2 4 POLYPHASE CURRENTS. [Exp. 



The total power at any instant is 

 ( i ) w = e a i a + e b i b -f e c i c . . . = $ei. 



Let e p be the instantaneous potential of any point P of the system. 

 Since it is known that %i = o, it follows that 



(2) e p i a -\-e p i b + e p i e . . . = e p ^i = o. 



Since (2) is equal to zero, it may be subtracted from (i) without 

 affecting its value ; hence 



(3) w>= (e a e p )i a + (e b e p )i b + (e c e p }i c . . = ^(e e p )i. 

 The total power at any instant is seen to be the sum of the products 

 of the instantaneous currents in each conductor and the instantaneous 

 differences of potential between the respective conductors and the 

 point P. 



The mean power W is found by integrating the instantaneous 

 power over a time equal* to one period, T, and dividing by T. 



w = f 



But each one of these terms represents the power, as read by a 

 wattmeter with current coil in series with one conductor and with 

 potential coil connected from that conductor to the common point P, 

 and the total power is the sum of the several wattmeters so con- 

 nected. For an w-wire system, n wattmeters are required, the total 

 power being 



W=--WW + W . . . W. 



n . 



When the point P coincides with one conductor, the wattmeter for 

 that conductor reads zero and can be omitted ; n i wattmeters are 

 then required. 



The method for n wattmeters, for n I wattmeters, and for two 

 wattmeters, is, accordingly, proved without reference to wave form 

 or the character of the load. This general proof was first given 

 by A. Blondel, p. 112, Proceedings International Electrical Congress, 

 Chicago, 1893. 



