POWER MEASUREMENT 329 



instantaneous currents at these same points. Then the rate of 

 displacement of electricity through wire No. 1 will be i\ and the 

 rate of doing work, or the instantaneous power will be iiVi, and 

 similarly for all the others. Therefore, 



p = iivi + i 2 v 2 -h . . . i n v n (a) 



In practice it is necessary to deal with potential differences 

 rather than with potentials. Let to be the potential of some 

 particular point on the system. In general, 



ii + 22 + *3 . + in = 

 consequently 



llVQ + I&Q ..''.+ Wo = 0. (6) 



Subtracting (6) from (a) 



P = il(Vl - VQ) + il(v 2 - V ) - . . . i n (v n ~ Z> ). 



The average power will be 



1 C T 1 C T 



P = j, I ti(i Vo)dt + jj I iz(v z vo)dt 



"> + f J { ^ Vn ~ V() ^ d 



i C T 



But -^ I i i(vi Vo)dtj etc., are the readings of the n wattmeters 



1 Jo 



connected as above. If the common point is on one of the n 

 wires at one of the terminal points of the absorbing device, 

 then one of the quantities in parenthesis will be zero, the cor- 

 responding wattmeter will read zero, and only n 1 watt- 

 meters will be required. 



The above demonstration is perfectly general and therefore 

 applies in all cases that can arise in polyphase power measure- 

 ments. However, the consideration of the cases which are of 

 frequent occurrence in practice is instructive. 



Designation of Wattmeter Terminals. As some of the mean 

 products in (26) may be negative, it is necessary that the con- 

 nections be so arranged that a negative deflection of the watt- 

 meter signifies that the reading should be subtracted when com- 

 puting the power. That there may be no confusion, the potential 

 and current terminals of the wattmeters through which the cur- 



