Ce ASTRONOMICAL ax» 
In plate I, figure IL, in the plain right-angled triangle BA C, 
right-angled at B, let C B be the femi-diameter of the earth, 
which call 1, the angle B A C the moon's horizontal parallax, 
the hypotenufe C A the moon's diftance from the earth's cen- 
ter in femi-diameters of the earth, to find which fay Sine an- 
gle BAC : fide B C :: Radius : hypotenufe C A. " 
Having found the moon's diftance from the earth's center, — 
there are given in plate I, figure III, in the plain oblique. 
angled triangle B A C, the fide A C — the moon's diftance from 
the earth’s center, the fide B C = the earth's femi-diameter, 
and the included angle B C A = the fhoon's true zenith dif- 
ance, to obtain angle B A C— the difference between angle 
BCA the true zenith diftance and D B A the vifible zenith 
diftance == the moon’s parallax in altitude ; tofind which, fub- 
tract angle B C A from 180° the fum of the three angles, the 
remainder will be the fam-of >the tv angles A B C 
eee. "Take the fh dnd dilferetice of Che Bdes- A C and 
; then fay, the fum of the two fides A C and BC : their 
Rain :: the Tangent of half the fum of the two unknown 
angles: the Tangent of half their difference. Subtract the: 
half difference from the half fum, and the remainder will be: 
the leffer angle BAC= the moon E nep * which: 
- added 
* The common method of deducing the moon’s parallax in altitude from her — 
true zenith diftance is by approximation ; finding the parallax for the true zenith. 
diftance as if it were the vifible, by adding together the logarithmic Sine of the 
zenith diftance and of the horizontal parallax: then adding the parallax thus found 
to the true zenith dilamce, and confidering the fim as the vifible zenith diftance, 
and then going over the work again ; but [have exhibited the above method as 
the direst one ; and it is but little longer than the other. | 
