EA oils X LIE. 
w 
HE OEE ERES EN, EI y EAE ERG 
Gaa aai i aiii a tnt ESTA SPs re eee wow A 
MATHEMATICAL PAPERS. 13 
added to the true zenith diangps, will give the "iere" 
D B A. 
= ` For the parallax in latitude and longi 
: Having found the moon’s parallax in altitude fuppofe it fet ` 
off plate I, figure I, upon the vertical arc from p to m towards 
the horizon, becaufe the vifible zenith diftance is greater than 
the true; then, the point will be the moon's vifible place, 
or her place as feen from fome given fpot on the earth’s furface. 
From $ to-L, through m, let the arc oL be drawn ; then, 
in the triangle pmp, the angle mp D = the diftance between £ 
- and e on the ecliptie is the moon's parallax in longitude ; and 
the fegment my, of the fide pm, is her parallax i in latitude ; 
to find which by fpheric trigonometry, there are given two fides 
and the included angle, viz. fide p i aus moon's diftance from. 
le of the ecliptic ; the fide the moon's parallax in in 
aftu, and cin p» m= meni at nest angle p> Z to 180°: 
Or it may be more convenient to anta the triangle LDm ; in 
which are given fides L » and ) z and the included angle Lpz, 
= A Z to obtain the fame things.. But the moon's parallax in 
atitude and longstude may be found more eafily, by the follow- 
ing method. he p mr upon the arc p> L ; 
then, [o will Be formed. a right-angled triangle ) mr, right- 
angled atr. As the perpendicular mr, in eclipfes of the fun, 
and even in occultations of fixed ftars by the moon, will al- 
ways be near the ecliptic, it may be confidered as paralla] to it, 
without any fenfible error ; confequently, the fide mr may be 
reckoned == the fegment ym. We may therefore call the fide 
» the moon’s parallax in latitude, and the fide mr, augmented 
in the ratio of the Sine of the moon's vifible co-latitude to ra- 
dius, 
