Of tie MOON from the SUN. 193 



To the logarithmic cotangent of half the fum of the appa- 

 rent altitudes add the logarithmic tangent of half their dif- 

 ference, and from the fum fubtract the logarithmic tangent of 

 half the apparent diftance, the remainder will be the logarithmic 

 tangent of a i ft arc. 



THE fum of arc ift and half the apparent diftance, will be a 

 2cl arc. 



THE difference of arc ift and half the apparent diftance, will 

 be a jd arc. 



To the log. tangent of arc 3d add the log. tangent of the 

 greater altitude, the fum, rejecting radius, will be the log. co- 

 fine, either of the angle itfelf at the higher object, between the 

 other object and the zenith, or of its fupplement to 180, as 

 arc i ft is lefs or greater than the half diftance. As the applica- 

 tion of the Jirji and third corrections depends on the quality of 

 the angles, it muft be obferved, that, if arc ift is lefs than the 

 half diftance, the angle itfelf will be found, and will be acute ; 

 but if arc ift is greater than the half diftance, the angle found 

 will be the fupplement of the angle at the higher object to 180% 

 and the angle itfelf will be obtufe, or greater than 90. Ne- 

 verthelefs, if the greater altitude is that of the Moon, the co- 

 fine thus found is to be ufed in computing thejirjl correction of 

 diftance. 



To the log. tangent of arc ad add the log. tangent of the 

 lefler altitude, the fum, rejecting radius, will be the log. cofine 

 of the angle at the lower object, between the other object and 

 the zenith, and will always be acute. 



THESE two angles being known, the feveral corrections of 

 diftance will be found as follows : 



i. To the arithmetical complement of the log. cofine of the 

 angle at the Moon, add the proportional logarithm of the cor- 

 rected parallax, the fum will be the proportional logarithm of 

 the firfl correction, which is to be added to the apparent di- 



B b ftance 



