GENERAL PHYSIOLOGY. 37 



CASE I. 



Suppose that the external resistance is so great in 

 comparison with the internal resistance that the latter may 

 be made equal to zero (ri = 0) C / =-^jt- = ~~ for one cell. 



Suppose that we arrange a battery of sixteen cells in 

 multiple arc. Experiment has shown that when a battery 

 is so arranged the internal resistance of the battery de- 

 creases in proportion to the number of cells and that join- 

 ing up cells in multiple arc is equivalent to simply increas- 

 ing the size of the plates. 



Our formula then becomes : 



C' = H^- : but_L=0;C' = _E_; C=C'. 

 ^+re' 16 



Therefore no advantage is gained by joining up cells 

 in multiple arc when the external resistance is incompara- 

 bly greater than the internal resistance. 



CASE II. 



Let the internal resistance be incomparably greater 

 than the external. 



Then for one cell: C =-r?-; but re = 0, therefore C = -?- 



-- n 



Join up 16 cells in multiple arc. The internal resist- 

 ance is thus decreased by the factor 16. 



C'= TJ^ ; re = 0; therefore C'=JL = ^0=160. 



l6+ re IT 



Therefore when the internal resistance is incomparably 

 greater than the external resistance the current increases 

 proportional with the number of cells joined in multiple 

 arc. 



CASE III. 



Let the internal resistance be so small relatively as to 

 be discarded. For one cell C = 



