428 Prof. W. E. Ayrton and Dr. W. E. Sumpner. [Apr. 



quality, and be hissing, there is considerable difference in phs 

 between the current and the P.D. between the terminals; further, 

 the experiments show that current is very far from being a sii 

 function of the time, although produced by a dynamo whose E.M.F. 

 normally follows a harmonic law. 



We do not purpose, in this communication, to enter at length into 

 these experiments on alternate-current arcs, but a few examples of 

 the experimental results that hare been obtained will be interesting 

 as illustrating the ready applicability of this new method of measur- 

 ing power to such investigations. 



In addition to the difference of phase of P.D. and current that may 

 be produced in the arc itself, there is the electromagnet to be con- 

 sidered by which the distance between the carbons is usually regu- 

 lated in arc lamps. This electromagnet will introduce lag betwt 

 the P.D. at the terminals of the lamp and the current passii 

 through the electromagnet and the arc in series ; and hence, evei 

 although the arc be perfectly steady, we find, even in the case of 

 Brush lamp especially intended for alternate currents, that the true 

 power supplied to the electromagnet and arc is 20 per cent, less than 

 the product of the readings of the ammeter and the voltmeter 

 attached to the lamp terminals, and which gives the square root of 

 the mean product of the squares of the current and P.D. 



If, however, the arc be between common carbons and be hissing, the 

 difference, we find, is much greater. With cored carbons this Brush 

 lamp requires a P.D. of about 35 volts to be maintained between its 

 terminals, but if these cored carbons be replaced by common 

 carbons and the arc be hissing, the P.D. between the terminals 

 of the lamp at once rises to 45 or even 50 volts, although the 

 current passing through the lamp and the amount of light given out 

 remain practically as before. And then we find that the true power 

 supplied to the lamp may be only one-half of the square root of the 

 mean product of the squares of the current and P.D., so that the 

 readings of the ammeter and voltmeter alone make the apparent 

 power twice as great as the true power. 



For the purpose of easily estimating the ratio of the true to the 

 apparent power supplied, formula (3) may be thus written, 



from which we see that the expression in the brackets represents the 

 ratio of the true to the apparent power supplied to the lamp or othc 

 circuit ab (fig. 1). Hence the percentage error made in assuming 

 that the power supplied to any circuit was the product of the am- 

 meter and voltmeter readings would be in all cases, whatever the 

 nature of the current or of the circuit, 



