Current and Potential Difference Analogies. 209 



MM. Blondlot and Curie, of making an electrometer with 

 two needles for the measurement of power, is the exact 

 analogue of the wattmeter method. For with the double- 

 needle electrometer (fig. 8) we obtain from a single reading 



the mean value of 



which is equal to r into the mean watts given to ah. Similarly 

 with the wattmeter (fig. 9) we obtain from a single reading 

 the mean value of 



Fig. 9. 



#1*3, 



which is proportional to — into the 



mean watts given to ah. 



While, however, the double-needle 

 electrometer gives us the answer 

 with perfect accuracy, the watt- 

 meter method is liable to inaccuracy 

 from the circuit cd not being strictly 

 non-inductive. 



Some years ago, at a meeting of the Institution of 

 Electrical Engineers, one of us published the formula for the 

 error made in using a wattmeter to measure the power given 

 by an alternate current to an inductive circuit. Not wishing 

 to cumber the pages of scientific periodicals with elementary 

 mathematics, it was thought sufficient merely to state this 

 formula without publishing a proof. But as our formula has 

 now been introduced into text-books, and as the appropria- 

 tion thereof by the writer of a well-known treatise has 

 led him to supply a proof of it involving an appalling 

 array of mathematical equations, we venture to offer a proof 

 which, although very simple, is perfectly accurate. We are 

 the more induced to do this because we find that this formula, 

 and its proof for the error due to self-induction in the sup- 

 posed non-inductive portion of the circuit cd, apply equally 

 well to all the nine methods of measuring power illustrated 

 in figures 1 to 9 of this paper. 



Phil. Mag. S. 5. Yol. 32. No. 195. Auaust 1891. P 



