Nipher — TJie Electrical Capacity of Bodies. 115 



= 8 i[i6^( Ql -Q,)'L_|_^ 



2 r x 2 r 8 ^ 12 ) 



This is the well-known expression for the energy of these two 

 spheres, in terms of their respective charges and capacities. 



If the spheres are brought near enough so that they react 

 on each other, the density will no longer be uniform on the 

 spheres. 



The total flow of force from the positive charge Q x and to 

 the negative charge Q 2 will, however, remain unchanged. 

 The potential of each body will, however, be changed. The 

 potential of each body can then be determined to any desired 

 precision by determining the successive images of the two 

 charges. Knowing the resulting potentials, the perviance 

 between the two bodies can be computed. 



The conclusion that the energy of an electrical system re- 

 sides in the medium has been formerly inferred from the 

 following considerations. The energy of any system is 

 usually represented in general by the equation 



W= r fVAVdv 



(13) 



This equation is the exact equivalent of (8) for AV is de- 

 fined by Poisson's equation to be 



d 2 V d 2 V , d 2 V_ . 

 & Y = dx^ + W + ~Mr-~~ p 



where p is the volume density of the medium. AV therefore 

 represents the flow of force from unit volume of the medium 

 and AV dv is the flow from an element of volume. If the 

 integration in (13) be extended through the volume of a tube 



VI 



of force the result would be -^~ which is the same as (8). 



