I W T
1 1
rcipeffing the motions o f tué pliinets,'and which are in-
'deçd thp'fomi'datioji o f ,;J1 allroïJomy.
. - i f f . .That ' th’e primary plan'ets^reyolve about 'thé; •iiîti'
In cllipTeSy having tiie'Tù'ii ïn'one o f ’ the foci. 2dly.
T h a t the fduares o f the periodic times o f all' the planets/
, 'have ‘the-fame proportion to eacli other as the cubts o f
théir refpeâiive mean diftanccs'.; 3 dly. That1 if a line he
ffiswn from the fujf ito a planet/'àhâ move as the planet
moves, it will defcribc about the fun, equal ateas in equal
. times; ^-Thefe ‘.principles which K ePLE^dednce'd.'from
/ obfervatioD, .S';ir I . N ewton' ' proved to be true from
the common .principles, of' ' motion, and his nbcorp o f
gravity.
, 9$. The periodic time o f theé'àrthi or thé rimfrin which
• the earth, mates a complete reybliifion-in her orbit,
'eafte& a/Ærra/revolution, it 36yd. 6h. 9'. 11",3. '
î'imejfroin “the earth’ s leaving jthe firll po in t o f arfp. a ll
{Re reiinns tOjt'tvis .^J-'jjedd this 'is called
a ironical rëvplûtîônj and 'this ffeing&efsathan her perio-
dic time,it follows that t h e çq ü i n o £t i a lp bi nTsdm oy e backwards
; and this motion is called ’the .prcccjfimi 'of the
equinoxes. The. time from tile "earth's leaving her apo -
gee till ihe xétùrns to' if , is.j6ja?r;6h. i f . 2" ; sand this
.bang greaterhhan her periodic time, it follows;tbat.her
apogee moves forward; this is -called3’her anamalijlic
ÿear. - r i
- fotn; T he foudwiiig tablé çrarams the relative nitan
diitanc.es .of the planets .from; tlie fun, ahuraiifg the
mean cifMrcelJof ' the earth to lie unily .; together 'wirh
their periodic times. 1
39. À table ó f the places o f the afeetifing nhfles oT
tij« orbits o f the plaiïets.fôrlïy^lj, with them motions
'in'l.o)?gÇutfe rèFipoyhars.
^Planets . J§„ Plapê^ç\f the Node.. |1 Mot. of.^od ?
vMérçury i, | IS, i 50, , 2Q'. - 43" j|.:.. i° . . i'2!.. çp'.'j
. Venus 1 . '2 . 14. 26. I<8 ' j - J i - ^1°
"M i r s ^ T -! i r i f - ;'ÏV¥).-- 4
Jupitel- j1 3: 7- J5 - 32 1 O- 59- 3°
j 'Satprn | 3- 2 I - 3*- 22 1 55- 30 ..
M . de la P lac^ Jgaijsl the place ÿ_of tthe. npdelofthe
Georgian planetjTjn^yâS,J o be 2®. iV . 4.7." ; ba t itsenvp
thon is .«at yethetfernnned.
.^ i c c . Actable ofJShMj^hpationsjof the.opbitspif this
planets to tlmecliptic-forthe year.-tyHS.;, with the variation
for npo'-yem-s.
t Phmets 1 TMéanTïift. . 1 ■ TeWodicTimes
Mercury 1 “q',3'87To- ■1 • ■ 87ft 15'- 43"»6
^eujis f . i t °>72333 . |.- .2241I. .)'Qh.A494-«sóri^
Earth- - 1 i ~--l',QOp& 0 1 ■ ]- - , 36yd. 6h. .9. X 1,6
Mara.- ■ 1 -1.523%-; j iy. 32id. 23h. 30. 35,6
jupaer - 1- - -5,20279 1 i.ly.‘3 i jd . - I4h '27. 10,8
•Saturn 1 1 29’y. 1743. ■ 'xK- '5 iJ .i 1,3
GeorgianI I , *9,18352 l;.8.37- ï ï ó i i8h.
- Place ó f Aphelia |' M ot. in lö ö ye;
Mercury t ] "JM ■ I 3°• • S3-' 5}< iv f ?-Vi 33'- +5"
ye-nuSé -et 1 êfÔ. ■É l 4 6, 42 jy?-,-4 -r~ -yr'jo 1
Earth f. t!3. Û «... ■ 37- .6 1■ I- 43- 15
Mars 1 t’î- I. '28. ?4 1 -5 i- '4°
Jupiter ' 1 ! 6. / 21. - S t J i 11- 34-. 33
Saturn r \^ 8 . ■ p r i i i l 1■' ' ; 'j - 7
Georgian.] I Jr. -. 16- m m ê l-r^rfrï 29^ - - ?
T, ‘ Planets . ■ 1-r. auaifiurio.0 Jr,,. ,.a .Variation..,. 4
~ rM~efGûi3y:--. - -| - 7?.. 0'. 0" 1 Ï, xf 2o 43
"V-éHiS J 1 1 V ^ i 47 £ . '
'■ ; Mars * ; 1 I . Ç-1. 0 f ÉaReBÉS -
x Jupiter 1 I ,liî> c& 'f. 1 .— =27.;m i m
' f .Satbm . ;v^ -i ’ ■ ' ■ H B i H
^Qjsotfgian 1 -0. 46. i, 20 kj»mm
.9 8 . : A table Of the places o f tfiehphïIiaoT thé orbits
for the'beginriitig'af TÿÿoVIwfth'tKéir môtiohi'!in,I80|^-
tùdein ifiô yéârs.
The. variation is that ari&g.,Jrom~ theory, as 'deters
-mined b y Iff be la G rJ nP e.. ThPofigm.+ „ ihows
that the inclination' incremes, and>tliLJfign— that,it :
•decfeafis.;
i ‘ .ifojtriif two.planets rerm^tnrewcplarorbits^to find'lhe
timefrOm conjahftion to sm|nn£ti(Hi. Tiet. iP=;the' perio-
dietimeofaauperiorp]unet,^“ the periodidtime o f ,vrin-';
feriorplanet, ICrthe.ti’ine required, Then P : 1 cravs:; y6oG:
. 360''’"the angle-oefcribedfcy the fuperior planetpnri day ;
' ' * / * : y [ . L V . t - ,
forthefame reafon, is the angle dcfcriben by tlul'infe-
• / - ; - * f * > v
ripr planet in y d a y 'j "therefore is the daily
1 1 ^ :' r I { I S i 1! p —V ? .7‘ 1 •
«angular velocOT o fth e inferior planetffrom the^perlbr,
or how inrush ’fhe former rj&edts from*, tne latter., evpry
cfay. . Now i f they,fet onr-from conjunction, .they will
rjeFuInJ nto/conjtin Cti© n-again, after the inferior '.planet
has gained one revolution', o r 366° 5 therefore 3fro°—
SBBSBbBh B 1 ill J $ l
360° K 3^o° « j day • t— tPp . ■ The ' rule therefore to
T T \ v « 1 | #pp-p-'
»findrfhe required timej theperimic times together.,
and divide ‘by fheir (difference. TJiiif'wili alfo give
■ the time betweeir tw.o oppoiitioQSy^crr between any two
fiirijlar fituations. T he txffie front- eonjundtion to conjunction
is called a fyrwdic revolution,
mm
I I ' f R O ©. ^
tyn, WfA 'ffjffpjipn' and M t lÉ
i /i Pheeno.ména. \ ’ >
;G--; T l O N. yiiin
io„6. tThe apparent diameter o f the moon is found,con-
tin:ua|l^^/to'vary* npw'tlie a'pparenVdiameter o f any very
diftanh'bbdyV varies inverfely as its dilta’nce. Hence, as
the ‘appai;entl’'diameter o f tne^mpe^f mcreafes, fhemuft
app:^racu -iKe' eartH,/ f!and when it decreafes, ihe muft
^m&d’e'f#4om Jthe ’ ear^hi’ This variation pf her apparent
to 2. T he tri’Qpufeèipg the' neafeft, 'and‘^ next' to the j
fun, the kiMx3 remarkable’“ ifi ourTyitem, and alfo 1
lafeful for the divluö.i^OT nd ^ tn|it^|pe •:]
4nc^t?^johömers were aMénM^e.
ffiohs/an.d the orbit which it 4 ë£cn’bes. ' T-M^nsotibli^óf i
the mo'o-n in its 01 bit about the eartK, is^fioiu'weftto eatl, 1
ahd¥tsrofem%feS^®’HÖ fSclinedJt a 1
motion o j the 'mbon is' alfo pHferved not [to be uniform, 1
and its diftance 'from 'the earth is found to vary; which 1
fhows that it doe^ not j evolve ii\-a^cirP^®o|M tlie eai th 3
in but il^imbtipn is -£ound.|p|:bfeh^au' e'llipfe,.'
• paving t'Kc earth in' 'pne' o f file ’foci. ‘ The p.ofition ‘of the
ellipfe is ohferved to be cpatiraually changing, the major
1 axri^'róit^b'eingiixed, dii% foraetmiei'dire'Ct^^cl 1
rfonietimesretrograde iw^pl’ei^he'-motro'n' j
i s ’dirVfl; arid it makes a oómple-tèreyplution in'a f j t t®
m'bré than;8f years.
found to change, that is, thh^ëlhpfë; n.Caj^r J
^ f0 a c|rcderth^au‘itls,W othebtimesi Tlfe inmn è^on s,s 1
!%|Bi^ ^fc|u^d like wife fubject to^ a.yari^yp^ifr^m^^^rl
/All^b'efe" irregularities arife ^^'myth&V^i3®-
?%urhing tbfe.ipooiils imption by itsi
s tffefflipfe'whi^|éhepi^%^Qej^rMék^ Mt'
Jtthèmid^is:iubjeCf \tda variation, -the Keriodi^tïme ^of the
:>raooh about,‘fee^earfh' will*;alfo. vary; in .wiTfr^-theH
- pioohV Qr'DTt' is dilated,«,and the periodic .time $ /in-
1 creafëd; and’in fummerj her ,orbitns^ntra6tea,.anqmer |
• periodic time is diminifhed. The periodic time o f the
'moon increases whilft the fun is 'm.hyfeg apb- I
‘ gee to his perigee^ and idëc^eafes"w hillt^e ^oyês^^hi-
' his.perigëc tó^is apogefe j ahd |h,e greateïf^fFerencé'ófl
the periodic t?ime^ is fopnd tö'be minutesl 1
104. Themi?/2« periödic time o f the moon IS 2lfa .'yh.
43^i' i i" ,5 ; ’’this-is' calftd her^fidèreal re^mib.Uj'JÏMng
• i^ è mean time from her leaving any fixed bar, till her
return to it again. Now it- is by bhfèrvVti9n, that
. the mean time from'hèr'ïejm^ till file returns
to it, is 2yd.. 13’h. i§ '. 4" ; hênee, the'moon is logger in
returning to nérapngeè^thaullie is in makings revolution
in her oVbit, and therefore Her apogee m'uft move J
forward. T h e ‘f»^n ta^e-^)W Imr leavirTg her nóde till I
file returns to'it!ag^iii,'is Ï 270. 5I1. 5'. 35'76, an“d tlii's
rbèing lefs' th^ri. her mean periodic time, it follows that fhe
returns to 'hér nbdè^^ïofe 'm llaas èó^nleted h ^ fevólii-
' tion, and therefore hér node|C muit havé a retrdgrade |
I motion.’ '
105. T h e time .between two mean com|| |b n C ^ f f lè , J
fun and .moon, ,or from new moon to new'"mp^ni funpof- j
Ifillp they* mp‘tiofi8 had both- péèn üniformy I
the ru}eïh'&fti;,ciej io i j ^ahirig ®^erS e ;the mean peri-,
odic timer ó f the moo‘n_ an a^ni/ as^ireadyVfia^^ we get
the mean time'‘from cörijun&ion to conjunction to' be
29'd. i 2b. 4 4 .4 i , 8 »"an d^ils. is^alïed’lier fynoefac revonr-
tion. , Xhe tfru* time from pew to 4nbw^ódn |wlir be
•fometimes greater and fometim.es^kfs than this. The
eaufes o f all irregul^niês will briefly explain.
aB^ees^exaSlf’ V ? t K ^ o u g h t to be the cafe,
if thembo^mbv’ed.' inf ah ellipfe about''the earth in brie
:b f 'theraore'Biat the rnobn moves
in an ellipfe abpft the cai th^fituated in one o f itS'foci,
a??Q the obferved variation
of theTf®m^s ’diameter. ’1 From fhe'variation o f
^hl.tftin’ s diam’eter, it appears in fW e mariner, that' the .
eartili m'ufl. revolve in an 'ellipfe ab;o'u'tFthc fun, having the
1 fiint'i|n'(bire IpfJ;rhe, foci-.' 1
107. Tlie eaith moving in .an ellipse‘&botft the fun in
i f JfoGuss, the riearcr the earth com''es'hp the fiin;1 «the
mbre it is attra^d^b^him^ and tJ^is aJitraClibri increafes
in the f a m ^ ' f a S ' b M f w l ^ d f f ^ f i e ' e dlftiihiihes 5 '
^ fq h ^ r e 'b f the
diftg^|increafe'S'. A s thel*ef6retire “earth approaches
the fun all the time it' moves 'from"'1th,e “aphelion to the
and cmfpinng 'pd.rt-
■ ly f \cbe11fcySeS''tne motion of .
fhe earth'; an’d when th e ‘ earth moves from perihelion
'|lo n^^Tmrt^' a^a iiiil the^earth s ^
molion, antl^dimihiflies its^mo¥ioriA Tims, ‘the velocity
ear!^lf mo^^rek'‘whiHf1 if 'moves from the aphelion
40 ‘ perihelion;' a^d'-debdeafes as muthr whilft if * moves
the moohmoves m an
’ |ell^fe^al^ur f a e ' e S n ^ i¥bcS8|'^fhe'’jnum,^m like
manner1by.tnef earth's ‘attra&ion^ Haye her'vdfbcityln-
; creaTed from^n^^dgee td®t^rrg^d^^d dedrrafed as
I much fi;om her perigee t'o 'apogeeM THefe are tlie prift-
■ Gi^rcaufgstof'Mie“ yatiapok-df:fh e Of tnb earth
4’ind^hmon. VfBut al tbemn jMemOdS, as well as
the earth attrafts it, the kttra^ti'o'h o f the' 8J1 will caufe
^another variation j' o f th e ' mbBm § | v|elocity: * Thus the
moon . being attra'Cfed hothT y the fu'ri ' anrl earth, th&y -
win/came great itTegulariues m KW^muon rarfa hence
it is'very difficult' o f ' tlie'mOon. -'
i tne fS § n f .phce? |hatis,' the /
place whei e fhe" would f f i d been i f heFmotion had been /
unifoira, it requiies notlefs than zd ’corfeCtiobs/ih order
’’^®geV the trudjTObl^tO a fiimgent^a&ree of accufabyC
Sia IfNEWTON . was the “firfr penofifWho pointed “du t
& tne;Tour£es^df|th^m irregularities ;. b u t' they ard 'or ’ a
nature;'too diffiemt to idniit
1 o wb v ie^tMf^mW' with, a :felefcbp
find ihat her' veiy ncraglrwMt.mpunpins and ca- .
' yitifcs j o f the
'IMffi1, ^ c e r t a i n parts areToundlto
^ ^ ^ ^ m a a -^ s^ fw a w o ^ f f it e to ’ the fu n^ > an^when
' the' fun becomes vertical ’ to any "of them, 'they1 are' ob -
nb^madow f fhel^therefore rpuft be moun-
'® i S ”^ ^|ier parts'are' ^ways oark on ‘that fide next the
i*fun,3arid' i l f i i m i n a t e n .^6® V jbefe there-
, 'fore' mu'ftrhe^c^S^^ .appearance o f ‘ the
^ r i^ jf rom ^ ‘its alte^ gJp^ fitpa tl^ja' ' ^
: re|p^qtf to .the fun'.1 'T h e tops o f tbemountafus nn-TtJie
- *'c 'K ‘ V & frk ‘