DISCHARGE OF A CONDENSER. 279 



If the values of p and of p are real, they should be negative 

 from equation (50) ; if they are imaginary, the real parts are still 



T^ 



negative, and equal to -. The real part of the exponent a 



e ae 



is then negative, and the ratio tends towards zero, when 



a 



tends towards infinity. As this is also the case with other terms, 

 the values reduce to 



If we assume / = ^> which gives ap + a'p' = Q, and replace the 

 exponentials by their values, we get 



ap 2 a'p' 2 



w cos -ytdt = + 



ap a p 



The total swing imparted by the discharge to a free system 

 will be 



from this follows 



p-p 



P 



p -p 

 The value of v is defined by the total discharge m Q. 



