Alternate Current and Potential Difference Analogies. 205 



The three-ammeter method has the advantage over the 

 three-voltmeter method, in that the dynamo need not give 

 a larger P.D. than that necessary to send the current through 

 ab; it is inferior to the three-voltmeter method in that while 

 it is possible to measure V l9 V 2 , and Y 3 rapidly in succession 

 by using only one voltmeter, it is, of course, impossible to 

 use only one ammeter to measure A 1? A 2 , and A 3 without con- 

 stantly interrupting the circuit, and hence it would be neces- 

 sary to accurately calibrate three instruments if this current 

 method were employed. 



But the main objection to this current method is that, as 

 Dr. Fleming points out, it does not possess the accuracy of 

 our three -voltmeter method of measuring power. For in 

 order that this three-current method may give accurate 

 results it is necessary to assume, to quote from our Royal 

 Society paper, " the entire absence of self and mutual induc- 

 tion from a circuit some portion of which is necessarily of a 

 solenoidal form." 



It is possible, however, to obtain a current analogue of our 

 three-voltmeter method which shall have the accuracy of the 

 three-voltmeter method itself. And as the general propo- 

 sition given in our previous paper tells us that the current 

 analogues of P.D. arrangements in series are current arrange- 

 ments in parallel, it follows that with this other method also 

 the dynamo will not be required to produce a greater P.D. 

 than that necessary to send the current through the circuit 

 the power given to which we desire to measure. 



The method is as follows : — In parallel with the circuit ab 

 (fig. 3) the power given to which 

 we wish to measure connect a 

 non-inductive resistance of r 

 ohms (in circuit with which no 

 instrument is placed, which would 

 necessarily make the so-called 

 non-inductive branch more or 

 less inductive). Let A 3 , A l5 and 

 V be the readings of the two 

 ammeters and the voltmeter placed 

 as shown, then, from the equa- 

 tions given in our Poyal Society paper, it follows at once 

 that the mean watts given to ab are 



:U*-K.*-IZ 



2 1 



A 3 ~ — A x 



m 



It is interesting to notice that if ab were the primary coil 

 of a transformer, it would he when the load on the secondary 



