Lamps with Direct and Alternating Currents. 479 



of the current could, therefore, he accurately measured by 

 this dynamometer, which is indicated by D in the figure, and 

 by knowing what fraction of the current passing through the 

 dynamometer D passed through the non-inductive voltmeter 

 V, the current passing through the lamp is known. 



Any error that might have arisen from a variation of the 

 light-standard was eliminated by taking successive readings 

 with a direct current produced by a Gramme-dynamo G, and 

 with an alternating current produced by a Ferranti dynamo F, 

 the switches 8 and s being turned to 1, 1 in the first case and 

 to 2, 2 in the second. The Gramme-dynamo G was also used 

 to excite the field magnets of the Ferranti, a suitable current 

 being obtained by a proper adjustment of the resistance p. 

 By means of the resistances q and t the direct and alternating 

 currents passing through the incandescent lamp L could be 

 respectively varied ; and it was found that if these resistances 

 were so adjusted that the reading of the dynamometer D was 

 the same in both cases, so also w^as the reading of the non- 

 inductive voltmeter V. 



It is known when power is supplied by means of an 

 alternating current to a circuit of resistance r ohms and co- 

 efficient of self-induction I secohms that 



number of true watts vr 



number of measured watts sjl^if 1 + t^t 2 



where the measured watts are obtained by multiplying s/K 1 , 

 the square root of the mean square of the amperes as measured 

 by the dynamometer, by -y/V 2 ^ the square root of the mean 

 square of the volts as measured by the non-inductive volt- 

 meter, and where t is the time between one alternation and 

 the next, or half a complete period. Therefore the 



number of true watts 



WA 2 V 2 



where in our case r and I are the resistance and coefficient of 

 self-induction of the carbon filament of the lamp. In the first 

 set of experiments a lamp with a looped filament was em- 

 ployed ; but the experiments seemed to indicate that the value 

 of I was not quite small enough to make the term Vir 2 

 absolutely negligible, or else that there was some slight 

 mutual induction between the dynamometer-coils and a small 

 brass vessel containing oil, in which moved a damping vane 

 attached to the moving coil. The results were therefore 

 discarded, and this vessel was replaced by one made of non- 

 conducting material, and all metal near the dynamometer 



