546 A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 



(39) Let n,, , be the roots of the equation 



(LN-M')n'+(RN+lS)n + RS=0 ..................... (16), 



and let the primary coil be acted on by a constant electromotive force Re, so 

 that c is the constant current it could maintain ; then the complete solution of 

 the equations for making contact is 



x ^n^_ (IS +N \^fS \ + s *^} ............ (17) 



Sn,-n t \\n l / \n, / n,n a J 



_ .............................................. 



S Hi-n^ l 



From these we obtain for calculating the impulse on the dynamometer, 



The effects of the current in the secondary coil on the galvanometer and 

 dynamometer are the same as those of a uniform current 



MR 



~*RN+LS 



i 

 for a time 



(+> 



(R + S>- 



(40) The equation between work and energy may be easily verified. The 

 work done by the electromotive force is 



Work done in overcoming resistance and producing heat, 



R]y?dt + Stfdt = c< (Rt - fL). 

 Energy remaining in the system, 



(41) If the circuit R is suddenly and completely interrupted while carrying 

 a current c, then the equation of the current in the secondary coil would be 



M -f 



y = c-^e 



M 



This current begins with a value c-, and gradually disappears. 



