ON MAPPING THE SURFACE OF THE MOON. 



Collecting the results, we have 



337 



b' = - 5 1 50 

 1'=- 3 12 57 

 C = -15 20 28 



Determination of the Arc fi. 



Having determined the selenographical latitude and longitude of the appa- 

 rent centre of the moon's disk, and also the angle which the meridian of the 

 middle of the disk makes with the circle of dechnation, we may ascertain the 

 latitude and longitude of the measured point by the aid of the arc yu (fig. 12) 

 on the spherical surface of the moon, which connects the measured point with 

 the apparent centre M. 



Fig. 12, 



£_aL 



For this object the following elements are required : — 

 Fig. 11, p. 234. /= the polar coordinate of the measui-ed point = sni r,i 

 fig. 12. 

 „ „ u= the inclination of/ to the apparent declination circle. 

 For obtaining the values, we have 



Fig. 11, p. 234,/= .jpj— , Unu= ^. 

 Fig. 12. n=m — \p. 



Fig. 12. E"= the distance of the moon's centre, C, from the place of ob- 

 servation, A. 



^=sin;/'. 



For — - we have 



E 



1 E" sin TT 



E^~E3-663' 

 in which 



E"= the moon's apparent semidiameter, to be computed by the following 

 formula : — 



R" = 



,, cos S' T, 

 cos a . K 



cos 6 



-, pcosd»'sin7r . Q.X /I ^" 



i— ^-- cos(a — 3)=(1 — m) 



cosS ^ ^ ^ ' 



