342 



ELECTEOKINETICS. 



[PT. II. CH. VIII. 



Now the activity of the electromotive force E pq is E pq l pq . 

 Forming the products for all the branches and summing, bearing 

 in mind that each branch appears twice, we obtain for the total 

 activity 



p=nq=n 

 2 2 



p q r s 



But since there is supposed to be no electrostatic energy, this 

 must be the heat developed in the system in unit time. The heat 

 is accordingly a homogeneous quadratic function of the impressed 

 electromotive forces. If we should solve the equations (n) we 

 should obtain the electromotive forces as linear functions of the 

 currents. Then forming the expression for the activity we should 

 obtain a homogeneous quadratic function of the currents, and by 

 our general theorem for the heating this must be equal to 



This might be obtained from the equations above by the aid of 

 certain properties of determinants. 



173. Wheatstone's Bridge. As an example of the above 

 principles let us consider the case of 

 Wheatstone's Parallelogram or Bridge- 

 It consists of four points connected by 

 six conductors, which may be represented 

 by the sides and diagonals of a parallel- 

 ogram, or more symmetrically as in 

 Fig. 69. 



Suppose that the only impressed 

 FIG. 69. electromotive force is in the branch 12, 



and that we require the current in the 

 branch 34. The equations (6) are 



OnVi + 12 V Z + C 13 F 3 + (7 14 F 4 = C, 

 C^V, + C*V,+ (7 23 F 3 + (7 24 F 4 = 



