ELECTROMOTIVE FORCES OF THE ELECTRIC ARC. 309 



Owing to various reasons, the above method was not suitable for these higher 

 frequencies; consequently a new method was devised similar to that used by 

 Messrs. FRITH and RODGERS,* based on the R.M.S. values of the superimposed P.D. 

 and current, and not on the instantaneous values of these quantities, with this 

 difference from Messrs. FRITH and RODGERS' method, that there was a criterion, when 

 a result was obtained, as to whether the arc was behaving like an ordinary resistance 

 or not. 



Basin of Method Adopted. 



Consider any apparatus A, fig. 1, which may have resistance and E.M.K. but no 

 self-induction or capacity, through which a steady direct current may be flowing, and 



Fig. 1. 



let there be mixed with the direct current an alternating testing current of R.M.S. 

 value C. 



Let V A be the R.M.S. value of the alternating part of the P.D. between the 

 terminals of A, and let r A and c be the instantaneous values of these latter quantities. 



The impedance of the apparatus A = \/ ( rr ->\~dt} \/ (-,( c*dt)=~VJG = I fL . 



\1 -II / / V \ 1 J () 



Suppose that the frequency of the alternating current can be made such that the 

 conditions of the apparatus are not in any way changed by the alternating current, 

 then if the apparatus has a true resistance it will be a constant, so that the 

 instantaneous values r A and c will have a constant ratio, i.e., will obey OHM'S la\v. 

 Then the wave-forms of V A and ( I will be similar curves and in phase, and the true 

 resistance of the apparatus = vjc = V A /C = I A . 



A criterion is now required that r A and c do obey OHM'S law, ami this is supplied 

 by the power-factor of the apparatus A, the power-factor being denned as 



For it can be proved that the necessary and sufficient condition that the power- 

 factor may be unity is that the wave-forms of V A and C are similar curves and in 

 phase, so that V A and c obey OHM'S law. 



Therefore if, when the current C and its frequency are such that the conditions of 

 the apparatus are not changed, it can be proved that the power-factor of A is unity, 

 then A has a true resistance numerically equal to I A . Further, in any apparatus in 



* 'Proc. Phys. Soc.,' 1897, vol. 14, p. 307. 



