CREW AND BASQUIN. — LUMINOSITY IN THE ELECTRIC ARC. 343 



If we consider the arc itself as having appreciable resistance, this time- 

 constant is still smaller. If, on the other hand, we consider the actual 

 circuit as equivalent to a circular one of equal area, the radius of this cir- 

 cular circuit will be 45 cm. 



Its self-induction * will be 



L = Ana (log I - 2) 



where a is the radius of the circuit, 45 cm., and R is the " geometric mean 

 distance " of the cross section of *the wire from itself, defined by the 

 following equation ; 



log R = \ogr — I, 



where r = radius of cross section of wire. 



Here r = 0.1 cm. Hence R = 0.7788 r = 0.0778. 

 Hence 

 Z = 12 X 45 [log 45 - log 0.07788 - 2] 

 = 12 X 45 X 2.3 [1.653 — 2.891 — 2] =: 12 x 45 x 4.35 = 2340. 



L 2340 1 



— = s = — 777r- sec, approx. 



R 2 X 10' 10000 ^^ 



In each of these cases it is to be borne in mind that the initial cur- 

 rent, the decay of which we are studying, is but a minute fraction of the 

 strength of the alternating current operating the arc. 



The conclusion of the whole matter is, that there is no evidence, either 

 from an examination of the arc or from electrical theory, that the current 

 in this short isolated strip persists for a length of time comparable to 

 one thousandth of a second. 



In fact, the instant the brushes of the interrupters have passed on to 

 the slate sectors, the whole circuit consists simply of two short pieces of 

 thick copper wire with one pair of terminals nearly in contact, the other 

 widely separated by a piece of slate carefully selected with reference to 

 its high insulating power. 



Further evidence will be furnished, by experiments to be described 

 later, for thinking that the phenomena which appear when the current 

 is off are quite independent of the self-induction of the circuit. 



It need scarce be added, that in place of the eye of the observer, in 

 front of the steel disk, may be substituted the spectrograph or the photo- 

 graphic camera. In this case, both arc and spectrograph are placed on 

 a large table with a long bole cut into the top of it so as to clear the 



* Gray, Absolute Measurements, Vol. II. Pt. I. p. 308, Eq. (119'). 



