388 



until a given strength of current shall be obtained, with different 

 dimensions, &c. of wire ; 



v=e 



, { x \ 

 i sin f vj J . 



kcp 



If / denote the length of the wire, and V the potential at the end 

 communicating with the battery, the final distribution of potential 

 in the wire will be expressed by the equation 



which, when h=0, becomes reduced to 



corresponding to the case of perfect insulation. The final maximum 

 strength of current at the remote end is expressed by 



or, when A=0, y= j-r 



Kl 



Hence if we determine A f so that 



/ ix\ e(i-)V*_ e -(i-*)V* 



SA, sm \v-- =-V - , A -, when x>0 and *</, 



the equation 



will express the actual condition of the wire at any time t after 

 one end is put hi connexion with the battery, the other being 

 kept in connexion with the ground. 



" We may infer that the time required to reach a stated fraction 

 of the maximum strength of current at the remote end will be 

 proportional to Ac/ 2 . We may be sure beforehand that the American 

 telegraph will succeed, with a battery sufficient to give a sensible 

 current at the remote end, when kept long enough in action ; but 

 the time required for each deflection will be sixteen times as long as 

 would be with a wire a quarter of the length, such, for instance, as 

 in the French submarine telegraph to Sardinia and Africa. One 



