IV.] THE VARIATION. 17 



, n 3 ""'" 



= - -,o + ^ 



77 Wi Q /*) 'M Y" 



/(' ^^ 't O I 't ^^ /( I 



^3 ,. 2 n(1n-ri} 1 



3n~ 8nn' + n'~ 



Calling = m, we have 



3 2-m 



a. = - 



2 ' \-m ' 11 



3 - 8m + m" 



3 2-m 1 3 m" 



'^-^'s-Sm + lim^ Ml )" 



n' m 



or, calling - , , or = m, , we have 



' n n' 1 m 



2 + m, 



1 

 3 - 2m, + - m, 5 



* 001 > " 



~ ' + 2 m '" 



These are convenient expressions, and, as it happens, very approximate. 

 If we wish to develope in ascending powers of m or m l} it appears that 

 the latter development will be the more convergent. 



n' 



We find by observation ='07480, very nearly. 



Hence a 2 = -00717,95, 



b. 2 = '01021,2= 2106"'4. 

 Hence the ratio of the greatest and least distances will be 



1-00717,95 : 0-99282,05, 

 and the greatest angular deviation from the mean longitude will be 



35'6"-4, 

 a very close approximation to the truth. 



A. II. 3 



