[ 2 7 + ] 
conds — — + r t x L r — rt x tabular cotangent of L S 
1146000000000 
The logarithm of the denominator 1146000000000 
is 12,059, hiftead of fubftracfting which, when the 
operation is performed by logarithms, add 0,941 
(its compliment to 13) to the value of the numera- 
tor found in logarithms, and fubftracft 13 from the 
index : the remainder will be the value of at in 
feconds. Q. E. D. 
A concife rule to find the diflance of the Moon from a 
zodiacal far, very nearly ; the difference of the longi- 
tudes of the Moon and ftar , and the latitudes of both 
being given . 
To the coline of the difference of the longitudes 
add the coline of the difference of the latitudes, if 
both of the fame denomination, or fum ; if of con- 
trary denominations, the fum of the two logarithms, 
abating 10 from the index, is the coline of the ap- 
proximate diftance. This gives the true diftance of 
the Moon from the Sun, being then nothing more 
than the common rule for finding the hypothenufe 
of a right-angled fphcrical triangle from the two 
lides given. But in the cafe of a zodiacal liar apply 
the following corre&ion to the approximate diftance 
thus found. 
To the conftant logarithm 5.3144 add the line of 
the Moon’s latitude, the line of the liar’s latitude, the 
verfe-fine of the difference of longitude, and the 
cofecant of the approximate diftance j the fum of 
thefe 5 logarithms, abating 40 from the index, is 
the logarithm of a number of feconds, which fub- 
ftra&ed 
