228 



KEPORT — 1866. 



Lohrmann (Topographie der Sichtbaren Mondoberflache, p. 27) gives 

 b'= (a— 90°), a being equal to the distance of the moon's apparent centre 

 from the pole (see section 11). This formula i? employed in the following 

 computations for determining points of the first order. 



Since the greatest value of B' is about 1° 32', and the greatest value of 

 (3 about 5° 5', it foUows that b' must change sign in each lunation (see sec- 

 tion 14). 



Investigation of Lihration in Longitude. 



18. Libration in longitude, or the selenographical longitude of the appa- 

 rent centre of the disk, is equal to the angle formed at the moon's pole 

 between the first meridian, or that from which all selenographical longi- 

 tudes are reckoned, and the circle of latitude (Moon's pole a-p'Lin fig. 6) 

 passing through the apparent centre of the disk. This angle is equal to the 



Fig. 6. 



Moons Pole 



^^cii, 



iptic 



selenocentric longitude of the apparent centre of the disk, reckoned on the 

 moon's equator from the ascending node of the moon's equator on the 

 ecliptic (which is equal to the longitude of the ascending node of the orbit 

 + 180°), minus the distance of the first meridian from the same point (see 

 fig. 6), where ?S (K^ fig. 2, p. 223) represents the ascending node of the 

 moon's equator on the ecliptic, L the selenocentric longitude of the apparent 

 centre «r, and L' the distance of the first meridian from ?g , or its seleno- 

 centric longitude. The distance of the first meridian from the ascending node 

 of the moon's equator on the ecliptic is, from the uniformity of the moon's 

 rotation, at all times equal to the moon's mean longitude, minus the longi- 

 tude of the ascending node of the orbit, or plus the supplement of the longi- 

 tude of the ascending node. Libration in longitude vanishes when the moon 

 is in the Kne of the apsides. 



19, "When the moon passes the point of perigee, the first meridian, 0°, 

 of selenographical longitude appears as a straight line, which cuts the centre 

 of the apparent disk. Libration in longitude then = 0°. Should the passage 

 of the perigee coincide with that of either node, the first meridian is pro- 

 jected at right angles to the equator, also a straight Une ; and the apparent 

 disk is in a state of mean libration, and may be represented on the ortho- 

 graphical projection, subject to the necessary distortion in the regions about 

 the limb. 



