﻿158 Prof. Burton and Mr. Wiegand : Effect of 



where I, J, K, A, B, and may be calculated as before and 



AK 2 -2BKJ+CJ 2 



(IK -J 2 ) 2 

 AJ 2 -2BJI-fCF 



7 = 



(IK-J 



2\2 



B(J 2 + IK)-AJK-CJI 



13 ~ " (IK-J 2 ) 2 



. • (12) 



For this case (a = 27", b=r, c = 3'5r), to acloseapproxi'nation, 



1 = 2-5, J = '79, 



A= -26, B = -27, 0= '21, K . . . . (13) 



a= -0035, £=-05 



The interest of these equations, (1) to (13), is twofold. 

 (1). Using the expressions for the forces we may calculate 

 whether in any given circumstances of size, charges, and 

 distance apart we shall have attraction or repulsion between 

 the two spheres. (2). In the manner in which the streams 

 are always charged we can obtain the effect of the charge on 

 the drop just leaving the unbroken stream on the value of 

 the charge given to the next drop to be formed. 



1. Although, as the accompanying photographs show, we 

 cannot be dealing exclusively with the simple case of two 

 equal spheres, the manner in which the attraction or repulsion 

 varies with the ratio of the charges on the equal spheres for 

 constant distance apart, or with the distance apart for a 

 constant ratio between the charges, will give some insight 

 into the similar effects for unequal spheres. The numbers 

 given in Table I. for c, u, and /3 are taken from Lord Kelvin's 

 results, and the value of the force between unit spheres is 

 calculated for various distances between the spheres and 

 simple ratios D : E from 1 : 1 to 6 : 1 . The curve in fig. 12 

 shows the relation between the force between two equal 

 spheres (D:E = 6:1) and the distance from centre to 

 centre ; i. £., the numbers of column 9 plotted against those 

 of column 1 . 



It is very apparent that as the spheres approach the forces 

 of attraction increase with great rapidity, while on the other 

 hand, as the distance is increased beyond the point of neu- 

 trality, the value of the repulsive force grows very slowly. 

 That is the attractive forces at small distances will be made 



