SCIENCE AND PRACTICE. 261 



When p = 0, 



I n = ...... (VIII. 



T 



or, when the circuit resistance external to the battery is in- 

 appreciably small, the intensity increases as the number of 

 parallel plates increases, and in working with such circuits 

 it proves that we do well to take elements of large surface. 

 Whenr=0, 



. wE E 



.\ n - - = - .... (X-A.. 



n P 9 



a very important result, which says that when the external 

 resistance p is very great in comparison with that of the 

 element, no greater intensity is obtained by increasing the 

 surface of its plates. 



Two other cases belong under the same head, but seldom 

 occur, viz., that of combining similar elements of different 

 sizes, and of combining elements of different electro-motive 

 forces in series and parallel. 



The resistance of similar elements of different sizes will, of 

 course, be different let them be r^, r 2 , r 3 . . . r n ; but the 

 electro-motive forces will be equal, and the intensity of the 

 current of each element joined up in series will be 



T* n f\ 



1= _ 5 __ .(X. 

 p + ^i + r 2 -f r 3 . . . . r n 



and that of any section in the circuit, the product of this 

 with the number of elements, or, 



l n = _ !L5 _ : _ . . (XI. 



9 + ^ -\- r 2 -{- r s . . . . r n 



But where these elements are connected up parallel, the 

 intensity of the circuit becomes 



r 2 T * _ T _n (X 



+_L + _L + ...._L' 



r z r s r n 



In the other case, where the electro-motive forces of each 



