412 



Mrs. H. Ayrton. 



P.D. and current SV/8A must be negative, although the resistance of the 

 arc is positive. 



It is found, from the above measurements of the cross-sections of 

 the mist, that the connection between m, the resistance of the mist,, 

 and the current, is of the form, 



If m varies directly with the length of the arc, then 



\ A A- / 

 Adding this equation to (1), we get 



, , p + ql s + tl 



for the whole resistance of the arc, which is exactly the form that 

 was found by dividing direct measurements of the P.D. between the 

 carbons by the corresponding currents. Hence there is no reason why 

 this ratio should not represent the true resistance of the arc. 



Under what circumstances 8Y/8A measures the True Resistance of the Arc. 



When the current is changed it takes some time for the vapour 

 film to alter its area to its fullest extent, and still more time for the 

 carbon ends to change their shapes, All the time these changes are 

 going on the resistance of the arc, and, consequently, the P.D. 

 between the carbons, must be altering also. Both these, therefore, 

 depend not only on the current and the length of the arc, but also, till 

 everything has become steady again, i.e., till the arc is " normal " 

 again, on how lately a change has been made in either. At the first 

 instant after a change of current, before the volatilising area has had 

 time to alter at all, SV and SA must have the same sign, just as they 

 would if the arc were a wire, but as the volatilising surface alters, the 

 sign of SV changes. If, therefore, a small alternating current is applied 

 to the direct current of an arc, it will depend on the frequency of that 

 current whether SV/8A is positive or negative. When the frequency 

 is so high that the volatilising surface never changes at all, SV/6A 

 will measure the true resistance of the arc, unless it has a back E.M.F. 

 which varies with the alternating current. 



The measurements of the true resistance of the arc made in this 

 way by various experimenters have given very various results, because 

 probably the frequency of the alternating currents employed has been 

 too low not to alter the resistance of the arc. A curve is drawn 

 showing how the value of SV/SA with the same direct current and 



