ON MAPPING THE SURFACE OF THE MOON. 



223 



larger scale, in each of which, there should be a point of the first order — 

 being apparent, this Appendix contains a form of computation based on 

 Encke's method, and modified from Lohrmann's and Beer and Miidler's 

 works, and as libration enters as a necessaiy element into the calculation, it 

 is preceded by an investigation of libration in latitude and longitude. For 

 the MS. from which the greatest part of this investigation is taken I am in- 

 debted to A. C. Eanyard, Esq., of Cambridge. I must, however, remark that 

 the formulae are derived from the ' Berliner Astronomisches Jahrbuch fiir 1843.' 



2. The investigation of libration consists of three parts, viz., that of the 

 angle C, or the angle which the meridian passing through the middle of the 

 moon's apparent disk makes with the circle of declination ; that of libration 

 in latitude and that of libration in longitude. The meridian passing through 

 the middle of the apparent disk should be carefully distinguished from the 

 fii'st meridian on the moon's surface, from which all selenographical longi- 

 tudes are reckoned both east and west. 



3. It wiU greatly assist in the conception of libration if the following 

 principles be borne in mind. 



Three planes being supposed to pass through the moon's centre, viz. the 

 plane of the moon's equator, the plane 

 of her orbit, and a plane parallel to the 

 plane of the ecliptic, the last will lie 



Fig. 1. 

 moot's Orbif 



■^■foon's jSquator 



between the others, and will intersect 

 them in the line in which they in- 

 tersect each other. 



In consequence of this law the 

 longitude of the ascending node of the 

 moon's equator on the ecliptic always 

 diflfers by 180° from the longitude of 



the ascending node of the orbit. The inclination of the moon's equator to 

 the ecliptic is 1° 32' 9", the inclinatioji of the plane of the orbit is about 5° 9'. 



Investigation of tlie angle C. 

 4. Conceive the moon's centre to be the centre of the celestial sphere. In 



Fig. 2. 



p Moon'sFole. 



Earth's Pole. 



Moon's 



[m Equator. 



fig. 2, 1' is the pole of the moon's equator, ISTj p m the mOon's' equator, Y" 2^i e 



