318 ELECTRICAL MEASUREMENTS 



and 



The three integrals are the mean square values of the three 

 currents and will be given by the readings of the dynamometers. 

 If Siemens instruments are used, 



KiD, -~ ijdt 

 i Jo 



where KI is the constant of the instrument and D\ its deflection' 



and similarly for the other instruments. 



Hence 



P = ~ (K.D, - K,D 2 - K 3 D S ]. (13) 



The result involves no assumption as to wave form. It does 

 assume that the resistance, R, is non-inductive. This cannot 

 be exactly true for the potential circuit contains the electro- 

 dynamometer. The use of hot-wire ammeters would render this 

 assumption practically true. P includes the power in D$. 



The results are greatly affected by the errors of reading. To 

 obtain the best precision in the measurement, the power wasted 

 in R must be equal to the load, an obviously impracticable 

 condition. 



This method is used in telephone investigations as an aid to 

 determining line constants. 



The Three Voltmeter Method. In this analogous method the 

 three instruments capable of measuring the mean square values 

 of the currents are replaced by three instruments which measure 

 mean square voltages. The connections are as shown in Fig. 184. 



The non-inductive resistance R is joined in series with the 

 load and the three voltages read, as indicated. 



p - ?r*** = I 



At any instant 



*>i = v z + v s and vf = v z 2 



