438 Poicer given by any Electric Current to any Circuit. [Apr. 



would be 4 per cent. Hence the true power would be 8 per cer 

 less than the apparent power. Or, in other words, to find the true 

 powor given to ab (fig. 1), we should merely have to diminish 

 \\V-ilr by 8 per cent, and the answer would be obtained. 



If r were unknown, and .1 the square root of the mean square of 

 Ihe current were measured instead, then to obtain the trne power 

 for the values of FI, F 4 , and V given above, we should diminish V\A, 

 the apparent power, by 8 per cent. 



We will finally consider what is the percentage error made in 

 estimating the power by the method last described, compared with 

 the percentage error made in taking the value of FI + Fj V. 



Let us assume that, on account of errors in the reading* of F lt of 

 F 2 and of F, or on account of inaccuracies in the graduation of the 

 voltmeter, the value of Fi + Fj F is taken as half a volt greater 

 than its trae value, that is, that this expression is erroneously 

 increas *d by 1 per cent, of FI if we assume V t to be 50 volts as above 

 Then y will be also increased by 1 per cent., and since the tt 

 power is obtained by subtracting from the apparent power 2y time 

 the apparent power, it follows that the power measured in this waj 

 will be estimated as 2 per cent, too low if the combined error 

 in measuring Vi + V 2 V be plus 1 per cent, of FI. 



VI. 



Measuring the Power given out by an Alternate-Current Dynamo. 



In consequence of the trouble usually experienced in correctly 

 measuring the power given to an inductive circuit, it is usual when 

 measuring the power given out by an alternate-current dynamo to 

 use for the outside circuits various resistances, all of which are as far 

 as practicable non-inductive. But as the construction of adjustable 

 non-inductive high resistances that will take large currents is a trouble- 

 some matter, we suggest the following as a convenient method of 

 overcoming the necessity of employing such a non-inductive circuit : 



Let the circuit external to the dynamo be ac (fig. 1), only a 

 portion of which is non-imluctive; then, if FI, F 2 , and F have tin- 

 values already given them, it is easy to show that the power given to 

 both the inductive and non-inductive portion of, ac that is, to tl 

 whole circuit external to the dynamo, is 



-(^'- 



And we anticipate that, if only a small portion be of the circuit ! 

 strictly non-inductive, this voltmeter method of measuring the j 

 given out by an alternate-current dynamo will give more accurat 



