ON MAPPING THE SURFACE OP THE MOON. 



231 



L'=l+supp. £3 (see section 18). For the formulae used in computing B see 

 section 11, and for A see section 7. These formulae have been employed in 

 the following computations of points of the First Order. 



The principal part of the libration in longitude is l—\ (see section 9), 

 which, besides changing sign in each lunation with respect to east and west, 

 changes sign also with respect to north and south by the motion of the moon's 

 apsides. 



Application of the foregoing investigations to the motion on the apparent disk 

 of the point at ivhieh the Equator i^ifersects the First Meridian. 



23. It now remains to inquire how the point of intersection of the moon's 

 equator and first meridian will be affected by the changes in latitude and 

 longitude which the centre of the apparent disk is perpetually undergoing ; 

 for as only the latitude and longitude of this single point are determined by 

 the formulae for computing the Hbrations, we do not appear to have at pre- 

 sent the means for tracing out on the moon's disk the curves representing 

 the moon's equator and first meridian for any other epochs than that of mean 

 libration, when, as before mentioned, they cross the disk in two straight lines 

 intersecting at the centre ; and this inquiry is perhaps the more important as 

 showing how necessary it is, for accurately mapping the surface, to have good 

 determuiations of points of the first order. Taldng, therefore, the spot on 

 the moon's surface at which the equator and first meridian intersect each 

 other, we may inquire the path it will describe on the apparent disk during 

 the changes of libration through one revolution of the nodes. 



24. In fig. 9 let W E N S represent a small circle concentric with the limb or 

 margin of the apparent disk of the moon, W E being a portion of the equator. 



Fig. 9. 



and N S of the first meridian in mean libration at the passage of the descend- 

 ing node and perigee respectively, and o the point of intersection of the two 

 (0° of latitude and longitude), and o' the position occupied by the point o by 

 the joint effect of both librations, o E will consequently represent the greatest 

 excursion of the point o in longitude, and o S that in latitude, the equator 

 being projected in the curve e' o' q, and the first meridian in co'm. The 



