force ; for on the latter depends the 

 amount of work obtainable from the 

 apparatus. By mean value of the elec- 

 tromotive force of an alternating current 

 is meant the electromotive force of a 

 direct constant current, which will, in a 

 given resistance free from self-induction 

 (say for instance, the wire of a Cardew 

 voltmeter), produce the same amount of 

 heating. It is necessary that the resist- 

 ance should be comparatively large, in 

 order to limit the current to such a 

 small value that the disturbing effect of 

 self-induction may be neglected. ' Let T 

 be the periodic time, then e, the mean 

 value of the electromotive force, is found 

 from the equation — 



T 



2 2 



/_ ( 2 n n z sin 2 n n t \dt = - — e', 

 ,R\ 2 / 2 R 



when It denotes the resistance of the 

 Cardew voltmeter. 



The solution of this equation is a 

 simple mathematical operation, and need, 

 therefore, not be given at length. The 

 result is 



