544 A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 



6nal strength during the time 2-^. This diminution of the current, due to 



induction, is sometimes called the counter-current. 



(36) If an additional resistance r is suddenly thrown into the circuit, as 

 by breaking contact, so as to force the current to pass through a thin wire 



of resistance r, then the original current is = , and the final current is 



-R + r' 



The current of induction is then % //7p^' \ anc ^ continues for a time 



2 -JT . This current is greater than that which the battery can maintain in 



fC T~ 7* 



the two wires R and r, and may be sufficient to ignite the thin wire r. 



When contact is broken by separating the wires in air, this additional 

 resistance is given by the interposed air, and since the electromotive force across 

 the new resistance is very great, a spark will be forced across. 



If the electromotive force is of the form Esinpt, as in the case of a coil 

 revolving in the magnetic field, then 



E 



* ' -*), 



where p* = R 1 + Up*, and tan a = - . 



Case of two Circuits. 



(37) Let R be the primary circuit and S the secondary circuit, then we 

 liuve a case similar to that of the induction coil. 



The equations of currents are those marked A and B t and we may here 

 assume L, M, N as constant because there is no motion of the conductors. 

 The equations then become 



(13*). 



