A S T R 
diameters, O the place of the fpeftator, H C R the ra¬ 
tional horizon, to which draw ZONK perpendicular; 
L the Moon, join LO, LC, L K, and draw C V perpen¬ 
dicular to LK. Now, to compare the apparent places 
feen from O and C, let us compare the places feen from 
Q and K, and from K and C. Put h — the horizontal 
parallax to the radius O C, or O N, which is very nearly 
O N O M Y. 
have bL : ba :: fin. P b X fib. pb 
hence CLK: 
//X^X cof. dec. 
coi'.KCN 
This there- 
cof. P p ■ 
, , cof. Lp —cof. Pi X cof. P* 
pb ; hence ba—b Lx-> r -: 
fin. Pi X fin. pb 
43y 
cof. Pi x cof. 
hya 
X 
cof. Pi cof. Pix col. pb 
~ cof. lat. 
hya 
fin. pb 
fin. Pi 
cof. Pi 
fin. pb 
• cof. Pi X cotan. pb 
cof. lat. 
by a 
cof. lat. 
X 
col. 23 0 28' 
cof. Moon’s lat. “ ^ X tan * M °° n ’ S lat ’ Bl,t ’ if 
CP be to CE as 1 is to 1 -\-m, and x, y, — the fine and co¬ 
fine of the latitude of the place, then a= 2 myxy ; hence b& 
—zhmx X- 
cof. 
2 3 
28' 
. rA , r , , „ fin. dec. x tan. Moon’s lat, 
cot.Moon’slat. 
The fign — becomes -f- if the declination and latitude of 
the Moon be of different affiedtions, that is, one fouth and 
the other north. The latitude here ufed is that feen from 
the centre of the Earth. This correction increafes the 
Moon’s difiance from the pole,/? of the ecliptic. 
To find the correction of longitude, or the angle 1 .pa, 
we have La—Lpa y fin. pL, hence L pa— — ; but 
iin. p L 
cL=iLx fin. i, and by fpher. trig. fin. Pi ; fin. p :: fin. 
P p ■ fin. i — -——; alfo Lb—zhmx ; hence Lpa— 
lin. Pi r 
equal to it, on account of the fmallnefs of the angle 
C O N. Let C 0=2 1, and C N (the fine of CON to that 
radius) —a, t— tan. of the angle KCN the latitude of 
the place; then rad. — 1 («-NK; hence, as h 
— the angle under which ON (which we may conlider as 
equal to unity) appears when feen direCtly at the Moon, 
we have hyta— the angle under which N K would ap¬ 
pear; therefore byi^-ta — the horizontal parallax of 
O K ; confidering therefore K as the centre of a fphere, 
and KO the radius, compute the parallax as before. Now, 
as the planes of all the circles of declination pafs through 
P p t in eflimating the parallax either from K or O, the pa¬ 
rallax in right afeenfion mull be the fame, becaufe K and 
O lie in the plane of the fame circle of declination; the 
only difference therefore between the effeCl of parallax at 
K and O mult be in declination. Now at K, the angular 
difiance of the Moon from the pole P is LKP, and the 
angular difiance from C is LCP; the difference of thefe 
two angles, therefore, or CLK, is the difference between 
the parallax in declination at K and at C, and this angle 
C L K is always to be added to the polar difiance feen from 
K to get the polar difiance from C. Now, CLK— hy CV ; 
but the angle VCK (=LCE) is the Moon’s declination, 
CN 
therefore CV=:CK X cof. dec. alfo CK 
alfo Lb—zhmx; 
cof.Ion. (( X fin. 23°28' 
cof. lat. ’ ~ cof. lat. 
fore is the equation of declination for the fpheroid, to be 
applied to find the parallax in declination feen from C, af¬ 
ter having calculated the effefl of parallax in declination 
for a fphere whofe centre is K and radius KO. There is 
no equation for the parallax in right afeenfion. To find 
how this equation-in declination will affedt the latitude, 
let P be the pole of the equator, p 
the pole of the ecliptic, L the place 
of the Moon feen from K, and b feen 
from C ; then b L is the equation in 
declination ; draw La perpendicular 
to pb, and ba is the equation in la¬ 
titude, and the angle ap L the equa¬ 
tion in longitude. Now, confider¬ 
ing b L and ba as the variations of 
the two fides Lb, pb, whilfi P p and 
the angle P remain conftant, we 
fin. py fin. Lp 
zhmx x 7. — yr, — 7 - r — ihmx y , , „ , 
fin.Pi>Xhn./?L cof. dec. <( X cof. lat. <J 
— (as the cof. of the Moon’s latitude may be confidered 
. . , , fin. 23 0 2S' . , 
equal to unity) zhmxy ——— -- x cof. Ion. (T . In 
col. dec. (J 
north latitude, we muft add this correction to the longi¬ 
tude feen from K, in the figure preceding the lafi, when 
the Moon is in the defeending figns 3, 4, 5, 6, 7, 8, but 
fubtratt it when in the afeending figns o, 1, 2,9, 10, n,to 
have the longitude feen from C ; and the contrary when 
the latitude of the place is fouth. 
According to the Tables of Mayer, the greateft paral¬ 
lax of the Moon (or when (he is in her perigee and in op- 
poiition) is 61'32"; the leafi parallax (or when in her 
apogee and conjunction) is 33' 52", in the latitude of Pa¬ 
ris; the arithmetical mean of thefe is 57' 42" ; but this is 
not the parallax at the mean difiance, becaufe the parallax 
varies inverfely as the difiance, and therefore the parallax 
at the mean difiance is 57' 24", an harmonic mean between 
the two. M. de Lambre re-calculated the parallax from 
the fanfe obfervations from which Mayer calculated it, 
and found it did not exaCtly agree with Mayer’s. He 
made the equatorial parallax 57' 11-4". M. de la Lande 
makes it 57' 5" at the equator, 56' S3’ 2 '' at the pole, and 
57' 1" for the mean radius of the Earth, fuppoling the 
difference of the equatorial and polar diameters to be — 
of the w hole. From the formula of Mayer, the equato¬ 
rial parallax is 57' 11‘4" with the following equations, ac¬ 
cording to M. de la Lande : 
57 ' 11 ’ 4 ' 
-3' 
7 * 7 " 
cof. ano. <T 
+ 
10*0 
cof. 2 ano. ({■ 
0-3 
cof. 3 ano. <X 
— 
3 7 *3 
cof. arg. eveCtion 
o *3 
cof. 2 arg. evect. 
+ 
26'Q 
cof. 2 difi. ([ a O 
I ’O 
cof. difi. (f a © 
+ 
O'?. 
cof. 4 difi. ({ a O 
+ 
2*0 
cof. 2 (apo. (J — 0) 
JU 
O * 2 
cof. 3 (apo. (1— O) 
+ 
1*0 
cof. (arg. eveCt. 4. ano. 0 ) 
4 * 
o -3 
cof. (2 arg. lat. — ano. <J cor.) 
— 
o-8 
cof. (2 difi (( a0 - ano. 0) 
•— 
°’7 
cof. (2 difi. (1 a 0 + ano. 0) 
+ 
o*6 
cof. (arg. evedt. — mean ano. d) 
0*4 
cof. 2 (&—©), or 2 (0 -f fup. $:) 
