25] RECIPROCAL OF THE MOON'S RADIUS VECTOR. 203 



on the two sides of the equation 



d(P) dg dP dg 

 d(e*)-d(f)-d(f)- d(e)' 



fi 1 F M K f 



we nnd -^ = -^ , as before. 



Similarly, by equating the coefficients of higher powers of y, we obtain 

 other relations between the coefficients of terms of higher orders in the 

 value of P. 



It may not be without interest to give here the result which I have 

 obtained for the development of the constant term in the reciprocal of the 

 Moon's radius vector. 



The expression includes, besides the terms spoken of in the foregoing 

 paper, an additional term depending on the square of the Sun's parallax. 

 Reintroducing the symbol a to denote the length before denned, which in 

 the paper has been taken as the unit of length, I find 



The constant term in - 



r 



I 179 97 757 40:39 34751189 31013527 



= " 48 W -162 m> 432 m ' 1990656 m ' 



,. 



* 



799 873 287849 268607 

 i m " 192 "'-32- 2304 W ~ 576 



5 5401 18527 



."1 

 l J 



a" 3 75 

 m + 128 



225 



where e and y have the same significations as in Delaunay's Theory. 



The method which I employed in obtaining this expression is closely 

 related to my first method, above alluded to, of proving the evanescence 



of the coefficients B and C. 



262 



