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XXVIII. Alternate Current and Potential Difference Ana- 

 logies in the Methods of Measuring Power. By Prof. 

 W. E. Ayrton, F.R.S., and W. B. JSumpnbr, D.Sc* 



I. 



IN a paper read by us before this Society on March 6th it 

 was pointed out that for every problem involving alter- 

 nate P.Ds. in series there was an analogous problem involving 

 alternate currents in parallel. This general proposition tells 

 us that we can transform each of the P.D. equations given, 

 for example, in our paper on " The Measurement of the Power 

 given by any Electric Current to any Circuit/' read before 

 the Royal Society, April 9th, 1891, into a current equation, 

 and so transform our method of calculating power by the 

 measurement of three P.Ds. into a method of calculating 

 power by the measurement of three currents. 



Fig. 1. 



Such a transformation of our equations has been recently 

 carried out by Dr. Fleming in the ' Electrician,' for May 8th, 

 and the method he arrives at as 

 well as the three-voltmeter method 

 of which it is an analogue are seen Fig. 2. 



in figures 2 and 1. If V x , Y 2 , V 3 

 be the readings of the voltmeters 

 in figure 1, and A l3 A 2 , A 3 the 

 readings of the three ammeters in 

 figure 2, and r the resistance of 

 the non-inductive portion of the 

 circuit cd in each case, then the 

 mean watts given to ah are re- 

 spectively, whatever be the nature 

 of the circuit ab, or of the current 



and 



£-(V-v I ».-v l ») 



* Communicated by the Physical Society : read June 12, 1891. 



