ASTRO 
And, in whatever pofition we take r, thefe conclufions 
will give the rule as flated above. If we confider yC as 
the equator, and y Q^the ecliptic, the demonftration will 
do for the fecond rule. 
If the body be the Sun at s', whofe right afcenfion and 
declination are given, to find its longitude; then fin. s'y'n 
: rad. fin. s'n : fin. ys', that is, fin. obi. eel. : rad. :: 
fin. decl. : fin. longitude. Or, cof. s'y'n : rad. :: tan. 
yn : tan. y s', that is, cof. obi. eel. : rad. :: tan. right 
afc. : tan. longitude. The Sun being always in the eclip¬ 
tic has no latitude. 
To find the Angle of Position. 
Let p be the pole of the ecliptic yL, P the pole of the 
equator y C, S a ftar; draw the great circles /iLC,/iSD, 
p PS BA, and PS p is the angle 
' v of pofition. Now, the angle 
P p S, or D L, is the comple¬ 
ment of longitude yD; the an¬ 
gle p P S is the fupplement of 
A PC, or of AC, which is the 
complement of the right afcen¬ 
fion y A of -the fiar; p P is the 
obliquity of the ecliptic; P S is 
the complement of the declina¬ 
tion, and p S the complement of 
J C the latitude of the ftar. Hence, 
if the longitude and declination of a ftar be given, w-e 
have fin. P S : fin. PpS :: fin. P p : fin. PS/>, that is, cof. 
ftar’s dec. : cof. its long. :: fin. obi. eel. : fin. angle of 
pofition. If the latitude and declination of the ftar be gi¬ 
ven, we know p S and PS their complements, and P p; 
hence fin. pS X fin. PS : rad. 2 :: fin. | x $P+ s /'+^PX fin. 
£ X SP+S/>—P/> : cof. PS/>*. Or of the right afcen¬ 
fion, declination, latitude, and longitude, of the ftar, any 
two being known, we fhall know three parts of the trian¬ 
gle P p S, and confequently the angle P Sp may be found. 
If S be the Sun, pS~<)c 0 , and the triangle may befolved 
by the circular parts. 
To find the Parallax. 
The centre of the Earth deferibes that circle in the hea¬ 
vens which is called the ecliptic; but, as the fame object 
would appear in different pofitions in refpedt to this cir¬ 
cle, when feen from the centre and furface, aftronomers 
always reduce their obfervations to what they would have 
been, if they had been made at the centre of the Earth, 
in confequence of which, the places of the heavenly bo¬ 
dies are computed as feen from the ecliptic, and it be¬ 
comes a fixed point for that purpofe, on whatever part of 
the Earth’s furface the obfervations are made. 
To find the Moon's Parallax, Take the meridian altitudes 
of the Moon, when it is at its greateft north and fouth la¬ 
titudes, and correct them for refraction; then the diffe¬ 
rence of the altitudes, thus corrected, would be equal to 
the fum of the two latitudes of the Moon, if there were 
no parallax ; confequently, the difference between the fum 
of the two latitudes, and the difference of the altitudes, 
will be the difference between the parallaxes at the two al¬ 
titudes. Now, to find from thence the parallax itfelf, let 
S, s, be the lines of the greateft and leaft apparent zenith 
diftances; P, p, the fines of the correfponding parallaxes ; 
then as, when the diftance is given, the parallax varies as 
the fine of the zenith diftance, S-.s:: P : p\ hence S— s 
: s :: P—p : />=-—-, the parallax at the greateft alti- 
tude. This fuppofes that the Moon is at the fame dif¬ 
tance in both cafes ; but, as this will not neceffarily hap¬ 
pen, we mu ft correft one of the obfervations in order to 
reduce it to what it would have been, had the diftance 
been the fame. If the obfervations be made in thofe pla¬ 
ces where the Moon paffes through the zenith in one of 
the obfervations, the difference between the fum of the 
Vol. II. No. 8 j. 
N O M Y. 43jj 
two latitudes and the zenith diftance at the other obferva- 
tion will be the parallax at that altitude. 
Tofind the Parallax of the Sun, GV. Let a body P be obfer- 
ved, as in the annexed figure, from two places A, B, in 
the fame meridian, then the whole angle APB is tire ef¬ 
fect of parallax between the two places. The parallax 
A PC ~ hor. par. X fin. PAL, taking A PC for fin. 
A P C, and the parallax B P C hor. par. X fin. P B M ; 
hence hor. par, x iin. PALf fin. P B M=APB, hor. 
par. = APB divided by the fum of thefe two fines. If 
the two places be not in the fame meridian, it does not fig- 
nify, provided we know how much the altitude varies from 
the change of declination of the body in the interval of 
the pafiages over the meridians. 
Ex. OnOftober5, 1751, M. de la Caille, at the Cape 
of Good Hope, obferved Mars to be i< 25-8'' below the 
parallel of A in Aquarius, and at 25° diftance from the ze¬ 
nith. On the fame day at Stockholm, Mars was obferved 
to be 1' 57-7" below the parallel of Aandat 68° 14' zenith 
diftance. Hence, if the angle APB is 31 -9", and the fines 
of the zenith diftances being 0-4226 and 0-9287, the ho¬ 
rizontal parallax was 23-6". Hence, if the ratio of the 
diftance of the Earth from Mars to its diftance from the 
Sun be found, we (hall have the Sun’s horizontal paral¬ 
lax. Now, from comparing the altitudes of the northern 
limb of Mars with ftars nearly in the fame parallel obfer¬ 
ved on the fame days at the Cape and at Greenwich, Bo¬ 
logna, Paris, Stockholm, Upfal, Hernofand, the mean of 
the whole gave 10-2" for the horizontal parallax of the Sun ; 
and, rejecting thofe refults which differed the moft from 
the reft, the mean was 9 842". From the mean of another 
fet of obfervations, the refult was 9-575". From the mean 
of feveral obfervations on Venus made in like manner, the 
parallax came out 10-38". The mean of the three laft 
gives 9-93" for the horizontal parallax of the Sun. Flam- 
ftead, from an obfervation on Mars, concluded the Sun’s 
parallax could not be more than 10''. Maraldi found the 
fame. From the obfervations of Mr. Pound and Dr. 
Bradley, Dr. Halley found it never greater than 12", nor 
lefs than 9". Caflini, from his obfervations on Mars, 
found it to be between 11" and 15". But the moft accu¬ 
rate method of determining the Sun’s parallax is from the 
tranlit of Venus over its dilk, already explained. 
If the Earth be a fpheroid, let E be the equator; draw 
GA», HBr, perpendicular to the furface, and compute 
the angles CAror LAG, and CBr or MBH; fub- 
tradt thefe from the obferved zenith diftances PAG, 
P B H, and we have the angles PAL, P B M. Now, 
CP: CA :: fin.CAPor PAL : fin.APC-- A X fin<PAL 
alfo CP : CB 
:: fin. CBPorPBM 
J5 S 
CP 
fin. BPC 
CjB 
