between two Electrified Spherical Conductors. 



291 



and, by using this and transformations similarly obtained for 

 the other parts of the expression for F, we obtain 



-p^[2:;r'(i''.-sJ-|-Js:;r'(Q«-'S<)]} as)- 



The quantities P^ Q^, S^ which occur in this expression, may 

 be determined successively for successive values of n in the fol 

 lowing manner : — By substituting, in (8), for p^, jo'^, q 

 values by (13), and eliminating /^, /^, g^, g^^ we find 



from which we derive 



„, ?'„ their 



W; 



■t7i+l= 5 -t. 



CL+1 



Sn_i = 



ah 

 ah 



ah 



s„— s„_i _ 



(*)• 



By giving ?i the values 1 and 2 in (13) and (8), we find 



Si= 



a6' 



(c). 



^^=—^6 ^' 



By these equations we have directly the values of the first two 

 terms of each of the sets of quantities P^, P^, Pg, &c., Qp Qg, Q3, 

 &c., and Sj, 83, S3, &c. ; and the others may be calculated suc- 

 cessively by the preceding equations. 



The polynomials which constitute the numerators of the suc- 

 cessive terms of the second member of (15) may also be calcu- 

 lated successively, by means of equations obtained in the follow- 



