IMPARTED TO A VACUUM BY HOT CONDUCTORS. 
whence 
505 
V 
= i (\/2c cc ~ A)2, 
A being a second integration constant. 
We have the further conditions : 
V = cc when x = 
V = when x 
which are satisfied if A^ = 
Taking the positive root for (since negative values are inadmissible) and puttin 
v-j^ = Nq/71^ we obtain 
- 1 2^^ 
N 
\n. 
AkJ'R.O 
(14). 
This equation gives the concentration (o-i) of tl,e corpuscles at any distance * from 
the plane when the temperature is maintained at 0° absolute. 
Returning to equation (12) we see that integration and substitution for v yield the 
electrostatic potential V in the form 
iwlUB 
If V = V(, for X = 0, the integration constant y is determined 
y = V„ + 2 iA 
SO that V is finally to be obtained from 
+ y- 
as 
0 + 2 log \ , 
71 
v = v„- 
"nIc„ ‘“S' { 1 + 
The electric intensity at any point x is given by 
(15). 
(lY 
dx 
2[27T'Re^ 
No/' 
\i 
1 + 
Rf? I 0 
Q—hi-iRB 
( 16 ). 
X 
and the charge on unit area of the radiating plane by 
cr 
= _ .1 _ K-Re\i., 
477 \dX/x=o \27rN, 
- iif/Hff 
(17), 
VOL. CCI.—A. 
3 T 
