28 ROYAL SOCIETY OF CANADA 
heated plate or the gas in its immediate neighbourhood, pass across from 
Ato iB. 
Let 7 = current per square cm. through the gas, 
n = number of ions per ce. at any point distant x from A. 
e = charge on the ion. 
4] 
2 

ladies J 
When the current is steady, the same current passes over any cross- 
section between the plates. 
dv 
dx 
i= Kne 
dv 
where A = velocity of positive ion for unit potential gradient and ae 
is the electric force. 
By Poisson’s equation, 
ar 
er 47 ne 
(See J. J. Thomson, Phil. Mag., 47, p. 465.) 
Eliminating n between these two equations, we obtain 
A dv | CALE E Fri PR 
AC rae te eK ae, J 
! dv\° 
Integrating (a) = An Eu: 
dv \2 
Now B is the value of (3) ut the surface of the heated plate and 
can be made as small as we please by increasing the number of ions pro- 
duced at the surface of the plate. This can be readily seen from first 
principles, for the higher the temperature, the greater the number of 
ions produced per second and consequently the smaller the value of the 
De dl : : 
electric field Te necessary to withdraw, from the neighbourhood of the 
plate, the number of ions requisite to convey the current. The potential 
eradient between the plates was experimentally examined and it was 
