OP ARTS AND SCIENCES. 227 



Investigations on Light and Heat, made and publisded wholly oa in paet with 

 Appropriation from the Uumford Fund. 



X. 



CONTRIBUTIONS FROM THE PHYSICAL LABORATORY OF THE 

 MASSACHUSETTS INSTITUTE OF TECHNOLOGY. 



XXVIL — THE INVERSE ELECTROMOTIVE FORCE 

 OF THE VOLTAIC ARC. 



By Charles R. Cross and Wm. E. Shepard. 



Preseutea June 16, 1886. 



The fact that the total or equivalent resistance of a voltaic arc con- 

 sists of two parts, the one constant for the same current, the other 

 variable in proportion to the length of the arc, was first made known 

 by Edlund in 1867 and 1868.* This total resistance, r, is evidently 

 represented by the equation r =. a -\~ bl, and if the constant a be 

 multiplied by the current, C, employed, the inverse electromotive force 

 is found. » 



Later researches have shown conclusively, with the silent arc, 

 throughout a great range of length and of current strength, that this 

 pi'oduct, aO, is approximately constant. 



The most recent results on this subject are those of Frohlich,t 

 whose results give a value of 39 volts for the quantity a G ; of Peu- 

 kert,t who finds a mean value of 35 volts for currents of 10 amperes 

 and over ; and Von Lang,§ who assigns a value of 39 volts. 



It has long been known that on the passage of the arc from the 

 whistling to the silent stage, as the carbons are separated, there is 

 a sudden rise in the difference of potential between them. At the 

 same time, the arc becomes much brighter and hotter, from which we 

 should naturally infer that the conductive resistance would diminish. 

 The current, however, is at the same time diminished. 



* Poggendorffs Annalen, 1867, vol. cxxxi. p. 586 ; 18G8, vol. cxxxiv. p. 250. 



t Elektroteclinische Zeitsclirift, 1883, vol. iv. p. 150. 



} Zeitschrift fiir Elektrotechnik, 1885, vol. iii. p. 111. 



§ Centralblatt fur Elektrotechnik, 1885, vol. vii. pp. 315, 446. 



