﻿the Poles of the Electric Arc. 773 



On the nature of P. 



8. For the purpose of explaining the observed mechanical 

 pressure, many hypotheses have been suggested *, starting 

 from different points of view on the arc mechanism, and a 

 conscientious discussion would* carry us beyond the limits of 

 the present paper. 



Without any assumption, it may be observed that of 

 course in the arc a loss of matter by each electrode and a 

 transport from anode to cathode occur, thus — on the anode 

 at least — a recoiling effect must be occasioned. Whatever 

 the nature of the forces propelling the carbon particles 

 may be, the recoil due to evaporation can be estimated as 

 follows : — 



Let N, fi, v be respectively the number of particles leaving 

 the crater in 1 second, their mass, and their velocity of 'pro- 

 pulsion ; then the considered recoiling effect is given by 



P = N/tw (4) 



By fju, v mean values are to be understood, for it is quite 

 improbable that all the particles possess the same mass and 

 are projected with uniform speed, therefore the right-hand 

 side of (4) is a substitute for an expression Xu/jlv, with 

 N = 2n. 



In calculating the repulsion P as a recoil effect, by a 

 formula similar to (4), Prof. Duffield assumes for v the 

 velocity of agitation of carbon atoms at the temperature 

 4000° C. of boiling, that is, 



18-39 . 10 4 \/ 1 2 \/^f$ = 2 ' 97 • 1Q3 cm./sec, 



18-39 . 10* being the molecular velocity oE H 2 at 0° 0. 

 It seems to me that this assumption is hardly defensible, as 

 will be best shown by means of the following analogy. If 

 we keep a compressed gas in a bulb, by opening a tap the gas 

 escapes, impressing a reaction upon the bulb, as in tur- 

 bines. The velocity responsible for this recoil is not at all 

 the molecular velocity of agitation (a function of the gas 

 temperature), it is the velocity v with which the gas departs 

 from the bulb (a function of the pressure difference in and 

 out of the vessel). The value v will be obviously less than 

 the molecular speed ; thus the pressure P does not reach to 

 the high range estimated by Duffield. 



* Besides the works already noticed, see a recent paper of Prof. A. M. 

 Tvndall, " On the Forces acting uoon the Poles of the Electric Arc," 

 Phil. Mag. xlii. p. 972 (Dec. 1921). 



