Resistance of the Electric Arc. 409 



between the terminals of the lamp and of the battery. This 

 last gives the back E.M.F., since the resistance of the 

 cells was small enough to be neglected. The P.D. at the 

 lamp divided by the current gives the resistance ; this is 

 plotted on the same diagram ; to make it clearer, however, 

 the scale of ohms is multiplied by 10. We have measured* 



the instantaneous -=-r- at various current strengths, and the 

 rtA to ; 



values of this are plotted in a dotted line. It is seen that 

 there is a very close agreement between these two measure- 

 ments of resistance. On the same sheet are plotted values 



dV 

 for the steady -r^. This differs considerably from both 



the resistance-curves. This leads us to see that the rapid 



excursions caused by the alternating current are not along 



the curve joining the steady values of V and A, but along 



a line which is everywhere more vertical than the tangent 



to the curve. This line is formed by joining the point on 



the curve to the instantaneous origin, which is distant from 



the origin of the diagram by an amount equal to the back 



E.M.F. at that particular current. Were the electrical 



excursions to travel along any intermediate path, the value 



dV 

 obtained for the instantaneous j-r- would be dependent on 



cl A. 



the frequency. As will be seen later, this is not the case 

 between the experimental limits of 250 and 7 complete alter- 

 nations per second. If, therefore, the arc, as has been affirmed 

 by various authorities, consists of a back E.M.F. and a re- 

 sistance, we feel justified in applying this method for the 

 measurement of its resistance, which has been found correct 

 in closely analogous cases. 



Now at very low frequencies indeed the electrical oscilla- 

 tions would travel along the curve connecting the steady 

 values of V and A ; and this is clearly the meaning of the 

 critical frequency which we have observed with cored carbons 

 (see p. 421), namely, that under the critical frequency the 

 superimposed alternations travel on the steady value curve 



dV 



and become identical with the " steady" — j • 



Several experimenters have obtained values for the resist- 

 ance of the arc which agree fairly well amongst themselves, 

 and which seem to show that the arc has a positive resistance f. 



* By method I. below. 



f An abstract of papers bearing on this subject was given by Mrs 

 Ayrton in the ' Electrician,' Sept. 13, 1895. 



