380 Note i i ; electrification of two disks 



whose coefficients are products of A's and B's, and in calculating these we 

 meet with the integral * 



I (i - p 2 ) m Po n (P) dp = ( i) n ...(24) 



Jo 2tn + 2n + i ! m n ! n ! n ! 



We have, therefore, for the harmonic of order zero. 



A i 



Surface-density on the first disk, <T O = - , where A is the charge of the 



2-n-a 2 /j, 



first disk. 



Potential at the surface of the first disk F n = A . 



2 a 



Potential at the surface of the second disk, arising from this distribution 

 of electricity on the first, 



I a* i a 4 i a 6 

 c\_* 3' 2 5? 



. i a 6 ~| 



= A -i +--!- f + &c. 



7 c 6 J 



- A 



3-4-4- 5-6^ + &c.] 



- &c. 



Order 2.- ff = ^ __ 



Potential at the surface of first disk, 



--^i^d/* 1 - *) 

 2 a * 2 2 v ' 



Potential at the surface of the second disk, 



. i 2 r 2 4 a 2 6 4 n 



"| = A.--K - &C. 



2 c* L3 5 5 7 c 7 9 c J 



i a*b* (i - /> 2 ) ra . 4 4 . 6 a 2 

 " 7 '* 



Potential at first disk, 



T/ - Z. j l2 3 2 [35 4 _ 30 , 31 

 1 4 ~ 2a A * 2 2 . 4* L 8 M 8 ^ ' 8J ' 



Potential at second disk, 



4 2 . 4 c s 7 9 7 9 



_ A ^aW-J?)r 2 _6_ & -i 

 2.4 2 2 c' L 7 9 J 



and so on. 



* I am indebted for the general value of this integral to Mr W. D. Niven, of 

 Trinity College. [See Sir W. Niven's memoir in Phil. Trans. 1879.] 



