Of the MOON from the SUN. 195 



rejecting ten from the index, will be the proportional logarithm 

 of a fourth correction, which, added to the diftance, thrice cor- 

 rected, will give the true diftance. 



THE following method of finding the angles at the Moon 

 and Star will perhaps be more familiar to fome ; as it is the 

 fame with the method commonly ufed to find the apparent 

 time from the angle at the pole between the meridian and the 

 Sun or a fixed Star j and though it is not quite fo concife as 

 the former, it has this advantage, that it gives both the angles 

 without any ambiguity. When- this fecond method is ufed, the 

 logarithms mould be taken to at leaft five places of figures, be- 

 fides the index. 



1. 1*0 find the Angle at the Moon. 



ADD together the apparent zenith diftance of the Star, the 

 apparent zenith diftance of the Moon, and the apparent di- 

 ftance of the Star from the Moon's centre ; take their fum, half 

 their fum, and the difference between the half fum and the ze- 

 nith diftance of the Star ; then add together the arithmetical 

 complements of the log. fines of the Moon's zenith diftance and 

 the apparent diftance of the objects, and the log. fines of the 

 half fum, and the difference between the half fum and the ze- 

 nith diftance of the Star. Half the fum of thefe four loga- 

 rithms will be the log. cofine of half the angle required, which 

 being doubled, .will give the angle at the Moon between the ze- 

 nith and the Star. 



2. To jind the Angle at the Star. 



A-DD together the zenith diftances of the Moon and Star, and 

 the apparent diftance, and take their fum and half fum as be- 

 fore ; but now take the difference between the half fum and 

 the zenith diftance of the Moon ; then add together the arith- 

 metical complements of the log. fines of the Star's zenith di- 

 ftance and the diftance of the objects, and the log. fines of the 



B b a half 



