﻿Electricity on Streams of Water Drops. 157 



being- repulsion or attraction according as the sign of the 

 total is positive or negative. As these formulae are perfectly 

 general they can be used to give the force between two 

 spheres for any values of a, b, and c. 



Kelvin* has published the values of the constants involved 

 in the case of two equal spheres at distances from centre to 

 centre from twice the radius of the spheres, i. <?., the spheres 

 touching, to distance four times the radius. In this case the 

 calculation is simplified because qn = $22- Putting 



1 1 



S^ = Ir and S^ = Jr, 

 Jr o 



where r is the radius of the spheres, Kelvin gives the 

 following equations to calculate the charges D and E from 

 the potentials u and v, and the force in terms of either u and 

 v or D and E 



J) — (Iu — Jv)r, E = ( — Jw + Ii?)r, . . . (6) 



~F = 2Buv-A(u 2 + v 2 ), ....... (7) 



F=^2/9DE~a(D^ + E 2 )[ ? (8) 



where I, J, B, and A may be calculated from as many terms 

 of the above series as necessary, and where <x and 3 are °iven 



by 



A(P+J 2 )-2BIJ , . B(I 2 + .P)-2AIJ 



(P_jy aud £=- (i»_jt)» • • ( 9 ) 



As a typical case, we have calculated, using the formulae 

 above, the corresponding constants for the case a = 2r, b=r, 

 c = 3*5r ; i.e., one sphere twice the other, and the distance 

 apart of nearest points half the radius of the smaller sphere. 

 Of course, in this case q 22 is no longer equal to q n and the 

 corresponding equations showing the relation between the 

 potentials and the charges, and the value of the force in 

 terms of the potentials and the charges, become 



J) = (Iu-Jv)r, E=(-Ju + Ki<)r . . . (10) 



where Kr = Sl/Q, r being the radius of the smaller sphere ; 



and F = - An 2 + 2Buv - Gv 2 , 



or F=^ 2 {-«D 2 + 2/3I)E- 7 E 2 } 



* Electrostatics and Magnetism, pp. 96-97, *f[ 142. 



I • • . (ii) 



