342-344] Physical Principles 299 



For by hypothesis CD A can form a closed circuit in which no chemical 

 action can occur, and therefore in which there can be electric equilibrium. 

 Hence we must have 



V C D+V DA + V AC =Q ........................ (266). 



Moreover the sum of all the discontinuities in the circuit is 



= V AB +V BC - V AC , by equation (266) 



= 'AS ~^~ VBC ~^~ 'CA 



= E, by equation (265), 



proving the result. A similar proof shews that we may introduce any 

 series of conductors between the two terminals of a cell, and so long as there 

 is no chemical action in which these new conductors are involved, the sum of 

 all the discontinuities in the circuit will be constant, and equal to the electro- 

 motive force of the cell. 



Let ABC... MN be any series of conductors, which includes a voltaic cell, 

 and let the material of N be the same as that of A. If ^V and A are joined 

 we obtain a closed circuit of electromotive force E, such that 



VAB + V BC +...+V MN + V NA = E. 



Moreover V NA = 0, since the material of N and A is the same. Thus the 

 relation may be rewritten as 



V AS + V BC +... + V MN = E ..................... (267). 



In the open series of conductors ABC ... MN, there can be no current, so 

 that each conductor must be at a definite uniform potential. If we denote 

 the potentials by V A , V B , ... V M , V N) we have 



V V V 



, V M VN Y MN 



Hence equation (267) becomes 



V A -V N =E. 



We now see that the electromotive force of a cell is the difference of poten- 

 tial between the ends of the cell when the cell forms an open circuit, and the 

 materials of the two ends are the same. 



A series of cells, joined in series so that the high -potential terminal of 

 one is in electrical contact with the low-potential terminal of the next, and 

 so on, is called a battery of cells, or an " electric battery " arranged in series. 



It will be clear from what has just been proved, that the electromotive 

 force of such a battery of cells is equal to the sum of the electromotive forces 

 of the separate cells of the series. 



