[ 276 ] 
cof. QP X cof. P R + fin* QP X fin. P R j 
whence fin. QP X fin. P R = cof. (Qj 5 — PR) — 
cof. QP X cof. P R j which being fubftituted above, 
gives cof. R Qj= cof. (QP — P R) X cof. P — cof. 
PR X cof. QP x cof. P -p cof. P R X cof. Q P = 
cof. (QJP — PR) x cof. P 4- verfe-fine P X cof. 
P R X cof. QP. Now put cof. (QJP — P R) X 
cof. P — cof. G, or the approximate difiance, then 
cof. R Q^- — cof. G, or (becaufe the difference of 
R Qjmd G is but fmall) G — R Q^X fin* ( G+ 
= verfe-fine P x cof. P R X cof. P Q nearly. 
Whence RQ== G — _ verl '- | ' ine P x cof. P R x cof^P 
nearly — G 
QJE. D. 
V. 
lirt. Cj + K Ci. 
f. P X cof. P R X cof. QP 
~ lin. G 
nearly. 
Note , the error of this formula arifes from 
takino- G — JL±_!L 5 -by which means it will always 
give R Q too great, nearly by the following quan- 
tity, L S q cof. P R X S q cof. Q P X cot. G X S q 
tan. 1 G. This comes to a maximum when G is 
6 o°, and is then = 4 X S q cof. R P X S q cof. 
P Q. If the latitudes of the Moon and ftar are both 
r° it is= 1". If the Moon’s latitude be 5 0 , and that 
of the fiar io°, it is = 4" 4; and if the latitude 
of the fiar be 1 5 0 it is = 10", 
XLIX. 
