408 Messrs. J. Frith and C. Rodgers on the 



the small increment of current produced. It must also be 

 borne in mind that the change in the current must be of so 

 short a duration that the form of the carbons is not in any 

 way altered. 



Apparently the only method which fulfils these conditions 

 is oue in which a small alternating current is used, super- 

 imposed on the main continuous current. This has the effect 

 of rapidly increasing and decreasing by a small amount the 

 current passing through the arc. It seems probable that the 

 effect on the arc of each small increase of current is annulled 

 by the decrease of current immediately following. In fact a 

 comparatively large alternating current maybe superimposed 

 on the main continuous current without producing any visible 

 effect on the arc. 



We are thus led to define the resistance of the arc as the 



ratio of a small increment of P.D. applied, to the small incre- 



dV 

 ment of current produced. This may be briefly written -jr. 



It is most important to distinguish this quantitv, which we 



dV 

 call the "instantaneous" -jt, from the tangent of the incli- 



nation of the tangent line of the curve representing the steady 



values of Y and A, which we will call, for the sake of clear- 



dY 

 ness, the "steady" -j-\* 



We have performed some experiments to exemplify the 



difference that exists between these two quantities; and also 



to show that in cases analogous with the arc, where, however, 



dV 

 the result can be verified, the instantaneous -7-^ found by 



superimposing an alternating current, gives correct values 

 for the resistance. 



In one of these experiments a glow-lamp, taking 10 am- 

 peres at about 8 volts, was placed in series with three I.E. 8. 

 50 ampere accumulators, and a current sent through against 

 the E.M.F. of the cells. This arrangement is just what is 

 wanted to test the method, namely a resistance in series with 

 a back E.M.F., both of which are functions of the current ; 

 and, further, the resistance can be separated from the back 

 E.M.F. and measured, and the result compared with the value 



dV 



obtained for the resistance bv the instantaneous -=-r- 



dA 



The result of this experiment is represented on PI. TIL 



Here are plotted the curves connecting the current and P.D. 



between the outside terminals of the arrangement and also 



