THE PEESSURE UPON THE POLES OF THE ELECTRIC ARC. 
131 
in the process of evaporation, we find marked disagreement between observed and 
calculated values :— 
Any reaction due to evaporation should be calculable from a knowledge of the 
number n of molecules of mass m which leave the pole in 1 second with a velocity of 
-v cm. per second. The product mn can be measured, but the determination of v 
presents some difficulty. Assuming that in the arc the carbon is at its boiling-point, 
and that the carbon atoms are in thermal equilibrium with the air into which they 
are escaping, fie.,[the carbon atom possesses the same kinetic energy as is possessed by 
an oxygen or nitrogen atom at the temperature at which boiling occurs, we have for 
the velocity of the carbon atom at 0° C., using the fact that the velocity of at 
0° C. = 18'39x 10^ cm. per second, 
V — 18'39 X 10* X \/^ = 7’5 X 10* cm. per second. 
Since the boiling-point of carbon is about 4000° C., the atomic velocity at that 
temperature = 7’5 x 10*x = 2‘9 7 x 10^ cm. per second. 
In experiments ah-eady quoted the amounts of carbon liberated from the anode 
and the cathode have been determined under various conditions of arc length and 
current strength {loc. cit.). 
In a typical experiment with an arc of 6 mm. length and a current of 10 amperes, 
85x10“^ grin, of carbon were lost by the cathode in 1 second, a much larger loss 
being recorded for the anode. Taking the above data the loss of momentum from 
the cathode per second = 8'5 x 10“*x 2'97 x 10’^ = 252 grm. cm. per secondfi 
On account of the nearly hemispherical curvature of the pole tip for an arc of this 
length only the components of the momenta along the axis are effective, hence the 
reaction recorded by the torsion fibre should be one-half of the above pressure— 
namely, 126 dynes. The observed value of the reaction, after correcting for 
convexion currents, under the same conditions of current and arc length, is 
2T8 dynes, which is not as much as 2 per cent, of the calculated value. It does not 
appear that we can account for the reaction at the cathode on any simple assumption 
which regards its cause as molecular or atomic projection. 
The Nature of the Particles Projected from the Cathode. 
It seemed possible to discover the nature of the particles projected from the 
cathode from the following considerations :—- 
If p is the observed pressure corrected for convexion currents, we have, assuming 
symmetrical projection from a hemispherical pole tip, or random projection from a 
small area on a flat pole face, 
2p = mnv, .(l) 
where m is the mass, v the velocity of each particle, and n the number projected per 
second. 
