, L e t .s- be. the place o f a fpe&ator, and draw the meridian
A t ^ , an<J^<± osTwpp<4? 1% fun f°. be ^f.V.fMtbe
meridian. Then when the earth ha made one ^volution
about itsuaxis, t*he fpettator at s wlH come again
into fhe fame £timrion,ipul | « m o u tlie fame Meri-
tdinn Psvae;
djan, becaufe he has moved forward in the eclipticstewards
L p i f therefore i» b£ the point Where the fan >s
when he next cornea tq th e meridian, or taflier when” the
met»di»ii overtakes him, ah,3 'yp.fi, idraw the meridian
Prmp.thcn the earth, alter it has made k’ ffyoffiiSdir
ahout its axis, has described the angle trJV before tjie
. feedbttpr.at 4 he brought afein m|o She- meridian Pmp
o f the fun. flow the angle vpr is mc^nred b y the ate
. fe , which is the increafe o f the fun’-s-right afcenfion fit
the time he'moves from a to m, or in fi true fila r d a y ;
hence, the length o f * Jrtu folar day is equal to the time of
the earth’ s -rotation about its axis, together with the lime o f
‘defcribing an angle equal to the increafe o f the fun’s right afcenfion
in a. true folar day. Now i f the fop movdd’ utii-
, fprrnly, and alfo in the equator T D ’li.S , this Increafe
ep woiild.be always the fame in the fame time, and
therefore the fila r days would be all equal; bntfhe ftm
moves in the ecliptip T C L , and'therefore i f it# motion
were uniform, equal arcs ( am) upon the ecliptic would
mot give equal arcs (ep) upon the equator. JBut the motion
o f the fun in'- the ecliptic is not uniform, and hence alfo
am, deferibed in a given timetpis fu b jeff to a variation,
and Cpnfequently ep is. fubject :to a variation. rHence,
the increafe ep o f the fun’ s right afcenfion in a true folar
day, varies from two caufes ; lit. Becaufe the ecliptic,
in which the fun moves, is inclined to the equator ; zd.
Becaufe his motion in the'ecliptic is not uniform; therefore
the length o f a trite folar day is fuhjeft to a continual'variation
; confequently a- clock which is adjufted
to go 24 hours for any one'true folar day, will hot continue
to ihow 12 when the.'fun comes to the meridian;
* As the earth deferibes an angle of 360°; 5i){.:;8",:kabout its axis
therefore 360»,. 59'.-8",z : 386°: : 24b. : 2}h. 56'. 4",098 the lei
o f a fixed' flat, over the meridian till «.returns >to it again.
becaufe the intervals by , the .d ock y$JT opqtigne; $iiwP
,:t4 i?-iptsrvd? -9$ tfee f%u^jpa^g0>ftvef fh.e gtenot
equal.-
80. A s the fun moves through 360° o f right afcenfion'
in daysi. thefiffir«. ü fis i dayjs;: I d a y : : Jufflf,:
I 59’• 8“, 2 the increafe o f figh t afcenfion in 1 day, i f
the increafe W91 e iliujfii'Uk'pivit. would he the increafe in
. a mean folar day, that is, if the folar days were all equal;
I fob they wouJ|ibe'all equal, it the fun’s right afcenfion
; itim.'eaihri uniformly, as appears by the laft article.’* I f
thgrpfire a clock.{)?; hdjiifted.'tjo fg d # 8 hg^rs r n j mean:
folar day, it will not-continue fitgpinGi^iWAth fhq fiu>-
that is, to fhow 12 when the fy q corner t^ th e msfidian,
becaufe the -true fila r days differ in length from a ipefn-
folar th e fiSPiigfls
before 12, and fpmttljhns after 12? ,and db-is difference is
; called. the, equation :o f time. j\ d ^ o k 1 thus ndj,uiietb is
fa id-tohs %^*|Sed,tp n p i j S b tim«. . fj'he;timf 5ron;n-
.by the d o c k .is cahed true or mean tirp,e; agd.that.-mown.
jb y the; fop,-«called apparent time ; tbps, ,when..the fq a
/cames,to>the>meriban,itisifeS?tph?4 ?,ft’d 9fH '# / ''t''
rent timet, Hence, the time ihown % f l c o f l r Mrlth“
.parenttime, aud'thqnefote a dial will dffferifrhra'.n dPWv.
by how much the- eqjinfion o f tqme is on thqt {lay.
-'H^hen-thertfetesyou f i t a 'b y ,Ä 9 dial, jmfi.mqitfee
what-the equation o f time, js.pgpn that day,'-.and
allow fa r hSj.ifbr, inflsraße; if,thg ^quaMqp bE,^ m.mv^S8»
and bhfi.pEatdibhi^ftSS^hsji the' fun, 'then -you .prüft
ifetiyBiW) jsatcb gri^imtfts before the time ihown by the
dial. . Now aftronqinera, ^hon;they.ucgm.gqtq:,{^jj|3 p f ’
.the equation of-timcifqr every day b^dhe-ye^r« % ,re ie
funsand clock together, jwbebj.beifu>n is at his apogee,
and täremth '^^ädda tei’SKhatia the^ifferenen hptw£?fi
the fqn and ,the «sloclt, fo r every:dayf.?tjipnp^^pÄjafert
them in a table, ftating.hosv much the clock is before o r
after the fun. For; the methods Of, makfig'tbdr:>9d.c{i"
. Jations»-we<®iuf: alfer the; reader, to ,
mentioned. The-imblmatron o f the ecpat®f t.0.ffe:9S?ip'r
tic, upop »hielt the equation o f time partly depends,
and the p lä c e o f -the fua’ s apogee, when theMdne^.aqd
. fumfet d^.together, being.bpihfnWsd to yary, the equation
«£> tune-fir- .the fame day#, o f -the ye a r,ypj-fy^ry.
f year -vary, and ■ ^jiefereribvmjjft.
year. Beudes ther^qe rwhentthe fup.;,is -in bis,apogee,
■ 1 there are three ojther timen o f the year when the, mock.
1 and fine agree^qu when bmukk vs&apparent times;ate the
■ fame. -
-*8f. Whenever it is required to make any calculations
from aftronomical tables, and the time given is apparent
■ time, the ^ equation- of.'tithe, muff be applied in oydtr to
convert it into mean time, and for that time the cqrapu-
tations mull be. made, becaufe aQ tables are conftrufted
for wean motions. Thus; if it w'ere required to find
in ft mean folar day of 24 hours, and an angle of 360° in afidtrcal day,
igth of a fiderea! day in mean folar rime, or the time from the palfage
the
Sny day at apparent rroonf itbe 'equation
o f time^nuffi. be apphed to 12 o’ clock, and tbfen the
ftlh’ s'place fhuft-be 'cbtnputed -frhtn «he "tables for ,tsbat
etiikr. 'A ll thh atbislts 'ih the Nautical Almanac, anfwer-
36g'to noon, fife Cbtftptrtedrin -dfls manner. -
&ri ‘the 'Sdfar-.Syfiem.
8'2. T he fun jis placed in, ‘tbe. ieentcr >of .the fy-ftemi
about which the planets revolve in thefoho(vving! order,
Tfckotring from 'the-ifun-r' mercury, menus, the earth,
-mars, juplter, fatuthi, and ‘ifhc'geargian ; tlr&fc:are fome-
times 'called primary planets. Some o f thefe planets
have bodies 'revolving 'about {them,; the -earth has qrne?;
Jiipiter - has fou r; fa turn bas'jfey&nv; 'and the geotgian
has fix ; > theft art called“fecorfdary planets, fatelliifs-,’ehr
moons. There afefalfd oth-ef bqdiea'whrch'resol’V'e about
|die jftini rea lly fiometc, which move in orbits vvery elliptical,
mid extend -to a very great .diftancc- beyond the
orbits o f the-primary planets. T he fun, the primary
planets, the. fecondary planets, and the comets, compofc
what is galled -the Solar Syflcm. The two planets'
which ar.e -nearer to: the -fun than the -earth is, are called
inferior p lanets; and the other five which are further
from the fun than the earth is, are calle i fuperior .planets.
A l l the .other 'bodies in the-heavens are fixed liars, and
at fuch immenfe'-diftances beyond the folar fyftem, that
their apparent relative fituations are not at all altered by
the motion-of,the earth in its orbit ; we may therefore
confidei- them ias' placed in-the, concave furface o f a
fphere, having the earth for .its -center ; and-to thefe
we refer the inorionr, o f the bodies in our fyftem. The
orbits.,of the:primai^r.planets are ellipfes, having-the fun
in fme rdfIt-be ffoei-;* but they are fo very nearly circles,
tha^Arkwirvprefcnt ppr.pofe, we may confider them A*
circles bavMg'Weif»n »»(MBMeBtffe
P
., 82. L e t 5 be 'th® luflv -E the earth, .aUdetttimAjjl ik
p f onefofqbe'im^rior-planejs, veWipip&nUfxuri
fphere o f the fixed Bars-; drzve f aSeP,
£rf?r -jE/S- be tangents' to the'orbit o f the1 planet, -and let
a, h, c, f , e, f , be- fo many -di-ft’eredl:: fituatiohs .
planet; then as vhq planets a le opaque bodies, that.half
which is next to the. fun,., is enlightened,fandr’the ofher
half is dark, as reprefefited in, the figure. 'The fituation
a is called inferior copjunQfon and 'fbe- R a tio n ,»
ci(lted'yh?«t2o*‘"ebnjua|SiJ39t M 9W' A k maaifeft, that a t q
>the dark part only o f the, planet is "towards -the earth,
and therefore the planet mthnn inyiffMe ; vat h,„'a part
" if the enlightened face is. towmdsqahe earth,-and therefore
part offthe. planet'wiirbe vffible, and will.look.Kke
th e 'moon before j t 'chides to its firft quarterat c, one
half of the e&ghteiiea,pari?bf the planet will jbe turned
towirds the earthy -and it .Swill feck like tfre moon at its
firft quarter,;- at d, more than half!the. enlightened part
ofibciptanjetpsip be 'towards the earth, arid It will look
hke the- riioon biitweenits fecond quarter and full; at e,
the |vhole enlightened part of the, planet will be next
|heVarth,8and tMjpl^iiet wijl appear to, ihipe witlj a full
facc,Jik-e tKe ’mQon.al.i,ts full ;and fio^n 6 through ƒ to
a, the appearancesswSl be t|ie fame ifi.ihe contrary or-
der.lr' Thlrc are the phinonuna which an-; inferior planeb
mul; hnvp j r*ndah,.jh5yfewigg, w n « and mercury with *
d 2 • ' ielefcope,