226 VARIABLE STATE. 



If we replace /, in all the terms containing r as a factor, by the 



2/7 



approximate value , which corresponds to the maximum T l of the 

 first wave, we get 





or finally 



The time at which the maximum is attained diminishes, 

 therefore, as the number of contacts increases ; the waves are thus 

 shortened, and the duration of the phenomenon is thus materially 

 diminished. 



A series of uneven numbers of equal and alternate contacts 

 of very short duration would thus produce along the wire an im- 

 pulse in the same direction as that of a single contact, but it would 

 be far shorter. 



235. For a contact of an infinitely short duration T, the potential 

 at a point at the time t is 



TT V -^-rs-z* 



j*i 



The value of the current is 



or 



V T a /*\!/ a \ a 



(10) I = . =. ( ) (2 i }e~t . 



P Jir 2ai\tJ \ t ) 



It is easily proved that the maximum determined by the con- 

 dition = is attained when 



