426 Prof. W. E. Ayrton and Dr. W. E. Sumpner. [Apr. 



FIG. 1. 



Let V }y F 2 , and V be the readings of the voltmeter when ap 

 between a and 6, 6 and c, and a and c respectively ; then, if W be tl 

 mean watts supplied to the circuit ab, we have in all cases, whatevt 

 the nature of the current, or of the circuit^ ab 





For, let Vi, v t , and v be the instantaneous values of the P.D. betwt 

 a and b, b and c, and a and c at some moment /, 



then v = t'i + v t (2). 



r . 



If a. be the current in amperes flowing through the circuit at time 

 f, then avj equals the watts w given to 06 at that time. But 



a = , 

 r 



since the resistance be is non-inductive ; 



Then, squaring (2) we have 



Consequently 



* = ^T (f **- 



- ! 



or 



the equation given above. 



If the resistance of be be not known, or if there be any fear that it 

 may be changed by the passage of the current, then an ammeter (an 



