25. 



NOTE ON A REMARKABLE PROPERTY OF THE ANALYTICAL EXPRESSION 

 FOR THE CONSTANT TERM IN THE RECIPROCAL OF THE MOON'S 

 RADIUS VECTOR. 



[From the Monthly Notices of the Royal Astronomical Society. Vol. xxxvm. (1878).] 



LET nt + e denote the mean longitude of the Moon at the time t ; 

 n't + e' that of the Sun. 



=nt + e n't e', the mean elongation of the Moon from the Sun. 



(f>, the Moon's mean anomaly. 



(j>', that of the Sun. 



T), the Moon's mean distance from the ascending node. 



c= jj and g = -j- , so that (l c)n denotes the mean motion of the 



Moon's perigee, and (g l)n denotes the mean retrograde motion of the 

 Moon's node, in a unit of time. 



Also let e denote the mean eccentricity of the Moon's orbit. 

 e', the eccentricity of the Sun's orbit. 



y, the sine of half the mean inclination of the Moon's orbit to the 

 ecliptic. 



m = , the ratio of the mean motion of the Sun to that of the Moon. 

 n 



/i, the sum of the masses of the Earth and Moon. 



