I 



891.] Power given by any Electric Current to any Circuit. 427 



alternate current ammeter, of course, if alternate currents be em- 

 ployed) can be inserted in the circuit;. Let A be the reading of this 

 ammeter, and which represents the square root of the mean square of 

 e current, then, for r in (1) we may substitute VJA, or 



A 



w* 



(3). 



When employing this last formula, the non-inductive resistance 

 may be that offered by incandescent lamps, since there is no objec- 

 tion to the resistance varying with different mean strengths of the 

 jurrent employed. 



This voltmeter method of measuring power was arrived at quite 

 idependently of the electrometer method referred to above, but an 

 lination of the electrometer method shows that it is practically 

 mivalent to simultaneous measurements of three P.Ds. 



III. 



The method which we have described for measuring the power 

 fiven by any current to any circuit may be conveniently employed for 

 leasuring the power given to an alternating-current arc, or to an alter- 

 iting-current arc-lamp. It is known that an alternating-current arc 

 juires a greater current than a direct-current arc to produce the same 

 jht with similar carbons; for example, a 10-ampere direct- current 

 imp requires 12^ amperes, or 25 per cent, larger current, when used 

 rith an alternating current. In a masterly paper on " The Theory 

 Alternating Currents," read before the Society of Telegraph 

 igineers, on November 13th, 1884, Dr. Hopkinson refers to a law 

 fiven by Joubert, that the difference of potential between the carbons 

 an alternating arc is of approximately constant numerical value 

 iroughout the period, and that it reverses sign discontinuously at 

 reversal of the current. Using this law as his basis, he works 

 Dut mathematically some very curious relationships between the 

 iriations of current and P.D. with time. 



Three of our senior students, Messrs. Kolkhorst, Thornton, and 

 r eekes, have been making a number of experiments on the power 

 ipplied to alternating-current arcs by using the method of measur- 

 ig power described above. From these experiments it would appear 

 mt the quality of the carbon employed affects materially the differ- 

 ice in phase between the currents passing through the arc and the 

 J .D. between the carbons. If the arc be quite steady and only give 

 )ut the rhythmic hum that accompanies a good arc, such as can be 

 )btained with cored carbons of proper quality, the arc appears to 

 it practically as a simple resistance, and M. Joubert's law does not 

 lold. But if the arc be maintained between uncored carbons of poor 



