464- M. G. KirchhofFow a Deduction of Ohm's Laws, 



The potential of all the free electricity is constant with re- 

 gard to all parts of each of the conductors : its value, how- 

 ever, will be different in the case of the first conductor from that 

 of the second; for theory teaches us, that if its value were the 

 same in both conductors, there should be no free electricity 

 present, inasmuch as the sum of all the free electricity is =0. 

 Now as regards the difference between the two values of the 

 potential in the two conductors, this might depend upon the 

 nature of the material of which the two conductors were com- 

 posed, and their form. I shall assume that it is independent 

 of the latter, and is that magnitude which is known as the 

 tension of the two bodies. Let u denote the potential of the 

 entire amount of free electricity in regard to a point in the 

 first conductor, and u% the same in regard to a point of the 

 second conductor; both u and u 2 must then be constant; if 

 then U 1} 2 denote the tension of the two bodies, we must have 



Z^— W 2 == \J \^ 2 « 



If we imagine several conductors, say three, so placed in 

 contact that the first conductor touches the second, and this 

 the third conductor, the electricity in them may always assume 

 a state of equilibrium. If we again denote the potential of 

 the total amount of free electricity in any point of the first 

 conductor by u v for one in the second by ti 2 , and for one in 

 the third by z/ 3 , and further the tension between one and two by 

 U 1} 2 , that between two and three by U 2> 3 , it is essential to 

 the existence of a state of equilibrium that each of the three 

 magnitudes, u v n^ and u 3 be constant, and that the equations 



u 1 — « 2 =U 1)2 



be satisfied, But if we assume that the conductors 1, 2 and 

 3 have been so placed in contact that each of them comes 

 into contact with the two others, electric equilibrium cannot 

 possibly always exist in them. Should equilibrium exist, 

 each of the magnitudes u 19 m 2 , and u 3 must be constant, and 

 the equations 



u 1 —u 2 =\J h 2 



U 2 U 3 = ^2, 3 



w 3 ~m 1 =U 3j i 

 must be satisfied. These equations, on addition, produce 



= U 1)2 + U 2)3 + U 31 ; 

 thence the tensions of the three conductors must satisfy this 



