﻿the Poles oj the Electric Arc. 775 



If we momentarily assume as known the net carbon con- 

 sumption in, i. e. the loss occurring by evaporation at the 

 crater surface in 1 second, we can write instead of (5), the 

 equation 



m = Avd. 



It follows from (4), with m = N/^, 



P = A . v 2 . d, 



or for unit surface 



P . A 



•■VI •-• ®> 



Taking p from Table II., we get a mean value 



V = 400 cm./sec. 



in a good agreement with the foregoing upper limit 650. 



If the observed p is half due to recoil and half to impact 

 of particles moving towards the electrode, v becomes still 

 less, i. e. 280 cm./sec. The values 400 or 280 mean that if 



400 an '—I 280 . AO , ,, , 



-nr^, i- e. bU per cent., or -rrr^-, &• £• 43 per cent, or the carbon 

 boO l ' b50 r 



waste occurs in the arc gap by evaporation, the calculated 



pressure agrees with the observed. 



10. Hitherto we have made no hypotheses on the electrical 

 nature of the particles issuing from the crater. It may be 

 pointed out that the repulsion P, owing to the intensive 

 evaporation due to heat, may be also produced from neutral 

 carbon particles carrying no current, a trivial phenomenon. 



If we assume, on the contrary, that the particles possess 

 an electrical charge, and that the arc mechanism may be in 

 the first instance reduced to a stream of positive ions of 

 mean charge e moving from anode to cathode and carrying 

 a current portion, al, and to an inverse stream of negative 

 ions (or electrons) carrying the rest (1 — a) . I, a system of 

 equations may be written *, from which it follows 



1=4 c»> 



* $., p. 85. To correct 6iW l = ±N 1 n l v l 2 = b 1 a l . IE. According to 

 Thomson ('Conduction'. ... p. 426 (1903)) the ratios a, {I -a) should 

 be proportional to the mobilities of the positive and negative carriers. 



