22Q 



REPORT — 1866. 



These formulae are employed in the following computations for determin- 

 ing the angle C and points of the first order. 



Investigation of Libration, 



12. In mapping the surface of the moon the orthographical projection ia 

 iised in which the centre is charactemed by 0° of latitude and 0° of longi- 

 tude. This point, of course, is that in which the moon's equator and first 

 meridian intersect each other. We have consequently to deal with two points, 

 a- or the centre of the apparent disk, which is the only point recognized in 

 the computations of libration, and the point of intersection of the first meri- 

 dian and the equator. These points coincide only when the line joining the 

 centres of the earth and moon passes through the centre of the apparent disk 

 in mean libration, which occurs in periods of 2-997 years. 



13. At any other epoch than that of mean libration the point <r is removed 

 more or less from the point of intersection of the equator and first meridian, 

 consequently as tr is the only point of the moon's surface turned towards the 

 earth to which the comiratations of libration refer, libration in latitude =: the 

 selenogi-aphical latitude of the apparent centre, and libration in longitude = 

 the selenographical longitude of the same point. 



14. When the moon passes the ascending node as seen from the centre of 

 the earth, the moon's equator appears as a straight line on the apparent disk, 

 and may be thus represented on the orthographical projection. Libration in 

 latitude then=0°. As the moon passes from the ascending node to the 

 greatest north latitude, the southern parts of the moon come into view, aiid 

 the equator is projected on the apparent disk as the lower segment of a 

 narrow ellipse, as given in an inverting telescope. All the appearances de- 

 scribed in this Appendix are inverted, lower for upper, &c. The east limb or 

 margin of the moon is seen in the telescope opposite to the right hand. The 

 greatest libration in latitude = the moon's latitude + the inclination of the 

 moon's equator to the ecliptic a b, fig. 1, p. 223. Were the moon a transparent 

 globe and the equator marked on it, the equator would be seen as a long, 

 narrow ellipse, widening and closing up between the passages of the nodes, so 

 that at the passage of the descending node the libration is again = 0°. 



Kg. 4. 



The same phenomena take place as the moon describes the portion of 

 her orbit south of the plane of the ecliptic, but in the opposite sense, the 

 northern parts coming into view. From this it will be seen that libration in 

 latitude changes its sign every lunation at the passages of the nodes. 



