434 
CB X fin.PBM 
astro 
and, as the parallax is very fmall, the 
CP 
fnm of the two fines will be very nearly the fine 
of the fum, therefore the fine of APB = 
CA x fin. PAL + CB X fin. PBM , 
■---5 l>enee CP = 
CAx fm.PAL+CBX fin.PBM 
fin. APB 
Or, let E QJbe the equator, P its pole, Z the zenith, 
v the true place of the body, and r the apparent place as 
depreffed by parallax 
in the vertical circle 
Z K, in the annexed 
figure; and draw the 
fecondaries P v a, 
P rb ; then ab is the 
parallax in right af- 
cenlion, and rs in 
declination. Now, 
vr : vs :: i (rad.) : 
fin. vrs or Z»P, and 
t/s : ab :: cof. va : 
i, hence vr : ab :: 
ZvP, 
va : 
a b 
vr \ 
fin. 
®rx fin. Z»P 
col', va ’ 
but vr—hor. par. X fin. vZ , and fin. vZ : 
fin. ZP :: fin. ZPd : iin.ZvP — 
fin.ZPx fin. ZPv 
„ , there- 
fin. vZ 
. lior.par. X lin.ZPx fin. ZPy 
fore, by fubftilution, ab — - 7 -. 
’ 1 ’ col. va 
Hence, for the fame ftar, where the hor. par. is given, the 
parallax in right al'cenfion varies as the fine of the hour 
abx cof. va 
angle. Alio the hor. par. — -—=-=r——rrrr-. For the 
D r (in. ZPx Ini. ZPw 
eallern hemifphere, the apparent place b lies on the equa¬ 
tor to the eaft of a the true place, and therefore the right 
afcenfion is diminifhed by parallax ; but, in the weftern 
hemifphere, b lies to the welt pf a, and therefore the right 
afcenfion is increafed. Hence, if the right afcenfion be 
taken before and after the meridian, the whole change of 
parallax in right afcenfion between the two obfervations is 
the fum (i) of the two parts before and after the meri- 
vr 
dian, and is therefore =—7-X fum (S) of the fines 
cof. va 
©f the two hour angles: and the hor. par. '* - ~ ^ ■. 
0 ’ r fin.ZPx-S 
On the meridian there is no parallax in right afcenfion. 
To apply this rule, obferve the right afcenfion of the 
planet when it paiTes the meridian, compared with that of 
a fixed liar, at which time there is no parallax in right 
afcenfion ; about fix hours after, take the difference of 
their right afcenfions again, and obferve how much the 
difference (d) between the apparent right afcenfions of 
the planet and fixed liar has changed in that time. Next 
obferve the right afcenfi«>n of the planet for three or four 
days when it paffes the meridian, in order to get its true 
motion in right afcenfion ; then, if its motion in right af¬ 
cenfion in the above interval of time between the taking 
of the right afcenfions of the fixed liar and planet on and 
oft' the meridian be equal to d, the planet has no parallax 
in right afcenfion; but, if it be not equal to d, the 
difference is the parallax in right afcenfion, and hence 
the horizontal parallax will be known. Or one obferva- 
tion may ,be made as long before the planet comes to the 
meridian, by which a greater difference will be obtained. 
But, belides the effect of parallax in right afcenfion and 
declination, it is manifeft, that the latitude and longitude 
of the Moon and planets mull alfo be affefted by it; and, 
as the determination of this, in refpefl to the Moon, is in 
many cafes, particularly in folar eclipfes, of great impor- 
N O M Y. 
tance, we fliall proceed to ftiew how to compute it, flip- 
poling that we have given the latitude of the place, the 
time, and confequently the Sun’s right afcenfion, the 
Moon’s true latitude and longitude, with her horizontal 
parallax. 
Let HZR be the meridian, y'EQ^jthe equator, p its 
pole; Y~C the ecliptic, P its pole; y' the firft point of 
Aries, H QJd the horizon, Z the zenith, Z L a fecondary 
to the horizon palling through the true place r and appa¬ 
rent place t of the Moon; draw P t, Pr, which produce 
to s, drawing the fmall circle ts parallel to ov ; let rn be 
perpendicular to P t, and draw the fmall circle ra paral¬ 
lel to ov, then rs, or ta, is the parallax in latitude, ami 
ov the parallax in longitude. Draw the great circles Py\ 
PZ A B, P pde, and Z W, perpendicular to pe ; then, as 
fticial points S or vf ; alfo draw Zx perpendicular to 
P r, and join Zy% p"f- Now y'E, or the angle y'p E, 
or Z pY) > s the right afcenfion of the mid-heaven, which 
is known ; PZ—A B (becaufe A Z is the complement of 
both) the altitude of the higheft point A of the ecliptic 
above the horizon, called the nonagefimal degree, and 
Y'A, or the angle Y'P A, is its longitude. Now, in the 
right-angled triangle ZpW, we have Z p the co-latitude 
of the place, and the angle Z p W, the difference between 
the right afcenfion of the mid-heaven 'fp E and 7’V, to 
find/>W; hence P W=zpW P, where the upper fign is 
to be taken when the right afcenfion of the mid-heaven is 
lefs than 180°, and the under when greater. Alfo, in the 
triangles W Z p, WZP, fin. W p : fin. W P :: cot. WpZ 
: cot. WPZ, or tan. A Py'; and, as we know y'o, or 
y'Po, the true longitude of the Moon, we know APo, 
or ZP*; alfo cof. WPZ, or fi’n. Y'PZ, : rad. :: tan. 
W P : tan. Z P. Hence, in the triangle Z Pr, we know 
ZP, Pr, and the angle P, from which the angle Z rP or 
tr s, and Z r, may be found ; for, in the right-angled tri¬ 
angle ZPr, we know Z P and the angle P, to find P*; 
therefore we know r x ; and hence (as the fines of the feg- 
ments of the bafe of any triangle are inverfely as the tan¬ 
gents of the angles at the bafe adjacent to which they lie) 
we may find the angle Z r x, with which, and rx, we 
may find Z r, the true zenith diftance; to which, as if it 
were the apparent zenith diftance, find the parallax and 
add to it, and you will get very nearly the apparent zenith 
diftance, corresponding to which, find the parallax rf; 
then, in the right-angled triangle rst, which may be con- 
lidered as plane, we know rt and the angle r, to find rs 
the parallax in latitude ; find alfo t s, which, multiplied 
by the fecant of tv, the apparent latitude, gives the arc 
ov, the parallax in longitude. 
Hitherto we have confidered the efteft of parallax, up¬ 
on fuppofition that the Earth is a fphere; but, as the 
Earth is a fpheroid, having the polar diameter Ihorter than 
the equatorial, it will be necelfary to (hew how the com¬ 
putations are to be made for this cafe. The following 
method is given by Clairaut: Let E PQ ^_p in this fi¬ 
gure, be the Earth, E Qjhe equatorial and P p the polar 
diameters. 
