l86 PROPAGATION OF ELECTRICITY. 



PART II. ELECTRICAL CURRENTS. 



CHAPTER I. 



PROPAGATION OF ELECTRICITY IN THE 

 PERMANENT STATE. 



198. PERMANENT CONDITION. When two insulated conductors, 

 at different potentials V and V, are put in metallic connection, 

 equilibrium can no longer exist positive electricity flows from the 

 body at the higher towards the body at the lower potential; a flow 

 of electricity, an electrical current is produced. If the charges on the 

 two bodies are limited, equilibrium is established after a time, which 

 is generally very short, and which depends on the nature and the 

 dimensions of the intermediate conductor; the current is then 

 variable with the time. But if by any means the two conductors 

 are kept at a constant difference of potential, a permanent state 

 is established, and the intermediate conductor becomes the seat of a 

 constant current. 



199. ANALOGY WITH THERMAL PHENOMENA. The analogy of 

 these phenomena with those of the propagation of heat between 

 surfaces, at constant temperatures in a conducting medium, is 

 obvious, and this analogy is expressed by identical laws in the two 

 cases. 



We have seen, reminding the reader of the principles of Fourier's 

 theorem (70), that if, in a medium which is a conductor of heat, we 

 take two near isothermal surfaces at the temperatures t and t + df, 

 the flow of heat dQ, which in unit time traverses an element of 

 surface dS, is perpendicular to the element, proportional to the dif- 

 ference of temperature dt of the two surfaces, and inversely as their 

 distance dn t and is thus expressed 



