HETEROGENEOUS CONDUCTORS. 2OI 



Thus, all electrostatical problems which have been solved for a 

 system of dielectrics, furnish also the solution of the corresponding 

 problems in the propagation of electricity. Such, for instance, are 

 the following cases : 



Concentric spheres (77). 



Concentric cylinders (80), or eccentric cylinders one of which is 

 inside the other (136). 



Parallel planes (81). 



Closed condensers of constant thickness (79). 



Successive concentric cylinders formed of different media (164). 



214. HETEROGENEOUS CONDUCTORS. We have also seen (167) 

 that, by comparing a dielectric to a medium whose specific inductive 

 capacity is /* 2 , and in which is disseminated little spheres of the 

 specific inductive capacity /*j, the medium thus constituted behaves 

 like a homogeneous dielectric, the specific inductive capacity of which 

 would be represented by the expression 







in which h represents the ratio of the sum of the volumes of the 

 small spheres to the total volume of the space in which they are 

 disseminated. 



In analogous conditions, the mean specific conductivity of a 

 medium of conductivity r 2 , containing small spheres of conductivity 

 <r 1? is expressed by the formula 



If the ratio of the conductivities of the spheres and the sur- 



*1 

 rounding media is very great, the formula reduces to 



In like manner, the problem of 150 will give the conductivity 

 of a system formed of three different media separated by two parallel 

 planes. 



