56 STATIC ELECTRICITY 



The total normal strain over any closed surface draun in 

 the medium is equal to the total quantity of the elect 

 tion within. 



The total quantity is, of course, the algebraic- sum of tlu- potttivc 



and negative electrification >. 

 If the surface is unclosed w 



\ It the surtace is ttOdOMa we J 



^? have a useful expression for the total 



1 i " i 



normal strain over it. 



FIG- 43. If Fig. 43 represents a unit tulx- 



with cross-section a and strain 1). 



Da = l. Let S be a cross-section making any angle with ,. 

 Then S = a/cos 0. If D N be the component of strain normal to 



S,D N = Dcos0. Then D N S = Dcos0 x ^ = Da =1. Or tlu 



COS (7 



total normal strain over any section of a unit tube is units. 



Now suppose that we have any surface through which n unit 

 tubes pass. The total normal .strain OUT their mis cut oil' by tin- 

 surface will be n. Or 



The total normal .strain over anv Mirtacr is equal to the 

 number of unit tubes passing through the surface. 



The transference of tubes of strain from one 

 charge to another when the charged bodies move. 

 We have seen that it follows from tin- inverse square law that 

 in an electric system occupving a finite region each 1 1 

 positive charge is connected with an rqnal ilrnu-nt of nr^atix*- 

 charge by a tube of strain. Hut if the- charged bodies mou-. tin- 

 pairs of elements connected may ch. 1 \M- 

 general way how this may occur. As an illustration 

 the case of a charged body originally near a condiu-ting tabh , 

 Fig. 44, with nearly all its tul- ,g down to the surface. 





Suppose that then an insulated conductor \*>. \ brought 



between A and the table. If B were an insulator the tubes would pass 

 through it. But the parts of the tubes within H \\ill disappear, 

 since a conductor cannot maintain any electric strain ; and \u- 1 

 the arrangement more or less like that in Fig. l~>. uhcrc HH 



