434 Prof. W. E. Ayrton and Dr. \V. E. ISumpner. [Apr. 9, 



But if the harmonic law hold for the current, the sum of Lp for the 

 arc alone, plus the Lp for the electromagnet alone, mast equal the 

 Lp for the arc and electrpmagnet, since p has the same valiu- in 

 case. Now it is obvious that the condition is far from being fulBlled 

 with the numbers just given. Hence the current does not follow a 

 harmonic law. 



It is interesting to notice that the Lp for the hissing arc alone is 

 actually greater than the Lp for the regulating electromagnet. 



The values given above for r, being obtained by dividing the true 

 watts by the mean square of the current in amperes, are the effective 

 resistances in ohms whether the current follows a harmonic law 

 not. Hence, by comparing the value of r for the regulating ele 

 magnet alone with its resistance in ohms, measured with a steady 

 current, we have a true measure of the waste of energy in the iron 

 core of the electromagnet due to hysteresis and Foucault cnrren 

 Now the resistance of this electromagnet for a steady current is o 

 0'065 ohm ; hence 90 per cent, of the energy given to the regnlati 

 electromagnet of this Brush' lamp is wasted in heating its iron core 

 when the frequency is 200. Here again we have a further illustrati 

 of the importance of being able to measure, by means of the simple 

 method we have described, the power given by any current to any 

 circuit. 



Added March 31, 1891. 



IV. 



The Best Value to give to the Non-inductive Resistance. 



In cases where great accuracy is required in the measurement of 

 the power given to a circuit, it is important to consider what value 

 should be given. to the non-inductive resistance (fig. 1), in order to 

 reduce to a minimum any error that may arise from possible in- 

 accuracies made in the three readings of the voltmeter, or on tb 

 graduation of its scale. 



Since W = ^-(F 2 - F, 1 - F,), 



dW = -(FdF-F^F,- 

 r 



where dV, dV\, dVy are the errors made in the estimation of the 

 three P.Ds. 



Let dV= eV 



dV, = eV l 

 dV t = eV t 



