436 Prof. W. E. Ayrton and Dr. W. E. Sumpner. ("Apr. 9, 



dW y/2 + 4(l+C080) 3 



W ~ 2e ~ 2C080 



dW 



We ~~ co80 





Now dW/We is the ratio of the percentage eiror made in measuring 

 the power to the percentage error made in measuring one of 

 the P.Ds. and the right-hand side of the last equation we find 

 equals from 4 to 5 for the values of the lag angle that occur ajj 

 ordinary practice. If then there were a positive or a negative error 

 of 1 per cent, in each of the measurements of F, Fi, and F 2 , tl 

 would be a probable error of from 4 to 5 per cent, in the measure- 

 ment of the power. The probable percentage error in the measure- 

 ment of the power being from 4 to 5 times the error in the 

 measurement of each of the P.Ds. arises partly from the fact tl 

 the expression for IF, being 



depends directly on the difference in the mean squares of the P.Ds., 

 and not on the difference of the square roots of the mean squares. 

 And as all instruments that are graduated for measuring the square 

 root of the mean square of an alternating P.D. such as a hot-wire 

 voltmeter, an electrostatic voltmeter, <fcc., really measure the mean 

 square and not the square root of the mean square directly, it would 

 be better, if such an instrument were to be employed for the method 

 of measuring power described in this paper, that it should be 

 graduated in mean squares of P.Ds. and not in the square roots of 

 the mean squares. In that case a similar line of reasoning to that 

 employed above shows that the probable percentage error in the 

 measurement of power by the method would be from 2 to 2'5 times 

 the error in the measurement of each of the P.Ds. 



It is, of course, clear that these errors to which we have been 

 referring are not errors in any way essential to the method proposed 

 for measuring power, since by the employment of an accurately 

 graduated voltmeter, by exercising care in taking the readings, and 

 if necessary, by repeating the measurements two or three times and 

 taking the means of the observations, the power can be measured to 

 any degree of accuracy desired. 



