﻿156 Prof. Burton and Mr. Wiegand : Effect of 



ratio o£ their diameters, and the distance from centre to 

 centre. A closer study of the values of the forces in various 

 cases opens up a whole vista of possibilities for the play of 

 either attractions or repulsions between the drops such as we 

 are considering here (see Kelvin* and Rayleight). 



It is hardly possible to treat mathematically the case for 

 more than two bodies ; even the problem of two equal spheres 

 at a given distance from each other offers an exceedingly 

 laborious solution. The formulae for the force between two 

 spheres of radii a and b, at potentials u and v respectively, 

 the distance from centre to centre c, have been deduced in 

 probably the simplest form by Lord Kelvin J by use of the 

 method of electrical images. For a system of two conductors 

 of potential u and v, bearing charges D and E respectively, 



D = q n u + q 21 v, ~E = q 12 u + q 22 v, . . . (1) 



where q n and q 22 are the coefficients of capacity and q 2 \ = qi 2 

 is the coefficient of induction. For the spheres (radii a and b, 

 at distance centre to centre c) 



111 



^ ii= p 1 "p 2 + p; + - ' 





(/22= Qi + o;" f i + -' 



, .... (2) 



111 



$21 $12— ~~ Q" 5" Q~' 



Ol I0 2 O3 J 





where the successive values of each of the P 5 s, Q's, and S's 



are given by the general formula : 





9 O 7 



C " — OL — r 



X»+i— —7 -X ?i — X„_! (3) 



The values of the first terms for P, Q, and S are deduced by 

 Kelvin to be 



a 



Qi ~p Si= ^' i 



p - c " n - c a q 



-«s, I " (4) 



a 2 b ' *** ab' 2 ' ^ ab x ' j 



The value of the force between the two spheres is given by 



*-l\*% +*-%+*%}, • • • ( 5 > 



* Papers on Electrostatics and Magnetism, 1884. 



f Sc. Papers, ii. p. 103. 



X Electrostatics and Magnetism, pp. 96-97, 51 142. 



