340 



ELECTROKINETICS. 



[PT. II. CH. VIII. 



between the corresponding points equal to zero. Let the current 

 from the point p to the point q be I pq , and let the conductivity of 

 the conductor pq be C pq , the impressed electromotive force E pq . 

 Then evidently 



The equation ( I ) may be written 



(4) I M =C M (E pq +V p -V q ). 



Substituting the values of the currents in the equation of 

 continuity (2) for the point p, 



(5) C pl (E p ,+ V p - V l )+C P (E ia + F,- F.) ...... 



Let us introduce a symbol C pp , denned by the equation 



form 

 (6) 



s=l 



The equations (5) may then be written in the symmetrical 

 n 



+ . . . + C 



If we add these equations for all the points of junction, the 

 result will be an identity, so that the equations are not all 

 independent. The equations therefore suffice to determine the 

 differences of potential between the junctions, but not the 

 potentials themselves. 



Since in the equations (4) only the differences of the potentials 

 appear, it is evident that we may choose one of the potentials 

 arbitrarily. Let us therefore put V n equal to zero, and use the 

 first n 1 of the equations (6), which are independent, to deter- 

 mine the potentials V lt V 2 ...... V^^. Calling A the determinant 



of the coefficients of conductivity, 



V21 ^1 



l, ni 



a 



2, ni 



i, n i 



