft^ That when panik! Ra]rs fall upon the pfame
Side of a pbtno-convex Lens, the (longitudinal) Aberration of
the extxtfnMT Ray is | of the Thkknefs, and is lefs than the
like^beiMlion caafed hy an^ Menifcos-dafs whofe concave
Side is expofed to the incident Rays.
. 34. StSMul^^ Wlhen the ^^id Glafles have their convex
Sidefr turned to the inddent Rays, the Abernction of the ex-
treme Ray Hi4he Ptefio-Convex is ^ of its Thicknefs, and is
JelNthto ihe-likt Aberration of any MenKcus in this Pofidon.
^^y^fAMfy;, Thiit a double-convex Glafi, whofe Radiaa
of the fi^ft Surface* on tf^ich die Rays fall. Is to that of the
leoQatt SuWiwe as 2 to 5; is juft as good as the Piano-Convex
in its beft Potion, the firror being in both i of their com*
fnon Thickneft.
36. Ftmribif^ When the Radii of a Double-Convex are
eqoaf , the Aberradoh is 4 of the Thickneis ; and therefore
fach a Lens iv not fo good as a Piano-Convex of the iame
Thickaeft in ^ %isft Pofidon.
. -i^/iFiflhfyi Beit if the Racfius of the firft Surface be to
diat of the fecond as 1 to 6, it is then the beft GUtfs of all,
itt AberrMsofl' then' b^H^ die leaft poflible, 'uik. 4| of its
Thicknefs. But if this beft Gbifs be tum'd with itsodier
- Side to the |lays» the Aberraticm will be -^, and therefore
becomes much worfe than before.
38. itxdfy. When a Piano Concave has its plane Side
tum'd towards parallel Rays, the Aberration of the ci^eme
^^p is alfo f of tl^e Thickiiefs ; and w)ien inverted it is only
Image
&%z Q E T r c s*^
^^fi WQtildibe forwi-*d fotnewhat larger atJfcff/y
fore the View not^fo plcafcnL; At T V ia placed
%.<irq^f;JPi^C(5 of Br^fs,: witl^a iJQfe:of aipro|)er
2^4 ibq>]Qd Si!U|ffi^cc:& arf i^..!:^ 6, the At><!naMi«ti« the-kaft
poiTiblc, i^/k. T4-, as above in the like Convex^. . ..
L^^ H^|iC6 the Ola^Tef of C(iiiu»on^peAai;iAiiOtt|^ tq hsve
fhe Figare of the Convex ia Jri, 17« .and thg£eH»Dd.Giaiq»
Y^ch ihprt'figbted Pe9|4« i^ft^ioiigbt t0 bo iitfilkiQilicariBt «
Ijre feil Hjention'iJ. , ; . \ 1
1; 4Q. Jn^U t|>6 above mciMiQn'd .Glaffin the &me Apeiturei
^^[^Kn^s, and focal DifV^u;e is {uppofed,.4^.ibat.th«|C:difT
^K v^ nothing \i\it the Figure arif^ng fconuthic^ vacioufi. MagaU
iud« and Poiuion of their R^dii r^^vejyu. B\^. lA^zMt
6i^jB> aft weii^vjc fbcw^, thf :Ai?<|Ha«on «auW hjrihe Figore
Ip^ara (ofsnaU a Fioportion to that: 1;^ the^ dificnmi: Kefraogi*^
l^y. of K^-ySf the Perfe£Uoa of* rf frft£kiiig Tel^deopet &••
comes defpera^e^ ai^d (san o^ljT adinis lof Iii^royffiiieiit b/ isit
Ci^afiog ^eir Length.
^^,4i, . Fiona, he^ce long Tclefccipe& becaari«iof,commin.Ufe »
mii^.&^i were the Jsnpravem^ou of this Soiti^thac for
viewing the celeflial Bodies . tha Tube* .<>f (he Tekftope was
^ro,wn afide» and a Method invented by Hii§mm of m|fca->
iring them with much greater Eafe, and of* a greater Lengtli.
"iox he QOntrived to fix the C^je^-Glafi upon the Top.^f ik
hx^g\k^\^t?Q\e^ anddireded its Axis* towards /any Qi^cA
by,aie?Qs of a Sil^-LiVe coming doiyn frpm^ the^Giafs to thcf
Eye-Glafs below. In this manner wete Teiefcopes made tt>
$JiqUngtJi.of,i^3JSect- .. ,♦...,...
, , 4z../rh^fe were calPd Aerifii'Iekfc^pe^ aabcitig ^kAyoAk-
0«Jt a Tpbe,. in .a dark Night \ for the Uic ofe a Tube^ is not
o^y to dired the GlafTes, but alfo (0 jopakje: the FM 'dark
y^hexe. the. Inpges of ,pl:yf£U are formed i for: i^ Telefcepes,
as well as in the Gtsy^r^ Qbfyurti^ wOr Ought feoiftve s<l<9tiiea*
L%bt come to the Eye than what proceeda from dur l^ttorea
made of, the 01^^ ^hroad. . . •. : w.
43. In order to underiland in what Proportion Telefcoyes
ar£ tO'be Ien§th^n'd, fo that they ihal} magnify m any pro-
pofed Degree wi(h the fame pifiiqdnefs and Brightne& el.th»
Objcd, . we are to.confider that the Indiftinftnefe of Vifion
confifts in Miy iica the ferjihh Image of a Lad Toi/t( in |ic
Ohjeii is n:i a ^dnt in tke Imog€y hut a, circ^r J^^i ^4
Size
O p T I c *• zB%
Sfeetocircumferibci die Image, and ct* eff^alf
fuperfluoas or ektmneom Ray«, that fo Ac Gbjedk
it^y iappear as diftind «!( poflH^. '
As' the Image is formM by Reflcftloft, the
Ookt two conagttoas Points in tht Objeft make two of thofii
Jlrets ift^tfa imge, whofe Ceniertf atie eontigaoos s -eAd there^
fore as thofe two Areas are mixM ahnoft entirely with each
other, the Reprefimtation of the fiid two Points in the Ob^
jiBft is not difthnabatconfuTed.
: 44* And fiace this is the Cafe with refpea to evcty od^r
Point in the Objedl, *tis evident there will be a Mixture of
To many Poinif of an CH>jea in ^tty Point of the confined
BKtore, as there are Porots in the Circle of Aberration^ fincb
the Center of any one Circle of Aberration will be G0Vei<4
by all other Circle of Abetration. whofe Cc^ers fW'^Ml
the ^FerimeltBriof' the 6xSt niention*d Circle ; or,' i«i* oIlM
W;ofdi, there will be fueh a Nunrber of Points in the Oll^
fnix'd m any one Point in the ^onfiifed Irilagei ai is ptapbr^
donfd to the Area of the Circle of Aberration.
45. Hence, fince this confufed Reprefentation of feveAl
Foists k one is iApreisM on the keana by^ the EyeGbfi,
and from thence eon?eyM to the Common Senfory, it appears
f^t fifi'IndiJH^nefi of an Ohjea is as tht Area of a Circle of
J^pratum imth Foius of a^elefcope^ or as the Square of ita
Diameter*. -\ :
JL '46. TolUudraj^ this* Matter, let A be a gitren Point, BC Plate
an QbjecVGla^of a Telefcope, BC A a^ Pencil of Rays co- XLIX,
ming from thrf'Bokit npon the Glafsi each Ray, AB, AC?, Fig. 5.
V^ill ^ fo refjraAed throu^ the Lens, as that the moft re-
frangible Part of each will meet and iitterfed each other in
Ae Point F in the A»s> the mean refrangible Part will go
to ci and theleaft refrangible Part .will meet and interfed the
snoft refrangU)le On each Side in the Points D and B ; there-
ftte DB will be the Diameter of the confufed Image or Cir-
'de«ofAbernitiO0S:49D^E,«id fits Center.
. 47. Let HI be the Bye-Glafs, and G its Center $ tlien
mil the Angle DGE be that under which the Circle of Ab-
ccrations is feen qat^ the £ye-Gla6^ and consequently at the
Eye, (as we have (hewn already). Bat this Angle is as the
Sobienfe 0£ diitCtiy; and aa the Perpendicdar G^ inverfely»
. Uiat is, DGE is as -pr- i for it increafes as D£ increafes while
\sc
Gf r^fnaioi the fame, and as Gr decteafes while D£ is con-
iUys
J^ofspf every Sort witl .1* united rwfly i» on^
Point, and wUI therefof&.adjpit of ftp £ye-GIafs
Y Z of a deep Charge,, or ftnall Fo(^ Dift^mce i
and fo the Power of magnifying wifl be,piX)por-
fiant; wherefore, finceDE is s^ways as the Angle DGE^
we have D^ ; ^, and ifo DE^ : £^^ But J>£' u u
the Area of the Circle of Aberration, and thercfprc ai the
Indiftinl^nefs of Vifion ; confequeptly the apparent IndHUnfi-
le^ofagiFeaObjeawill^beas^ — . ^
48«, Timef<3^Q tlie Diftinanffs-.^f .Vi&w. wi^ be 4»
sr^i or, becade DE r=: iS CB tire Diameter of die A-
|»ertim of the ObjeaGlafi^ therelbrie 3E* will beas Cfi^ 2
iadib^die Diftiaaaels of a gnnen O^eA wil^udwa^ i?e at
^^, that is, M the Sfiari tf the fnudTMftanu of thetye^
Clafs direSly^ ^and as the ^ptare if the Diameter or Ana of
lAiJpertUiifimlfitfely.
** 49. if then itt any onefefrading Tdefeope thie Diffiodb-
tit& of an Obje£t be reprefented by n^» and inaDy other
Tdlefcopc of the fame Sort by -— - ; then if ^-i- =5
^, we have BC* x Cr* =^ SC?- x Gc^, or BQ x Cr =
9C X Or ; and therefore BC : S€ :: Gc :Gc; that is, tmoo
i^frii&ing Telefcopa Jhe^ an OijeA e^uaJfy difinBy nvhen the
'Dhffte^ersof the Jpertures of the^hjea-Glaffes are a$ the focei
Plfiemees hf the Bye-Glafes.
50. In reflefting Telefcopes the Diameter of the Circle of
I . . ... : y3 ' j,3 - , 1 •
Abenations was PQjs: -^^ =%;? » (fc^potor*D 3= za ss
pfametcr of the Slphere j fee Jrtule 24 ) whence PQ^ =;;;
~. Let F = focal Diibnce of the Eye-Glafs, then t)^
, PQ5 *i • '
fcdHBnftnds ^ of Viflcm wHl' ba as ~^ (Ankte 47.)* iS? /
I.* ■..♦/.
^6 ... .. -
;,j ttpnall^
Optics, i 83
ci(^mlly greater ; for it will be ia a Prc^mtioit
compounded of -^ and -j-** if ^^ly one Ey^
Glafe Y 2 be ufed. Thus, in Numbers, fuppofc
Qj zx, 12 Inches, flG = 3,5; Gk = 18,
^d ^/ = I ^ then will — x — = =6i,7(
5r. Therefore if the ikme Psuts ih another Tekfcope ef
AitSoit be iippdcirttA by -^ rs.— ;L— ^ oni face did
Kftinafaefs in each will be at ' < > *™^ — 6— 5 *^*«^ »
^ y y
we fdppofe^^ Objea feen equally diftrnfi in both, we Atll
have D^F"^ x y*^ = D^J* x/, or D»Fy3 5s i>*Fy^4
Hence I^ = ^^ •• fc • ^ 5 **^ ^» ^efiiaing Telefcopafiiw ak
Oljea equaliy Mftina^ when the focal Difianca 9/ fhe £jg»
Qit^et^n w th§ Qihsof fht Omrntmnff tb$. Imrg§ SftemU^m^
Ohjea Mttak^ £nnigd iy the SfKwe 0/ the Dimmer ef th
Sfheres to which they or 4 greutid, er by the Sqitari tf the focal
Diftauce of the Metals-,
52. In any Telefcope or I)oidiIe Ificrofeo^, the BH^jjbU
nefs of a given Image will be as the Qoantiiy of L^hc bff
which it is ihewn; that is, aa the- Area of |hc Ap^ure ex
the Objefl-Glafs, or a^.the Squ^e of the Diameter.
53. Alfo, if the Area of the Apert«»e of aa Objcft-GliA
be ^en^ the firightne& of the Image will be inverfely m
ita Ai^a, or Square of its Diameter or Breadth : For the Ide
the Area of the Pidure is» the greater will be its BngbitBda
by the farae Quantity of Light. 7
54. Therefore when neither the Apertures of Uie QhSk$
nor the Ampliication^ of the PiAore are given, or die fiuse,
the Brightnefs is as the Sqjagre of the Diameter of the Aper-
tures diredly. and the Square of the linear Dimenfions of^
ihe Pidtires inverfely;
55. Hence in all Sorts of Telefcopes a given Ohjed ap-
pears equally bright, when the Diameters of the Ape^uret
are as the linear Dimenfions of the Pidlures : But the Pi^ure
Jb larger as the focal Diftance of the Objed-GIafies is fo, and
tfp arthe ibeal JOifiaooe of th^ EyeGlafs is \tb ; therefore
. ; nearly;
»a6
Optics.
jtpBmif ; Whence hy fiach a Telcfcbpe the I>ngth
ofaftObjed: will bccidgnified go times, t^e Sur-
face 2500 times, and the Solidity 125000 times ;
yi^t the Tekfcopc not above 20 Inches long; an
EffeO: equal to that of a refFa6ting Telefcope 16
Feet in Length*
\'Ai to At CapteraOifcuray. and Mdgic Lani-
;^.lin^.Dinieiifioi)« of Pi&ifcs aie lu tbt focal D^bnees of
the O^ed^laiTes diieaiy, and as the focal DiOances of tlie
£ye-Giaffei inverfely. Let thefe be reprefented by. P«M F»
tod {,/, in any two Tdefoepes; let D, 4 be tke Diameters
of the Apertures, and L, I, the linear DlqieiiiioQi of the
¥ F
t'iSkaxes ; then we have D : d n L: i i: -j • -7:9 when Ob«
jedsappeaiieqiiallf bright xri both. * - '
c6. Hence, fince the Brightnefs of a Pidure or Image is
jvt D* f^ . F
asg (^/. 54.) =^pr-» 0>ecaureL= j by the laft)
therefore If D or f be'^aeh increiifed in ftn^^Ratio, the Di-
llinfbefs will ivmam the fame as before, (by Jrt, 49 ) and
the linear Dimenfions of the Image will be diminifh^d in the
fame Ratio, (fince L is inrerfely as f) but the Brightneis of
the Image will be increafed in the quadruplicate Ratio of
what it had before. For,
' jf7/ Suppofe P Of thd focal Length of the Telefcope given,
then the Brightnefs of the Figure will be in this Cafe aa
D^ f ^ ; and if D and f be increafed each in the Ratio of i
txi /*, th^n will th^ Brighttoefs be in this Cafe as «r* D* f *«^
zzD^f*^^; fo that the former Br^tneis is to this as D^f^
to D^f^>»\ that is, as i toi»^; which Ratio js quadrapli*
cate.of the Ratio i to atr.
F
58. 9eeaufewehadl>: y, or J}f : F, when Obje£U ap^
pear equally bright, (by^/.cj.) and when they are Akwh
equally diftkdt we hadD:f (by^/. 49)2 therefore in le^
£»{tiQg Telcicopes of vasiona Lengths, that Obje^s may ^
l^ar eqoalty bright and equally diftinA, it is-requiidtetmit.
jy* i F, and f» ; F, Or that D : f : •¥> that is, the Dia^
mtiif tf the Jpirtmrt anda^o the focal length if the Eye-GUfi
Jkmldea^ he at the Sptare Roet of the fb^at Dijianee or tengt^,
rf the Tele/cope. ' '
f
Opt I cs* 'i'Bj
hrH^'Xi^y both pcrfoim their JSflfe&s by afingle
X^ns '^ t}}^ former bang oaly the ObjeftvGkis'Of
a long Telefgope applied in a Sciaptric Ball to At
Hole oJ^a Window- Shutter^ in a dark^nVi Room ;
which ^ivcs a Jively Pifturc of all the* ObJeAs
59. In thb Cafe likewife the £jiiMr Dimnfions rf ihe HBure
•r Image 'ure in tbefam fubdupUcate Ratio of the Length of tbi
TeUfcopei bccaufc^ |ls was flicwn, [4rt. 55)^* ^^" ^^"
ma&Qw^0xt diredljr as tbe Diameter of the Aperture, wlMch
is here (hewn to be as the Sqaare Root of the Length of the
Tekfcope.
60. In Kfleding Teleftopes, when tbe Diflittanefi b pteR,
we have t : i^. and therefore y^ : D»F. (See -*/iV/f 51.)
Alio when die Brigtitnefi it g^ven we ]iave y : -^ [Jrt. 55,)
therefore F:—.. Hence, when the Diftinanefs and Bright-
D'
nefi are bodi:guren» we fciwe jr* ; (D*F) : -^, or jr* : D',
orjr:D*.
61 . The linear Dimenfions of the PiAoie -^ were as y ;
that is, in this. Cafe, § : ]>^ and therefore D *. Pp^ ;
i?
whence F : — : D*. Hemo in refloBing Ttkfccfa of,£f-
furem Lengths a gwiM ObjeS nviH appear equaily MftinB and
hrighty mobtu ihiDi^unaers <f the OljeQ^Metals are as the BU
fnadrate Roots of the Cuhes of the Dtamttirs of the Spheres Or
focal Lengths of the Specula i or; 'mhen the focal JHftances of
the Bye-Glaffes are as the Sifmadrate Root of the focal Diftamce
tfihi Specula. ; ^ :>
. 6a. MfimAmg t» the Theorems in Jrt. 48, 49^ l/U^Ifm*
gens calnilattd a DAle of the lincir Apertorg of the Ofcjofifc^
Glaft, the focal J>itanc!e of d» fi^^iafi, and the liMor
AmplificaticMi or .magmfying Power of the l^elefeope; fram
one which, he fotind bf £xperience was obnft^nfted in the .^eft
Manner. I have reduced his RUnland Meafivsa to l^agBfi^
Teec« Indies^ and DecifflidParts^ atfoUowi*
which
2^8 Optics.
Whkh. lie before it, in true Perfpeflriw,' but in afi
jmertidPofitumj on a wlute Sheet or Plane held
I
>««/
Um^J
F»«/ J
.
Dijttmu
pertm'* of
Diftaitt ej
Magmfyr
tftht
the OijeB-
the Eye-
ii^F0tv
Ghfi.
Glafi.
Glafi.
tr.
,
Feet..
Inch. Dec.
Inch. Dec.
1.
0,y4S
0,605
20
. 2
0,76
0,8+
27,6
3
0.9+
1,04
33.5
4
i»o8
1.18
39>S
5
i.ai
uii
44
6
».3»
1,45
49
7
>.43
1,58
53
8
MS
1,69
55
9
1,62
i.7«
59
lO
'»7i
1,88
6«
»S
2,IO
2,30
76
20
2.43 .
2,68
88
30
3.00
. 3,a8-
108
40
3*43
3.76
125
r
3.84
4,20
140
60
4,20
4,60
152.
70
4.55
5.00
164
80
4.83
5.35
176
90
5.»5
5,65
187
100
5.40
5'95
197
IZO
i.90
6,52
2t«
6 J. Sinc<$ h has been ihews tiiat the Errovs irifa^ 'fitwi
tbe diiFerent RefrangiUlity of Rays, and, of eonfeMrade die
IndilUadhieft of Viiion l^ r^Maag TekibDpe» ft lb veij
great, a Qgefiion nHif be put. How it comes to pafe Ol^v^
appear through fuch Telefbofies ib diftkuEk at tfae)r do ^ To
which it maybe anfwer*d, 'tis becatife the ermk Ri»yr mno
not uniforiidy fcatter*d over ail the Axek of tift CiRloof Ab-
crratioa/ but coUefted nimitely more deafely ia- the Ceater
ihaa in any other Part of that circular ^pace, groiriag tmrwi
and rarer towards the Circnurfbrence, wtBre, inr comparifi»v
(hey are uiiaitely rare, and afftd not the S^fe any where
but in the Center^ and v^ near it, o& thataoobiint.
64. Tis fijthcr to be «bfcr99d, tfaa^die4Mft hiiiibioiia of
: ^ at
Optics. 289
flt the Focal Diftance of the laid Glafi : And on
the other hand, the Ma^ic Lan thorn is only a large
all the PrlfmatJc Colours arc the Yellow and the Orange ; thefc
afifedl the Senfes more ftrongly than all the reil put together ;
and next to thefe in Strength are the Red and Green. The
Blue compared with thefe is a faint and dark Colour, and the
Indigo and Violet are much darker and fainter; fo that
thefe, compared with the ftronger CoIoUrs, arc little to be
regarded.
65. The Images of Objedls are therefore to be.placednot
in the Focus of the mean refrangible Rays, which are in the
Confine of Green and Blue, b^t in the Focus of ihofe Rays
which are in the Middle of the Orange and Yellow, there
where the Colour is moft luminous -and fulgent; that is, the
brighteft Yellow, that YcUow which inclines more to Orange
than to Gl-een.
66. Now it has been Ihewn {Awiot. CXVIII. 9.} that the
Diameter of the Circle in which both thofe Colours will be
contain'd is but the 26cth Part oi the Diameter of the Aper-
ture of the Objed-Glafs; and farther, about \ of the brighter
Halves of the Red and Green (on each Side) will fall within
this Circle, and the remaining \ without it, which will be
fpread over twice the Space nearly, and^ therefore become
much rarer. Of the other Half of the Red and Green, about
one Quarter will fall within this Circle, and \ without, and
be fpread through four dr five times the Space, and therefore
become much rarer. Alfo this extreme Red and Gccen is.
much rarer and darker than the other Parts of the fame Co-
lours ; and the Blue and Violet being much darker Colours
than thefe, and more rarified, may be quite neglc^ed.
67. IlenCe -the lenfible confufed Image of a lucid Point is
fcarce broader than a Circle whofe Diameter is the 26otii
Part of that of the Aperture of the Glafs, if we except the^
dark mifty Light round about, which we fcarce regard. And
therefore in a Telefcope whofe Aperture is 4 Inches, and
Length 160 Ytfity it exceeds not 2|'', or 3''; and in aTe-
lefcope whofe Aperture is 2 Inches, and Length 20 or 30
Feet, it may be about 5^ or 6", and fcarce ilbove. And th:s
anfwers well to Experience ; for it is obfcrvable that in Tcle-
fcopes of 20 or 30 Feet long, the Diameters of the Fixed
Stars appear to be about 5^ or 6*^, or at moil not more than
8'' or 10''.
68. Now if we fuppofe the fenfible Image of a lucid Point
to be even a z^5otk Part of the Diameter of the Aperture of
290
• Optics*
convex Lens, with a (hort Focal Diftance, 1?vhiclt
by' being placed at a proper Diftance from fmall
the Glafsy yet wUl this be hiach greater than if it were only.
from the fpherical Figure of the Glafs^ 'viz, (in an 100 Foot
Tclcfcope) in. the Ratio of -i- to — — — , w of 1206
250 72000000
to I. (See Jrt, 20^ 21.) Therefore the Image of a lucid
Point would Ml be a Point, but for the various Refrangibi-
hty of the Rays ; and this alone is the invincible Obflacle ta
perfedl Viiion by any refrafting Inftruments.
PI XLIX ^9* '^^^ magnifying Power of a refra£iing Tclefcope is
pjg ^ ' thus eftimated. Let AB be the Objedl-Glafs, and CD the
^* ' Eye-Glafsj and let HFI and GFM be two Rays coming
from the extreme Parts of a diilant Objed, and crofling each
other in the Center F of the Glafs AB. Then is the Angle
GFM =: IFM that under which the Objeft appears to the
naked Eye; but IBM =: CKD is that under which the
Image appears as magnified by the Eye- Glafs CD. But the
Angle lEM is to the Angle IFM as LF to LE, or <i/ the
focal Diftance of the Ohjea -Glafs to the focal Diftance of the
Eye-Glafs ; and in that Proportion is the Objefl magnifiedy-as
was oblierved before in Jrt. 55.
fig, 7, ' 70. The magnifying Power of a reflefling Telefcope is
" thus computed. The parallel Rays K B and L E are reftedied
by the large Objedl Metal AF to its Focus <r, where the
Image IM is form'd ; which Image is defined by two other
Rays NQj PQ^ coming from the extreme Parts of the Ob-
jed at a remote Diilance, and meeting in the Center of the
large Speculum at Qj for it has been (hewn that the Objedt
and its Image both appear under the fame Angle from the
Vertex of the Mirrour. (Annot, CXXV.)
71. ^ow if/ be the Focus of the fmall Mirrour GH,
fuppofing the Image were formed in the faid Focus/, (that is,
that both the Foci a and / were coincident) then the Rays
proceeding from the Image IM will proceed parallel after
Kefieclion, and produce dittind Vifion of the Image, which
will then fubtend an Angle lOM at the Center O of thtf
Speculum GH; which is to the Angle IQM, under which
the Objeft appears to the naked Eye, as aQj^o aO or/O.
So that the magnifying Power would in this Cafe be as
fO
jz. But to inpr«a((t ^U magoitybg Power, the Image IH
a:gnfpafent-
\
Optics; 291
tranfpareftt-coJour'd Pidurcs or Figiifes, JForms a
large *id furprizing Image thereof at a grdat Di-
•
& not plated in the Focus of the fiiiall Speculum; bat sU jI
fmall Diftance beyond it; by which means the Ray? coming
from the Image to the Speculum GH will be rcfleded con-
verging to a diftant Focus R, where a fecondary large Image
IM is form'd from the firft Image IM; which Image IM is
feen under the fame Angle lOM with the former from the
Center of the Speculum GH, but from the Center of the
Eye-Glafs TV it is feen under the hrge Angle ISM. But
the Angle ISM is to the Angle lOM as OR to SR ; where-
fore the fecond Ratio or Part of the magnifying Power is that
73. Confeqoently, the whole niagnifyhig Power of thfe
Tclefcope is ^^x --^ (becaufe in this Cafe fO becomes
aO). Or, in other Words, the Angle NQJP, under whidi
the Objea appears to the naked Eye, is td the Angle ISM,
under which the krge magnified fecondary Image /M appears
to the Ey; through the Eye Glafs, as f^:^!^. Such is
aO X SR
the Theory of the Telefcopc firft contrived by Dr. 7. Gre-
gorie^ and therefore caird the Gregorian Teie/cope; but it re-
ceived its lafl Improvement from the late Mr. HatiUy^ and is
how in cbmraon Ufe.
74. A fmall Alteration was made in the Stni^ure of this
Telefcopc by Mr. Caffegrain^ viz in ufing a convex Specu-
lum GHy inllead of the concave one GH. Now if they are
equally fpherical, that is, if they art Segments of the iame
Sphere, then vvill/ be alfo the virtual Focus of the ConvcjC
G H ; and if ail other Things remain the fame, the firft Image
I M will be virtually the fame as before, and the laft Image.
IM will be really the fkme ; fo that the magnifying Power of
this Form of the Telefcopc is ^^-~-, which is equal td
that of Grtgorie^s Form.
75. And to fhew this is tL curidiis Propofition, I (hall give PLXtlX.
the following eafy Demonftration thereof. Let HD £(e a Fig. 8.
concave Speculum, and EC a convex one, both described
with the fame Radius CD, on the common Axis BCD : The
Point N, bifedUng the Radius CD, will be the Solar Focus*
to eath Spe^uluta. Let F be a radiant Point, from whence
T i ftancei
292 Optic «•-
ftance -, in order to which, it is ncceflkry to illu*-
minate thiem very ftrongly with the Light of the
a Ray FH 15 incident upon the concave Mirronr in H, or to
which the Ray K E incident upon the convex Mirrour tends ;
both thofe Rays will be reile&ed to the fime Point B in the
Axis, and in the fame Line EB. Laftly, let GF be an Ob-
je£b ; the Image thereof ab form'd by the Concave is equal
to the Image A B made by the Convex. This is evident from
dr dr
the Theorems , , = /, and • = /, thofe Spe-
zd-^r r — zd ''
cula refpe£tively.
76. For as // =r FC, CB :=/ in the Convex ; fo in the
Concave let FD = 2), and Y)^z=.F\ and then we have in
the former d \ f v. zd-^-r : r, and in the latter D : F::
r — zD\r. h\xi D'==id'\-r, tYitxtioT^ zD z=z zd-^-zri
.whence r — zD =z 2//-|" '"» confeqacndy d : / :: D : F^
that is, CF : CB :: DF : DB. But the Objed and Image
are to each other in the fame Ratio in either Glafs; and
therefore fince the Obje^l is the fame iii both, the Image wiH
be fo likewife, or A*B = ab,
Plate 77' 'S*'" -5^^ Ncivton Order 'd this Telefcope to be made
XLIX. in a different Form or Manner, as follows. AB'JD was a
Fig. 9. large o£logonal Tube or Cafe ; E F a large polifh'd Specu-
lum, whole Focus is at ^ ; G H a plane Speculum truly con-
centered, and iix'd at half a Right Angle with tlie Axis of
the large one. Then parallel Rays ^E, ^F, incident on the
large Speculum EF, icflead of being refleded to the Focus 0^
were intercepted by the fmall plane Speculum GH, and by
it refleded towards a Hole cd m the Side of ihe Tube, croC-
iing each other in the Point O, which h now the true focal
Pomt ; and from thexicc they proceed to an Eye Glafs e/^
placed in that Hole, whofe focal Dillarxe is very fmall, and
therefore the Power of magnifying may be very great in this
Form oi the Telefcope ; becaufe ihe Image I M is made by-
one Reflwdion, (for that of the plane Speculum only alters the
Courfe of the Rays, 2.i\i\ adds nothing to the Confufion of the
Image) and will for that Reafon bear being viewed by a Glafs
of 2i very deep Charge, in comparifon of an Image form'd .
by differently refrangible Rays.
78. This Telefcope is a very good one, as to its Effed or
Performaiice, but is not fo coaiinodious for common Ufe as
^liofe of the Gregoiian Fcr.iJ, and is tlierefore now pretty
jnuch-laid aiide. They who would (ee a larger Account here-
i . : Candle
Optics. 293
Gandle thrown on them by another very large and
very convex Lens (CXXIX).
of may confult Sir Ifaac^s Optics, and fercral Tbilofophical
Tranfailionsy where he deicribes it at large, and the Reafons
)vhich induced him to make choice of this Stra^are rather
than that of £)r. Qrcgorte: Or fee a compendioos Accoant of
the whole in the latt Edition of Dr. Gregwie^ Elements of
Optics.
(CXXIX) I. The Camera Obscvra, or Darien^dRoom^
IS mside after two different Methods ; one is the Ohfcura Ca-
mera or Darkened Chamber at large, and properly fo call'd ;
that 15, any large Roopi or Chamber made as d^rk as poffible,
fo as to exclude all Light but that which is to pafs throogh
the Hole and Lens in tne Ball fix'd in the Window of the faid
Room.
2. The other is in fmall, and made in various Ways, as
that of a Box, a Book whofe Sides fold out, ^c, for the Con-
veniency of carrying it from Place to Place, for taking an
Optic. View in Pifliire of any propofed Place or Part of the
Country, Town, fsV. and hence it is call'd the Portable Ca-
mera Ohfcura.
• 3* 1 he following Particulars are to be attended to in this
Philofophical Contrrvance. Firft^ That the Lens be extreme-
ly good, or frtfi from any Veins, Blebs, ^c, which may dif-
torc and bu'emifh the Pid^ure.
4.. Secondly^ That the Lens be always placed dire6Hy againft
the Obje<5l whofe Pifture you would have pcrfe\^!y formed to
contemplate ; for if the Olafs has any oth^r Pofition to the
Object, the Image will be very imperfect, *indiftin6b, and con-
fufei
5. Thirdly Care ought to be taken, that the Ball be fufE-
clently large, and the frame in which it is placed not too
thick, that fo there may be faificient Roon> for turning the
Ball f^vzry way, to take in as n^any Objects as poffiblc, and
to render the Ufe thereof mofl complcat.
6. Fourthly y The Lens ought to be of a juft Magnitude
or Aperture ; for if it be too fma'il, the Image will be obfcure.
9nd the minute Parts not vifible at a diftance for want of re-
quifite Light. On the other hand, if the Aperture be too
large, the Image will be confufcd, and become indiftindt by
too much Light.
. ^. Thcrctore, Fifthly^ if by Experience I find that an
T 3 The
?94 Optics.
The Solar Micr^fcope is of the fame Kind with
the Magic Lanthorn •, only here the Objefts are
yery fmall, and ftrongly enlightened by the Sijn
Aperture of 2 Inches Diameter is beft for a Lens of 6 Feet
focal Diitance, I know (from what has been faid in the la^
Jnnotation) that the Diameter of any oth^r Lens of a dif-
ferent focal Diftance ought to be in tho ful)duplicate Ratio of
6 to the fdid focal DiHance, that the Object, or its Image
rather, may be equally bright and diftinft in both.
8. Sixthly y We ought not to attempt to exhibit a Pidure
pf Objeds in a dark Room, unlefs the Sun fhines upon or
lirongly illuminates the O^jeds ; for mere Daylight is not
fafHcient for this Purpqfe, the greated Beauty in this Phseno-'
menon being the exquiiite Appearance and Contrail of Lights
and Shadows, none of which can appear but from an Objedl
placed in the Sun-Beams ; without which every thing looks
^ark and dull, and makes a difagreeat^Ie Figure.
9. Therefore^ 5f«i/f«//fi^, the Window, pr that Side of the
Boom where the Sciopcric Ball is ufed, ought to look towards
that Quarter diredlly upon which the Sun ihines, that fo the
illumined Sides of Objeds may prefent themfelves to the Lens,
juid appear more glorious in the Pi^lure. .
lb. Eighthly y Hence it is eafy to infer, that the beft Time'
f)f the Day for this Experiment is ?ibout Noon, becaufe the
• 8un-Beams are then ftrongeft, and of courfe tlie Piflure mod
luminous and dillinft : Alfo that a North Window is the beft \
fhough for viewing the Shadows in greateft Perfeftion, aii
]paft or Weft Window will anfwer the End beft.
1 1. Ninthly y As the Image is form'd only by the reflcftecji
Rays of the Sun, fo due Care (hould bp taken tliat none ojf*
the Sun's diredl Rays fall on the Lens in the Window ; for if
fhcy do, they will, by mixing with the former, greatly dif-
turb the Pii^ure, and render it very confufed arid unpleafant
^o.vicw-
12. Tenthly^ As white Bodies refledl the incident Rays mbft
copiously, and black ones abforb them moft ; fo to make the
Pi£lure moft perfed it ought to be received upon a very whitq
Surface, as Paper, a painted Cloth, Wall, fsfr. bordcr'd
round with Black, that fo the collateral Rays which comp
from on each Side the Objedl may be ftifled, and not fuiFer'4
to difturb the Picture by Refleaiqa.
13. Thefe are the neceflary Precautions for the due order-
ing Qf the ypious Circujn(l:apces of this Experiment. I ftail\
through
Optics. 295
through a concave Lens ; they are alfo magnified
by a fmall Lens, of a very fliort Focal Diftance,
that the Images may be thrown large and diftinftly
now enumerate the {evtrH principal Pk^tnomena of the Dark
Chamber. The Firft of which is, that an exad and every-
way fimilar Image is formed of an exteinal Objedi ; for Pen-
cils of Rays coming from all Points of the Objedl will repre-
fent thofe Points in fuch a Manner and Poiition as will be vexy
proportional and correfpoodent to their refpeflive Pofitions
and Diftances in the Obje^, fo that the Whole in the Image
ihall bear an exaA Similitude or Likenefs of the Objed in
tvtry Refpedt.
14. The Second Pb^enomenon is, that the Image will bear
the fame Proportion to the Object, whether a Line, Super-
ficies, of Solid, as their Difbmces from the Glafs refpedively :
This is evident from what has been faid relating to the Effect
of a convex Lens. Hence the larger the focal Diftance of
the Glafs, the more ample will be the Pi^ure of the fame
Objed, but the lefs will oe the Space or Compafs of the Plan
or Perfpeftive View.
15. The Third Pb^enamenon is, that the Image or Pidure
of the Objed is inverted; and this is not the £fFe£l of the
Glafs, bat the crofiing of the Rays in the Hole through which
they pafs into the Room ; for if a very fmall Hole were made
\n the Window> Shutter of a darken*d Room, the Objeds
without would be all feen inverted, thofe which come ^om
the upper Part of the Objed going to the lower Part of the
Image, and vice ver/d. A{1 that the Glafs does is to render
the Image diftind, by converging the Rays of every Pencil
to their, proper Focus in the Pidure, the Poiition of each
Point be'ing the fame as before.
16. Tht Fourth Pb^enomenon is the Motion or Reft of the
feveral Parts of the Pidure, according as thofe of the Objed
^re in either State. The Reafon of thb is ytry obvious ;
and (his it is that gives Life and Spirit to the Pamting and Por*
traits of Nature, and is the only Particular inimitable by Art*
And indeed a more critical Idea may be form'd of any Move-
ment in the Pidure of a darkened Room, than from obferv-
in^ the Motion of the Objed itfelf : For Inflance, a Man
w(^lking in a Pidure appears to have an undulating Motion,
or to rife up and down every Step he takes ; whereas nothing
of this Kind p o^ferved in the Manhimfe)f, as view'dby th«
T 4 on
1396 Optics.
on the oppofite Wall of a darkened Room r
"Which, it well performed, is one of the moft ex-
quifitely curious and moft delightfully furprizlng
1 7. The "Fifth Phenomenon is tfee Colouring of the Oftk
VtSure\ every Piece of Imagery has its proper Tints and
Colours, and thofc always heightcn'd and rcnder'd more in-
tenfe than in the Objed ; fo that in this refped it is an Im-
provement of Nature itfelf, whereas the Art of the greateft
Matter can only pretend to a diftant Refemblancc and faint
Imitation. The Reafon why the Image is coloured is becaufe
the feveral Points of the Objeft refleding feveral Sorts of co-
lour'd Rays to the Glsfs, thofe Rays Will give a Reprefenta-
' tton of thofe feveral Points lerpcctively, and in their own Co-
lour, and therefore in thofe of the Object ; but thofe Colou/s
will be heightened, becaufe they are crowded into a lefs
Space.
II. The Bixth Thanomenon is the Claro Of euro, as the ltd*
ham call it ; that is, the Jnrenfity of Light and Shadcfw in the
PiClure: And this, as well as the Colouring, is greatly height-
ened above what it is in the Objedi, by reafon of the leffir
Area of the Pifture. Here every Light and every Shade is
exprefsM in its proper Degree, from the moft brillant in the
one, to the moft jetty Black of the other, inclufive of a won-
derful Variety in the feveral Parts, arifmg from the difFt;rent
Situations of the feveral Parts of the Objccl, and the different
> Angles of RefleAion. A juft Imitation of Nature in the
Diftribution of Light and Siiadows is perhaps the moft diffi-
cult Part of the Art of Painting, and on which its greateft
Perfedion depends. '
19, T\ie Sc<v€nth Vhismmerion is the Optical TerfpeBifve, or
Projedion of the Image, which is not in Piano, or on a Plane,
' as in common Perfpedive, but on a Surface defcribed by the
Revolution of a Conic Srciion. about its Axis, as is evident
from '^hat was cbferved in .^nnot. CXXV. Therefore, though
in general a plane Surface is made ufe of, and may do vtry
vvcll in large Repr? fentations, yet in fmaller ones, as thofe of
the PortdhU Coisnsrus, it is necenhry, to have the Image or
Piflure compleiit, or every where well defined, that it be re-
ceived upon the Surface of an Elliptic Fi:^ure\ and fuch as is
fuited to the middle Diftance of the Gbjeds. But this is a
Nicety which few will think worth regarding, who do not
aini at a very jrreat Accuracy indeed in what they do.
^0. I iliall finiib this Subjedl with an Obfcrvation jhat may
EfFcds
Optics. 297
Effefts that can be produced by any Optical'In-
ftrument whatfoever (CXXX).
be ufefal to PerTons concerned in Drawing, and that b, Tbaf
if an Obje^ he placed juft tnvice the focal Diftancefrom the Gla/s
ivithout, the Image *uiill be formd at the fame Diftanct from
the Glafs twithin the Room^ and confcquently nvill he equal iH
Magnitude to the OhjeSl itfelf The Truth of this is demoir-
♦ftrated in Amot. CXXV.
21. Although every thing that has been faid of the CAmtra
'Ohfcura is plain enough in itfelf to be underftood, yet as a
Reprefen ration thereof may facilitate the Idea, I have here
given a Diagram for thatPurpofe; where A BCD is the Plate IJ«
Profpeft of a Houfcy Trees ^ &c. EF a darkened Room, or Fig. i.
Camera Ohfcura ; on one Side is the Picture GH of the faid
View inverted, fbrm*d by a convex Lens in the Ball fix'd be-
fore a Hole in the other Side IK at V. AH which is fo ealy
'that nothing more remains to be faid to explain it.
(CXXX) I. The Solar Telescope and Solar Mf-
CRO SCOPE, as they ought to make a Part of the Amufement
of every Virtuofo and Gentleman, fo they defcrve a Particu-
lar Account, and the feveral Ways in which they are ufed
merit a particular Defcription, which I fhali illaflrate by a
Draught of each.
2. The Solar Telescope is applied to Ufe in the fol-
lowing Manner. A B reprefents a Pait of the Window-Shutter Fig*, 2.
of a darkened Room, CD the Frame, which (by means of
a Screw) contains the Scioptric Ball £ F, placed in a Hole of
the faid Shutter adapted to its Size. This Ball is perforated
with a Hole ahcd through the Middle; on the Side bc\% .
fere w'd into the faid Hole -a Piece of Wood, and in that is
fcrcw'd the End of a common rcfrafting Telefcope G H I K,
with its ObjeA-GIafs GH, and one Eye-Glafs at IK t and
the Tube is drawn out to fuch a Length, as that the Focus of
each Glafs may fdl near the fame Point.
3. This being done, the Telefcope and Ball are moved
about in fuch manner as to receive the Sun-Beams peirpendi-
cularly on the Lens GH, through the cylindric Hole of the
Ball ; by this Glafs ^ty will be colledled all in one circular
' Spot/v, which IS the Image of the Sun. The Lens IK is
to be moved nearer to or farther from the faid Image /», as
the Diftance at which the fecondary Image of the Sun is
to be form'd requires, which is done by Aiding the Tube
|KLM backwards and forwards ii^ the Tobe LMNO.
Then
^^S Optics.
Tlfen of th^ firil Image of the Smi » will be fermM a ft^
cond Image PQ^ very large, laminoas, and diftindt
4. In this Manner the Sim^s Face is viewM at any time,
without Ofence to weak Eyes; and whatever Changes hap-
fien therein may be daly obferved. The Sf»is (which make
io rare an Appearance to the naked Eye, or thioagh a fmall
Tdeicope in the common Way) are here all of them confpi-
f uoos, and eafy to be obferved under all their Cir^umilanccs
of B^inning to appear, Increafe, Diviiion <^ one into ma-
ny, the Uniting of many into one, the Magnitude, Decreafe^i
Abolition, Dkappearance behind the Sun's Diik, i^c.
5. By the Solar Tei^cfife we alfo view an Eclipfe of the
Sun to the beft Advanuge, as having it in our Power by this
xneaos to reprefent the Sun's Face or Dilk as large as we
pleafe, and confeqaently the Ecllpfe proportionably confpi-
caous. Alfo the Circle of the Sun's Diik may be fo divided
by Lines and Circles drawn thereon, that the Quantity of tbe
Edipfe eftimated in Digits may this way be molt exa6Uy de-
termined : Alfo the Moments of the Beginning* Middle, and
End thereof, for finding the Longitude of the Place : With
Several other Things relating thereto.
6. The Tranfits of Mercury and Fenus over tbe Face of
the Sun- are exhibited moft delightfully by this Inftrument.
They will here appear truly round, well defined, and very
black i their comparative Diameters to that of the ^Sun may
this way be obferved, the Dire£lion of their. Motion, the
TimeB of the Ingrefs and Egrefs, with other Particulars for
determining the Parallax and Diftance of the Sun more nicely
than has hitherto been done.
7. By the So/ar Teie/cepe you. fee the Clouds moft beauti-
fully pafi |;>efore the Face of tiie Sun, exhibiting a curious
SpedUcle according to their various Degrees^ of Rarity 'and
Denfity. But the beautiful Colours of the Clouds furround-
Sng the Son, and refradling his Rays, are beft feeh in the
Pitlure made by the Camera-Gia/s, The fine Azure of the
$ky, the intenfely ftrong and various Dyes of the Margins of
Clouds, the Haloes and Coronals, are this way inimitably ex-
piefs'd. And fince the Prifmatic. Cplours of Clouds, fo vari-
oufly compounded here, make fo noble and delightful a Pha?-
nomenon, I have often wonder'd to fee no more Regard had
^hereto by Painters, whofe Clouds (though near the Sun] are
feldom or never feen tinged or variegated with thofe natural
Tints and Colours.
8^ I cannot here omit to mention a very utoffitai Ph^en^me'
ifon that I obferved about ten Years ago in my darkened
Room. The Window look'd towards the Weft« and the
' ' Spir^
Optics." 29^
Spire of Chicbefter Cathedral was dire^y before it, at the
Diftance of about go or 60 Yards. I ufed very often to di«
vert myfelf in obferving the pleafant Manner in which the
8un pafs'd behind the Spire, and was edipfed by it for fdme
time i for the Image of the Spire and San were vtty large,
being made by a Lens of 1 2 Feet focal Diftance. And once
as I obferved the Occultation of the Sun behind the Spire,
jud as the Diik difappear*d, I faw feveral fmall, bright, round
Bodies or Balls running towards the Sun from the dark Part
of the Room, even to the Diftance of zo Inches. I ob-
ferved their Motion was a little irregular, but rectilinear, and.
feem'd accelerated as they approached the Sun. Thefe lumi-
nous G]Qbules> appeared alfo on the other Side of the Spire,
and preceded the Sun, running out into the dark Room, fome-
times more, fometimes lefs together, in the fame maimer as
they followM the Sun at its Occultation. They appear*d to
be in general about ^V o^ an Inch in Diametcv,. and there-
forie mull be very large luminous Globes in fome Part of the
Heavens, whofe Light was extingoiihM by that of the Sun,
fo that they appeared not in open Daylight j but whether of
the Meteor- Kind, or what Sort of Bodies they might be, I
could not conjefture.
9. The Solar Microscope (faid to be the Invention of
a German^ from whom at leail it had its Name) is a inoft ca-
rious Improvement in Optics, and deferves to be greatly va-
lued ; as it is the befl Method which Nature will admit of,
pr Art can furnifh, for magnifying and exhibiting very fmall
tranfparent Objedls to the View of Spedators.
10. To this End it has been contrived very commodioufly ^u^ lt
in feveral different Forms, two of which I fhall here illufbatc pjg -
by Diagrams. The firfl is as follows : AB is a ScAion o( ^' V
the Window-Shutter of a dark Room, CD of the Frame
containing a Scioptric Ball ^F; in the Fore- part whereof is
fcr%w*d the Tube GIKH, at one £nd of which is a Lens
G H, which by converging the Sun-Beams into a narrow Com-
paq does flroiigly enlighten the fmall Objed ab pUced upon
a Slip of Glafs or otherwife in the Part of the Tube NQ.
where a Slit is made on each Side for that Purpofe. Within ^
fhis Tube there flides another Lin«M, which contains a fmall *
magnifying Lens ptn*
I f. By moving the exterior Tube IGHK one way and
the other, the Glafs G li will be brought to receive the Rays
of the Sun diredUy, and will therefore moft intenfely illumi-
nate, the Objea ab. The other Tube LM being flid back-
wards and forwards will adj«ft the Difhoce of the fmall Lens
mnf fo that the Image of die Objeft ab ihall be made very
i * * diftina
loo
Optics:
iiSilnSt on the oppofit^ Side of the Room at OP; and tlie
Magnitude of the Image will be to that of the Obje^ as its
Diftance from the Lens mn is to the Diftance of the Objeft
froitt it, as has been Ihewn in Jnftot, CXXV.
1 2. Thus for Example : Suppofe the focal Di(!ance of the
Lens mn to be i Inch z=: r, and let tha Didance at which
it is placed from the Obje6l be i,i == ^; then if the Lens be
double, and e(|ually convex, (as ufual) the Diilance of the
Image will be z= / = no; therefore the Image
will be I ID times larger than the Obje^ in its linear Dimen-
iaoas, and x lo x i lo =: 12100 times larger in Sarfac^, and
la Solidity it will be 110 x 110 x no =; 1331000 .tia:^e&
laigei than the Obje^.
*3.. If the Lens, inftead of i Inch, were but 4 ^ Inch
local Diilance, then would the Diameter of the Image be
twice as large, or 220 times larger than the Objedt ; and the
Superficies 4 times larger^ 'uiz. 4 x 12 100 =1 4&400; and
the Solidity 8 times larger, vis^, 8 x 1331000 = 10648000^
that is, above 10 Millions of times larger than the Objed.
14. Once more ; for very ikiaJl Obiedls we may ufe a Lens
^ of an Inch focal Diilance, and then the Image at the fsune
DiiUnqf^^lfre/pre will be in Diameter 4.x 110 = 440 times
lafger than tii(j Ob^'ed ; in Superficies, 1 6 x 1 2 1 00 = 1 93600
tiiiies larger 4p'and in Solidity, 64 x 1^331000 :== 85184000
times larger ; that is, any folid imall Obje£l ^ will at the DU
^ance of 9 Feet 2 Inches, by means of a Lens ^ Inch focal
Diilance, be magnified above 85 Millions of times.
15. Or morcdireftly thus: Let th« focal Diilance of the
I>Ouble-Convex mnbe ^zz r, ^nd let the Diftance at which
the Image is form'd be 12 Feet or 144 Inches =j^» thea
■ ^-^ z:zdz=i 0,2504, whicKtherefwe may be taken fori
of an Inch ; coniequently the Dil^nce : of the Image k' 576
times the Diilance of the Oib}ed.from the Lens, and fo muck
larger will it be in Diameter, «Qd in Surface it will be 574,5f
,5^76 rr 331 776 times larger, and in Solidity it will be 576 -x
576 X 576= 1911:029.76 times larger: Or,, a fmall. Blopd-
Globule, or other folid Particle, will :be magnified above 19 1
Millions of times ; an EfFecl prodigious, and incredible ,ti>
thofe who are not converfant with GlafiTes , or . underihnd . not
.the Rules of Optics.
16. If the linear Diraenfions of the Image be nicely takes
by a By-ilander with a graduated Scale of equal Parts, ib^
I>imen£on of the Objefk will be known of CQoiie fromtlufr
JUift<inc«s^ pi thf Image a&d Ob]e& from, tbe Leas i 4n4 in «^-
. . cecdi)ag^
Optics; 301
<^<li«g fmall Obje^s, fuch as the Pores of CoVk, the Paiti<>
des of Blood, Ammakula in Semine, Sec, there is ao other
Way of meafuring them fo well : And thus the Solar Micr^"
fc9pe becomes a Micrometer ia the la& Degree of poiEble Me»*
furadon.
i 7, The Form of this Inftrument, as it has been Hitherto
defcribed, is chat which I have contrived for my own Ufe,
and for theirs who regard more the general Convenience thaa
the Grandeur of an Apparatus, However, that thofe of a
■ diiFerent Tafte may be gratified, the common Form is to be '
very much commended for their Ufe ; of which it will Ik
iui&cient to give a bare Defcription, iUuftrated by a Priot.
18. This Iniirument confilts of feveral P^ts, 'vix. A, a Plate LIXw
fquare Frame of Mahogany to be fix'd to the Shutter of. a Fig. i«
Window by mrins of the Screws i , i . To this Frame is ap-
plied a circular Cqllar B of the fame Wood, with a Groove
on its Periphery on the Ootfide, denoted by .2, 3. Thb Col-
lar is connected by a Cat-Gut to the Pulley 4 on the upper
Part, which h turned round by the Pin 5 within. On one
Part of the Collar, on the Outfide, is ^en'd by Hinges a
,XiOoking-Glafs G in a proper Frame, to which is fix'd the
jointed Wire 6, 7 ; by which means, and the Screw H 8, k
may be made to Oand in an Angle more or lefs inclined to
the Frame. In the Middle of the Collar is iix'd a Tube of
Brafs C, near two Inches in Diameter ; the End of which,
on tlie OutTide, has a convex Lens 5 to collect the Sun-Beams
thrown on it by the Glafs G, and converging them towards
a Focus in the other Part, where D is a Tube Aiding in and
out, to adjuit the Objed to a due Didance from the Focus.
To the End G of another Tube F is fciew'd 4»ne of Wilfon^
Single PocJut Micrcfccpa, Containing the Objedl to be magni-
fied in a Slider ; and by the Tube v, il.ding on the fmall
r£nd £ of the oiher Tube D, it is brought to a due focal
Diilance.
19. The great Artifice and Conveniency of this Solar Mi-
|:rofcope i?, that by means of the Glafs G the oblique Rayj
of the Sun are made to go ilrait along the dark Room pa-
rallel to the Floor, inftead of falling upon it. Thus let A 8 F^. x,
denote a Sedion of the Looking- Glaf§, and SC the Rays of
the Sun impinging upon it at C, by which they are remedied
to the Lens D, and from thence converged towards E to illu- /
minate the Objedl to be magnified ; fo that the Beam of Light
goes from C to E in the Direction parallel to the Floor, in-
Itead of falling on it in the Diredion SG. By the Pulley
4, 5, the Glafs is turn'd directly to the Sun, and by the
joixued Wire and Screw at H it. is elevated or depreijs'd^ ib as
302
O p t I c s.
• to bring the Glafs into the Portion AB required, ^here fkii
Angle of Incidence ACS is equal to the Angle of Refleftion
fiC£. Mr. Uberklum, a F ruffian Gentleman , was the firft
who invented this Method of magnifying Objects, but with-
out the Looking -Glafs, which was afterwards added to it.
The Theory of this Contrivance and the Magic Lanthom is
the fame ; only here we make ufe of Sun-Beams inftead of
Candle- Light, and the Objed and magnifying Lens of the
fmalleft Size.
20. Another mofl egregious Contrivance of this Sort we
have from the late learned Dr. s^Gravefande^ which, he calls
by the Name of Heliostata, from its Property of fixing
(as it were) the Sun- Beam in one Pofition, inx, in an horizon-
tal DireSion acrofs the dark Chamber all the while it is in
Ufe. It is an Automatim^ or Piece of Clo^-work, whofe
t^LLIII. P^^ ^c ^ ^<^Uow. A A is a Frame in which a metalline
Speculum S is fufpended, moveable about its Axis by means
of two fmall Screws at ««. This Frame is fbc'd to tlfe Piece
C» which being hollow is moveable upon the cylindric Shaft P
about the Irbn Pin e, (See the Part by itfelf ) This Pillar P is
fix'd to a triangular Bafe or Foot fet perpendicular by th6
three Screws B, B, B.
21. On the Back-part of th6 Speculum is fix*d a long cy-
lindric Wire or Tail D, in a perpendicular Pofition. By this
it is conneded to the fecond Part of the Udioftata^ which is
a common Thirty-Hour Clock, reprefented at H; the Plane
of which Clock is parallel to that of the Equator in any
given Place. This Clock is fuftain'd on the Column FG, in
which it is moveable up and down by a thin Lamina or Plate
that enters it as a Cafe, and fix*d to a proper Height by the
Screws d^ d, at the*Side. The Whole is truly adjulled to a
perpendicular Situation by means of the thrfee Screws I, I, I,
in the Tripod LLM, and the Plummet (^ whofe Ci^V muft
anfwer to the Point 0 beneath.
22. The Axis of the Wheel, which moves the Index NO
over the Hour. Circle, is fomewhat large, and perforated with
a cylindric Cavity verging a little to a conical Figure ; and
receives the Shank /^ of the (aid Index NO very clofe and
tight, that by its Motion the Index may be carried round. In
the Extremity O of the Index is a fmall cylindric Piece n^
with a cylindric Perforation to deceive the Tail / of the Fork
T,' yet fo as to admit a free Motion therein. In each Side
6f tiie Fork are feveral Holes exatlly oppofite to each other,
in which go the Screws r, r, upon whofe fmooth cylindric
Ends moves the tubular Piece R 6n its Auricles m^ m.
ty Whtn ^hc Machine is to be fix*d for Vk, anothcf Parrt
15
Optics. 303
is made ufe of to adjuft it $ which is caUM the Fvfitort and
is denoted by the Letters VXYZ. The Cylinder C is re-
moved with the Speculum from the Foot P, and the Brafi
Column VX put on in its ftead, and adheres more ftri^y to
the Pin /, that it may keep its Poiltion while the Machine is
I eoniUtuted.
I 24. On the Top of the Column, about X as a Center,
moves the Lever Y Z, fo that it may be any how inclined to
the Horizon, and keep its Pofition. The Arm YX may be
of any Length at Pleafure, but the Arm Y Z is of a peculiar
I Conflrufiion, and of a determinate Length. To this Arm»
which extends no farther than j, is adapted a Siding-Piece
Zat iharp-pointed at Z. By tlm the Arm XZ is determined
1 to a given Lengthy the Piece Zx being iix'd by the Screws
I 25. Upon thu Arm is drawn the fhort Line *vx^ by whidk
1^ it may be lengthened in the Whole, and is tIts of the whole
I Length- XZ. when (horteft. The Reafon is, this Ann is al«
I ways to increafe and decreafe in Proportion to the Secant of
^e Sun's Declination to the Radius XZ when fliorteft; but
the Radius is to the Secant of 23"" 30^ (the Sun's greatefl De-
^ dmation) as 1 0000000 to 10904411, or as .100 to 109.
j 26. Now the Reafon of this Conftrudion of the Arm XZ
I is to find for aiiy given Day the Diflance of the Center of the
Speculum S from the Top / of the Style /N, which muft
ever be equal to the Secant of the Sun^s Declination ; for it
muft always be equal to the Diflance of the Top of the faid
Style / from the Center of the Cylinder R in the Fork T,
and that is ever equal to the faid Secant of Declination.
27. For fmce the Style /N and the Fork T are in a Por-
tion parallel to each other, therefore the middle Hole in the
Sides of the Fork being (as they muft be) of the iame Height
above the End of the Index O as is the Height of the Style
NTy 'tis evident that on an equinoctial Day the« Sun's Rays
will pafs diredly through the Perforation of the Piece R, if
it be put in a Pofition parallel to the Plane of the Ecliptic, or
chat of the Clock ; and alfo that the Top of the Shadow oi
the faid Style will fall exa£lly on the faid Hole.
28. In this Cafe the Top of the Style is at the leaft Di-
fiance from the central Point of R» and therefore may be re-
prefented by RmSus, while in any other Pofition above or
below, the Diftance will increafe in Proportion to the Secant
of the Angle which the Rays make with this firft or middle
Ray, that pafi by the Top of the Style, and through the
Hole R.
2^. Now it may be demonfirated, that on any Day of the
Year,
304 Optics,
Year, if the Clock and its Pedeflal be fo fix*d that the Lindi
of XII be exadlly in the Meridian, and that the Pofition of R
in the Fork be fuch that the Sun's Rays go diredly through
it» and the Shadow of the Style's Top fall juft il^n the Hole 9
moreover if the Diflance of the Center of the Speculum S
from the Top of the Style / be made equal (by the Pojitor),
to the Di^ance of the central Point of R therefrom ; and
lailly, the Tail of the Speculum DE paffing through R ; if
then the Clock be put into Motion^ the Index N O fhall car-.
ly about the Tail of the Speculum in fuch a Manner^ that at^
all Times of that Day when the Sun can coipe upOJi ^e Spe-.
culum it will refled the Rays conflantly in one and the fam^
Pofition and Diredion all the time without Variation.
50. The Machine thus coiiflituted is placed in a Box of
CsJe, and kt in a Window with one Side open, expofed to
the Son, and all the other Parts clofe ; fo that when the Room
is made dark, and the Solar Microfcope fix'd to the Fore<
part of the Box in which the Heiiojiata is placed, juA againfl
the Center of the Speculum to receive the reflefled horizon-^
tal Beam, all the E^riments of the Darkened Room are thei^
performed as ufual. This is a very ingenious Conflrudlion
of a Solar-Microfcope Apparatm^ and full of Art, but, I fear»
too expcnfive arid troublefome for common Ufe. However,
'tis eafy to fee that; this Machine is capable of being greatly
reduced \ for it may be made to anfwer the End very well
without a Clock ; alfo the Speculum may be Glafs inftead of
Metaly and all fix'd on one Foot or Pedeftal : But this I
leave to the IngCQuicy of the Mechanical Reader.
LECTURE
F
i
Astronomy. 305
LECTURE XL
Of Astronomy ; c^nd the Ufe of thi
Orrery and Cometarium.
Of the Universe ; aH iNFiNitV of Systems;
of th& Ptolomaic System ; the Tychonic
System ; of the Copernican or Solar
System t>f the B^orld. The Extent and Con-
ftitutnt Parts thereof Arguments for the
Truth thereof Demonstrations of its
Truth. Of the Suit 'y /A<? Primary Planets;
the Secondary PJanets, or Moot»/s. The Co-
j METS. Of /^^ Magnitude^ Motion, Maculse^
6?r. oftheSvs. 0//i>^ Number, Order, Mag-
nitude, Diftances, fcfc. of the Planets ; tbeif
Periods -, of the Nodes, Inclination, and Aphe-
lia of their Orbits. Of the Moon, its Pha-
fes, Period, Diftance, Magnitude, ^«i Light
Of the Satellites or Mdons of Jupiter and
Saturn. Of Saturrfj Ring. 72>^ Mathema-
' tiCAL Theory of the CELEstiAL Motion,
j w/'/i^ Calculations ^»i Examples. Of the
[ Orrery; an biftoricaUceount of the Invention
43;^i Improvements thereof A DefcriptioH of
the Akm ILL AKY Sphere, Of the Motiom
of the Earth about its Axis, and about the
Sun. The Vicissitudes of the Season^ ex-
Vol. IL U plained.
3q6 Astronomy*
plained. Of the various Lengths of TiAti
and Nights, ^be Third Motion of the Earth ;
the great PL>tTONic Year j the Recession
/?///&^ Equinoxes explained. A Calculation of
the hotteji Time of the Day. The Doftrine of
Solar and Lunar Eclipses fully explain'd^ by
Calculations on a MatKematjca! Theory, ^
Explanation of the Astronomy of Coi^ets.
A new Method for Conftruftion of their
Orbits. CalculatioBS relating to, Jbe.tt^Jbfile
Theory of Comets. An Analytical Inveftiga-
tion of their Elliptic Orbits. Of their Tails,
onA all other Phenomena accounted for on the
genuine Principles of Phyfics.
I SHALL, in this Lefture endeavour to exhibit
to you a jufi and natural Idea of the Mun-
dane or Solar Syftem^ that is, the Syftem of
the World ; confiding of the &un ; the Fri-
^ mary Planets j and their Secondaries^ or Moons \
the Comets -, and the Fixed Stars ; accoirding to
the Hypothefis of P/Z^i^^^rtfj among the Ancients,
and revived by Copernicus: Which Syftem is
fully proved, and eftablifli'd on the jufteft Rea-
foning, and Phyfical and Geometrical Conclu-
fions, by all our modern Aftronomers (CXXXI).
(CXXXI) I. B7 the Universe we are to underftand the
wkole Extent of Space, which, as it is in its own Nature 6ve*
xy way infimte» gives as an Idea of the Infinity of the Uni-
verfe^ which can therefore be only in Part comprehended by
uit And that Part of the Univerie which we can have any
Notion of, is that which is the Subje^ of our Senfes ; and ofv
this the Eye prefents u$ with an Idea of a vaft ^tended Pro-
The
Astronomy. 307
iTrtE itioft celebrated Hypothcfes, or Syftems
df the World, are three, viz. (i.) The Ptolo-
iHeany invented by Ptolomy^ an ancient Egyptian
Philofopher, which aOigns fuch Pofitions and Mo-
tions to the heavenly Bodies, as they appear to
ipe^y and the Appearaiice df various Sorts of Bodies diffis
minated through the fame.
2. The infinite Abyfs of Space^ which the Greeks call'd
the T^ •«>, the Latins, the Imtne, and we the Uni'uerfe, does
nndonbtedlf comprehend an Infinity of Syftems of moving
Sodies round one very large central one, which the Ronuau
caird M^ and we the ^un. This Collection of Bodies it
^refore properly caird the Solar System, and fometimes
the MuNi^AKB System, from the Latin Word Mundus, the
WarU.
3. That the Univerfe contains as many Solar Syftems of
Worlds as there a^e what We call Fix^d Stars, feems reafona-
ble to infer from hence, th^t our Sun removed to the Oiftance
of a Stnr would appear juft as a Scar does, and all the Bodies
inoving about it would difaj^ear entirely. Now the Reaiba
why they difappear is becaufe they are opake Bodies, and
too fmaU to be feen at fo great a Diftancc, without an intenfe
Degree of Light ; whereas theirs is the weakeft that can be«
as being firft borrowed and then reflected to the Eye.
4. But the Sun, by reafon of his immenie Bulk and innata
Light, which ^ the ftrong^ft poilible, will be vifible at aa
immenf<» Diftance ; but t^e greater the Diflance» the leif
bright it will appear, and of a lefler Magiiitude : And there<f
fore tv^ry Stir of every Magnitude may probably be a Sun
like our own, infivming a Syftem of Planets or moving Bo^
dies, each of wbi<;h Qiay be inhabited like our Earth with
various Kinds of Animals, and ftored with vegetable and
Other Sd[>ftanees.
^. In this View of the Univerfe, an auguft Idea arifes in.
the Mind» and worthy of the Infinite and Wife Author of
Nature, who can never be fuppofed to have citeated fo many
glorious Qrbs to a^ifwer (6 trifling a Purpofe as the twinkling-
to Mortals. by Night now and then; befides that' the far
greateft Part of the Stars are never feen by us at all, as will
be farther Aewa when . lite .come to tii^at of thofe oeleftial
jSodies.
6. Whea therefore Mofit teUs us/ th^t /« thi Befftming
U a the
3o8
Astronomy.
the Senfcs to Jiave. (2.) The Tychonic Syjim^
or that of the noble Danijh Philofopher, Tychn
Brabe. (3.) The Fythagorean^ Copemican^ or
Solar Syjlemy above-men tion'd. Of all which in
Ordeft(CXXXII,\
God created the Heavens and the Earthy it is to be andexHood
in a limited Senfe, and to mean on]y the Makings or rather
Nenxj-making^ of our Terraqueous Globe j for 'm exprefsly
&id that the Earth in its firft State was a Chaof^ (in Hebrew
V^y\ ihrii Shafetefs and Void) which probably might, be
only the Ruins of a pre exiftent Globe, inhabited by rational
Creatures In the fame maimer as fince its Renovation. And
though it hh faid, God made /w* great Ughtiy the 5«» and. the
Moott, it ddes not follow they had no £^f{ence before that
Tiix^, * any more than it <]08s that the Stars had not, which
he fe faid to 4iaYe iriade alfo. •
7. Now if the Stars had no ExiHence before the Mofaic
Creatipn, then were there rto other Syfiemsiof Worlds be-
fore oiir oWn ; then mufl ail the Iȣnity of Space have been
one eternal ^bfolute hnne oxEfttft^Sface tiil chat Tine, and
G(x) who inade the Worlds muft be fuppofed ^ have made
them all at once: -Which Suppofitions are too extravagant
and unreafbnable, and' therefi^ cannot be the Senfe of chat
' Paffage of Scripture ; whiefa 1 think can be no more than thb»
that when God had formed the Earth into an habitable Globe»
he gave it fuch a Poficion and Motion about the Son, '^nd
about its own Axis, as ihould caufe an agreeable Variety in
the Lco^thof Days and Nightfc, and in the Temperature of
the Seafoiis of the Year: All which wdi be (hewn to have
their Exiffetlce and Diftinaion refulting fvosi' thefe Principles,
and no other, in the Sequel of rht No«esf4o this Leawel^
(CXXXIIJ I. I have thought it expedient'toilIuftrate.tfce
Idea of the three remarkable Syftems of the WofcW above-
mentiOhM by proper Diagrams.; in the ¥\AM wUchiyou
PL LIV. view the Difpofition of the Heavenly fiodies according, to
Tx%. I. the Hypothefis of CUmMus F^ehmatirt a iwEMo% Mathema-
tTdan and Ath'om>it)er of F^ufium in Egypt^ wtho lived in the
£rft Part of the fc^coAdrCeatury after £btr^. r .
- 2f Thk was lirH^ iavciitied and adUmred to chiefly becaufe
it feem^d to correfpond with the fenfible Ap^Marances of the
C^leiUal Motiom. They took it for granted that the Motions
The
Astronomy. 309
The Piolomean Syftem fuppofes the Earth im- Pj- L^^-
moveably fix*d in the Center, not of the World * ^*
only, hut oi tht Univerfe \ and that the 5<^», the
MooHy the Pianets, and Starsy all moved abotit
it from Eaji to H^eji once in twenty-four Hours^
in the Order following, viz. the Moom^ Mercury^
Venusy the Sun^ Mars^ Jupiter^ Saturn^ the Fix^d
Stars , and, above all, the Fignciept of their PW-
mum Mobile^ or the Sphere, which gave. Motion
to all the reft. But this was too grofe and ab-
which ttoie ^toSki apjpearM to hftve were Aich ;(s they truly
and really p^rform'jfi i and not dreaming of anj Motion ia
the Earthy nor b^pg ispprizcd of the DilUo^n of ahfolun^
relative^ or afpdriia Molicn, they could not make a proper.
Judgment of fuch Matters, but were under m N^c^i&ty of
being mifled by then* very Senfe«y:,fQr want of proper Affift*
a&ce whieh Aftcr*Ages produced. --^
3. ^Tis itafy to obfirrve thcgr had.AO Notion of any other
Syfbpm butottr own^ nor of any other World but the Earth
on which we live. They thought nochiog lefs than tb^ all
Things were made for the Ufe of Man ; that all the Stars
were contained in one concave Sphere^ and therefore at an
equal Diftanoe from the Earth ; mi that the Primtm Mobik
was circufflfcnbed by the Cabm Sfftfyrmm of a cubic Form,
which they fuppofed to be thcjie^u^n, or blifsful Abode of
departed Soals.
4. It would icarce have been wcrth while to have faid fo
mnch about fo abfiird an Hypothefis; (as this is qow well
known to be) were it not that there are flill numerous Re-
tainers thereto, who endeavour very zealoufly to defend thp
fame, and that for two Reafons principally, luz, becaufe the
Earth is apparently fixed in the Center of the World, and the
Son and Stars move about it daily i and alfo becaufe th9
Script«ire a&its the Stability of the Earth, the Motion of the
Sun, (fc. ' ,
5 . Thefe two Argumentsmcrit no^articular Anfwer/jt is fuf-
ficient, with refped to the firii, toiay , that we are aiTar 'd Things
may (yea mull) appear to be, in naay Cafes, what they really
lire not, yea, to have fuch Affedions and Prop^ies as are ab-
ipltttely contrary to what th^ realjy pofle^. Thus a Perfol)
U 2 furd .
^Ip A S T RO N O M Yf
furd to be received by any learned Philofophcr,
^fter the Difcoverles by Obfcrvations and Inftru-
ments which acquaint us with divers Phjcnomena
qt the heavenly Bodies, altogether inconfiftent
with, and, in feme Things, exaftly contradido-
ry to, fiich an Hypothefis ; as will be fhewn by
the Arguments adduced to prove die Truth of
the Copernican Syftem.
pl/LIV. The Tychcnic Syftem fuppofed the Earth in the
F'g' ^- Center of the World, that is, of the Firmament
fitting m the Cabin of a Ship under Sail, will, by looking out
at the Window, fee an apparent Motion of the Houfcs, the
Trees, ^c. on the Strand the contrary way, but will per-
ceive no Motion at all in the Ship. Alfo a Perfon fitting in
a Wind-Mill, if the Mill be tprn'd about, he will fee an ap-
parent Motion of the upright Poft the contrary Way, but
will no; perceive any in the Mill itfelf.
6. All thofe C^fes are exaftly parallel to tha( of the Earth,
(the Reafon of which has been (hewn in the former Part of
this Work, Jnnot, XX.) and it is as rational to' alTcrt the Ship
^nd the Mill are really quiefcent, and the other Bodies pod-
tively in Motion, as k is to in^ft on the Motion of the Sun,
and the Earth's being at ReH in the Center.
7. As to the Scripture, as jt was never intended for an In-
toution of Al*ronon>y pr Philofophy, fo nothing is to be
underftood as ilriftly or pofitivcly aifertcd in relation 'thereto,
butas fpoken Only agreeably to the common Phrafe or vulgar
Notion of Things. And thus Sir Ifaac Ncmjton himfelf would
always £iy» the Sun rifcs^ and the Sun fets \ and would hava
iaid with Jfjhus^ Sun fiand thou fiil!^ &C. though he well
knew it was quite contrary in the Narurc oi the Thing.
$. How ridiculpuj a Thing does Pqpery appear to be tp
all rational Minds, or to thpfe who are at liberty to thinks by
infilling on the literal Senfe of Scripture fo rigidly in the Ex-
prefiiou, T/^/V u my Body! And is it not equally abfurd to
jnainrain that the Earth fiands vfon Pillars^ only becaufe we
read fo in the Bible ? What an aukward Shift/ are thofe cele-
brated Mathematicians MefT. Le Seur and Jacqtder obliged to
make, in their Commentary on Sir Ifaac % Pnncipia I The
^ditor;^ forfooth, is here the Coipmet^utor on all thofe Part^
/
Astronomy. 311
of Stars, and alfo of the Orbits of the Sun and
Moon ; but at the fame Time it made the Sun
the Center of the Planetary Motions, viz. of the
Orbits of Mercury^ Veniis^ Marsy Jupiter^ and
Saturn. Thus the Sun, with all its Planets, was
made to revolve about the Earth once a Year, to
folve the Phenomena arifing from the annual Mo^
tion ; and the Earth about its Axis from Weft to
Eaft once in 24 Hours, to account for thofe of the
diurnal Motion. But this Hypotbejis is fo mon-
that relate to the Earth's Motion, or Copernican Syftcm: And
bccaufe their Declaration is fomcthing vtry Angular in its
Kind, 1 (hall here give it ui their own Words.
PP. Le Sbur & Jacquier Declaratio.
Krwtonus iu hoc Urtio libra Telluris mot4e hypoibefii ^rffumit*
Autoris PropoJttiaHes aliter txpikari non poterant^ niji tadem fuo'^
quefoBa hypothefi. Hinc alienam coaili fumus gerere per/onam ;
ca^terum lath a fummis PontiJUibus cmtra Telluris Motum JXicrt'
tis nos obfequi profitemur.
In Engli/h thus:
^< Netvton in this Third Book has aflumed the Hypothefis
<* of the £arth*8 Motion. The Author's Prc^fitsons are
*' not to be explain*d bat by making the iajne Hypothefis
** alfo. Hence we are obliged to proceed under a feigned
<^ Character ; but in other RefpeAs we profefs ourfelves ob-
" fequious to the Decrees of the Popes made againft the Mo-
" tioo of the Earth."
' 9. By this it aj^ears how well many People underftand the
Troth, who yet dare not to profefs it. But to conclude this
Head : There is no Authority equal to that of Troth % the
common Opinion, the literal Expreilion of Scripture, the De-
crees of Popes, and every thing elfe muft give way to plain
and evident Demonftration ; of which we have abundantly
ibfiicient for eftabliihing the true Sydem of the World a-
{^infl all Opposition.
10.' The rytHONic Systbm is reprefentcd in the next pi. ny^
Diagram. This had its Original from Ty^bo Brake, a No- pjg ^^
Weman of Denmari^ who lived in the latter Part of the laft
X^encury ; he built and anade his Observations at Vrenabut^^
U 4 ftrouQy
312 A 8 T RO N O M Y.
(troufljr ab&rd,. ;w4 C^nuary to the great Sin^li**
city of Na(uce, jinf} in &>w^ refpcfts "even contra-
d\£tory to.^pp^^r^nces^ .tb%t it ohuin^d but Iktlo
Credit, ^ .foon. g^ve way to
TbnteLVf The Coperman, Syfiem of the World, which
fuppofes^the Suti' IK> poflfefs the central Part ; and
that about it revolve the PUnUs and Comets in
different Periods of Time, and at different Di-
ftances therefrom, in the Order following, viz^
(CXXXIII).
(i. p. Cel^ial Tower) in thp Ifland of JTs^ or HusMa, Thi«
rbilofopher, though be approved of the, Ofemican Syftem,
yet could be not reconcile himfelf to the Moi^OB^f the Ear b ;
and beings on the other, hand, convinced ibe Ptohmeau
Scheme in Part could not be true» he contrived one dilFerenC
ffoxd either, which is reprcfented by the next Diagram.
11, In this the j^arth ha^ do Motion albwed it, but the
Annual and Diurnal Pha^nomeria are folved by the Motion of
the Sun about the Earth, as in the Pichmak Scheme ; and
thore of Mercury and Vevu$ are folved by tbis Contrivaf.ee,
though not in the fame Manner, So iimply afi4 naturally, as
in the Copermcan Syftem ; .as is ea/y to obfervc in the Figure. ,
12. Afcer this Scheme bad been propofed foroe time, it
received a Corre£lion, by allowing the Earth a Motion about
its Axis, to account for the Diurnal Phsenomera of the Hea^
i^ens; an4 fo this came to be call'd'the 5/W-7>^i&^wV5|^<^«.
But this was dill wide of the Truth, and encumbcr'd with
fuch Hypothefes as the true Matberaatici^ and genuine Phi-
Jofopher could never rel^fh. Therefore both thefe Syftems,
^Tid all others at length gave way to the True Solar SyfteHl,
%Q be morp fully defcrib^d in tjie following Note«. '
(CXjtXtlT) i. 'J'he SoL,AR.SYST$Hrf as^it ianQw taiight^
y/as in fome part invented by ,the Ancients^ perhaps by Py^-
(has;^rfs himfelf; fpr thougji Dio£cnes Laertim itti writing biJ
Lire fays no more of him than his ajferting Jthi Antipodes tf,
thg,EartL ytl Arijhtle t^lls us tl^it the SeJipf^-the Pythsi^
rfans taught thai the Ear^ 'w/fs carrdeJ about nbe Centir (via.
fhe Sun) 'afHo»g the Statfs^ (J, e^ the Planets) #wf iy fuming
p^bcut (irs A^j5] caufi^ Pp^ Olid ^kkl- Jien^^; il.iame ,t9 hft
r
Astro no m y. 313
1. Mercvrt, at the Diftance of about 32
I^IIions of Milesi revolves about the Sun in the
Space of 87 Days, 23 Hours, and 16' Minutes.-
II. Venus, at the Diftance of 59 Millions of
Miles, in 224 Days, 1$ Hours, 49 Minutes. .
III. Th«e Earth, at thf Diftance of abdut
82 Millions of Miles,- in 365 Pi^ys, 6 Hours, 9
Minutes, or Sydereal Year.
call'd the Pytha^gorean Hypothesis or System 0/tii
World,
2. But fomc of thcfc, 'tis faid, allow'd only one Morion
to the Earth, 'vix. the cRurnal \ while Others, as Tbilolaus^
Artftarcbus the ^amian, Plato in his advanced Age; alfo 5/-
leucfu the Mathematician, and others, maintained the Earth
had two Motions, the diurnal about its Axis, and the arm'ucd
Motion about the Sun. Hence it is alfo call*d the Philo*
LAIC System.
3. But the Aftronbmy of thefe early Ages died in its In-
fancy, and was buried in Oblivion for many Ages after ; till
^t length it bf gin to be rcvivq^ by Cardinal Cufa, who wrote
in pefence of it, but to no great Purpofe, till after him it
was cfpoufed by the celebrated Nicholas Ccpermcus^ a Canon
of Thorn in Fol^Jh TruJJia, where he was born A.D, 1473.
Thia Gentleman undertook to examine it thoroughly, and ex-
plain M by it^ the Motions and Phenomena of the Heavenly
Bodies fo well to the Satisfatflion of the Learned, that he
was generally followed therein by the principal Aftronomers
of that and the following Age ; as Kheticus^ Rothmannus^
Laujbi^gius, Sclckardiufy Kefthrm^ Galileus^ and numberlefs
others. From thi» Time it was call'd the Copernican
System.
4. After this arofe divers great Men, as Gajfendusy firw* .
fius^ BullialduSf Ricciolus, the two Cajpms^ Mr. Hugens^ Hor-
rQx, Biftop Ward^ Mr. flamfteed. Dr. Halhy, Dr.. Gregory^
Dr. A>//, and, above all, that fuperlative Geniu^ Sir J/aac
Newton \ who aH of them, with the grcatefl Pains and Dili-
gence, applied themfelves to make Obfervations, to. invent
Jnftruments, and toinveftigate the Phyfical Caufes of Celc-
jlial Phenomena ; in which they fo happily fucceedcd, efpcr
cially the laft great M^n, that the mture. Extent, Order^
§nd CpnlUtution of all and ^very fart of the SoUr Syftpm,
IV, Mar?,
314 Astronomy.
IV. Mars, attheDiftance of 123 Millions of
Miles, in 686 Days, 23 Hours, 27 Minutes, or
I Year, 321 Days, 1 7 Hours, and 1 8 Minutes.
V. Jupiter, at the Diftance of 424 Millions
of Miles, in 4332 Days, 12 Hours, 20 Minutes,
oraltnoft 12 Years.
VI. Saturn, at the Diftance of 777 Millions
both of Planets and Comets, became fo well defined, flated,
and eilablifhed, as to admit of no Conteil or Scruple, with
any Man properly qualified to underhand it ; and which there*
fore ought for the future to be called the Newtonian
System of the World.
Plate LV. 5* '^^ System (no longer now to be calPd an Hypothec
Jis) is reprefented in a Plate by itfclf, with the Orbits of all
the Planets and Comets (hitherto determlnM) and at their
proper Diftances from the Sun, reprefented by the central
Polftt ; it being impoffible to reprefent, eitlier by an Inftru-
ment or Diagram, the true Proportion both of Magnitudes
and Diflances of the Sun and Planets, as will appear by what
follow?.
6. For it muft be allowed, that to render any Machine or
Delineation ufeful, the lead Part ought to be vifible : and
one cannot well aiCgn a lefs Bulk for the Globe of the Moon^
than what is here reprefented in this Plate ; which being fix'd
upon, the Magnitudes of the Planets Mercury ^ Vinus^ the
Earth, Mars, Jupiter, and Saturn and its Ring, muft be fuch
as are Ihewn mider the refpedive Names in the Plate; and
with refpeft to thefe the Sun's Bulk or Face will be repre-
fented by \he exterior Circle of the Diagram, which here rc-
prefents the Ecliptic? in the Heavens, and is nearly 9 Inches
' in Diameter.
7. Now the Diameter of the Earth in this Scheme is x^ \
pf an Inch, its Semidiameter is therefore 5-5 ; and the Di-
ftance of the Earth from the Sun's Center is about 200QO Sc- t
inidiameteis. But 20000 x ^^ = 1000 Inches = 83-5 Feet;
and Ante the Diftance of Saturn is near ten times as great, it j
is evident the Extetti or Diameter cf a Machinf to exhibit the '
Jfiverai Farts of the Solar Syftem in their due Propartion of Di*
fiances and Magnitudes (though no bigger than thofe here A£igf^d)
ivill he at hafi i6oo Feet^ or n^ore than a garter of u Mile *
And cojifcfuoiilj the Circupijereuce of Saturn'j Orbit 'will Metk-
ture "-Jin near a Mik^
of
A s T HON o M y. 315
of Miles^ in 10759 Days, 6 Hours, 36 Mi-
nutes, or nearly 30 Years.
VII. The Comets, in various and vaftly ec-
centric Orbits, revolve about the Sun in different
Situations and Periods of Time, as reprefented in. .
the Sclieme of Mr. Wbipn'% Sokr Syftem
(CXXXIV).
8. In a much leTs Compftfs incjeed the Diflances might be
reprefented very well in Proportion, but the relpe^ive Mag?
Aitodes can no otherwife be (hewn than by fuch Globes or
^aphkal Delineations as is the Plate of the Diagram under
Confideration. Another Thing which cannot be properly re-
prefented in fuch a Pla^ is the Inclination of any Planetary
Orbit to the Plane of the Ecliptic, especially the Orbits of
the Comet8,v of whofe Pofitions we can by no means this way
get any Idea. The feveral Parts therefore of the Solar SyJIem
jpiuft be explain'd and illuftrated by diftinft Theories, with
proper Figures adapted to each : And this will be the Subjed
of Che following Notes.
(CXXXIV) I. The Periodical Times of the primary Pla-
iietB Sir Ifaac Newton has Hated in Days and Decimal Parts of
a Day, as follows :
87,969,2. 224,6176. 365*25^5- 686,9785. 4332,514.
. 1?
10759,275.
2. The mean EHdances of the Planets froiH the Son are
thus flated by Sir If&ac :
According to KepLr^
B ? © ■ • ^ V h
38806. 72400. 1 00000. 152350. 519650. 951000^
According to Bullialdus^ . .
3858J. 72398. looooo. 152350. 523520. 9S4i.9H.
According to the Periodiad Tiaieft,
38710. 72333. looooo, 152369. 520096. 954x306.
3. Before we can fliew how the Periodical Times and Di-
Aances of the Planets are found, it will be necef&ry to pre-
mife the following Things, via. Tht Orbit of a Planet is not PI. LVI.
« ib^ Flam of the Efliftic. Thus tet A N LO be the Orbit Fig. i .
of
3i6 Astronomy.
of a Planet P, and let BCET be the Earth's Orbit, which
is in the Plane of the Ecliptic ; then will one Half of the
Planet's Orbit lie above the Plane, as NLO, and the other
Half NAO below it.
4. I'he tnvo Planes, therifori, ttf'fhe Flamfs Orhit and of
the Eciiptic <will interftSi tmt anoihtr^ i^ch Interfedion will
be a Right Line, a« NO ;? aftd thtsf^ is calPd the Une of the
l^odts^ Ae Ixodes being tii€>t*ro Points N*and O, iri which the
Planet di^fbetods^belfiw/'^r afceads above, the Pkn^ of the
Ecliptic: WhcAce O is eatt'd ^<^*AfcenMng iW<?, apd N the
Dejctnding Node.
5. Let the Curve N>wO be defcribed in the Plane of the
Ecliptic perpendicularly u&der the Half- Orbit NLO; then
is the Curve 'NiwO (aid to be the Prtj^aUn of the Plancfe
OMt NLO on thi Pltme of the Eclifticy and^ the frojeffed
Place of the Planet P, or its Place reduced n the Ecliptic.
6. Thb Angle LOm meafores the Inchneuim if the Pleme
of the Planet's Orhit to tl>at of the . BcUptio i which i» attb
caH'd the OhHqieity thereof. The pefpendiealkr Diftanee P^
h the Latitude of the Plamt from the Pkae'iof the Etiiptk;
tmd hm » the greateft Latitude, if LO Of LN be a Quarter
<rf* a Circle. Alfo the Dillaacc of the Plaftift from the Node,
^h. PO, is caird the Argumntof Latimdt. - -
' 7. Di^w 6P, S/, and TP, T^, and joNi ST| then is the
An^cf PS/ the true Latitude fecn fi-om the Sim at S, and
therefore call'd the Heliocentric Latitude » «»d the Ang^e PT/
is the apparent Latitude, ot that which is feen :fi«in the Earth
at T, and is therefore caird the GeocetOric hatittuk,
. 8. The true Di^nce of the Planet ftidtit^ithe Sun and
Earth is meafured by the Lines SP and PT ^bat %f ahd'T/
arc 6iird the Curtate Diftances. Alfo in the T>iang?B S^T,
the Angle STp is caird rtlt Angle ef Ekng0tUm\ bi Diftancc
of the Planet from the'Sftn. The Angle SpT }f$ call'd the
PfirallaSftc Angle, as being that under w^ich the Scmidia-
meter of the Earth's Orbit is fe^ j and the A»gfe /ST at
the Sun is ufually call -d t&e Anglo of Cmmytation,
9. We may now pftkeed toihew the Mediodi of deter-
mining the jPmM^<i/f««f^" of a Planet j which ^Rwy be done
cithei" by the Gottjunftions or Oppcfitions ^of the Planet to
the^un*' Thus, for Example, obferva well the Place o\Ju-
pitef in' (tit Ecliptic at his Oppofition to the Sun, and alfo
wheti he comes to be in Oppdttion to the Sun a^ain 2 and
note* ivdl the Time that lapfed between. Then ffy. As the
jfrch defcribed htfween the tiuo Oppojitions is to the 'whole CrV-
tumfcrcncty fo is the^ime- im tA^hi^h thkt Arch ^was deferred to
. . (he Periodical Time, rcry nearly j for if will not b^ cxaftly fo»
begittfe
Astronomy. 317
becaofe the Motion of a Planet is not quite ui)ifonn» as
moving in an Ellipfis^ and not in a Circle. In the (ame man-
ner you proceed for an inferior Planet.
10. But a more accurate Method is by obferving ni^Iy
the Time that elapies between the Planet's being twice fuc-
cefiively in the fame Node, (which may be eailly known^ be-
caufe in that Pare of its Orbit the Planet has no Latitude)
and-that wiM be the Periodical Time of, the Planet; for in
one Revolution of a Planet, the Nodes '(if they- move at al^)
will not move feniibly» and may therefore be eileem'd as
quiefcent.
11. In arderto eiBftiate theJDiftaAces of the Planets, we
proceed for Venus and Mcrcuryinihe following Manner. Let
the Place of the Planet in its greateft Elongation from the
Sun be duty obfenred, the Difference between that and the
Sun^j Place (as iieen from the Eanh) will be the Qgandty of
the greatejl.ElongatiQp, or of the Angle ATS, wich u&p^Bi
to the Planet i^am. in her Orbit at, A. And fim the C^it
of Fems is nearly. circular, the Line T A will touch the Orbit
in the Pomt A, ami fo the Angb T.AS will be,* C^ghc ope. .
Suppofe the Angle AT^.=. 47 lilrgrees hy Obferration ;
then if we put the .Diftance of the Earth ST =z 100000,
iay. As Radius 91 Sine of 90^ is to the Sine pf 47^, fo is
TS = 1 00000 to SA=: 73O0O» nearly the Difiance of
Venus from the Shu.
i a. in like manner may the Diflance of Mgrcwj from the
Sun be determined in the Grofs, \m not fo nearly as that of
Vemf^ becauie the Orbit is much mere excentric or elliptical,
and. therefore the Asigle TRS will not be a Right one. Its
Quantity therefore muft be found from the Theory of the
Motions of Mircury founded on Oyisrvadons; and from thence
the third Angle T£$..will be known, and coniequently the
£ide SA, wluch }»/tiie DilbuK:e of Mmury from the Sun.
. 13. In tkr Su^^etior Planets this Matter » not quite ib
, eafy ; however, there are divers Methods by which it' m;)y
be done, by havju&g-^the Thectry of the Ea^h kpown, which
• gives the Side ST; and by Ob|f<^rvaiion the Ang^ STP it.
known^ which is ithe.IDtfefeeneeof the^Q^ocentric .Place of
the Sun and Planet ir (hen ibere Demaws only the. Angle SP,T
to be foaodf >ifchieh Aftronoinrrs Xhew how to do ifeveial
Wftys^ oneof which it peculiar to Jufiurj beiog do))c by
' means of oneref )m Sttutiites^ at will be ihewp wh^ we
tieatof them. ...<...
.J '4^ Aslhaveia this Note mentiotifd the Inclination of
the Planets Orbitft to the Pkno of the Ecliptic, I ihall gise
the Quantity thereof for eadi Planet as follows :
The
6 59
2.CL
3 23
s
I s^
a
I 20
o
2 31
3P
«
H
42
^Fjtms —
n
14
»5;
Mars ■*—
H
i8
29
7«/tf/#r —
So
7
>9
Sat^m —
do
21
49
318 AsTRONOMYi
"Mercury is
i/^«j — - —
Tli« ladiaaltcHi of the Orbit of {Mars
fjufiter —
^SaturJi -— —
15. A1A> the Line of the Nodes in the feveral Pkneta^
Orbits kdetermlfied; and the Place in the Bctiptic of ^
Afcendiog Node f^ each Planet is as follows :
00
^ /. . . 54
For,<Mars — « 18 2q 54
54
54
16. The Diftancea of the Planets from the Sod as AoY^
determined a^e reduc^le to EttgHfi^ Miles, by firfl finding the
Earth's DiBanoe m that Meaiiire ;. and this is done hj finding
the Quantity of the Sun's ParailaK^ that is, of the < Angle vop-
PI. LVI. der which tlte'£anh's Semictiani^er aj^ars at the Son. ^Thiis
Fig. 2. let S be the Center of the Son, and C ihe Center of the
Earth DEP ki her Orbit AB| the Angle DSC is that which
we (peak of, as being that under which the Semidlameter
<^D of the Eanh appear^ at the Son.
1 7. To find this Angle Ailronomers have attempted V»-
nety of Methods, bat have as yet fioand none that will deter-
mine it exadly ; however,, by many repeated Obfervations of
Dr. Haliey it is found to be not greater chaa 1 2^^ nor lefe
than 9^^. Wherefore io|^ (the Mean} has been fixi'd upon
as near the Truth, whicb we muil be contented with tlH
Moj^ 26, 1 761, when Femes will tranfit the Sun's Di&, by
which means the fame Gentlemian has fhewn the Sun's Pa'-
rallax may be determined to a great Nicety, *vi»i. to witUi
a 5oodth Part of the Whole. See PM. Tr^, N^ 548,
abridged by 7ftw/, Vol. IV.
1 8. Suppofing therefore the Angle DSC = 10^ y^*', afid
the Side D€= i ; then £iy,
As the Tangent of DSC i c/ yy'^' a= 5, 706764
Is to Unity. DC as.i =s OyOooooa
So is Radius . 90^ s: 10^00600
To the Side SO =r 19657^8 sc 4,29323:6
Then 19657,8 Semidiameters of the £arth anthiplied b%
4000 gives 78631200 Ei^ii/lb Miks for the Dtflance of the
Sw).
19. Not the Dlfiances only, bat alib the Daaniieters of th*
Planets
Astro nomV* 315
Planets are to be invcftjgated, by meafttring their apparent
Diameters with a Micrometer adapted to a good Telefcopc.
\ Thus the San in his mean DiHance will be found to fubtend
an Angk of 32' 12" zr. 1932^ and the Earth at the Sim
fubtends an Angle of zi^ (being double the Angle DSC).
Therefore the Sun's Diameter is to the Earth's Diameter as
1932 to zXy f.h^ i^ as loooo to IQ9.
20. Agsiio.: Mr. P(mnd (w^th lh« Hugenian Tekfcepe of
123 Feet) found Batman fubtended ^n Angle of i6^« There*
fore if Saturn were brought to the nacan Diftance of the
Earth fr^m the Siin» his apparent Diameter would be m-
creafed in the Ratio of ^^ to i j that is, its Diameter
100000
Would be fcen under an Angle equal to ?il — ^ x 16* =s
! ... o * 100000
i i^zJ'6\oq6. Whence the Sun's Diameter is to Saturn'^ as
\ I932'': i52:/64096,:: loooo : 790.
I 2 r. The fame Oentlnnan meafured Jupiter^^ apparent Di-
j ameter,' and found it fiibtcnd an Angle of 3.7* j wherefore
I Juftter at the Diftance of the Eardi would fubtend an Angle
! equal to ^ x 37''= 102/417, Hence the Svft'a real
1 ^ lOOOOO ^^ ^ ' T- /
\ Diameter is to that of 7«///fr as 1932''' : 192/417 :: looOo :
! 99^-
22. Hugenius meafured the Diameter of Mars when neareft
the Earth, and found it did not exceed 30^ ; and that the
Diftance of Mars from the Earth was then to the Sun's meam
1' Diftance as f^ to 41. (See his Syftema Satumium,) Therefore
M»s removed to the Difknce of the Sun would fubtend an
I r
[ Angle equal to — x 30* = 10/9756. Whence the Dia-
( 4|
j meter of the Sun is to that of Mars as 1932^ to 10/9756 ::
i loooo : 57.
23. Dr. Halley colle^ed from the Appearance of Ftnm
in the Sun's Difk, Mrjf 26, 1761, that Venus feen from the
Sun at her mean Diftance would appear under an Angle of
30^; coniequentl/y at the Sun's mean Diftance ihe would
j appear under an Angle equal to ^^^?^ x 30'' = 2 r/6QqQ.
lOOOOO ''^^
Therefore the Son's real Diameter is to that of Femis as
1932^ : 21/6992 :: loooo : 11^.
\ 24. The (iaine learned Gentleman by the like means finds
^ Mercury at his naean Diftance fabfwd an Angle of 20'"^, and
therefore at the Sun an A&gle <if ^ ^'^ x zo" = 7,''742.
■ * lobooo ' '^
, Where-
320 ASTRONOMV.
Wherefore the Diimmimi of fhe Sm zxAMereuty are ih
K^^z" : 7/742 :: loooo : 40.
• 2$. There ave other Phaeoomena of the Planets to be ob-
lm«l, imsa wheoee kvtmX importaAt Dtlcoirerie.s have been
loada in the Phyikal P«rt q§ Aikoftoaif . Thus the Son and
lome Pianets, when view*d with a good Te2efeope» appear
to have dark Spol^ on their Surface 1 by th«ie Spots thofe Bo-
dies are fonad to have a Motion aboat their Axis^ and the
Pofition of their Axis with refpe^ to the Vhatt of the Eclip-
tic is by this means determined.
26. Thefe Spota are moft numeroos and eaiUy obfervtel in
the Sun. It 'i& not uncommon 10 fee l;hem in various Forms*
Magnitude?, and Numbers, moving over the Sun*s Diik.
They were iirfl of all diicover'd by the lyncean Aftronomer
Galileo y in the Year i6io» foon afftr he had ftnifii'd his new-
invented Telcfcope.
27. That thefe Spots adhere to or float upon the Surface
of the Sun, is evident for many Reafons. (i ) For many
of them are obferved to break out near the Middle of the
Sun's Diik j others to decay and vaniih there, or at fome
Diftance from his Limb. (2.) Their apparent Velocities are
always greatef^ over the Middle of the DiOc, and gradually
flower from thence on each Side towards the Limb. (3 ) The
Shape of the Spots varies according to their Pofition on the
feveral Parts of the Diik ; thofe which are round and broad
- in the Middle grow oblong and flender as they approach the
Limb, according as they ought to appear by Che Rules oJF
Ofties,
28. By comparing many Obfervations of the Intervals of
Time in which the Spots made their Revolutions, by Galilei^
Caffinl^ ScheiniTy He'velius, 'Dt. Hali^j Dr. Dirk^rn^ and o-
thers, it is found that 27 Days, 12 Hours, 20 Minutes is the
Meafnre of one of them at a Mean : But in this Time the
Earth defcribes the angular Motion of 26!* .22' about the
Sun's Center; therefore fay. As 360*" -|- 36** 22' is to 360**,
fo is 27d. izh. 20' to 25d. i5h. 16'; which therefore is
the Time of the Sun's Revolution about its Axis.
29. Had the Spots moved over the Sun in right lined Di'-
redions, it would have fhewn the Sun's Axis to have be^
perpendicular to the Plane of the Ediptic i but fince they
move in a curvilinear Path, it proves his Axis indiQed to the
Axis of the Ecliptic ; and it is found by Obfervation, that
PI. LVL that Angle is equal to f ^o' i tha^ is, if 6Dp»ffmg through
Fig. 3. the Center of the Sun C be perpendicular to thu Plan^ of the
Eafth's Equator HI, then will the Axis of the Sun's Motion
AE contain with that Perpendicular Ae Angle ACB s= 7*
3C/
Astronomy. 321
$6' =r GCI, the Angle tHikh the Bqaator of the^an GP
makes with the Plane of the BclipCic.
30. And the Points in wyckn Plane {Aling thtoogk the
Perpe&dicular B Dand Axis AB cuts the Edipticne in die 8ik
Degree of Pijits on the Side' next the Son's North Me A,
wod tonkqaaxlf in the 8th Begree of f^9 on the odiAr
Side next the Sooth Pole B. Sthemer had decefmtncd the
Ao^e BC A to be 7 Degrees, and Caffim made it 8 by hk
Obfervations ; which is the Reaibn why 7^ 30' is chofen for a
Mean.
5 1. As to ^ Magnitode of the Spots, it is very confi-
d^fHtble^ as will appear if we obfeire that ftmie of them are
fo large as to be pUinly vifible to the naked Eye. Thus Ga-
MtQ faw one in the Year 1612, and I know two Gentlemen
who have thas ¥iew*d them w^hin 20 Years paft : Theft
Spots muft therefore fubtend at leaft an Angle of i Minute.
•Now the Diameter of the Earth, if removed to the Son, woidd
fubtend an Angle of bst 20'' ; hence the Diameter of a Spot
jnil vifible to the naked Eye is to the Diameter of the Barth
as 60 to 2Q, or as 3 to i ; and therefore the Sor&ce of the
Spot, if circular, to a Great Circle of the Earth as 9 to i. '
Bat 4 Great Circles are eqtial to the Eatth's Supe^des s
whence the Surfiace of the Spot is to the Surface of the Earth
as 9 to 4, or as 2^ to i .
32. Gajfendus fays he ftw a Spot whofe Diameter was
equal to V^ of that of the Sun, and therefore fubtended an
An^le at the Eye of i' 30^ ; its Surface was therefore above
5 times larger than the Surface of the whole Earth. What
thofe Spots arci, I believe 00 body can. cell ; bat they ieem to
be rather thin Sorfaces than folni Bodies, becanfe they lofis
the Appearance of SoUdity in going off the Diik of the Scn«
They refemble fomething of the Nature of Scum or Scoria
fwimming on the Surface, which are generated and diflblved
by Caafes little known to ns.
33. Bat whatever the Solar Spots may be, 'tis certain the)f
are produced from Caufes very inconfiant and irregular :
For Scheiner in his Ibfa Urfina, which contains near 2000
Obfervations upon thefe Spots, fays he frequently faw $0 at
once, but for 20 Years after {vix. betweei the Years 1650
and 1670) fcarce any appeared. And in this Cettury thd
Spots were frequent and numerous till the Year 1741, when
for three Years fticceffively very few appeared. I (aw but one
in ail that Time ; and now &ice the Year 1744 they have
again appeared ss ufaal.
Vol. If. X 34. Thefc
322 ASTEONOMT.
34. Thefe Maaia or daik Spots aie not peculiar to die
Sno; tbqr have b^ obloTcd aHb in cbe Pluieis. TluisfV-
mu was obienred to have fevcral \rf Signior Bkmdtim^ the
Pope*t Domcftk Prelate, in the Year 1726 ; bjr which he
determined herltevohition aboot her Axis to be performed in
34 Bays and 8 Hoais ; end that her km is indined to the
Pluie of the Ecliptic in an Angk of i^ Deg;rees; and laiUy,
that the North Pole of this Planet £ices the 20th Degree of
Afuaiut.
35. As in Femu^ fo in t/lart^ both dark and bright Spots
have been obferved by GaliUo firft, and afterwards Jb^ Signior
Caffimy Dr. Ucok, MiraliB, Mr. Rumer^ and others. By
thefe Spots the diurnal Revolution of Mwrg about its Axis is
deeenmned to be 24 Hours and 40 Minatesi and that the
Axil is nearly perpendioiiar to the Pbne of its Qibit.
36. There feems to be good Reafon to coodode Mm-s is
enconpafled with a large Atmofphere ; for Caffini oUerved
a Fix'd Star, at the Diilanee of 6 Minntes from the Difk of
Marsy became fo faint before its Occnitation, that it cocdd
not be feen with the naked Eye, nor with a Telefcope of 3
Feet ; though Stars of that Magnitnde are plamly vifible even
in Contad with the Moon, which for that Reaiba ieems to
have no Atmofphere.
37. Jufittr has had his Spots obfenrable ever fiaoe the In.
rention and Ufe of large Telefcopes ; and from repeated Ob«
fervations they fhew Jufiter*s Revolution about its Axis is in
9 Hours and 56 Minutes. Befides thefe Spots, Jupiter has
the Appearance of three Zones or Belts encompaiffing his
Body, fometiffles more, fo that his Diik (eems clouded with
them : What they are, no body yet can tell. The Axis of
this Phnet alfo is nearly perpendicular to the Phme of his
Oibit.
38. Ctmfideringthe large Magnitude of 7s^/^f, andhisihmt
ditnmal Rotation, the Equatorial Parts of his Surface muft have
a prodigious Velocity, which of confequence mufl caufe him to
beof afpheroidiealFigure (as wasftKwn of the Earth). Ac-
cordingly Cajfini found the Axis of the Equator to be to that
of the Poles as 14 to 15 ; but Mr. Pound %ktTsmd% more
exaftly determin*i' them to be as 12 to 13, agreeable to Sir
Ifaac Ngnvton^s Computation.
39. Siatkfn by reafon of his great Diftancf on one hand»
.and Mercury by reafon of his S^iallnefs and Vicinity to the
Sun on tiie other, have not as yet had any Spots diicover'd
on their Surfaces ; and confequently nothing in rehttion^ to
their dtamal Motions, and Inclioations of their Axis to the
^bafs of iheir Orbits^ lAn be knows.
These
Astronomy* 323
These are all the heaVenly Bodies yet knowii
to circulate about the Sun, as the Center of their
Motions ; and among the Planets, there are three
which ^re found to have thtir fecanJary Planets f
Sateltitesy or Moons^ revolving conftantly about
them, as the Centers of their Motions, (X^XXXV)
(CXXXV) t. Of die £x Primary PlancUi we find but
three that arc certainly attended with Moons, wk, the Eartbt
jfupiter^ and Satum } for though Mr. Sb§rt has given, an Ac*
vxxmt of a Phienomenon that he obferved fome Years ago,
which feems extremely like a Moon about FiMu^ yet as it
was never obferved before nor fince through the bell of Te-
lefcopes, I can by no means think it was a real Moon : Howt
ever, that fhe Reader may uie his own Judgment, I refe^
him to the Account given of it in the Plnlrfopbicml Tram/'
a3iom*
2. The Diflance of our Moon from the Earth is deter-
mined by her horizontal Parallax, or the Angle which the
. Semidiameter of the Earth fubtends at the Moon, «/«. ^ b. r vf
Angle AOC, which is the Difference between the true Place ^; ^V*
of the Moon*6 Center O when in the Horia^n, and the ap. '^E* 4*
parent Place thereof as view*d from the Surface of the Eaith
at A. The former is known by Afiionomical Tables, the
latter by Obfervation : And the Quantity of this Difference
or Angle at a Mean is p' \z" = AOC.
3. If therefore we uy. As the Tangent of 57' 12'^ is ui
Radius* fois ACr? i to COszSOfi; this will be the mean
DiAance of the Moon in Semidiametei^B of the Earth. There^
fore fince one Semidiameter of th^ Earth contains 39SJ
Miles, ^e have 3982 x 60,1 = 23931892 == CO the mean
Difiance of the Moon.
4. The Moon*s apparent Semidiameter MO meafures (at
her mean Diftance) 15^ 38^^ =: 938^^ by the Micrometer^
which is the Quantity of the Angle MCO. The Earth's
Diameter therefore is to the Moon's as 3432^^ to 938^^, that
111 as 109 KQ 30, or as 3,63 to i. Wherefore — x 7964
109
2s: 2192 Milei in the Moon's Diameter,
$.. Therefore H» Face of tlie Earthy as it appears to thB
Imnari^ns^ is to the Face of the Moott as ic appears to os*
X a Th«
324 ASTRONOMT.
THsEARtH, which has only ^^^ikfo^rerolv-
ing about it, in 27 Days, 7 Hours, 43 Minutes,
at the mean Diftance of about 240000 Miles.
as 169 X 1C9 to 30X 30, 'uht. as itSZi to 900,- orTis 13,2
to I. And the real Bulk of the Earth is to that of the Mooa
as 109 X 109 X 109 to 30 X 30 X 30, ofiz. as 1295029 to
270D0, that is, as 1 295 to 27, or as 48 to i very nearly.
6. Sir l/aac Newton mentions the Atmofphere aboat the
Moon, but other Aftronoraers think there is Reafbn (not ^o
faya Demonftration) for the contrary ; For Mfere there an
Atmofphere of Air like ours, it mull necefHyily obfcure the
Fix*d Stars in the Moon^s Appulfe to them ; bat it has been
obferved that this never happens ; on the cou^ary they pre-
ferve all their Splendor to the Moment of their Occolcationy
and then difappear inftantaneoufly, and in the fime Manner
they recover their Light when they appear again on the other
Side. And this I am very certain of from the late remarka.
We Occultation of Jupiter, which I obferved with a good rc-
fledbing Telefcope from the Beginning to the End wi3i all the
Attention poffible, becaufe I was very defirous to be fatisfied
about that Matter ; and all the Phenomena confpired to con-
vince me^ there was nothing like an Atmofphere about the
Moon.
7. That the Surface of the Moon is not fmooth or even^
but diverfified with Hills and Vales, Contincfncs and Seas,
Lakes, (fc. any one would imagine who views Her FztSe
through a large Telefcope. That fhe has Variety of Hilfe
and Mountains is demonltrable from the Line which bounds
the light and dark Parts not being an even regular Curve,
as it would be upon a fmooth fpherical Surface, but an irre-
gular broken Line, full of Dents and Notches, as reprefented
in the Figure : Alfo becaufe many fmall (and fonic large)
bright Spots appear in the dark Portion, ftandfng out at feve-
ral fmall Didances from the boundary Line ; which Spots in .
a few Hours become larger, and at laft unite with the en-
lightened Portion of the Dilk.
8. On the other hand we bbferve many fnftall Spots inter-
fperfed all over the bright Part, fome of which have their
dark Sides next the Sun, and their opposite Sides very bright
and circular, which infallibly proves them to be deep, hoUow,
round Cavities ; of which there are two very remarkable
ones near together on the tipper Part, and may be view*d
exceeding plain when the Moon is about four or &^e Days
old,
Jupiter
Astronomy. 325
Jupiter is obfervcd with a Tckfcope to have
four Satellitet^ which move about hira in the
Times and Diftances following, viz.
9. To meafurt'the Height of a Lunar Mountain is a cu-
nous Problem, and at the dime time very eafy to dk€t in the
following Manner. Let C be the Moon's Center^ EDB a PI. LVI.
Ray of the S\iri touching the Moon*s Surface in D, ard the Fig. c.
Top of a Mountain in B. Draw CB and CD; the Height
of the Mountain A B i$ to be found. With a Micrometer in
a Telefco^fe find what Proportion the Difbnce of the Top of
the Mountain B, from the Circle of Illumination at D, beirs
to the Diameter of the Moon, that is, the Proponion of the
Line DB to DF ; and becaufe DF is known in Miles, J^^
Will Be alfo known in that Meafure.
la. Now admit that DB : DC :! i : 8^ as id one of the
Hi!Is it'wili'be; then DC* + Wh^ = 64 + i :=: 65 r=:
CB* ; whiicc 1/65 = 8,062 = BC; wherefore BC —
AC = 8,o6» — 8 = 0,062 cr AB, the Heigit of the
Mountain required. Wherefore AC ; AB :: 8 : 0^062 ::
8000 : 62. And flnce the Moon*s Semidiameter A C ==:
1096 Miles, therefore 8000 : 62 :: 1096 : 8,5 nearly. This
Mountain then being 8| Miles high, is near three times higbdr
than the highefl Mountain on the Earth.
1 1 , Again, the Cavities are proportionably large and <}eep.
Lhave obferved Cavities in the Moon more than the' roOdth
Part of the Moon's Diameter in Breadth, which is abont
£oo Miles upon the Moon'ii Surface ; their Depths appear
ykewife proportional. The Lunar Cavities therefore prodi-
giouHy exceed the Height of the Mountains; and confe-
q jently the Surface of the Moon has but ^ttle Similitude to
tlie Surface of the Earth in thefe Refpe^s. '
1 2, Since the Moon's Surface appears to ^e fo very moun-
tainous and irregular, it has been a Queilidn, how it cornea
t > pais that the bright circular Limb of the Diflc does not apr
p.^ar jagged and irregular, as well fts.the Curve bounding the
light and dark Parts ? In Anfwer to t^is, it muft be confider*d»
that if the Surface of the Moon Hadji^ut one Row of Moun-
taira placed round the Limb of the.Diik, the (aid bright
Limb would then appear irregularly indented; but fince the
Sjrfoce is all over mountainous/ an4.$j;ice the vifible Limb is
t) be confider'd not as a fingle curve Line, bu| a large Zonp,
h iving many Mountains lying |one behind another from (he
Ojferver's Eye^ 'tis evident the Mountains in fome Rows be-
X 3 Thb
3^6 . Astronomy.
Th^" Firjlm i Day i8 Hours 27 Minutes,
at the Diftance of 5^^ Semidiameters of Jupiter^
ing pppofite to the Vales in others, will fill up the Inequali-
ties in the vifible Limp in the remoter Pans, which dtminiih
to the Si^^t and blend with each other, fo as to conftitute
(like the Waves of the Sea) one aniform and even Horizon.
13. Whether there be Seas, Lakes, f^c. in the Moon, has.
been a Queftion long debated, bot . no w^ concluded in the Ne-
gative : ror in thofe large darker Regions (which were
thought to be Seas) we view through a good Telefcope ma-
ny permanent bright Spots, as alfo Caverns and empty Pits*
whofe Shadows fall within them, which can never be ieea
In Seas or any liquid Subilance. Their dark and duiky Co-
lour may proceed from a kind of Matter or Soil which reflects
(light lefs than that of the other Regions.
14. Thefe Spots in the Moon have continued always th9
fame unchangeably fince they were firft viewM with a Tele-
scope ; though lefs Alterations than what happen in the Earth
iti every Seafon of the Year, by Verdure, Snow, Inundations,
^d the like, would have caufed a Change in their Appear*
ance. But indeed^ as there are no Seas nor Rivers in the
|4oon, and no Atmofphere, (o of conrfe there can be no
Qouds, Rain, Snow, or other Meteors, whence fuch Changes
pight be expelled.
15. Since (as we have ^wn) the mean Dijiance of the
Moon is about 60 Semidiameters of the Earth, at the* Di-
fiance of the Moon one Degree of the £arth*s Surface will
. fubtend an Angle of one Minute, and will therefore be vi*
fible } but fuch a Degree is equal to 69I Miles, therefore a
Spot or Place 70 Miles in Diameter in the Moon will be juft
yifible to the naked Eye.
16. Hence a Telefcope that magnifies about 100 t!imes
will juA difcover a Spot whofe Diameter is t^^ of 70 Miles,
^r -/^ of a Mile^ or 3698 Feet : And a Telefcope that will
fnagnify 1000 times will ihew an Objed th^t is but -f^^ of a
Mile, that is, whofe Diameter is but 370 Feet, or little
^ore than \zo Yards; and therefore v^ill eafily fhew afmall
Town or Village^ or even a Gentleman's Seat^ if any fuck
fhere be.
17. The Time which the Moon takes up in making one
Revolutk>ti about the Earth, from a Fix*d Star to the fame
. figain, 16 27 d. 7h. 43^ which is call'd the Perisdictd Montiu
^at the Time that pa^Tes between two Conjundtions, that is^
from opf New Mo^n to another, '» ^ual tp 29 d. lah^
Body
Astronomy. 327
Body from hisCenter^ as meafured with a Micro^
meter.
44' 3^ which is callM a Syno£cal Moutb : For after one Re-
volution is finiih'd, the Moon has a fmall Arch to defcribe to
get between the Sun and the Earth, becauTe the San keeps
advancing forwards in the Ecliptic. Now this Sorplos of
Motion takes op 2d. c h. i^ 3^, which added to the Perio-
dical Month makes the Synodical, according to the mean
Motions.
18. The Moon moves about its own Axis m the fame
Time that it moves about the Earth, from whence it comet
to pafi that (he always (hews the fame Face to us : For hf this
Motion about her Axis jafi fo much of her Surface » tnni*d
towards us conftantty, as by her Motion about the Earth
would be tumM from us.
19. Bat fince this Motion about the Axis b equable and
uniform, and that about the Earth (or common Center of
Gravity) is unequal and irregular, as being performed in an
Ellipfis, it muft follow, that the fame Part of the Moon*$
Surface precifely can never be Ihewn conftantly to the Earth ;
and this is confirm^ by the Teleicope, through which we
often obferve a little Gore or Segment on the Eaftem and
Weftem Limb appear and difappear by turns, as if her Body
librated to and fro ; which therefore occafionM this Phaeno-
menon to be caird the M^otCs Uhration*
20. The Orbit of the Moon is elliptical, more fo than
any of the Planets, and is perpetually changing or variable^
both in refpeft of its Figure and Situation ; of which we fliall
treat more largely in another Place. The Inclination of the
Moon*s Orbit to the Plane of the Ecliptic is alfo variable,
from 5 Degrees to 5° 1 8^ The Line of Node^likewife has
a variable Motion from Eaft to Well, contrary to the Order
cf the Signs, and compleats an entire Revolution in a Space
of Time a little lefs than 19 Years. Alfo the Line of the
Apfiies^ or of the Apogee and Perigee^ has a direft Motkm
from Weft to Eaft, and fini(hes a Revolution in the Space of
about 9 Years. All which will be more copioufly treated of
when we come to exj^ain the Phyficai Caufes thereof.
91. The Phafes of the Moon in every Fart of the Orbit
are eaiily accounted for from her different Situation with re*
(pe£l to the Earth and Sun : For though (O an Eye placed in pj^ LVL
the Sun (he will always exhibit a compleat illuminated Hemi- ^ig. 6.
fpAere, yea in refped to the Earth, where that Hemifpheie
it viewNi in aU Degrees of Obliquity, it will appear in everjr
X 4 The
338 AsrROKOMY.
The Second in '^Thys^ 13 Hoars, ijMmates,
at ihe'Diftaoce of *9 ScmidiameteTs. ^
The yiWri in 7 Days, 3 Hours, 42 Minutes
Degree from the g;reateft to theleafl; fo tint atEooFartat
allof die enlJgfateDM Surface can betel. At P a Isctk Part
of ick tam*d towards the Earth, aad from its Figore it is
then laid to be JbinteJ, At G one Half of the caiigfaten'4
Sor&ce is fntned to the Eanh,,and (he is then laid to be ^if-
cboimfid^ and in her £ifl Qnarter or ^madrgnwn. At H a
p3it more than half is turned to the Earth, and then ibe k
laid to hcgMotts. At A her whole illiuiiBed Hcmi^here is
feen^ being then in OffoJaUm to the Smtf and dius is called
the FuUMaon. At B ihe is again gibbMUy but 00 the other
Fart ; at C (he is again dkhoUmjed^ and in her laft Qiiarter ;
at D (be is horned^ a^ before ; and then becomes svw i^wn
at P# M^bere (he is in €cijut»Qim wit)L the'Sun*
22. If MN be drawn perpcndicolar to the Line SL joiii-'
ingcbe Centers of the Son and Moon, and OP p^rpendico.
lar to the Line TL foining the Centeis of the Earth and
Moon, 'tis evident the Angle OLM in the firft Half of the
Qx\fiiL, aod PLN in the feamd, will be pioportiofial to the
Quantity of the illaminated Di(k turn'd towouds the Earth;
an3 this .Angle is every where equal to the Aogk ETI;,
which is^ call'd the ElMgatun $f ^bt l^n from the Son.
2^' To fiod what Qoantiry of the Moon'a jrifible.SucJfoce .
is illu(l'ate(] for any given Time, we are to con(ider that tho
V}' LVI. Circle of iiliimination £FC is oblique to the View every
yig* 7* whese (bot at G and A), and therefore by the Laws of tb^ .
Orthographic Proje^ion (which fee in my Eliments rf aU Ge-
pmetry) it will be proje£led into an Ellipfe whofe longed Axis
is the Diameter of the Moon BC, and the Semiconjogate isv
Tlh-zs^ Coiine of the Angle of Elongation FfiP. Henct
f P :;= Verfcd Sine of the faid Angle. But from the -Nat
ture of the Circle and EUipfr we have LP in acoal^anr Ra^
tio toEPv wherever the Line PO is (Irawn perpendicular txi
B ; therefore ahb aL^P = PO has a confUnt Ratio to FP.
But (by. E£(lid V. 12.) the Sum of 4M the Undt OP zsi.jlrm
tf the CircU it t9 th Su9» of ^U tie Lines F? =: Arem.of tkt
iiluminatni Bmt^ euJhe Diameter oftkt Circle O? to the Verftd x
Sine of the Eiengatitm F P.
24. Af the Moon iUominatei the Earth by a reflex Light*
fo does the Earth the Moon % but the other Phapnomena wiU
^e fl#rei4 for ^ fnoll part, I {hall recopiUi theff^ for th^
/
Astronomy. 329
at the Diftance of h-A? Semidiainctcrs.
The Fourth \ti 16 Days, 16 Hours, 31 Mi«
nutes, at the Diftance of 25 ^j, Semidiainctcrs
(CXXXVI),
Reader*s Curiofity as feUowi. (i.) The Earth will appear
but to little more than one Half of the Lunar Inhabitants
(2 ) To thofe'to whom the Earth is vifible, it appears £xM»
or at leafl to have no circular Motion, but only that which
refults from the Moon*8 LibraHom. (3.) Thofe who live in
the Middle of the Mooi^^^ vifible HemiTphere fee the Eartii
diredly ^vpr their Heads. (4.) To thofe who live in the
Extremity of that Hemifphere the Earth feeros always nearly
in the Hari;von, buc not exadly there, by reafon of tne Lihra^
tifi/i. ( c.) The Earth in the Conrfe of a Month would have
^1 the iame Phafes as the Moon has. Thus the Ltmariaw
when the Moon is at E, in the Middle of their Night, fee
the Eaith at Fai/^ or (hining with a full Face ; at G it b i^V
chotofm/ed, or half light ai^ half dark ; at A it is wholly
dark, or AW ; and at the Parts between thefe it is gibbous.
(6 ) The Earth appears variegated with Spots of different
Magnitudes and Colours, arifing from the Continents, Iflands,
Oceans, Seas, Clouds, Uc (7.) Thefe Spots will appear
ponfbintly revoking dbout the Earth's Axis, by which th^
lAmarians will determine the Earth's diurnal Rotation^ in the
fame n^anoeras we do that of the Son.
(CXXXVI) I. Galileo firft difcover'd the Saiillites4Xi
Moons of Jwfiter^ in the Year 1610; and call'd them Me^*
eta Sidera^ or Medicean Stars, in honour of the Family of the
]^din, his P^o^s. The famous Piece call'd Sidtrms Nam"
dffSy in lyhich he particularly de&ribes the Difcovery of thefe
Stars, he dedicated to Cosmvs Medicos II, the fourth
Great Dnke of Hetmria..
2. The Orbits of JupUer*^ Moons lie nearly in the Plane Pl. LVI,
of the Ecliptic, which is the Reafon why their Motion is ap- pjg, g^
parently.in a right Line, and not circular, as it really is. To
underftand this, let S be the Sun, T the t Earth in its Orbit
TH^ I the Planet Jt^erm hb Orbit AIB, and in theCen-
ter of the four Orbits of his Moons* Then, .becanfe the
Plane of thofe Orbits does nearly pafs through the Eye, the
l«al Motion of the SattlUn in the Per^hery will be apparent-
ly in the Diameter of the Orbit, . which is at Right Angles tp
^t fiii^e^oiiiiag th^ Q^at^ of the Bard» and Jufittr.
SATURff
336 ASTRONOMY*
Saturk has fifte Moons ; and befides them a
ftiq>ciidoiB Ring (urrounding his Body, whofe
Width and DiftMce from Saturn* % Body are equal
aqd computed at upwards of 20000 Miles. ' The
Periodical Times and Diftances of the Satumian
MoofiS) in Semidiameters of the Ring, are as
follow,
) . Thus fappofing the Earth at R Jf DC be drawn dinmgli
the Center of Jupiter perpendicular to R I, the Motion of
each Moon and their Places will appear to be in that Line.
Thus if the exterior Moon be at E or P, it will appear to be
at I, either upon or behind the Center of Jupiter 5 if the '
Moon more from E to K, it will appear to have moved from
I to L; and when it moves from K to C, it will appear to
move f^om L to C. Again, while the Satellite moves from
C to M/ it will appear to move from C to L ; and as it goes
from thence to F, it apparently moves ftom L to I. Thus
a!f& on the o6ier Side the Orbit, while the Satellite de&ribes
the Quadrant FD, its apparent Motion will be fi-om I to Di
and then from D to I again, as it comes from D to £.
* 4. Whence, fince this is the Cale of each Satellite, it ap«
pears that while each SateHite defcribes the remote Half of its
Orbit CPD, its apparent Motion will be dire6l, or from
Weft io Eaft along the Line CD ; and while it defcribes the
6ther Half DE C, its apparent Motion is retrograde, or ^m
Eaft^ to WM back again along flie fame Line from D to C«
S^ thdt eath Satellite traverfes the Diameter of its Orbit twice
in each Revolution.
5. The Moons of Jupiter {etenSfy (hew the fame Phirfet
to him as oars does to us. They di&ppear from our Sig^t
fometimes, (6 that *tis very rare to have all the four in View
at once C nor is it poffibie to know which Satellite in Order
yon fee, but from the Knowledge of the Theory and Cakn-
fatloh, betatiie the remote^ Satellite may appear neareft to
l^piier, and the contrary, as is evident from a View of the
Figure.
6. Theie Moons, like our own, fofler an Edipfe ertrj
i\mt they eome to the Shadow of Jupitrr, as at F. Alfo,,
fhppofing the Earth at T, the Satellite at'G will nndergo an
Occultatlon behind the Body of Jtfiter, as is evident from
the Sciieme. Again, a Satellite will fproetimes lofe its Lnilre
as it pafiiss ^rtr the enBghten^d Diik ojf its Psimary ; as wheA
Thb
A S T ROKO M Y, 331
The Firft^ ox ininoft, revolves about Saturn
ia i Day, 21 Hours, 18 Minutes, at the IManoe
of near 2 Semidiameters of the Ring.
The Second in 2 Days, 17 Hours, 41 Minutes,
at the Diftance of 2 f Semidiameters.
The ?J/ri in 4 Days, 12 Hours, 25Mmuies,
it 18 at E and N, and the Earth ia R and T. Laftlf, one
Satellite at O may difappear behind another at K, or caofe
Ibiotktr to 4iiappear behind it at M.
7. The Ohfervationft by Telefcopes hatre been earned fo
far as to make it veiy probable that all the Satellites do reaily
reVdve about their own Axit, by means of Spots which they
have'difcoverM to belong to them, and which by their KfotiM
caufe a great Variety m the Brightnefs of the Satellites, and
fofnetimes do almoft. obfcure them : For which fee Mr. Psinut^
Oifirvati^ns on J^es's jihidgmeni of the Phihfifkksl Trmtf*
0Bi9m^ Vol. rVi. p><^7*
8. By means of Jvpiter*% Satellites feveral noble Frobkoii
in Natural Philofophy have .\n eafy and elegant Solution \ tho
Pirft of which is, tQ ietermiw the RaH% of tbe VtUtity ofligki*
The Manner how this is done I have ellcwhere fliewn *. Sem
jiimot CXII. The Secpnd is, to dtHrmine tki UffgitttJe ^-«
Flacefrmt aitf propofed Miridmn ; which is eafily done by the
following Method. Let the Moment of Time in which the
Satellite enters the Shadow of Jupiter be calccdate d for the
given Meridian from Tables of iu Motion ; then let the Mo*
ment of Time be wellobierved when this Immerfion happena
lit the propofed Place ; the Difference of thefe two Momenta
tum*d into Motion will give the Longitude of the Place, al-
lowing 1 5 Degrees for eveiy Hour, i JOsgree for every 4
Minutes of Tune, 'or ,15 Minutes of a Degree for every Mi*
nute of Time, a
9. The Third P^blem is, u fitd the Difattce ef Jupiter
^m iht Smt, This is done as follows : Let the nud^e Mo-
snent of the Occultation of a Satellite at at G be obfenred,
and again the middle Moment of the following at Pf. thin
wtU give the Time in which the Arch G F is defcribed. Then
iky. As the Time of the whole Revolution is to the Time
now found, f» is the whole Circle or 360 Dcjat9i to the
Degrees and Minutes contained hi the Aith FG ; which ia
theMore the Meafore of the Angle FIG, or its equal TI3»
Vir^ich |8 th^ FteaM9fti9 Angle It 7«;^ $ w)^
at
- I
232 Astro no m y.
at the Diftance of 3 ^ Semidiainetets.
The Fpurib in 15 Days, 22 Hours, .41 *Mi-
notes, at the Diftaace of 8 Semidiaoaeters.
The Fifth in 70 Degrees, 22 Hours, 4 -Mi-
nutes, at the Diftance of 23^5, Semidiameters,
(CXXXVII).
the Diflance of Jvpitsr from the Son IS is known, .by what
half b^en (hewn in Jmot. CXXXIV» - v^
(CXXXVII] I. Though GalUfo's Teldcope was (uif^
to diftover all Jufiter*^ Moons, it would not reach ^ahirn^s^
they being at two great a Diftance. Bat yet this iags«:ioiii' ^
Obferver foond S^ftm, by reafon of his King, had a v^iy
odd Appearance; for his Glais was not good enough tO: ^n
hibit the true Shape of the Ring, hat only a confufed Idea.#f
that and Satum together, which in the Year 1610 he adver*
tifed in the Letteis of this Sentence tranfpofed : Altiffimmm
Plamtam tergeminum obfervavi ; i. e. / have ubfcfved S^tum
t9 ha^i three Bodies,
. 2. Thb odd Phacnomenon perplexed the Aflronomers yerf
l^uch^ and various Hypothefes were form'd to refolve it ; all
which {eem*d trifling to the happy Hugeahu, who applied
himfelf purpofely to improve the Grinding of GiaiTes^ and
perfe^ng long Tele^pes, to arrive at a more accurate No-
tion of this Planet and its Appendage. Aca>rdingly in tha..
Year 1655 he condruded a Telefcope.of iz Feet, and view^
ing Saturn divers times he diicoverM fomething like a Ring
encompafling his Body; .which afterwards with a Tube of 23
Feet he obferved more diftindly, and alio difcover'd a Sa-^
tellite revolving about that Planet. This Hugetdan SateUito
is die fourth in Order from Saturn.
%, In the Year 1671 QfJJini difcover'dthe third and fifth,
and in the Year 1686 he hit upon the £rft and fecond, with ,
Tubes of 100 and 136 Feet; but could afterwards fee all
five with a Tube of 34 Feet. . He callM thcfe Satellites Sf4^
ra Lodofcea^ io honour of Louis U Grand, in whpfe Reign ^d
Oj)fcrvatory they were firft difcover'd.
4. In the Year i6$6 Hugens publtihM his Diicovefy in re^
lation to Saturn z Ring in the Letters of thb Sentj^nce iraoT-.,
pofed, vi^. Jnnsik cingitur tenuis flane, nmfpfAm cokeerjnte, aj
EcUpticam inclinato \ that is, Saturn is encompafi^d, hy ^ tkn
Plane or -Ring, n§ 'wbere iobering to his Body, and ineH^ed to
fhi Plant pf the Bcliftic. Thjs {n^linfuioi^ of the Ring to (h^
These
Astronomy. 333
These are the conftituent Parts of the S^lar
Syfiem^ which is now received and approved as
the only irue Syjiem of the U^orld^ for tlie foBow-i
ingRcafons (CXXXVIII).
Ecliptic is determined to be about 3 1 Degreed iy tk^Wt
Roemer^ Picard^ Campam, &c. though by a Method ii6t Vorjr
definitive. , ,
5. HoH-ever, fince the Plane of the Ring is indincd to the
Plane of the Earth's Motion, it is evident when Satitr^ is fo
fi:uated that the Plane of his Ring paiTes through the Earthy
we can then fee nothing of it ; nor yet can we fee it whea
the Plane pafles between the Sun and the Earth, the dark
Side being then tum*d to us, and only a dark Lift appears
ufpon the Planet, which b probably the Shadow of the Rin^,
In other Situations the Ring will appear elliptical more o^
lefs ; when it is moft fo, the Heavens appear through the ^Jf*^
liptxc Space on each Side Saturn (which are calPd the Anf^) >
yea, a Fix'd Star was once obferved by Dr. ClarkeK Father
in one of them.
6. The Nodes of the Ring arc in 19** 45' of hrgo and
Pi/ces. During Saturn's Heliocentric Motion from 1 9* 4 j'
to the oppoiite Node, the Sun enlightens the Northern Plaq^
of the Ring, and *viciffim,
7. Since Saturn defcribes about one Degree in a MontK^
the Ring wiK be vifible through a good Teleicope tiH within*
about 2 5 or 20 Days before and after the Planet is in 19*^ 45^
of Firgo or Pifces, The Time therefore roay be found hy an
Ephemeris, in which Saturn feen from the Earth Ihall be in
thofe Points of the Ecliptic ; and likewife when he will be
feen from the Earth in 19" 45' of Gemini and Sagittarius,
when the Rinjg; will be moil open, and in the beft Pofition to
be view'd.
8. There have been fome Grounds to coiije£turc that Su^
tttptH Ring turns round an Axis, but that b not yet demon*
ftrable. This wonderful Ring in fome Situations does aUb
appear trouble ; forCa^ntin the Yean 675 obferved it to
be bife^ed quite tound by a dark elliptical Line, dividing it
as it were into two Rings, of which the inner one appeared
bnghter than the outer. This was oftentimes obferved after-
wards with Tubes of 34 and 20 Feet, and more evidently
in.the Twilight ot-Moon- Light than in a darker Sky. Sec
PbiL Tran/. abridged, Vol. 11. p. 221. 222.
(CXXXVHI) I. The fagacious K^Ier was the firft who
dticover'd this great Law of Nature in all the Primary Pla-
L It
L._...
334 AsT*RONOMY.
1. It is moft fimple, and agreeable to die Te*
nor of Nature in all her Aftions ; for by the two
Morions of the Earth all the Pbitnomena of the
Heavens are refolved, which by other Hypotbefes
me incxpKcabk without a great Number of other
Motions, contrary to philofophical Rcafoning by
RuleL
II. It is more rational to fuppofe the Earth
moves ^x>ut the Sun, than that the huge Bodies
of the Planets, the ftupendous Body of the Sun,
and the imrhenlp Firmament of Stars, Oiould all
fliove round the inconfiderable Body of the Earth
every twenty- four Hours.
III. The Earth moving round the Sun is agree-
able to that general Harmony, and univerial Law,
aat»« and nfttrwank the Afironomers obferved tliat the Se-
condaries did likewife regulate xkeit Motions by the fame
law. I have afready exhibited the Mathematical Theory
thereof in Aamt, XXXIV. 1 1, and given an Example in the
Earth and Femu, And that the fame Law holds in the Syftem
0f yufkir^% and S'aturft's Moons^ will appear from the fol-
lowing Inftances.
2. The £rft of Ja^ter^ Moons is at the Diflance of 3| of
y^ter^^ Diameters from his Center, and revolves in 42
Hotirt. The ontermoft defcribes its Orbit in 402 Hoars;
therefore &y« As 1764 (the Square of 42) is to i6i6o4» (the
Square of 402) <b is ^i^ (the Cube of a|) to aearly
t!^222Z, the Cobeof $ori2t, theDiftanceofthefoonh
Satellite ; which anfwers to Obfervations.
3. Or thus analytically by Logarithms. Let L zs. Lop-
rkhm of the Period of the fiift Satellite, L z^ Logarithm of.
ail^y other Satellite's Period, and D and 4^ the Logarithms of
then: Diftancesj then will it be aL : 2/ :: 3D : 3^/, and
therefbce zL 4* 3<^=^ 2/4- 3D; whence we hare d:n
D ^ «/ ^ |L. For Example^ in the firft and fecund ^
which
2
r
Astro no m y,
ivhich all other moving Bodies of the Sjrftem ob-
fcrve, viz. That the Squares of tbepmoAicalimes
are as the Cubes of the Dijiances: But if ihe Sun
^ move about tte Earthy that Law is deib'Ofld,
and the general Order and Symmeoy of Na^e
^. interrupted; fmoe according to that Law. the. Sun
would be fo far from revolving about tile Sdlth
in 365 Days, that it would require 00 Icfi than
^ 5196 Years to accomplUh one Revokition.
^ IV. Again : Did the Sun obferve theumver-*
fal Law, and yet revolve in 365 Days, his Di-
fiance ought not to be above 3 10 Semidtamctcrs
of the Earth; whereas it is eafy to (Mrove it is
really above 20000' Semidiameters diftant from
us/
tellites of Jupiter^ Cajptd obferved the Diftaaoe of the iirft
<^ in Semidiameters of Jupiter to be c|, whofe Lopantlmt it
"* Of 753353- The Periods of thoie Satellites give •!/££
' 2)32459, and -yLzi: 2,122851; from whence we get dsi
^ 0,95509, the Number correfponding to which is 9.07ft Ae
I Dillance of the fecond Satellite, agreeing wonderfully with
Obfenration.
^ 4. Now iince the Moon turns round the Earth, if the Sun
: did likewife perform his Circuit about it, their Motions woold
undoubredly be regulated by the fame Law with all the i^.
Bat the Period of the Moon is 27 Days, that of the Sun
365 ; the Diflance of the Moon 60 Semidiameters of the
Earth 1 therefore fay. As 729 (the Square of 27) is to 133125
(the Square of 365;) fo is 216000 (the Cube of 60) to
39460356^ the Ci:d>e Root whereof is 340, which ought to
exprefe the Sun*s Diftance in Semidiameters of the Earth.
But we have (hewn the Sun b really diftant from the Eiatth
near 20000, ((ee ^xmo/. CXXXI V. 18.)
5» Admitting the Son to be at the DHlance of 20000- Se-
midiameters^ his Piritdieal Timi would then be mOre than
450 Years, if its Motion were governed by Kepkr^s Law,
and compaied with that of the Moon; foray 21 6000 (r^'6o')
aa to 8000000000060 (;=: 20000') fo is 729 (= 27^) to a
335
.gg6 A 8 T RON O M/ 1*
V^ The Sun is the Fountain of lightatid Hdti
^ll(uch it irradiates through all the Syftem ; and
therdbre it oi^t to be placed in the Center^
that fo all the Planets may at aU doies have it in
an uniform and equable Manner : For^
VL If the Earth be in the Center, and the Snn
and Planets revolve about it, the Planets would
then, like the Comets, be fcorched with Heat
when ncareft the Sun, and frozen with Cold in
the'u" Apbeliay or greateft Diftance ; which is not
to be fuppofcd.
VIL If the Sun be placed in the Center of th^
Syftem, we have then the rational Hypothciis of
the Planets being all moved about the Sun by the
univerfal Law or Power of Gravity arifmg from
Namber^ the (quare Root of which is 164320 Diys = 450
Yean neariy, which is the Periodical Time of the Sun'sRe^
volution at that Difiance, and moving according to the UnK
ver£d Law.
6. This beautiful and harmonious Syftem, or Frame of
the World, fufficiently recommends itfelf from the Principled
of right Reafon only ; fuppofing there were no fuch Thing
as abfohite Demonftration attainable in the Cale. It is there-
fore very furprizing, to obferve, how few among thofe who
are not Mathematically learn'd, can be induced to believe,
and acquiefce in this Dodrine of the Earth^s; Motion, and;
Stability of the Sun. Copernicus^ above 200 Years ago, men-
tions the. zealous Father LaStmtius^ asridkoling thofe who
aflcrted tl^e Spherical Figure of the Earth. Therefore, fays
be, it is not to be wonder'd at if fuch Sort of Pepple fliould
ridicule Us. And whatever the Popes may have iince de-
creed, 'tis certain, this Dodlrine was fo far from being then
reputed heretical and damnable, that this great Man dedi-
cated his Book to Pope Paul III. becaufe by his Holinefs,
Authority, and Learning, he might be fecured againft the.
Calumnies of ignorant Gainfayers ; yea, and appealed to his
Holtnefs at the fame Time for the Ulefulnefs of his Dodlrine
even to the EcdeiiaiUcal Republick. His Words are, Mathi-
liis
A S T R ON O M Y. 337
His vaft Body ; ana eircry thing wiH anfwcr to the
Ijawsdf ei«:ukr Morion j and central Forces: But
acberwife >yc are wholly in the dark, and knowae*.
tl^ag ^f the Laws and Operations of Nature.
VIII. But happily we arc«bl€ to give not on*-
If Reafon^ but dmot^rative PrUfs^ that the Sun
does pofiefs the Center of the Syftem^ and that
the Planets move aboi^t it at the Diflance and in
the Order above alfign'd: The firft of which is^
That Mercury and Venus are ever obferved to have
fwo ConjunSlions with the Sun, but no Oppqfition ;
which could not happen, unlefs the Orbits of thofe
Planets Jay within the Orbit of the Earth
(CXXXIX).
mata Matbemaiith firibttntur, quibus {*f bi noftri Labores^ Jt
f^ nom failit vfitMy nniihuntur etiam Reipubiiae Eceiefmflic^
eamhiore alipiid^ ct^us Principatum tua SanBitas nunc temt,
(CXXXIX) t. What relates to the Cotijunaions and Op-:
positions of the Planets will be eafily underftood by a Dia- ±x
gram. Let S be the Sun; T the Earth, V Fenus, and M Mer^ PI* ^VIL
cttty^ in their feveral Orbits. Now 'tis evident that when
Fenus and Mercury are at V and M, they will be ieen from
the Earth T in the fame Pan of the Heavens with the Son^
n)ix. at W, becaufe they are all pofited in one Right Lin^
T W ; and this is talPd the Lomotr or Inferior C»njun£iion.
2. Again : When Femu and Mtrcm^ comfe to the Sitnacion^
D and O, they are again in the fame Right Line joining tkd
Centers of the Earth and Sun, and are therefore again itai
in the fame Part of the Heavens with him ; and this is call'd
the Upper or Stiperior Conjwtaicn, Utr6 'tis evident, tbofd
two Planets, muft appear twice in Conjun6iioii with the -Sad
in each Revolution, to a Spe^top-on the Earth at T, whkh
we at prefent will fappofe tb be at Reft.
3. Hence we have an. infallible Proof that the Orbits of
Venus and Mertury lie both within the Ol-bit of the Earth;
Alfo the Orbits of Mars^ Jtif^ter^ and Saturn inuft lie without
$he Orbit of the Earth ; for otherwiib they could not cicbi^
bit the Af^)earanGC they do of alternate Conjundltons and
. Voh. ih Y IX. Thb
Xl^.
A S T R 0,N0 M Y.
IX. The ficond isy That Marsy. JupttCTi and:
SaiurBf have each their ConjtmHions aod Oppefe^
iims to tke Sun, alternate and fucceffivejy ;'
which could not be, unlcfs their Orbits were cx-^
terior to the Orbit of the Earth.
• X. In the third Piace^ The grtateji Elongation
or Dfflance of Mercury from the Sun is but about
ao Degrees, and tliat of Venus but about 47 ;
which anfwers exa^ly to their Diftances in the
OppefiiioQS. Thos let Mars be in his Orbit at Y, *ti6 evi-
dent when the Earth is at T, that Planet >vill be feen in Con«
jaodion with the Sun, and will be then at its greateft Di-
Ibfioe from the Earth.
4. But when the Earth is at / between the Sun and Mffiip
^6s plain they muft appear in oppofite Parts of the Heavens,
becwife a Perfon at t viewing the Sun at S muft look diredly
, t0 tfafi contraiy Part to view the Planet at Y ; and in this Op-
pofition to the Sun Mars is neareft to the Earth : AU whicJk
is fo evident from the Scheme, and fo exactly s^eable to
the Phenomena of thofe Planets in the Heavens, that any
Perfon muft be ibangely oblHnate, and incapable of any Sort
of ConviAion, who cannot fee the ConfUtution of Nature,-
and the Diipofition of the Planeury Orbits, are fiich as are
2Jbove delcribed.
^. But farther: If we divide the Diflance of the Earth
from the Sun, *viK, the Line ST, into a hundred or a diou*
fuod equal Parte, and place the Orbits of Feadt and Mtr^^
cMfy at the DiHance of S V =: 724, and SM z=: 388, and
then draw T A, I'R, to touch thoie Orbits in the Points A
afld R} then 'tis plain the Angles ATS and RTS will mea-
fiire the greateil DiHance at which either .of thoie Planets can
be feen from the Sun; becaufe the vifual Ray paifing to the
Pljinet in any other Part of its Oibit will* lie nearer to the
Liae TS W, and theiefore fliew the Planet nearer the Sua
t^smji^hen at A or R.
STNow *tis found by meafuring thofe Angles geometri-
cally in the Diagram, that the Angle ATS = 47 Degrees,
and RTS r^ 20, very nearly ; and this agrees exa^y with
their obferved greatejd Diilances or Elongation from the Sun
in ch^ Heavens. Hence it is that M(rany is {o rarely feen,
tod Vims but dt celtain Times of the Year^ whereas if the
Syftcm
As Tib HO u Y. 339
Syftem above affigrt'd i But in the Pt^meak Sf-
ftem, they ttiight and would fometimes be fcch
r8o Degrees from the Sun, viz. in Oppofitien
td him.
XL Fourthly, In this Difpofition of tfie
Planets they will all of them be fometimes much
nearer to thfe Earth than at others; the Confe-
tgoence of which is, that their Brightnefe and
Splendor, and alio their appAtent Diameters^ will
rfitrth were at lkt% and in the Center of the Pknccmrjr Qr-^
knx$j thofe Piaiieti woald be ieen in all Pofitions and Di-
ifauiC8ȣtim the San, in eveiy refped like the Moon ; and
therefore 'tis perfe^y iurprizing, how any Man can reift
-ittfih glaring Evidemde of Truth on one hand, and Falfliood
on the other. . . '
7. We have already fhewn, that the apparent N^q;aitiide
and firightneis.of an Obje£k decrease as the Square Diftance '
increafel ; therefore the Magnitude of P^emus feen at V is to
that as it appears from D in the Proportion of TD* to
TV*, that is, as 1724* to 276*, or as to i nearly. And
when Fenus is meafured in both thofe Didances with a Mi^
crometer in a Telefcope, the Numbers (hew the perfeft A-
greement of this Syftem with Nature itfelf
8« Thus alfo the apparent Magniluds of Man when his
Difiance is rY, is to that when his Diftaace is T Y, as T Y*
to / Y* 5 that is, as 2523* to 523*, or very nearly as to i . ^^
And this we know is true in Fad, by meafaring the Phuiet
in both thofe Diitances. It is likewife obvious to commoa
Senfe ; for Mars in his neareft Diftance appears fo large that
he has been often miftaken for Jtipiter^ whereas in his great*
eft Diftance he appears fo fmall as fcarcely to be diAingoifliVl ,
from a Fijc*d Stan
9. From what has beea faid of the Phafes' of the Moon»
^tis eafy to uiiderftand that Fenus ztid Mtrcvfy muft have near-
ly the like Appearances. Thus when Fenus is at V, all her
illumined Hemifphere will be tam'd diredly from the Earthy
and fhe will then be New. As fhe paflfes from V to A iho
Will appear bomed. At A (he will JheW juft half her enlight*
en-d Surface to the Earth, and appear bifea^^ or ^choto^
iniftd. Ff#m A to D ihe wifi appear- moi^ an4 mwtgiibous $
Y 2 be
340 Astronomy.
be propdrtionally greater at one Time than ano-
ther: And this we obferve to be true every Day^
T^iis the apparent Diameter of Venus^ when
greateft, is near 66 Minutes, but when leaft not
more than 9 Minutes- and a half j oi'Mars^ when
greatefti it is 2 1 Minutes, but when leaft no morjp
than 2 Minutes and a half ^ whereas by the Pto-
lomean Hypothefis they ought always to be equal.
XIL The fifib is, -Tliat when the Planets are
atod at D would appear a /^k// enlightened Hemifphere, w^
k not that ihe is then loft in the Sun*fi Blaze^ or hid behind
his Body : All which Phafes return again in the other Half
of the Orbit. The fame Thing is obvious in Mercury ^ and
Man ihews part of thofe Phafes i but Jufiter and Staum ap-
pear always with a Full Face, by reafon of their very great
Diflance.
10. The Appearance of Venus in the Day-time for feveral
Days together, in fome certain Years, pot the fagadous
Dr. Halley on refolving the following TProbleni, nnz. To find
the Situation of Venus in reffeB of the Earthy wohen the Area
of the illuminated Tart of her Dijk is a Maximum, I fludl here
p^t the Solution as he has propofed it in the Philofophicsd
Tranf anions J N° 349 j and alfo the Demonftration, which
the Dodtor omitted.
flate 1 1 . In order to this, let S be the Son, V the Planet Venus
LVIII. in the Situation required, T the Earth, and TV her Diftance
Fig. I. fought. Pot T6 = <?, SV = ^, TV =2 at, and on the
Point V with the Radius VT defcribe the Quadrant TA 5
from T let fall the Perpendicular TB» and put BV=::ii
then A B =.;r — ^ =: 1;, the Verfcd Sine of the Angle T V A.
Now (by Emtid IL 12.) we have a* =.^* + ** + zhd^
whence A^ -— 2^^ = ^* •+• ** » ^"^ by adding zbx on each
Side, «*+ zhx — 2^^/ = ^* + 2^;f + ;r*i thatis, «* +
^hv^^^h^ -\-zbx '\'xxzz:.r. Then r-—tf* = 2^0/ = j;
and mnltiplyiog by 2;ir we have J^bx'v =;; %xs^ whence ^bx ;
s :: zx I *vi thatis, /^bx : h^ -^zhx-^-xx — «* ;: 2TV:
AB :: the Diameter of a Circle to thf Verfed Sine of the
eacteiior Angle T V A.
12. But in any Situation B of the Planet V4nus the Arch
pf Illumination af is equal to the Arch bd^ which meafttrcsr
the exterior Angle b^d. And it ha^ been fl)cwn» that tht.
View d
AsTRONOMYt 341^
viewed with a good Telefcope they appear with
different Pbafes^ or with different Parts of their
Bodies enlightened. Thus Venus is fometimes
ttew^ then korned^ after that dichotomizedy then
gibhuSy afterwards /«//; and fo increafes and dc-
creafes her Light, in the fame manner as the .
Moon, and as the Copernican Syftem requires.
, XIII. The /ixth is. That the Planets, all of
them, do fometimes appear direSl in Motion,
Area of the nvho/e Dijk of the Planet is to the Area of the in*
lighten d Fart as the Diameter of a Grcle to the Verfed SiHt tf
the Arch of IllumnaHon^ and therefore as ^bx to b^ -J^zhx-^
13. But the Area of the whole Diflc. is every wktre at
— i therefore^ as ±b^ : i.^ + 2 i^r + ** •*- «* ,;; — :
XX ■ . -r ^^
h* + Zbx+X* tf* ,., . ,^ r> r Ml i_ '
— r! — .. ;' ■ ■> which in all Cafes will be propor-
tional to the enlighten'd Area of the Dlfk. And to deter-
mine this a Maximum its Fluxion mufl be := 0^ or the nega-
tive Pans thereof be equal to the affirmative, that is, that
• ^bx + 2XX X ^bx^ =: izbx^x x ^* + zbx-^^xx — '«*;
and dividing all by ^bx'^x, the Equation becomes zbx^
j2;r*=: 3^*4" ^^*+ 3-** — 3^*- Confequently ^hb*^
^.bx-^ xxrz $aai whence we get ;r := V^ 3 «« + ^ —
2^ = 427.
14. If therefore we take 427 from the Scale of equal
Parts ST, and fet from T to the Orbit of Fenus, it will in-
terfedt it in the Pointer ; and drawing Tx, it will give the
Angle xTS = 40 Degrees nearly; which Ihews that when
Fenus is 40 Degrees ditlant from the Sun, before and after
her Inferior Conjun^ion with him, ihe then fhines with tho
greatefl Luilre poffible. '
15. In this Poiition we fee not much more than ^ of her
Diik enlightened, and yet fhe fhines with fo great a Loftre as
to furpafs the united Light of all the Fix'd Stars that appear
with her, and cafb a very firong Shade on the horizontal
Plane, and may be feen in the full Sun-ihine of the Day ; a
Phaenom^non very extraordinary, and which returns bat once
fn ei|l^t Year?,.
Y 3 to^-
342 Astronomy.
fomctimcs retrogradej and ^ other i\vm%ftatiaHa^
ry. Thus Venus^ as fhe paffes from her greateft
Elongation Weftward to her greateft Ebngation
Eaftward, wi)i appear direStJn Motion^ but retro^
grade as fhe paffes from the latter to the former %
and when Ihe is in thofe Points of greateft Di-'
ftance from the Sun, flie feems for fome time Jfa^'
iknary: All which is neceffary upon the Coperni-
16. The different Dlreftions in which the Planets appear
fo move in the Heavens is an irrefragable Argnonent of the
Truth of the Sol^r Syftem ; for in the Ptohmean Sjrftem they
would be feen to move with their Uue or real Motion, and
}n their Diretlion according to the Order of the Signs from-
Weft to Eaft, in every Part of their Orbits, and that alwayi
in an equable Manner ; whereas now we obfcrve'them move-
fometimes from Wefi to Eaji^ when they are faid to be dtreSH
in Motion ; fometimes from Eaft to Weft^ when they are faid*
to be rstrograde^ or to go backwards ; and fometimes they
appear not to move at all for a certain Time, when they are
faid to be fiatioi:(iry : And laftly, the Motioft of" a Planet*
when iSre^ is always much flower than when it is retrograde.
1 7. Now all thefe Phenomena are not only explicable by,*
fcut npceffarily follow from, the Copemican Theory. Thn*
with refpc6l to tjie Pljinet Mercury^ when at R he will appear-
it his greateft Diftance from the Sun among the Stars at Q^
being feen in the Line TQj but as the Planet palTes from R
by N to O, the vifual Line TQ^will continually approach
the Line T W, in which the Sun appears at W ; and when
the Planet is come to D it will be in Conjundion with thet
Sue, and will have apparently defcribed the Arch QJW ill
the Heavens. After this, while the Planet moves from O to
2, it will appear to go in the Heavens from W to X, ftill
|he fame Way as before 1 ^nd b^caofe its apparent Motion
agrees with thp true, it is all this while din^i.
1 8. But when the Planet inoves from Z to M, the Ray
TX will return, and deffrribe the Arch X W back again; and
f^a the Planet moves from M to R, the vifual Ray will keep
^^ving on from W to Q^; and fo in the PaflTage of the Pia-«
net through the Part of its Orbit ZMR it will appear to
inove in the Heavens through XWQj the fame Arch as be«
fore, bat in ^ rftro^rad^ Dire^ion.
cm
A 8TX)OM)OM y./ 343
ami i^p^kffis, but canaot Jiappen in any other.
. ,XiV, Th5 fififenih is. That the Bodiesof Mer-i^
f^ »nd F^nuf^ in their lower Conjun6lions with
the Sun, ve bid Mind the Sun*s Body ; and^ to
the upper Comjanjftiops, arc feen to pais over the
Sun's Body or Difk in form of a ilack rcwtdSpfft:
Which is neceffary in the Copernican^ but impof-
fible in the P/^ii?;»f^» Syftem.
19. Now becaufe the Tangent LimJ dr viibal Rajr TQor
TX coincides as to Senfe'witli the Orbit of the Planet for a
fmall Diflance on each Side the Points R and Z, as ixOiSk m
to b^ and from € to di therefore the Planet when it arrives at
.a will appear to move in the Tangent from axo b^ during
which Time it will be feen in the fame Right Line T Q» and
eCXkAfcqnentiy in the fame Point QJa the Heavens : So that m
its. Motion from ato b it. muii appear flatimary^ or without
any M£)tion ; and the fame is to be obferved in moving from
V to d^ when the Planet is .in that Part of its Chbit.
20. Henqe we . obfervc, .that in Mercury and Fenus^ the
Places R, Z, and A, G, of their greateft Elongation are tiiofc
in which thqy are fiationary. It is in.thefe.two Points that
we can at any time \ttMfrcury i, and it is in thofe Points that
we fee Venm fuch a glorious Morning-Star er Phofph^rus at A,
and fuch a fpjendid Evening-Star or Hr/perus at G. Henoe
we ob^ve, ,that from the Tinac Fmuj js a Morning-Star in
her greateft Elongation at A. to the Time of her berog an
IJyening-Star in her greateft Elongation at G, fhe is £ri£i in
Amotion : Confeqgently^ half the Time of her being a Morn-
ing or Evening, Star fhe is direS, and the other half r^M-
^rade.
^i, AJfo it is eaiy to obfcrve, that fince the iame Arch QX
is dclcribed in Xinie^ very nnequal, njiz. in the Times the
Planet defcribes the. very unequal Parts of its Orbit ROZ
and ZMRy the VeloQQr of the Motion in the former Cafe
inuft be much.lefs th^ that in the latter; that is, the Planet
whea^aSiV/^ inoves apparently much flower than when it is^
rstr^rade,
^i?,2. Jf we confidcr the Difpofitions of the Orbits of 4|^
ifuperior Planets, we ft»Il obferve the fame Pbaenomena »|^
tbem^lfo. Let S be the Sun, ACH the Earths Orbit, ™^
JMK that..of M.,, .«ul.,OI.Q.A. Fu«uun«.t of Stars. LVIH-
Y 4 XV. The *
J44 A STRON oil y.
XV. The eigbih\%y TKat die Times in whkrh
thcfe O^JsriKS^/^/Kf , Oppofitimu^ SUUums^ mARe-
fragradaiions of the Planets happen, arc not ftich
^ they would be, were the Earth at Reft, in its
Orbit ; but precilely fuch as would happen, were
th&Earth to move, and all the Planets in the
Periods above a^ign'd them i And therefore fbiy^
and no other ^ can be the true Sjftem of the World ;
through Mars at M diaw QMG and OMC, to toodi 'tli^
Earth^A Orbit in G and C. 1 hen becaofe die Earth and Mars
do both move tiie fame Wajr, but the Earth vcij qiiic^ in
refped of Maru all the Phaenomena will be the verf &mt
|f we fuppofe Mars to be at Refl, and the Earth to move
with the Difference of their Velocicies.
23. Let Mars then«be at Reft in M, and the F^rth begfp
her Motion from G. At G the Planet will be feen in the
Line OQ. among tlie Stars at Q^ When the Eanhis at If,
Mars willbe feen in the Line HP, among the Stars at P. Ill
the fame manner at A/B^ and C, the Planet will be proje^-
ed to the Points L, N, O, in the {^vens. Therefore white
the Earth defchbes the Fart of its Orbit G AC, Ma^s wiH
appear to mpve through the Ardi of t)ie Hdivens QLO;
.wbi^h being from Welt to Eaft is according to the Order of
the S^ns, and the Planet will be £rt& in M9ti§m.
2^ fi)it as the Earth proceeds from C to D, Mars will ap-
pear .to move from O to N ; and as the Earth goes on through
E, F, to G, Mars will appear to return by L, P^ to Q^, and
fo mcafujre back again the iune Arch as before : And thus
daring t^e Earth's Paifage from C to G, this Planet will appear
rarogra^f I which therefore muft always be the Cafe when
.he s in Oppoiitibn to the Son and neareft to the Earth, as in
Conjunflion he is always Jht^ in Moiion ; and when the Earth
15 in^C or C, the Planet muft appear for fom^ Time Jfationa-
ry, foi; the Reafons mentipn*d in Jri. 19. The mane mav
be (hewn ofjuptttr and Saiurn ; but as the Earth has a mucn
greater relative Velocity in refpeA to Jupiter than it has with
rcfpjd IP Mars, the Times of the Conjunaitim and Oppofitions^
as alfo of i\\e progreffi^ff and rfgreffiife Moiimst m\\ be mo^e
frequent in Jupittr than in Mars^ and for the fame Reafon
^ ' will happen oftencr in ^turn than in Jupiter.
"■•^* • ^5. Again: Another Ph^nomenon^ which infallibly proves
• ; ' and
Astronomy. 345
and' it willflaiid the eternal Tcft of future Ages,
for, MioHTY^is THE Force of Truth, and
SHAtt PREVAIL* •
But though die Planets all move round the
Sun in Orbits' commonly fuppofed circular , yet
are they not exaftly fo, but elliptical, or in form
of an Eli^ipsis, which Figure is vulgarly call'd
the Truth of the Copernicfm Syftem* is, that Fam^ and jlf/r-
cury fuffer an Occultatlon behind the Sun's Diik, when the/
^re in the remoteft Parts of their Orbits, as at D and O; ba(
this can never happen in the Ptolomean Hypothefis, becaoie
ther^ the Orbit of the S^n is foppofed exterior to the Orbits
of thofe two Planets,
26. All theie Pha^nompna of the Planets plainly pro?^,
that the £arth holds that Place in the Heavens which the pre-
fent PhUofophy afligns her; but to (hew moreover that (he
}ias not only a Place among (he Planets, bat likewife that (he
is carried in th^ fame Manner wi(h them about the Sun, w^
need only obferv^, that the Times in which thefe Pheno-
mena happen to the Planets are no ways fuch as they woulj
be were the Earth at Reft, but fuch as they muft neceflarily
^8 f^ppofuig At Earth's Period abont the Sun to be in 365 1
27. For Example: Suppofe Fsuus at any time in Con-
junclion with the Sun at V, then were the Earth at Reft aK
T, that v^ry Conjundion would happen again when Fiuus had
made jufl one Revolution, that is, in 225 Days; but every
pne knows this is contrary to Experience, for a much longer
Time than that lapfes between two Conjundions of the famr
Kind ; as there evidently muft, if we fuppofe the Earth to
have a Motion towards the fame Parts in the fame Time ; be*
caufe then, *tis plain, when Fenus comes again to V, the
Earth will hav^pkfe'd in that Time fropi T to fome othcf
Part of the Orbic, and from thi» keeps moving on, till FcMtu
gets again between ic and the Sun.
28. What this. Surplus of Time is may be eaiily eftimated»
.\>y fnppo&ng the Earth to be at Reft in her Orbit, and Ftfou
to move with the Difference of their mean Motions. Thus
the daily mean Motion of the Earth is 59^ 8^^ and the daily
piean Motion of Femu is i" 36' 8^. The Difference of thcfc
mean Motions is 37'^ thfreff^re fay, As 37^ it to the whole
an
2^6 Astronomy^
znOvalj asABPD, defcribed about two Centen
S, F, caU'd the Feci, or Focal Pmnts of the Ellipfe
The Point C is the Center ; A P the Axis* or
Jongeft Diameter ; and BD the ffiorteft Diamc-
*ter: Andiaoneof thcfeFocus*s. f^/z.S,. the Sun
is placed, about which the Planet moves i<i the
Orbit ABPD(CXL). : '
Cirele or 360^ == 2t6oc/, fo is i.Day to ^83 Da/s^ tbe
Time between two Conjun^lions as required, viz. i Year ■
and 2 1 8 Days^ in which Time Vcntu performs a little more
than i\ Revolutions. In the fame Manner the Time way'
be found for any of the other Planetary Conjanftions, Op-
pofidons. Stations, Retrogreffions, l^e.
27. Thefe Arguments are plain, and eafy to be andcr-
Aood; Bioft of them require no raorc than common Obfer-
ration, that is, in other Words, comTnon Stnfi. To be igno-
lant of the Truths here fpecified, is to fhew an unaccountan
b!e Inattention to the molt obvious and glaring Phacnomena
©f Nature : And if People arc not convinced by thefe Proo^^
k is not becanfe they cannot^ btst becaufe they ^Unoi-^ ana *
therefore, $i Fopufus <vult dtdpi, dcclplatur.
(CXL) 1. We haTC hkherto confider'd tfa Phenomena of^
the Heavenly Bodies without regard to the accurate Form 6f*
Aeif Orbits, whicli is net drcidary but ifltffical ; yet that it
is irery Kttle fo, even ki the moil eccentric Orbit, as that of
Mtrtury, will appear by comptTing their Eccentricities Witlir
tlk^eir mean Diftances from the Sun . Thus fuppofe the meah
^Hftan<[e df the Earth from the Sun be diridcd int'6 looci
MutJ Parts, then in thofc Parts we have, *
InMcrcMrjt, CS : DS :; 80 : 387 :: 1 : 4»»4
'^r^nus^ CS : DS :: 5 : 725 - 1 : 144,6
' * EitttJb, CS : DS ::' 17 : 1000 :: 1 : 19
Mars^ CS : DS :: 141 : 1^:24 :: 1 : io,S
Jupitir, CS : DS :: 250 : 5201 ;; 1.: ao,8
Saturn^ CS : DS :: 547 : 953? u 1 : 17^4
2. It t» /ottnd by Experience that the Otbks of f he Phnets
Plate ^^ quicfifent, or thatf the Line of the Jpfde$ A F always keeps
LVIir ^^ *"^ ^ ^°"® Pofition wiA rcfpect to the Fix'd Stars:
pj - * And the Jfhetium^ or Point A, poffefies dtfferCBt Pofeta m
^* the Ecliptic in the fereral Orbits as idiowK
Hence
A s T * o N o M y/ 347
Hswct^ whcta the PJanct is ki tBiiPwnt P, it
is neardfl: the Sua» which Fotnt is^ for that Rea-
In Mgraifyiy
t ij 44 oo
}Ib M^Sf
• / * if*
hnMs,
- 4 «9 54
Ju^iT,
•^ 9 9 SV
BMh^
i:f 8 i lo
SAtwrUj '
^ ^7 49 SV
3. That the Earth^s Orbit M elliptical is well known from;
common Experience ; for were the Orbit circular, the Son^*
apparent Diameter would always be eke fame \ but we find
it is not, for if it be meafared with a Micrometer in Winter-
time, it will be foaod cooiiderablx liarger than in the Sum*
mer, and it will be greateil of all when the Sun is in the S*
o^ ):f , (which (hews that is the Place of the Jpheliam) it be-r^
ing then 32' 47^; whereas when the Sun is in the %^ aH ^^
his Diameter is but 31' 40'^
4. Hence It is evident that the ikn is really nearer to ua
in the Midft of Winter ,than in the Midfl of Summer ; but
this feems a Paradox to many, who think the Son muft necda
be hotted when It is neareil to os, and that the San is appsi.
rently more diftant from us in Decern hir than in June, As t9
the Sun^s being hotter, *tis true rt is fo to all thofe Places
which receive his Rays dire£lly or perpendicolarly, but .-we
find his Heat abated on account of I he Obliquity of the Rap,
and his Ihort Continuance above tlie Horizon at that Time*
And as to his Diftance, it is only M/ich refpedl to the Zenith
of the Place, not the Center of tlie Earth ; fince it is plain,
the Sun may approach the Center of the Earth, at the fame
time that it recedes from the Zenith of any Place.
5. Agreeable to the Son's ncancr Diilance ia the Winter^
we obferve his apparent Motion b then quicker than in Sam*
roer ; for in the 8* of Vf it is abcnit 61' fet Day, but in the
8"" of 2s his Motion is but ^^^ J^er Day. Accordingly vm
find the Summer Halfl Year S Days longer than the* Wintet
Half- Year, as appears by the following Computation.
S tr M M E R Ha/f^' Year includis V/ 1 N T £ R Haff- Tear tndudet -
■~ •-. -^ Days,
In March
21 J Days
JfrU
30
Mof
3«
June
30
July
31
Jugufi
3»
Stftmher
12
Somraer-Half
186^
Winter-Half
i7»4
The DifFercncc
' 8 Oayi.
In September
18 .
Oaoher
3«
Novemher
%^
December
3«
January
3«
february
?8
Match
95
fon.
^48 A S T R O N O M Y*
fc^, caird the Peribetion: H^re, therefore^ t^c
Xttfiaion of the Sun is ftrongeft, his Light and
%., For thci Son's attradling Force 'being one Part of diQ
ia(d(| of the Planft^ Motion, and this Force always in-
tb'eaimg and decreaiiiig in the inveHe Rati6 of the Squares of
the Dil!ances, *tit evident the Velocity of the Planet will al-
#a^s be greater the nearer it is to the Sun, and 'vice werfd^
I&nce the Motion of a t'lanet is eveiy where unequable, be-
ing conilantly accelerated as it pafles from A by D to P, and
in the other Half from P to A it is retarded. '
7. Yet Is this unequal Motion of a Planet regulated by ^
certain immutable Law, from which it never varies, which
ij, ^bat a Une drauan frvm the Center of the Stm to the Cdr-
ter of the Planet dots fo tno^e ixj'ttb the Planet about the Sum^
that it defcrihes elliptic Anas al<ways frtfparfional ta the fimeff
That is, if when the Planet moves flow^ll it defcribes the
Ardi A A in a given Time, and when it moves quickeil 1^
defcribes the Arch ^P in tlie fame Time, then will the trili-
neal Area ASa be equal to the other trilineal Area ^SP.
Plate ' ^' ^^ dcmonftrate this, let the Tinae in which the Planet
V Ylll inqves through the Periphery of its Orbit be divided ihtd
J. * equal Parts, and fuppdfe that in the firft Part it defcribed anjj^
-rig. 4. Rjgijt Line AB, by the Projedile Force in any Dircftion and
the Centripetal Force conjointly; then in the fecond Part of
Time h would proceed in the fame Right Line to r, if nq-
thing prevented ; fo that Br = AB, as is manifeft from th^
fiitc Lanjo of Motion,
9. Draw the Right Lines S B, S^, and the Triangles A B S and
BrS will be equal, as having equal Bafes AB, Br, and the
iame Altitude of the Vertex S. But when the Body comes
to By let the centripetal Force ad with a new Impulfe either
<qual to the former or unequal, and let it caufe the Body to
decline from the Right Line Be, and defcribe the Right Linq
JE^C; draw Ce parallel to BS, meeting BC in Ci an4 at
the End of the fecond Part of Time the Body will be at C,
andf in the fame Plane with the Triangle A SB. Join SC, and^
/ becaufe of the Parallels SB, Cr, the Triangle SBC will be
<qual to the Triangle SBr, and therefore equal to the Tri-
^h|!e SAB. B/ the fame Way of Reafoning, if nhe cen-
tripetal Force ad fucccffivcly in the Points C, D, E, caUfing
the Body in each eqijal Part of Time to defcrib^ the Right
' Lines CD, DE, EF, fsfr. the Triangles SCD, SDE,
SEF, Cs^r. will be equal, and all in the fame Plane.
10. la ^qval Times, therefore, equal Are^ ar^ defcribedi
Heaj
A ST %rO NtO m v. 349
fieat gretjtefti and his apparent Diameter largeft s
and in this Point the Planet muft confequently
^and, by Compoiition of Ratios^ iny Soms^f Areas 9ABS|
SAFS, .are to each, other as the Times i^ which they are
defcribed. , Let now l;he Number of Trianjjles be increa(e4»
and their Breadth he dimwUk'd.fn in/if itumi then will their
Perimeter A OF be ultimately a .Curve; And thereCbre the
centripetal Force, by which ,the Body is < drawn perpetoall/
from the Tangent; of this Curve, a^ inceiTantly ; and the
Areas defcribed are alfo in this Caii^ proportional to the
Time^ of their, Defcription., /, .
; ^ 1 1. Hence the. Velocity of the revolving Body or Planet
is ^y&ry where inverlely as the Perpendicular let fall from the
Center ^&tp the Tangent of the Orbit in tlie Place of the
Planet. For the Velocities in the Points A, B, C, (^c. are
s^ the Bafes of the Triangles A B, BC, CO, bfc. as besiy
the Spaces, defcrlbpl in the fame Time; and the Bafes of
equal Triangles are reciprocally as their perpendicular Alti-
tudes i and therefore fmce in the evanefcent Triangles AS Bp
AS.C^ fefr. the Right Lines Ac, B^, Ce, isTc become Ta«-
gents to the Curve in the Points A, B, C, ^(. 'tis manifeft
the Velocity inthoTe Points will be inverfely as a Perpc^dic^•
lar from S let fall upon thofe Tangent Lines produced.
1 2. Hence alfo it follows, that the Times in which e^ual
Arphes are defcribed in any Planeury Orbit are diredly as thgie
Perpendiculars, becaufe they ate inverfely as the Velocities.
5 .15. If two Chords of very fmall Arches defcribed in the
f^jne Time AB, BC, and DE, EF, be compleated into the
Parallelogfams ABC V and FED Z, and the Diagonals BV
^ E Z be drawn ; then will thofe Lines tend to the Suq[ or
Renter S, and be proportional to the centripetal Force : Poi;
^fi Motion BC and £F is compounded of BV, Be, mi
EZ, E/j but BV = Cr, and EZ = F/i but Cc and F/
were geiierated by the Impulfes of the centripetal Force is
B,.and E, and are therefore proportional to themj and. cpn-
fequently fo are B V and E Z.
14. Draw the Diagonal AC, and it wiU bifed the Line
BV in ii confi^qqitly the Sagitta Bi is as the centripetal
jporce by which the Arch ABC is defcribed, whofe Chord
is AC. .
15. Hence Jf a. Body revolve in any Curve AP; about Plate
an unmoveable Center S, the Force in any Point P will be LVIIL
ID that in any other Point /as gp.^^z to ^~^. ' ^* *•
move
'35° A S T R 04f O M Y*
moVc with rjic grcateft -Velocity; But In the
Poific A, * wh<!re die Planet is faitheft diftanc from
Sot tbe Siigk^ QR, f r, (which call % j,) are aa the coo&i^
petal Forces (F, /,) in P and /, when the Times (T, /,) arc
.given, (by the M) that is, SisiiFz/. fiat when' die
Forces are giyeri, the Sagitta will be as the Squares of the
Times, «w». S : i :: TT : //.^ Therefore when neither the
Hmes nor the Forces are the iame, ic will be S : / :: F x T^ :
./x /*; and fo — : 4 " F = / And becaufe' the effiptic
Areas SQP and Sf^ are as the Thnes in which they are ije-
foibed, therefore when the Arches PQ^and ^f aie Adefi-
nitdy fciall, wt have T : / :: ^SP x QT : IS/ x qt ::
S* X QT : S} X qt. Confcquently we have, «s F ^/-:;
«P*xQT*'S/*xf^» : '
' 1 6. Let 3 V be a Perpendicolar let fall from S upon the
Tangent PR jproduc^d; then will the centripetal Force bf as
g-^^^, becwfe the Reaangle SY x QP = SP X (^
for the evansfceht Arch QP is coincident with the Tangent
PR, and ma/ therefore be edeem'd as the Bafe of the Tri-
angle SPQ, whofe Area is either 4 sip x QT, or 4QP x S Yj
therefore S P x QT = QP x S Y. Which was to be flicwnA
Plate * 17. If the Orbit were a Circle, as PQVF, and PV a
LVIII. Chord drawn through the Center of Force S; then drawing
Fig. 6. the Chord QM in fuch manner as it may be bife£ied in £.
by the Chord P V, we have QK» = V K x PK, (by Eudzti,
ill. 35.) but in the vaniihing State of PK it will be VK =
VP, and QR = PK (by Jn. 1 3 ) ; alfo QK = QP, there.
foreQP* = VPxQR. andPV=^i whence, in this
QR
Cafe, the CMtral Force will be inverfely as SY* x P V.
18. Wherefore, fince the Velocity is as ^--, we have SY*
O I
Is the Square of the Velodty inverfely; therefore the ccdtri-
petal Foree is as the Square of the Velocity direflly; and thd
fehoid PV inveifely.
19. Hence if the curvilinear Figure APQ^be given, aitd
* ■ eiiy Point *S to vi^hich the centripetal Force is cofttinualfy di-
• ' 4 te£M; the £aw of tHe centr^)etal Force may be f6und^ by
which any Body P perpetually drawn from a right-lin'd Courf^
ball be decain'd in tbe. Peximeter of that Figure, anil by re-
'■ ' ' the
AstronomyI \ 35^
the Sbn,' (for that Reafda caU^d the JpBiUmi)
^evcry thing i$ jufl: the reverfe: And in the
vtallyiil{<faiil4eftribe icv ^Uc, l3i]F^iii{«liiig tile Value oTtk*
20. Por Example : Let a Body if re^oohve in the Circumfe- Ptoe
nnci tf A Grck^ ''tis required to find Ae La^M of the CintripHal LVIlL
fifrce iekdt^g to kry given Foini S. ' Let PY be a Tangent in Fig, 6.
tfae P(»iit P, and S Y the Perpendicular, and VP die Cjioid
paBing throa|;h S. Let V A be the Diameter (^ the Circle,
and jwn A P. Then is the Triangle S Y P fimflar to the Tri-
angk VAP ; as may be (hewn from EucL III. 32. There-
Are A^.: PV;: SP: SYi confequemly S^L?!Z sSY,
•Bdft ii-4rr^=SY*xPV, which thetwfereiscs the
A V ■
centripetal Force inverfelj; but becauft AV^ is a givea
Qaaiitity, we have the faid Force reciprocally as SP* x P V.
21. A^Wki.Laithei'e^redj^^wdthelfiwrf the cattri"
feted Force hy which a B^t^ tj meved, /o mt to defirrihe the efut- Fig. 7,
emgu/ar Spiral P QS ahout the Cemter $. In this Cafe all the
Angles aie given in every tnlineal Area SQP, and therefore
Hlfo the Ratio of all the Sides in the Figure SPRQT ; there*
O T • QT
fore the Ratio of ^=^ is given, whence —^s- x OT is as
QT; that is, <becaui« of the given Ratio of QT to PSI
QT*
—- is as SP. And this Ratio wfll be conflant, let the As-
QR
gle PSQ^be changed in any Manner whatfoever: For let
QR = a, when th^ Angle f SQ is conftant, and QT = hi
but when it is variable, let QRr=jf, andQTzrjr; the*
<by Lem. 1 1. of frrjtdjf.) it will h& a . x :: h* :y*, whence
h* «* QT* QT*
--- c= '^ r:: ^^^r=:. I w4iich il»ws that -^^ wiU alwa^
a X QR QR
QT* X SP*
the fame as at firft, «if&. as SP. Therefore
QK.
will become SP'; coniequently the centripetal Force QR
wHl be inverfely as S P' .
22. Let a Body revoi<Qs in an Elites APQ. hy aFerceevi- Fig, 8.
ey ivhere direSedto the Center Ci it ie reqmrea to find the La^w
^f that Farce, Let Qp be drawn parallel to the Tangent
FR, and PF perpendicuhur to KCi and pandU to PF join
Points
352 Astro n om y;.
Points B or D it is ill its mean Diftanoe ffonf
the Sun.
CQj the Jtft as before. The ri^t-angkd Triangles QT V
and PF C arc fimilar ; for the Angle Qj/C = PCF, (by Eu^
€Ud, XXIX. I .) therefore QT : C^ r: PF : PC ; aod (^T x
PC = Qy X PF. But QT X PC is equal to twkc the Tri-
angle PQC, which is a conilant Quantity, as bemg propor-
tional to the conilant Particle of Time in wliich it is defcribed.
Alfo in the Ellipiis DK x PF is a conilant Quantity Y^/rC^-
mcs). Therefore DK x PF is.to QT x PC, or Q5; x PF,
that iS) DK to Q^, in a given Ratio, wherever the Point P is
taken in the EllipSs. Hence alfo the Ratio of DK^ to Qji^
is a conilant one : But in the EUipiis DK* : Oo;* ::.PG* :
Pv X «iG (per Conies), Now becaufe Qp :i= QR; and th^
Difference between Gv and GP is infinitely fmall, therefore'
Pi/ X *z/G = QR X PG ; whence PG* is in a conilant Ra*
lio to P G X QR, tl^it is, QR 9r the antripetal Force is every
mibere in a conftant Ratio /* PG, or to PC, the t>ifiance front
the Center.
23. Hence if the Center C of the Hiipfis were to go off
to an infinite Difhuice, the EUipfis would be changed into t
Parabola^ in which the Body would move, and che Forc^
now tending to a Center at an infinite IMftance would become
Suable, or the fame with Gravity^ according to the Theory
Galileo, And if the Parabola ihould be changed into an
Hyperbola^ the Body would move in that Curve by the fame
Law of the Force nqw changed from a centripetal to a cen-
trifugal one, becaufe now it caufes the Body to recede from
the Center.
PI. LIX. 24. Lailly : Let it he required to fad the Law rf the Force
ivg, t. tending to one of the Foci of an Mipfu. Draw SP to the Fo-
cus S, and PH to the Focus H, and HI parallel to DK.
Kow becaufe CS =: CH, we have SE = £1; and becaufe
the Angle HPZ = SPR, (per Comes) and HI pazallel to
PR, therefore the alternate Angle PHI zn FIH, and fo PI
z= PH; confequently EP = ^^"^^^ = AC, from th*
, ■ * . , -
G'enefis of an EUipfis. Let the Latns Return, of the £llipfi«
2BC*
be L = -TTT-f (becaufe 2 AC : 2BC :: aBC ; L) andQv
interfea PS in x. Then becaufe QR = ?x, and the Tri.
angle Fxv limilar to the Triangle PEC, we have Pa- : ?v :i
PE (= AC) -.PCs therefore Qjl ; Pv :: AC : PC ::
Now
A ST RON O M Y, 353
Kow though the Planetary Orbits are really el-
i^iicalj yet is the Etcentriiity C S, in moft of
L X QR : L X Pof, (Tbeorem I.) Again, L x Pa/ : Gv 5^: vP
:i L : G<v. {Theorem XL) Alfo, Gi;x>P : Qjp* :: PC* :
I>C% />^ Ow^; Tbeorem III. Again, Q5* : QT» :: PE* :
PF* i but when the PoinU P and Q^coinddc, it it Q5* =:
Q^*, and PE* = CA*; wherefore then Qy* : QT* ::
CA* : PF*. Now becaufc PF x CD = AC x BC, (per
Comes) therefore PF* x CD* = AC* x BC% andfo AC* i
PF* :: CD* : BC*j confcquently Qj/* : QT* :; CD* :
SB^. (Theorem IV,)
25. Thefe four Theorems fct feparatety as below.
Theorem I. L^ QR : L x Pi;,:: AC : PC.
II. L x P*p : G v X •i/P :: L : Gv.
III. Go; X *i;P : Qo;* :: PC* : CD*,
ly. 02/* : QJ* :: CD* : CB*.
It 18 evident, by joining all the Ratios we have L x Q^ :
(ij* :: A C X L X PC* X CD* : PC X G^ X CD* x CB*i
but becaufe AC x L = 2BC*, we have Lx QJt : QJ* :•
2 PC : G V. Now when P and CLcoincide, 2 PC := Gv^
and then L x QJl = QT* ; and multiplying each Side hy
^, we {haI14iave L x SP* = v ^^" , Therefore the
centripetal Force is as L x SP inveriely ; or, becaufe L issi
given Quantity, it will be diredlly as — ^ •
«6. I ihall now fhew what Ratio the projeflile Forcd
Which caufes a Body 16 diefcribe a Circle has to that which
(cateris paribus) canfes th6 Body to defcribc any ComcSe/lion,
Let us afhime this Ratio tQ be that of )? to i $ and putting
^aj^nd 2^ for the tranfverTe and conjugate Diameters of the PI, ht^i
Conic Se6lion AN, the Circle being AIH, iuppofe the Right pjg^ 2.
Line E F to move parallel to itfelf, and the Points a and d
therein fo as to defcribe the Curves At and AN ; and let the
Dillance df that Line from AB be call'd x, *vix, A£ rr ;ri
and let i</ =: AH the Diameter of the Circle.
27. Now V^zdk ^•^^x:=zEJ in th6 Ciitic, and — x
; a
V2tf;r =t= A* = Ea in the Conic Seftion. The Fluxion^
H
of the Ordinates E</ and TE.a, ^iz. ^ xxx^ ^^ ^
354 Astronomy.
them, fo extremely fmall, as to be almoft infehll*
bic ; and therefore their Motions may be look'd
X % X
;, will be as the Velocities in tytty Point of
the Curves in the Diredion £F or AB. Bat th^fe Fluxions
d — X h a'=^x f-^^jx. L ^ \
are as — p and -^ x ^ " ^ ■ :♦ (maiding by — n J
and therefore when £F arrives to AB, or jr=0, the Ratio
d
of thofe Fluxions or Velocities will become that of -7=1
L . a . h
to — X , — * or as V ^/ to •'T^ in the Point A. Where-
a Vza V a.
_ h
fore V d : "7=- :: i : » ; whence we have nnad = hi.
V a ,
28. And when xzizdzz AC, the Difbince of the Center
6 y hh
of Force, we have — V zax =p xx^=.fz=. — become
*+- d
zad'=t='ddz=Lhhz=.nnad. Whence we get ^ = • *"*■
*z — «*
and^= ■"ZL.-^« Having therefore the Diametets ta
Vz — n"-
and zh, the Conic Se£iion is given in Specie.
29. Now becaufe Unity, or i, reprefents the proje£Ule
Force to defcribe a Circle, the Force n mzy be any other
Number greater or lefs to defcribe a Conic Sedion. And firfl
let 11^ =: 2 2 then will a = ^-^^^^ — = ^^^^^ = Infinite, or
2 — «^ 0
the Center of the Curve will be at an infinite Diftance from
A, and.confequently be the Parabola AN.
30. If the Value of «3 be between i and 2, or if » be
any Number between i and V^T, then will the Conic Sedion
be an EUipfc between the Circle AEFH and the Parabola.
AN, having the Center of Force C in the upper Focus next
A, astheEllipfe ALMK.
34. But if « be any Number lefs than i, the Curve will
ftill be an EUipfe, but within the Circle, having the Center
of Force C in the lower or remote Focus, as the Ellipfis
AIGO.
upon
#
As TtoUdut^ ' Jlj
ii{)on is ctfcfddr^ and as fuch reprefented in Of-
32. Againi if ii^ be greater than 2, or n greater thad
4^Ty them w91 a be negatke 1 cbnfe^uandy the Curve ivill
be an tidterUldi as AO.
33. Laftly ; if n* = c, then * = ^^ZZli^ ass ^^ and
# 2S: 4/; that isi tf the projedile Velocity bfe dimiaifliM ^i
4/fJmihtm, then the Cunre or Traiedory will become the Right
JLme ACi or the FnjtBd^ wiU delcead direaiy to the Cen-
ter of Force C.
34. Let A S3: the Axa of nay Bllbfe/ S^ $, /, tke Areas fi, Ltjj^
^ the Seaors ASB, BSC, CSD, C^c. and T, ?; #i the pj« ^
Times in which they are defci-ibed ; then we have 8 : ^ ::
T : 7; and S : J :: T : /, and fo on for every Se^dr thiou^
ahe whofc Area. Therefore S : T :: S+ 5 + / : T + T+
¥ :: Sum of all the Se^lol-s : Sum of all the Times in which
4hty are deftnbed ; fo is the whole Area A to the Periodical
Time P lof a whole Jlevoludoa. Confequently, S x P qs
T X A, and P sr —^5 and in a given Partfcte of Time
*r, we have P as — • -
o
35. By Jrf. 25, we have ihfe principal tatus ReAum L ::£
Or*
^—^9 but in a given Timtl the cchtripetal FoKe QR is ai
^^ ; wherefore in a given Time L : QT^ k SP* ; and fy
L^ : QT k SP : S, the Sector ASB defcribcd m a giveii
Time. Whence P : — ^ j therefole A : t x L^, that is, Tibi
dna ^ an Eilipft it in ibi SuhkfikMfe Jikik oftkilatai
Rectum and Periodical Time coft/oinfly. »
§6> Npw let 4 31 Tranfverfe Axis, apd j=s Conjugate t
dien (by Comes) a i b z: i i Li and fo 6^:sZiaL^ and i sr
k I 1 ■
a^ X L^; wheftce ^it zsza^ x L"^. But the Reaanglea x I i
At the Area oif the Eilipft, (by Cmcs) therefore a^ x L^ :
A : P X L^, (by Art. 35.) that isi li^ : P ; or, The Periodic.
(^i fimt kin the SefytnpHcate Rntio of tin Tranfiverff ir greater
^4^s 4f the EiUffe.
$f. HeactthePerie<KeaITimewiUbet^ftmuiaHthe
Z 2 rw««
356 Astronomy.
xeries and Diagrams, widiocit any fenlibk Er^
ror.
Specia of an Effipfis fifom a Riglit Line to a C&de defcribed
npon the ikme tranfverie Diametet; or, more partkularif,
the Time of defciibiog the Seml-EUipfe AED will be the
fame a« that of the Semi-Ellipfe ADD ; and the fame alio
^ the Time of defcribing the SemiCitde APD, which is
Ofoly one Species of an EiUipfis, where the Foci coincide with
-the Center N, and the SemirCdojag^ NO becomes the
Semi- Diameter NP. Lafily, when the Semi-Elliple ADD
degenerates into a Right line AD hf diminiihine the Semi-
Ccmjogat^NO/«/^ii£r^«r, and the Focns recedii^ to the
.£nd.<^ the Axi^at JD, it is plain the Time of deibibing tha
Xine AD is fttU the fiune.
PI. LIX. * 38". The Velocity of the rcvolvmg Body P is as -^, S Y
»«S-
being a Perpendicahr let fell on the Tangent FY from die
• Center of Force S ; for the Velocity h ever as the iinali Ardi
QP deiojbed in a given Time. Sat QP = PR, in its evar
seicent Sute ; and becaofe of the Right Angles at T and Y,
and the Angle QPT = YPS when the Points q. P, coin-
dde, the evanefcent Triangle QP T will be fimilar to PS Y ;
and therefore give QP (= PR) : QT ;: PS : S Y j whence
TR^L^LlSZ. But SP X QT : L*; therefore PR:
SY ^
■ , That is. Tie Vehcitj is in the Sulduflitate Ratio of tie
Latus Re£tam direSly^ and the Perpendicular inverfefy.
39. Hence the Velocities in the greatefl and leaft Diffainces
A and D are in the Ratio compounded of the Diflances S A
and SD inverfely, in the (ame Figure where L is a given
Quantity ;, becade in that Cafe the DUlances.are the Perpen-
diculars.
' 40. Therefore if a Circle D E C F be defcribed at the fame
DiftanceSD^ becaafe the Circle is: that Species of £llip&
. whofe Latus 'RtSlum is equal to the Diameter 2 DS, and iince
in this Point D the perpendicular Dlftance is the fame in both,
the Velocity of the Body in the Epulis at the Point D is to
tliat of a Body defaibing the Circle in the Subduplicate Ra-
tio of L to 2 DS, or as V^X to V^ 2 DS ; and .the iame may
be fhewn with refped to the Velocities at the other Point A.
41. To^SPnipfure the Velocity in ^ EUipfe at the mean;
Astronomy. 357
The Orrery is, therefore, an adequate Re-
prefentation of the True Solar System, and
Diftance B with that of a Body dcfcribing a Circle EF at K. LIX.
the fame Difknce CB from the common Focus S, let R= Fig. 6«
Radius of the Circle = AC = CD = SB, and let B z=
leffer Semi-axis BC, which is here equal to the Perpendicular
S Y to the Tangent in the Point B. Let the Velocity in the
EUipfe be V, and in the Circle n; ; and as L = Lotus ReSum
of the EUipfe, fo z A is that of the Circle ; therefore (Art, 38.)
1 ——1
V:^:: i! : 1^, or V^ : v* :: il : L^:: Lx A: zBV
B A B* A*
But becaufe {by Comes) A : B :: 2B : L, therefore 2B^ =
A X L; confequently V* = v*, and fo V = v. That is,
The Velocity qf the Bodjf in the EUipfe in the Point B is equal f
that in the Grcle EF defcrihed nmitb the mease Diftance SB.
42. It has been ab-eady fhewn (Art, 29.) that the Velocitjr
of a Body in the Vertex of a Parabola is to that in a Qrclg at
the fame Oiflance from the Focus, as V^T to i. And be-
piufe every thing that has been fhewn relating to the Motion Fig. 7.
in'^n EUipfe may be demonfbated alfo of the Parabola and
Hyperbola, (See Princip. Lib. I. Prop. XII, XIII.) therefore
in the Parabola the Velocity wiU be every where at P at a
Perpendicular S Y let faU upon the Tangent PY reciprocaUy*
And (by Conies) SY* : SP, and fo SY : V^PS; therefow.
The Felodty in the Parabola nuill be every where as ^^» ^'«
(he Subduplicate Ratio of the Piflatfce inverfely.
43. We have alfo fhewn (Annot. XXXIV. 13.) in a Circle
whofe Radius is <i, P = Periodical Time, V =;: Velocity,
that yP =;«, and V:?:-^, and therefore V* = ^; bat
• P * r
alfo P* : fl', [ibid. 1 1.) whence V* :%i^i therefore
a^ a
V : ^-L. Therefore the Velocity (V) in the Circle AGHI
a
is to the Velocity in the Circle EPF defcribed with the Ra-
dius SP, as V' * to v'-iL 5 or V : V :: V^ : l/AS =;
AS SP
V^Jl. But the Velocities in the PqintsjA and P in the Pa-
rqbol^ alfo arc in the fame Ratio ofV^SPtol/iL(by 42.) j
Z 3 givo
^38 Astronomy,
gives a juft Idea of the Nnmher^ MotionSy Order^
and Pofitions of the heavenly Bodies : But the Pro*
COnfequently, Tbi Velocity in the Parabola af tie Vertex A it
to th( Velocity in the Circle in the fame Difiance AS, as the Ve*
bcity in the Parabola at P is to the Velocity in the Qrcle defcrihed
^t the fame Diflance SP| that is, in the Ratio ev^ where of
V^T to I.
44. Again; the Velocity in the Circle whoffs Radios 14
iSP is to the Velocity in a_Circle whofc Radius is S P, as
VSP to VlSP, or as i^ 2 to I ; confequcatly. The Veh-
fity in the Parabola at P is equal to the Velocity in a Qrcle <whofi
^Uf is iS?.
PL LIX. 45* '^^^ «ng»l» Ytlodty qi a Bpdy P revolving in any
Fiz 8 * ^^> that is, the Angle which is made at the Center S^
^*' ' ' fvraj. PSC^ by the Radius VeSlor SP dcfcribing in a given
Time the Arch PQ, is as QT diredUy, and as SP inverfely ;
that is, the Angle PSQ^: /Sjf j: ^ : ^. This is eafy
to underftand when weiconfider, that any Angle is greater as
die Arch PQ^or pq^ dcfcribed in a given Time, is fo 1 and
|efs in Proportion to the Diftance SP and sp, becaufe the Ve-
locities with which thofe Arches are defcribed are inverfely as
the Perpendiculars BY, Sj, to the Tangents in thofe Points ;
and when the Arch^ QP and fp are indefinitely fmall, we
inay efleem thexp equal to the Lines QT and ft. Whence
the Propo&ion is evident.
. 46. Henee the angular Velocity at P and / is as ^^ an4
» ^ ; for the Seftors PSQ^and /Sf, being defcribed in th^
bp
fame Tiije, are equal ; whence QT xS?z=r jtxSp. Therer
fe«QT:,/;;S^:SPjandhenc§f:|l::||:|!,;
Fig. 9. 4^' ^""^^ *^® ^^* ^* ** ^^ ^® EUlpfe ABD let ftll th(f
'*_ Perpendiculars SY, sy, to the Tangent Yy in the Point P|
let the centripetal Force tend to the Focus S ; ^nd let C B b^
the lefler Semi-axis. Then will the Velocity (v) in B be to
the Velocity (V) in P, in the Ratio of VT? to V^SP. Fo^
V : «; :; Ce : SY AJrt. 1 1.) whence V* : •«* ;: CB* ; S Y*.
portion
Astronomy. 359
portion of Magnitude and Dijlances of the Planets
is not to be expedtcd from the Orrery, but by
But (by Comes) BC* = S Y x /;; therefore V* : a;* :: SY x
/y : SY* :: sy: SY. But becaafe of the fimOar Triangles
SPY and s?y, it is sy : S Y :: jP : SPj wherefore V* : v* ::
s?:S?i confequently V : a; :: V^j P : VSP.
47. Prom what has been faid it appears, that the Motion
of a Planet in its Orbit is very oneqi^al and anomalous ; and
this Anomaly or Irregularity of the Planet's Motion is in it-
felf very irregular alfo, being fometimes more, and fome*
times leis than at others. And in order to explain this, it will
be requifite to compare it with an equal and uniform Motion
of a Body moviftg in a Circle. Let therefore the Ellipfe
AEBF be the Orbit of a Planet, whofe Focus is S, its greater pi, ux^
Axis AB, and lefler OQ^ On the Center S, and with the pig ,q/
Difhnce SE, (which is a mean Proportional between AK and
OK, the two Semi-axes) defcribe the Circle CEGF, The
Area of this Circle will be equal to the Area of thcJEllipfe,
as I have ihewn in my Elemetits of Geometry.
48. In this Circle let us fuppofe a l^oint to move with an
uniform or equal Motion through the Periphery CEGF, in
the fame Time that the Planet defcribes the Ellipfe; and
when the Planet is in ii% Apbelium A, let the circulating Point
be in C, and the Motion of this Point will reprefent the equal
or mean Motion of the Planet ; and the Point will defcribe
round S Areas proportional to the Times, and equ^il to the
elliptic Areas the Planet at the fame time defcribes.
49. Let now the equal Motion or angular Velocity in the «
Circle be CSM, and take the Area ASP equal to the Sedor
CSM; and then the Place of the Planet in its Orbit will be
P; and the Angle MSD, the Difference between the true
Motion of the Planet and its mean Motion, is the Equation,
and is caird the Profihapharefis^ from its being added to or
taken from the mean Motion, to obtain the true or equated
Anomaly.
50. Hence the Area AC DP will be equal to the Sedor
DSM, and therefore proportional to the Frofthapharefts% and
confequently where thb Area is biggeft, there the Profba"
fh^erefis or Equation will be' greateil, or a Maximum ; which
evidently happens when the Planet arrives at E, where the
Ellipfe and the Circle cat each other. For when the Planet
d^^fcends farther to R, the Equation becomes proportional to
the Difference of the Areas ACE and xktER, or to the Area
CJBR«i i for when tl\e Planet is at R, let the Point be at V,
Z 4 Deli.
360 Astronomy.
Delineation, as in Mr. fybifioH\ Solar Sjftem ;
anddicScaorCSVwinbeeqaal Co diecllqidc Area ASB,
|)iatis»ACE + C£RS = C£RS + «ER-|-«SV; con-
fJEqacDtlr AC£--»£R = ikSV = »RBG.
51. IntbeFm&tfiSrMtliecqit^liocioBaQdtlietrveMa^
of the Planet coincide, becaofe the Semkiicle C£G an^
Semi-ellipre AEB are equal, and are deibibed in tlie &me
Time. As the Planet defceiided from the ApbtUmm A to the;
Teribeliifm B, fU Motion was flower, or le& than the mean
Motion; in which Cafe the £qaation or Profibapb^erffis is to
ht /ubirnaed Uom the mean Motion, to get the true Motion
and Phwe of the Planet.
52. Bat darinff the Afcent of the Planet ^m the Fertbi'
Uum B to the Jfibelium A, its Mo^gn will be qaicker than the
mean Motion^ as might be (hewn in the iame Manner as
fbove. In A the Velocity is leaft of all, and in Bmateft^
as we have ibewn ; and in £ it is equal to the m^an Velocity
in the Circle. For when the Planet is in £, let the Point be
in >nr, and let the Area ESjsr and Sedor ntSf be defcribed in
the fame infinitely fmall Particle of Time, and therefore equal
to eac]} ofher ; for £i& x Sir =: (Ei& x S£ =) mi x «S i bu^
&£ = /;{$, therefore '^b:=zmii therefore the angular Ve-
locity ESiifr at E is equal to the angular Velocity mSi, which
^ the mean Velocity.
53. In order therefor^ to find the Equated or true Ano-
maly from the Mean, we are to find the Pofition of a Line
SP that (hall cut off the elliptic Area ASP, to which the
whole Area of the l^llipfe has the fame Proportion as the
whole Periodical Time of the Planet has to the Time givci^
PI. LIX. in which the elliptic Sedor was defcribad. Or if AQB be 1^
fij;. II. Semicircle defcribed on the longer Axis of the pDipTe, we
inuft draw from S the Line SQ^ which Ihall cut off the Area
A 8 C^ to which the Area of the whole Circle is in the above-
mentioned Ratio ; for then a Pfcroendicular Cj^H will cut the
Elltpfe in P, fo that the Line pS being drawn, the elliptic
Area ASP will be to the Seftor A SO as the whole Area of
|hc Ellipfe to that of the Circle, as is mewn.
54. To cut an Ellipfe or Circle in tliis Proportion was the
famous Problem long fince propofcd by Kepler, which is folved
as follows. Upon QC, produced if required, let fall the
Perpendicular SF; the Area ASQ^is equal to the Sedloc
A C QjLtid the Triangle QS C, that is, equal to J QC x A Qjj-
IQC X SF J and becaufc iQC is a conftant Quantity, the
Area ASQ^will be proportional tp AQ^-|" SP. Hence ij
where
Astronomy* 36J
where the feyeral Orbits of the Planets are
laid down in their proportional Diftances from
f^^ take the Arch QN = SF, we havcthc Arch AN pre^i- •
tional to the Time or mean Anomaly of the Planet; which
WfS can eafily iind by haying the trae Anomaly given.
55. For Example ; m the Orbit of Mars we have QC :
6C :: 152369 : 14100; and becaafe the Length of an Arch
equal to Radius is 5 7^295 7$^ iay.
As the Radius QC = 152369 == 5.18298$
Is to the Eccentricity SCzr 14100 = 4.149219
So is the Length of the Arch 57^,29578 5= 1.75807 J
To the Length of an Arch B, . 5*,3oa 5= 0.7245 1 2
Then fay.
As Radius SC 90* 00 = 10.00000
Is to the Sine SF of the Angle? «
SCF=:ACQj^ which fuppofc 5 S© 00 <= 9.698973
So is the Length of the Arch B = 5*,302 =: 0.724313
- To that of the Arch QN=rSF= 2^65I = 0.423282
56. Therefore A Qjf QN =: 30''+ 2%65 1 =; 32* 39' f^
Thus from the eccentric Anomaly ACQ^we gain the meav
Anomaly AQjf QN = AN, which is proportional to the
Time ; and the Reverfe of this, »i«. frojp tjie mean. Ano-
maly AN given, to find the eccentric Anomaly ACQ, is to
\^ ^onc by the Method of Infinite Seritf, as follows. Let
the Arch NQ=:jr, the Sine of the Arch AN be = ^, the
<po.fine=/, and the Eccentricity SC = ^. The Sine of
the Arch AQ^is equal to the Sine of the Arch AN — NO,
equal to the Sine of the Arch AN — y, which Sine is thi^
exprefledby aConv. Series, *— t^ — — + -^^^ —
I 1.2 ' 1.2.3
•j-^ , &*f . as Dr. Keill has (hewn in his Trigonomitry.
57. Call that Series /, then Radius (i) : Sin^ of AQ(/J ••
gC(^):SF=0^)NQ; therefore j^ =^/ =^^—€f&_
|f:^ + €25^4.J^y!L.6fr. CoiifequemIywehaver# =
1.3/ 1.2.3. • '•2.3.4 ^ / 6 -^
.^62 A S THO NOM Y.
the Sun; and their Magnitudes comparatlTcIy
with each other^ and with that of the Sun, ex*
TX7> = «,^ = *, -^ = ^-^^ = -'5 and the
^T/S — ••» 2 1.2.3 1.2.3.4
Equatiott will bcccwne » = tfjF.+ ^jf* — cy^ — </y*, OTr.
wiicb reverted giTcsi = — « r«* -4 i-^m^,^
ifiillliili^**, £^^. Of, by fubftkttting tke Vahci
ef * and W; ^ = J. * — _L , J + -t «» ^ -ii «», «3ff.
5?% But if the Aick AN be greater than 90 Degrees, and
le6than27Q, then^f = «=j-.l^ + ^ +^ —
42!, bfc. And then tf^= 1 --* A, and^=: ^ ^ -^4..
24 "^^ "^ tf 2«* •
^, OV. This Series cxpreffes the Arch ON in Parts, wherc-
of the Radius contains ipoooo; but tiy have it in Degrees
and Farts of a Degree, fay,. As Radius (i) is to this Series (1),
fo is the Radial Arch S7%29578 (R) to QN z=j in Degreeai
l&ati»,/=/R=?— •« raj' +~x»^ ^^•
59/ Now the -^cxy firft Term of this Scries — « is fuffir
a
cent to determime the Anomaly of the Eccentricity in almoft
ftll the Planets nearly enough ; for in the Earth's Orbit, where
CQj CS :: i : 0,01691, the Error is only a loooo Part of
a Degree. For Example, Let the Arch A Qj:^ 30® ;
rXheLog, of the Eccentricity CS = |'=i. 8.228244
Then 4? The Log. of the Sine of A N == e-=z 30° = 9.698970
t The J^g. of Radial Arch R zr 5 7%295 = i . 75 8 1 z?
The Sum is the Log. ^^ x R, or R« = 9.68523^6
$ttbdu€t th^ hog, m u-zzi -^^fg =: 0.0065 r^,
R«
There remains the Log. of — =:jf = o>4774 = g^SyS^zz
a
But 0,4774 Parts of a Degree are equal to 2 ft' ^8^ ; there-
fore AN -^ Nq=' 'yf r- 28' 38'' -^ ?9*» 31' ^2'^-= ACL
pr?fsM
AsTRONOMTf 363
prcfsM by the outmoft Circle of the Scheme
(CXLI),
IHT Angle ACQ, tht eocentfi^ Anomafy* In the Tmngb
QCS, having two S^es QC and CS, and the included An-
gle given, we find the Angle CSQj= iff 3' 7^
60. Now making 2CS =? SH Radius, we have QH :
PH (:: CE (= AC) : CD) :: Tangent of ASQ : Tangent
of ASP = 29"* z' 54', the equated or co-equated Anomaly
irequired» And that this is fuffidently near the Trach» let na
R«*
^ the Value of the fecond Term of the Series, nfix. — r.
tor
Thus, the Logarithm of -^ =:. 7.920800
a
Multiply by — — — — - %
The Produft is the Lcgarithm of -^
= .5.841600
= 9.678923
The Sum is the Logarithm of l~
Subdttd the Logarithm of 2
= .5.52052^
= 0.301030
R«'
The Logarithm of the fecond Term — - =s .5.210402
To which Logarithm anfwers the Number 0,000016, or the
T^e-Q-^ P^^ o^ ^ Degree I too fmall to be regarded. An4
in the Orbit of Mars and Mercury the two firft Terms — -—
n
r will determine the Value of jr to more than any necef-
fjwy Degree of Exa^bcfs. ,
. (CXLI) I. TheORRERT (thougb a modem Name) has
fomewhat of Obfcurity in refjped of its Qrigb, or Etymolo-
gy ; feme Perfons deriving it from a Greek Word which im*
ports to fee or <uietw^ becaufe in it the Motions of the Hea-
venly Bodies are all reprefented to the View**, or made evi-
dent by Infpedion : But others fay that Sir Richard Steele fiift
gave this Name to an Infbument of ^his Sort^ which wat
^lade by Mf . R/awley for t{xe late E%rl of Omr^^ and lhew*d
Thb
364 Astronomy.
The principal Ufe of the Orrery is to render
the Theory of the Earth and the Moon eafy and
intelligible •, and to evidence to our Senfes how
all thofe Appearances happen, which depend on
the annual or diurnal Rotation of the Earthy and
the monthly Revolutions of the Moon: As, the
Variety of Seafons, the Viciflitudes and various
Lengths of Days and Nights, the Manner of So-
lar and Lunar Eclipfes, the various Phafes of the
Moon, fcfr.
In my Orrery^ which is of a peculiar and moft
elegant Strufture, the Earth in its annual Motion
paffes round by a Circle, on which is engraved the
Calendar y and the Ecliptic \ and the Plate which
carries the Earth about has an Index on the op-
pofite Part from the Earth, to fliew the apparent
pnly the Movement of one or two of the Heavenly Bodies.
From hence many People have imagined that this Machine
owed its Invention to that Noble Lord.
2. But the Invention of fuch Machines as we now call
Orreries, and Planet ariums, is of a much earlier Date.
The firft we have any Mention of is that of Jrcbimedeu ge-
nerally caird Arehimides*^ Sphere ; though it was morethaa
what we now-a-days call a Sphere, which is an Inftrument
confiding only of large and fmall Circles artfully put together ^
but this famous Machine of Archimedet was of a more com*
plex Nature, and confiiled of a Sphere, not of Circles, biif
of an hollow globular Surface of Glaft, within which was a
Piece of Mechanifm to exhibit the Motions of the Moon, thq
Sun, and the Five Planets. This CicerQ affcrts in his Tufcu^
3. But the mod (popio^s and accurate Defcription of thU
Sphere is that of Claudian, in Latin Verfc. Th^s the Ppc^
fings:
Jufiter in parvo cum cerneret athera «vitrte^
Rijity & ad Super 05 talia diSia didit.
jpuccine mortalis progrejfa potentia cur a f
Jam meui tnfra^U luditur ^rbe labor^
/ ' Place
Astronomy. 365
Place of the SUtt in the Ecliptic j for every Day of
the Year ; and one Turn of the Winch carries the
Earth once round its Axis, and the faid Index over
the Space of one Day in the Calendar : So that
ty this means the true Place of the Earth, and
the apparent Place of the Sun, alfo the Place and
Phafes of the Mcion, may be readily Ihcwn for
any Day required.
. The Orrery-Part^ containing the JVbeelWork^
is placed within a large and moil beautiful Armil-
LARy Sphere, which turns about upon its Axis,
with a fairly-engraved and fUver'd Horizon,
which is alfo moveable every way upon a moil e-
legant Brafs Supporter, with four Legs richly
wrought •, at the Bottom of which is z, noble large
filver'd Plate, with a Box! and Needle, and
JurkpoR^ rerumfui JUentf legefyui Deorum^
Ecce Syracufiui tranftuUt artefmex.
Jnclufut ntariis fanadatwr ffiritus afiris^
Et w*uum certis motibus urget efus.
P^currit frofrium mtntitus Sigmfer atfmtm,
Etjmidata novo Cynthia menfe redit.
Jamquefuum 'vohvtns auiax indufiria mwtdum
Gaudet, & hwnand fidtra mente ngifm
^mdfalfo mfmtem tomtru Saimcma ndrwT
^nmla Naturae parva referta -manus.
4. This Machine appears from hence to have been fufE-
^endy grand and aniverTal, as comprehending all the Hea*
venlv Indies, and exhibiting all their proper Motions ; which
it all that can be &id of oar common modern Qrneries. *Tis
true, this Orrery o£ Archimedes was contrived to reprefent the
Ptohmnie Syftem ; but the Mechanifm and Nature of the In-
firoment is the iame, whether the Syftem of Ftokm;^^ or G-
fmrmcus^ or any other be reprefented by it.
$. The next Orrery we have any Mention of Is that of
Pefidomus the Sfic^ in Garo's Time, 80 Years before onr
Saviour's Birth : Concemmg which the Orator, in his Book
I>£ Nat, DMy$m, has the followiog fdSsLg^.^^md Jl in Sey-
Compass,
366 Astro NoMr^
C6MPAiSj with the Names of all the PmiJ
finely engraven in Words at Length. The Cir-
cles of the Sphere are as follow.
The EojifiNOctiAL, which divides thtf
Sphere into two Parts, viz. the Noribern and the
Scutbem Hemijpberey and is fo call'd, becaufe
when the Sun con>cs to pafs over it, (as it Ao^
twice every Year) the Days and Nights an tbei
equal. This Circle is divided into '3 60 Degrees^
cali'd the jRjyjfc/ Afc^n/im of the Sun or Stars.
The Ecliptic is that great Circle which
leprcfents the apparent annual Path of the Sun
tiitXMigh the Heavens. It is divided into 1 2 equal
Parts calPd Signs^ confifting of 30 Degrees eadi^
Whqfe Names and CbaraBers arc as follows i
I. Aries^ the Ram, r ; 2. Tdurusy the Rill f$ ;
ihianif aiU in BHiaimkmt Sphari^ ttHqmi iuUHt bine, quioM
nuper famliaris nofttr effeck p9fidoimm^ ctjtu fingulte ^onverfio^
nes idem efficiunt in S^It, £sf i« Luma^ & in ^uffi StMs^erran--
tibus, quod efficitur in CaU fingdis £tlntt £^ aoSibus ; quis in
tUa barbarie dubim^ qtdn eaSfLerm fit perfe^it BaHeue? That
18^ ** If any Man (hould carry this Sphere oi Fojldoniuj into
** Scytbia ot Britmn, in every Revdutton of which the Mo-
*' tions of the San» Moon, and Five Planets .were the fame
** as in the Heavene each Day and Night, whd in thofe bar-
** barous Countries could doubt of its iMcing inifli'd (not to
^* fey aauated) by peifea Reafon V What can be a nore
genuine Account of a compleat Orrery than thu? And, faf
the w^y, what would Gcm^o tay, wen he now to fife horni
the Gmve« and fee hb Bif^barms JBritak aboundag ii Dr»-
. dcs of vanovfl Kinds and Siecs I «
6. From this Time we hear no more of Orrcriet ami
Spheref» till about 5 to Years after G&rj^, when the famous
Se^erinus Boethius^ the Chfiftkm (though Rmmt) Philofephe)[^
18 Aid Xb lave contriired ontfc whioh nnJbrit: King of the
Qoths wrote to him about,' and defoed it for hii BMher-ln*
Law Gnndibuid King of Bmpm^ ; i& whith Le^r he caUs
k Machinam MtmdDjfrmfidam^^'^Cttkm g^fiMkf'*'''tUf9imXM'
\
Astronomy* 367
J, Giminij the Twins, n -» 4. Cancer^ the Crtb, * 5^'
5. Leo^ the Lion^ «l ; 6. ^^^Vy^? the Vir^n, ^ \
7. L/^i^, the Scales, «& ^ 8. Scerfio^ the Scor-
pion, iti 5 9. Sagittsriusy the Bowman, * 4
10. Qtprkom^ the homed Goat, t:f ^ 11. Jqwi-^
riusy the Watcrer, iC? • 12* Pifies^ the Fifties, X.
The Ecliptic interfefts the Equino&ial in the Be-
ginning of Jries and Librae in an Angle of* 23
Degrees, ^9 Minutes. In this Circk the Longi-
tude of the heavenly Bodies is reckon*d* The
Ecliptic is the Middle of
The Zodiac, whkh is a broad filvct^d
Zdne, encompafling the Sphere to five Degreea *
on each Side the Ecliptic -, fo caliM from the Fi-
gures of the feveral Animals^ or Conftellations of
the Signs J with which it is adorned and embelUfli* A
fenSum ; Att w, a Machine fregitant *witb the Vminrft^^^Hf.
portable Heaveny--^a Compendium of all Thfrtgs. Whit fflOft!
can be (aid of our Orreries ?
7. After this fucceeded a long Interval of Barbarifm and
Ignorance, which fp deluged the Literary World, that we
find no InihiDces of MechamYm of any Note till the Sixteentk
Cei^tuiy, when the- Sciences began again to revive, and tbt
Mecnsmical Arts to floimfh. Accordingly we meet with ma-^
ny Pieces of corioas Workmanlhip about this Time ; and in
^ Alirottomical Way particularly is the fiately Clo^ m hi$
Ai^e%'8 Palace at Hampton- Courts made in Henry the Eiehth'i
Time, J: D. 1540, by one N. O. This Ihews not onfy the
Hoor of the Day, but the Motion of die Son and the Mocm
dtroiigh aH the Signs of the Zodiac, with other Matters de^
pending thereon ; and is therefore to be efteem*d a Piece oJT
Orrery^Work.
8. Such another is mentioned by Heylln at tl^e Cathedrd
Church of Limden in Denmark ; but the mod comideiable at
this Time is that Piece of Qock-Work in the Cathedral of
Strajtwrg in Alfaee ; in which, befides the Qock-Paxt, is th^
C^left^l Globe or Sphere, with the Motions of the Sun,
liocm^ Platiett^ and Fix*d StSM^s, ^c. It iVas finilh'd- in ih^
This
368
ASTRftfJOMV*
TUs Zone comprehends wixbin it the PiahS oi
Orbits of all the Planets.
The Meridian is a great Circle pafling
tjirough the Poles^ and cutting the EquimSitU at
Right Angles ; fo call'd, becauie when the Sun is
upon any Meridian, it makes the Meridies^ Mid-
Day, or Noon, to all Places under it. Of thefe^
there is one call'd
The General Meridian, within
which the whole Sphere turns, and upon .which
are engraven the Degrees of Latitude j beginning
and proceeding each way froni the Equinoctial to
the Poles. To this Circle the Sphere isfufpend-
cd ; and bdng moveable within the Horizon^ the
Sphere may be elevated or reSifiedfar the Latitude
cfatg Place k
y^ar 15749 and is much fuperior to that pompoas Clock al
i^M/, which alfo contains an Otrery-Part.
9. Abont the Beginning of the Seventeenth Centoiy this
Sort of Mechamfm began to be greatly in Vogue, and Spheres
and Orreries were now no uncommon Things ; though Or-t
reries bore an exceffivc Price till very lately. The firft large
one made in London by Mr. Ronuley was purchafed by King
George 1. at the Price of 1000 Guineas ; nor has any of that
large Sort, which contains all the Klovements of Primariea
and Secondaries^ been fold for lefs than 300/. at any Time
fince.
10. There have been various Forms invented for this no^
Hit jtoibimient^ two of which have principally obtained, wx^
t^e tUni\fpi>encal Orrersy and the Whole Sphere ; though the
Onery at firft was made without any Sphere, and with oidy
the Sun and the £arth and Moon revolving about it ; but thii
was too imperfeft a State^ and they foon began to invcH: it,
fome with a Hal/Sphere, foj^ne with a Whok ot Compleat
sphere ; for otherwife it could not be an adequate Keprefenta^
tion of the Solar Syilem.
11/ Th^ Hemifpherical Orrery has lieen made in greatet
^mnbcn than <iigr eth^r, on account of their . being ,inadf
A 's t ft b fi b Ri V.' 369
THEHoRizoNis that broad filver'd Ffame;
br Circle, which contains the whole Machine^
ttioveable every way within it: It is fo call'd be-
caufe it bounds our Sight in the Heavens, and di-
vides the Sphere into the upper and lowef Hemi- /
fphere. Updn this Circle are curioufly cngravcii
the Ecliptk Sighs and the Calendar^ for readily
fiiiding tKe Sun's Place for any giver! Day or
Time. On this Circle is alfo reckoned the Am-
pJitude of the Sun^ &c, .
T HE Points where the Ecliptic interfefts the
Equinpftial ire call'd the EquimSlial Points^ or
Equinoxes, bfccaufe when the Sun is in them,
the Days and Nights are equat. As the Sun is irt
one df them in the Springs it is caird the Fernal
much cheaper and eafier than thofe hi a Sphere of the fame .
Si;&e ; there being a vail Difference between p/acinj^ an Himi^^
fibere on thi fiox of an Orrery^ and diffofing an Orrery in a
large moveMe Spkfr€, But then the Idea given us by the
former is very nniiacural and impeifedi ; and 'tis furprizing tQ
think they (hduld have fach a Run as they ha^, Mr. Wright
having made 'between forty and fifty of that Sort £nce the x
Death of Mr. Rowley his Mafter. . And though I incline to
think few more of that Form will be made, yet as they have
liad fo great a Name, I have thought proper to give the
Reader a View of one in a Print.
12. This ill judged and erroneous Form of an Orrery had
tiiis BfiFedt with thofe who knew the Nature of fuch Machines
very well, that fome applied themfelves to conftrufl Orreries
in a Compleat Sphere^ others invexited fiich Inilruments as
ferved to Exhibit the Motions of the Heavenly Bodies fepa«
rately» which they accordingly calPd Planet ariums, hu--^
i^ARiuMs, ^c. and others declared againft all Orreries ini
general, as giving falfe Ideas of the Syftem of the Worlds
«fpecially as the Magnitudes and Diflances of the Heavenly
J^odies could not be reprefented by thehi in their proper Pro- '
|>ortions.
13. But they muil be fuppiofed to reafon yciy weakly, who!
» ydti 11. A ai Equinox i
370
Astronomy-
Equinax i and in the other at Autumn^ it is caird
the Autumnal Equinox.
' The Beginning of Cancer and Caprk&rn are
caJlM the SolfiUid Poin^s^ or the Solstices; *
which is as much as to fay, the Stations of the
Sun^ becaufe when the Sun is in thofc Points, he
feems ftationary^ or not to mme for fome Days i
The firft is the Summer^ the other the Wintef
Soljtice,
The Meridians which pafs through the Points
above-nieation*d are call'd the EquinoSial and
Soljiitial CoLURES refpeaively. They divide
the Sphere irxo four ^artersy in the Middle ot
the four Seafons of the l^ear, .
The LelTer Circles of the Sphere are the Tro-
pics and Polar Circles ; which are all parallel
objeft an inconfidcrable Deficiency in any Inftramc^^? ^
ita mod important Ufes, No one ever decried an ^^^^^^
becaufe an abfolute Vacuum was impofliblj- ^^»«* ^^ •
0f a Telekope, becaufe we cannot f(
Planets* And on the other hand, to ri
by Parts, or in a piece -meal Manner,
one of the
phy. Th^^^netarian
toon bei
the oni
SyileTH
of the
Kind
b/e
the
Astronomy; ^7
to the EquiDoftial, and are two on either Side.
^he Northern tropic is that of Cancer i the
Southern y ihtf of Capricorn ; as paffing thro' the Be-
ginning of thole Signs^ They are diftant from the
Equinodial 23 Degrees, 29 Minutes^ and include
that Space or Part of the Sphere whith is Call'd
the Torrid Zone on the Terreftrial Globei becaufe
the Sun i$ at one Time or other perpendicular over
fevery Part, and elttreniely torrifies or heats it.
Within 23 Deg; 29 Min. of each Pole lie the
PoJarGtcksi df which that about the North Pold
IS call*d the Jtffic Grck^ becaufe of the Conftct
lation of the Beair in that Part; and the other a-
bout the South Polci the ^tarHic Cirde. They
include ttefe Spaces wJiich are ciird the Frigia
Zones^ by reafon of the intenfe Cold which reigqi
follows. Let DCH be a P^ of the Earth's Orbit, C it» PlatI
Center, EC the Axb of the Ecliptic; E its Pole, CP the LXV
Axis of the Earth, P ita Pole i through the Points E and P Fig. i
draw the great Circle EPA, meeting the Ecliptic A L in A ;
the Arch P A meafures the Inclination of the Axis of the
pf the Ecliptic, V«- tl^c Angle PCH^
Vfervation to be aboat 66** 30', and
ntal Arch EP or the Angle PCE =i
o!e P from the Point £ defcribe a Icflfer
fill be parallel to the Ecliptic ; then if
be dire<aed at any particdl^ur Thne tb
bfervations of naany Ycars^ tha^ it wiljl
.ded to the Poyit P in the Hearens, boc
e be dire^^lfid to fome other Point Q» (S
-= I Degree; and ^erefore m the Space
5920 Year% the Point P or Pde of the
je the Circle PFG atoout the Pole of th<
A Revolution is call'd the Great Tear.
e of this Cubical MofiM of the Earth's Axi*
all the Aftronomers and Phflofbphcrs before
'a Time, none of them being able to gaefi
A a z iri
37.2
A S T R O N O M Yrf
in thofc Regions the grcateft Part of tStt Year;
Tbofe Spaces which lie between the Tropics and
Polar Circles, on either Side, are callM the Tem-
perate Zones, as enjoying a mean or moderate De-
gree of Heat and Cold.
The Circles above are effentialto the Sphere ;
befides which there is the ^adtant of AUitudei
for fhewing the Height of any Luminary above the
Horizon •, and a large and mofl: beautiful Ho-
rary Circle and Index, fhewing the Time corre-
fponding to the Motion of the Sphere : Alfo the
Solar Label, for fixing the Sun to its.proper Place
in the Ecliptic.
It is eafy to conceive, that the Sun will always
enlighten one Half of the Earth ; and that when
the Sun is in the Equinodial, the Circle which
from whenee it could proceed : But this divine Geometer foon
invefligated the Caufe thereof^ and demonftrated it to refalc
from the Laws of Motion and Gravity, that is> from the
Spheroidical Figure of the Earth i for were theEai^th a per-
fe£l Globe, its Axis would always remain parallel to itfelf^
and have no fuch Motion. See the Principia, '
1 8/ From this Motion of the Earth's Axis follow feveral
remarkable Phenomena ; as Firfl^ a confiant Change of the
Pole-Star ; for 'tis evident, if any Star fhould chance to co-
incide with the Pole P at any time, it will after 72 Years be
left at the Diftance QP, or one Degree Weflward, and the
Star at (^becomes then the North Pole- Star.
1 9. Secondly^ The prefent Polar Star will in time be on the
South Part of our Meridian ; that is, the Star, which fup-
pofe at prefent a; P, will after 1 2960 Years be at G, which
being 47 E^grees (in the Arch of a great Circle) diftant from
F, will be on the South Part of the Meridian of London^
which fuppofe on the Earth's Surface ztb. For if TR be
the •Equator, then .the Latitudp of I^« Ti&=: 51® go^i
and its Complement hp =? 38° 30',; thpyefore gp-r-^P =
47'' — 38° 30' == 8° 30' = g/j, the Diftance of the prjcfent
NortLStar towa,fds the ^Quth at that Tim^. .
terminates
A S T R O N O MY. 373
terminates the enlightened and darkened Hemifpberes
(which is caird the Circle of Illumination) will pafe
thro* the Poles of the Earthy and alfo divide all
the Parallels af Latitude into two equal Parts.
But fince the Earth nioves not in the Plane of the
EquinoStial^ but that of the Ecliptic^ the Axis of
the Earth, will be inclined to that of the Ecliptic
ia an Angle of 23 Degrees 29 Minutes ; and
therefore the Circle of Illumination will, at all o-
ther Time$, divide the Parallels of Latitude into
two unequal Parts.
Now fince any Parallel is the Path or Trad
which ^ny Place therein dcfcribes in one Revolu-
tion of the Earth, or 24 Hours; -therefore that
Part of the Parallel which lies in the enlightened
Hemifphere will reprefent the Diurnal Arch^ or
20. Thirdly y The Circjc EPA paffing through both the
Pole of the Ecliptic and JEquater will be ih^,,SoIftiti(tl Colitre,
and A the Splftitial Pointy when the A^ds of the £a|th points
to P; but after yz Years, \^hen it points to Q« then. the
great C1FCI9 EQB will be the Solftttial Colure^ and ^ the ^#A
Jlice^ for the fame Reafon, And hence alfo the Eqmno&ial
Points (whiph are always 90 Degrees diitint from the Solflices)
mufl'move in the fame Time through the fame Arch, the
fame Way, nnz. Weft ward.
2i".' Fourthly^ Hence *ti3 evident, all the Points of the
Ecliptic do move backwards, or Weflwards, through one De-
cree every 72 Vears ; which Motion is faid to be in, Antece*
dintia^ and is contrary to the Order of the Signs : As the
other Motion, by which the Planets are carried round the
Sun, is f^id (o be in Confequentia^ or according to the Order
of the Signs, «i/|«. from Aries «y» to Taurus y , Gemini n » feff»
And' this retrograde Motion of the Equino6Ual Pointy is called
the Recejpon of the Equinoxes,
22. Fifthly y This Reccffion of tjie Equinoftial Points, and
indeed of the whole Ecliptic, is the Cade of the flow appa-
rent Motion of the Fix'd Stars forwards y for fin<» the (cvct
ral Circles of Longitude by which they arc rcfcrr'd to the
A a 3 l^^tk
m
ASTRpNOMY^
Let^tb of the Day ; and that Part in the dark H^
mijpbere will be the N^Slumal Arcby or Length of
the Nigbty in that Parallel of Latitude.
Henc?, when the Orrery i$ put into Motion,
t*e Earth moving with its Axis always parallel /<?
iifelf^ yet ^Iv^ays mUned to tbe PUate cftbe Edip-
)ic^ will fometimcs haye the Ncr^bem Parts tum*d
mor^ direftly to the Sun, and moft enlightened j
fmd at other times the Smthern Parts #ill be fo.
Hence various Alterations of Heat and Coldy and
Length of Days and JNightSy will enfue in the
Courfc of the Revolution of the Earth about the
Sun, which will conftit^itc all the Variety of Sea-
fans^ as will moft naturally and etridently be fliewn
*^ the Qrrery, as follows (CXLIL)
Edlptic ^re continjially (hifting backwards^ the Stars» which
Hre immoveable, imuft with refped to thc^e Circles hav^ their
!l>i^iiK:e, that is, their L^ngitbde, conftantly increaiing from
^he foil Point of Aries. Thus aK the Conftcllations do eonti-
^uaHy change thdrPlftces at the Rate aforefaid: The brigh(
9car of jfriei, for Inftance, which in Hipparthui^t Tinae was
iicar the Vernal £<}uhK>x, is now removed near a whole Sign-
{' r JO* Eaftwfiird, and is in the Beginnme of faurus b '» and
'durus ift got into Gemni n i and thus aB the Conftellationt
pf the Zodiac have changed t|ieir Places, and pdiTefs different;
l^igns frdm what they formerly did.
<CXLII) 1. Though thcfc Things are plain p aPcrfoi^
fiiio has his Eye on an Orrery » while' he hears pr reads thi^
Accoant of, the Nature and Manner of the Seafons, and thcf
Variety of Day an^ Night, yet Ideas of this Sort are not fo
^afy to be obtain :d by mere Reading and Cogitation only, uii*
tsft aflifted by a proper Diagram or Reprefent^cion j whicl)
therefore I (hall here fubjoin and explain.
151. LX. 2. Let S be the Sun, A BCD the Orh/'s Magfmu Or annual
Path of the Ekrth about the Sun. In this Orbit the Eaftl^
is reprefentcd in four fcvcral Ppfitions, in ^hc piijlft of ih«t
' rr " Y^.
A 8 T ItONOrM ¥• 375
We will firft give the Earth Motion in the firfl:
Pdnt of Ubra ; the Sun will then appear to en-
let Ariesy and this will be the Vernal Equinox %
for now, the Sun being in the Equina ffial^ all Parts
of the Earth will be equally enlightened from Pole
Jo Pole, and all the Parallels of Latitude divided
Into two equal Partes by the CircJe of Illuminationf
Hence the Days and Nights will be equal, and
the Sun's Heat is now at a Mean between the
f%Hlr Seafons refpeftiv^ely. On the Earth are drawo tl^t &•
^^1 Circles and Liiies as follow.
i ^CQ^The Equator.
TOR The Tropic of Cancer.
FML TTie Tropic of Cfl^r/Vtfrff.
iibc The Norfh Polar or Araic Circle.
d« f The South Polar or Antaraic Cirde.
EQD The Parallel of L»«ifc«.
NCS The Earth's Axis.
iCf The Axis of the Ediptic Plane.
• 3. As the San is fi4}pofed to bjc at fo great a Difiahce, that
the Rays coniing from it do arrive at the Earth nearly paraU
hi, they will t^erdfore illuminate iFery nearly 'one Half of
the Globe of the Earth, abftrading from the Refraction of
rhe Air. And if we are fuppofed to view the Earth circur
lating about the Sun at a verv great Diflance in the Pofitiona
reprefented in the Sdieme, we ih^Il have all the enlightened
Fart ttimM to the Pye on the Equinoctial Day in the Spring,
but on that in the Autunrn we fee only the dark Part ; as oq
ehe Summer and Winter Solftices we fee qnly half the lighi(
iiina dark Hemifpheres refpeCtiyely : And accordingly thft
Earth is thus reprefented in the Figurt.
4. But (as I find by Experience) the bcA Way to convey _
an Idta of the Seafons, and Day and Night, is to reprefenc
the Earth alfo in Pofitions exhibiting the vifible Hemifpherc
equally divided mto the light and dark Parts, or femicirculaf
Areas, as in the next Plate ; and to compare thefe l^th to^ PI. LXI«
Sther in the Defcripdon. To begin therefore with the Sir
ition of the Earth m the Spring and Autumn.
5. In either of thefe Cafes, *tis evident the Sun is in the
nane of the Equator ^Q* and therefore equally dijiant from
each Pole of the Wqrid ; confcquently the Circle of Ilium' Fig. ^zL
Ajil 4 greateid
37^ A S T R 0 N Q M *.
greateft and the leaft : All which ParticUlar3,con-
flitute that agreeable Seafon we call the Sprino^
the Middle of which is lhe>«fn by the Index to -bj
fhe I lib of Margb.
^ As the Earth paffes' on from Weft to Eaftj
through I4hay Sforpio, and Sagittarius^ to tlic
Beginning of Capricorn^ the Sun will appear: from
the Earth tp moye through the oppofite Signs of
the Ecliptic, viz. Aries^ TauruSy Gmi^iy to tbq
n^fithn wj}l pafs through both the; Poles, {^, S ; and therefpr^
every Place at ah equal £)iilance on either Side will h^ve a^i
equal Degree of the Sun's Light and Heat. And as the
Earth revolves upon its Axia, every Place muft defcribc a
Circle parallel to the Equator, one Half of which will be in
' the light, the other Half in the darJk. Hemifphere ^ and as
Parts of the Circlp mcafure the Day and Night, ij, is plain
they muft then be equal. Thus in the Equator, thcj Diurnal
Arch QC is equal to the Nodlurnal Arch CJEi in the Tro-
. pics RO and LM are equal to OT and MP; in the Lati-
fude of Eifgland the Day EG is equal to the Night GD ; and
b in ail ot^er 'Parw. '
6. Hence, by the way, we inay obferve, that had the Sun
always moved in the Equator, there could have been no i)i»
verfity of Day and Night, and but ope Sfafon or the Year for
ever to all the Inhabitants of the Earth. No Alteration of
Heat or Cold, fo agreeable now both to the Torrid and the
Frozen Zones; but'thp fame uniform eternal Round of un?-
^^ variable Suns had been cur uncomfortable Lot, every w^j
'^' :' Contrary to that Difpoiition we find all Mankind fonn'd y^it^,
of being delighted and charmed' with Variety to an ex^eme
begree. The Obliquity of the Ecliptic is therefore not to
be look'd upon as a Matter of Chance or Indifferency, but
V in Inftance of Wi^^lo^i ^"^ Defign in the adorable 4«thor of
Nature, who does nothing in vain.
' 7. If wfe confider the Earth moving on in its Orbit, with
its Axis N S always parallel to itfelf, till it comes into the
Summer Situation, we fhall there fee, that by thist^arallelifm
cif the Axfs all the Northern Parts of the Earth will b^
PI. LX. brought tpwai'Ss fhe Sun, which will in this Cafe be in the
rl. LXI. hane of the Northern Tropic, and his Rays perpendicular
Fig. I. upon it, as at R. The Ci|cjp of JllumjnatijA a^f ^'U novj
^ - V • • - -. '= - .t , •• ; : • Begin-
A fr'B»air 9M Y. 377
*egfti0Uig of Cancer • ^ dtorin&'wlridi Tirtie, by the
tinclined Fofition of the Earth's Aids, the Northern
Parts Kriil be gradually turned towaitis the Suii,
md the,' Sontibem Parts from it; whence the Sun's
Rays will fait more and more dircdkly on the
forfper, wd pafi througha fbll Icfi Quantity of
%\it Atmafpberei but in thci iS(>«/*tfr» Parts» the ,
reverfe. Alfo in the Northern Pzrts the Arches
pf the Parallels- in the enlightened Hemifpbere ^^'Al
be jp fttch a Site, a» to inc)|ide tiia North Ppleouid ^li ^boi|t
it to the Diftance N A = 23° 30^ ; and on the con^ary tp
pcdud^ the Sooth Pole S, and Sotithern Regions to the fiune
Diltanc^ Sf. The Northern Climates mufl therefore now
'have tlvsir Summer, and the Southern Climates their fTinter i
as yn'A appear more particularlx if we confider,
8. Tirfti The Sun-Beams fall more perpendicularly upop
any Northern Parallel than upon the fame Soothfrn P$ral-
lely and have thcfrefpre ft ihorter Pai&ge through the Atmo-
fphere. Thus, Jfor In^pe, in the Parallel of England B,
let the Rays ill. kg^ be incident, on the Atmosphere mnisk h
aiKl /; thei^ will their PafTage i&£, ig^ be Sorter than it
would be in the fame Latitude Southwards, and therefore wiQ
notbe fo much refra6ted, blended, and abforbUj and con-
fequently their EffeA will be more confiderable and fenfible.
Again, as. Riiys are more.perpicndicular, they will ftrike witji
a greater Force ; alfo the nu^re will fall on a given Space ;
on both which Accounts their Effedt, in refpcd of Light and
Hjpat, willbie greater.
9. Secondly, As the Earth revolves about its Axis, every
Place in North Latitude will defcri^ a greater Part of its
parallel ifi the enlightened than in the dark Hensifphere ; or»
|n other Words, the Day will be longer than the Night. Thus
in the Northern Tropic th^Diumal Afch is R Y, the Nodtui-
pal YT, whiqh is Jcfi than the other by the Difference YQ. »
Again, ^ in the Paiallel of london the Length of Day is fhev^
by the Arch £Z, of the Night by ZD, which is fhorter
than' the Dav by (he Difference G Z. And laflly, at the Po-
J^r Q\xdf( cba it is all Day, no Part of that Parallel lying
within the dark Hemifphere a^Ef. On which Account it |s
pvident the^ Light and Heat of the Sun is greater in any Place
'j}i X^qrth Latitude now than at any oth^ Ti|nf ff tb^ Y^V-
Cpnt^T.
37^ A 8 * i fir N O I* Y^
continually tncreafe, mi thofe in the iMrl one
dectea^ fhewing the conftam Increafe of tiie
DayS) and Dccreafe dExht Nights: AM which
will be in cjieir gneareft D^ee wheti the Sun is;
mtiyed to Cancer ^ and therefore thatt Will be the
^fiddle of that Seafon we call S^iii^£ft, in N^-
them Latk$^'^ but tn Southern laHtude cs^ry
Ihirtg will be the levcife, and thdir Seafon Jt^ir.
TlHE J^crtb iF^igid Zom is now wholly en-
. i ....
ft IS tderfeft^e nt^ the IDfiflft of theStfinmef.Sddbn fai all.
tat N^kthbfti Cliknates. ,
lo. In yi^ Sonthcrn ftot of the World it & l$^^ff, ft*
tbe ftme Kearpm rererfed; ^'^. becauf^ th6 SoaS itays i^
mote obli^aely tjic^t ; they therefrt-e pafs thwogh ^ ^tater '
Quantity of the Atmofpheit, on which accotrtt they are ttiof©
r^^iiased, blcmted, and ftifled, and thei^ Efl^^l; wt^keti*d.
A1A> a lefs l^nantity of the Sol^ Rays wili fall on a given
Spiiee, arid each Ray flrike whh a fefs Foitc. And laftly,
^e JXiratioft 6f theif Prefence iviil be fhorter than that or
>^ix Al^ettce, or the Day will be fhorter dim the Night; as
in die Soathem Tropic the Day is LX, bat the Night XP,
hmge^ by the Difierence MX i which biSerence h fUfi greater
^ farther ybu p), till you come tb the AtUArBU CiKle d^f,
where there 14 no Da]^ at all/ and all tidthin to the Soorii
iMe S is itfvoSv^ in Night, of greater or lefs Duration.
m. F6t tiie fame Reafons, when the Earth arrives to the
<)ppe€tfe t'alt tyf its Orbit, it will be Sum m eh to aH the Soa-
them Climates, and Wintsr in the Northern, ft is evident
n. LX. tbis tadft hecdiartly happen by the ParaDelifm of die Eai'th^s
PL Lxi. Axis, and the Chhrige of her Place in the Orbit : Jy whic^
Vk. 3. flfeslns tht ^tth now illuinines tliat very Half oiT difc Gbbe
'^* which in the othW-Pdfitibh Was dai^; and whence it foilows,
that in all North Laltitt/dcb the I^tength of the Says »mv are
e^ttal Mb the Leto^h of the Kights /fc», and n^r^ tv&Jh in
8toath Lktitnde^. Thtis the Day (in the Paralld of Eitffand\
£Z s= DZ, the Night in the Summer Seafbn; and the
fftght now, vh:. ZD = ZE, the Day at that Time. All
which Things ate too plain from the Schemes to want &nhei^
Explicatiion.
12. Thus the VicMittodcs ^nd Variety of the Seafons, aid
•f £)ay «^d Night, appear in general ; ^ to txhibit the ia^se
lightened.
AsTRONdMV, 379
li^tenM, and the Pole tumM tow^ds the Siift
fs far as poffible ; but trow a:s the £arth move's
on, the North Pole returns, die Dhirnal Arches
begin gradually to decrcafe, and the No6hirnal
to incrcafe; and of confequence the Sun*s Ra^
fall more and more obliquely, and his Heat pro-
portionally diminilhes^till the Earth comes to Jries^
when the Sun will appear in Libra -, and thus
produce an Equality of Light and Heat, qf Day
|ft ah eTpecikl Manner for any pardcDkrHaee, asZMtinr, an- p], LXII^'
^er Schtsme is neceflaiy, wherein the Sphere (hah have the Fig. i.
fat^e Pofiti<m with ^efped to chat Place, as the Earth itfelf
his. Thos let j£ N QS be the Earth ; 2 wffl be the higheft
ftint, dr Place t>f Lon^-, HO the Horiroh, and N th^
IpWeft Point or Antipodes; an4 4^Q^tfae Eqoatof, TR and
PL the two Tropici, ac and if the two Polar Cirdes, as
|>efore.
13. Then when the Sun is In the Plane of the Equator at e,
die S^i diurnal Arch^ or half the Length of the Day« wifl
|)c reprefcntied by JEQ ; and thaj of the Night jjy CC^
which h equal to the former. In this Cafe the Angle ^C^^
^ich thteaWs the Altitude of the Sun above th6 Honzoa
\o, is ^r 50' z=:he.
14. Again: When the Sun is m the Tropic TR, and con-
fequently neareft to the Zenith of London^ the Semi- diurnal
Ardi is then 'Ipl, which is longer than the former in the Pro*
portion of the Right Ang^e ^NC = 6 Hours, to the ob-
fixfe An|le i£NF dr 8 Hours 16 Minutes; NES being an
Hour-Cirde 4^wn Sirough the Point I, and mt^rfe^ing the
Equator m E. The Semi-nqiturnsd AitJi is IR, and equal
in Time to the Angle EN(^:± 3 Hoursr 44 Minutes, th«
Complement qf the other tQia Hours.
"" 15. Lailly: When the ^|m appears in the Southern Tro^
pic at'P» and moft remote fix)m the Zenith of L(md9n^ the
Semi-(fiurnal Arch is then PK, e<{ud to the An^Ie ^ND =
3 Hours 44 Minutes nearly^ equal to the Night when the
Sun was in the other Tropic ; and the Semi-nodumal Arch
K L at this Time is evidently equal fo the Semi-diurnal Arch
T I at the oppofite Time of th^ Year.
16. Whenever the Sun comes upon the LmeNS, repre-
^^% the Hout-Cifde of Six, it is theif ^ix fCkiJt^ as at
38p Astronomy.
and Night, to all Parts of the World, Thi§ will
be the Middle of tne Seafon call'd Autumn, and
that Day the Autumnal Equinox. ,
But 9S the Earth goes on through ArUSj Tau-
rus^ andGeminiy you will feethe Sun paft through
the oppofite Signs oi Libra^^ Scorpio^ Sagittarius.
The North Pole is now in the dark Hemifphere,
and the Frigid Zone is now mcjre and. more obr
fcureci. therein : AH Northern Latitudes continu?
X in the Saiomer Tippic, before Sun-fet at I ; and at B in
^he Winter Tropic, after Sun-fet at K. Alfo when the Su^
comes upon the Line ZCN» (which represents th^Pjim
Vertical, or Aximutb of ^aft and Wefi) it is then due tafi,
and Weft, which happens ^t V in the Northern Tropic, after
Six in the ^orning» and before Six in the AfternooUj^ and i^ut
%ferfaziW in the Southern Tropic*.
17. It is found by Obfervation, that the Air is not abfor
Jutely dark, till the Sun is deprefs'd about 1 8 Degrees below
the Horizon, a;/^. at /, that is, till the Angle hCizzi 18® =s
HM ; and drawing MV parallel to the Horizon HO, it will
reprefent the Circle at which the Crepufculumy or Twilight,
begins and ends, in the feveral Poinjts where it cuts the Pars^l-
iels of the Sun's Declination, as at G in the Tropic P I4, an4
at F in the Equator. But fince RO ==: PH =^ 15 Degrees,
the Arch OR is lefs tlian O V, and fo the Tropic TR will
not tou^h th^ Circle M Y at all ; which fhews that for fome
Time in (he Middle of Summer there is no dark Nigbi: An^
this happens bet>yeen May 12 and July 1 1 . See my Synop-
sis Sci E N T I i CoE LE sT 1 s, ou a large Imperial Sheet.
18. Moreover it is evident that CF=: KG, becaufe PI^
.is parallel to -^Qj the Time, however, of defcribing CF
and KG will not be the fame ; from whence it appears there
is a certain Parallel in which the Twilight will be the haft of
all, and another in which it will be a Maximum or greatejf^
The former is when the Sun has 6° 7' South DccSnation,
'viz. in Li6ra ^ or Piftes K 17° 3o'» which happens Febru^
ary 22, and September zj, in the prefent Age : And 'tis plain
the Twilight is gj;eatcft of all in the Parallel whi^h touches
the Point V, on May 12 and July 11, as aforelaid. Note,
How the Time of the leaft Duration of Twilight is invefti-
satcd'rjlay be feen in the beft manner in Dr. Gresory^^ Element^
gradually
AstronomV. j8i
gradually tnrning froth the Sun ; and his Rays
fill more and more obliquely on them, and paft
through a larger Body of the Atmofphere : The
• noSlurnal Arches continue to increafc, and the
diurnal to decreafe : All which contribute to make
the difmal dreary Seafon we call Winter ; the
Midft whereof is fhewn by the Sun*s entering the
firft Scruple of Capricorn ort the lotb of Decern*
her^ as by the Index may be feen.
of Afironomy ; and I would have given it here, but that it Is
very tedious, and In itfelf a Matter of little Importance.
19. It is a Problem of miich greater Confequence and
Curiofity, to determine the Ratio or Proportion of Heat which
any Place receives from the Sun in apy Day of the Year. Iq
order to this it muft be confidered, that the ^antity of Heat
•will be as the Time^ if we fuppofe the Sun to have the fame
Altitude ; and as tht Sine of the Altitude , if the Time be the
t fame. Therefore if neither the Time nor Sine of the Alti-
tude be given, the Quantity of Heat will be' as the Redtangle
j or Produd of both.
20. Therefore \tt a ±2 Sine of the Latitude j£ss; its
Co-fme (or Sine of « N) 1= ^ ; the Sine of NS = r, and of
its Complement (or Declination) SD =: ^; the Sine of the
Hour from Noon (or Angle mUt>) zn at, its Arch iED =
SK, and Radius = 1 ; then is V^T^^^TSfAr =; Co-fine of the \^j
Angle «NS, (a;/^. Sine of the Angle DNC) and (per Spbe-
, rics) we have be i/i-^xx ztz adz=. Sine of the Sun's
! Altitude SB; which multiplied by the Fluxion of the Arch
of Time == k will produce the Fluxion of the Sun's Heat,
. ^%. z X be V^ I — x^ =±= a d. Or, putting be z=, g;
\ V I — Af^ =z h^ adz=.f we have the Fluxion of the Heat
y zsc^ X X gh -±zf
\ 21. Now to find the Value of «, let ABzzs;, BE its -
I Sine,. EC thcj Co-fme, and Radius CB; and fuppofe FG fyf^i.
(drawn infinitely near to EB, and B D parallel to A C ; then p. i
'tis evident from the fimilar Triangles EBC and BDG, That '^^S- ^n
EC : BC :: DO : GB, ox b \ \ :\ x \ k, whence % =
LXVI.
Fig- S-
'/_
-r-; wherefpre f xgb =i=/= xfz±:-f- = Fkurion of
Lastly :
3|8i AstnoNdMti
LAstLY : As the Earth journeys 6n frorii
^cncc through Cancery Lea^ and l^rgOy the Surt
appear; tp pafs through Oipricorn^ ./fjuartiisy and
Pifies'^ ?in4 all Things chaiige their Face. The
]^crtksr» Climes begin to return, and rcceiirc
lnore diroSkly the enliTening Beims of the Sun^
whofe Meridian Height does now each Day in-
treaf^ i the Days now lengthen, and die tedioiis^
Nights contrail their refpedivc Arches ; and e-
i}^ Hcatj. ^hofc Fltmt is xg s&i/i, which th^refojre k u
the Qgdptif^ of float from Noon to ths given Time, a» re«
22, From th» Theorem We may calculate the Heat of
may Day ia the Yeir in any given Latitode required ; ofwhidi
I (ball give th? feveral following afefi4 £)ampjes. ift it be.
Required /4 ^^/r^/r /i^ Hsor £|f an E^uvto^ial D^ iaukr tbi
iquater^ In this Cafe the Lautode of the Place. is Nothings
therefqi^ az^oi CQnfeqae|»tl]^/e = «</« ^ o. la the othec
icmmhg P>rt ^g =?: xic^ i:;^ I, cz=2 1 ; therefore thei
Heat will' be as ;r ; and fince the Semi-diurnal Arch ia 90 De-
8rees« the Heat of the Half- Day will be aa x= i| and o^
It whol^ Qay the Heat is as 2.
. z^. I^t the Heai of am EqtUn^Qial Da^ hi repHrid far tbk
tatiiudi of^i^ 30^1 then becaufe in this Cafe there is no De-«
dination of the Sun, ^=0, and fo adxz=i o. And iince
N S = 90®, we have cz:z\i and fof the Semi-diurnal Arch'
=: 90^9 M dt I alfo ; therefore the. Heat is as ^ :=: 0,6225
2s Co-fine of the Latitude; which for the. whole Day i^
1,245, and which is to that under the £quino£ikl as i^ to 2^
iaarly. At the Pole bts^o^ therefore the Heat of an Eqnt*
ti^aial Bay at thq Poles is Nothing. Laf|ly, m tl^e Lajdtnde
of 60'' the Heat of fuch a Day is half that under the Equa-
tor, or I ; becaufe then ^ = ^ Radius, or 0,5.
24. In the next Place, let us calculate the Hiai ^f the Sum^
Mir 7rofkal D^. Here we have the Time of j the Day
8 Hours 1 2 Minutes nearly i therefore, the Arch of the Equa-
tor which cafies the Meridian in that Time is 1 23** r= %. Andf
Wcaufe when Radius is i the Circumference is 6,283184
1^ r- r 1- r ^ o « 6,28318%
therefore fay. As 360 : 6,28318 :: % ; ^ =s
3R9
6^01745329^, the Length of the Arch z in theMeafure o#
Very
AsTROitOMY. 3S3
Very thing confpirea to advance tht delightful
Seafon of the Spaing, the Midft whereof ia
fhewn by the Earth's returning again to that
Point, where firft we gave it Modon.
Ahh thefe Appear^mces of the Sealbns, &r.
are (hewn as well for (he Southern t^fifudes^
whcrq u the (amc Time they happen in Order
juft the tevwfc tp what we have now otjfonred
f0r the Northern^ Thits, when it if Summer with
Tilf l^i^ganitun qf » s: u|'' ^ ^.089901
Tl^ LqgVrj^ of « = si"" 3(y s: 9.99354*
x4i^ Jafgvithin of 4iz^zi' ^of zfi 9.600700
Total, tlie Logairiduii of qdt^ cs 0,^98 s 9.895944
«{. Then for the other Pitt of the Theorem^ tiz. xtf,
we have
The Logarithm of » s= 57^ 00^ c= 9.923591
The Logarithm of i^ =s 38® 30^ :;= 9.794149
The Logprithm of r s= 66"" 30^ s 9.962398
Total, the Logarithm of iit sz 0,4788 = 9.680138
'^ Therefore the Heat of half the Dajr it 0,6698 + 0,4788 =:
1^1486; and of the whole Day it is 2,2972, almoft twice as
great as that of the Bqninodial. Daj with i», and greater
dian the Heat of fuch a Day to thoft who live under the
Bquator.
26. To find the Bjcpreffion of the Winter Tropical Dayi
we have die Semi-diomal Arch 9=57*', aQd the reft the
fine as before. Therefore
The Logarithm of 3bb:57^=: ■•75587$
The Logarithm of 0,0 1 745 = 8. 24 1 795
The Logarithm of .iii/=s 9.494244
Total, the Logarithm of aJ% 3c 0,3104 = 9.491914'
Thaixhe'^adx = 0,4788 — 0,3104= 0,1684, and ta
± X 0,1684 = 0,3368 = Heat of the whole Day, which is
almoft 7 times \tb than that pf the Somm^r Tr6pic.
27. The Sum of the Heat of the two Troj^ical Days it
•^2972 4- 0,3368 5S 2,6341 which is greater than the Heat
US,
^84 AstkokokY.
vi; if is Winter #ith them, and they have their
Ddys (hortcft when ours are longeft; fuld wtf
vtrfa. AH which is mott diftindly fcen in the
Orrery.
• At the fame Tim6 the Earth is going round
the Sun, the^ Moon is fcen confttotly circulating
round the Earth ohce in 29 Days arid i, half;
'Which Days are number -d dn i, filvef d Circle,
ahd ftiewn by an Indej^* mbVirig oVer them. Thus
of two Eqoinodial Days with tts, which is but 2,49. Henofif '
by means of the Obliquity of the £diptic» we who live be-
yond the Tropic have mach more of the San^s Heat than
we coald have enjoy M had the San movedalways in the Equi-
ndoftial. And on the other hand, it will be found by Calcu-
lati6n» that for thofe who live between the Tropics and the
Equator, the Sam of the Heaf of ahy t\^o oppofite Days of
the Year is Jefs than the Heat of two Equino^ial Days; and
therefore the Heat of the whole Year is lefs in the prefenC
Qsfe^ t|ian it would be from a confbmt EquinoAial Sun.
. 28. Lallly; let it be required to calculate the Heat of a
Polar Day ^ or that under the Pole, for the Tropical Sun. In
this Cafe A = o, and xg = xhc =: o ; alfo azui. Whence
the Heat of any Day under the Pole will be as d^ or Sine of
Diclinatiotf, becaufe x is here always the fame, viz.. sl Senti^
circle J or 1 80 Degrees. And under the Pole the Value of ^»
is thus exprefied for the Tropicdcl Sim.
The Logarithm of ^ss 23** id = .9.600700
The Logarithm of ss =: 180 = z,2^^2yz.
The Logarithm of 0,01745=8.241795
Total, the Logarithm of dz = 1,252 == 0.09776.7
The Double of which is 2,504; which therefore exprefiea
the Heat of a Tropical Day under die Pole, which is greater
than the Heat of any Day in any othef Latitude. Hence we
iee the Extreme of Heat, as well as of Cold, is found in the
iame Place, 'viz. under the Pole. .
, 29. It is Problem of another Sort, To Juui nuben the Heat
u a Maximum, or greatefi of all^ in any given Day, In or-
der to folve this, let the Semi-diurnal Arch = a, i8=: Arcl^
eS the Hour from Noon, If z^ Redbngle of the Sines of La-
titude and Declina(i(U)i and c ;:=; Heftangle of (htiir Co-iine^.
AsTRONOMt. ^85
feath Day of the Moon's Age, and the Pbqfis
propcf thereto, are fhcwn for any required Time i
and alfo why we fee always one and the fame Face
of the Moony viz. on account of her turning about,
her own jixis in the fame T^mefhe takes to revolve
about the Earth.
A G A IN z By placing a Lamp in the Orrery;
and making the Room dark, we fee very natural^
ly how the Sun is eclipfed by the New Moon, and
Then (per SpBeria and i/tjtmii Siria) we have the C6-fin^
of the Hour from Noon =; 1 — 4as* + ^9l^ — yi^**. ^c.
and the Sine of the Sun's Alcitode nic — ir«* -f" iV^**"""
'7l^fi®,f^r. -f.^. Thismultipli^bytf-^^^ ^^ + ^^"^
iacz,"- — iex^ + 4^acx^ + ^T^cx^ — jhsacx^ —
'jk-^ex'^i^c. '\'db'\'»bi which therefore is poportional
to the Sun*8 Heat. And this is greateft when Jts Fluxion i^
eqaal to Nothing, viz. ex -^ bz, — acxx, — \c%^i, -f^
Jtff«^a:-|- A^**^ — -m^ck^z, Vc. = o. Then divi-
ding by sc, c + b — acx — icvi^ -{- ^acz^ + ^^cx^ -^
Tj^tff«S£sfr. = o; whence 1^ = «+-?-«* i-jgi
ac * 2a 6
^ -i-«* 4. — «* = A. Now puttiiJfr r r= i*., / —
Z4a ^120 r o 2^
T^^fz=i ^. 0;=: 5 by reverting the Series wehave
6 24 « 120 ^ '
i = A— /-A* -^ zrr — / x A' + S**' — jr' — / x
30. Frorii this Theorem it will be eafy to compute the
Value of x, or the Time from Noon when the Heat is greateit
dn any gtve9 ^^y- ^or Example: Let it be required for
the Day of the Summifr Solftice in the Latitude of 5 1® 30^^
when the Declination is 23"* 30^. Thenfince {h^Jrt. 24; 25.)
iVe have a =: 2,146, b = 0,3121, c = 0,5709, b + c:=:
C^Sg, and ac = .1,225 '» therefore -Xi =: A = 0,7207.
ac ^
Whj*tice by the three firft Terms of the Series we &dl hav^
i:zz A — r A* +, 2,rr t- / x A' = 0,7862. Therefore fay;
Ab the Circomfereace 6»28| : 560'' :: 0,7862 : 4j'' nearly^
386
AsTROJlOMy*
the Shadow pafling over the Difk of the Earth j
ind alfo how the Moon, at Full, is cclipfed by
pafling through the Shadow of the Earth. Here
aifo we fee the Manner how Murcuiy and Venus
tranfit the Sun's Face in form of ^ dark round ^of ;
and alfo why they can never appear at a great Di-
ft^nce from the Sun -, dnd various other Pbano-
memj of the like Nature (CXUII).
Whence, by allowing 1 5° to an Hour, it appears that the b9t-
tefi Time of the Day u Three o'Ckck m the J^tet
(CXLIII) I. The Doarine of Eclipses is next to be ex-
S*ain'd. The Suli being a luminous Body, valUy larger than
e Earth, wHl enlighten fomewhat more than one Hialf of
it, and caufe the Earth to prq)e£l a long conkal Shadow^ as
t^l. LXII4 ^ reprefented in the Figure, where S is the Sao, E the Earthy
Fig. a. and hBD its Shadow..
2. In order to find the Extent or Magnitude of the Earth*s
ShadotVi the Lines being drawn fu in tl^ Figuit, in the Tri-
angle SBM, the outward Angle SDA=: DSB + DBS,
die two inward and oppoiite Angles ; but the fii^, idz. DSB^
is thftt under which the Earth's Semidiameter CD appears at
the Sun, which is not fenfiblei therefore l>Bj, the %emi-
angle of the Cone, is equal to ADS, which is the Angle
Under which the Sun^s Semidiameteir A S appears at the Eal'th,
which in its mean Diibnce is 1 6 Minates.
3. Hence we can find the H^ght' of the (hadowy Cone
CB; ifbr in the Right-angled Triangle CBD there is given
the Side CD=: i, and the Angle CBD = 16 Minutes;
therefore to find the Side CB,. fay.
As the Tangent of CBD = oo"* 16' = 7.667849,
Is to the Radius 90 00 =z to.oooooo^
So is Unity i =: o. .
To the Length of the Side CB = 214,8 = 2.332151'
4. The Height of the Earth's Shadow tcing at theincaBf
Diilance of the Sun 2^4,8 Semidia<Q^rs,.when the Sun h
at its greateft Didance it will make CB^ 2 1 7 Semidiameters
of the Earth, which is its greatefl Height. Hence we fee
the Height of the Shadow is ^ar ;n^^« tims u great as tte
Astronomy. 387
The Come t arium is a very curious Machine,
which exhibits an Idea of the Motion or Revolu-
tion of ^ Comet about the Sun ; and as this Sort
ineait Difbnte of tbe Moon, or 60 Semidiameters : Bat the
Height of the terreftrial Shadow falls hx ihort of the Difbuioe
of Siars, and therefore can iavtrive no one of the heavenly
Bodies bitt the Moon.
5* After the fiune manner it may be ihewn that the Ang^
of tbe Moon's Shadow (ind indeed of all Spheres whofe Se-
midiamteen bear no fenfibk Proportion to their Diftance from
the Son) Is of the fame Dimenfions with that of the Earth ;
whence thofe Cooes are fimihur Figures, and fo have their
Heights pro|)ortional 00 the Diameters of the Bafes. There-
fore fay. As the Dsaneter of the Earth 100 is to the Dia-
meter of the Moon 28^ (6 is the Altitude of the Ealth's
Shadow 2i4»S to the Altitude of the Moon*s Shadow 60^^
6f the Earth's Semidiameters. The Shadow of the Moon
therefore will juft reach the Earth in her mean Difbnce, which
ftoanlkot do in her Apogee ; but in her Perigee it will involve
a Audi Part of iht Bartik's Surhct.
6. Befides the dark Shadow of the Moon, there is another PI. LXII*
v^rd the Pemtmbra^ or Partial Shadow 1 to reprefent which Fig. xl
let S be the Sun, T the Earth, D the Moon ; and let KCF
and ABE be.two Lmes touching the oppofite Limbs of the
Son and Moon ; then 'tis evident that CFEB will be the dark
or abfelute Shadow of the Moon, in whicb a Ferfon on the
Earth's Sur&ce between F and £ is whoUy deprived of thdi
Sun's Light. Moreover, let KBQ and ACH be two other
Lines touching the Skies of the Sda and Moon altematdjr^
and interftfting each other in the Pomt I above the Moon.
Then #ill HCBG be the Femmbrm above-mention'd, and is
the Fri^um of the Cdne GIH) fvr 'tis Evident that a Part
of the Sun wiH be leen and Part thereof hid to a Spedatoc
osi die Earth's Surface bfctw^en F and H, andBandG; 6r,
in other Words, the Smi hi thofe Parts of the Earth will ap*
fC^ ovly fartia/Iy eclifffij.
7. To oaicdate the Angle of ^i Cone HIG, draw SB,
then in the obtiqae Triangle BIS, the external Angle BID
k etfaal to both the mward and opposite Aa^es IBS and
ISB I but ISBis that under which the Semidiameter of the
Moon nppears at ^e Sun, and ii thtrefbfe itifeiiiibly fmalli
whence the A'n^ BID s= IBSovKBS sr the apparent
Sbaidiametcr of die San* Theme&re the Part of tht re
Bh 2 ^f
388
. Astronomy.
of Motion is not perform'd in circular ^ but very
elliptic Orbit Sy^io in this InRrument, a pecu*
liar Contrivance by elliptical Wheels is necet
fary to effcft it ; which as a great Curiofity
bcal Cone C IB is eqoal and iimilar to the dark Shadow of
the Moon.
8. Let U8 now fee how mach of the £arth*s Surface can
be at any time involved in the Moon*s dark Shadow* or the
Quantity of the Arch £F. In order* to this, let us fuppofe
the Sun to be in Apogee, and the Moon in Perigee ; and in
that Cafe the Height of the conical Shadow will be about 6i
Sexnidiameters, and the Dii!ance of the Moon about 56 ;
Hate thatis, (in Fig. 4.) DK = 61, DT = 56, and TE = i.
LXII. In this Cafe alfo the Half-Angle of the Shadow TK£ =:
15' 50^^ as being lead of aU. Thereibfe fay.
As Unity, or the Side TE =1=0.
Is to the Side TK = 5 =: 0.698970
So is Sine of the Semi-angle TKE = 15' 50*= yM^ii^
To Sine of the Angle /TEK = i** 19' 10^ = 8.36aao&
. Wherefore TEK + TKE = ATE= AE = i^ 35', and
fe F£ = s"* 10^ = 190^ = 220 Miles Statate-Meafure ;
which is therefore the Kameter of die dark Shadow on the
' Earth's Surface when greateft.
9.' After a like manner you find the Diameter of the Pe-
imnbral Shadow at the Earth, as GEPH, when greateft (oi
aH, that is, when the Earth is in Piribelk, and the Moon in
her ^f ogee I for then will the Sun's apparent Diameter be
equal to 16' 23^ =; TIG, the greateft Semi-angle of the
Cone ; and thence we ihaili find I D sc: 584 Semidiameten of
the Earth. In this Cafe alfo the Diftance of the Moon from
the Earth is DT = 64 Semidiatfieters. Therefore, As TG
= I : TI= 122^ ;: Sine of the Angle TIG= 16' 23*^ :
' Sine of the Angle IGN = 35« 42'. But IGN = TIG +
ITG,andfoITG = IGN — TIG = 35°25^ thedow-
. ble of which ia ^o\s^d = GEFH =: 4900 Englijb Milea
nearly.
10. Since an Edipfe of the Sun proceeds from an Inter-
pofition of the Moon,'^.*tis evident, if^he Sun and Mooo
W€fe always in the &ne Plane^ there-^onkl neceflarily be an.
Edipfe of the Sun every* time the JMoon .came between, the
Sun and Earth, that is, at eviery iVku Mwu. For IttX be
Fig. 5. the Sun^ T the Earth, and. FBGH the: Moon's Orbit in the
Piaae of the Ecliptic \ then whexi the Moon comes to be at B
will
Astronomy. 3S9
Will be fhewn, together with all Parts of the"
Machine, in my new Conftruftion thereof..
The Comet here reprefented is that which
appeared in the. Year 1682, whofe Period
in the Right Line TX, which joins the Centers of the S(ii|
and* Eaith, it will be exadly imeipofed between the Sun and
a Spe6btor on the Earth at V ; and fince the apparent Magr
nitude or Diik of the Sun is the fame nearly with that of the
Moon» it moft neceflarily be hid l>ehind the San*s Diik at that
Time, and fb edipfed from the Sight of the Spefbtor; and
this Bittft be the C^fe whenever the Moon conies into the iaid
Line or Point B, <wr«. every New Mooh.
11. But if (as the Cafe really is) the Orbit of the Moos
be not in the Plane of the Elliptic, but inclined thereto un-
der a certain Angle, there may be a New Moon, and yet no
Eclipfe of the Sim at the fame Time. To illuSrate this^
let ABCDE be a Ciide in the Plane of the Ecliptic, de-
fcribed at the Difbnce of the Moon's Orbit AGH, and in-
terfedUng Che fame in the^Points B and D, making an Angle
themwxth as ABF, whofe Meafare is the Arch GC, as being
90 Degrees diftant frpoi>the angular Points or Nodes B and D.
1 2. Now *tis evident, if the Arch G C be fomewhat greater
than the Sam of the apparent Semidiameters of the Sun and
Moon, then at G, and.fcmie Difhmce from G towards B,
tiier^ may be a New Moon, and yet no Eclipfe of the Sun,
becaiife in this Cafe' the Diik of the Moon G is too much ele-
vated or dejbefied above or bek>w the apparent Difk or Face
of the Sun C to touch it, moch lefs to - hide or edipfe any
Part thereof ; as is evident from <the Figure. •
• 1 5. At a certain Point M in the Moon's Orbit, the Moon
Will have a Latitude equal to the Sum of the Semidiameters
of the Sun and Mooim and therefore when the Moon is New
in that Point, ihe will meat to a Speflator in the Point Z to
touch the Sun only ; mm whence this Point is calPd the
EcHptic Limits inafmuch as it is impoffible there (hould happen
a New Moon in any Fart between this and the Node D (on
e^h Side) without edipiinig the Sun lefs or more ; as you {e\
the Partial Eclipft at K, and the Total Eclipfe in the Node it-
^If B. . .
*. 14. What we have hitherto faid has been with regard to
the PhdmomefM of an Eclipfe of* the Sun as they appear to a
Spedator tm the Earth's Snr^ce, in whofe Zenith the Moon
(hen is, and where thex;e is no Refraction to alter the tm^
Latitude of the Moon : But where the Moon has any Lati-
■^ Bb 3 »
39© Astronomy.
is 75 Years and a half, and therefore will again,
appear in 1758. By this Piece of Machipery is-
Ihewn the unequal Motion of a Comet in every
tttde, there the Procefs of calculating the Appeaiances of a
Splar Edipfe will be ibmewhait more complex, on aoeouat of
tl^ Variatioii of the Moon*8 Lati^e and Loogitude ibr eve-
ry different Altitude^ and coofequently every Moment of the
Eciipfe.
PLLXIII. 15- Bat that I may give a clear Idea of this Affair of Re-
Fig. I . fraaions, let AB P Im» the Sqrfaoe of the Earth, M the Moon,,
S the Sun^ feen ft<Mn th< Qmter of the Earth T in the &me
Point of the Heavens with the Moon, and confeqnently an-
trolly tcliffyd to a Spe^ator at C, in wfa»fe Zeiylth the Moon
is : fint to a Sp^ .^tor any where elfe fituated, the fame Phtt^
n^enoH will not ]||ppen in th^ fame Circamlbnces, if at all.
Thus a ^p|e£tator at B will view the Moon in the Diie^on ot .
4e Right Line B MN, an4 fo her appreat MacfS in the Hea-
vens will be at N, where it is evident her upper Limb wiU
but jail touch thf k)W!er Limb of die Snn, and fis wiU not
edipfe it at ajit : B^t to a Spedator any ndicn between Band-
C the Sun will appear tp bi^ partudfy ici^dkb or mote; as
yon go from B towards C. '
16. This AKh SN in the Heavena is caH'd the Paraliax^^^
or Difierence between the true ^o^affaxet^ Place of tl\e Bqtv
dy at M» and is equal to the Aag^e &M N or BMT. NovT
this Angle oc Parallax is co^fiaotly diminifhing, at the Ph^»
mmenon at M approachet towards the Zenith at £, wha« it
trntirely vaaifl^s; but i^creafes as it approaches the Hofizon
at G^ where it is greateft of all, ^ is there cali^d tiie tbri-
mmutl Parallax^ which in die Mobn amounts to a wkolt P/-
^#i>, as was (hewn Anmt. CXXXV.
17. It is here obfervabic^ that the Pa»lfa»e always deprcffca
the Objea, and therefore when the Moon haa North Latitude
it is dimiaitbedy but the Sooth Latitnde is increaied, with re-
fpea to us $ and fo the Edipdc Limits are variable in every
particular Latitude. Bpt a Selar Eciipfe vdaj in an abfohue
Marnier be bed repre^nted by a Projedion of the Earth's
Diiky and of the Sedion of w dark and penumbrai Shadow
of the Moon, as they appear (or would appear) to a Speda^
tor at the Pittance of the Moon in a Right Line joii&ing the
Centers of the Sun and Earth.
1 8. In order to this, we are to find the Dimenfiras of the'
a^arent Semidiameters of the Earth, dark Shadow, and Pi^
Part
ASTRONOMY. 391
Part of its Orbit, and how from thence it moves
yrith a retarded Velocity till it arrives at the Jipbelion
Point, where it moves ftoweftof alJ j and from thence
it is feen continually accelerating its Motion to-
nmtm. it tbtDiftaocs c^ the Modq. A^ to the ifirft, <vix.
the Earth* s SemtSameter^ it is equal to the Moon^s horizamai
/Wtf/kr« at we have ihewn. Thm of the dark Shadow is
thm eftimated : Let C he tlif Center of the Mooq, D,B its RLXIII,
Dhuiirter, BHB ttstdark Shallow, and KAL tt|e Penura- fig, 2.
bial CmP^ Then let fiF be the Diameter of die Fnymira
a$ |)ie Easth, 1^ IG that of the dask Shadow, and dnw
CGaodCE; then i& the Ang^ CGBsBHC+HCG,
apdrfiai QCH = BGG--* BHC ; that is, theamuent Semi-
d^am^ter of the dark Shadow is equal to the Diftrence be-
ttKeeti the appaienf Semidiameters of the Moon and Sim.
(Se» ^frif. 3 and 5.) v .
pg. In like manna the Ai%IeECHsDEC+ DAC,
^nat hf the appamnc Semidiomecpr of the Pimmhra ^t the
EjiTlh it ^nal to the Sam of the apparent Semidiameters oF
the MSWA and Sun. (See Att. 7.) Now the Semidiameters of -
the San and Moon, and alfo the Moon*s Horizontal Parallax,
a^e aU >ea^y calculated for the varipos Diftances of the Son
and Moon from the Earth, and for leafl;^ mean, and greateil:
Eccentfkjiies of the Looar Qrbit, In the AfirsntmcalTid^lis,
20. Therefore let AE repreient a fmall PpriioA of the Fig. 3.
annual Orbit, and FH the vifible Path of the Center of the
Xtunar Sb%dows, which will ^nca^ly correfpond to die Pofition
of the Moon's Orbit with refp^d to the Ecliptic in the Hea-
vens ; and therefor^ the Point of Ij^teifedtion S wi)l be the
Node, and tl^e Angle {) Q E the Angle of Indication of the.
Lunar Orbit to the Plane of the Ecliptic, which is about 5
Degrees.
^i. Hence if j^lPQS r^prcfcnt the Diijt of the Earth (ac-
cording to thp Orthografbic Pr^e^ien) in the fcveral Places |^ ,
B, C, i)| whofe Semidiamet^r is made equal to the Number
of Minutb in the Moon^s Horizontal Parallax at the Time of
the ^linfe ; and if in the Path of the Shadows in the Points
£3 , K, rf , 0, we defcribe ^ fmall Circle whofe Semkiiameter.
is equal to the Difference between the Semidiameters of th^.
Sun and Mopn, that fi^Il bp the prcular Setiion of the Moon's
dark Shadow at theDiftance of the Earth: (by Jrtic/e 18.X
Laftly, if on the fame Center we dcfaibe a larger Circle^
whofe Semidian\iq^er is equal to the Sum of the Semidiame-
ters of the Sun and Wfoon, that ihall reprcfent the Seftion of
B b 4 wards
393 As T R O N O M ¥•
wards the Pmbelium^ in fuch manner as the Law^
of Attraftion require. The Comet is reprefented
by a fmall Brafs Ball, carried by a Radius VeStar^
fhe Fenumbral Shadow, ^y Art. 19.) and is here &wn hf *
tl^e dotted Area/
. 22. Here then it is evident, if the Moon, when New, be -
at the Diiboce QG from the Node, the Benumbral Shadow
will not fall near the Earth^s Difk, and ib there cannot poffi-'
bly happen any EdipT^. If the Moon's Diftance from the
j^ode be equal to S3N, then the Penumbral Shadow Will jilft •
touch the DiQc, and confequently QC the EcijftU Umift
which may befban4 a&fpUpws. The^Liae NC,- as being
the neareft Piflance of the Centers of the Shadows and Dilky '
is perpendicular to the Path FH, and is equal to T C -f N T
— 62' 10'' 4* 1^21'' + 16' 2^^, 'viz, the Supi of the Mo<Mi-a.
H<»:rzQntal P^allax, and of the Semidiameters of the jSun
ao4 Mpon, all of them when greated : Alfo the Angle N 3 C,
iifben leaft, is 5^ ^d. Therefore in the Right-angled Tri-
angled NsC, to find the Side QC, we. have the following
Aiudogy^
' As the Sine of the Angle N C C = 5*^ 30' = S.98 1573
Is to Radius 90® 00' =: 10,000000-
^ is the Logarithm of theSide N C=: 95^,5 == 1 ,980003
To theLogarlthmofthe Side S3 €='996^4;^ 2.998430
24. The Ecliptic Limit, therefore, is 09$',4 := i6® 36',
beyond which Biilance from the Nqde & th^re can be n9
Edipfe ; and within that Diftance, if the Moop be New, the
Shadow will fall oh fome Part of the' Difk, as at B ; where all
thofe Places over which the Shadows pals will fee the Sun
edipied, in part w^ by the dotted Penumbra! Shadow, bu(
totally by the dark Shadow ; iand the Sun will be centraliji,
eclipfed to all ttoft Places over which the Center of the Sha^
dows pafleth*. " • . v . . - .
24. If the Moon be new in the Nod^ itfcif, then will the
Center of the Shadbws pafs over the Center of ibe^ Dilk, as
l^prefented at g? . In this Cafe if the ^pp^ni; l)iameter of
the Moon be greater than that of the Sun^^'the I'ace of the
Sun will be ivMfy ohfcuredto all Parts' over \yhich the Centeir
BaiTefs ; but if not, the Sun will only be centrally eclipfed^ bu^
nis Circumference will appear a hri^t Anntilui^ or. luminous
Astronomy* ^ 393
or Wire, in an elfiptic Groove^ about the Sun Iij
pne of its Foci ; and the Years of its Period are
ftiewn by an Index njoying with an equable Mc^
Ring, whofe Width will be equal to the Difference of the
])iameten of the LuiiMnarie».
25. As the Difk of the Earth is here projeOed, itreprs*-
fents the Cafe of an EclipTe on ao E^noOialDiy, fo that
A K is the Ecliptic, i^Q^ the Equator, X Y the Asds of the
Sdiptic, FS the Axis of the Equator or of the Earth, P and
S the Nqi^ and South Poles ^ be&des the Trcqpics and Polar
Circles, l^r/e repref«nted by Right Lines, as in thecomiiiQii
Analimma, And by thofe who underftand this Prc^edion, the
Djik of the Earth an^. the Pailage of the Shadows oTer it
may be exhibited for any Place of the Sun, or Declination of
the Moon; for which fee 9y Turn Trigmumgtir's Gmde,
Vol. II.
26. Lunar Eclipses are not quite (b complicated in
Theory, nor near, fo tedious and difficult in CalculatioiH as So-
lar ones. The latter are only apparent y the former nalhjmchi
that is, the Moon is really deprived of its Light, aodi±ere*
fQre mufl; appear obfcured to all the Inhabitants of the Eartk
^qu§Ily, by whom (he can be feen ; where^ the Sun, not bc^
ihg deficient in Light, will ever appear Vefplendent to thoft
who do not happen to live on that Part of (he £arth where
tne Lunar Shado>vs pafs.
27. As a hmar EcUpfe is pccafion^d by the |mmeifi<m ef
the Moon iqto tlje Earth's Shadow, we have only to calculate
t}ie apparent Semidiameter of the Earth's Shadow at the Moon,
in order to delineate an Eclipfe of this Sort. Thus let AB Plate
be the Earth, T its Center, AEB its Conical Shadow, DC LXIIL
t^e Diameter of a Sedtion thereof at the Moon ; ai\d drawing Fig. 4*
TD, we ixave the outward Angle ADT =DTE-f DfiTj
therefore pTE= ADT — DET; that is, the AngleDTE.
lender which the Semidiameter of the Earth's Shadow at the
Diilance of the Moon appears, is equal to the Difference be-
tween the Moon's Horizontal ParallaJi^ ADT, and the Semir
ifiameter of the Sun DEF. '
23. If therefore AE reprefent the Path o( the Earth's pjg^ m
§haJo\Y at the Diftance of the Moon near the Node ©, and ^
FH a P^rt of the Lunar Orbit, and th^ Sediop of the Earth's
Shadow fee delineated af Q, B, C, D, and the Full Moon at
Cf . I, N^ (^ ; ttei} 'tis evident, where the leaA Diftance of
tne Centers of the Moon and Shadow exceeds the Sum of
Jheir Scmidiaraetiprs/' there (:an bc^no Eclipfe of the Moon»
m
A S T R^ NO MY.
tjoii over a graduated filver'd Circle : The WhdJe
being a juft Reprefentation of the prefent Theory
of thofe prodigious and wonderful Pb^^nommt of
the Planetary Syftem (CXLIV).
as at D. But where that Diilance is Mi, the MoetkmtA hih
pait^ o& whofly inyohred in the Sliad«w, and fe fnffer an
£clq)fe» at at B and 9 ; m whkh latter Cafe the Moon paffes*
0¥er the Dkraeter of the Shadow.
. 29. But in a certain Fo&apn of the Shadow, as at C, tke^
Iffil Diftance of the Centers NC is equal to the Sum of the'
fienridianicters} an4 therefore BQ it the EcUptk Limit for^
Loni^ Echp^s: To' find which, we have NC =c 65^ la^-
nearly whe« greateft, and thie Angle N 8 C =s s"" oo^ T^ne^
fixre&y, ' ^
. A& the 6ino of |he Angle N.8 C 3= 5'' 00' ss %,<^^o;l<^6]
litoRa^iixsj ^ 90^^ oo' z= 10,000000
SoisjtfaeLogaritlunofthe Side NCsB 63^2=: 1.S00717
TodieLqganthmof theSide sC^z 725^225 2,860421'
Henc*, if the Moon be at a iefs Dxfknce A-om the Node e!^^
diah 7^5' 2= 12** 5^, there wiU be an EcDpfe'; othcrwift?
Aone can happen.
' 50. If the Earth had no AtxtiOfphere, the Shado'Otr woulcf
be abfolutely dark^ and the Moon inyolvigd in it <j[uite invii!-'
file ; bat by sieans of the Atmofphere many of the Solar Ray $
aiOfelradM into and mixM with the Shadow, by which the
Moos' is rendered vifible in the nui^ of it^ and of a duflcy.
ptd Colow;
\ (CXLiyj 1. I Ihall here preftnt the Reader with as largo'
a Compeiidiam of the Newtonian Cometographt as
the LUnks of this Work will permit, or, perhaps, as he majf '
Iwve an Inclinatkm tp read. $ir Ifufte has made the Doctrine'
or Afirmmy of Comtts the laft Part of his immortal Princifia^
aid declares it tt> be by ^ the qo^ difficult and* intricate
Part of Philofophy.
a* A Comet is a Swt of Phnct revolving about the Sun,
iii a vesy eecentrk C^bit or EUipfls,^ and which confequently
appMWthes veiy near the Son ip one Part of its 0(bit, and
fooedes to a very remote Piftance from it in another. Henc^
^tis evident) they moft undergo extreme Degrees of Heat and
Cold. Hence it appears that the Comets are foud^ cpiopad, fix'd^
''* \ apd
ASTEONOM V. 39;^
IliddandUc BffdiM, «pd not aVMHW ^ 9Atli»^ «f (U
Sarth, Sun, or Planicu, as h^ t>Ofa ofinQy fiippoftd i l^ocai^fcr
if k wecd ^cb, it q^oft iacyitahly b^ diffipattd ^ 44^^
iapMBngfaiipiurduiJIuA: Fof^ Difbincoof tlioOWftof^
1680 19 /VfiffAi wp fo finril, Hm '^ 90BGd.vc4 i| JDoi^c of
Heat ^vit xoQO taqiet greitter than tba^ of ^4-1^ Iron-
3* Yet are thty not io ^*4» butduit tlieyfoika 4p^ ti^'
Id^ Y9fmu; wUc^ ac firft, while the Cqmfl i| y«t a greai^
vay from the Sun, fnnroiiiMi the Sp4t ^ Fonq of ^n Atmo^
fptK»p, wrt^egw to ?#»4w*P Comet v»ble. A» thcCa^
met approaches nearer the Sun, this VapoiMr be^ to ^iJBeiul
funf^ the Head qr Viulmt, to iieights gwf t^ sm4 groatf r, as
the Coinet gets ^pixtr and neaier td the ^^ u4 wkf^i^fff^
aaazi^js Streains pf Ught we wfiifiDy call thew TW^. . AA
Mfhii^ hi.^y to conceive fr^fn a View of the figure* *
4. I^he^e Tails alfo ar^ fo foe and taufluci^, iha^thf Sjtm-
2^edi$i>^y viahle tlirough them. As^they rifii.ft^M ti^i
Head and afcend, they become rtrified, ^nd gro^ brpadei. to-
waidt tlip oppfar End. The Form of the Taii is weUknawA
to a]] poMT living who iaiv the )ate Comet; in whioh. wo ob-
fisrv^d tho Tail ba^ a finaU Flewre or Cutrataret, as (hey alt
have, ' being c^nveoc on the anterior Part, aod concavip \i^kA^
which arii^ fiDm the twolbki Motion of thfs Partidef of tkir
Tail, thf one of the Afcent fiom the Head. th9>other being
the prog^fliye Motion ^n cowmon with the Nttckm itfeHI
Bat as thf former is much the gr^ateft, fo its DkeOciom is b«t
liul^ a^ta'd.by thf l^tter^ and (o the Foiition d the T#il hnl)
« little cd>lique and incurv^ted.
5. As to th(s CanTe of the ATQcnit of the Cometaqr Va*
ppur or Tail towards the Parts oppofite to the $nn> tbeie iMvo
been various Surmifes aad CoDJeiaare3» £br fo I call theau, aa.
no( being attended with Cert?iin|y and DemonSr^non. K^f^
afcribes it to the A^ion of the Sun's Rays^ rapidly cacrying
the Matter of the Tail away, with them. An^ Sir ^auc doet
not thiols it diiSboent to Reafon» to fiippofe the fiibtil ^Ahr
in thofe fref Spaeee may yipUt to the AOion tod Difefiion of
the Sua-Sf 411^. It « certain bom Exptnmenta^ chat the 80*
lar lU^ys coH^d by a Bnming^Glafi to a Foa»» impel light
and poadMlons Bodiesi vciy noubly» even fo at ta make theiif
vibrate b^dcw^rds and forwards : And though this Impidfion
of the R9ys of Light witt^ us, in out ffoA Medium^ and oi^^
our |luggilh M^tter^ be' inconfiderable; yet in thofe fret
$P^^a» and on the CabtU Effluvia or fine Partidea of the Cor
Piscary Atfuofphere, it nnay be very great. I know there
ar^ other and later ({ypothdes to account for the Motion and
F^rm of ^ Comet's T^jl ; bat on Fjaminafton they appear
ts
3^6 Astronomy.
to be infSfficienty improbable; and anphilofophkal^ afAldi^re*'
fore^ifluin not trouble the Reader with them. -^
6. The Bodies of Comets are yeiy fmall, amd above the
Orbit of the' Moon, as is evident froih hende, that they have '
• no perceptible hoHxontal or diHimal Parallax y aiid whch vic?w'd *.
widi a Telefcope at their neareft DUtabces appear le(s than to ^
the uaked'Eye, by having the Splendor of their Talfi talGcn.
tMy and that of the Atmofphcfre abated by being ndl^nified'/'
The Nuetfus of the M Comet meafured but a few Seconds,'
IQ I found by meafufihg the A^ofphere by' a Micrometer^
jmd taking a proportion^ Pan. -
7. On the other hand, by theif annual Parallax ^Rey are'
]^ved to defcend wi^fai' the Regions of the Plteets' ; they-
aifo appear fometimes £re3 and flower than they really move,
ibmetime^ retrograde and fwifcer thain the true Motion, and
laffly they are- fometimes ftatimary i all which Phschpmena
itrife from the fame Caofe» as were befdre explain^ ^ th^
Planets. (See ^Mr^/. CXXXIX )
' 8. Since the Comets by Obfervation are found to deicnbe-
curve tMk^ about the Sun, ' they ifnuft be drawn by fomeTorice '
Hom a rcflilineal Courfe by the firH Law of Motion*. And
fince tl& Force in all the Planets tends to the Sfan, as being
tike largeft Body in the Syftem, therefore alfo this Force in thfe
Comets^ refpe^ the Sun in a more immediate ManHer, as be«
mg fo mCich lefs than it than mdt of the Planets are. And
ySdyi an this Force in the Planets is inveffety in the duplicate
Ratio •( the Diilance from the Sun, thte fame Law is up-
doubtedly obferved by the Comets, which are in bthter Re-
fpe^ Bodies iimilar to the Planets. The Comets therefore
ifiove in Conic Sections about the Sun, having their Foci ii|
the SofiV Center. (See ^»<7/. CXL )
' 9. Hence, if Comets return in an Orbit,* thoie Orbits muft
be ElUfJesi and their Periodical Times will be to' the Peri«
odical Times of the Planets in the feiquiplicate Ratio of the
principal Axes : And therefore the Comets being for the moft
part beyond the Planetary Regions, and on that account de-
fcribing Orbits with much larger Axes than the Planets, re-
volve more ilowly. Thus if the Axis of a Comet*^ Oibit be
4 times as long as that of Saturn's Orbit, then would the
Time of the Period of the Comet be to that 6i the Planet as
1 V^ 4 to I , or as 8 to I ; tnz. 8 x 30 1= 240 Years.
10. Since it is found by Obfervations that the Cometaqr
Orbits are extremely eccentric, and that the Portion Which a
€omct defcribes during the whole Time ^f its Appearance is
but a very fmall Part of the Whole, the Renter of fuch aQ
^Ilipfi^ being removed to fo vaf^ a Diilance inuft occafion t£e
C^nratijr^
Astronomy. 397
Curyatare at each End to be vaftly near that of a FaiaboU
liAving the (ame focal Diftance ; and confeqaentty the Motion
of a Comet may be calculated in a Parabolic Orbit without
m&y fenfible ferror
1 1 . Therefore the Velocity of a Con^et in Peribeiio {in%. in Plate
the Vertex of the Parabola P) is to the mean Velocity of a LXIV.
Ranet defcribing a Circle about the Sun, at the fame focal Fig* !•
Diftance SP, as •T to i. And fuppofing the Earth to be
that Planet, let us put the Radius of its Orbit SP = 10000O9
and dien fay. As the whole Periodical Time of the Earth
365|istothewholePeriphei7 6283i8,foi$ i Day to ifzo^z
Yzxt& defcribed in one Day ; and in one Honr it will defcrite
^1,67 Parts. But as i : ^T :: 1720,2 : 2432,747, the
Parts defcribed by the Comet in one Pay ; and fo the Parts
defcribed by the Comet in one Hour will be 101,364.
12. Whence if the Latus Reaum LR of the Parabola be
equaljto 4 times the Radius SP of the Earth's Orbit, and we
put S P* =: 1 00000000, the Area which the Comet will de-
scribe each Day, by a Ray ^wn to the Son, will be
12163734 of thofc Parts, and cachHour an Area of 50682J
of thofe Parts. To demonftratjB this we moil coofider, that
the Square of the Diametejr of any Circle is to its Area at
.1 : 0,7854 :: 4 : 3,14159; therefore the Square of Radius
or PM = 1 . Whence the Area of the Circle is to the (aid
Square PM as 3,14159 to i. And the Rectangle PL s= z»
But the Parabolic Area PLS = — PL = i.x2 =-i.
3 3 3
Hence this Area PLS is to the Area of the Circle as — to
3
3,14159. And if the Velocity of the Comet and Planet at
P were the fame, the Time in which the Comet would de-
feribe the Arch of the Parabola PL would be to the Tkne ift
which the Planet defcribes iu Orbit in the iame Ratio of ^
_ 3
to 3,i4i$9. But thefe Velocities are as • 2 to i; there-
fore the faid Times will Ixj^x -4=. to ^iiiliS, that i^
31/2 «
aii/— = i/— to 3,14159. Wherefore&y, As 3,14159:
I o 9 '^
i/JL :: 365 D. 6H. 9' : 109 D. 14H. 46', the Time ia
whi?h the Comet wiU defcnbe the Arch PL. If then PS*
s= PM 5= iQooooooo, wc have the Paiabolic Area PLS =x
133J3333J
3^8 A S T R O N O M Y.
<33333S33 Parts defcHbed in 109D. 14H. 46^ and thttt-
foft the proportional Parts for a Day and Hour as above.
13. What thbf^ diumal and horary Arenas are in different
Parabohu may bethas ihewn. Lttfrq be a Parabola fimikr
to the former PRQj then will the Time T of dcfcribing the
Atch Pk be to die Time t of dfefcriblng the limilar Arch fr,
as the Periodical Time P of defcnbing a Ciide bn PS to the
nribdical Time p of deieribing a Chide on fs, by the bft
Article. But P:^j:PS* ://*:: R^:r^:: T : ti aifothe
£milar Areas PRS = A, and/rS = «, arc as the Squares
of their like Sides PS and /S ; that is, A : « :: R^ : r\
Now fince in the fame Figure equiil Spaces are defcribcd in
^qoal l^imes, whatever Nomber of Days or Hours are coa^
tam*d In T and t^ the Areas A and a will con&ft of as many
equal l^arts reipktively} and which therefore we may caU
the^Piaittf A^aftdi-Flftof «, or^andji ib that ^:
A a R^
^••T-r-R^K
14. Let Ae QgadrtliM Area PSR of the Paraboh PRQ^
be ditided into 100 eqnal PHrts, thit is, let A = 100; then
^SBiofthofeParis, andfo— :R\ Again, let N be
t&eNmxSbeirof thofePirtsdeltribedin i Day; then will Aa
diun^il Area 1)e N X ~ : A : N X R* : ^X (by Jrt. 1 3.I
109 1
therefore N : — r.
Ri
15. In like manner k is Ibewn, that if the Qgadiantal
Area/rS of the Parabola fr^ be divided into an 100 efc4
Parts, and/S=:r, and n = Number of thofe Parts in the
dhimal Area $ then n : -r-. And fo N : « :: :_:--. s
rl Ki ri I
«=: N X -v^ if R = SP= I, or the Radius of the Barth*i^
OAit. ;
: r6. On tfcefc Pnndfics tfie Gmnkft Caki^u* depesdsr ftt^
in any Parabolic Orbit the Quantity « == N x -^ is the'^dBUri;-
lial Area, and may therefore be e(feemed the mM» MoiUn cii^
An9nudf of the Coni<6t for a Day; which multipli^ by tlieu
Time (<jcpi:efi'd in Diys) before or aft^ir the Coniel & in Perl *'
\
Astronomy. 399
&//o dt P, Will give the whole mean Motion or Afea ^R(2§
for any Place of the Comet Q^in its Orbit. In order to this
we muft have the Time afcertain'd from Ofafervatbn when
the Planet was in Peribelto at P, and alfo the Perihelian Di-
ibnoe SP from the San; «s alfo the Place in the EeKpticat the
fime Tim«, the Pofition of its Nodes, and Inclination of its
Orbit : All jvhieh Partioiiars for z^ Oomets the ladtftrf of
the great Aftronomer of this Age has fupplied, 'vi%. Dr. ffaA
hy^]xi\^%CMna^rafhtai Which I have tniliftiibei« «id added
thereto the fame Things for the laft Comet, as they were de-
termined by the Reverend Mr. Uiih^ frerii the OUervitiOns
iof Mr. Profeflbr BU/s oi Oxford^ at the Obfervatory of the
Righit Hoto. the Earl of Macchsfieli^ at Sheriem^ in O^ord-
ftnfe*
17. Prom th6 Mace oF the Codfrt CLdraw tJA perpendi* PLLXIV.
cnkr to the Axis ; and let ^5 be a Tangent to^ Curve in p|» 2.
the PaiHt Q, ^^ BQdrawn pernendicular thereto ; then by
the NflCax« of the Parabbk we Ws ABss 8R» die t^m*
Lotus R€3um. And putting the ^given Area P QS 3tt tf » and
AQjssjT, we have yV-*' + -J-* = «» or*'-|-3;r=: izai
which Cubic Equation refolv*d gives the Ordkiatt AtJU and
thence we have PA; but P A + PS =z S<^= DiAanct of
the Comet from the San» which therefore is given, lliere-
fore in the Triangle S AQ^ rqrht-angled at A, we have SQ^
and AQ^to find the Angle QSA } and dies PSQdtt Angle
from the Peribelium is known. When this is donej all the
Other Partitttlars are Ae fame as m the Planaay Calouhu.
18. Thefe are the Prhiciples er Elements <tt Calctilatioa s
which we ^H now proceed to iHdb-ate by Example, that fo
the fraxis may not remain fo (fifiicDlt and obibure as it hae
hitheitd httti I and w^ flutH make choke of the la!l Comet
for this Rirpo^y wht)li? yman Anomaly or (Uurtfal Area is in the
firft Pfaccr to be dttemrined.
' 1 9. In Older to tfais^ we havts the coiftam iSxtiu Motion of
a Contset moving in e Parabola, tt^hofe Perihelion-HManoe
PS = R = 1 =: Semidiametcr of the Earth*s Orbit, was. N=i
Ml »j"'^^r|^^/ ** 0^1 at«, ii«ihele lA/ffMrn^.^dotzZ
is therefore always at hand for cenflant Ufe.
20. The Perihelion-Diftance PS = r =r 0,22206, and its
Logaridua 9>34647a» es in the Tadok, for the Comet of
I74f . But we have iti mean Anomaly « = N x -^ (by-4r..
r^
itde iS'h diereforc to find n by Lo^^ithms the Procefi tt
isi;>llowf:
The
400
A S T R ON O M Yi
The Logfirichm of Perihelion-Difbmce r = g»^4.6^yi
Which multiply by — — 3
The Fcodadl is the Logarithm of r' = 8.039416
Divide by 2, the Qaotieiit is Log. of r^ =: 9.019708
Arithmetical Complement is the Log. of -^ ir: 0:98029^
ri
To which add the Logarithm off N = 9.960128
The Log. of Mean Anomaly «= 8^718 =r 0.940426
21. Having thus obtained the JUumal Area^ if we multiply
this by any Number of Days and Decimal Parts of a Day, it
will give the Area PRQS, or mean Anemalj, for the given
Time. Thus let it be required for January 23 D. 6H. i Vi
D. H, M.
Then from the Time of Perihelion, Feb. 198 12
iSubdttd the given Time, Jan, 236 11
The Difiereftce will be 27 2 i
Wherefore to Log. of diomal Attz 8,7x8 = 0.940420
Add the Log. of the given Time 27,0833 = 1.432702
The mean Anomaly requved == 236,1 =: 2.373122.
22. Having therefore the Area PRQS = 236,1, we cai\
find AQj=: jr, from the Equation *^-t"3;if= izai for if
iirhen the Quadrantal Area t^SR is 100, we put SR = ;r =: i^
then 'tis plau), jr^ 4" 3* =.' + 3 = 4= '*« in that Cafe.
Therefore when the mtan Jnomafy is but ji^ Part of this,
we have ;r^ -|- 3^ = t#? = 0,04; which will be a conftant
Multiplier for reducing any given Anomaly to. fit it for the
Equation. Thus 0,04 x 236, i = 0,444 =:;r^-[-3jrinthe
prefbnt Cafe, which reiblved accoriung to the ofual Methods
gives ;ir =:: 1,65 nearly.
AQ*
23. Then by the Nature of the Fkrabola — ^ = AP s
■V^^^'^^ = 1,3612. Alfo AP + PS= SQ= 1,8612,
the Diftaoce of the Comet from the Sun for the given Time.
But to exprefs this Diftance in the fame ?arts as the Son's
mean Diflance from the Earth contains 1,00000, wemuu
«oniider that the Perihelion- Diftaace PS s^ 0^222061 whence
A i T R 6 « o M f^ 4oi
&k s«£ 0,444^2. WbirfforefiiT, As 4 :p,444t2 :: i,86i2 :
6^82650^ the ExpreiEoti required •
. 24. In^ie R^-angled Triangle QAS, kviog all the
Sidea, w9MtheAiigl»Qi8A:^62''|6i^i wkeoce the oB-
tufe AfigU PiQj^ I i7" 33^', which is due HelioceBlric
Diiiaacc of the Coltiet from tha Perihelion. Now £nce the
Perihelioo. is ip £k 1?* <2' 5J^ if we fiibdaa 4 17** 33' 30*,
ve hiave the Heliocentric Longitude in ^ 19° 39^ 25'.
25- Alfo the Descending itoJi is in tri 15* 45' 20^ from PLLXlV*
wMch TubthdE^ the Comet's Plaise now found, the Difference Fig. 3«
1 47**. 05' ^5^ is the DJiUnce of the Comec from the Node.
let the Line of the Nodes be SS^A s ^ben, fince the Peri**
Ixelion P fa 151** 27' 35^ diikant from the Node fl,, it will be
but 2^^ 38^ z^' diilttnt from the Node O • If then from the
Apgic QS A == 6z'' }6i' wd^ficdiia PS?J :±e 28** 58' z^' =
Asa, we fhall havt QSfl, = 30** 58' 5^
, i6f f roin QJet fall the Perpendicular Q|^ on the Line of
Npdes % tiien in the Right-angled Triangle QSN, having the'
Angle at 5 and the Side %Q^ we can find QN as follows.
As Radius 9P* = 10.000000
' ' :TotheSlni6ftheAfigle<iSN=±33*j8'i=: 9.747J74
Sb is tiie Side SQj= 0,82650 = 9.9.17227
■ Tothfc Length of tht Side C^N zn 6,46200 1^ $.66460!
27: Again : In the Right- inglcd Triangle QND we hard
Hit Side jiow fonnd <2[hr, and the Angle of the Inclination
of the Comet's Orbit <iND = 47* 9', to find the Side or
Pcrpenditukr QDi Thus Ay;
As Radius 90^ = io.oooooo
Is to thc,Sine of Inclination QNDi= 47^*9'=: 9.86513*
So 18 the Side Q^ zsL 0^46200 =£ 9.664601
To the Perpendieu[Ur (^ =: 0^33860 =: 9.529739
28. W^ can now find the Heliocentric Latitude of the Co*
inet; or the Angl^ (^Di for
As the Side QS=s 0,82650 Sir 9.9x7227
Is fo.th^ Side C^ = 0,33860 zz: 952^739'
-SoisRadius^ 90*^^ io.cobooo»
. TdKneofHelioC. Lat; <iSD=: 24** li' lic 9.612511^
.29. To find the Comet's Curtate Diiiance from the Sun*
W)c. SD, we hate this Aodogy froai the RightaAg^ed Tri«.
, As Radius ^ * 90* =± to.oooood
Tothe Sineofth^An|^SQp±£65''4^sS: 9.960051^
So is the Side $0=0^8265022: 9.9117227
To the Curtate Di&ance SD = 0,75380 ;5= 9877279/
Vox. U. . C c 30. Ta
402 AsTRONO^^tV;
30. To find the Side ND m the Right-angled Triangle
QND, fax.
As Radius • 90® == lo.tiooooo
To Co-fine of Inclination DQNnr 41** 51'= 9.812616
So is the Side QN.iz: 0,46200 £= 9.664601
To the Side DN = 0,31420 ±1 f 497217^
31. Then in the Right-angled Triangle NS D we ean fincf
the Heliocentric Pluck of the Comet in the Ecliptic, or Ahgjie
DSN, thus: •. • . . ' V
As the Curtate Diflance SD = 6,7,5380 m 9.877274
To the Side NJ>r;: 0,31420 == 9.497217
So is Radius 90®::= ib.oo6ooo
To the Sine of the Angle DSN =: 24^ 38' =. 9.619938
. Therefore to the Place of the Node 5^, « 1 5* 45.^ 20*^
Add the Angle now found 24 38 00
The Sum is the Helioc. Place in the Ecliptic, n i o . a 3 20
32. The next thing to be doncis td find the Place of fhe
Sun, and coniequently of the Earth in her Orbit forthei given
Time; which is calculated from the .Tables in the ufual Me-
thod as follows :
Mot.ofthiSun.
S. 0 / //
1741. 9 21 I 58
3. II 29 17 00
Jan- 23* 00 22 40 12
Hours 6 . H 47
Min. II 27
M/. ofFtrihelim. .
. s. *» 1 «
3 8 13 30
2 30
3
Mean Mot. 10 13 14 24
Equat.add. i 7 39
— - 3 8. 16 3 .
10 13 14 24 .
True Place 10 14 22 3 74 58 23 M.Anom.
33. The Sun's Place being found in r: 14** 22' 03^, the
Earth's Place will be in the oppofite Part of the Ecliptic,
a//«. in ^ 14** 22' 03'' at T. If therefore from this we fiib-
trad the Comet's Heliocentric Place at H, we fhall have the
Arch HT = 63^ 49' 43'' = DST, the Angle of Commuta^
tiom And as the Earth's mean Anomaly is 7S. 4** 58' 23^,
the Logarithm of the Earth's Difknce ST will be 9,993947.
Sut Sl3 is alfo known; therefore we can find the Angle
DTS, or Elongation of thc^ Comet from the Sun, thus :
. . As
A s T^ It o. N o M sr^ ^03
. As the feum of the Sides ST + 3D =2 1, 74060= o.t4SH^
IstbtheirDifFercnce ST — 80 = 0,23240= 9.36620
D-4-T '.-»'•
^«otk«Tang.ofi.4kcApg.—=^i-^= 58^ 00'= 10.20421!
D T
"To Tang, of f their I>ifF. — ^ — ^it: 12^*03' c=: 9.329898
. : .^. Hence 58* + 12^ 03' = 7a" 03' = TDS, and 58*
— . L2? 03' = 45° 57' =s STD, or Longitude of the Ca-
met from the Sun; which added to the San*8 Place at I gives
ikKt<h9centric Longitude, of the Comet at L, in <r oo** 19^
And to find the Geocentric Latitude, or Angle DTQ^ we have
this Analogy :
, As tl^e Sine of Commutation TS D =r 64" oo'^ = 9. 953650
; Is to the Sine of Elongation ST 0 = 45* 57^ = 9.856568
^ Sp is Tang, of Helio. Lat. D S Q= ^4* 1 1* = 9.652656
To the Tang, of Geo/brt. DTQ^= 19* 46^ = 9.555568
•35. Thus yon have the whole Procefs of Calculation^ as it
relates to the Phaenomena of a Comet moving in a Parabola
near the Vertex, and is the fame with that ufed for the Pla-
nets (from the 25th Article inclufive). And though it is cer-
tain (from what will be fhewn by and by) that this Comet
^oes not deicribe a Parabola^ but an Ellipjli, yet the com-
puted ^Longitude and Latitude are the fame which the ComeC
was obfervcd to have at that v^ry Time ; whence the Accu-
racy of this Method fufficiently appears : But as it is thus li-
xnited to a Parabola, and only one fmall Part of that, and
cannot be extended to determine the Axis of the Orbit, or
the Time of its Revolution, I (hall here fupply this great de-
ficiency by (hewing a direct and geometrical Method of Com-
putation of all the Phenomena of a Comet moving in any
Conic Sedlion^ which was firfl invented by M. Bonguer in
l^m Pari/. An, 1733 ; which Method I (hall explain, illu-
ftrate, and exemplify in the following Articles.
36. Let A KB I be the Trajedory of a Comet, AB its PI. LXV*
tongell Axis, IK the fhortcftT S, F, the two Fw/, in one Fig. i.
of which the Sun is at S ; C the Place of the Comet, CS its
Oiftance from the Sun ; DC£ a Tangent to the Curve in the
Point C ; Cf the Space pafs'd over by the Comet in a fmall
Particle of Time; SD, FE, Perpendiculars from the Foci
to the Tangent : And draw SG parallel to DE, and join FC-
Alfo let ANO be the elliptic Orbit of apy Planet; S, f, its
Foci. Laftly , let A L B be a Circle deicribsd on the longer Axif ^
AB; APTB a Redangte about the Ellipfis A IB; and
AQRB as the Square about the Cirdo ALB; and put 80
C«2 =*, .
464 ASTRONOMft
'iSidi SD=:^, Crs^ the Time ia wUch it is ddo^
a&/ The longer Axis of the Cometary Orbit AB = j(^ of
|he Planetary Orbit AO = q^ the Circle defcribed on the'
&me Axb A V O s /^; the Periodic^ Ytttie of ^ Comet ts ty
and mt of the Planet = sr.
J7. The Space Cc iefcfibed, f^ DiflMice SC, and th^
^ngle SCD, are all known by Obfervation, and therefore
givexi Quantities. The meaA Diflance of the Comet is AH
£r |jr, an4 of the Planet is Ag s= \q. And- becaofe the
Sjuares of the PeriotBcal Timet art as the Cubes of the meast
Diftances^ we have \q^ : ix^ :: h* : t^ 1 and thnefbre t si
If v^JL. (^««,^. xxxiv. II.)
38. It is neceiTary now to find another Expreffion of the
periodical Time t, thus : Becaufe Cc is a very fmall Portion
of the Orbit, it may be efleemM a Right Line, dnd die
SeftOr CSf as an cvancfcent Triangle, whofe Area JSD x Cc
zszibeis given; but as the AieiL iheh to the T\mef fo is
die whole Area of the EMipfis A KBI ss A to the whole Pe-
f
nodical Time t; that is, t sz fv- x A.
i&e
39. Now in order to determine the Area A, we moft find
the Semi-conjugate HK, thus: Becaufe AB= SC + FC,
therefore FCz:ix — a; and by &niiar Triangles SDC aad
FEC we have SC : SD :: FC : FE, tkfct is, a : * :: x^a i
hx—ab _ p^^ and therefore FG = eFE — GE)J
a
' ' . Again, SC : CD :: FC : CE ; oi^ : I/**— **
Hence D£ or SO =s
ix-^zab
bx^^zab
I therefore FS =s
4 ab';fc r\^j^^^^+a^x—b''x^
= -/ r-2: — -— ^-t . And therefore SH=:iSF
CS"
-"*^ -,
40. Moreover, by the Nature of an ElIMv SK =s
AH
Astronomy. 40^
AH =? ix, and therefore i/SK* — SH = H^ =;:
^i;r * ^^^ ^ ^ ^ = — V 4PP — a*; tbere-
4^ ^
fore IK == iHK = ^ ^^0x^a^. Confeqaendf,
ilii^ax— tftf = APTB, the Semt-Area of *e EHipfey
* Le^ Qj= Diameter of the Cirde AI^B, ind P it* Periphc.
ly : then fince (LH ^ P = ^QP u the Area of the Cirdc,
we fliaH have Q; : iQP (:: iQ^ : iQR) :: AQRB :
ALB :: APTB : AIB :: f : i,f. Tbaxu. f* ' iff »
i^i^ax—aa: ^ •«* — «»= AIB. Bot^AIB;^
.-A-.tl
AIKBz:;: A=: -^^V^ax— ««; therefore the abovf
Expicffion t = -4" A = ^^ V^tfx— iftf. Then t =5
— V^ — r= i/a* — ««. And, redodnfi; the EqoatioQ,
q q aeq «» * »
^get^= ^^-/^ ^ ^*i = AB, the prmcipal Ans of
|he Se6Uon, or Trajeaoiy of the Coipet.
41 . If we fubftitute this Valae of x in the Equation abo?»
fort, wegmBhavets? /^ ^ ==-.| = the Periodic
<cal Time. Alfo bccauf^ the'Conjugate I K = _ i/i;^— «a
^ f , tiierenire 4? = ■ . i-;,^ ss 'v^ /..^ . ^ i
w|ience c s=: IK =:: 2 ^^w v^.
42. From thefe Equations it plainly appears, that when
the Velocity of the Comet is foch that/*^»y =: ae^n^^ the
Axis X is infin^e^ and cqnfequently the Trajeftory will be a
Parabola ; but if /;«*«* be greater than/*/*^, it will be an
IJyperboIa ; in both which Cafes the Comet can never return :
feut in all Cafes where/*/* £ is greater than /ii*»*, the Co-
met v^ill def^ibe SlH^esi among which we reckon that of
4o6 Astronomy.
the QrcUt where ;r = 2« = ^^ ^^ ^ ^ ^ ^» and hence
f p q — r«*»*
< = Cr=:'^^X, the Arch of the Circle defcribed in
cne Day.
43. Let the Planet we fuppofcd to dcfcrlbe the Ellipfis
ANO he the Earth; then will its mean Diftance 4f =2
1 00000 equal Parts \ and {o q-zz 200000, and / =: 6283 iS.
Alfo the Periodical Time n =: i Year ; and then if Cr be thf
Sp^cc defcribed in oqe Day, we have / =^ -r^ — r-—- =
365,25;65
6.6027378. Then alfo the other Expreffions will become
for the prmcipal Axis * = ?9' 8^6^99 JfS ^ x ^ ^d fo,
591826599535— -2^*
4750560000 X a\
the Periodical Time t == 1"'
5918.26599535— «^**
44. Hence it appears, that if Obrervations could be made
fufHciently exadl to determine the Diftance of the Comet, and
the Space it moved over in its Orbit in one Day, then the
Axes of the OrSit and the Periodical Time of the Comet
may as well be computed as thofe of a Planet ; but this is a
Matter of the greatefl Nicety ^ and of courfe the greateft
Difficulty, becaufe the eUlpt'tc Orbit of a Comet, if it be fuch,
can fcarcely be diftinguiib'd by Obfervation (however well
inade) from a Parabolical Orbit, in all that Part of the Orbit
which the Comet defcribes during its Appearance. Hence the
Quantity ae^ will generally come ont either equal to, or
greater than the Number 591826599535, and fo gives the
vixis X infinite or negative : And if it chance that ae*" be lefs
than the faid Number, then if a or ^ be not defined to the
lall Degree of Exaftnefs, the Axis ;c, and Periodical Time t,
will be \txy different from the Truth. . But more of this in
another Place.
45. A Parabola therefore is fully f^ifficient to account for
all the Circumilances and Phenomena of a Comet's Motion
during the Time of its Appearance ; as Sir Jfa^s^^c has (hewn
with refpeft tp the Qomets of i664:, 1680, 1682, 1683,
1723, an^ Mr. Be^ts for the iaft Comet of 174I. And that
^^he Reader ipay fee the wonderful Agreement between the
.Theory (though grounded on the ParaboUcai flypothejii) and
the Phaenomena pf Longitude and Latitude of the Comet
' by Obfervation, I (hall here fubjoin a Tabje exhibiting the
Y*UTie both by Computatior^ and Obftrvation, and the Dif-
ferences between ^hem feverall^ for ca^h refpefliv^ Tiw Of
©pftrv^tion,
A S T,R O N O M Y.
407
>743-
M .M 4* M M
V* V» ON ON Ov*^
V>4 ^ h> OA V>4 OA
V» M V^ (.^ -v^ *4
»743.
Ml*'** *• —
u» u^ On oa m
^ ON 00 On 00 OvnO
hi »4 O OS N K> 1^
sO M o u> O O O
to
»743- ?
O* N M h» M
v^ 4h. v^ wn wn JJJ
^/ ^^ iUS \^ ^/ ^/
^k ^^ ^^ ^K ^K ^K
M M •-• 14
U4 o» M 4k v^
*N] vO k* O t* ^>
(4* »■« v#i o» -^ 0»
•N) ^k. O 0^«-^ **>!
•^-5<s ^ss
O O o» u> -^> -^ -^
M M M IM 1^ V>» Vl
->4 \0 *^ OOnO "^ h»
v^ 4k v»» -fw M 4k
-s-^-?-?-?
O O - N 4*-
•^ 4^ N t4 O ^
M M M M M
00 0 v^ ONVl >0
M -M M •-« i-l M M
0 vO NO NO vo NO 00
M M M M »*
00 GOV! vj VI
0
V>1 >4 04. 00V>4 *-n
4i.4^ « « V^
14 h> ON«^ v» »4 \0
sO nO ^^ M (^
«<*
;>»4k4^ -K «^ 0
sO 0 »-^ 0 0 0
4^ t>» •>> OA <>» v>a
vj 0 ^ "^ M - VI
vn»4- 0 -
^
xxxx^x
'^^T^'^":^:^:^
^-^s-s-^
M M ^4 U
o» N/^ ►• o» 4k. *-
0 6 w o» 4^ -^. -^»
00^ u-E^
VI vO v>A 0 N N
V|\0 VI 00 ON ** N
VM V^ U 14 0
i-« •-« ON N 00 ON
^ - 0 N « K*
wa ON 0 VI 0NO4 ^
V^ M M tA
*^ ON4k ONO»
n S
00 0 Wri On VI sC
NO NO ^ ^ NO NO 00
OQ 09 VI VI Vi
^ M 4k U4 K) V»4
ON 004^ vO 4»' 4*'
4k 4^ - « vo
14 ^ S^l V^ U» l<) NO
Ul \^ v>»
vO 00 On •-• 0»
M «. 4^
o» 00 0\V| v-n h)
(4 - 0 ^ W NO V>4
wrt 4^ 04
0\V»4 OOVI VI
H
M ^ N « i-r -1
On«^ On ONWrt \0
++ 1 I I I
»- N O* •- 14 N *i
^>4 VO •-« Os '^ VI NO
■1-+++++ 1
+ 1 1 1 1
t-5
OQ ...
• P
M t4 v>A Ud OA i:^
44. 00 "^ VI wn 00
(^ M 04 U^ hk ^ 14
»-a NO VI 4^ O 00-^
till I +[+++++! +
- O 4^ 00 On '*
I I
r
o:
s p»
4oS
As T R O N O M v.
Flate 46. Havmg thus ihewn the feveral AflNsdioas of a Coinfit^^
!LXV. Motion, I (hall conclude with a Word or two in relation tq
Fig. 2. their fSls. The Atmofphere of Comeu confiding of a verjr
fine Vaponr, wilF, when the Cofnet is m its Jfieiion, be nw*
ly fpherical, and its Denfity greateft. As the Comet ap^
jproacfaes the Sun, the Sun*s Heat ept^r^ the Atmofphere, aw^
rarifies it by degrees, caufing at the faine time the fineftPir^
to rife from the Comet, like the Flame from a Candle^ to*
Wards f he Parts averfe from the Sun ; and as the Comet comef
iiparer and nearer the Sun, this Fume will rife and extend it-i
if if to greater and greater Lengths, and make what is call 4
the Tiw/of the Comet; fo that when they are riew'd' with 4
Tclefcope, the iViri^^w, Atmofphere, and Tail of a Comet
appear much like what is reprefented in the Figure.
47. The Length of the Tail is thus found by Obfervation^
fig. 3- let Sbe the ^pn, C the Comet, T the Firth, C# the Cor
iliet's Tail ; draw TS, TC, SC, and Te touching the En4
of the^Tail, and meeting the Line SC j>rodaced in £. The
f lace of the Sun and pomet being known, ' the Angle TCB
i^ known (for TCE ^ ST C + CST). JiVo the Angle of
Deviation £C^ is known from Obfervatipn ; whence TC^ i|
known. Moreover the Angle CTIp is known alfo by Obi-
ftrvation. Therefore in the Triangle TC/, having the tw<j
Angles TC/ and Cf/, and the Sidp TC, (from the Thea-
iiy) we can iind the Side C/, whioh u the Length of the
Tail. And thus they have been found to be 40, 6o» and 80
Millions of Miles.
, '48. Draw Se cutting the Comet's Orbit in ili then becaufi;
the whole Motion of a' Particle ffom C tq / may be refolve4
intp two Motions Cd and f ^ 'tis plain, ^ce d^ is that dt-
jtedily averfe to the Sun, the pO|net would have poffefsM the;
f oint d when the Partide at / firfi: rpfe ffom the Nudetu, |f
the Motion had been every where iti the Direction of 8/, s|s
|he Lme S/ kept moving from S/ to S£.
49. Fut fince this is not the Cafe, but the Particles move
Jn the oblique Direj6lion C<^ thierefore parallel to Qe draw
8 F cutting the Orbit in D, and join De ; then will the com-
pound Mption Ce\ ariiingfrom the prog^rcffive Motion of thp
Jomct in the Direction CD, aftd its Motion of Afcent in the
►ire^lion C /, give the Point D for the Comet's Place when
:i\ the Particle at / began to afcend from' the Nuehus,
50. Now the Time in w|iich the Comet defcribes anjr
given Part of its Of bit DC may be found from the Theory^
Jnd cdnfequently the Time of the Aicent of the Tail of a
Comet from the Ifjicient tQ t^^ Extremity /. Jhus I hav^
Astronomy.
^i{h'4 a cmpUai Cmfiaduim •/ the Nemttoniaii PbiUfify
p/ Courts.
Jampatei hwrific^ put fi wa JUxa Cmitu i
Jam noff mframMr ^^f>aii PtinmnM Afiri. ^
])r.H4LLtY;
APPENDIX
4*9
AT P E N D I X
T O
LECTURE XL
Of Time, and its Measure hy the Celcftial Mo-
iians. Of iie Year Tropical and Sydercal^
and the ^intity ef each. The Time of the E-
Q^uiNOXES and Solstices determined by Calcu^
lation. Of Days, Natural and Artificial. The
Eqvation^- of Time expUan^d. Of Weeks.
Of Months,^ Periodical and Synodical. Of
Old and New Styk. Of Cycles ; the Cycle
eftbe Sun, /iWDominical Letters; /i&^'ME-
TONIC Cycle, or Cycle of the MooN^and Gold^
EN Numbers. "The Cycle of Indiction. The
Pionyfian Period, or Pafchal Cycle. The Ju-
fian Period. 72^^ Aftronomical Principles of
Chronology, by Sir Isaac Newton, ex-
plained and exemplified.
I. TT shall here give the Reader an Idea of
■ of the Year, as the 'grand and original
JL Meafure of Time, and derived from the
Aftronomical Principles of the Earth *s Motion ;
and then aftei:w^rds confider its Subdivifions and
Xiftributions into lefTer Parts, as Months^ T>aySy
Hours^
A P P E N D I X, Srr. * 411
Hours^ Minutes J Seconds^ Thirds^ &c. for the Pur-
pofes of common l4fe, and the Ufcs of Chrono^
logy, HiftorjTj and other Sciences.
2. T 1MB is in itfelf a flowing Quantity, mca-
faring the Duration of Things; ai^ its Flux is
always equable and uniform ; and therefore to efti-
mate the Quantity of Time, we fhould meafurc
it by fomething that is in its own Nature always
of one and the fame Tenor. For this Purpofe
we have no Expedient fo convenient as that of
Motion ; and becaufe the Meafurc of Time ought
to be permanent, we can find no other Motion
fit for this Purpofe but that of the Heavenly
Bodies.
3. Among thefe, none of the Motions are fo
obvious to every Body, and plain to commcm
Senfe, as that of the Sun and Moon ; which there-
fore have been agreed upon by the Confcnt of all
Nations for this End, and indeed this feems to
have been a principal Part of the Defign of their
Creation. For we are told they were appointed
for Times and Seafons, for Days'' and for Tears^
Gen. i. That is, the Sun by his Diurnal Motion
affords the Meafure for Days, and by his
Annual Motion tKe Meafiire for Years; and
the Moon, by her Revolutions, gives the Meafurc
of another Part of Time we call Months.
4. For it is a compleat Revolution of thofe
Luminaries that conftitutes a Year, a Month, and
a Day in the Abftraft, or abfolutely confider'd.
Hence it is neceflary to confider the Point which
is tQ be efteem-d the Exordium or Beginning of
^ijl Appendix
dieft Revohmons. And this, wi;h refpe& tatho
Aimusil Revohicion of dip San, is £b(M in th^Kt
Foinc of die Ediptic which is die Beginning of
Ari€S'^ and die Tim^ which the Sun takes in gor
IPg from^ and retiming to (his Point ag^in, i$
oUrdaYjAR.
5* Ai,$o the Space of Tinie wirich the Sui|
^ takc& tQ crompleat pne Revolution shout the Evth,
is c^'d a Natural Day^ or the Nycblbemrm^ ixkj
eluding a Commoa Day and Night ; which Space
pf Tinie is fubdiyided into 24 equal Parts, we
frail Hours ; and each of thefe are again fubdi?
Fided into 60 equal Parts or Minutes ; each of
fhefe again into 60 other equal Parts callM Sc-
^nd Minutes, or Seconds; each of thefe into
Thirds, and fo on in a Sex^efimal Sybdirifioei
fer any leflfer Parts of Time.
6. Now, if this firft Point or Beginning of
^fies were fixM, each Annual Revolution of the
Sun would be conftandy die iame, and therefore
a juft ^nd equal Meafure of the Year, which j^
caird the Periodical 25wr, as being the Time of
the Earth's Period about th$ Sun ; and which con-
li(ls of 3^6 s p. 6 H. 9' 14''. For fo long i$ tte,
Eftrth iq departing from any fixed Poiat in thp
Heavens, and returning to the fame again.
7. But fince, as we have fhewn (^Anmt. CXLJ.)
the fcveral Points of the Ecliptic have a rctro-
frad^ Motion, *tis eafy to underftand, that by this
cceffion of the Eqijinox it will, as it were^^ nii^t
^he Sun, and caufe tb^t the Sun Ihall arrive to the
Equinox^ or firft Point of Ap^h before his Re-r
yolutior^
ioLtioTvtit XL 413
Voiutidn is c(>mpleated. Aod ttverefore Ah Space
of Tim€ (which is call'd the fr^pical Ttsr) is not
£6 k>ng as the former 1 for by Obfervations made
at the Diftance of many. Years of the Time of
two Eq^^npxes, and dividing the Time ehpibd
between by the Number of Rievolutions^ the Quo-
tient will fliew the Qyanti'ty of this "Tropical Teat
to be 365 D. 5 H. 4?' sV'^ ^^ch is 20' ij" k&
thanthe Periodical Yev»; .
8. The Bcginnii^g 9f the Year prTiine whca
the Suii enters the EquinoK is thus d^termmM by
pWeryation. luCt ABC be a Pottioa ^f tbfe Er Pl.LXVt
iquino&ial, and DB£ an Arch of the.SQlijAiC^ ^%-^
then with a very nice iQjftn^ment take thp Ifi/sdr
dian Altitude of the Stm^ the Day before and afcer
the Equinox; the Difiereace between thcie Alti-
tudes and that of the Equator will be the Sun's
DecHnation on tfaofe two Days, which ftippofe to
be AD and EC; which being thus known^ and
the Angle of Obliquity ABD = EBC=22'29'^
we find the Arch D B and £ B ; and dicre£bre we
fay, AsDB+EBistoDB,fois 24Hour8lothe
Time between the fifijl Qbfcrvation and Moment
of the Sun's Ingrefs to the Equinodti^ iPoint B«
'^. But the Quantity of 1^ Tropical: Year is
better defined from a Cakuhition of the MomeifiB
^f thp Solftfccs. The {Qvention of which cunooi
and mofl: certain Method was owing to pur late
celebrated Dn Halky% and is founded on aneafy
Obfenratioii, atid therefore praftidable by any Pcr-
ibn but moderately ikill'd in the Conk Geometry*
The Method is as follows : Let A VO rcprrfcnt pig. ^
afinaU
I
i4'i:4 Appendix:
a ffflall Portion of the Tropic, which the Eclif^
tic RVM touches in the Solftitial Point V. Sup-
pofe- the Sun at feveral Times near the Solflice
be ih the Ptrints K^ I, L, V» C, M,N, then wift
the Right Lines T L, ID; B C, E M, GJV. (per-
pendicular to the Tropic A O) be the Deficien-
cies of tKe Sun's Declination at thofe Times froni
his gceateft Declination in V.
10. And from the Elements of Geometry, the
Sobfefifts -TL, DI, i^c. of the Angle of Con-
ta<ffc A VK, are as the St|uares of the Conterrtiin^
'■■'■-'■ An*^s'V£:, yii fe?fr that is, of the Lines VT*,
- V D,' tt'f . which 2tw; liearfy equal to thofe Arches.
Now when theSun Vin L, part of its -Path- that
Day will be the Line LtTi; and when in M, the
Line I M, drawn parallel ta . A O. Let V Q.be
partbfthe-Solftitial Coliirc; thc^awe have VT=t
LF, and VD-GI, ^c. alfo vlc=iTL, VG=
D I, iic. whence L F» : I G* J: V F fO*^ G, (^c. fo
that the Figure K VN has really theVf^pe^y of
a Parabola, and may be taken for fucl^o without
any fenfible Error. \
II. Therepore let difee Points F, G,v ^» ^^
the Ajos V Q^ be determined by Obfervatiofiii*us j
let ah'ht an upright Objeft, ac the Groui^^^- O""
Horizon, and f i a Plane fet nearly perpendlt^^^f
to the Sun's Rays at Noon. Then Itt the Rain's
^. /> f , on the Plane mark the Shadow ofc^ ^
Apex ^, on three feveral Days at Noon \ iup^°^
two before; and one after the Solftice. By | *^^s
means wc have the Proportion of Diftance l'^-
twecn the Points F H and F G, for as fb xfaS'-
to Lbct d r e-:XL 4*^
F H : F (5. By the firft Obfervatiori ' from the
Point H the Sun's Place at K 13 giTcni by tW
fdcond, from the Point F,wc have the Pfe(i atL;
arid by the third, having G, we hav^'thi Point
M in. the Curve.' -' •'* *'^ ^ '^ *" '' * * ^ •
12. Now let the' Time between thie'dtitiiid '
fecond Oh(tvrmoiiKT{z:iY^TLyi^aH\^^^^
betwteen^hefccond ah4 third Qbfentatibn TEj^=
LVM)=i*, FHr^i^,'P<5=t£/,ahd^TVW;f=
the Time' betweeti ihfe fecohd OMervatibn and
the MeiBftit of thi^^^ftieei* to bc'^fei«ii(l''^-^lieh
AVii=^+^, and-V^£t=*— i; krid' Idi'the 1m^
SasffeffUm of the Parabola.be f. •'^Keh (pef HE^i
jw>/we have >f*iiVF;xj>, and therefore* 'VFrri
^*'^^T rVivyr" ' Vu'' '^* + *^* + ^* "" i
^. , In Uw Manner yHa;= r- — -^^ • and
VG= ^lr::;!£f±£, therefore FH(=;VH—
• .•\ ^ . • • • •' .
y F)«=» C^^;=ar,arKi FG(=Y.G^VF)=
T — ! — =</; wfl^crore^sc — .=— — : .
and! recjucing the". Equation, we have ;*• =
l^tp^
; = T V> the Time ro^iredi
13. But if the Order of the Obferyations be
fuch, as that fheOtfervation of the Shadow of
the GHomon in / is exaftly in the Middle between
thofeoFthe Shadow in b and'^-, then will AT =
T E, and fo ^ = b; and the Equation Will become
f = TTT} — = T V J which gives this Analogy,
2d
i^l§ . A i» P £ K DIZ
2d^zcic'^d::a:9f^ chat is, 2FG4»iFHi
GH::AT:TV:
14. I fliaU illuilrate thti Calculation bjr an £x^
ample qf each Cafe. In the Year 1500^ Bim^rd
Walker^ in. the Month of June^ at Nuremierg^ob-
jbrved.the Chord of the Son's Diftance fiom the
Zenith by aJarge Inftnurient, as follows;
Jwa 2,45467") <:7^ 8.44975 •
June; 9, 44934? ^ <7^^ "^ 44883
7«a^jt6, 44990/ C7««^ i^j 4499^
The Differences of theife Chords are eqpial very
hear to the fmall Diftaoces FG and FH; there-
fore r=j 5^3^ afid i/ss56,^and t— iJ=:477;and
fince the Time was 7 Days between QbferVatioB^
therefore assy. Whence we hate 11782
477 •• 7- ^ ^^- 20 H- 2^, which added to th<e Time
of the middle Obfervation)* gires futie ij D. 20 H;
if for the l^inle of the Sblftice.
15. Again, by the 6ther tfirce Obfervations,
we haveiftti07, ^=9i, r-^t/=:i5, and«t=r4j
wherefore fay. As 398 : 15 : : ^D, == 96 H, : 3 H.
37', the Difference between the a* Obfervatioiii
June 12, and the Moment of the Solftice, ^hich
therefore inuft be June iiD. ioH. 23', whictt
is but 21' different from the former. The Time
of the Tropic therefore, in Amo 1 500, we may
conchjde was Jtme n D. »oH. li'.
16. We will now give an Example df the
former Method by the Shadow of a Gnomon 55
Feet high, which Gajfendus at MarftiUes naade
ofe of for determining the Pro|X)rtion cf the
Gmmoa ta its Sdftitial Sbtdc. This ht did u¥
I
h Lecture XI. 417
tht; 'feir 1636; and die Eiperiihents trere a^
Here indeed the End of the Shadow, inftcad of
being received on the Plane c J, perpendidilar to
the Rays, was taken on the Horizbhtal Line, where
the Points /, f, hj are fefc^rrM to F, G, J7, in
three of. the Obfervations ; yet is the Ratio be-
tween FH and FG the fame nearly as the Ratio
between/^ and fg^ becaufe the Rays at that Di-
ftance from ^, in fo fmall an Angle, differ little
from parallel Rays. , . , ,
I y. Hence tHe Cafe of the Problem is ftill die
fame.^ Therefore, let the Shadow, on Jiine 19,
hcaH:=i^iy66', ontheiift, tfF=3i75i;andbn
the 22d, tfG=: 31759; then 2^=30, 2d=zi6^
c — i= 7t and ^ == 2; ^ =± i -, then the Theorem
i^* — da*
— — — 7-= 0,274 = 00 D. 1 7 H- 25^ which
2ad'^2lfC
is the. Time by which the Solftice preceded the
fecond Obfervation. The Solftice therefore wai
on June 20 D. 17H. 25^ N.S. or ^une 10 eI.
17 H. 25' Oj.
18., The biffererice between the Tinie of this
and die other Solftice is i D. 2 It. 47'; oif
which iD. iH. 12^ arifes frona the Deficiency,
bf the Length of the Tropical Year frbrii that of
the jfulian Year, (as will by and by appear) and
. the other Part i H.45' from the Progrcflioh of the
Vofe.H; Dd sm*'i
4i8 • A p.p B N » IX
Sun's Apogaeum during that Space of Tiin^
viz. 136 Years.
19.- The Days are the next Part of Tinic wft
fliall confider. Thefe may be divided into Solar
and Sidereal Days. The Solar Da^ is that Space
of Time which intervenes between the Sun's def *
parting from any one Meridian^ and its Return
to the fame again. But a Sidereal Day is the Space
of Time which happens between the Departure
of a Star from, and its Return to the fame Me-
ridian again. And each of thefe are divided into
24 equal Parts, or Hours.
20. Because the Diurnal Motion of the Earth
kbout its Axis Is equable, every Revolution will
' be performed in the fame Time; and therefore all
the Sidereal Daysj and the Hours of thofe Days,
will be equal. And on the other hand, the Solar
Days are all unequal, and that On two Accounts,
viz. becaufe of the Elliptic Figure of the Earth's
,Orbit, and becaufe of the Obliquity of the Eclip^
tic to the Equator.
Hate 2 1 . Th IS will appear as follows. Let S be the
J.^V'- Sun, AB a Part of the Ecliptic, A the Centre
of the Earth, and M D a Meridian' whofc Plane
paflcs through the Sun. Now in the Time of
one Revolution about its Axis, let the Earth be
carried ^bout the Sun from A to B, and then the
Meridian will be in the Pofition m i, .parallel to
the former MD. But 'tis plain, the Meridian
9nd is not yet direfted to the Sun, nor will not^
till by its angular Motion it has attained the Si-
tuation ef^ dcfcribing the Angle eBm^B$Ai
whence
iO LkiCTURB XI. 419
^yence it appears that all the Sdar Bajs are longer
bun the Time of one Revolutiod, or Sidereai
Day.
,22. If the Earth revolved in the Plane of the
Equator, and in a Circle about the Sib, then
would the Angle A S B, and coniequently the Ah-
gle eBm be always of the fame Quantity, and
therefore the Time of defcribing the faid Angle
leBm would always be equals and fo all the Solai:
£>ays would be equal among themfelves. But
neither of thefe two Cafes have Place in Nature.
23. For. by the Earth's Theory, founded qit
(he niceft Obferjrations, the Orbit is ah Ellipjis^
and therefore (as we have (hewn) her Annual Mo-
tion cannot be cquablei or the Angle A S B de-
fcribed in the fame Space of Time will not be
equals for in the Aphelion, the Velocity of the
Earth will be Icfi than in the Perihelion, there-
fore alfo the Arch A B will be lefs, and cdnfe-
quently the fimilar Arch em^ and therefore alfb
the Time of defcribing it ; whence it appiearsi the
Part of Time to be added to the Sidereal Day, to
bompleat the Solar Day^ is always vanable.
24. The other Part of the Equation of Time
(and mofl: confiderable) is that which arifes from
the Plane of the Earth's Orbit or Ecliptic being
inclined to that of the Equator of Plane of the PUte
Diurnal Motion 5 to ekplain which, Xtt^yf^ be hf"^^
a Semicircle of the Ecliptic, and <r H ^ of the
Equinoftial, S the Centre of the Sun, and A that
•of the Earth in the third Quarter of the Ecliptic j
bf the Meridian paflSng through the true Sun S,
Dd 2 and
f\ 1.>.
42b • A P i* E N D I X-
.and Its apparent Place at I in.the fifft Quarter of
the Efcliptic V 2s,
. 25. Suppose, now, the Motion of the Earth
in eVfcry Refpeft equable, and firfl: that it fat out
from ift, and proceeded in the Equator in a given
Timt to D, the Sun would apparently defcribe in
tlie faiiie /Time the Arch of the'Equktor ^ li
Again, fuppofe it fat out from the fame Point ^y
and fpent the fame Time with the fame equable
Velocity in the Ecliptic, it wpuld arrive to the Point
A, fo that the Aith ii: A= ^it D, and V 1 = r C.
*then.^is evident, as the Earth revolves about its
'Axis from Weft to Eaft, the Meridiah of any
Place will firft arrive at the Sufi I in the Ecliptici
dhd afterwards at the Sun C in the Eqtlinoftial j
that is, the Time ofNoon by the Stin in the E-»
cliptic will be looher than that NbOn which wodld
Happen by the Siin in the Equinodial ; and that
iy 'the Quantity of the Arch i&D tUrh'd into
Jtime.
' 26. Now the Arch Z^ D =: B C is the Difference
of the Sun's Longitude v I or v C, and his Right
Afcenfibn TB; Draw ge parallel to D.C,* and
the Angle e A/ will Be equal to* the Angle DS b^
and the Arch if firailar to the Arch D^ -, there-
fore the Time in which the Meridian i^/ revolves
into tifqi^^^feh^-^; is that which is to. be ad-
ded to the Eflxpfe^^ to ^tt^tt it with the
Time of the Equmoftial Noon^ in the firft and
'third Quarters of the Ecliptic. ' In the fecond
iuid foifrth Quarter, the faid Equation is to be
:;■■ '■■' ' ^ - ' . '■ fo^
/(7 L E C T U R E XI. 421
(i}btraacdi as would cafily appear by making the
^ijje Cpnftruftion liierc. . ,
': .2f> Nqw' becaufe in differcnt^Parts of the
Quadrant this Arch Db otBC is of a different
}-iCBgth, the Equation of Time mil b< a variable
Quantity J. and therefore fince. the Mbtion and
7HX^e meafured by the Sun in the EguinpfUal is
^Iwa^ equal, (therje being nothiqg tp ipal^e it
otherwife) it foUpws, that the I'inics (i. e.. fhq
Days) meafured by the Sqn ui the Ecliptic muft
Ip always J qnequal; or, in other Words,. thi9
Solar Days are fomctimes Ihorter, fon:ietimes Ipng-
er, than the fqual Time meafured ou{ in fl^e. &)^7
poftiaJ.
: 2i. It has; beei^ fliewa already, that the
True Motion of the E^h precedes . the Mean [in
the firft Semicircle of Anomaly, and is preceded
by the Mean in the fecond. Therefore while the
E?if th is gping from the Aphelion to the Peri-
I^elion^ or while the Sun apparently moves from
the Apogseum to the Perigaeum, the Apparent
^ime will be before the Mean, and in the other
Semicircle of Anomaly it will be after it. The
Difference of thefe Motions converted into Time
i&.,the Equation 0/ Tim in this Refpedt, and is tq
be.fqbtraaed from fhe Apparent Time to gain
the Mean, or added to the Mean to gain the Apr
parent, in the firft Semicircle of Anomaly, and
Vice verfa in the latter,
\, 3*9. Now both thefe Parts of the Equation of
Time are calculated by Aftronorners for every De-*
gccaof Anomaly, and for every Degree of the
, -; D d 3 Sun'a
^iz Appendix
Sun Js Longitude ia the Ecliptic, and- difpbSsA Uf
f wo feveral Tables, with Dntftibns for adding and
fi^trallingy as the Cafe requires; fo that at all
times the true or equal T\mt may be had. And
from thence it appears that the apparent Timcy
pr that fbewn by the Sun, viz. by z Suhr^al^Ji
but four Etays in the whole Ye^r^ the lame -^^ftth
the mean or equal Time Ihewn by a goodCJSr^/l
ptWdtcb^ viz. about April the 4th, June the'6th^
Jugufitht 20th, and December tht rgtk Alfoa-
boutthe 2id of Off^her the Equation is great6^
of all m the Year, being then about 16^ ii*f,
Oocks being then fo much flower than Sun-dials. ^
30. As the ?olar Days are unequal, the Hour^
muft be foof courfe \ zsA hence it appears, tha^
there is no natural Bo^y which can by its Modon
mcafure.Time truly or equally; and the only
V^ay to do this i3, by the artificial Contrivance of
Clocks, Watches, Clepfydrae, Heur-Glaffes, ^sJV.
3 1. In different Parts of the World, the natu-
ral Day has a different Beginning* The ancient
Egyptians began their Day at Midnight, as do alfo
fhe modern Nations ot France^ SpainyGreat- Britain^
, and mod Parts of Europe. The JewSj with the
Germans^ i^egin their Day at Sun-fetting. The
Babylonians began theirs at Sun-rifing. And the
Aftronomers begin the Day at Noon, and reckon
pn to twenty-four Hours, and not twice twelvCjj
as we do by our Clocks in civil Life.
32. A Week is another common Meafore of
Time confiftlng of fcven Days; and becaufe the
' Ancients fuppofcd the fcven Planets had an In^.
' " fluenoe;
to Lecture XI. 423
Auence upon the Earth and all terreftrial Things,
they allotted the .firft Hour of each Day to the
Plittiet they fuppofed then to prefide; from whence
the jfeveiai Days of the Week received their
Names. Thus Sunday was Dies SoliSj \. e. the
{Say pf the Sun% Monday was Dies Ltpue^ i. e«
the Day of the M(wn ; Tuefday was Dies Mortis^
i^«. the Day a^Tuifco or Mdrs^, Wednefdof was
JW« M^curiij i. c. the Day of Wooden or Nkr-^
CUfy,\.Tburfday .visc$ Dies Jovis^ i. c. the Day of
fb^fi-Gtyupitmr j Friday was Dies Veneris^ \. e, th^
Day/ oLEriga or Fenus\ and Safurdaf was Dies
Sdiurmikt. thc/Bay of Saf urn.
^ A Month is another Part of Time, fo
caU'd froln the Moon, becapfe it is the Time of
tier Revc^tion about the Earth, and is therefore
alfo callM a Lunation. If we refped the Re-
volution of the Moon from any fixed Point in
t;he Heavens (as a Star) to the fame again, it is
^ird a Periodical Months and confifts of 27D.
7 H. 43'. But if we regard the Time that paffes^
between one Conjundtion or New-Moon, and the
nQX£ following, it is call'd a Synodical M^^^ w4
1$ equal to 29 D. 12 H. 44' 3''.
34. These now mentioned are the jyhrononU*
MlTiarSy Months^ and Days ^ But thofeufed in
f:(»mmon l4fe are fomewhat different. Thus the
Civil Month is a Space of 28, ^9, 30, or 31
Pays, and 1 2 Synodic Months make 354 DaySt
which is caird a Civil Lunar Year ; and a Qvil So-
lar Year is the Space of 365 Days. Therefore
to ec^u^e the Gvil Lunar to the Solar Tear^ ii
I - P d 4 Pajrs
424 A F P EN D IX >
Pays are to be added, which were call'd by tb(i
Creeks JEpagmeu^^ and by us the EpaSs. . ' r
35. The Qml Soli-Zmar Year of 365 Days,
being fliort of the true by 5 H. 48' 57^Voccafioii?d
the Beg^ning of the Year to rim forwards th»*
the Seafbns one Day nearly in four Yearsy andiii
1460 Years through all the Months 06 the YesMii
On this Account Julius G^far ordainW that every
4th Year ^i|i!^ iXgi fhould be added to Fehiua^^
by caufing the 24*^ Day to be reckonW twcej
^nd becaufe this 24'^ oi Februarys was tieo$iictK
(Sextilis) be^re the Kalends of A&n-*, there >yere
In this Year two of thoie Si^tUeSj -wluch' gave the
Naine oT ^^//Zf to this Year. : The Ycar^ttius
correfted, wks fpom thence called thtJuiymTieiiar, '^
36. BtfT the fi^i Hours, added hfJuUUiOefari
\% too muc6i that is; exceeds 5 H, 48' 57'' by^ri'j'^i
ind therefore ^e Sun each Year begins his Coufrijl
1 1' 3'' before the Juliian Year is ended, whijch irf
^31 Years amounts to a whole Day. tience at
the Council of Nice^ A. D. 325, (at wfeeh- the
Time of Eajier was fix-d) thie Vernal Equinox be-
ing upon the 21"^ Day of ^Manb^ it was found in^
the Year 1582 to happen on«hfe ii'> of Marcb^
io Days fooncr than before; >' ' 1 .; . •
37. Fopt Gregory XIII. thought the Kalenda^
too erroneous, and refolved to reform i?, by rcftor-s
ing the Equinox to its former 'Hace in this Y^^*
'uiz. to the 2 1 V of Marcbl To do this, .he« tooK
10 Days out of the Kaleifidar, by ordering the 5*^
of OSioier 15^1 to be called the 15*** ; arid tq[
nrcvcqt the Regrcfs of the Equinox for the f^•»
to L E C'T U R E XI.
fiire, otda^'d every loo**** Year to confift of only
giSj Days, i;*crcasm>the 7«fi^ it iias "^^^y as
being Biffisiiik. This Reformaddn is therefocp
called &e Gr^orian Amount, or Ntw*Slile,. and
is jiSoShi^PapiJis in Itafy^ Spain^ Frtmcej Germany^
and by fome Protefianis abroad j but we^ftHl re-
tain t\it sJuUau Year, and call the Reckoning by
.38. Sracs. the Co^mcil of Nice^ tothe prefent
'Year 1746, there have elipfed up^^rds of 1421
years^ by which means the Equinix ^oes in the
OM-Stifc, at this ti«ne;faU on the lo'^ofA&rck^
and the yultan Account is 11 Days later than the
iSreg^an. But ev6i tht^r^orian Emendation
is not fCifiieietiti^fQr Whereas by that four Dzys in
4O0 Years are reje&ed, a confideraWe Error is
jdomnaitted ; for the odd 1 1^ g\ by which the Ju-
iim Year exceeds the Truth, will not amount to
more thatfthree Days in 39 1 Years* . If therefore
at the K^d of every 391 Years we expui^e three
Days^^the Eiquinox wilj very nearly always keep
jcht^ f^n|c Day of the Month.
.39. In Comp4tajiQnaof Time, we find it nc-
ce£&ry to fix upon fpfne realarkable'Trai\fa6tion,
cxr memorable Event, for the Exordium or Begin-
m^g of the Reckoning; tl^fe ^rc caJlrdEppCHA'a
or -Slfi a's, Thus fome compute from the Crea-
fim. pfiib^.Warld: The ancient Grecf:s from the
I^ilUfion i>ftht Olympiads^ beginning jj6 Yearsf
befo^ C^iRisT : The Romans ,from the Building
f£,Iioj^^^ about 750 Ycars,before Christ.' '. Thp
42s
^aj6 A P P EN D I X .
CbaldMtsmAEgyplans v&d ^JEraafNakm
mffar^ foeg;inning A ante. C. 1752^. The Wurkifif Et
pocltt. is dierjJEfi)fra or j^^
^22. The Pirjhn JExz isi catt'd nfiegirA AiJ C
£^2. And that of die Ckifiianr^ die£Erttr«j^
<3tr/}?5tfince which Time we redkon 1 746 Ytos*
\ 40. Besides the Meaibtie of Time b/ CotnoBiOB
Years, wcfind it became neceffary to intnoduce^he
Ufe of Cycles (/. e. Circles) of Tear4\ as the
Mffcnic Cycky the Cytle of ibt Swij the Xlycbif
Indi^Un^ and the JfUian Pef^cmt(pmr\A^ of
an the pefll. Of each of thefe 1 fhtfllgive thcf foK
lowing fhort Account?. ^
41. Thb Cycle* of the SYruawfes hence? If
the Number ^6^ be dividfed by* 7,* it will have a.
Remainder of i, which (hews the laft Day^ofdw
Year is the fame Day of the' Week vwth the lirfh
^ow it was always cuftomary to place againft the
feven Daj^ in the Week, the (even fkft Letmi
pf the Alphabet, A, Bi C, D, E, F, G, and theA-
fore, as they were cdntinued thro* the Y^r, it'i^
evident the fame Letter toufl< ftand again^ the
firft and laft Day of the Year; viz^ theLettef A.
♦ 42. HfiHcE, if the 1*^ cfj^mfidfy be %^un^
Iby, the Letter A will point out ail the Sundays «
that Year; and fince tie i^^ of January in the
next' Year 4s M^Wtfjr; the firfl itow&Ty will be or^
the 7'*^'agarrift ^hich ftands the Letter G, which
therefore will be the Sunday Letter fof aH thatYtar.
Again, the firft Day of the following Year being
' "Tuefday^&ik firft Sunday vnt. be onthe 6'^ againft
to L E c ^r ir R B XI. 42.7
)jrhich ftands the Letter F, which therefore iadt-
cates the Swtdays thro' that Year, and fb On;
i¥hence *m e^y to obferye, that die Letters which
point Off t the Sundays in every Year unll be in
^ retrograde Oder, viz. A, G, F, E^ fc?r. And
becaufe thefe Letters ihew the Dies Domini^ or
LofJ^s-DofSi they have b^en call'd DbMiNicAt
•LitrTBft-Sv . -^ . ' ' .
43, Now, if all the Yeat* were dommon ones*^
the.fasietJbetter wcmld not be the Dwninicaiy or
the' §tnnda^s would iiot be upon the fame Days of
the Week, till after a Cycle or Revoiution of
ft^cif Yeafc; iahd flnce every 4*'' Ye4p has a-DaJr
ettracfdijMry, thii Day wijl interrupt UteSucceft
lion of the Dominical Letters^ and caufe that
the fame Days will not be fhewn again by the
iame Letfcrs after a CycU' of feven Years, but of
4x jr:?j,2S. Years, which is call'd the Ofck of the
44. BipAuSE iff eveiy Biffesitik Year the 24**
pr 25*^ oi February is reckon*d twiee^ and both
thofe Days have the fan^c I^ter, it follows, that
that Letter which fhpw?d the SUtfdays before the
24*^ otpel^uaty wil} nof (hew it afterwards, and
tliwetefore in every fuch Year there will be twp
Dominical Letters, For.E^ainipIe, the Year 1 744.
was B^extik^ Jmyfry, i. Sumic^^ the Dominical
Letter Aj but the 24*^ o^ February being FricU^
ha^ t]he Letter I?, arid alfo Saturday the 25'^^
therefore Sun4ay, the 26*tmuft have G, which for
that /reafon was the, Swid(g LfiXXxx the remaining
^p^tpftheYear* ' * 45- T^
^^§ . A P F EN p I,?
45. To fin(i What Year of the C^ck the
pr^eiit ivgny Year of Christ is, add 9 to the
^ivtsp Year,' (b^caufe the firft Year ef Chrjst
was the ;9'> of the Cyclp) and divide^by 28, the
Remainder is the Year oixkcQcle required. Ex-
ample:; The Year 17464-9:= 1 75§»*^*'75$
l^^dediy .2$, Ipayes 19, t^iYear. pf,the.Q'^^<«-
quired, whofe Dominical Letter \& E, apcoEiiiqg to
the following- TaWe; : .7 •.'•:.'.,. ■':\. .^>.
Qck : I.. 2. 3. 4. 5: ^.-'T*.^'. 5».vlo..ini|ai
-2)«». £r/.^'E.D. c* d.F.Eg ^»: a: g.
(3?r/^ ^3.. . 14. I5.;i6,. i.7, 18.; I9,:2Q,.3t.
D^«». Z;^: D. C. B. ^ 'R E.''D.-^
'Cycle : 22. 93. 24. tS^'^^' ^7- 28. , .;
Dm.L^t. a: g. f. ^ c. b; a. . .1 :
46. T»E Metonic CycleJ (<b caU'd from the
Inventor Meton) otherwife calrd xht Cycle of
the Moon^ is a Period of nineteen Years, after which
the New and Full Moons were fuppofed to tetu^-n
on the fame Days ot the'Mqnth,. and Hours, a;
before; becaufe if the Solar ^nd Lun^ Year be-
gan together alt any TJtpe., thefe Years being to
each'othfer ^? 3^5 to 354, could not; coincide *-
gaih'aY tteir 'fi^giriniijt'g 'tijl after z (j^rtgin Time,
viz. 235-Luriations;* whlclt ifriake 6j^^^ D. ^6H.
'3i'45''",aftd. In nineteen: $olar years ai;fc 695^ D.
•18 H. 5 the DSf^fepce 'b^^^^^^ 15"
fliews the 'two Yearj'wyi ^en begin again vety
pearly* at 'th'e^ fame ^ime, and 'the j^evi('v^^
/O L E C T tJ R E *XI. 439^
, Modns com6 toiXnd again upon the farrie Days of
the Month.
4.7. Yet this Deficiency of an Hour arid half
\n\\ cauferiie''iV>a; and Full Moons to happen fd
much foonet'-cwch-Q'^/^ in the Heavens than by
this Reckonings* arid, this* :in 304 -Years amobntt
to a whoIe-Dajryand thti^OTe?att^^
happen alipoft five Days (boner than they Aould
\do, bythe Rule fettled by the Ntcene Council for
Ifinding the fame by the Golden Numbers-, the Na-
ture and Ufe of which are to be underftood as
folWs.
48. Taking any Year for the Firft of the CycU^
the Ancients obferv'd all the Days on which the 1
"New M;(7»j happenM tliro* the Year, and againft
* each fuch Day they placed the Number i ; in the
1* Year of the Cycle they did the like, and to each
Day of the New Moon annexed the Number 2.
In like Manner to every New MooH Day in the
3* Year of the Cycle they fubjoinM the Number 3 ;
.'and fo on,' thro* all the Yedrs of the Ofcle, This
being done for one C^cle^ the fame Numbers were
fitted to the Kalendar to fhew the New Moons
in-cich Year of any future Cycle ; and, upon Ac*
count of this their excellent Ufe, they were itt
^Cold:, and were therefore callM the Golden Nunh
ters for thofe Years refpeftively.
49. But becaufe thefe Numbetl; for the ob-
ferved New Moms are not of lafting Ufe (as a-
bove Ihewn) the beftvway of difpofing thefe Num-
't)ers'-is by the Mie&n Lunations^ as they may be
*'^ /• ^ found
4 Jo Ar t EU Dik
found from i^ftronomical Tables for cich It tar
of the Cyckj which are the fame in every Q^cU^
wd do not vary greatly from the true. But, how-
ever advantageous this may be in civil life, we are
not toe3cpe£tthisInnovationfhould takeFlaoeinthe
liturgy of the Church of Engkind;wbkh flill conti-
nues to compute theMoons^ itdoes theEquinoxes^
by the old erroneous Rule eftablifhed by the Cbun-
cil of JV/Vr, which are calTd Ecclefia^ical Nm
Moou^ in Contradiftinftion to the true ones in the
Heavens.
50. Besides thefe, there was another Period
caird the Cycle of Indiction, confiding of x^
^ears; it was fo caird, becaufe the Numbers of
this Cycle indicated the Time of Eaficr. But as
this Cycle ha3 no Connexion with the Motions of 1
the Heavenly Bodies^ I fhall fay no more of it
here, but refer the Reader for a farther Account
of this and other Matters purely Cbramlogical^ tp
the Authors who have wrote on Cbronolegy^ or,
if they pleafe, to an Epitome of that SciejKe in
my Pkilological Library of Literary Arts and
S£iences.
51. The Dion ysian Period is one that ii
made by multiplying together the Cycks of dip
Sun and M^on^ and therefore confifts of 53 ^ Year^
for 18 X 19 = 53^. After the Completion of this
Period, not only the New and Full Moons return to
the fame Days of the Month,butalfo theDaysbf the
Month return to the &me Days of the Week; aijd
therefore the Domnical Lttter^ atnd t^e jMavfa6k
Fcafis
io L EC t U R B' XL f$Z
i^eafts att return again in the £une Order. Ifcnce
<his Cycle was call'd the Great Paschal Cycle.
52. The Julian Period is the laft I ihall
mention," and the largeft of all* confifting of 798a
YearS) being compofed of the Cycles of the Sun^
Moon^ and IndiSion\ thas 28 x 19 x 1 5 = 7980.
The Beginning of this Period -was 764 Years be-
fore the Creation, and is not yet compleated; and
therefore comprehends ail other Pemds^ Qfcles^
and Epocbas^ and ^ Times of aU memomble
Adtions and Hiftories. It had its Name from its
Inventor Julius Scaliger^ who has eternized him«
felf thereby.
53. I can't conclude thisEfi^y^ without lay-
ing before the Reader the j^ommkal Principles
of Chronology, which Sir I/aac Newfan xnsikts
life of for fettling the Grand Epocha of the jir*
^onautic Expedition^ and which he makes the Balls
of his Chronology. He obferves, that Eudoxm^
in his Dcfcription of the Sphere of the Ancients*
placed the Solftices and Equinoxes in the Middles
of the ConftcUations Aries^ Cancer, CbeU^ and Ci*
pricorn: And alfo that this Sphere or Globe was
firfl: made by Mufieus^ and the jt^erifms deli*
neated upon it by Chiron^ two of the Atgonauts.
54. Now it has been /hewn, that by the Pre-
ceflion of the Equinoxes the Stars go Jback 50'^
p^ Ajmum. And fmce at the End of the Year
1689, the EquinoStial Cohere paffing thro* the
middle Point, between the firft and laft Star of
. Jtus^ did then cut the Ecliptic in b G" 44'^ it
is
43J^ Appendix *
is cridenti that the' Equinox had then gone
back g6* 44'; therefore, as 50'' is to one Year, fo
^ iS"" 44' to 2645 Years, which is the Time fincc
the Argonautic Expedition to the Beginning of
the Year 1 690 ; that is, 955 Years before ChrisIp
is the jEra of the Argandutic Expedition:
55. But our great Author is mpre particular
and fubtile in this Affair. He finds the Meafi
Place of the Colure of the Equinoxes and Solfiices^
by confidering the feveral Stars they pafs'd thro'
among the other Conftellations, ^ follows, ac«
coiiding to Eudoxks.
$6. In the Back of Aries is a Star of tfie 6"^
Magnitude, iliark*d y by Ai^^; in the Ehd of
of the Yeir 1689, itS Longitude was 8 9"* 38' 45'' <
and the Equmoftial Coldre piffing thro', accord-
ing to EudoxttSy cuts the ficliptic in « 6* 58' 57''.
^ 57. In the Head of Cetus are two Stars of the
,4*^ Magnitude, call'd » and 1 by Bi^er. Eu-
fdoxus*s Colure paffing in the Middle between tKerii,
.cuts the Ecliptic in » 6** 58' 51", at the End of
the Year 1689.
' 58. In the extreme Flexure of EHdaAus there
•^as formerly a Star of the 4'** Magnitude (of ktfe
it is rcferr'd to theBreaft of Cetus). It is the only
• Star in Eridanus^ thro' which this Colure can pafs ;
its Longitude was at the End of the Year 1689
^ is"" 22' ic", and the Colure of the Equinox
paffing thro' it cuts the Ecliptic in 1$ 7* ix' 40",
$g. In the Head of P^/m, rightly delineated,
is a Star of the 4^^ Magnitude, call'd t by B^jf^rj
io L p c t p R » iJCi. 43 j
its Longitude w^ 8 23' 25' 30" at the End of
the Year 1689 » *« ^ Colure of the Equinox
paffing through it cuts the Ecliptic in « 6® 18*
5f
60. In the Right Hand of PerfeuSy rij^tly de-
lineated, is a Star of the 4'' Ms^tude, whde
Lon^tude at the End of the Year i6B9 was IJ
24" 25' 27'', and the F^uinoftial Colure paffii^
through it cuts the Ecliptic in b 4* 56* 40".
//
r« 6 58 S7
61. Now the Sum of all theie )b 6 5S 51
five Plates of the CoIureX « 7 12 4O
w«. , ib 6 18 57
C« 4 56 40
Is = I z 26 05
The 5*' Part of «rhich is =« 6 29 13
#hich is thferefore die Mean Place, in which tlj^
Colure in the End of thd Year 1689 did cut the
Ecliptic.
62. After a like Nfanner he determines th<J
Mean Place of the Seljlitud Summer Coluire to be it
5* 28' 4<", which as it is juft 90 Degrees from
the other, fliews it to be rightly deduced. The
Eifttinoxes having then departed i* 6° 29' from
the Cardmal Points of CS^iroHy fliews that 2628
Years hare elapfed fince that Time, wluch is
more correft thain the former Number {JrfitU / j.)
tho' lefs by only feventeen Years.
63. Bt fome other Methods^ of a like Nature^
he alfo fliews the ^ra 0/ the Argtnauts fxa^t to
be placed in that Age of the World | and having
^« fix'd
434 Appendix.
fixM this moft antient Epocba^ he makes his Com-
putation with Reference thereto in the future
P^rt of his Book.
^4. And thus our great Author has with his
dufual Sagacity, fo condu£):ed his Defign, as to
make his Chronology fuit with the Courfe of Na-
ture^ with the Principles of Aftronomy^ with Sacred
Hijiory^ with Herodotus^ the Father of Profane
Hiftory, and with itfelf. And tho* many have
thought fit to cavil, and find great fault with his
Chronology, yet, how little Regard ought to be
^ paid to them may from hence appear, that Sir Ifaac
Nezvton was undoubtedly equal to any Man in aU
the comfnon Salifications of a Chronologifty and
vajlly fuperior to all in thofe which were effential.
Gentlemen fhould have the Modefty not to cri-
ticife on the greateft Man that ever lived, till
they have convinced the World, at leaft, that they
underjiand him.
LEC^
45^
LECTURE XIL
7ibe U/e of the Globes*
Of the Globes in^eneraL The Circles of the
Sphere defcribed. The Positions of the
Sphere, T*he Solution of Problems on
the Celestial Globe. T'he Terrestrial
Globe defcribed. Problems on the fame. Of
the Constellations of the Northern and
Southern Hemisphere. Flamfted*j Cata^
tOGUE of the Stars. Of the DistANCE and
other Phsenomena of the Stars, u^ Calcula-
tion of the furprizing Velocity e?/ Light.
Of the Abberration of Light, and the Te-
lefcopic Motion of the Stars by Dr. Bradley.
The pRiNCii^LES of Gnomonics, or Art of
Dialling demonjiratedj by <?, Dialling*
Sphere. Aftronomical Doftrine of the
Sphere, and Method of calculating Spheri-
cal Triangles. The HarVes1*-Moon ex-
plained. How to find a MEtiiDi AS hifiE. The
Figure and Dimensions of the Earth deter-
mined by adual MenfuFation ^/ ^ Degree un-
der the Arctic Circle arid at Paris. A new
Calculation on that Head. Of the Ortho-
graphical Projection. Of the Stereo*
graphical Projection. IT/^^ Globular Pro-
E e a jedipn.
1^3^ ^^^ ^I^ ^f '^^ Globes.
jcftion. Of Mercator*s Chart, and a new
Method of CanftruSfif^ tbe^ttNe tf Meridio-
nal Paris by Fluxions, ^e Nature of the
Rhum^-Line invefHgated^ and applied in Sail-
ing. A new Map of the World on the Glo-
bular Projeftion. A Map of the Country in
Lapland where the Arch^of the Meridian was
mafuredby the French King^s Mathematicians.
IN this Le6hire I fliall explain the Nature and
Ufe of both the Globes^ by giving you a fuc-
cinft Account of the Nature and Defign of
each, and a Solution of the principal Problems that
are ufuall^ perform'd thereby,
flate Each Globe is fufpended in a General Meri-
LXVm. ^jj^^ and moveable (within an Horizon) about
* its Axis, in the fame manner as the Armiltary
Sphere of the Orrery ; and the Circles of that
Sphere, already defcribed, are laid on the cor-
refponding Parts of the Surface of each Globe ;
and are therefore fuppofed to be known.
The Surface of the Celestial Globe is a
Reprefentation of the Concave Surface of the
Starry Firmament^ there being depifted all the
Stars of the iirft and fecond Magnitude, and the
moft :noted of all the reft tliat are vifible. So
that by this Globe we may fliew the Face of the
Heavens for any required Time, by Day or
Nightj throughout the Year, in general; or in
regard to any particular Bpdy, as the Sun^ Mooft^
Planety or Fix'd Star.
The
Tie Vfi of the Globes. 437
The Stars are all diipofed into G>n£bellations»
under the Fornis of various Animak, whole
Names and Figures are printed on the Paper which
covers the Globe ; which were invented by the
ancient Aftronomers and Poets, and are ftill re-
tained for the fake of Difl:in6tion and better Ar-
rangement of thofe Luminaries, which would be
Qtherwife too confiifed and promifcuous for cafjr
Conception, and a regular Method of treating on
.thefn (CXLV),
(CXLV) 1. The Surface of the Celestial Globe msy
be efteem'd a juft and adequate Reprcfentatio& of tlie conpive
Expanfe of the Heavens, notwith^ding its Convex!^ \ for
'tis eafy to, conceive the Eye placed in the Center of tHe
Globe, and viewing the Stars on its Surface, fqppofing it
made of Glafs, as fome of tlieoi are i and alfo, that if t}oles
were made in the Center of each Star, the Eye in the Center
of the Globe, properly pofit^, would view through each of
thofe Holes the very Stars in the Heavens reprefented by
them.
z. Becaufe it would be ImpoiTible to have any diftind or
r^ular Ideas or Notions of th^ Stars in refpeS of their Num-
ber, Magnitude, Order, Oiflanpes, ^r. without firft reducing
them to proper Claiiies, anci arranging them in certain Forms,
which therefore are call'd Ast^risms or Constellations ;
this was done in the early Agw of the World by the £rfl'C^-
fervers of the Heavens, and thofe who made Spheres or De-
Jine^tions; of whom Sir Xfaac Nnwten reclcons Ci?ir<m the
Centaur the &rfk who for^*d the Stars into Conftelhtions^
about the Time of the 4rg9naiaic Expedition^ or foon aft^ ;
and that the feveral Forms or Aflerifm were, as it wer^, fo
many iymbolical Hiftories, or Memoris^ls of Pe^fons ^sA
Things renuirkable in that Affair. Thus Jri^s^ the IU91, is
cosunemorated for his Golden Pleecty and was made the firft of
the Signs, being the Enfign of the Ship in which Phryxus
fled to OlchU. Taurus, the Bull, with brazen Hoofs, tamed
by Jafon ; Gemini, the Twins, vix, Caftor and Pollux, two
of the 4rgonauts ; the Ship Argo, and Hjdrus the Dragon, (if c»
which aU manifeftly relate to the Affairs of that Expedition,
which happened about jforty or fifty Years after SoUmon^s
Death.
Ec 3 Iw
438 The Ufa of the Globes,
In order to underftand the following Problems,
it will be neceflary to premife the following De-
finitions in relation thereto, viz.
I. The Declination of the Sun and Stars
is their Diftancc from the Equino£fial in Degrees
of the general Meridian, towards either Pole,
Norfb or Sourb.
II. Right Ascension is that Degree of the
Equinoftial reckoned from the Beginning ofJries^
which comes to the Meridian with the Sun or
Star,
III. Oblique A$cension is that Degree of
.(he Equinoftial lyhich comes to the Horizon
when the Sun or Star is rifing : And Oblique
Defcenjion is that Point which comes to the Ho-
^•izon on the Weft Part, when the Sun or Star
3. By thi§ n^eat^ they could make Catalogues of the Stars,
record their Places in the Heavens, and call them all by thciir
Names. Hifparchus is faid to be the firit who framed a Ca*
talogue of the Stars, which was afterwards copied by Ptolo-
myy and adjufted to his own Time, A, D. 140. The Num-
ber in this was 1026. After this Ulu^ Beigb made a Cata.
logue of 1022, reduced to thfc Year 1437. Tycho Brake refti-
fied the Places of 1000 Stars; but his Catalogue, pub]ifh*d
by Longomontanus^ contains but ']'j^^ for the Year 1600.
Bayer publifh'd a Catalogue of 1 160. Hevelius compofed a
Catalogue of t888 Stars, adjufted to the Year 1660. But
the largcft and moll compleat of all is the Britij^ Catalogue
by Mr. Tlamflejf containing about 3000, of which fcarcc 1000
. can be feen by the naked Eye in the cleareft and darkeift
Night. They are reftified for the Year 1689. They arc
diftinguifh'd into feVen Degrees of Magnitude, in their pro-
per Conftellaiions ; ^hofe Names, Latitudes, and Longitude*
here follow,, together with th^ Number of Stars in each, and
of each particular Magnitude, as I have taken them from the
third Volume of the Hiftoria Cceleftis, Note, The firfl La-
titude is South, the oth^r Northj» in the Twelve Signs, unfefs
SWfc'4 tQ the contrary.
Tie Ufe of the Globes,
is defcending or fetting in an oblique Sphere.
IV. Ascensional Difference is the Dif-
ference between the Right and Oblique Afctn-
V, The Longitude of the Sun or Star is an
Arch of the Ecliptic, ^between the firft Point of
Aries^ and that Point of the Ecliptic to which
the Luminary is referred by jthe Meridian palfing
through it ; and is therefore reckoned in Signs and
Degrees of the Ecliptic.
439
4. The Conftellations of the Twelve
Si
CMS.
Names.
Long,
0 /
Lat,
0 /
?
I
2
3
4
5
6
7
Aries,
^z6 48
«2I 06
00 01
12 31
65
0
I
2
S
6
28
^i
Taurus^
yi6 49
n26 36
18 27
09 46
»35
•
I
4
'3
21
44
s«
Gemini,
ni4 II
2512 33
10 07
13 18
79
I
2
4
6
12
32
22
Cancer.
2o22 49
ai2 19
10 19
14 59
71
0
0
0
6
7
39
«9
1^0.
aio 57
:2o 42
07 39
17 38
95
2
2
6
'5
10
SO
Virga.
TJJiOO 10
rG»?9 23
06 24
21 24
89
'
0
5
10
15
45
. 9
2
S
i
2
Li^rom
ino4 II
. 28 35
18 34i\^
II 27 S.
49
I
2
7
S
ti
5
21
25
Scorpio,
nX26 48
4^2o 46
12 ^6K
'3 57^
5^
0
2
2
12
Sagittarius,
4^22 55
VfzG 29
lo 59
07 31
50
0
I
5
6
11
*3
Capricernus,
Vf27 26
:r2i 29
08 5a
07 27
5'
0
0
3
3
9
34
Aquarius,
;ro7 24
H2I 57
21 04
23 02
99
I
0
4
7
3'
5°
6:
Pt/ces,
Kii 06
r26 47
23 06
09 05
109
0
0
'
6
?.7
54
21
£e 4
VI. Th5
44^ "^^ ^f^f^f fbe Globbs.
VL The Latitude of ^ Star is its Diftance
from the Ecliptic towards the North or South
?olc.
VII. AhpIitude is the Diftance at which the
Sun or Star rifes or fets, from the' Eaft or Weft
Point of the Horizon, towards the North ot
South.
VIII. Azimuth is the Diftance between' the
5. TheG»)|^^/(^/iM/Qf tkeNOATRERvHEMllPBEItK'
Andromeda,
T 3'aq
»i8 4
»5 55
49 53
66
0
3
2
12
«3
Ajuila cum An-
timo.
VfZQ 46
£7 8 6
10 5
4J ?7
70
1
0
10
7
»5
32
5
Anfer cum f^ulu.
vy2o 20
H I ?4
37 3$
47 46
34
0
0
0
4
»?
18
0
JjUft^Ct*
an az
asi2_3o
2 29
32 >3
68
I
2
I
10
18
3»
5
Bootes,
flH22 34
taoo 54
25 .5
60 33
55
1.
0
8
10
II
'7
8
-*-..-i
Caffhpeia.
*rii 6
n '8 . 4
38 18
59 S3
56
0.
0
5
7
9
30
5'
Camel9pardus.
mo 40
OB to 39
29 24
45 43
58
0.
0
0
4
18
»7
9,
3
Opheus.
<V><Jo 39
«26 37
59 32
75 27
35
40
0
0
3
7
8
H
C9ma Birenices,
twi6 S3
^ 4 38
,5 .4
33 56
0
c^
0
8
H
•4
4.
Cofona S eft in.
moo 58
20 54
44 *«
56 25
21
0
I
0
6
8
16
0.
Cygntfj.
yf*o 55
X23 17
37 39
74 «o
107
0
I
6
21
3»
48
0'
Deipbiw.
5: 8 49
16 31
23 00
33 44
18
0
0
6
0
2
9
I
Draco.
Ptrttam
Grttimf.
57 «3
87 25
49
0
I
7
8
«3
«9
I
£y»W!Btf,
20- 9
»5 13
10
0
0
0
4
I
5
0
^^^^
The Ufe of the Globes.
North Point of the Horizon, and the Point where
fhe Vertical Circle, paflSng through the Body of
fhe Sun or Star, cuts the Horizon.
IX, The Ai,titude of the Sun or Star isit$
Height above the Horizon, nieafurtd in the Der
grees of the ^adr^mi cf Altitude^ or moveahj^
Azimuth Grcle.
441
HercuUt.
^28 725 15
X28 2969 33
95
0
0
II
«5
3«
38
0
leoMiHor. ®^9 ^ 9^»
WR 4 4 30 50
53
0
0
I
5
11
33
3
Lacerta.
X19 +9143 '*
6 27I55 34
16
0
0
0
3
6
7
0
Lynx.
028 24
a 9 45
17 3
40 39
44
0
0
0
3
12
21
<
tyra^
W 3 35i54 28
26 14I66 13
21
I
0
2
2
5
11
e
Ptrfeus. C. M.
» 8 8
,ni« 48
11 17
41 13
67
0
2
S
11
«5
28
6
figafus.
~23 37
«r 7 '7
9 >5
44 24
93
0
4
3
10
«3
58
5
^sgitta.
Yfzo 00:3s W
^ 8 37'43 «5
^3
0
0
0
0
4
I
.8
p
Serpens OpbUi-
«l 7 38
VII 31
7 59
42 28
59
I
7
6
3
32
10
Scutum.
W 0 23
10 8
4 59
18 17
7
0
0
0
2
4
I
»
0
Strpeutariusj or
Opbiucbus.
"I27 58 6 54
kf I 2937 18
69
0
I
7
«5
13
26
7
Triattgttltm.
W 0 s
13 15
13 55
20 34
»S
0
0
0
6
0
5
3
35
I
58
7
9»
4
zo
TJrfa Major.
nio 41
A 6 58
17 6
61 3
215
yrfa Minor.,
n2i 43
«.i7 >9
65 42
77 50
24
0
0
0
4
3
5
6
6
^Utiut Venattci.
MR 0 s
25 43
52 S2
33 56
1
0
2
5
>4
3
^. A
442 ^he Ufe of the Globes.
X. A Star is faid to rife or fet Co/micalfyj when
it rifes or fets when the Sun rifes.
XI. A St^r riks Jcronicallyy if it rifes when the
Sun fets.
' ; Xlh A Star rifes Heliacally^ when it emerges
out of the Sun-beams, and is fcen in the Morn-
6. Conjiellations in the Southern Hemisphere.
Ara cutnThuri-
hulo.
Sis 6
27 18
23 5
37 «5
9
0
0
I
6
2
0
0
Jrgo^ or JVtfO/w.
2524 57
an 2
22 24|„
49 14,1 *
0
0
4
6
6
9
0
Jpus. .
* 9 45
.21 24
44 32
62 4
Q
0
0
4
3
.4
0
Cams major.
If 3. 7
az25 12
'34 44', 2
59 H!^
I
7
6
-4
0
II
5
3
Cants minor.
OS 16 48
il 0 49
23 47I *
I
0
3
9
1
Cetus.
H18 36
* 42(78
34 '4-
0.
2
.9
44
4
Centaurus , um
Lupo.
-a=2S42
niza 30
21 59: ^
0
I
0
p
0
6
9
I
I
0
0/
1
Cameliofttis,
tn,i6 30
t 3 39
63 35
75 24
1
|.0
0,
0
Coimia Noahi.
\
ni4 54
s 6 46
55 42
60 41
10
0
2
0
I
6
I
0
'
Corona Auftr.
Jtf i'i8
10 14
12 28
22 36
12
0
0
0
I
3
8
0
Cor*vta.
<b 6 26
«3 3
10 91
21 44
10
0
0
.3
„2
2
3
0
Cratar.
tteiQ 26
=0= 3 58
II 18
22 42
11
0
0
0
8
2
2
0
ErJJanus^
V16 38
nil 15
18 26
54 33
68
0
0
12
....
'5
20
20
0
I
0
Grus.
~'+ 54
18 2
39 43
4' 55
3
0
0
0
2
I
Hydrus..
Jtf26 59
V 3 37
64 10
78 5
10
0
0
4
2
3
r
0^
Jng
The Ufe of the Globes.
443
ing before Sun-rifmg: And it fets Heliacally^ when
it is fo near the Sun that it cannot be feen.
XIII. A Right Sphere is that whofe Poles are Hate
in the Horizon and the Equinoftial, and all its i".^^^^' ^
Parallels cut the Horizon at Right Angles. *
XIV. A Parallel Sphere is that whofe Poles
co-incid^ with the Poles of the Horizon, or Ze-
Lepus.
n 644
28 9
34 45
45 46
19
0
0
3
7
3
6
0
Mufca,
Tn,i6 20
22 22
55 "
58 47
4
0
0
0
2
2
0
0
Mamfceros.
1129 34
51 10 50
'3 »3
3> »«
19
0
0
0
10
7
2
9
Orioff.
n 7 32
gzi; II
3 II
54 4
80
2
4
4
25
20
25
0
Pa<vo*
^24 7
vy24 41
36 ti
SO 49
14
0
I
3
s
4
I
0
Phoenix.
SS29 47
K24 '4
31 39
55 5
"
0
I
5
6
1
0
0
Pifcis Volant.
^11 19
67 52 g
82 35
0
0
0
0
-7
I
0
Rohur Carolime.
^ 3 34
m 7 6
S' ^|l2
72 I2i
0
I
2
7
12
0
0
Sextans.
ai9 59
11)113 5
19 43'
0
°
0
I
7
32
I
0
Toucan.
a; 3 «6
22 43
45 27
59 46
'
0
0
4
2
3
0
Triangulum.
J^ 5 35
17 2
41 32
48 I
5
0
I
2
0
-I-
2
0
0/
■ i.
Xiphias,
^ 7 36
«i8 32
70 12
88 14
6
0
0
I
2
I
2
0
7. In the Zodiac^
Jn Northern Hemifpbere^
In Southern Hemtfph£rey
gum of all the Stars.
Naw.
I
2| 3.1 4 1 5 1 t)
7
943
1511
547
7
4
4
II
23
20
43
93
56
94
227
136
169
356
145
445
695
176
174
113
10
30oi|i5|54|i92|4S7|67o|i3i6
297
nitk
444 7^^ ^fi ^f *^ GtOBBs,
ntib and Nadir \ and the Equinodial with the
S. The Ufe of fach a Catalogue of Stan is veiy great i
for {rom hence we learn, (i.) If aay mw Stars at any time
appear, which have never been obferved before, (2.) If any
Scar, which now s^pears, (hall in Time to cooie disappear.
(3.) If the ntw Star which (hall appear be the fame with a
Star that has dKappearM formerly ; and therefore, (4.} If the
Stars have any periodical Times of Apparition. Heocf
(c.) The Means or Method of predidiog the Appearing or
jpifappearing of Stars. (6 ) By a Catalogue of the Stars we
compare their refpedive Places, Situations, and Diftaccef with
)£afec (7.) By tkis means we alio compare and detennine the
^ trse Pla^s and Motions of the heavenly Bodies in general,
And of the San, Moon, Planets, and Comets in particular,
with many other ufeful Purpofes it (erves befides.
J. Now it is a^ually Fad, that fome new Scars appear,
that others difappear ; yea, that they change their appa-
rent Magnitude, and difappear by decrees. Htpparcbvf th^
£rft of Men pb&rved a new Sur, ( 1 20 Years before Cbri/t[
which occafion'd his making a Catalogue of the Stars.. Ano^
ther is faid to have appeared J. D, 130 ; another A, D. 389;
pne exceeding bright in the 9th Century, and another in the
Year 1264.
10. But the fir9i ne%p Staty of y/hich we have any gO0||d
Account, is that in the Chair of CaJ/topeia^ firft obferved Iw
(^9meiiuj Gemma on the 9th of November 1 572, and by ^ych9
Brake on the i ith. Sir Ifaac Nenuton fays it equalled Venifs
in Brighcnefa at its ia^ Appearance, and gradually declined
in its Luftre, till it totally disappeared in the March fQllowin|;«
'irhis Star is fupppfed to be the fame that appearM in t$e
Years 945 aqd 1264, having its Period about 310 or 320
1 1. In Aug. 13, 1596, Z>. Fabricius obferved another new
Star in the Neck of the Whale i and though the 17th Cen-
tury this Star was obferycd tQ appear ana difappear perio<i|]-
qilly, it^jPcriod feeing e^ual to 33^ Days. The Phsenome-
^ of this and the like Stars are (uppofed to 1^ .QwiQg.tQ.the
•{Spots on their Surface, which fometimes in9rcafe and fome-
times decreafe, in the manner as we have obferved they do
. on the Surface of pur Sun.
12. For that the Stars are r^lly Sunsy and have each a
Syftem of Planets, ^c. about them, like ours, can be no
Doubt to thofe who underfland the Hules of ReafQuing rigtitf
^)r, as I have before pbfervcd, Armat. CXXXI. And therein
The life of the GLt)Bfis. 445
Horizon i and all the Parallels parallel thereto.
fore as they revolve about their Axis, thofe Spots may caofe
a great Alteration of Luftre, and ibmetimes wholly obfcare
them for a time^ But it is no Wonder if Bodies at fuch a
Diflance fhould have Appearances produced by Caufes quite
unknowil to us. See more on this Head in Dr. Lwg^i Afir^»
13. As to the Diftance of the.Fix*d Stan« we had but
(inall Hopes of any Eftiroation of it, till Dr. Bradley began
Ills Ob&rvations on them with an Inih'ument (b very exafi,
as that he is of Qpinion, if the Parallax of a Star amounted
to but one iingle Second, he muft have obferved it; and
therefore that fuch a Star muil be above 400000 times farther
Trom us than the Sun. ,
14, For if S reprefent the Sun* T the Earth, ATE its pL LXVi
Orbit, and R a Star at fuch a Diflance SR or TR, that the Y\% iu
•Semidiameter of the Orbit ST fliall fubtend an Angle TRS ** ^
= 3c/^^ or half a Second, then we find the Diitence SR
by this Analogy :
As the Tangent of the Angle TRS == yJ"lsi 4.371911I.
Is to Radius 90° = 10.000000
So is the^un's Difiance ST =: t =: 0.000000
To the Diihuice of the Star SR s: 424700 = 5.628086
15. But the Diilance of the Sun ST == 20000 Semidia*
meters of the Earth (fee Atmt, CXXXIV.}; and . fuppofing
SR=:(TR=:) 400000 ST, then is the Diflance of the
Star from the Earth TR z= 400000 x 20000 == 8000000006
Semidiameter« of the Earth, or 8000000000 x 4000 -sz,
320000000Q0000 Miles of Englifb Meafure. Hence it ap-
pears, that though the Velocity of Sound be fo very great
as at the Rate of 1 142 Feet fer Second, or 7000000 Miles
f€r Jnmtm^ yet it would take up 45 7 1430 Years to pals from
the neareft Star to us. A Cannon-Ball would take up twice ^
that Time to pafs from us to the Star ; (fee Jnn9t. XX V. 4.)
yea. Light itfelf, with the inconceivable Velocity of i ooooooo
Miles ^ Minute, takes up more than 6 Years in coming fronk
the Star to us. Therefore how immenfely great muft thoft
Luminaries be^ which appear fo bright, and of fuch different
Magnitudes, at fuch inunenfe Diftances !
16. The different apparent Magnitudes of the Sean are
owing to their different Diilances from us. Had we Telefco-
pic Eyes, we fhould fee many more. Se*viniy Stan, aitd
«orei have been difcover*d in (he PUiadgj (commonly call'd
XV. Am
446 ^he Ufe of the Globus.
XV. An Oblique Sphere is that, one of whofc
the Seven Stars ; and all that Trad of the tleavens called the
Mlky Way (or Galaxy) is well knowti to be owing to the Rci-
fulgence of a prodigious Maltitude of Stars difleminated thro*
thofe Parts of the Univerfe, though at fo great a Diftance as
to be invifible to the naked Eye ; yet are diey diftemible in
great Numbers through a Telefcope, and motf in Proportion
as the Infbument is better.
1 7. Hence likewife we account for that particular Phaeno-
menon we call a nebtdoiu Star, or doudy faintiih bright Spots
that appear like Stars in an indired View ; for in order to
this you have no more to do than«only to direft a good Te-
lefcope to any one of them, and you will be agreeably far-
prized with a View of a great Mdtitude of very fmall Stars,
^hich were the Caufe of the luminous Spot to the naked Eye.
18. To the ytry fmall apparent Magnitude of the Stars
we owe their conftant Tnmukling ; for being, but lucid Points,
every opake Corpufcle or Atom floating in die Air will be big
-enough to cover and edipfe them, when they get in the Right
Line between the Star and the Eye ; which Alternations of
momentary Occultations and Apparitions make the Twinkling
of the Stars we now fpeak of.
19. I ihall here give a fiiller Account of the fmall elliptic
apparent Motion of each Star about its true Place, which I
have already begun in a former Annotatim, And in order to
-underftand the Force of the Argument, the following Repre-
Wate fentations are neceffary, n)i%. Let S be the Sun, A BCD the
LXV. Earth's' Orbit \ and from S fuppofe a Perpendicular erefted,
Fig. 5,6,7. as SP, paifing through a Star at P. Now if the Speftator
were at S, he would view the Star in the fame Perpendicular,
and in its true Place P, projedled in the Point/ in the vifible
Surface of the Heavens. But if the Spedator be carried
about the Sun in the Circle A BCD, whofe Diameter is fen-
fible at the Diftance P, or fubtends a fenfibl^ Angle A PC,
then in the Pofition A he will fee the Ph^enomenon P in the
Right Line A? a, projedled in the Point «. For the fame
Reafon, in the Points B, C, D, the Star will appear in b^ c, di
. fo that it will feem to have defcribed the little Circle ^^ri.
20. If the Diilance of the Star SP be fo great, that the
Diameter of the Earth fubtends no fenfible Angle, but ap-
pears as a Point, then will alfo the fmall Circle ahcd become
infenfiblei and all the Lines A P, BP, {ffr, may be efteem*d
perpendicular to the Plane of the Ecliptic, and be direded
CO t^ic fame Point in the Heavens with the Perpendicular SP,*
Pokj
The Ufe of the Globes. 447
Poles is above the Horizon, and the other below
\ as to Senfe. So that in this Cafe the Star P would ever ap«
pear in the fame Point/, if Light were propagated in an In-
ftant.
2 1 . But if in this very Cafe, in which the Star is fo re-
mote. Light be propagated in Time, or with a <:eruin Ve-
locity^ then as the ^rth deicribes its Orbit a Spectator will
fee the Star in an oblique Diredtion^ and not in the Perpen-
dicular, as we have formerly fhewn: That is, if GF be a
Tangent to the Earth^s Orbit in B, and BE perpendicular to
the Plane of the Ecliptic in the Point B, then while the Earth
moves through the indefinitely fmall Arch G B, a Star at £
^ will appear to move from E to /, or to be in ^ when the Earth
arrives at B.
22. Now iince the Diftance SB is but a Point with re(jpe6l
to the great Diftance SP of the Star, it follows, that we
may refer the Spe^bttor from the feveral Points A, B, C, D,
to the central Point S, for obferving the Fbammena of the
Star at P, which will not be alterM thereby. Therefore V
sa be parallel to AC, and you make the Angle Y^a equal to
^ the Angle EB/, 'tis plain the Star P mnft appear in «, in the
Diredtion Sa. Alfo when the Earth is at D, the Star will be
leen in the oblique Direction Sr at r, the Spe&tor being re-
fcrr'd to S.
23. For the like Reafon, *ui%. becaufe hd is parallel or
alike fituated in refped of 1^%^ and to the Tangents in D and
^, therefore the Star at P will appear in d and h when the
Earth is at C and A ; and fo during the Space of one Year
the Star P will appear to defcribe a fmall Circle adch^ fuppo*
£ng the Star in the Zenith £ of the SpedatOr ; but if the
Star be at any Diftance from the Zenith, the iaid linall Cir-
cle will become an EUipfe, as in Fig, 7.
24. Thefe fmall elliptic Motions of the Stars occafion*d
their Dedinations to vary, and alfo their Diftances from the
Poles of the World, and that by the Space of 20^^ on one,
Side and on the other. Now this could not happen on any
account of Refradion, becaufe the fame thing was as well ob*
ierved oi Stars near the Zenith, where there is no Refradioo^
as elfe where fituated. Nor could it refult from any Nuta^
Hen of che Earth's Axis; for that would have made the equal.
I>iflaQces of the Stars on oppolite Sides of the Pole unequal^
which never happened.
25 . Neither can this be a Paralla^ic Motion of the Stars ^
§or then while the Lanhdefcribed the Half of its Orbit ABC^
44^ 3^^ IJfe of the Globes*.
it\ and the £quino6tiaI and its Parallels obliquel]^
cutting the lame (CXLVl).
tbe Star would dedcribe.tlie Semicirde ahc\ whereas it i^
focmd by Obfervation, that the Star defcribts the fiud Semi-
' ^circle abc while the Earth de&ribes its Semi-Orbit BCD. (See
^ Art, 22, 23.) Therefore itmuftarifefotelyfieomiir fV^cf/f^
iAfht htaring afit^k Frfvrtkm I9 the a$aatal MatioM §/ th
Earth i whKh aoeouits for all the Pb^tmrnma to the greatcft
Exadnefs, without any the leaft DiiBciilty or Imrkacy i aa
they may fee who will confnlt the Profijbr't own Accopat in
the Tnmfa^ionSf and what Mr. ^jmfm and Mr. Mm Lamiti
have wrote on this Sobjed.
(CXLVI) I. The thiee Pofitiohis of die Sphere here de-
Mate fcribed are repidented info many Figures; thefixft of which
LXVII. is the Dirta or Right Sphere, which is proper to thde Peojde
Fig. I. <H^y who live under the Equinodial Circle JEQ^ becaufe to'
them the Poles of the World P and Swill both be in thetio-
rizonHO«
Fig. 2. 2r. The fecond Figure reprefenti die ParaUdSfbere^ wha-e
the Axis of the Eaith PS is perpenditttlar to the Horison» ot
the Pkrfes P, S, are in the Zemth and UaMr. This Jofidon
6f the Sphere is peculiar to the Parts of the Earth under each
Pole } whofe Inhabituits» if any there were, woiiM perceive
no circular Motion of the Son, Moon, or Phuneli, nor any
Motion (^ the Stars at all. Bot this moft b^ underftood of
a Perfon ftanding predfely on the Ends of the Earth^s Axis^
t^liich are the only Ppints on the Earth's Smfite which have
no real Modon, and conftquently winch can produce no ap*
parent Mbtion.
1^%- 3* 3- '^^^ QhUfui SfbiTi b reprefented in the third Figuie.
In this the Axis of the World PS makes an Angle P£d
with t&e Horizon HO, of a gveatcr or Mler Number of De-
grees aeoordiDg to the Ladtude of the Place. Hence itnp-
pears, that all the Inhabitants of the Earth have fuch.a Pofi^
tion of the Sphere, except thrfe onder the EpumSUU and
Hie Poles.
4. The Arch PO meafinpcs die Ahitude or Height of the
Px)le, or what is commonly callMthe Pole's BUvatimi and
this Arch PO is ever equal to the Latitude (rf'thePhce &Zi
as will eafily appear dius : It is i£Z 4. ZP =: (^P = Qjia-
. drant=r) ZP-f PO = ZO; if therefore from the two
•^uaiqoadnnCsi&PsZOyou fabiaft Ac oMnnonPM
The Ufe of the Globes: 44.9
The Problems on the Celeftidl Globe arc the fol-
lowing.
P R O B. I. To reBify the Globe:
Elevate the Pole to the Latitude of the Place,
ind every thing as direded under PRO B. 11. of
the Terreftrtal Globe^ which fee.
PR OB. II. To find the Sun's Place in the
Ecliptic:
Find the Day of the Month in the Calendaf
on the Horizon, and right againft it is the De-
gree of the Ecliptic which the Sur* is in for that
Day.
PR OB. III. To find the Sun^sTitcliY^ATion t
Rectify the Globe, bring the Sun*s Place in
the Ecliptic to the Meridian, and that Degree
which it cuts in the Meridian is tlie Declination
required.
or Arch ZP, the femainmg Ardhes ^2 = ^O ; whic& Wat
to be ihewh.
5 . Hence appears alfo theReafon of the Method of redifying
the Sphere or Globe for any given Place Z, or Latitude ^Z,
*vix. becaufe if the Pole P be elevated fo high above the Ho-
rizon as the Place is diflant from the Equator, the (aid Place
will then be the highefl Point of the Globe, and confeqaent-*
ly that to which alone all the Pb^enomenaof the Heavens and
the Earth, in fuch a PoiitiOn of the Globe, can agree.
6. Hence alfo we obfervc, that the Coriiplenynt of the
imcitude ZP is equal to the Elevation of the Equator ^H
above the Plane Of the Horizon. For i©Z -f- ZP = (iEP
= ZH=i) '^LjB^Mlit therefore fubducl the common
Part ^Z, and there remains on each Side ZPitr i£H;
which was to be fhewn. Whence the Angle ZEP =
i^EH.
7. Any Great Circle of the Sphere pafUhg through the
Zenith and Nadir Z and N, as ZEN, Z AN, arc caird ^.
zimuths or Vertical CtrcUs '» of which that which paffes through
the Eaft and Weil Points of the Horizon, as Z E'N, is caird
VoL.IL Ff PR OB.
450 5fi5^ Ufe of the Globes^
PROB. IV. to find the $U^s Right As-
cension :
Bring the Sun's Place to the Meridian, and
the Degree in which the'^Meridian cuts the Equi-
nodial is the Right Afcenfion required.
PROB. V. To find the Sun's Amplitudz:
Bring the Sun's Place to the Horizon, and
the Arch of the Horizon between it and the Eaft
er Weft Point is the Amplitude, North or South.
PROB. VL To find the Sun's Alt IT WE far
My given Day and Hour:
Bring the Sun's Place to die Meridian; fct the
Hour-Index to the upper XII i then turn the
Globe till the Index points to the given Hour,
where let it ftand ; then fcrewing the Quadrant of
Altitude in the Zenith^ lay it over the Sun*s Place,
and the Arch contained between it and the Hori-
the Prime VtrttcaL The Aich of the Horizon A£ is tlie
Amplitude of a Phaenomenon emerging above the Horizon at
the Point A; this is call'd the Ortinje Amplitude^ becaofe it is
rifing ; as on the Weftern Side it is call*d the Occt^e AmpU*
tude^ becaufe it is there fitting. The Arch AB meafured by
a Quadrant of Altitude Z A is the Altitude of any Cele&i^
Body at B, above the Horizon.
8. As I judge this a proper Place, I fhall here explain the
Philofopbical Principies of Gnomon I cs, or the Art £^ Di ai^
* LiNQ. In order to this we are to coniider, that as the Time
which palTes between any Meridian's leaving the Sun and're^
tnniing to it again is divided into 24 Hours, {o if we con-
ceive a Sphere to be conftru&ed with 24 of thefe Meridians^
the Sun will orderly come upon or be in one of them at the
Beginning of every Hour. Such a Sphere may be reprefent*
Hate ed by the Figure PDS6, where the feveral Meridians aie
LX VII. reprefented by P i S, P 2^8, P 3 S, and fo on to twice 1 2« or 24
Fig. 4. in all.
9. Since thefe Meridians divide the Equinodlial into 24
equal Parts* each Part will contain juft 15'', becaufe 15 x 24
ZOfI
TbeUfe of de GloHes, 451
ton will give the Degrees of Altitude required.
PROB. VII. To find tbi Sun's Azimuth for
oftf Hmr 9f the Dof:
Every thing being done ds in the laft Pfoblenii
the Arch of the Horizon contained between the
North Point and that where the Quadrant of Al-
titude cuts it^ is the Jzimuib Eaft or Weft, as
required. '
P R Ofi. Vlil. Ta find thi Time wbeti the SuH
rifes orfets:
FiiiD the Sun's Place for the given Dayi
bring it to the Meridianj and fet the Hour-Hand
to XII; then turn the Globe till the Sun's Place
touches the Eaft Part of the Horizon, the Index
will fhew the Hour of its Rifing: After that^
turn the Globe to the Weft Part of the Horizon,
jc 360^ rs the whole Cirdls ; and fince all the MeruJiiUift
paTs through the Poles of the World, the Planes- of thofd
Meridians all interibdl each other in One common Line PS» ^.
ii^hich is the Axis of the Sphere, therefore the iaid Axis PS
is in the Plane of each of the li Meridians.
10. Suppofe Z to be the Zenith of any Place, as London^
and D W B £ the Plane of the Horiason fixM within the Sphere^
conilru6^ed with the (aid iz Meridians ox Hour-Circles^ 1,1^
^9 2, 3,3, 4,4j ^c, then will the Axis of the Sphere PS pais
through the Center of the Plane at N, fo that one Half Nl^
will be above the Plane, and the other Half NS below it.
ti. Sappofe n6w this DisdUng'Spbere to be fafpended hf
the Point Z, and moved about fo as to have the Points D and
B exadly in the South and North Points of the Horizoi>, and
£ and W in the Eafi and fTifi Points ; then will the Sphere
have a Situation every way fimilar to that of the Earth and
Heavens with reipedt.to the given Place Lotidon, and the Axis
of the Sphere to that of the £arth. ,
1 2. Therefore the Sun fhining oh fuch a Sphere will be
attended with all the fame Incidents, and produce all the fame
Effe^i as would happen if the faid Sphere were at the Cen-
F f a and
452 ^he Ufe of the Globes.
and the Indek will flicw the Time of its Setting
for the given Day.
PR OB. IX. To find the Length of any giveH
Dof or Night:
T H I s is eafily known by taking the Number
of Hours between the Rifmg and Setting of the
Sun for the Length of the Day ; and the Refiduc^
to 24, for the Length of the Night.
PROB. X. t:o find the Hour of the Hay ^hav-
ing the Sun^s Altitude given i
Bring the Sun's Place to the Meridian, and
fet the Hour- Hand to XII j then turn the Globe in
fuch manner, that the Sun's Place may move a-
long by the Quadrant of Altitude, (fix'd in the
Zenith) till it touches the Degree of the given
Altitude ; where flop it, and the Index will fhew
tcr of the Earth, or the Center N of the Sphere coincided
with the Centefof the Earth 1 becaufe the Diflance betwixt
the Surface and Center of the Earth is infenfible at the Di-
flanco of the Sun.
13. Now 'tis evident, as the Sun revolves about fuch a
Sphere, it will every Hour be upon one Half or other of the
12 Hour- Circles ; <i;/%. from Midnight to Noon it will be on
thofe Parts of the Circles wnich are in the Euftern Htmifphere^
slnd from Noon to Midnight it will pafs over all thofe in the
Wefiern. It is alfo farther evident, that while the Sun is in
the Eaftern Hemifphere it will be firft below and then above
the Plane of the Horizon, and ntice 'verfa on the other Side.
14. Again : When the Sun is upon any one of thefe Hoar-
Circles, by ihining upon the Axis it caufes it to caft a Sha*
dow on the contrary Side, on the Plane of the Horizon, on
the nether or upper Surface, as it ^ below or above the ^d
Plane. This Shadow of the Axis will be precifely in the Line
in which the Plane of the Hour- Circle would interfedl the
Plane of the Horizon : If therefore Linos were drawn through
the Center N, joining the Points on each Side the Plane where
the Hour. Circles touch it, as 4N4, 5N5, 6N6» l^c. the
on
The life of the Glober. 453
ion. the Horary Circle the Hour required. ^
PRO B. XI. To find the Place of the Mooii
or any Planet, ^for any given Hay :
Take Parker's or fVeaveHs Epbemeris^ and '
againft the given Day of the Month you wil) find
the iDegrec and Minute of the Sign which the
Moon or Planet pofleffes at Noon^ under the Ti-
tle of Geocentric Motions. The Degree thus found
being mark'd in the Ecliptic on the Globe by a
fmall Patch, or otherwife, you may then proceed
to find the Declination^ Right Afcenfion^ Latitude^
Longitude^ Altitude^ Azimuth^ Rijtng^ Southings
Settings &c. in the fame manner as has been fhewa
for the Sun.
PR OB. XII. To explain the Phenomena of the .
Harvest-Moon.
In order to this we need only confider, that
Shadow of the Axis will fall on thofe Lines at the Beginning
of each refpedive Hoar, and thereby indicate the Hour-Circle
the San is in for every Hour of the Day.
15. Thefe Lines are therefore properly call'd Hour-Unesr
and among the reft, that which repreients the Hour of 1 2 at
Noon is N B, half the Meridian-Line D B ; whence it ap-
pears, that the Hour- Lines ^)^ i, N2, N3, ^c, which ferve
for the Afternoon, lie on the £aft Side of the Plane, and ate
numberM from the North to the Eafl ; and on the contrary.
16, It alfo appears, that as the Sun's^ Altitude above the
Plane is greater or le(s, the Number of Hour- Circles the Sua
will poiTefs above the Horizontal Plane will be alfo greater
or lefs. Thus when the Sun is at S in the Equino^ial, its
diumalPatb for that Day being the Equinodlial Circle itfelf
JEEQW, 'tis plain, fincc the Arch iEE = EC^ the Sun
will apply to fix Hour-Cirdes below the Horizon, and to fa.
above it, in each Half of the Day ; and conlequently, that
on that Day the Shadow will occupy but 12 of the Hourr
Lines on each Surface of the Plane, beginning and ending
at$.
F f 3 when
454 2^^ ^ ^f t^^ Globes.
when dig Sun is in the Beginning o^ Aries, the Full
Moon on that Day muft be in the Biginning of
Libra: And fince when the Sun fcts, or Moon
rifes, on that Day, thofe Equino&ial Points will
be in the Horizon, and the Ecliptic will then be
leaft of all inclined thereto, the Part or Arch
which the Moon deforibes in one Day, vi%. 13
Pegrees, will take up about an E[our and a Quar*
tcr afccnding aboye the Horizon ; and therefore
* fo long will be the Time after Sun-fet, the next
Night, before the Moon will rife. But at the
oppofite Time of the Year, when the Sun is in
?he Autumnal, and Full Moon in the Vernal £-
quinoXj the Ecliptic will, when the Sun is fetting,
nave the greatcft Inclination to the Horizon ^ and
therefore 1 3 Degrees will in this Cafe foon af-
cend, viz. in about a Quarter of an Hour ; and
1 7. But when the San is m the Tropic of Cancer y its di-
urnal Path for that Day being the Tropic itfclf TCRF,^'t^
manifefl tiie' Sun in the Forenoon afcends above the Plane in
paffing between the Hoar-Circles' of 3 and 4 in the Mornings,
and defcends tielow it in the Afternoon between the Hours of
8 and 9 ; Therefore on the Summer-Tropic the Shadow wil(
pafs over 16 of thofe Hoqr-Lines. And nfke merfa, when
the Sun is in the Winter-Tropic at O, its Path being then
OG JH^ it rifes atqve the Plane betwe^ 8 s|nd 9, and leaver
it between 3 and 4.
1 8. From what has beei^ faid 'tis ^dent, that if the Cir-
Plate cles be fuppofed removed, and only the horizontal Plane re-
LXVII, main, with the Half of the Axis NP above it, in the fame
{■*ig. r, Pofuion as before, then fhould we have cqniHtuted an Hori-
zontal Dial, every way the fame with thofe in common
Ufe, as reprcfented in the next Figure, with only the Addi-»
tion of a Subftylc PO, to render the Style NP very firm.
19. Hence appears the Reafon why t^t Gmpion orStyl^
NP in thofe Dials is always direftcd to the North Pole, and
filways contains fuc)i an Angle PNO with the Hour of i^
N fi as 18 ^qu^ to t^ie L^tita^e of cite Place : I^^ftlya th^ R<^%*
. ' ^ fo
The Ufe of the Globes. ' 455
h long ^ftcr Sun-fct will the Moon rife the next
D^y after the Full : Whence, at this Time of the
Year, there is much more Moon-Light than in
the Spring ; and hence this. Autumnal Full Moon
came to be caird the Harveft Moony the Hunter's
or Shepherd* s Moon : All which will clearly be
(hewn on the Globe.
P R O B. XIII: To reprefent the Face ^f the
Starry Firmament for any given Hour of the
Night:
Rectify the Globe; and tqm it about, till
the Index points to the given Hour ; then will
all the upper Hcmifphere of the Globe reprefeiKt
the vifible Half of the Heavens, and all the Stain
on the Globe will be in fuch Situations ^ exadljr
corrcfpqnd to thqfe in the Heavens ; which piay
therefore be ealily found, as will be fhewn«.
^n why the Number of Hoar- Lines on thefe Dials exceeds
not 16, and are all drawn from 6 to 12 and 6 again on the
Northern Part, the xefl on the Soathem ; and why the Hour-
Iiine of 6 lies diredlly Eafi and fTefi, as that of 12 does
N^rti jaxid South.
20. If a Plane be fix*d with the fame Sf^ere in a Vertiosl f\2Xe
Pofitioo, or p^rpendicolar to the Horizon^ and coinciding witl^ LXVII.
the Plane of the Priine Vir^cal^ i. e. ^ng fall South and jp^g 5^
North ; ^en will the Axis PS dill pafs through the (l^enter of
the Plane N, and the lower Semiaxis NS will by its Shadow
mark oat the Hour- Lines on the Southern Sar4ce» and die
upper Semiaxis N P will do the fame on the Northern. Thefe
Hour-Lines are determmed in the fame Manner as thofe on
the Horizontal Dial } and it is plain, the Sun cannot come on
the Southern Face of this Plane before Six in the Mominc,
nor (hine on it after Six in the Evening.
21. Alfo it is evident, that all the Hours before Six in d^f
Morning, and after &at Night, will befhewn on die North-
eita Face or Side of das Plane, for the Thne of the San*s be-
ing above the Horizon in any Place. Hence the Reafon of
» Vl'ma South and Nertb KtrtiaU Dial eafily appears ; the lat,
" Ff 4 J^ROR,
4s6 7%e Ufa of the Globes,
PR OB. XIV. ro find the Hour when any
known Star will rife^ nr come upon the Me-
ridian:
RECTit V the Globe, and fct the Index to XII-,
then turn the Globe till the Star comes to the
Horizon or Meridian, and the Index will fliew
.the Hour required.
PR OB. XV. "Tofind at what rime of tht
Tear any given Star will be on the Meridian
at Xll at Night:
Bring the Star to the Meridian, and obferye
what Degree of the Ecliptic is on the North Me-
ridian under the Horizon ; then find in the Ca-
lendar on the- Horizon the Day of the Year a-
gainft that Degree, and it will be the Day re-
quired. (CXLVII).
Fig. 7.
Hate '^^ ®^ which is here reprefented apart from the Sphere, with
LXVII ^^ ^^^^ NS, Subdyle^ and Hour- Lines: And the fame may
be conpeived for a Nmh ErtH Dial.
2Z. The Gwmon, NS contains an Angle SND = ZNP
with the. Meridian or Hour- Line of 12, w«. ZD, which is
exaflly the Complement of the former PNB to 90 Degrees;
or the Elevation of the Gnomon h in tkeCt equal to the Com-
plement of the Latitude of the Place : And what has been
faid about the Reafoo of the Hour- Lines is the fame for the
Half- Hours, Quarters, ^V. Likewife if the Rationale of a
DireSl Squth Dial be underilood, nothing can be difficult to
underhand of a Dial which does not &ce the South or North
diredlly, but decline^ therefrom any Number of Degrees to-
wards the Eail or Weft. But they who would know more of
the Mathematical Structure and Calculations for all Sorts of
Dials may jiaye Recourfe to the Second Volume of my Twng
7rigonom£ter% Guide, Qr other Books on that Subjed.
^ (CXLVII) I. I ihall here reprefcnt the Cafes of th«fe
.Agronomical Problems, as they are performable by the Cir-
, cles of the Celeftial Globe, Qs. by the: StsreograpHtal j?w-
pciion of ifee 'Sphere 49 Planq. Xhitf
.♦ . \; These
T^e Ufe of the GlobesI 457
These are the cYiiti Problems on the Cekjiial
Globe t We now proceed to thofc on the Tep-
rejirial', but fhall firft premife the following De-
finitions relating thereto.
I. The Latitude of any Place is its Di-
ftance from the Equator towards either Pole ; and
is reckoned in Degrees of the General Meridian,
beginning at the Equator.
II. Longitude is the Diftance between the
Meridian of any Place, and the firft or ftanding
Meridian, reckoned m the Degrees of the Equa-
tor towards the Eaft or Weft.
III. A Qlimate is a Space of the Earth's
Surface, parallel to the Equator, where the Length
of the Day is half an Hour longer in the Parallel
which boynds it on the North, than in that which
terminates it on the South. '
IV. A Zone is alfo a Divifion of the Earth's
Surface parallel to the Equator, in regard of the
different Degrees o^Heat and Cold^ which we have
defcribed in the preceding Ledhire.
V. The Antoeci are thofe Inhabitants of the
Earth, who live under the fame Meridian, but on
qppofite Parallels, and are therefore equally di-
Let ^ N QS be the Genenil ^endiaQ* piate
N S the Axis of the Sphere. LXVIII,
iEQ^thcEquinodiaiLine. ' Fie. i.
HO th& Horizon of London.
So C J:f the Ecliptic, or Sun's Path.
2 D the Frime Vertical^ or Aximuth.
EP the Axis of the Ecliptic.
N AS an Hour-Circle or MeridiaD,
^ AD an A^^imuth ^irc^^!
<Jant
45^ ^^ W^ ^f '^ Globes^
fiant from the Equator. Their Noon^and Mid-
night are at the &ine Time ; the Days of one are
equal to the Nights of the other ; and their Sea-
fons of the Year are contrary.
VI. The Periobci are thofe People who live
under the fame Parallel^ but oppofite Meridians,
The fame Pole is elevated and deprcfs'd to both ;
are equally diftant from the*Equator, and on the
fame Side \ when Noon to one^ it is Midnight to
the other; the Length of Days to one is the
Complement of Night to the other, and the con-
trary, and the Seafons of the Year are the lame
to both, .4t the iame Time« '
VII. The Antipodes arc thofe who XwtFeet
fo Feety or under oppofite Parallels and Meridians^
They are equally diftant from the Equator on dif-
ferent Sides; have'tlft contrary Poles equally ele-
vated ; the Noon of one is Midnight to the other 5
the longeft Day or Night to one is ihorteft to the
other J and t^c Seafons of the Year are contrary^
VIII. Also the Inhabitants of the Torrid Zone
are call'd Amphiscii, becaufe their Shadows fall
' on both Sides of them.
IX. Those of the Frigid Zone are called
E YP a Circle of Longitadc.
gs I So the Trppic of Qanar.
VfVfiht Tropic of Capncem.
2, By means of tkofe Circles various Spberical Triangles
^re formM for Cakulation, Thus let A be the Place of the
San in the Ecliptic ; then in the Right-angled Triangle AXC
vrehave
C A the Sun*8 Placi,^ or Longitude from |;he Ej^uinox Q«
AX the Sun's DttUnatm Kortl\.
?£RlSCXi^
T^e Ufe of the Globes, 45^
Per I SCI I, becaufc their Shadows faU all around
them.
X. And the Inhabitants of the Temperate
Zones are call'd Heteroscii, becaufc they caft
fbeir Shadows only one way.
XL A Cqntinent is the largeft Divifioq or
Space of Land, comprehending divers Countries *
^d Kingdoms, not feparated by Water.
XIL An Island is any fmall Traft of Land
furroundpd by Water.
XIII. A Peninsula is a Part of Land enr
compafsM with Water all around, except on one
Part, which is caird
XIV. An Isthmus, being that narroyr Necif
of Land 1 which joins it to the Continent.
XV. A Promontory is a mountainous Part
of Land Handing far out in tlfee Sea ; whofe Fore-
part is cali'd a Cape^ oxHead-Land.
XVL The Ocean is the largeft Colleaionof
Waters, which lies between, and environs the
Continents.
XVIL The Sea is a fmaller Part of the aque-
t)us Surface of the Earth, interceding the Iflands,
Promontories, ^r.
XVIII. A Gulf is a Part of the Sea every
CX the Son's Higbt Jfien/hn.
ACX the Angle of Obliquity of the EcHptk,
3. And fappoiing the Sun lifing in the Horizon at M oi|
fhe Day of the Summer Tropic, and NMS an |f our- Circle ;
then there h fofm*d ^e Right-angled Triangle ^0|tf, in
Ifyhich we have
J^O = iEZ = the laiit^ of the Place Z.
MQ the Amplitude from the North.
19 M ^e Qomplem^nt of (l^c Soa^s Decliiuiihn IIM.
where
a6o The Ufe of the Globes.
where environed with Land, except on one finall
Part callM
XIX. A Strait, which is that narrow Paf-
fage joining it to the adjacent Sea.
XX. A Lake is any large Quantity of ftag-
n^nt Water entirely furrounded by Land.
The other Parts of Land or Water need no
Explanation.
I SHALL now proceed to the Solution of the
moft,ufeful Problems on the Terrejirial Globe ^ firft
premifing that ibe Latitude of a Place is equal to
the Elevation of the Pole at that Place ; for if the
Arch of the Meridian between the Place and the
Pole be added to the Latitude of the Place, it;
makes ^o Degrees ^ alfo if it be added to the
Pole's' Elevation, or Arch between the Pole an(l
Horizon, the Sum is 90 Degrees : Whence the
Propofition is evident.
P R O B. I. To find the Latitude of any Place:
Bring the ^iven Place to the Brazen Meri-
dian, and obferve what Degree it is under, for
that is the Latitude required.
PR OB. II. To reaify the Gkbe for any giwn
Plaoe:
ONM the Angle of the Hour from Midnight.
OMN the. Angle of th^ Sjia's Pojition.
4. On the fame tropical Day the Sun is at I at Six o' Clock,
becaufq the Hour-Circle of Six is projedled upon the Axia
NCS ; therefore in the Right-angled Triangle ICK we havft
I K the Sun's Altitude at Six.
C K the Aximuth from the Eaft at Six.
CI 'the Declination North.
ICK the Latitude of the Place,
Rai««
The Ufe of the Globes'. 46 1
Raise the Pole fo high above the Horizon, as
IS equal to the Latitude of the Place; fcrew the
Quadrant of Altitude in the Zenith \ find the Sun's
Place, and bring it to the Meridian •, fet the Hour
Hand to the upper XII ; and place the Globe ,
North and South by a Needle; then is it a juft
JReprefentation of the Globe of the Earth, in re-
gard of that Place, for the given Day at Noon.
P R O B. III. To find the Longitude of a given
Place,:
Bring the Place to the Brazen. Meridian, and
bbftrve the Degree of the Equator under the
fame, for that expreffes the Longitude required.
P R O B. IV. To find any Place by the Lati-
tude and Longitude given :
BfeiNG the given Degree of Longitude to the
Meridian, and under the given Degree of Lati-
tude you will fee the Place required.
PROB. V. To find all tbofe Places wbtcb
have the fame Latitude and Longitude with
thofe of any given Place :
Bring the given Place to the Meridian, then
all thofe Places which lie under the Meridian have
the fame Longitude: Again, turn the Globe
round on its Axis ; then all thofe Places, which
5. Again; when the Sun on the fame Day comes to the
Prime Fertkat ZCDy his Place when due Eafi and fFiftu
at G ; therefore in the Right-angled Triangle GBC we have
GB the Sun's Deilination North.
GC the Sun's J/tituite when Eaft or Weft.
BC the Hour of his being due Eaft or Weft,
BCG the Latitude of the Place.
6. Suppofe the Sun in the Horizon at M once more ; thea
hi the Right-angled Triangle MCR we have ,
.pafs
462 Tbe Ufeof the ClobSs*
pals under the fame Degree of the Meridian with
any given Place, have the fame Latitude with it.
PR OB, VL I0 find all tbofe Places wberi
it is Noon at any given Hour of the Day^ i$t
any Placet
Bring the given Place ta the Meridian; ie€
the Index to the given Hour; then turn th^
Globe, till the laid Index points to the uppeif
Xll ; and dbferVe what Places lie under the Brals
Meridian, for to them it is Noon at that Time. .
PR OR VII. When it is Noon dt any oni
Place^ to find tvbat Hour it is at any otbef
git) en Place: *
« Bring the firll given Place to the Meridian^
and fet the Index to the upper XII ; then turn
the Globe till the other given Place comes to the
Meridian, and the Index will point to the Houi"
required;
PR OB. VItt Fot any given Hour of tbi
Day in tbe Place wbere you are^ to find tbi
Hour of tbe Day in any otber Place :
Bring the Place where you are to the Meri*
CM the Amplitude from Eaft or Weft.*
MR the DeclinattOH North.
CR Xki^ Afcenjumal DifftrtfUi.
R CM the Co'LatiituU of the Place.
RMC the Angle of Pafition,
7. In the oblique Triangle AZN we havd
ZN the Co^Laiitude of the Place Z.
An the €$' Declination. *
AZ the Complement of the Altitude A P.
ANZ the Hour from Noon^ equal to iBX.
AZN the Azimuth from the North.
And ^he fame may be done fin: any ^tar at A, or thy othet
. Kacc.
dian^
The life of the GLOBfiS. 463
^aii, let the Index to the given Hour ; then
turn the Globe about) and when the other Pla(^
comes to the Meridian, the Index will ihew the
Hour of the Day there, as required.
PROF. IX. ^0 find the THfiance hetweem
awj two Places on the Globe in Englifh AGles:
Bring one Place to the Meridian, over which
fix the Quadrant of Altitude i and then laying it
over the other Place, count the Number of De-
grees thereon contained between them; which
Number multiply by 69 and a half, ^the Num-
ber of Miles in one Degree) and the Produdt ia
the Number of Englijh Miles required^
P RO B. X. To find bow any one Place bears
from another i
Bring one Place to the Brafs Meridian, and
lay the Quadrant of Altitude over the other; and
it will ftiew on the Horizon the Point of the
Compafs on which the latter bears from the for-
mer.
8. laSiy, let Y be asy Star, then in Che oblique Triangte
YNE we have
YE the Co-Latitude of the Star, viz. YS.
YE the Co'DecUnation of the Star.
NE = j£ 25 = the Obliqmty of the Ediptic
NE Y the Star's hmgitude in the Ecliptic.
EN Y the Hour for Midnight.
9. For the Canons and MeUud of Calcalation I fhall refer
the Reader to the Second Vokme of my Young ffigonomettr*%
Qmdey what I have done being as much as the Nature of the
SubjeA at prefent requires : And thofe who have no Globes
inay folve moft of thefe (and many other) Problems by my
Synopjis Scientiie Cahftisy at a very iinall Expence, and with
^e greateft Exadlnefs.
10. The Reafon of the Fbamamtmm we call the Harvest-
Moon is extremely eafy by the Globe, and may alfo be rc^
PROB.
464 7^^ Ufe of the Globes.
PROti. XI. To find iboje Places iowbicb the
StiH is vertical in the Torrid Zane^ for unj
given Day:
Fill D the Sun's Place in the Ecliptic for die
given Time, and bring it to the Meridian, and
obferve what Degree thereof it cutS| then turn
the Globe about, and all thofe Places which pals
tinder that D^ee of the Meridian are thoie re^
quired.
PROB. XIL To find what Day of the Tear
the Sun will be vertical to any given Place in
the Torrid Zone:
Bring the given Place to the Meridian, and
mark the Degree exaftly over it; then turn the
Globe round, and obferve the two Points of the
Ecliptic which pals under that Degree of the Me-
ridian: Lallly, lee on the Wooden Horizon, on
what Days of tha Year the Sun is in thofe Points
of the Ecliptic ; for thofe are the Days required.
Plate prefented in a Diagiam dias. Let H O be the Horizon, JE Q^
LXVIII. ,the Equinoaial; then will Tr be the Ecliptic, when the Be-
Fig. 2. ginning of. Jries is in the Weflern Horizon ; but when the
other Equinox is there, /R will be the Portion of the Edip-^
tic. On the Vernal Equinox if a Fall-Moon happens, it will
be at C in the Eaftem Horizon at Rifmg ; in one JDay the
Moon will defcribe the Arch Cr; wherefore the following
' Night fo much Time will intervene between Six o^Clock and
the Hour of the Moon's rifing, as is fpent in the Motion of
the Globe while the Arch Cr ia afcending above the Ho-
rizon.
II. Whereas at the oppofite Time of the Year, in%. at
the Ataumnal Equinox, if a Full-Moon happen, then the next
Night the Moon*s diurnal Arch to be elevated above the Ho-
tizon is C^ =: Cr; but £nce the Poiition of CI is fo much
nearer to the Horizon than Cr, it will afcend much fooner
above it, viz> in about one fifth Part of the Time, and fome*
PROB.
The Ufe of ih GlobeS. 465
IPROB. XIII. To find tbofe Plates in the
North Frigid Zone^ where the Sun b^ins to
Jhine confiantly without fetting^ on. any given
Day between the loth of March and the loth
of June.
Find the Sun's Place in the Ecliptic for the
given Day ; bring it to the General Meridian,- and
obferx^e the Degrees of Declination 5 then all thofe *
Places which are the fame Number of Degrees di-
ftant frbto the Pole, are the Places required to be
found; •
PR OB, XIV. ro find on what Day the, Sun
begins to Jhine confiantly without fetting^ on
ar^ given Place in the North Frigid Zone^ and
how long.\
R E c T I F r the Globe to the Latitude of the
Placei and, turning it about, obferve what Point
of the Ecliptic between Jries and Cancer^ and
alfo between Cancer and Ubra^ co-incides with
the Nordi Point of the Horizon ; then find, by
times in lefs, becaufe the Moon^s Orbit fometimes makes a
greater Angle with the Horizon thim TCH =t: aCr, axfd
fometimes k lefs Angle than ^CH =z iiC^» Bat for more
on this Sabjedt fee my Pbilofipbital Grammar.
1 2. Becaufe in many Cafes it is abfolutely neceflary to have
aMERiDiAN-LiNfi at hand, I fhall here fhew the bell Way
o^ making or drawing fach a one on any Plane where the
Sun can f&ne, thus. Let a ftrait Brafs-Piii of Steel- Wire AB pi^^
be fix'd upright in the Point A, On which Point ^s a Center lxVIII
you had before dcifcribfed fcveriil contentflc Circles, as CDE, p-^ -
FGH, £ffr. Now to make the Pin AB exaaiy perpendica- ^*
lar, let three Points be chofen in the outmoft Circle, as F, G,
H, in which plac^ one Foot of the Compafies, and extend
the- other to the Top of the Pin B. The Pin is to be bent
6ik6 vny and the dther^ till the faid Point of the Comjpafles
Yqu. IL G g the
466 ^e Ufa of the Globes^ ,
the Calendar on the Horizon, what Days the Sort
will enter thofc Degrees of the Ecliptic, and they
will fatisfy the Problem.
PR OB. XV. ^0 find the Place over which
the Sun is vertical^ on any given Day and
Hour:
Find the Sun's Place, and bring it to the Me-
ridian, and mark the Degree of Declination for
the given Hour^ then find thofe Places which
have the Sun in the Meridian at that Moment ;
and among them, that which paffes under the De-
gree of Declination is the Place defircd.
PR OB. XVL To find^ for any given Day
and Hour^ thofe Places wherein the Sun is
then rifing^ or fetting^ or on the Meridian ^^
alfo thofe Places which are enlightened^ and
thofe 'Ibhich are not:
Find the Place to which the Sun is vertical at
the given Time, and bring the fame to the Me-
ridian, and elevate the Pole to the Latitude of the
will fall nicely on the Middle of the Top B from each Point
of the Circle' F, G, H, and then is the Pin well adjuilcd.
13. Then obferving in the Forenoon where the Top of
the Shadow AC touches any one Circle, there make a Mark,
as at C ; and then in the Afternoon make a Mark at E, where
the Shadow's Point is in the fame Circle again. Then bifedl
the Arch CE in the Point D, through which and the central
Point A draw the Line AD, and it will be the Meridian Line
required. If this be d6ne in feveral Circles, the Operation
will be the more exa^t and certain.
Plate .14. I have here added the Figures of the Celeftial and
LXVIII. ;T€rreftrial Cflobe, with all the principal Circles and their
Fig. 4, 5 . Names, . as they are reftiiied for the Latitude of London,
. . Note, Thefe Globes are made and fold by Mr, CuJ^ee, at the
C lobe and Sun mFhft-ftrett. ' '
Pkcej
The Ufe of the Globep. 467
(Place; then all thofe Places which arc in the
Weftern Semicircle of the Horizon have the Sun
rifingy and thofe in the Eaftern Semicircle fee it
fitting:, and to thofe under the IV^eridian it is
Noon. Laftl/j all Places above the Horizon are
enlighcen'd, and all below it are in Darknefs or
Night.
PROB. XVII. ^eBaydndHourofaSolai'
or Lunar Eclipfe being given j to find all thofe
Places in which the fame will be vijible:
Find the Place to which the Sun is vertical at
the given Inftknt, and elevate the Globe to the
Latitude of the Place ; then in moft of thofe Places
above the Horizon will the Sun be vifible during
his Eclipfe; and all thofe Places below the Ho-
rizon will fee the Moon pafs^ through the Shadow
of the Earth in her Eclipfe.
PROB. XVnt The Length of a Degree being
given y to find the Number of Miles in a great
Circle of the Earthy and thence the Diameter
of the Earth:
Admit that one Degree contains 69I EnglijB
Statute Miles; then multiply 360 (the Number
of Degrees in a Great Circle) by 69-j, and the
Produdt win be 25020^ the Miles which mea-
lure the Circumference of the Earth. If this
Number be divided by 3.14165 the Quotient will
be 7s6^j% Miles, for the Diameter of the
£arth«
G g t PROHj
468 The life of the Globes.
PR OB XIX. rbe Diameter of the Earth
hein^ kHtrahtj to find the Surface in Square
Miles ^ and its Solidity in Cubic Miles:
Admit the Diameter be 7964 Miles; then
multiply the Square of the Diameter by 3. 141 6,
and the Produft will be 199250205 very near,
which are the Square Miles in the Surface of the
Earth, Again, multiply the Cube of the Dia-
meter by 0.5236, and the Produd 264466789170
will be the Number of Cubic Miles in the whole
Globe of the Earth.
PR OB. XX. To e^prefs the Velocity of the
diurnal Motion of tbt Earth:
SiNCE a Place in the Equator defcribes a Cir-
cle of 25020 Miles in I4 Hours, 'tis evident the
Velocity with which it moves is at the Rate of
1042! in one Hour, or 17-^^ Miles ^^ Minute.
iThe Velocity in any Parallel of Latitude decreafcs
in the Proportion of the Co-Sine of the Latitude
to the Radius. Thus, for the Latitude of London^
51 deg. 30 niih. fay.
As Radius — p-;. _ — 10.000000
To the Co-fine of Lat. 5 1 deg. 30 m. 9794149
So is the Velocity in the Equator, 7 ^. ^^^ ,c
,-, M. '_ ^_ 1 2.232046
17^5
To the Velocity of the City of 1
Londm^Yoiyi. - ^ ^ 2-032195
That is, the City oiLonddn moves about die Axis
of the Earth at the Rate of lo^ Miles every
Minute of Time. But this is far fliort of the Ve-
locity of the annual Motion about the' Sun; for
that
The Ufi of the Globes* 469
that is at the Rate of 60000 Miles per Hour, or
about 1000 Miles each Minute, fuppofing the
Diameter of the annual. Orbit to be 82 Millions
of Miles (CXLVIII.)
(CXLVIII) I. I might here (hew how the feveral Sphe-
ric^ Triangles are fonn*<d for the Sokicion of moll of thefe
Geographical Problems^ as I ^id before for the Afirmamcal
ones ; but as the Method is the fame, I need not again repeat
it. However, to facilitate the Ideas of the above Defini-
tions, bfr. I have added (as before mentioned) a Print of each
Globe, as they are niade with new Improvements by-
Mr. K. Cufiei in FUetftreet. The Rationale of the feveral
Methods of folving Problems of this Sort cannot be weU
fliewn without an Bye npon the Globe, and a Praxis cum w-i
nw voce of a Demonflrator.
2.1 fhall here fubjoin a few Things relating to the Magni-
tude of the Earth, and the Dimenfions of the feveral Parts,
together with the Manner of acquiring the Knowledge there-
of. Fir/l then, the moil natural, eafy, and certain Method
of doing this is, by firft nuafuring the Length ef a Degree of
-Latitude in the Meridian of any Place ; becaufe if the Mea-
fure of one P^gree be once found, the £arth being fuppofed
round, *tis plain all the other Meafiircs m^y eafily be deduced
frodi this.
3. Thus if I take the Height of the North Pole-Star in
this Place with a very good Quadrant or Sextant, and then
proceed direfUy Northward or Southward, till by the fame
Inffarunfcnt I £nd the faid Star raifed or deprefled juft one De-
gree ; then ^tis evident I muA have pafs*d over juft one De-
gree on the Earth's Surface, which therefore might be known
by adual Menfuration, were it poffible to find Aich a Part of
the^rth-s Surface as is exadUy even and fpherical, and truly
in the fame Meridian.
4. Now (his b fcarcely to be expeded any. where,, ex-
cept in fuch a Country as Holland^ which is levels and when
over-flow*d with Water, and that frozen into Ice, the icy
Surface may be near the Truth ; and a Degree meafured in
the Meridian upon this Ice muft of courfe be pretty exadt, il
due Regard be had to Refra£Uons in taking the Height of
the Pole. Thus SnelUus. actually meafured ^e Difbmce be-
tween a Tower at Leydeu and another at Soutenvode three times
over, and then a fbait Line in the Meridian on the Ice«
wrhence by a Trigonometrical Procefs he meafured a Degree #
G g 3 THgRg
470 l*he life of the Globes.
Theile is a geometrical Method of defcribing
the Superficies of the Celeftial and Terreftrial
Globe on a Plane ; and this is call'd the PrcjeSion
bat as (bme Mii^kes bad been made ifi the Calculations, the
indefatigable Mr. Mufcbenbroeck attempted the Thing anew,
and form'd Triangles upon the fdndamental Safe of SmUiuf
in the Year 170O9 and found 57033 Totfij to a Degree.
5. Now this was but 27 Toifes lefs than had been found
by the Royal Aqidemy of Paris ; and this was but little ^^
ferent from the Meafure of a Degree fome time before by
pur Countryman Norwood, which refulted from his meafuring,
' the Diflance between London and Tork, which he did in th^
Year 1635 ; and according to him the Length of a Degree
it 694 of Engiijl^ Miles.
6. Mr. Grea'ues compared the EngHJh Foot taken from the
Iron-Standard in Guild-HaU^ London, with the Standards of
divers Nations. The Proportion between fome of Uiem is
as follows :
The Englijh Foot, i.ooo
The prefent Roman Fopt^ 0.967
The Gr/cK^zff Foot, / 1.007
The Ptfw Foot, 1.068
The Leyden or Rhinland Foot, I -03 3
The Bologna Foot, 1.250
7. If the French Meafure of a Degree, *uiz, 57060 Toifei,
f}e corrected by making proper Allowances for the PreceJJum
» of the Equino^esy the Jf^erration of Light in the Stars he made
life of, and the RefraSion of Light through the Air, (all which
. iv^re negleded by Picard) the true Meafure of a Begrep at
Paris wSl be 56925,7 Toifes.
8. Now iince the &mous Coj^ni and Sir I/aac Nrwton had
both of them ihewn the Earth could not naturally have z.fphe-*
rical Fornix but muft be a Spheroid; and fince thefe great Men
differed in their Account^ of what Sort this Spheroid was, Sif
Jfaac ihewing it to be an Oblate Spheroid, and Cajffini ftrongly
contending for the Oblong Spheroid i the King of France was
nobly inclined to have this important Affair decided^ and ac-
cordingly order*d the Length of a Degree to be mecdiired at
^he Equator, and at the Polar Circle ; that by comparing them
yrith the Length of a Degree near Paris, it might be known
whether the Earth were (£long or ^at towards the Poles.
^ '9. Upon this Bufihefs he order'd two Voyages, one t» Pe-
p, .the other to the Araic Circle, The Succeis of the for-
mer is pot y^t known, thofe who m^df it not being hear^ of
The Ufe of the Globes, 471
of the Sphere in Piano : Thus, one Half of the
Globe is projedled on one Side of the Plane, and
the other Half on the other 5 and if the Plane be
till lately ; and returning in Time of War they were diiperTed^
and their Papers fuppofed to be loft or conceals as yet, for
none are to be found in the Ships that fell into Englifi Hands.
But thofe Matbematiciam who weAt Northwards finilh'd their
Deiign with great Accuracy^ and have fbce publifh*d an Ac-
count of the fame.
10. And fince a Determination of the Figure of the Earth,
^nd its Dimenfions by a^ual Menfuration^ is a Problem of
the highefl Concern in Navigation, Aftrononvf^ Geography^ Le^
welling, Hydraulicsj &c. 1 think it quite neceflary the Reader
fhould have an Idea of the Manner in which this was effeded
by the French Mathematicians, and which therefore I fhall
give from the Book entitled The Figure of the Earth deter-
mind. Sec. by Maupkrtuis.
1 1 . The arduous Tafk was perform'd in Lapland by Mef-
lieurs C/airaut, Camus, Le Monnier, Maupertuis, the Abbe Otf
thier, aijd M. Celfius of Upfal. They fat out {qx Stockholm,
and from thence for, the Bottom of the Gulph of Bothnia-
iBeing arrived at Torne^i they began their Work ; for from
thence they fat out, July 6, 1736, to reconnoitre the Coun- Plate
try, of which I have here added their Map, by which the LXIX.
AiFair is made eafy to underfbmd.
«2. After twelve Hours Voyage up the River, they c^me
to the Hamlet Korpikyla, and from thence through the Foreft
they went on Foot to the fteep Mountain Ni'uja, whofe Sum-
mit, (a bare Rock) they made their firft Station. Farther up
the River they met with another high Mountain caU'd Ava-
faxa, on the Top pf which they built a Signal, They then
went up the River Tenglio, and crofs'd a Morafs to the great
Mountain Horrilakero, where they built another '5/gW. From
hence they return'd back again, and in their Way crofs'd the
Forefl to another very fteep Mountain caird Cmtaperi, which
afforded a very fair Profpeft to all the reft.
13. After this they went fome to one Part, and fome to
another, and built Signals on the Summits of other Moun-
tains, vix. Kakama, Pullingi, Niemi, and Kiitis, near the Vil-
lage Pello. Then taking the Angles which the Vifual Rays Fig. 2,
made connefting the feveral Signals by a Quadrant of two
Feet Radius, furnifti'd with a Micrometer, they conftituted a
Heptagonal Figure TC APQN K, extending from the Tower
of the -Church of Tgrnm at T, to Kittis at Q^
G g 4 that
472 "The Ufe of the Globes.
that of the Ecliptic or Equinodlal, as in the
Cafe of the Celeftial Globe, thcfe Projcftions are
then caird the Celeftial Hemifpberes. But with
< 14. A)id becaufe the Trath of their Work may the bettef
SLppeai-^ I ihall here fet before the Reader the Sum of all th^
^ngles^ of which the feveral Angles of the Heptagon did
(ConfiJft, «i//a5.
T-
The Angle
CTK =
24 22 S4.S
CKCT =
37 9 '2
9-
The Angle TCA =:
<KCH =
100 9 56,8
<JHCA =
30 56 53.4
3-
The Anglp CAP ==
cCAH =
Ihap =
112 21 48,6
53 45 56,7
CAPH =
3« 19 55.5
4-
The Angle APQjsr
<HPN =
37 22 2,<
<jNP(i,=
87 52 24,5
S-
The Angle
PQN =
40 14 52,7
CQNP =
S» 53 4.3
<5.
The Angle QNK?=
<PNH :?=
93 5»5 7.5
^HNK =
«7 n 53.3
CNkH =
9 4« 47.7
7-
The Angle NKT =;
<HKC =
43 45 35.6
CCYLT z=i
The Sum of all.
i|8 28 12
900 1 37
15. Bat imce thp Angles of any Polygon are equal to twice
^e Number of Right Angles that the Figure has Sides, aba-
ting 4, therefore the Sum Of the Angles of a Heptagon is
1^ — ^-^z 10x90° = 900®. Hence if their lie^tagon
had been taken pn a Plane/ it woulxi have exceeded the Truth
|>ut by i' 37^' j Wt fince the Figure lay on a convex Surface,
the Sura ought to be a little more than 900®. And thence it
appears to what a furprifmg Degree of Ex^dlnefs they attained
m this Undertaking.
16. Now in order to meafure the MeriMan-Line QM,
which lay through the Middle of the Heptagon, or rather the
Line q m, which was tlie corred Dillance between the two
l^^rallels where they made t\it\x Jftronomical Obferwations with
^ Sedor, (whofe Accuracy is incredible, and of a Strudlure
|iot here to bedefcribed) I fay, in order to'm^afurc this Line
^X£i, it was nvceflary to begin with Tome Bafe Line to be firft
" : - je^^^
T%e Ufe of the GlobesJ 473
regard to the Terrcftrial Globe, they are gene-
rally made on the Plane of the General Meridsan
or Horizon^ and then they arc commonly call'd
of all meafuredy and then to compute a fundameptal Trian-
gle or two, for the Grounds of their future Work.
17. Thus they pitched on the Diflance between Nimifiy
and the Village Poiki^ for the Ba/e Une B^, becaufe it lay
^ong the River, and could be moft accurately meafured on
the Ice« It was meafured twice over» and
Toifit. Feet. In.
The firft Menfuration gare " 7406 5 o
Thefecond — ^ — - *— 7406 5 4
The mean Length therefore is — 7406 5 2
18. Havmg this Bafe Line known, they calculated the
two Triangles A B^ and ABC» from which they found the
Diflance t)etwe^n Jvafaxa and Cuitaferi to be 8659,94 =1
AC^ from whence they proceeded to find the Sides and An-
gles of all the other Trifingles round the Figure, as AHC,
A HP, PQN, CTK, fcff. and from thence having found
the Sides AP, PQ^ NK, KT, TC, they form'd the Right-
angled Triangles AEP, AFC, PDQ, CGM, by drawing
£F, GC, PD, at Right Angles to thel'arallels paffing thro*
Qand M, and parallel to the Meridian Line QM ; and the
fame they did on the other Side the Figure, as is there re-
prefented.
19. Having thus meafured the feyeral Lines^ they were
found as follows.
PD == 9350,45 On the other Side,
A£ = 14213,24 Nd = 13297,8s
AF = 8566,08 lLLz=L 24995,83
CG =: 22810,62 Kg = 16651,05
Total, 54940,39 •'-^— — • 54944^76
5494o,39
Therefore at a Mean the Meridian Line is QM = 54942,57
2q. By very accurate Methods they deduced the Length
of the Line qm 1= 55020,09 Toifes, and the ftillmore cor-
f e£b Diflance q u = 5 502 5,47. But this Diftance or Arch qu,
by the niceft Afh-onomical Obfervations and Corrections, was
JFound to be equal to 57^ 28^,67 ^^ ^ Degree. Therefore^
As 57' 28^,67 is to 55023,47 Toifes, fo is 60^, or i Degree,
|o 57f 37>9 Toifes in one Degree at the JxSic Cirde.
4-74 ^^ ^ ^f ^^^ Globes.
Maps of the World: And-the fevcral Circles, ancj
Parts of the Surface of one Hemifphcre, are fo
delineated on the faid Plane, as they would ap-
21 . If therefore from the Length of a Degree here, nna.
^t the jfrSic Cirde, — — 57437>9
you fubdua the. Length of a Degree at? ^^^^^ ^
Paris, hyPicard. —1 ^5^9^
the Difference will be — 512,2 Toifes^
Qr 3282,878 Feet of Englifi Meafure.
22. Hence, having the Length of a Degree, the Radios
of Curvature is found for any Part of the Elliptic Meridian.
Fqr let ft denote that Radius, then it is 3,1416 : i ::
366 : 2R :; 180 : Ri therefore R = -, or R ==
3tHi6
^8ox 57437>? ^oifes, for the Curvature of the Earth's Sur-
3,1416
face in the Latitude 66^ zd at Lapland \ and in Prance the
Radius of the Earth's Curvature is iR = '^Q^S69^5>7
3,1416
Toifes ; or in EngUfi Miles thofe Radii are R = 39949 and
^=3958,4..
23. We are now prepared to affign the Proportion of the
Axis of the Earth to the Diameter of the Equator from this
aAual Menfuration ; in order to which we mull firfl of all
premife fome Theorems^ which refult from the Properties of
Plate ^^ Ellipfe. Therefore let EP^ denote the Elliptic Surface
LXVIII ^^ ^^^ Earth, E^ the Diameter of the Equator, and CP th^
' Semi-axis of the Earth. Let A I be the Radius of Curva-
ture to any Point I of the Ellipfis, IF a Tangent % and draw
HI and ID perpendicular to CP and CE. Take the Arch
I/= I Degree, and draw At and the Perpendicular id i
there A is the Center of a Circle touching the Ellipfis in the
Points I, i. The Angle lBE=:DIFisthe Latitufle of the
Place L Now put z = CE, » = CP, ;r = CD = HJ^
jr = DI ; and let i, /, j, denote the Radius, Tangent, anq
Secant of the Angle IBD; and lafUy, let AI = r.
t\g. 6.
Zj^. Therefore
I
/^ -f- 1 = J*, and fo /* — J* = I. Theer.
l.et
2
«* : «* 2; i:a, V ^ = a. Theor. 11.
Hence —
3
— z=z azz=zp^ the Parameter. TJbe$r, 111.
4
I :s::y:l¥:=^sj. 7kor.IV.^
pe
ar
The Ufa of the Globes, 475
pear thereon to an Eye placed in the Pole, or
imiddle Point, oT the other Hcmifphere. Hence
it will come tq pafs, .that the Stars and Conftel-
Alfo
And
And
Then per Conic f
That is,
Alfo becaufe
That is.
We have
Therefore (9)
Pence —
And alfo
Since (14}
Wherefore
Whence alfo
therefore alfo
Becaufe
Thcref. Conv.
Whence
Alfo we have
Wh. conjointly
Again —
Conv. and Inv.
In Species
Thatjs,
Whence(i5,i8)
^hence alfo
S I :t ::y:DF z=:tj. Tbeor. V.
6/: i::IF = /;:IB = ^. Tbior. Vh
7 / : I :: J : DB = i. Tbeor. VII.
8 ED X D^ : DI* :: CE» : CP\
9 «J5 — XX :yy :: zx : uu :: i : a. 7beor. VIJI. .
10 CD : CE :: CE : CF, per Conies,
11 X '. % 11 % \ X •\' tjj
12 »z = J)f* -|-'J'^» ®^ z* — ;r* = tyx.
13 I I a II tyx ly* :: tx \ y>
yzizatx, OT X ^ — . Tbeor, IX.
^ at
ax = L — DB. Tbior.X.
t
l6U z=i at x» V g* = ;ip* + xty = jt* rf- at'^ x*.
17 «*=;&* XI +att, \'%z=.x\^l+att, Tb.Xl.
i8;p* = — ? , V;r = -:=:^=:. 7*«r. XII.
9y =
i + atf
atz
Vi +att
Tbeor. XIII.
i/i 4- att
DC : DB :: x : ax :: i :a :: g* : «».
CD:CB:: i : i — « :: Ci/: C^.
D^(=^I):B*:: i : i—a.
GI : gl :: BF : DF, becaufe IGi : FBJ.
GI:B*:: BF:DF— iiDF.
GI : Bb :: AI : AB :: BF : DF— «DF.
IB : AI :: BD + iiDF : BF = BD + DR
iI:r::L^atj:L + ,y,
i+tf// : I +// =
t
s^y s^ax
U.
t+at^
i + att i,+ tf//l
n. XIV.
rx !+«''* J r*xi+«// ^
XV.
lations
476 ^e Ufe of the Globes*
lations of the Hcmifpheres, and the Paita of
Land and Water in the Maps, arc not reprefentr-
cd in their natural and juft Diftances, and in their
Therefore
Wtcnpc alfo
For^yother7
Lat. we have i
Whence it is
Therefore lafi!/ 35
3«
32
33
34
^7 I. ^7 ,
+ r^ate
ti =
Thear.TLVI.
tfTjBT-^tfrT
r^xi+att r*xi+«tt
zz = jr-lr =:
^a'
r"y 83 -|- r^attss = t^ss + t^attss.
-r-* ss
T-i&fiv. XVIIL
r7//8s — nrttj/
2;. From thefe Theorems we can calculate whatever re-
lates to the Figure and Magnitude 0/ the £arch ; and firft to
determine the Value of a, or the Ratio of x* to n*, that is,
of CE to CP. In order to this, we have r, /, t^ for the La-
titude 66'^ 20' at Laplandi and r, s, t, for the Latitude of
49^ 22', being the Middle of the Degree meafured in France,
(See Jrt, zz.) For having r == 3994, and r := 3958,4;
% a
whence by Logarithms we have r^ ss = 593,6, and x^ss =:
1552^9; alfo r^//8s =:: 3090,1, and i^tlss = 2io9»
Therefore a = 5|2!i=:* Whence we get a : « ::
313,22 : 309,72 :: CE : CP, Therefore by Menfuration it
appears, that CE exceeds CP in a greater Proportion than
that of 230 to 229, as was obferved in the Scholium of Jn-
npt. XXXIV.
26. Hence we have jczz CE
— rp — !L?LLi^
(by Lo-
garithms) equal to 3971,1 Miles; and.fo the t)iameter of
the Equator is equal to 7942,2 Miles. Whence, becaufe
-^rztf, uz:i »i/ a z=: CP = 3926,2 Miles; and fo the
Axis of the Earth is equal to 7852,4 Miles; fo that the
Equatoral Diameter exceeds the Axis by 89,8 or 90 Mil^^
«lU5
The Ufe of the Globes. 477
due Magnitddes ahd Forms, as on the Globes
themfelves: Yet moft of the Problems of cither
which is near tfirce* times as much as tl^e Theoiy gaTC U.
See Jnnot. XXXIV. 36.
27. In any given ^Latitade the Radios of Curvature ia
found by rbnnm XIV, idz. r = "" "^ ^ j and, becaufe
I + atti
under the Pole P the Angle IB E is a Right one, / and / will
in that Cafe become infinite and equal ; and therefore r ^
as
•j^ = 4016,6 Miles, which is the greateft of all; And
under the Equator that Angle vanifhes, and there /= i, and
/=:o5 and:for = ^z = 3881,8 Miles, theleaftofalL
28. The Radius of Convexity being known, we find the
Length of a Degree in any Latitude by this Analogy j As
180 r 3,1416 :: r : ~^ = the Length oi the Degree
jfe^uired. Thus under the Equator we have hlAl^ ^
180
3881,8 == 67^ Miles, for the leaft Degree; and under the
Pole we have ^*|^^ x 4016,6 = 70t\j Miles, for die
greateft Degree of Latitude : A man Degree therefore h
68^92 Miles. Thus alfo a Degree in the Latitude 49® 22^
is '^g^ X 3858,4 = 69,087 Miles; and in the Latitude
66* 20' it is ^''^' X 3994,1 = 69,709 Miles.
I oO
29. If. the Length of a Degree be known, the Radin8.(^
Convexity may be determined, and thence the Latitude of
» a
the Place by Tbeor. XVII. // =z ^'^ — ^'^^'^ fo, jf ^
I Tangent of an Angle be known, the Angle itfelf, that is,
1 . the Latitude, is known alfo.
I 30. Hence alfo the Radius of any Parallel of Latitude may
! be difcover'd; for, by Theorem XII, HI=:CD = ;r =
[ «
• jL ' and 180 : 3,1416 :: * : a Degree of Longitude
fa the given ParaUcl. In the Equator ;r=Kj hence 1^^^
180
Globe
478 7he Ufe of the Globes.
Globe are performable on thefe artificial Pro-
^ 3971,1 = 69,309 Miles^ tKe Length of a Degree in the
Eqaator.
3 1 . Hence the Circamfeieiice of the Earth under the Equa-
tor is 360 X 69,309 = 24951 Miles. I mi^t now proceed
to csdcidate the Sur^ce and Solidity of the Earth as^a Sphe-
roid ; but the Prooefs would be tedious, sind anfwer no great
I'nrpofe, enou^ having been faid for 'any Perfon to form a
proper Idea of the Magnitude and Figure of the Earth. I
conclude widi obibrving, that there is aooiit 2\ Miles between
the greatefl arid leaft Degree of Latitude within the Compafs .
of our oomsBon .Charts : Sij^n then. If our ^hnrj rf Nmn-
Ration y founded upon an Hypotbefis of their being all equal, be not
Hfery errmuom ; And ^ it be not nec^fj to bave erie ^fre^ed
dcterdit^ to tbefbregoing Meafurei ?
Scholium. '
3^2. Sinte writing the above, I have met with a Trcatife
on this SdbjeA by the Reverend Mr. MvaDocH, who haa
determined the Terrefb-ial Spheroid nearly the fame as above ;
tht DifEereoce between the Square of the Seraidiameter of the
Equator and Semiaxis being by his Calculation 22, and by
mine 21,6 (Art^ £5.) And as he has giren ns a TtU^of the
Degrees in the Quadrantal Arch of tl^ Meridian both in the
Sphere and Spheroid, with their Diferehces, I have here inr*
lerced it lor the Beader^s Satis^t&ioa and Curioiity. .
33. AT htv^^'of Arcs ff ibe MeriiRan to the Spbemd,
in Minutes of the Equator •
D.
Spheroid.
Sphere,
Diff.
p.
Spbertid.
Sphere.
Dif.
I
.58-7
. 60,0
1-3
12
704.5
720.0
»5r5
z
U7-3
120.0
2.7
«3
763-3
780.0
16.71
3
176.0
. 180.0
4.0
M
822..I
840.0
;7-9.
4
234-7
240.0
S-3
is
»6
880.9
900.0
19.1'
5
293-4
300.0
6.6
939-7
960.0
20.5
6
3S2I
360.0
79
17
998.5
1020.0.
2i»$:
7
410.8
4ZO.0
5*
18
1057.4
1080.0
22>6
8
469.6
480.0
to.4
>9
1116.3
1140.0
23.7
9
52-8.3
540.0 .
11.7
2P
1175,2,
1 30O.O
24.8 •
lO
587.0
600.0
13.0
21
1234.1
1260.0
25.9
II
645.8
. 660.0 '
14.2
22
1295.0
1320.0
27-.0
jedtions^
The Ufe of the Globes. 479
jeftions, by thofe who underftand their Nature
D.
Spheroid.
Sphere,
Diff,
Z).
57
Spheroid,
Spberi.
Diff.
23
^1352.0
1380.0
28.0
29.0
3370.0
3420.0
45.0
24
141 1,0
1440:0
58
3435-1
3480.0
44-9
^5
14.70.0
1500.0
30.0'
59
3495-2.! 35400
44.8
26
1529.0
1560.0
31.0
60
3555-3
3600.0
44-7
27
1588.I
1620.0
31.9
61
3615.5
36^0.0
+4-5
28
1647.2
1680.0
32,8
62
3675-7
3720.0
44-3
29
3>
1706.3
1740.0
33-7
^>3
3736.0
3780.0
44.0
43-8
1765.5
1800.0
34.5
^•4
3796.2
3840.0
1824.7
i860 0
35?
■
65
3856.5
3900.0
43-5
32
1883.5
1920 0
36.-I
66
3916.8
3960.0
43-2
33
1943. 1
1980.0
36.9
67
3977.2
4020.0
42.8
34
2062.4
2040.0
37.6
68
4037-5
4080.0
4*5
35
2061.7
2100.0
38.3
89
4097.9
4140.0
42.1
36
2i2i.e
2160.0
39'0
70
4158.4
4200.0
41.6
37
2180.4
2220.0
39.6
71
4218.8
4260.0
41.2
38
39
2239.8
2280.0
40.2
72
4279-3
4320.0
40.7
2299.2
2340.0
40.8
73
4339.8
4380.0
40.2
4c
2358.7
2400.0
4'. 3
7^
4400.3 1 4440.0
39-7
4'
42
43
44
45
46
47
48
49
5£
2418.2
2460 0
41.8
7S
4460,8 1 4500.0
39.2
2477.7'
2520.0
42.3
42.7
76
4521.3 1 4560.0
38.7
2537.3
2580.0
71
4581.9 1 4620.0
38.1
2596.8
2640 0
43.2
78
4642.5 1 4680.0
37-S
2656,6
^700.0
43.4
79
4703.' ! 4740.0
36.9
2716.4
2760.0
43.6
80
4763.7 ; 48fX5.o
36.3
2776.2
2820.0
43.8
81
4824.3 1 48^0.0
35-7
28359
2880.0
44.1
82
4884.9
4920.0
35-'
2895.5
2940.0
44-5
83
4945-5
4980.0
34-5
2955-3
3000.0 44.7
84
5006.2
5040.0
33-8
3015.2
3060.0 144 8
85
506 c;. 8
5100.0
33.2
52
ii
54
55
*6
3075-0
3120.0 I44.0
86
<;i27.5
5160.0
325
3«35-o
3180 0 I45.0
87
5188.2
5220.0
3. .8
31.2
3.! 94.9
3240.0 I45.1
88
5248.8
5280.0
3254.9
3300.0 J45.1
89
53095
53400
30.5
33H-9
3360.0 45.1
90
5370.2
5400.0
29.8
anc
480 The life of the Globes.
and Uie. But thefe Tliii^ will be beft undef^
flood from a View of thofe Prints, and a Speci-
men of the Praxb of their Ufe (CXLDC).
{CXiiX) I. The Solotion of moft of diefe Gbogra-
^HiCAL Problems may be peiform'd by a Trigmnutriad
CalcmlatioUf as is evident from the oi^inal Diagnmi we be-
fore made ufe of for the Sdudon of J/rmnmU^ Prwbiemi,
Thus if A and Z be any two Places on the Surface of the
Globe, then in the Triangle A ZN we have
Plate ZN the Ca-Latitude of the Race Z.
LXVIII. AN the Co-Latitude of the Place A.
Fig. I* Z A the Diftame of the Places A and Z from one ano-
ther.
ZN A the Differtnee pf UngUudi.
AZN the Angle of Pofition, or Biothg of A from Z.
Z A N the Angle of Pofiticm, or Biarmg of Z from A.
2, After the fame manner may Problems of Navigation
be folved; and iddeed the only true and natural Way pf
Sailing is upon the Jrcb of a Great Grcle, which gives the
iieareil Diflance between any two Places on the Surface of
the Globe ; and therefore the nearer a Ship keeps to the Atcti
of a Great Circle, the fhorter will her Way or PaHage be
from one Place to another. Thus in the fame Triangle
ZN A, if it be propofed to fail from Z to A, the Ship oug&t .
to be direded upon the Arch ZA. But in order to be ac-
qnaintjcd with this Methdd of Sailing,- the Doflrine of the
Sphere muft be well linderftood ; therefbre I (hall refer the
Reader who defires it, to Vol. II. of my Tou/ig ^rigmometer^s
Guide.
, 3. However, I (hall here fubjoin the Pbiiofipbical Princi-
ples of all Kinds of Geographical and Nauticad Maps and
Ch aUts : And firft I ihjdl diew the Nature of what is caird
the Orthocra/phic Projection, of the Sphere. Let
Pig. 7. ABD^bc the Primitive Circle, or Plane of the ProjedUoh,
which we may fuppofe to be a Meridian; and let AED be
a Great Circle elevated above the Plane in any Angle B A £.
Suppofe this Circle to be projedled On the Plane into the
Curve A F D, by Perpendiculars paffing through every Point
thereof; it is required to find the Nature of the projedled
Curve AFD.
4. In order, to this^ let EF and IG be two Perpendica-
lars ; draw GI parallel to C£, and HI parallel to CF, and
Gg to CI; and from g let fall the Perpendicular ;g/&; then
fi the Right-angled Trianglei G H I equal and fimilar to gbQi
and
TZtf Ufe of the Globes. ^i
^ gJ^Q, iSr fiinilar to BFC. Vfhsn&xtt ,piitting AC =
EC±i4r, CI=i;r, 01=;^; CF=?^, an<Lftl = y; then
by the Property of tic Circle we have. A t x I D = G I*,
lliati», jrjr = a«-H.;ri, andjr^: •a^ — ;r*a=Gl5 but
GI : HI :: (^C : ifrC ::) EC : »G, that «, yiy ixai ij.
^efprc y= -j2! 5= ^i/a^^tc'', wiuchihcwstbcCojnre
a " a
AF Dto be^an EUh/t, whpfe Semi- axes are AC and C P.
, .c« Hence the Circles of a Sphere viewM at an infinite^
CiftariQB are prcnefted into ilR^s, Thus the Grcle if Iltu-^
mnailojum |he Diik of the Moon is an ElU^fis^ as obferved
Amot,^ CXX^. 23. Thus alfo a Sphere (et in the Snn*
Seams will have its Circles all projected iiito elliptic Sha-
dows. And hence it is we conftniA the Oaf h oca A phi d
l^RdjECTioN, call'd the Analemma; which fee in my
forc-^iced Book.
:^.^/Now bccarfe CE : CF :: Radius : Co-fme of ECF,,
It. appears that the Semidiameter CE of eveiy Circle is pro-'
jeif^ed into the C^-fine F C of its Elevation above the Plane'
of ProjipifUbn. Hence alfo it appears, that in this Projediod
the fame Number of Degrees m a Right Circle, as B C &^
wiU be projected into very different Portions of the Diamete^
of the Plane BE. Thus 10 Degrees from the Pole 6f th^
t^irimitive will be |>rojeded into th^ ArchCK, but id De-
grees froin the Periphery will be projefted info E M. But
CK is to EM as the ^ghi Sine of io Degrees to the Verfei
Sine of the fame; that is,, as 1)^36 to 152, or nearly as I2
to I. Hence the Reafon why the S|$ots in th^Sun appear to
move fo much faller over the middle Pafts of the Di(k
ihan on the Ouciide, and why thdif-' Motion is always une*
^ual i with other Phenomena of the like Nature. -
7. TheSTEREpoRAPHic Projection of tHe S^iierM Pi. LXJi.*
is that on which ouir Maps are commonly made; and depends Fig. i »
on this Principle, That if the Plane of any Meridian te fup-
pofed the Plane of the Projedlioii, then in Eye fdaced in one
Pole of that Meridian will project afl the' Circles in the oppo-
site Hemifphere into circular Arches on the faid Plane. Th^s
let A ODE be any Meridian; then the Diameter AD, di-
viding it into the upper and nether l)emi(phere, is caird the
tine of Meafures ; and an Eye plated at the Pole E will pro-
je£t every Point B, F, G, in tHe oppofite Stmicirile into the
Points H, I, C, into the Line of Meafures AD, by the Vifuif
RaysEB, EF, EG.
8. Hence if the Arch AB == FG ±z 10 Degrees, thea
will their Reprefentatives in the I^ine of Meafures 1^ A H znS
Vdt.ll. HK tC|'
482 7h Ufe of theGto^t%^
rCs anil the Pdiit^ Hand I are tiidfe t^oitigh whkki^^^
des of to Degrees and of 80 Degreed io Sft in Prdje^iob/
^i%, die Circles GHE and GIE» a» is evidKhtfrdtt^ c^iUMei:^
ift{ the Figum. Hence the Reafin wky. rite Menditis ifo aft
Ue liiearef tp eack other in ^ middle Pkh^ t)£ t>eMaf> tfisti^
on the Outfides ; and confrgnrnrly, ^hy ther feveral Parts of
idit Earth cannot be duly ^epreTenci^dnoitludr Wb^ eifehei^ irf
jefpad ^ Ma^tude or Polition.
, 9. Oh E as a Center deicribe the. Aix^H CW; aWl drat^^
the line E K s the Arch G K wia 1>6 proj^fted Into th^ I^
CL,, which is the Tangent of the. Angle CBL. feufth'tf
Angle CEL is equal to Half the Ahgle <jfQ%^ m Ardi
GK; therefore any Arch GK is prdjefted* hito a Lfne' CL
equal to the Tangent of Half that Ar6h. i)encd the'Llne
CD \& caird the lane of Ha//'Ta»ge«tsi^Tef^€&.6f the Qua-
drant GKD. . ' . •
104 On this Projeftion ^re uCoally n^ade aiD tire Map$ of
Ae W^rld in two Hemffphcrts 5 there is klfo aftqlft'eV ckll'd
the Globular pR.QJECTioN', wherein all the Meridians
are equally diHant, as they are on the Gldbe itfetf. ^hey
are circular Arches her^» as in the liail Pro]ed1'oti» atfd are
^rawn after the fame manner, but are not prOje£ted by thd
l^ye on the Surface a« they are. By this Sort of Maps th6
feveral Parts of the Earth have their proper Propoftibil t>(
Magnitude, DiAance, and Situation afllgn'^d nearly as 0n th6
Globe itfelf. As this Sort of Map is for that Reafon very
Plate, ufeful, and not common, I have given one here for the Rea»-
LXXIV. d^r's Ufe, corredfcd from the lateff Obfervitions.
. II. Befides the foregoing, there is another very ufeful fro-
jeftion, generally made ufe of for Charts, Ind foniethnes fot
Maps ; it goes by the Name of Merc a tor's Proj ECTioif,^
. but was firft invented by Mr. WrMt long before. In this the
Meridians and Parallels are flrait Lines, and the former equi^
diHant from each other. Hence in tSis Way the 0egrees of
liOngitude in every Parallel are the fame, and equal to tfaof^
ih the Equator ; alfo the Degrees of Latitude are all mie-
qual ; both which are contrary to what they are on the Globe.
Therefore Maps of this Sort do not exhibit the true DUnen-
fions or Proportions of the feveral Parts of the Earth ; how-
ever, they are very ufeful on divers Accounts ; and that which
I have given from Dr. Halhy to illudrate the Account of the
Winds is of this Kind.
iz. But the greatefl Ufe of this Projedlion is in Sailikg ;
TO T YY I^ll therefore (hew how it is conflrufted in the following
«. LAX. j^anner. Let A B be an Arch of the Equator contaiii^d be-
'*g- 2. i^^jj jyjy ^^^ Meridians AP^ BP, meeting in the Po^b P of
the
The l/fi vf the Glqses. 4-S j
£Ke Sphere, wk>fe Center i$ C. U^ the Pbinu A and ft
Itt thert be ereaed the ^erpdidkulan AH ^ BI^ asd ItC
Ji> E r^ieftnt an Arch 6f anjr Parailei between €iitt (kme Me<
ndianai rfraiv CA and CB, KD and K£ perpindicailar t6
PC; tliMdgk Daiid£ dxaw CP, CG, JAd jok FGj kft-
]y, let fall the Perpendicular t)L.
15- Now the Ardi Afi in tlie Eqdatoir h to the fimOaf
Ardi of the Farillel D£ a* AC to DK» or a$ Jtadius to.tfae
Co-fiae of the Latitode A D. Soppofe now . the Meridian^
AP, BP« to be ia part projeded inco the Ptrflendiculan AH
and BI; tlhea wHl cfae Arch DE be prc^efttd into PG =;
AB ; Iwt in thb Cafe D£, th natural Length tftht Arth^ k
io "BG its frotr4aed Umih, as ihi RmBus CD U the Secam
€:F»/.aeLatiiiidi, or Z ^he Co-fiu hQ to tht J^^iFidrCDl
iot GF : (CD =:) AC .t DC : LC.
\^ Bat in whsbtevsr Proportion die Degrees of any Pa-
iaillel ate increafed or dimmiihed by a ProjaAiOn in iVa«#» ki
the fame Ratio ought the Degrees of Latitude alfo to be ia^
isreaftd <6r dia^n^ed 1 otherwsTe «he tf^ ^Hiring tini Di-
Jlances oiVhiCti would be loft, as in the Cafe of the Plain
^art^ where th<J Degrees 6f Latitude are all equal, ne
Ptgrees, therefore, of Lat^ff/de in Mercator*/ Chart incnafe in.
Trtfor^vshrf iht Spcant 0^ the Latiti^ to the lUJius. . .
15. But. that the .Reader may fee hew (itth.a Meridian is p|^ LXXi
prpje£lt3, let ft CH be a Quadrant of the Primitive Circle, pjL -'
Ind RQ^a Dikmeter ; dr^Cw QS ; then will the Arch SH be ^' ^*
|>n)jea)?d ilit6HI» and RS inco AI| bat A I is the Tangent
of I RS (by Art. 9.) Let ST and CI be perpendicular to
'AH, ibd *aw the TaAgents S V, C K, to the Points S and
C, meeting AH produced in V and K. And let HI r= x,
HS±='«j, andAp^T.
, 16. Then becanfe AT : AH n AH : AV, it is AT x
A V cit AH* 5' for the fame fceafon it is AI x A K == A H*
^"KT % A V. Whereibrc A V : A K :: AI : AT (= SB)'
J: QJ : QS. Let Qj be drawn infinitely near to QS, then
?iri2:4, and li)c±x^ and hccaufe the Angle A^Qjr;
"IS = ISV = QjS, therefore the Triangles QJ/ and
^xare (In their nafcent State) fimilar, and theipcfore QJ -^
@ :t Ii : Si :: AT : « :: AV : AK; confequcnfly, it b
7i V X '« = A K X *•.
17. JBut AK X ;Ir is tlie Fliaionary Reaangle of what is
t^m^i k Yigure of Secants, which inay be thus explained. Let fig /
It Cfcr t^ a Quadrant as before, H C an Arch, of which let
cH^ Setatit be equal to IN, rightly applied as an Ordinate to
(he j^feifs VLl^izjei and if this be conceived to be done
?</r kfiif Pdrit In fhe Quadrant, we ftall have a Curve BN P .
Hi* 2 fiefcriBidf
484 TbeUfe of the GLOBfisl
Jefcnbed by the Point N, which appears to be a r$Qa0gdii^
Hypirbola by compleating the Square A B. Now drawing * »
infinitely near IN, we ihall have IN xinzzzlNxx (=
AKxx)z=: Fluxion of the Area IHBN, which is com-
poTcd of all the Secants belonging to the Arch HC, and is
therefore call*d a Rgurs of Sicants.
i8. Now the Fluxion of the Area IHBN is to the Fluxion
of (be Reftangle IHBD as IN x ;Kr to ID x x, that is, as
IN to I D =5 AR. vhc. as the Secant to the Radius. There-
ibre the Areas thein&lvcs are in the iame- Ratio ; that is, the
Area IHB : R x ;r :: S : R :: Z : «, fuppofing Z reprefents
the Arch z protraded. In the fame numner it is fhewn,
that the Fluent or Area belonging to the Fluxion A V x % is
to R X se as Z : js ; but this latter Fluent of A V xxis equal
to the Area IHBN, becaufe their Fkixions are equal (by
j^/. 1^6.) Therefore IHBN : R x ss :: Z : k; confequent-
]y, IHBNxJS = RxKxZ> whence IHBN = Z when
R=i-
19. But the hyperbolical Area I NBH is the Logarithm or
Mcafure of the Ratio of AH to AI, that is, of -.^ =
I — ;r
»-, ii^pofing / 5= Tangjent of i the Gonplement of. 0.
But any Hyperbofical Logarithm is to the Tabular Logarithm
of the fame Ratio; as 2,302585, (*fc, to i ; therefore the
Tabular Logarithm of -^ x 2,3025.85 =INBH = Z gives
the Length of the protrafled Meridional Arch, anfwering to
the Natural Arch z or HS.
20. Therefore, if A and a denote a Greato' and a Leffer
Arch, beginning from the Equator ; then the Length of their
Difference A -, « will be H^ - hEllh^ 6t
2,^o2$Ssx — ——,OT 2,302585 X /— T. That is.
From tbi Tabular Logaritbm of i tbe Complement of tbe Lejffer
Arcb a, fuhdaS tbai of tbe Greater Arch A ; tbe Differenct
multiplied iy 2,302585 nvill give tbe Meridional Parts of tie
4rcb h — a,
21. As I am upon a SubjeA of this Nature, it will be pros-
per to obferve, that iince the Ship^s Courfe is or ought to b^
upon a Rhun^'Une, which makes equal Angles with every
Meridian, therefore the Differences of Longitude will be the
),ogarithma of the Tangents of the Half-Complements of the
Latitudeei;
The Ufe of the Globes. 485
Latitudes, as may be thus ihewn. Let i£Q^be a Qnadfaot p] lXX.
of the Equator, P the Pole of the World ; ?&, PA, PB, pjg 5.
l^c. the ieveral Meridians preceded in Phmo, and JEabc^ Sec,
a Rhumb-Line making equal Angles iEaA, MbB, &c. with
every Meridian.
22. Then if we make Mk = AB = BC, Vc and veiy
fmall, then may the Triangles M?a^ M?h, MFc, &e. h6^
tfteem'd re^ineal, and will be fimibr ; and therefore ^P :
Fa :; ?a : ?6 :: P^ : Pr, and fo on. Now if iE A ex-
pound the Ratio of «P to iSP, then becaafe the Ratio of
^P to ?M is double the Ratio of a? to Pi£, and MB ==
2i£ A, therefore ^B wiU expound the Ratio of h? to MP.
.Again, becaufe c? : M? = $ x a? : MP, and MCz=z
SMA, therefore MC expounds the Ratio of rP to ^P;
and fo of the reft.
23. Therefore the Arches uE A, MB, MC, tfr. are the
Logarithms of aP, iP, cP, (ffc. in refpeft of PM. But
^ A, MB, i^c. are the Differences of Longitude made in
failing from M to a, or b, &c. ; and dP, bP, £Jfr. are Tan-
gents of half the Complements of the Latitudes Aa, Bb, 8x.
(See jirt, 9.) Tbere/sre tbi Dtffermeet if Longitude infmiing on
any Rbumb are the Legarithm of the Tangemis of the naif-
Co'Latittides.
24. Hence the Rhumb-Line has acquired the Name of the
Logarithmic Spiral. Hence alfo it follows, that any table of
Logarithmic Tangents is a Scale of the Differences of Longitude
onfome Rhumb or other. Thus the Tabular Logarithms of
Tangents in prefent Ufe are Differences of Longitude on
that Rhumb which makes an Angle of 51^ 38' 9^; and the
Rhumb which makes an Angle of 71^ 1' 42^, is, the fame
for Neper^^ Logarithmic Tangents. They who would fee the
Demonfb-ation of this, as alfo how a Table of Meridional
Parts is from hence conibruded, and Ukewife how all the
Problems of Navigation may be folved by the commop Ta-
ble of Logarithmic Tangents only, may cqnfult my Log a-
RrTHMOLOGi A. See alfo Philofo^cal Tranfa^ions^ N^ 2 19,
where the Theory is given at hirge by its Inventor D>. Halley.
Scholium.
25. I have here added a Table of Meridional Parts, cal-
culated for the ObUte Spheroid by the Rev. Mr. Murdoch, in
his new and learned Treatife of Mercators Sailing applied t9,
the true Figure of the Earth, By this the Reader will be en-
abled to projed a true Chart for any Part of the £arth*s
Surface^ and to folve thereby the feveral Problems of Sa\liip|g ^
Hh 3 €^
^4-86 STA* Uje of th Globr^
to ckltneate Maps of Coimtrtet, and to appljr tlMtn fisr va-
rious other Purpofes of Narvigatim, Geograp^j and Afirm-
mf. Not are the Errors of the comm^ Spherical Projeakma
ib very finall in many Car<^»' as to be inconiidenible and n6|
dangerous. . For Infiance/ if i, Ship f^s from Sovth Latitnddr
"t^"* to North Latitude )o% and t&e Angle of the Cour(h be
43^ J tlien the Difference of Longimde by the common Tii-
ble would be 3206^, exceeding the true JDi^ence 3 141 1^
65' or Miles. Alfo the Diftance fyird would be 4512, eic-
oeeding the true Dtliance 4423, by '^9' or Miles: WhtcJi
Piffeiences are too great to be negle^ed. For other In*
fiances offqchaConedionof the Charts, I rthi to the Att-
thorns admirable Book above niefttioD*d. (Ste Schql. i4
A«4/.CXLVUI,)
27. A Table of Mm^ianal Parts to tU Sphmd 01^
Spbire^ nvitb their Digerencis.
p.
Sfnroid
Sfitr*.
Dig.
D.
Spbtrnd.
Spbirt.
Dtff.
I
S8.7
60.0
'«-3
22
13*5-3
•353-7
28.4-
2
1 17.3
1200
2-7
23
1389.0
1418.6
39.6
3
176.1
1 80. 1
4.0
24
?453-3
1 484. 1
30.8
4
234.9
240.3
S-3
«5
1518.0
1550^
33.0
1;
293.8
300.4
6.6
26
',583-3
1616.5
3?-2
6
35^.7
360.6
7-9
?7
1 649. 1
1683:5
34-4
7
411.8
4S1.0
9.2
s8
1715,6
T7JI.3
35.6.
8
471.0
481.5
lO.f
*9
.782.7
1819.^
36.8
9
530:4
542.2
11.^
30
1850.5
1888.4
37-9-
10
J89.9
603.0
«3-'
3'
1919.0
1958.0
39.0
41
649-7
664,.!
14.4
32
1988.2
2028.3
40.1
12
709.6
725-3
^S-7
33
2058.3
2099.5
41.2.
»3
7698
780.8
17.0
34
2129.0
2171.4
43.3
14
830.2
848.S.
18.3
35
2200,8
2244.2
43-4
'5
890.9
910.5
19.6
36
2273.4
2317.9
44-5
16
95«.8
97*-7
20.9
37
2347.0
2392.6
45.6
'7
1013.1
1035.3
32.2
38
2421.6
2468.3
46.7
18
1074.8
1098.3
23.5
39
2497.2
2544-9
47-7
«SI
M36.?
ti6i.6
24.8
40J 3573-9
2622.6
48.7
2C
H99.2
1235.2
36.0
4ij 2651.8
2701.5
49-7
21
1262.0
1289.2
27.2
«-«
|4'<! [-2730.9
2781.6
50-7 1
77>e Ufe of the Globes.
487
D.
Spheroid.
Sphere.
Diff.
z>.
68
69
SpberoiJ,
Sphere.
Diff,
43
2811.3
2863.0
S'-7
5403.9
547.40
70.1
44
2893.1
2945.8
52-7
5560.2
5.630.8
70.6
45
2976.2
3029.9
53-7
5723-5
5794-6
7^1
46
3060.9
3"S 5
54-6
7c
7>
5894.4
5965.9
7^'S
47
3147.2
3202.7
55-5
6073.7
6145.6
71.9
48
3235.>
3*9«-5
56-4
72
6262.4
6334.7
72.3
49
3324.8
3382.1
57-3
73
6461.6
65343
72.7
SO
3416.3
3474-5
58.2
7^
6672.6
6745-7
73-»
5»
3509.7
3568.8
59-'
75
6896.8
6970.3
73-5
52
3605.3
3665.2
59-9
77
78
7136.2
7210.0
73.8
S3
3703.1
3763.8
60.7
7393.0
7467.1
74: 1
54
3803.1
3864.6
61.5
62.3
7670.1
7744-5
74.4
55
3905.7
3968.0
79
8c
81
82
79709
8045.6
74-7
$9
4010.9
40739
63.0
8300.2
8375.2
75-0
57
S8
4118.9
4182.6
63.7
8663.8
8739.0
9H54
75-2
75-4
4229.8
4294.2
64.4
9070.0
59
4344.0
4409.1
65.1
83
9530.2
9605.8
75.6
60
4461.5
4527-3
65.8
«4
1 0061. 1
10136.9
75.8
61
4582.7
4649.2
66.5
85
10688.7
10764.6
75-9
62
63
4707.8
47750
67.2
86
1 1456.5
11532.5
76.0
76..
4837-'
4904.9
67.8
87
1 2446.0
12522. 1
64
4971.0
5039-4
68.4
88
13840.4
13916.4
76.0
65
5109.8
5178.8
69.0
89
16223.8
16299.5
75-7
^6
5254.0
5323-6
69.6
90
37.75.'
Hh4
APPENr -,
* I
APPENDIX:
*
COMTAINIMO A
Phyfico-Mathematical Theory
OF
Lunar Motions and Irregularities,-
OF THE
JVJoTioN of die Earth'& Axis,
AND
Precession of the EoymoxEsj
AMD THE
Computation of the Quantity of Matter,
-Density, Weight of Bodies, &c.
On the SuKPACS of the
SVN, EJK.TH, JUPITER, and SATURN.
yf 5 the SuhjeSis treated of in the enfuing Appcn-
•^ lUx ctuUuQt ^eU be mugbt int$ the Boty of
fhe Book amof^ the Annotations, and an the vioft
important Part of the N^wtpi^^n Philofophy? they
could not on any Account he omittedy and therefore I
have hi(e adfidx^ them ta ^pteat a Sy&em of that
Science. Anil have taken fuch a Method as I hope
will he found not mly fforf natural and concife^ hut
much more adapted to render thofe difficult and intri-
eato Ideal jr»^ tp h dppr^^^ed ly the intiSigent
Reader,
46?
APPENDIX,
T
j.^TP^ H E Motion of the Moon about thg
Earth U fimilar to that of the War-
ters of the Ocean revolving about
fhc Earth's Center, To fhew this fame Things
muft be premifed ; a$, firft, Thai the AttraShn
of the Earth upon aufy Particle of Water is the
fame as it would be^ wer^ the whole ^antity of
'^Matter contrasted into a Point in its Center. For piitf
let ABGO be the E^rth, C its Center, P aPar^ J^X^C
ficle at any Diftance PA from its Surface ; let *
PG be drawn through P and C, and BO the
Diameter of ?^ny Circle BDQE> or Scdion of
the Sphere perpendicular to the Axis PG.
2. NowputPN;=tf, BPax; thenPB*—
PN*=f;f* — <a? = BN% which is as the Area of
the Ofircle BDQE-, the attrdding Force whereof
is %xi^ and is proportional to the Quantity of
Matter or Number of Particles which ait on the
Corpufcle P in the Periphery of the Area, an4
in Dire(5liQn8 fimilar to PB. And fince theFofcc
of Attraftion is as the Number of Particles (2Xi)
?nultiplied by the Force of each Particle, which
13 as fome Power (») of the Diftance {x\ there*-
fore 2 ;¥^ )j y« =: 2 ix"^^ '\ « will be as the whole
* ""■^" ' "' ' " ' pr
4^4
Appendix.
or abfolute Force of thofe Particles, that is, in
the Diredbions PB.
3. But the Force reprcfented by PB is re-
Iblvable into two Forces PN and Bff, of which
the former only canfes the Corpufclc at P to ap-
protficli the* Sphere. Therefore as PB : PV ::
ap : /I s: 2*x« + « : 2axX^j the Force with which
the Particle at P is attrafted in the Dire£Hon
P N ; the Fluent of which - — p — ' (when cor-
n+ 1 ^
refted) is the whole Force of all the Particles in
the Area of the Seftion' BD OE, to atiradt the
Corpufcle P in the Diredlion PC.
. 4. I fay, the Fluent ■ mull be corre6t-
^ »+i
cd, for it is at prcfent too great -, becaufe when
the Area of the Seftion becomes a Point, or
x^ay then this Fluent has the Value - * ■■ ■
n+ I '
which therefore muft be deducted from the ge-
2 ax^^^
ner^l Fluent — r and their DiflFeitnce
r , or r :;?
n+ I » + I
PNxPB«+» — PN-+* .„^
: ' — ; : 9 will be as thp Forces
IX -f- I
of any circular Areas BDOE attrafting the
Corpufcle P in the Direftion of its Axis P C.
5. Now fmce in Natural Bodies this Power in
any fingle Particle is tnverfely as the Squares of
the Diftancej therefore « = -r-i, and fo the abovp
Expreffion
A p t fi N ]) I xir 4^^
PN
Exprcffion of. the Force will become i — ^^.
6. Now if we put AC = f, PA = r, PC:±
r + r=— , PB= r + «f, and PNac^j then
AGxAN = 2rx;f— r = A0% and I*A*-|^
AO* + 2PAx AN = (rr+2r;f--2r£: + 2rjf
— 2 ^f =) PO* = ^* + 2 r;f + X*. Hence 2 rjr
+ 2 r J == 2 r* + 2 r ^ -f 2 f ^ + ^*> ^d j^ = ^ +
— .-- — :- = -^ 7 (becaufe ^ = 2r +
2 r). And becaufe the Force of Attraftion in the
PN
circular Plane whofe Diameter is BO is i ~'pB
— I — ==r, if wc milt
tiply this by the Fluxion of the Diftance, visa.
^^ , we ihall have -^ — ^-— ,
b bb
2 TX^ "4" "Ix'
whofe Fluent tt is proportional to the
Attraftion of any Segment BAO of the Globe
upon the Particle P,
7. Hence, when;r = 2r, the ExpreflSon will
become 2—, or fimply ti, for the Attra6lion of
the whole Globe. Whence it appears, thzt the
attraSlive Forces of fiherical Bodies are to one an-
other in a Ratio compounded of their Quantities of
Matter. dire£lfy^ and as the Squares of the Diftances
from their Centers in^verfely. And therefore fincc
the
^^ A p P Bjr i> I X.
the Number of Particles only, and their Diftance
frcan the Center, enter the Exprcflikm of the
Foroe, it is plain the EfFcd will be the &me
Upon a Corpufcie P placed any where withoiit
ftte Surfa» of the Globe, as if the whole Mafe
of Matter were contra6ted into sL Point at ks
ienter. ^E.D.
8. T 6 apply this : If all the Matter of the'
Earth were contra&ed into the Center, and the
Waters of the Ocean were to continue their di-
smal Rotation the fame as they now do, they
would then be affedied in the iame manner by
the Earth and Moon as they now are, an4 have
all the fame PhcnofueM. And therefo^ if ft
iBody, inftead of revolving at the Diftance of
^ E«rth*s Sarfeiee <bo« its Center; were td RF-
volve at the Diftahte'of the Moon, every thing
*^oald foippen in ^ fimilar Maiinfer, and the Ef-
iefts 6f the E^Uth and Stah in dilhu'bin^ ihelVfo-
tion of ^e Satellite would be like thofe whichr
are produced in the Motion of the Water by
the Earth and Moon, but onty in a lefs Degree. ,
^. An^tfitii Thing to be prettiifed is, tfiaft
the Moon revolves not about the Cefiter of tht
!feai-A ^k fhe Cefiter of its Motion ; and tJicrefore
in ord^ to confider its Motion in the beft Man^
ner, we muft determine tTie Diftance to which
the M^on ftwft b6 rdiftfevcd from the Center o^
the Eard\ at Reil, (airf <xyftfider'rf as Oit Center
tif its Motion) thit it »ay tt^Wt about It ih
the &ifcfefi»rtedi:s* Tim ^ii it takes tif) tiow,;
togcthef
togpthe^ with the Earth, iti re^lviiig «bcH»( M
tomtACKiCtmet d/ Gra9i(:f, S<>e'.<^«^. K^Vi
10. Ir order tdthta,k(D be <hiD JXfian^ci
titb Moon from the coamOtt Center 9C Oi^^i^
«nd i^that ct.thc £arth £f6m it; «hm v^ P.-f ^
^ th$.Pift^M:e of d^Mmn froggipdie Eardi;
which, at a Mean, h 6ok iSemidiainei$n< i lUcm
let4rsc;DiAtod$ Kqtiufedi <hm beqairfc thC; at- ^ .,
ti&dllAg Faroes (Ffcitdf) in any mo iiS^tpait . - f
Diftahcli art as thfe S^ptores of thofe.Pi^ca
faiverfefy. We hafve ^:(\:k*i I>-\-d\ Agiai,
becaufe ijhe periodkat Time itt-glvvn^ br (keJiamt
in boili C^es^ wis have the Fbices ptapoHraiMd
Mi the Biftances ftoiii the Ceiaets of Mboctt(
(See ^«>/. XXXIVO thettfon Ft f ;: D: aJL
Confequently D :*::;»• r 0 + /, thiwifbit **
4= D+/ X D •, and Airftiplyihg by t> 4- 4 ^
have jc* x b + d = D+/ xD; Whence t>+<f :
D :: D+T : «* j therefore ♦^^4^^.: ^D ::
D + J : *. But D + «^ : P :; the Q^antiiSy of
Matter in the Earth and Moon tsgether > the
Quantity of Matter in the Earth aioae } that ifi»
ds 4o^T to 33rt^i, Whence f 40^ s ^39,3'
y. 6o;5 : 60 3=x, li^D Dffifit^ a$ ^idfkh.tbi Men
<moiM rnotht about tit Moftbat R^ m ^ fame
^me it mvf ides.
11. These Thi^ pf9%ni6£k, kt S beijw Sun» FL LXX.
T the Earthy and F a S^Uite itfirolying about ^^'7-
i^ and let SK bi the Adean DiftaOorof the Sa-
tellite or Moon from: the Sun; and ex^t^fund tiK
«ieoekn<tiv» Foree, -by. whid|r it is. msxSoed x»-
wardr
496 App BHDIX;
4raxiU the Sun S. And take SL:SK::$K^f
SP*;-andS^/:S*::S*i(:S/»v then Ihall S L, or
S /, expound the accektative AttraAion in any
Difiance 6f the Satellite S P or Sp. That is, the
Force '^t Pis CO the Force at ^asSL .is toS/$
forSK=S*,andSK^ = SLxSP*=S/xS/>*j
therefore 8L : S^::S/>* : SP*.
PL LXX. 12-' Join PT and pT and draw parallel
F^. 8. thereto the Lines LM and Im^ meeting ST in
M'and m. And tl» Attra&ion SL, S/, is re-
folvahle into two ptbers SM and LM, and Sm
and Vim* Hence the Body P is urged with si
Sirerfold Force '^ "(Hz. (i.) That by which it is
littrafted or tends towards T, arifirig from the
jnutual Attraftion of the Bodies T and P. (2O
The Force. LM, or /», by which it is likcwife
urged towards T. : (3.) The Force S M, Sw, by '
which it is urged towards S, or attraded in Di-
rcdtions always parallel to ST.
13/ By the fifft of thefe Forces the SitelJitfc
ought to dcfcribe an Ellipfis abotrt T in One of
its foin^ and therefore Areas proportiohal to thie
Time, as is evident from what was demonftrated
in Amotat. CXL. This is upon Suppofition the
Body T was fixMj but the Cafe is the fame, fup-
pofing it tnovtablc with the Body P about a conn-
mon Center (which is really the Cafe of the Earth
-. ' 1 andiWi?^»^asSif ii'2wipJViw/^;rhasihewnin^^^^
- XX. andxxK Ub. t. o£ tht Princ^ia.
14, The fccond Force LM, as it c6nfpires to
impel: the/ Body in the IXreclion PT, is to be
Mdtd xm the forn»er, an4 ca^ufes that the Body
A p p B !* D I X. 497
fiiall ftill dcfcribe Areas propmiofui td tbi Tttni.
But becaufe this Force is not in the inverfe Rado
of the Square of the Diftance, it will, com-
pounded with the former, caufe the Curve which
the Satellite defcribes to deviate from an Elliptic
Form', and the more fo, ceteris paribus^ the
greater the Proportion is which this Force bears
to the former, 'fhefe Forces LM, /», have
PT
been fhewn (Annot. LXXXIV. 9.) to be as ~j
and-^— ji and therefore increafe and decreafe
with the Diftance P T or />T.
15. LastlV, the third Force SM^ impelling
the Body P in Diredions parallel to TS, will
compound a Force with the former two, that is
not direfted from P to T, and fo will caufe that
the Body P Ihall no longer defcribe Areas pro-
portional to the Ti^es (as we have fhewn.) It will
alfo augment the Aberration of the Orbit from
an Elliptic Form^ on a double Account, viz. both
becaufe it is not direfted from P to T, and alfo •
becaufe it is not inverfely as the Square of the
Diftance PT. For the Forces S M : S A :: gLj
:s^::Sp^:SP^ Thefe Errors therefore are Icaft
of all when the fecofid and third Fotces (efped*
ally the thitd) are fo, the firft Force remaining
the fame.
16. Let S N expound the Force by which the
Body T is accelerated towards S 5 dien if the
I i Forces
4^9^ Appendix.
Forces S M and S N are equal, they^ by attradfc:
ing the Bodies T and P equally, and in paraflel
Lines, will caufe no Alteration in their Site or
Pofitions in refpedt of each other. But when the
Force S M is greater, or S w leffer than the Force
SN, the Difference NM, or Nw, will be that
alone by which the Proportionality of the Times
and Areas, and alfo the Elliptic Form of the Or-
bit, will be difturbed. Hence when N M or N»i
is nothing, or' lead of all, the aforefaid Pertur-
bations will vanilh, that is, when the Body P is
nearly in the Points C and D of Its Orbit.
17. We have hitherto fuppofed the Body P
PI. LXX. revolving about T in the fame Plane with S ; let
^^' ^' tJs now fuppofe it to revolve in a difierent Plane,
and let the* Semi-Orbit CAD be above, and
CDB below the Plane, in which are the Bodies
S and T. In this cafe the Force LM will have
the fame EfFeft as before, viz. will only tend or
impel the Body P from Pto T. But the other
Force N M, by aftiilg in a Direftion parallel to
ST, and therefore (when the Body Pis not in
the Nodes C, D,) inclined to the Plane of the
Orbit PAB,.will, befides the above-iiiention'd
Error in Longitude, induce an Error in Latitude,
or difturb the Inclination of the Orbit.
: 18. For let P y be drawn paraJlel to N M, and
let Fp be the Space through which the Satel-
lite P would move in its Orbit in a fmall
Particle of Time, exclufive 6f the Force NM;
and by ..the Force N M alone luppofe it in the
iame Time moved through the Space Pr> thea
Appendix. 499
totopleating the Parallelogram Prsp^ and draw-
ing the Diagonal P J, tliat will reprefcnt the real
Motion, and s the true Place of the Satellite at
the* End of the faid Time: But 'tis cedent the
Isineola Pj is not in the Plane of the Orbit
CAD.
19. Hence it follows, that by the Force NM
the Body P will be accelerated in its Motion from
G to Aj and from D to B^ and retarded as it
pafles from A to D, and from B to C; For let
P; be drawn parallel to NM, and expound that
Force, then continuing T P to r, and drawing qr
perpendicular thereto, the Force Pj becomes rc-
folved into the two Forces rP and r j; of which
the former, ading m the Difcdion PT, docs not
difturb the Planet's Motion in Longitude, nor the
equable Defcription of Areas: But the other Part
r y, afting in the Direftion r j, confpircs with the
Motion, of the Satellite P in its Orbit, (as being
parallel to the Tangent ab) and therefore ac-
celerates its Motion in Longitude. By t|^ lame
way of reafoning, by making the like Conftruftion W-LXXI^
between A and D, it will appear that the Motion ^*2- ^*
of the Satellite will be there retarded^ the Force
r q being on that Side in a contrary Diredtion.
20. Again, as the Planet paflfes from D toB^
it will be again accelerated j for let pj here ex-
prefs the Force N«i, which is now negative, or
afts in a contrary Diredtion to the former NM,
that is, from p to j, fuppofing^ j parallel to^Nwj
for then ts confpires witK the Motion of the
Planet in the Direftioh of the Tangent cd. In
I i 2 tb«
500 Appendix*
the (ame manner it is fhewn the Planet is tetanfed
in going from B to C, by the contrary Direction
of//.
21. Hence alfo it appears, that fince the
Body P is conftantly accelerated from C to A,
* and from D to B, the Velocity of the Satellite
will be greater in the Points A and B {ceteris pa-
ribus) than in the PcMnts C and D.
12. The Orbit alio will {cherts paribus) be
more convex in C and D than in the Points A
and B; for the fwifter Bodks more, the lefs they
defied from a Right-line Courie in a giren Time*
Moreover, in the Points A and B, the Force ILM
. and N M are direftly contrary to eadi other, and
their Difference NM — LM = KL, will be as
the Force which draws the Body from T towards
S; and fince this Force KL is greater when the
Body is at A, than whea at C or D, the Bod^
will there be lefs urged towards T, and fo will
lefs defleft from a Right Line. The fame may
be fhenn when the Body is in the Point B by the
Force * /. See Amot. LXXXJV. 20.
23. Whence the Body P will (caeteris paribus):
recede farther from T in the Points C and D
than at A and B ; as is eafy to oblcrye from the
Figure of the Orbit, which is lefs curwd, and
therefore nearer to T at A and B, than at C and
D. What is here faid is upon Suppofition that the
Orbit (exclufive of the perturbating Forces) is a
Circkj and not an Ellipjs^ which Cafe will be con-
j^der'd by and by,
2jy B]Bi.
A P P B N D I Z« 501
24. Because the centripetal Force of die cen^
tfal Body T, by which the Body P is retainM in
its Orbit, is augmented in the Points C and D by
the addicitious Force LM» and diroinifh'd in the
Points A and B by the Force KL; and becaule
KL is always greater than LM from C to A
(and double thereto at A, See A/mot. LXXXIV.
20y 21, 22,) and from A to D, (where it be-
comes equal to it,) therefore the centripetal Force
(F) is upon the whole diminifliM by the Aftioa
of the Body S. And becaufe F : ^, by Am$ot.
XXXIV. 6.) therefore the Radius TP (a) re-
maining the fame, the Periodical Time (P) of
the Planet will be augmented by the A&ion of
the Power KL; and becaufe in that Caic P:
— =, it appears the Periodical Time will be in-
•F
creafed in the Subduflicate Ratio by which the
Force F is decreafed.
25. Ac A IK, fuppofing the centripetal Force F
to remain the fame, (as we ihay when KL is very
fmall with refpeft to it, Annot. LXXXIV. 22.)
then however the Diftance PT {a) may vary,
we have r P* : tf ', or P : ^ •"2?. Therefore when
neither the Diftance {a) nor the centripetal Force
F are conftant, we have P^'-tss-: V-^r; thatis,
the Periodical Time (P) mil be in a Ratio com'
pounded of the S«fquiplicate Ratio of the Di- .
lij ftancc
50Ji Appendix.
ftance^^', and the Ratio -7=:, which is £\hi
■ i/p^
duplicate of that by which the central Force F is
ihcreafed or diminilhed by the Decreafe or Inr
creafe of the Aftion of the diftant Body S.
26, From what has been faid, it follows alfo^
that the Ams of the Ellipfis defcribed by the Body
P, or Line of the jipjiiesy has an angular ModOn
backwards and forwards by Turns, but its Fro-
grefs exceeds die Regrefe-y and by that Excefs it
is upon the whole carried forwards, or in Confix
queniia. For the Force by which the Body P
is Urged towards T in the Points C and D, where
the Force MN vaniflies, is compoiinded of the
Force LM, and the ceptripetal Force or At-
(raftion of the Body T. The former Force L M,
if.fhe Dift^nce PT be ihcreafed, increafes nearly
in the fame Ratio; and the latter Force (F) is in-
verfely as the Square of that Diftance, viz. as
5— J whef efore the whole Forpe is as P T +
* I *
27. Now Fj T P4. |j«- is a lefe Ratio than F ;
PY?. For Example: Let the Ellipfis (when the
Satellite is in the Quadratures) be A PB, and the
Axii be ABi the Diftances from the central
Body T Jet b? P T ; C T :: 6 : 5 ; then the cent
Iripetal Force at P wil^ be to that at C as 25 to
■ ' 3U
Appendix. . 50^
5$; bpt the additional Force (LM) at P is as
PT = 6, and at C as TC = 5; therefore th6
eompound Forces at P and C are as 25 4- 6 : 35
-|- 5i or as 31 to 41, which is a left Ratio than
25:36, Forag25;36;t3i:i ■■ =44,64.
25 ,
But the Ratio 31 : 41 is lefk than the Ratio 31 ;
44,64.
28. Hence, fince when the Force at P is ^
^~i, the Planet dcfcribes an ElHpJts PABs and p^^^*
when the faid Force is as^^, Ae Curve is the
Equiangular Spiral Pr J, (by Annot.CXL,) 'ttse^
vident tjie Satellite will with a Foixre as PT4-
«-=r? defciibe an Oval Vaq ftill more curved than
■ <
the Ellipfis, and therefore will lie within it. Now
were the Planet P to fet out from any Point P (in
which the Radius T P cuts all the three Curves
in one common oblique Angle) and to proceed
lirft in the Spiral Path from P towards s, the
Radius T P would conftantly interfeft the faid
Curve in the fame Angle as at P. But fecond-
ly, if it proceeded in the Elliptic Arch fix>m "p
towards A, the Angle TPA would continually Fig.$.
be altering and approaching nearer to a Right -
Angle, which \k would make when it arrived in
the Point A. Laftly, if it fet out in the Oval
P jj, the faid Angle TPg would alter much fafter
^dapptpach mpre quickly to a Right Angl^
I i 4 which
504 A P F E N D I X. •
which happens in the Point «, bccaufe of its
greater Curvity, or Deviation from the Spiral Fs^
29. Therefor? by this compound Force the
higheft Apfis A will be removed backwards to a^
or the Axis of the Eilipfis AB will recede into
the Pofition at 5 and this will be the Cafe every
Time the Line of the Apfides comes into Square
with the Sun.
30, On the other hand, when the Satellite is
in the Syzygical Line CP, it is urged with 4
Force in the lower Apiis C, which is equal to the
Difference between the centripetal Force arid th^t
Cxpreffed by KL j and in the upper Apfis it is
equal to the Diffi^rence between the central Force
and*/; which kl is as PT or AT, as being
double thereof; therefore the conipound Force
^bout the upper Apfis is as ^^7^ — PT, which
is a greater Ratio than that of F : p^^ ; or, in
Numbers, 25 — ?6 : 36 — 5 :: 19 : 31, But 19
J 31 is a greater Ratio than 25 to 36; whence
the Path of the Satellite Paq is not fo much
curved as the Eilipfis PAB, and therefore lies
between it ^d the Spiral Prj; and therefore as
"the Radius moves from P towards A, it fooner
jnakes a Right Angle with the'EUipfe at A, than
with the Oval Faq^ which happens at a. The
Lbde of the Apfides AB therefore goes forwards
fn this Cafe, s^nd becomes 06.
^u A^jD becaufe the ablatitious Part il is
twice d» grc^t ^ the ^idititioys Part Im for th?
vppef
Appendix* 505
upper Apfis, and KL= 2LM for the lower-,
therefore the Ratio of the compound Forces,
which is greater than the Ratio of the Squares of
the Diftanccs inverfely, will upon the whole pre-
vail, and caufe a progreQlye angular Motion of
the Line of the Apfides.
32. Hence *tis evident there is a certain Point
between the Quadratures and Syzygies, where
the Apfides are quiefcent ; to find which, let P
be the Place of the Satellite in the Apfis required ;
through P draw Pq equal and parallel to NM or
TM, and produce it to K, then is P j = 3 PK.
; (Amof. LXXXIV. 21.) From q let fall the Per.
pendicular qr upon T P produced, and the Force
I Pj is refolved into two others Pt* and gr; of
I ' which J r, by afting perpendicularly to the Ra-
j dius, does neither accelerate nor retard the Mo-
I tion of P towards T i but the other Part Pr,
acfHng direftly contrary thereto from P towacds r,
diminiflies the central Force of P towards T.
But the Force L M or P T augments it ; the Point
r therefore where Pr = P T is that required. Now
becaufe of fimilar Triangles TPK and yPr, wc
I luve PT : PK :: Pq (= 3PK) : Pr = PT, in
the Cafe propofed. Therefore 3 P K* = P T* j
I whence PT:PK:: ^^ : 1.
I 33. Hence wc have this Analogy; As V"^
' : I :: Radius PT : Sine PKof the Arch CP =
I 35*" 16'. The Point, then, where die central
I Force is neither inaeafed nor dimi»ifhed by the
pprce of the Sun^ «nd cwifcquently where the
^o6 Appendix.
Apfides are at Reft, is at 35** 1 6' on each Sida
the Quadratures, or at 54** 44' from the Syzygies
on each Side 5 fo that the Apfides do in each Re-
volution of the Planet {€ at eris paribus) go back-
wards through 141*' 4', and forwards through
218*^56'.
W.LXXI.' ^4, Since the Progrefs or Regrefs of thfe Ap-
* ^' fides depends on the Decrement of the central
Force in a greater or leffer Ratio than that which
is duplicate of the Diftance in going from the
lower Apfis A to the upper one B, and alfo on 9
fimilar Increment in returning from B to A, and
is therefore greateft when this Proportion of the
Force in the upper Apfis to that in the lower Ap-
lis does moft of all recede from the inverfe du-
plicate Ratio of the Diftances ; it is evident that
the Apfides in tl^eir Syzygies by the ablative
Force KL will go forwards more fwiftly, and
more flowly in their Quadratures by di? additi-
tious Force L M.
^5. For let the abfolute Force of Attradlion
in T be = ^, then becaufe this is every where in
the Ratio of ^^ at the Body P, the Force by
which the. Body P is atfra^ed towards T will be
?SKTpT- Again, if the Satellite P be within
^4 Degrees of the Syzygies A or B, its Force is
difturbed by an extraneous Force (^), which i$
every where as KL or it/-, therefore this pertur-
batjng Force is ^xKWpr ixkl\ i^ that the
^^ ' • Force
Appendix. 507
Force upon P in the Points J?zndp (within that
a
Limit) is every where in the Ratio of pnn» — -
i % KL to -=t; — ^ X */; which Ratio, when P
pi
a
i§ in the Points A and B, becomes -r^ — ^ x AT.
to g^ — ^x BT, (becaufe then KL : * / :: AT :
^T, and TP = AT, and ^T = BT, as has
been fliewn. ) Now this redliced to a common
Denomination is TQ*xa — i^xAT^ tp AT*xa
36. Now this Ratio recedes ib much the moi^e
from the Ratio of TB* to AT% or ^^^to
^^, by how niuch a^-^bxAT^ recedes from
an Equality with a — b x T B% or by how much
AT is lefs than TB; that is, when the Line of
the Apfides is in the Syzygies, as in Fig. 5. In H-LXX?.
this Pofition therefore the Apfides wiU go for-
\^ards fwifter than in any other.
37. But when (in this Cafe) the Body P is in
the Quadratures C and D, the additional Force
LM becoming equal to CT = TD, and CT
4- TD being here leis than in any other Situation
of the Apfides, (as Fig. 4.) from the Nature of
an EUipfis, therefore the Ratio or Quantity of
the pertprbating Force thence arifing will be leaft
ef all 5 and CQnfcqvien^ly the Apfides will recedp
flower
5o8 Appendix.
flower in this than in any other Situation. Hence,
upon the Whole, the Excefe in the Progrefe of
the Apfides will in this Situation be greater than
» in any other.
P1.LXXI. 38* If the Line of the Apfides be fituated in
f * • the Quadratures, then for juft contrary Caufes the
contrary Phaenomena will happen ; that is, they
will recede moft fwiftly when the Satellite is in
the Quadratures, and proceed moft flowly when
it is in tbt Syzygies. So that in this Cafe the
Regrcfs might exceed the Progrefs, and the Ap-
fides upon the Whole be moved in Antecedeniia^
were it not that the Force K L, by which they
go forwards at A, is near twice as great as LM,
hf which they- go backwards when the Body is
4t C. See Art. 24.
39. The Excefs of the progreffive above the
regreffive Motion ef the Apficjes will be aug-
mented, if the Bodies P and S move both to-
wards the fame Parts \ for then the Apfides will
, continue a longer Tune in and near the Syzygics,
than if the Body S were fix*d : And on the con-
trary, as their Motion would be contrary to that
of S when P is in. the Quadratures, fo thp Time
of the Rcgrels will be fhorter ; therefore the Time
by which they go forwards will, upon the Whole,
be from hence very much iricreaied.
40^ From what we have demonftrated {Ari.
28, 29, 30.) it is evident, that if a Body in de-
f ig- 7t fccnding from the upper to the lower Apfis be
urged by a centripetal Force, which increafea
ttiore than in a duplicate Ratio of the diminifli^d
' ' Diftauc^
Appendix.
Diftance fr6m the Center, it will defcribe a Curve
Acb interior to the EUipfe ACB, and confc-
quently more eccentric, inafmuch as the Ratio of
TB to T A is increafed by being changed to the
Ratio of TitoTA.
41. On the contrary, if a Body itt& out from
the lower Apfis B towards the upper A, and is
attrafted every where with a Force that decreafes
more than in the duplicate Ratio of the incrcafing
Diftance ; then, being Icfs attraded than it would
be in the Ellipfe, it will defcribe an Orbit exte-
rior to the Ellipfe, as Bi^ ; which alfo is more
eccentric than the Ellipfe, becaufe Tia to TB is
a greater Ratio than T A to TB.
42. By the fame Way of Reafoning we fhew
that if in the Defcent the Force be increafed in a
Ratio lefs than that of die Square of the dimi-
nifh'd Diftance, or in the Afcent it be diminifh'd
in a Ratio lefs than the Square of the increafed
Diftance, the Orbit defcribcd will be M^ eccen-
tric than the Ellipfe,
43. Therefore when the Satellite P is in the
Quadratures C and D, if the abfolute central
Force be to the abfolute additional Force 2^ a to
», we fliall have the whole Forces at C and D,
in the Ratio of ^ + »xCT to ;~^ + ^^
TD; which is as TD*xiJ + » xCp to Tc^
a + nx TD'. But this is a lc6 Ratio than that
of TD* to TC% becaufe CT is greater than
T D. Therefore in that jPart of the Orbit where
the
5^9
. ^lo Appendix.
the addititious Force L M takes place, the Eccen^
tricity will be diminifhed, by Art. 42.
44. Again ; fuppofmg the Satellite in the Sy-
zygies PQ, then the Force in Q^will be to that
at P as T^^a^bxTQl to TQ^xtf — ^
xTP% which Ratio is greater than that of T P*
toTQ*, becaufeTCtis lefs chanTP; where-
fore in and near the Syzygies the Eccentricity of
the Orbit will be increafed, (joy Jrt. 40, 41.)
The Eccentricity therefore of the Orbit wfll be
twice changed in every Revolution of the Satel-
lite.
W.LXXL ' 45. If the Apfides be fituated m the Quadra- *
^«- 6- tures, then, becaufe the Ratio of TD to TC iS
greateft of all, the Eccentricity of the Orbit will
be lead of all, {Art. 43.) Again-, when the Af^
^^'g' 5- fides are in the Syzygies, the Eccentricity is the
greateft of all for the fame Reafon, viz. the
greateft Difparity of AT and TB. Hence the
Eccentricity of the Orbit is continually increafing
as the Apfides pafs from the Quadratures to the.
Syzygies, and vice verfa.
46. It lias been already fliewn, {Art. 17, 18.)
that if the Plane of the Satellite's Orbit be in-
clined to the Plane in which are the Bodies S
and T, the Motion of the Satellite in Latitude
will in no wife be difturbed by the Part LM of
the extraneous Force, but only by the other Part
N M, and not by that neither when the Nodes
are in the Syzygies ; but when they are in tlie'
Quadratures this Perturbation is^ greateft of all-
47. Foft
Appendix. ^511
47. For let P be the Satellite m its Orbit Pl.LXXt
tAt>, inclined to the immoveable Plane CFD ^'8-^-
in any Angle ADF; ajid let PS expound the
Force of the Body S, attradting the Satellite in
the Direaion PS. From P let fall the Perpen-
dicular Py to the Plane CFD, and draw the
Right Line TjS ; then the Force PS is resolva-
ble into the Forces S^ and P J ; of which the for-
mer, being in the faid Plane CFD, does not
difturb the Satellite's Motion in Latitude; but
the other Force P j, being perpendicular to the
Plane CFD, is wholly fpent in drawing the Sa-,
tellite from its Orbit CAD towards it, and there-
fore is proportional to the Force by which the
Motion in Latitude is difturbed. But the Force
Pq is evidently greateft when STD is^a Right
. Angle, and is nothing when that Angle vaniflies.
48, When the Nodes are in the Quadratures
C, D, as the Satellite P pafles from the Quadra-
tures to the Syzygics the Inclination of the Orbit
IS diminifh'd, and it is increafed in going from
the Syzygies to the Quadratures, For let P j (as
before) reprefent the extraneous Force NM, and
the Direftion of its A^ion; we have fhewn
that the Body P will dclcribe the Uneola P j in
, a fmall Particle of Time by the compound Force,
which Lineola f* j is not in the Plane of the Or-
bit CPD, but dcflefts from it towards Pj; fo
that the Satellite really moves in the Plane T Px,
which produced will not meet the Plane E C F in
C, but in another Point ^, towards the Oppofi-
.Cioii B,
. ^ 49. For
512 Appendix.
Plate 49* For with the Radius TP defcribe tha
LXXIL Circle E C F D m the fix'd Plane palFing through
* '• T and S, and in the Plane TPj the Arch of a
Circle Fc interfering the other in c. Now bc-
caufe the Force NM is very fmall compared with
the central Force, therefore the Angle CPr, the
Inclination of the Planes CPT and csTj is ex-
ceeding 4hiaU, and the Arch Cr an infinitefunal
Quantity 5 therefore fince PA is a finite Quan-
tity, the Sum of the two Arches PC + Pr is
lefs than C A + A D, or a Semicircle ; and hence
in the fpherical Triangle CP^ the external An-
gle PC F is greater than the internal oppofite
Angle J?cC. (See my Tcung Trigonometer^s Guide^
Vol. II.) That is, the Inclination of the Plane
CAD to the Plane CFD is greater than the In-
clinatipn of the Plane cVT thereto; which was
the firft Thing to be fhewn.
50. In like manner we prove, that as the Bo-
dy P goes from the Conjunftion A to the Qua*
drature D, the Inclination of the Orbit will be
Increafed ; for if,, in this Cafe, through the Points
P and 5 we dcfcribe an Arch of a Circle m the
Plane TPi^ the faid Arch Vsd will meet the
Plane CFD in the Point d between F and D 5
and the exterior Angle P^F, the new Inclination
of its Orbit, will be greater than the interior op-
pofite Angle PDF, which was the Inclination
when the Satellite was at A ; which was the fe*
cond Thing to be ihewn,
51; Hence 'tis evident, that in diis Situation
of the Nodes the Inclination of the Orbit is leaft
df
A P P E N D I X, 513
of all when the Satellite is in the Syzygies at A,*
and that it returns to its former Magnitude at the
next Node ; for the fame Things are in the lame
Manner Ihcwn when the Satellite pafles through
the remoter Part of its Orbit DBC.
52. Hence alfo the Nodes in this Situation
have 2L retrograde Motion^ or are carried back-
'wards from the Site DC to ^r, in half a Revo-
lution of the Satellite ; and they recede as much
more during the other Half-Revolution.
53. If the Nodes K, L, are in the Oftants af- Plate
.ter the Quadratures t and D, then, (r.) The In- i*.^^^^-
clinatioh of the Plane will be conftantly dimi- *^* **
nifh'd in paffing from the Node K to the 90^^
Degree at H or G. (2.) It will be increafed du-
ring the Motion from that Point to the next Qua-
drature D or C. (3.) During both thefe Tran-
fits, or the Motion from K to D, or from L to
C, the Nodes go backwards. In paffing from
the Quadratures to the next Node the Inclination
of the Orbit is diminifli'd, and ^the Nodes go
forwards. The firft, fccond, and third are (hewn
2^s before, [Jri. 49 — 52. j and the fourth is thus
demonftrated.
54. When the Satellite P has pafe*d the Qua-
drature D, the Power NM becomes negative,
or a£ts in a contrary Diredion with refpedt to T,
and hence the Lineola Pi defcribed by the com-
pound Motion deflects from the Arch of the
Orbit Pp towards the Side B A; therefore 'tis
plain, the Arch of a Circle Pj/, defcribed with
the Radius T P in the Plane T P/,' will meet the
VoL.U, Kk Circle
514 Appendix.
Circle F L B in a Point / between L and B ; then,
as before, we fhew the Angle P/F is lels than
the Angle PLF; and the Node L has, during
the Motion through D/, gone forwards to /.
The fame Things happen in the Tranfit from C
toK.
55. FnoM-what we have demonftrated it ap-
pears, that during tho^ whole Tranfit from the
Node K to the Node L, the Inclination of the
Orbit is more diminifli'd than increafed, ^nd the
fame Thing happens on the other Side in going
from L to K } therefore tRe Inclination is always
fefs in the fubiequent than in the {Receding Node*
And this will be the Cafe, more or lefs, where-
cver the Node K is placed between R and S. .
Plate s6. When the Nodes are in the other 06bnts,
LXXII. ^/jj between S and V, and R and W 5 then,
* ^* (i.) While the Body P is pafling from the Node
to the next Quadrature, the Inclination of the
Orbit is increafed, and the Nodes go forwards.
(2.) In pafling from the Quadrature to the 90***
Degree from the Node H or G, the Inclination
is diminiih'd, and the Nodes go backwards*.
(3.) In pafling from thence to the next Node, the
Inclination is increafed, and the Nodes dill go
backwards. The fecond and third are demon^
ftrated altogether as before, (yfr/. 49.) and the
firft is thus ihewn.
57. The Satellite being at P, between K and
C, the Direftion of the Force NM is that of P j;
whence the Uneola P j, dcfcribed by the com-
pound Fprce, will deflc6t from the Arch P^.of
.the
Appenpix* 515
the Orbit towards the Side V R ; and confequent-
ly a circular Arch defcribed on the Center T
through the Points s and P, in the Plane TjP,
will meet the prin^itive Circle VS R in a Point k
between K and S* Therefore the Angle siF is
greater than the Angle PKF ; and the Node K
is carried in Confe^entia from K to k. The fame
Thing is (hewn for the other Part of the Orbit
LGK.
58. Hence it appears, that fince the Nodes
go forwards only while the Satellite is between the
Node and the next Qiadrature, and baclcwards
while it paffes from thence to the next Node, the
Hodes in each Revolution go hackwards more than
forwards 'j and therefore, upon the Whole, the
potion of the Nodes is abfolutefy backwards^ un,
kis they happen to be in the Syzygies, where they
are quiefcent ; becaufe in that Cafe the Motion in
Latitude is not at all difturb'd by the Force NM
and confequently where the Inclination of the Or-
bit is the greateft of all. (See ^/. 4^.)
^^. All the ferrors in the Satellite's Motion
hitherto defcribed are a little greater in the Con- ^
junftion of the Bodies P and S,* than in their Op-
ppfition ; becaufe the generating Forces N M and
LM in the former Cafe are greater than N« and
Im in the latter ; as we have ftiewn in Annotation
LXXXIV. Art. 9, 10, II, 12. Alfo it is there
ftiewn, that each of the d'ifturbing Forces NM
and L M is inverfely as the Cube of the Diftance,
and therefore become greater when the Diiftance
JCk2 ST
5i6 Appendix.
ST IS lefs, viz. in PeribeliOy and left as rheDi-
lllance increafcs, viz. inJpbelio.
60. Of thefe difturbing Forces, (ince NM is
nc^r twice as great as LM, therefore the Dimi-
. nution of the central Force will exceed its Aug-
mentation doubly ; and fo, upon the Whole, the
Satellite P will be lefs attrafted towards T by the
joint Forces of S and T, than by the' Body T
alone •, confequently the Satellite defcribes a lai^er
Orbit, and it's Period of Revolution is greater.
61. In all that h^s been faid, if S be the Sun,
* T the Earth, and P the Moon, the Theory of
the Lunar Motions and Irregularities is contain*d
in the foregoing Articles. And as this Theory
refults from the Laws of Attradion, and was firft
excogitated by Sir IJaac Newton by reafbning
a Priori ; fo it is found no lefs confonant to the
Experience and Obfervations of Aftronomers :
' For from thence it appears, (i.) That the Moon
defcribes not a Circle but an Ellipfe about the
Earth. (2.) That the Eccentricity of the Lunar
Orbir is variable, being when leaft but 43619 ;
when mean, 55237; and "when greateft, 66854
©f fuch Parts as the Radius contains 1 000000.
(3.) That the Moon's Apogee goes forwards in
the Syzygies, and backwards in the Quadratures ;
but upon the whole it goes forwards, fo as to
compleat a Revolution in about nine Years.
(4.) That the Moon's Orbit is inclined to the
Plane of the Ecliptic in a certain Angle.
(5.) That this Inclination of the Lunar Orbit is
variable.
A P P E N I> I X. 517
variable^ being when lead 5% and when greateft
5** i8^ (6.) That the Nodes of the Moon go
fbnaetimes backwards, fometimes forwards, and
are in the Syzygies -quiefcent. (7O That the
Motion of the Lunar Nodes is upon the whole
backwards^ at the Rate of 20'' per Armurnj and
fo as to compleat a Revolution in about 18 Years
and a half. Such is the furprizing Harmony of
the Newtonian Theory with J/ironomical Obferva-
fion, even in ibis moft difficult Pari^ that Halley
might well fay,
Intima panduntur vi£li penetraUa CaU^
Nee Idtet expremos qvue vis circumrotat Orbej,
And,
Difcimu^s hinc tandem qua cauja argentea Pbcebe
Pajibus haud^aquis graditur-y cur fubdita nulli
HaSenus Afirongmo numerorum fr'^ena recuftt\
Cur remeant Nodi^ curque Jnges progrediuntur.
62. The fame Method of Reafoning, by which
we have explained the Tides j and the Lunar Theory^
does alfo furnifli us with a Phy/icaJ Explication of
the Motion of the EartFs Axis. For let us con-
ceive numerous Bodies,* fuch as P, to revolve V^tt
about the Earth T, at an equal Diftance, in equal p. ,^
Times, and in a Plane inclined to the Plaae of
the Ecliptic, *tis evident each one will be afFedted
with the fame Motions as the Body P. Again,
Let us fuppofe their Number fo increafcd as that
they become contiguous to each oAer, and there^
Kk 3 by
5i8 Appendix*
by form a fluid Annulus or Ring of cohering
Bodies.
63. Then fincc each Part of the Ring, ob-
ferves the fame Laws of Motion with P, and be-
caufe while one Part is fo attrafted as to augment
the Inclination of the Plane, the contrary Part is
afFeded by a contrary Force to diminilh it, there-
fore the IncHnation of the Plane will always be^
variable, and governed by the Difference of the
Fortes which aft upon it in contrary Parts.
64. Therefore fince the greater Force al-
ways prevails, the Parts of the Ring which are in
the Conjundion and Oppofition will move more
fwiftly, and accede nearer to the Body T than
thofe in the Quadratures (by Article 21, 22.) And
the Nodes of this Ring will be quiefcent in the
Syzygies, but in any other Situation will go back-
' wards, and fwifteft of all in the Quadratures (by
>fr/iV& 47— 58.) Laftly, the Inclinatiori of the
Ring will be every where analogous to that of the.
Lunar Orbit ; and confequently its Axis will in
each Revolution ofcillate to and from the Axis of
the Ecliptic, and be carried backward by the Re-
trocelTion of the Line of Nodesi
6^. If the Quantity of Matter in the Ring
were to be diminifh*d in any Ratio, the Motjons
' would all remain the farrie, as depending on the
attradlive Force of the central Body T, which
is dill the fame. If the Diameter of the Ring
be diminifli'd, the Motions will be in the fame
Ratio diminifh'd alfo 5 for Effeds will be as their
Caufcs.
Appendix* 419
PT.
Caufes, But LM : ttt^ ; and, bccaufc TS is
STxLM
conffanr, LM is as PT, Alfo MS = — ^^
= ST; therefore MS is as ST, a given Quan-
tity • (See -^»»^/. LXXXIV. 9, 11.) Coniequei^-
ly the Motions of the Ring will be every where
as the diminifti'd Diftance P T.
66. Suppose therefore the Diameter of the
Ring to be diminifli'd fo far as to be equal only
ta the Diameter of the Earth, and the Body T to **g.„
be ipherical, and every way enlaiged till it e- pjg ^^
quaird the Bulk of the Earth ; then would the
Ring of Bodies coincide with and be contiguous
to the Surface of the Earth, and would alio co-
here to it. And fuppofe the Plane of the Ring
made an Angle with the Plane of the Ecliptic of
23 Degrees and a half, then would all the Mo- .
tions of the Ring continue, only in a leffer De-
gree ; and would be communicated to the Earthy
becaufe it adheres firmly thereto; for the Earth
equilibrated in ^ther will jrield to any Motion
imprefs'd upon it from without. But the Mo-
tions of the Ring being now communicated to
the Body of the Earth, will be farther diminilh'd
in Proportion as the Mafs of Matter to be moved
is augmented,
6y. Now this Circle or Ring of Bodies en*
compafling the Earth by Suppofition is aftuaJly
the true State of the Earth ; for we have (hewn
its Diameter through the Equator ^Q exceeds
Kk4 the
520 A P P E N D I X. ^
the Length of the Axis ND, (yfwwA CXLVIII.)
and therefore it is furrounded by a Zone of Mat-
ter upon the Equator analogous to this feign' d
Ring of Bodies, and which mull of courfe pro-
duce the fame Effefts. ,
68. Hence in the Equinoxes, that is, when
the Earth's Nodes are in the Syzygies, or when
the Line of the Nodes {viz. the Equinoxes) pafe
through the Earth and Sun, the Inclination of
the Equator and Ecliptic, that is, the .Angle
-SITE or FT H, is greatcft of all; and from
this Time it grows lefe till the Sun arrives at the
50*^ Degree, (or Solftice) when the Line of Nodes
are in the (^adratures, and then it is lead of
all.
6g. Therefore twice in a Year the Inclina-
tion of the Ecliptic and Equator is diminifhM,
and twice again rcftored ; and the Nodes (or
Equinoxes) conftantly go backwards, and carry
the Axis of the Earth T H with a retrograde
Motion about the Axis of the Ecliptic TF,
tracing out! the Circle, or rather vermicular Curve
HIGR in the Heavens among the Fix'd Stars.
. 70. Again; the Plane of the Equator is in-
^ clined to the Plane of the Moon's Orbit, for the
latter makes an Angle of but about 5 Degrees
with the Plane of the Ecliptic ; and therefore the
Moon (though a lefs Body than the Sun, yet be-
ing nearer) produces a greater Effedl than the
Sun on the. Equatorial Ring or Zone of Matter,
and fo augments all the aforefaid Motions of the
Earth's
Appendix. ^^^\
Earth*s Plane and Axis. Sir Ifaac Newton has
fhewn (Prop. XXXIX. Lib. III.) that the Part of
the annual Receffwn of the Equinoxes^ which is
owing to the Sun,* is 9^ 7*^ 20^^ and that which
is owing to the Moon is 40^ 52" 52^^ ; there-
fore by the joint Influence of the Sun ^nd Moon
the Equinoxes recede yearly about 50^ 0€*^ 1 1^^ ;
which is likewife verified by the Obfervations of
Aftronomers for 2000 Years paft. See Annota-
tion GXLI.
71. I SHALL now explain the Method ufed by
Philofophers for computing the Quandties of
Matter, Denfities, Weight of Bodies, fcfr. in the
Sun^ the Earthy Jupiter ^ and Saturn^ by means
of Satellites revolving about them. In order to
this let Q»^ y, exprefs the Quantities of Matter putc
in the two Bodies A, B ; alfo let G, g^ be the re- LXXIIL
fpedtive Forces of Gravity at the equal Diftances
A C and B D. Let T, t; be the Periodical Times
of Bodies revolving about A and B at thofe equal
Diftances -, and let T, /, be the Periodical Times
of Bodies revolving at the unequal Diftances AC
and B E, which call D and d.
72. Then in the given Diftances AC, BD,
we have Q^: qiiG ig {Art. 7.) But G : ^ ::
^ : ^ (by Annot. XXXIV. 6.) Whence Q^:
J :: rp» : 5r»", and multiplying the latter Ratio by
D' D'
D% we have Q^: y :: .pn : ^i' But becaufe T^
j;22 Appendix.
: /• :: D* : ^, (ibid. Art. ii,) therefore -^ =
-^5 confequently, Q^: J - ^^ = t?' That is,
ffif ^antities of Matter in anj txoo Bodies are
in the compound Ratio of the Cubes of the Biftances
direSfy^ and Squares of the Periodical Times in-
verfefyj of Bodies revolving about them.
73. Int this Calculation the Bodies ,A and B
are fuppofed at Reft. We confider the Sun at
Reft with refpeft to Venus^ and Jupiter and Sa-
turn in re(pe& of their Secondaries ; and we have
reduced the Diftaiice of the Moon to 60 Semi-
diameters, at which ftie would revolve about the
Earth at Reft. Now let the Diftance of the
Earth from the Sun be put — — 1000
then Venus revolves about the Sun at Diftance 723
the 4*^ Satellite of Jupiter at the Diftance 1 2,4775
the 4^'* Satellite of Saturn at the Diftance 8,5107
the Moon at the Diftance 3»054
rof Venus is 19414160^
The PeriodicaMof the Jovian Sat. 1441929^
Time ^of the Satumian Sat. 1377674^
^of the Moon, 2560580^
74. Now fuppofc the Quantity of Matter in
die Sun be loooo, then for that in Jupiter fay^
. 723- 12,4775
19414160'' 1441929'^ ^ "^ ^
(Ijy Art. 71.) the Dcnfity of Jupiter compared
with that of the Sun. By the feme Analogy the
reft
Appendix. 52^
reft are found, and in each they are as follow.
In the Sun^ Jupiter^ Saturn^ Earthy Moon.
loooo. 9*305. 3>250. 0,0512. 0,0013.
75. Now if thefe Quantities of Matter are di-
vided by the Squares of the Diameters of thefe
Bodies, the Quotients will be as the IVeigbt of
Bodies on their Superficies^ (by Anmi. XIX/ 3.)
The Diameters of the Sun and Planets fee ia
yinnot. CXXXV. Then thefe Gravities will be
as follow.
hitheSun^ Jupiter, Saturn^ , Earthy Moon.
loooo. 936. 519, 431. 146.
76. In homogeneous, unequal, fpherical Bo-
dies, the Gravities on their Surfaces are as tbeJDi*
ameters^ if the Denlities are equal (^Annotation .
XIX. 3. J But if the Bodies be equal, the Gra-
vities will be as the Denjities^ becaufe they will be
as the. Quantities of Matter, which in this Cafe
are as the Denfities {Annot. XVIT.) Therefore in
Bodies of unequal Bulks and Denfities, the Gra- •
vities will be in a compound Ratio of the Diame-
ters and Denfities. Confequently, the Denfities^
will be 0S the Gravities divided by the Diameters \
and therefore in the feveral Bodies as follows.
In the Sun^ Jupiter^ Saturn^ Earthy Moon.
loopo. 9385. 6567. 39539- 489"-
77. As it is not likely that thefe Bodies are
homogeneaJ, the Denfities here determin'd are
not to be fuppofed the truey but rather mean Den-
fities^ or fuch as the Bodies would have if they
were
524 Appendix.
werQ homogeneal, and of the fame Mafs of Mat- .
ter and Magnitude.
78, Let F,/, be the Forces of the Sun and
Moon to move the Sea ; D, d^ their Diftances
from the Earth ; then F : / :: j^ : ^. (See/.46.
Vol I. and AnnoL LXXXIV. 9, 11.) Let B, *,
be the Bulks ; R, r, the Diameters ; and N^ n^
the Denfities of the Sun and Moon ; then will
Q^: q :: BN : in :: R'N : r'm {Amot. XVU.
and XIX.) wherefore F : / :: -^ : ^. ILaftly,
let A, 4, be the apparent Diameters of the Sun
R T
and Moon 5 then will A : <i :: -=r : -j ; becaufe
any Body appears larger the bigger it is, and
}efs in proportion to the increafing Diflance;
R* r'
therefore A' : «' :: -gy : ^. Hence P : / ::
A' N : a^n. Confcquently, N : » :: ¥a^ : /A^ ::
A'' a'
79, But (according to Sir Ifaac Newton) F :
/:: I : 4,4815. (See Annotat. LXXXIV. 28.)
And A : tf :: 32' 12^ : 31' i64^ (at a Mean, by
Obfervation), That is, A : ^ :: 3864 : 3753.
^1 r ^T ' 4.,48i5
Therefore N : » :: ■ ^ ^ : r •• loooo :
4891 1, the Ratio of the Denfity of the Sun and
Moon, as aboye Ihewn, Art. 76.
80. The
Appendix. 5^5
80. The Quantities of Matter being Q^: q ::
R^N . r%^ (/&f. 7«.) and with refpeft to the
Earth and Moon, N : » :: 39539 : 489 11 ; and
R : r :: 109 : 30, (Jnnot. CXXXVL 4.) there-
fore Q^: q :: 109* x 39539 : 30' X4891Z ::
39,31 ; I :: 0,0512 : 0,0013, as determined in
JrL 74.
81. The Weight of Bodies on the Surface of
^ the Earth and Moon are in the compound Ratio of
the Diameiers and Denfities^ {Art. 76.) that is, in
the Ratio of 109x39539 to 30x48911, or as
431 to 146, (as per Art. 75,) or as 3 to i
nearly.
82. Having the Quantities of Matter in the
Earth and Moon, the Diftance of th^ common
Center of Gravity is determined : For the Di-
ftance of the Moon from the Earth's Center is to
this Diftance as 40,3 1 to i ; which Ratio is more
accurate than that of 41 to i, made ufe of in
I Annot. XXXVL Art. 2.
j 83. The Theory we have here been explain-
ing is applicable to any Syftem of three or more
Bodies, as well as to the Sun^ the Earthy and Moon,
Thus the perturbating Forces and Irregularities of
Motion in the Syftem of the Sun^ Jupiter^ and
I any of his Moons, may be eftimated in nearly the
' fame Manner, {mutatis mfitandis) as alfo thofe of
I the Suny Saturn^ and his Satellites •, and laftly,
I between the Sun and primary Planets^ by putting
L the Cafe more generally, (as Sir Ifaac does) in fup-
y pofing bgth S and P to revolve about the fix'd cen-
tral
5a6 Appendix.
tral Body T, which we may fuppofe to be the
Sun, and S and P any two of the Planets at plea-
fure. Therefore, to ufe the Author's own Words
(in another Cafe) for a Conclufion: Ufus igUur
hujus "Theoria latijjime pateti, *6? lati fatendo Veri-
tatm (jus evincif.
AN
AN
I N D E X
To the Two Volumes.
N. B. ITbe Numeral Letters denote the Volume,
and the Figures the Page of that Volume.
ACTION and Reamem
yjf ^qual, i. 57, 60-- 62.
JEdipilt^ >• .325—330.
JEta^ ii. 425.
Amal Pulfcs, ii. 95. their
Properties, 9^ — 104.
Air^ a Fluid >»f^rriJ, ii. a,
its Generation, 3**9. its
Weight, 4— 19» 34— 45-
its Elafticity, 10 — 26,
39— •44. I>eiifity,2o— 33.
its Pf eflbre on a human
Body, 31 — 34. -its Prcf-
fore the Caufe of Water
fifing in Pomps, Syphons,
CsTr. 38—44. neceflaryfor
BefpiratiOn, Animal Life,
Flame, Sound, l^c. 45—
50. Condenfation thereof, .
51, 52. Rarefadion there-
of, 68, 71.
Air^Gun defcribM, ii. 64—68.
J^r-Pumpt a Rationale of the
feveral Phaeiromena of Ex-
periments on it, ii. 37^—
51. the Stfu£tarc and MfS
of it, 63—68.
. AmpUiuie of Projedion, i. 8o.
AMofyic Method of Philofo*
phizing,,i. 3,4.
AngU of Incidence «id Re-
flexion, ii. 149^-152;
Aphelion of Planets^ it. 350,
351.
Aquetm Hamour of the Bye,
ii. 249.
ArtbimediC^ Screw, i. 305,
306.
Armiliqry Sphere, ii. 365.
Afirmumcal Principles of
Chronology, ii. 431.
Atmofyhere^ ii. i, 2. its Alti-
tude, 20—33.
AthraQioH^ i. 10, 12, 1 3, 14^'
how it differs from Repul-
fion, II. of Cohefion, the
Laws of it, 14 — 32. of
£learicity, 33, 34. of
Magnetifm, 35 — ^41. of
Gravitation, 42—46. the
Caufe of the Tides, 326,
343-
Autumn Seafon, ii. 378, 379,
38b.'
^&/«nw«/ ^Equinox, ii. 380,
INDEX.
B.
JDALANCE. Praportiona],
Falfe, Romaw, i. 109.
Bar9mitir^ the^tnidare and
I Jfe of feveral, ii. 10-^19.
Bellows, ii. 87, 88.
Biffextile^ ii« 4C4.
Bundnfr-Glafi, the Nature of
it, 11. 139—148.
' c.
nAM^RA Oi/cmra. the
Nature of it, ii. i86 —
• 296.
tlapillaty Tubes, the Pbxno-
nAena of tfaem confider'd,
1. 19—26. Capillary Sy-
phon, 29.
Carriages, the Theory of
Wheol-Carriages, i. 167—
* i7S-
Cafaraa of defceiidittg Wa-
lter,. 1.-282 — 287.
Catoptrics, what, ii^23i.
Celerity of Motion, what,,
i. 50.
Ontral Forcti, i. 83—94.
Cen/re of Ofcillation and Per-
coffion, i. 71, 74, 75. of
Magnitude, Motion, and
Gravity, i. 96—105.
Centrijfugal and ' > Centrifetal
Force, i. 85.
Okronilegy. Agronomical Prin-
ciples thereof, ii. 43 1-—
434- . ^^^
Chrenometer. its Ulc, i. 75.
Grcle, Horary, ii. 372. of
Illumination, 373.
Circular Motion, i. 83 — 94.
G'l;// Lunar and Civil Solar
Year, ii. 423.
Clocks, the Nature and Prin-
ciples of them, i. 129—*^
140..
Cohejkn. Attraftion thereof,
i. i^^lt.
Celiy what, ii. 141, 142..
Colom^s, original, how ihany,
ii. 163 — 166. the Theo-
ry of them, 186 — 226.
C»btrej, ii. 370.
CometSt jL 315. theDofirine
of diem, 394 — ^409.
CemetariuM. its Ufe, i. 140
—144. ii. 387—394. the
Mechanifmof it defcribed,
i. 142- 144«
CompofitioH zsA Refolution of
Motion, i. 58, 59, 60.
Ill — n6.
Concord, what, ii. 116.
Concave Mirroun, ii. 234.
Lerfes, ibid.
Conden/ation of Air, ii. 51,
Conduits, i. 255, 256.
Conjun£iion and Oppqfitioii of
the Planets, ii. 337—346.
Coutroverjy. a famous one,
i. 173— .»78-
Conwex Mirroors, ii. 234.
Lenfes, ibid.
Copermcan Syftem explained,
ii. 312—333. Arguments
for the Truth of it, 3 34—
345-
Crane, the Properties and Ufe
of it, i. 284 — 287.
CryflalUne Humour, ii. 250,
252—255. •
Gr//ra^ explained, ii. 54—55.
Curve. Parabolic, i. 8i.
Cycli of the Sun« ii. 426-—
428. of the Moon, 428 —
430. of Indi^on, 430.
Pafchal, 430, 431.
Cyckid. the Nature and Ufe
of it, i. 71— 74» 78* 79»
8q.
D. DAMPS,
1 N D fe X
t)AkPS, 1/31. ii.47.
*^ Days, SoUr and S^de-
teal, ii. 4189 42Z.
DiMfity of the Air, ii. 20—23.
. of Bodies in the San, tBe
£arth» Jufter^ and Saiumy
how computed^ ii. 521 t9
the End
JDiapa/on, ii. 116.
Diapente^ what, ii. llj.
toiatfffaron, ibid.
Diatonic Scale, i&V.
Dipping Needle, i. 35. .
Di'uing Bell defcribed^ ii^ 5 1
—57.
DiiifiUlity of Matter, i. 8.
Domnical Liftieri, ii. 426—
428.
E.
pARt thfe Struaurc of it,
ii. 89 — 93.
Xartbf the Figure of it^ i.
90 — 94. Motion of it!
Axis, ii. 517.
IfarthqualkiS, i. 31.
Ebullition^ i. 31.
Eccentricity of a PJaneti H.
^ 353— 35^-
xr^<7, whati ii. 104, 107-^
Illr
Echoes, the DoOrinfe Of them^
ii. 385 — 394.
Etiifticy and its Twelve Signs^
^ ". 366, 367.
Elafiicity^ in Solids, the Caofe
of it, i. 27. of the Air,
ii, 10—26.
Eliaricity, Attradion the^-
^o^i. 33»34- ,
ElUpfisy the Figure the Pla«
, nets defCribe, ii. 345-363.
EnfintSi i. 122 — 126. I^cwii^
AanC^ Water-Engine/ 289
Vot.Ii.
-I311. the Niitdre df (hi
Fire-Engine, 309 — 311,
Theory of Mr. Nt-wct*
tmtn'^iw — 320. Thfcorjr
of Captain Bavtry%^ 321;
322, 323. Imjprovemenc
di^reof bj NU.PayMe, 323^
^ 324* 325-
w^, ii. 4^4.
£pocha, what, ii. 42 j.
Equation of Timd» ii. 419—
. 422.
Eqiti&hrium of Fluids, L 254;
EqmMoSieJt ii. 366.
EjUdnoxes^ ii. 369.
E'uaporaHon accounted for^
i. 28
Exfanfion, of Metals, i. 76—^
78.
Exflofim^ i. 31,
Extenfivn^ what, i. 5;
^y€y a Defcription of it, li^
249«— 2 5 3 . its Defects, ana
how to remedy them, 253
pErmentationi i. 30. Iks Ef-
ftas,*ii. 5— 8. depend!
on the An*, 49^ 50.
Frgur ability of Matter, i. 7, 8;
Figure of the Earth, i, 90—*
94. of Fluidf, 187, 188.
K///r, i. 29 ^
Fw, what, ii. 138^ — 143.
Eire Engine,. Ste Mngitu,
Fits of afy RefletUon and
, Tranfmiffion, ii. 180— 185«
Fixity^ what, i. i7.
Flame, See Fire*
Fbti^li, their Nature arid Pro-
perties, i. 180 — 205. all
incompreffible except Air^
181—183. gravitate upoS
6ne another; 182—184.
their Frcffurc, 184—20$^
h\ thii^
INDEX.
tbeir MotioQ, Canfet and
Laws of it, 253 — 34i. ^
ffy of the Common Jack, L
ii%, I29» 130.
/i^Vr^» how accounted for^
F«6Kf, diferent Rays have
dtferent ones, u. 167—
179. Real, Virtaal, Nega-
tive, and Afirmative, ii.^
233—240.
Ftmttains, the Origin of them
whence, i. 259 — 266. the
Theoiy of Natural ones,
i. 269—274.
FriSiow, the EfisOs of k^ i
FriBiomJ^^biib^ i. 12$.
Frigid Zont, li. 3^1.
G.
/2JGE, a DeftripCioii of
"^ the Sea-Gage, ii, 23—
s6.
Catfs of a Lock, i. 162— «
167.
' GoUen Number, li. 429.
Qr»mtatiM^ the Laws of i^
»• 42f 43-
Gravity f how to find the Cen-
' tie thereof, i. 96, 97, &r.
Specific of Solids and'Fla-
, kU, i^i— ^31.
Grfgorian Account, ii. 424,
425.
Hiir9, Problem concemiDg his
Crown, 226— -230.
Horary Circle, ii. 372.
HorixM, ii. 369,
^orftXMi/tf/ Amplitude of Pro-
jedion, i. 80.
Hour^ what, ii. 412.
Hydraulics J what, i. 252, 2$3.
Ufeofthem, 280 — 282.
Humours of the Eye, ii. 250
—253.
Hydrometer^ i. 206—209.
HydrofteiHc Paradox, i. i9i-«
197, 205, 206. Bahnce,
207—224. Problems, 224
—230.
Hydroftatics^ 1. 179, i8a.
their Ufe, 231, 232.
Hygrometer, the Ufe of it, tL
6z, 63.
I..
yjCK, die Common on*
J defcrib^Bd, i, 127, 136.
Jitd'fiau's^ the Theory of
them, i. 269—274. Afo-
meuta of them, 270-279.
Velocities and Diffamces of
fpouting ones, 273 — 286.
lu^etus ofProje^n, i. So*
lucJiutd flui€, 1. no, 115.
Juiiau Year, ii. 424,
u.
TTAll, 1. 29.
•*-* Halo's, how fortn'd, ii.
211—229.
HarMonical?tOfettion^ ii. 1 1 9
—126,
Harmofty^ what, 11. 1 18.
Htat, whence, i. 31, ii. 138
—143.
JT^ if ^S of Motion, I. 54.* *
62. of the Pkbetarjr
Syftem, 86, 87. 313—
337-
teu/es^ the feveral Species of
them, ii. 234. the Ruks
of their Foci, z^z^z^S.
£fv^ defaibed, i. 107—109,
III— 113.
Levity, abfolute, impoffibl^^
i. 44, 202.
ligth the Nature of if.
^ • H. f2^
INDEX.
it. 1^9—134. its Velocity,
1 32^-1 38. its Power and
Meet, 136— -143.
Une, what, i. 5. oftbeAp*
fides^ its Motion, ii. 502—
508.
JjQmdfiemt^ its Properties, i.
, 35— 4»-
Lock apon a River, i» 162—
166.
L0ganihmc Cartre» ii. 1 1 1-««
116.
LooktMg-C^ifi, ii'24ou
M.
KfJCHINES, fimple,
i. 106. compound, 122
• —126. the grcatcft EflFed
of one, 125—128.
Magk Lanthom, ii. 286—^
293.
MagHtt^ natural and artificial,
-i. 35— 41. ^
Magnitude of Bodies, i. c, 6.
Matter, its Properties, 1. 4— r
II. Quantities of it in Bo-
dies on the Surface of the
Sun, Earth, Jutiten, and
Satttm, how computed^ iL
52 ly i^t.
Meebankalfowen^ i. io6.
Mechanics, its Objefl, i. 47.
the fiindamentd Aincipit
thereof, 107.
Miloe/^, ii. iiS^.
MJtifig of Bodies, i. 28.
MeriMan, ii. 368.
iAethodsdi Philoirophizing, I.
3, 4. of invelligating the
Effeas of Gla&s in re-
Beaittg and refraaing the
Rays of Light, ii. 231-^
■ 250.
Meteers, i. 28.
Mttomi; Cycle, ii 428> 420,
4|o, ^
li£cr9mittr, B. 265, 270,
271.
Microfcafis, Single and Com-
pound, ii. 26 1 — 267. Na-
ture and Theory p{ them,
263 — 273. Solar Mido-
fcope, 294—304,
Mills, the Principles of Wa-
ter-MiUs, i. 144—154. 4
Defcription of Dr. Bar-
iw's. 151— 154. the The-
ory of the Sails of Wind-
mills,' 155— 161,
MirrQurt^ Concave and dm*
vex, ii. 234. their Proper-
• ties and £fe6ls, 234-242^
Mohility of Matter, what,
i. 9.
MAmtntum of Bodies, i. 5 1^
173—178.
Monocb^rd, ii. 117, 118,
Moarst il. 223—229. Theo*
ry of its Motions and Irre-
gularities, 491 — 117.
Mootu of Jitfter, ii. 325?^-
331. of Saturn, 33&-«
336.
Motion^ its Nature, Kinds.
- and Affiedions, i. 47-!-r5i.
Laws thereof, 54---62. of
Bodies in Facno^ 63^:66.
in refilling Mediums, 2 3 3 - .
251. CH& inclined Planet
and curved Surfaces, 66-^
70. of Prcjcdiles, 80—
85. Circtdar, its Nature
and Ufes, 83-94, Per-
petual impoflible, 107, 108.
. pf Fluids, h0W,caufed».am{
the {.aws ci it, 253-255.
Mufrbenbroek, l^is Experiments
routing to Cohefion, !. 1%
li. his Experiments rela-
ting ta the Expanfion of
Metals, 77.
Mufiil^i^tnnp^ Urn Vibm*
\aI z |aon%
INDEX.
fioDs, ii. 11)— ii6. Di-
vtfion of Lines, ii. 117,
118. ,
Jdufical Chord, the Motion
and Tone of it explained,
ii. 118 — i2Z.
N.
fJAtural Day, what, ii.
Jffeedle, Mag;netic, Dipjping,
' i. 35 Variation of it, ii
36-38.
^twepiftfiH^ his FirC'Engine,-
i 31 T, 330.
Vtvujham^ his Water-Engine^
I 289—311.
VtvQ Stil^, ii. 424, 425.
QCrAYl. what, ii, 116.,
O/^Stiie, ii. 424, 42 j.
OpMcity^ how occalion*d, ii.
Optics t what, ii. 231.
Qrgan of Sight, ii. 249. pf
Hearing, ii. 89-^93.
Origin of Springs and Foun*
tains, i. 259—266.
Prf/7» and its Ufe, i. 140.
"357—386.
Qtacoufiiciy ii. I IQ«
T>Ar.ih(fia, i. 81, 82.
il'/*tfif Cyple, ii. 430,
43«- .
Pc»)ir/', {Mf ) hifi Improve-
ment of the Fire-Bngi^e,
i. 323-325
fenjkiums^ the DoArine of
them, i. 70—79. th^ com-
• pound Pendulum; i i 6tt
120.
9^hilUi^^ ii. 347, 348.
Fmod^lHm^^ 2. 430. Ji^
. iiaxt 431.
Ptrio^ical Year, ii. 412.
Pnfttmal Motion impofllble,
i. 107, 108.
Philofofhy^ its £n4 Uid Ufe,
i. I.
VhiUfifhixing^ Rules and Me-
thods therpof, i. 2, 3.
Fif€$ of Conduit, i. 255, 256.
P^M, Inclined, i. 10—16.
Plaiutarium, its Theory an4
Stra£tiirf, L 140^142. .
Piamets^ Primanr, their Dif-
taoces and Revolutions, ii.
312. Secondary, their -Dif-
tances and Revolutions, 3^3
— 363 Stationary, Dircd^
Retrograde, 341, 342.
PJeHk^, abfolute^^ abfuid, i.
44* 45? ..
Puiumalics^ ii. 2.
PoUr Circles, ii. 371.
Polarity of the Loadftone^
'• 35-
Prtjfure of Fluids, i. 182-7
195. of the Air, ii. 31 —
34i 38-^44-
JVfW/'/tfofMechania.i. ^07.
Problems in Hydroftatics, L
zz^^z^i, a curious one^
ii. 34-36.
fniiaiUs^ the Oofkioe of
them, i. 8o«-r$5.
Ptolom^ean Syttevi explain*4
and dtf*proved, ii. 309:<p
311.
Pulity^ iu Power, i. iio^
116.
£aimf^, com^pdon one* i. 287,
288, 297. Theory of
- Pump-Work, 288, 296.
Forcing, Lifting, aqd Me^«
curia), 297.^305.
Putrefaakn^ ii. 49, 50.
fyroipit^r, i. 76-78^
I N D E x;
Q^
# VAD RjiNT of Altitude^
*V^ a. 373.
R.
p J IN, Its.
Rainiow, its Caafe «c-
plaiji^d, ti. 209 — 227.
Earifamw of the Air, 6%^
Rays of Light, parallel, con-
verging,, diverging, ii. 232.
^§a£pg'WaJfcs^ ii, 25^^
262.
Kecoiling of Guns, i. 63.
RefleSm of Light, ii. I44-*
ReflepfihiHty of Rays, varioas,
' ii. 175— »99-
J£g/^tfi?i>«of Lightj ii. I53-T
166.
Refrangihthly of Rays, yjiri-
ous. ii. 156—174.
Rtpulfion^ 1. II
jRefervpir^ i. 255 — 259.
i^^axrr^ of Mediums, i. 233
—251.
Rejpiratiofi explained, ii. 47.
Retina of the Eye, ii. 251.
Rivers, the Running of them,
i 256 — 259.
RoISfig Cone ^nd Cylinder^
1.97. ' ".
Rmving with Oars, i. 63.
Ru/es ojf Philofophizing, 'i. 2.
• 8.
VAIIS. the Theory of
^ thofe of a Wmdmill, u
' 155-161. of^Shtp^ i6a.
Sap, i. 25, 26, 29.
'SdttJlifes, See Moons.
ta<uery, (Captain) Ikis Flflt-
Etrgine, i. 321—323.
^^.^^ itsPower, i, i|o*it6»
ttafim of the Yctr, ii. 574
SicntwH of Attimal Plttidt,
i. 26, 29.
Siffu of the Ediplic^ iL 366^
367.
Smowt i. ^8.
Mmr Micraftope, ii. C94-«r
304. Tclefcope, 397—
299. Sytem. See Syjttm.^
Soldering aocounted for« i. Z%\
Solid, what, i. 5. -
SoMiy ci Mact^, i. 6.
So/ftices, li. 370.
Sounds, depoodenc on the ASr^
n, 50. a genend Account
of them, 83-->93. priiict*
pal PhsenOmena of chem^
^3^96. how and to what
lidance propagated^ 94.
100. Velocity thereof, 100
— 106. Ztf^v/ thereof, 104
«.i07. ioud, low, grave
andacote, 112, 113.
Sfacif abfoiute and tehttiYe^
i. 48.
Sfeay»g'TrmHfet,u. 109, Pii
-.116.
Sfod/c Gravity of Solids and
- Fluids, i. 210—231. the
F'rinciple of this DoAnne
explak*d, i. i98r-<oo«
BftSiuiis, convex and <«m*
cave, 2.257—261.
Specubm. See Mirromr.
SpHngS^a^n, n. 375.37*-
Spring of ^e Air, ii. 39—45.
Springs, the Origin of them»
i. 257 — 266* Pef«raiial|p
Intermitting, and ReciprOr
eating, i. 964, 265.
^4^/^47, x^rSted-yaitl, i. ro9«
Stp^orifbome Tobe* >!• 109,
111—116.
Summer Seaibn, ii. 376-379«
Stforj^ifs, I. !•
INDEX*
* convex, L 187, 188.
twmmii^, hfyw peHbiiii*d«
' i. 63. of Bodies in Fluids^
107-20C.
sjtahitic Method of PJuloIb-
phizittg, i. 3, 4.
$S^, Qipilkuy, i. 29. die
. Nature of it cxplainM^
s66— 069, 284—287.
^'«5P'» »• 37-
^«ff of the World, ii« 306—
309. Ftohrndtantx^ta^d^
309, 311. Tjfhomc ex«
iiUiiiM, 3^10-^3(2. C^-
iMM» e3Cf4ftiB*d, 3»*-333-
. Arguments for the Coftrm'
. €4tt$, SH-345. reprefcnt-
cd by the Qnw;, 3S7r-
. 36J.
^JfLB of Speciiic Gm-
Tities, i. 214—220.
Tamta/us-Ct^ i. 268.
Te/e/copi, Refraam|,itsStra.
^ure and linpemdtioD, ii.
268-298. Reilefting, its
' StrnAiire and Ufefulneft,
' 277-286. Solar, 297—
lin^erat^Zian% u.' 372.
Unmrntttr^ the feveral Soitl
thereof, iir 57— 6>2«
Vhunder^ i. 31-
fUa^ the Theoi;^^ them ex-
. - |^am*d, L 326^343.
fime^ what» and the Meafure
. of it, ii. 41 lA
Snv, ii. 112.
JorriciUian Tnbe, U. It*.
fmidZoxnt^ ii. 371.
franjpmrentj^ how cauied» iL
147-151.
ftv)»rVi of Gatrc^ and Catn^
€9rn, ii. 370^ 37^,
TrapkalYeu, it. 412—417;
Tnimpa, Speaking, ii. 109,
. 111-116.
Tuigs^ Capillary, i. 19—26, ^
TjciroMicSyitemg ii. 310—312.
V. •
prjCUUM, neceffiuy, I.
9, 44, 4$. Motion of
Bodies therein, 03—66.
t^apottrs^ how raHed, i. 28.
FaruUiom of the Needle, i*
36-38.
Pegetatiom^ i. 26, 29*
Felociiy of Motion, i. 50. of
Fluid?, 275^ 276. ofWindiy
ii.8i7-88.
VihriU^nji dt Mnfical Strings;
\ jL i{3— 116. a focprizing
'^ Experiment thereof, 124—
.127.
Tis Tneriist of Matter, i. loJ
Fis 'Vivut and Fis wurtua^ u
"74»»7S-
Ftfion^ the Theory of it, it.
250—262.
Fitreous Humour, u. 249.
Vmfiut 11. 116.
UMt'verfi, itt Extent, si. 30&r
308. . '.
f^lcafuTs, L 27,31.
W. ,
PfTJTCHES^ thePrind-
pies of. them, L 129^
135.
W4Kttrt a Method of rai&ig
it by Heat and CoU, i. 307,
. 3C>^ - '
Water-MiUs, X 144-* 154. *
'Jjr^ir'EngiMi of Mr. JVni;-
Jhmm^ i. 289-#3ii.
Waves q{ Water, hpw |^<^
. pagated, ii. 96-99.
JFavu of. Air, their rroper<»
INDEX.
Wtdgt^ its Power, i. xto,
1 16.
Wuk^ ii. 242 » 243.
^^i^f of Bodies immeried in
Raids, i. 197 — 200. oa
the Surface of the Son,
Earth, Jmfiier^ wad Saturn,
how compated^ ii. 521,
tfTr.
THfeel and Axle, i. 1 10, 1 16.
^W Carriages, the Theory
of them, i. 167-— 173.
»W, ii, 73. principal Phae.
nomena thereof, 73— 7.8«
the general Caufes of it,
76—81. General Trade-
Winds, 79, 80. Velocitf
of th^ Wind, 81—88.
Wthd-l^Us, the Theory of
their SaUs, i. 155 — i6i.
Wind'h^rmunit^ ii. 115.
^Mtf«rSeafon, ii. 380, 381.
Y.
y^MJ^R, Periodical and
Tropical, ii. 412—417.
Civil Lonar and Civil So*
lar, 423.
ZODIAC, ii. 36/:
Zoiut, u.37^37^*
FINIS.
^^l 1 0 ]^2Si
T
l
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