190 TREATISE ON ALTERNATING CURRENTS. 



giving simultaneous readings /i, L, L A , and let i'i, i 2 , 13 be corre 

 sponding instantaneous values. 

 Then 



t'i = *2 + 4 

 therefore 



^2 = tf + t a a + 2 a 



therefore 



' / O ' O * O\ 



a ia = s(*i - HT ~ V) 



A " Z? C -c 



FIG. 79. 



But ri% is the instantaneous P.D. between B and 0, therefore 

 the power given to BG is 



T 



l ( T . . 



rj/* 



where T is the periodic time of the currents. That is, the power 



given to BG is 



Unlike the three-voltmeter method, this method requires extra 

 current, but not additional voltage, and is, therefore, sometimes the 

 more convenient method of the two. 



134. A Dynamometer Method. An electrodynamo- 

 meter is similar in construction to the wattmeter, except that the 

 two coils are constructed of wire of the same thickness, and are 

 usually connected in series, so that the same current flows through 

 both, in which case the dynamometer reading multiplied by a con- 

 stant gives the mean square value of the current. 



