232 



PROCEEDINGS OF THE AMERICAN ACADEMY 



TABLE VII. 



Current = 10.04 amperes. 



From the measurements as given in the tables, curves were next 

 plotted on a large scale for each mean strength of current, with the 

 separations of the carbons as abscissae and the corresponding resist- 

 ances as ordinates. 



These curves were in all cases found to be composed of two straight 

 lines, the intersection of which corresponds approximately to the point 

 at which the arc, as it is gradually lengthened, passes from a whistling 

 to a silent one. The curve for the whistling arc is the steejiest. 

 Hence, for the curve corresponding to each sti-ength of current there 

 are two different intercepts and two different angles made with the 

 axis of abscissiie, according as the arc is whistling or silent. Since the 

 intercept gives the quantity a in the general equation r =. a -\- bl, 

 which quantity being multiplied by the current gives the correspond- 

 ing value of the inverse electromotive force of the arc, it follows that 

 for any particular current there is a definite ojiposing electromotive 

 force for the whistling arc as for the silent arc, whatever its length, 

 but that the former is different from and less than the latter. Also, 

 there is for the whistling arc, as well as for the silent arc with any 

 definite current, a definite value of h, and hence a simple proportion- 

 ality between the variable portion of the equivalent resistance and 

 the length. The values of b are greater with the whistling than with 

 the silent arc for the same current strength. 



From the curves plotted as described, the linear equations of the 

 two branches corresponding to the silent and whistling arcs were 



