fin. P fin. A 
[ 246 ] 
fm. P fin. A 
^ 1 + 2 fin. P (cof.D-cof. A 
V 1+4 fin. Pfm.. A + D 
2 
fin. — — — ; fince cof. D-cof. A =2 fin /~ T ' — fin.- — 
2 22 
This being found without any logarithmic compu- 
tation, we {hall find tang. E a = 4 fin. P fin. -— - - fin. 
— — , if A^D, and hence we may eafily compute 
fin. p r: fin. P fin. A cof. E; but if A we {hall 
find cof. F 2 — 4 fin. P fin. fin.— — ? and hence 
r , fin. P fin. A 
fin. — - — - — 
r lin. i* 
§ 6. Similar formula? maybe found for cof. />, but 
as the angle p is pretty fmall, one might eafily fall into 
fome error by the ufual tables of logarithms. I fliall 
not fay what would be the amount of this error of 
having furnifhed the manner of avoiding it ; but this 
remark has not, I think, as yet been made in aftrono- 
mical calculations ; and I have found it of great confe- 
quence in computing eclipfes, where the difiances to be 
found are very fmall arches. 
§ 7. It may moreover be obferved, that if A = D, 
fin. p-=: fin. P fin. A; hence in the fame cafe, 
and f'^p, which feems very odd ; but the moon then 
is below the fenfible horizon. 
Theory of the apparent Diameters of the Moon . 
§ 1. Firft the exprefiion of horizontal diame- 
ter of the moon, or of the diameter feen at the 
horizon, feems to me too vague ; for one ought to 
underftand by it the diameter feen at the center of the 
terreftrial 
