SCIENCE AND PRACTICE. 413 



I and /! representing the lengths of the wire ; B, and 1^ the 

 corresponding radii of the insulators ; r and r L the correspond- 

 ing radii of the conductors ; and n and % the electro -motive 

 forces or numbers of similar elements. 



From these three equations some very important conse- 



T> 



quences are deduced. Supposing that - of one cable is 



equal to - of another, a special instance of which would be 1 



if different lengths of the same conductor were covered to the' 

 same thickness with different insulating materials, 



4) . . K : K, = n I : n, I, 



and, further, the same number of elements in action in both 

 cables, that is, n = n l9 



5) . . K : K, = I i I, 



If the batteries are not the same, but the lengths are 

 l=l lt 



6) . . K : Xj = n : n t 



For the relation of the times^ t and t lt which the charge- 

 current takes to appear at the farther ends of the two 

 cables, Professor Thomson and Dr< Siemens have arrived at 

 the proportion 



7) 

 In case 



If, besides, I = ^ the lengths are the same 

 9) . . f.t^rfir* 



or, if, instead of the lengths being the same, the conductors 

 have the same diameters, r =. r 19 



10) . . #:# 1== p : / 



