132 DE. W. G. DUFFIELD, MESSRS. THOS. H. BURNHAM AND A. H. DAVIS ON 
Assuming in the first instance that each particle carries a single electronic charge, 
e, and that electrons alone are responsible for carrying the current between the poles, 
the current C in absolute units is given by 
C = ne.( 2 ) 
The potential drop, Y, across the pole face is, on this assumption, due to the 
projection of these particles, whence their kinetic energy is equal to that derived 
from the source of current supply, and we have 
VC = ^inv^ .(3) 
From ( 1 ) and (3) 
■ YC 
V = -j 
p 
whence from (l) and (2) 
2 
Duddell"^ has found the values of V at the anode and cathode of an arc 6 mm. 
long carrying a current of 10 amperes to be 167 and 6‘1 volts respectively, both 
being electromotive forces acting towards the poles. These are electromotive forces 
across the pole faces and are distinct from those within the vapour in the arc-gap. 
We have already set forth in Table X. the values of p for a similar arc employed 
in this series of experiments, and, by substitution in the above formulm, we derive 
the values of ejm and of v, which are recorded in the final cohimii of the same table ; 
for the cathode the mean value of ejm is 6‘4 X 10^ E.M.U. The values of e/m for 
electrons and for hydrogen atoms are 177 xlO'^ and 9‘58 x 10® E.M.U. respectively, 
and, if carbon is quadrivalent, e/m for that element is 3'2xl0®. Even without 
further refinement of our assumptions, the experimental evidence is overwhelmingly 
in favour of the projection responsible for the reaction being electronic rather than 
molecular. 
We expect to find electronic projection from the poles of an arc, because the 
intense heat may occasion thermionic action, and the richness of the arc light in 
waves of short length is favourable for photoelectric action. 
Electronic emission is thus in accord with expectation, but it is at first sight 
surprising that it should be capable of producing a measurable recoil. 
It has been assumed in the foregoing that electrons carry the whole of the current, 
but the case for an atomic drift of positively charged atoms on to the cathode has 
already been considered by the writer (see “ The Consumption of Carbon in the 
Electric Arc—No, 1,” ‘ Eoy. Soc. Proc.,’ A, vol. 92, p. 122 (1915)). If we assume 
that half the current in the neighbourhood of the cathode is carried by such atoms 
(which may be supposed to contribute no more to the pressure than do the gas 
* Duddell, ‘Phil. Trans. Roy. Soc.,’ A, vol. 203, p. 305, 1901. 
m 2p \p/ 
