IMPARTED TO A VACITTJM BY HOT CONDUCTORS. 
501 
It we sujjpose the surface ot the hot conductor to he perpendicular to the axis of v/,, 
then the total number of corpuscles which hit unit area of the surface per second is 
fT f’ 
'^0^' — X*—GO ' 
We now suppose that there is a discontinuity in the electrostatic potential at the 
surlace of the metal which is great enough to prevent the escape of the corpuscles at 
low temperatures. If the work done by an ion in passing through the suiiace layer 
is (f>, tlien the discontinuity in the potential is (p/e, where e is the charge on an ion. 
We have further, by symmetry, 
1 off) 
e ay 
I a<p 
e dz 
= 0, 
the surface being perpendicular to the axis of x. 
Moreover 
rmc = — 
c<t> 
dx 
whence Un 
aJ ^ cl) 
^ Hi 
(4), 
where a,, is the normal component of the velocity of the corpuscle after it has escaped 
Irom the metal. 
It is evident from this that not all the corpuscles which strike the surface of the 
metal esca])e from it, hut only those which have a normal velocity component which 
is > Hence, to get the total number -which pass through the surlace layer, 
Ave have to integrate ex}jression (3) Avith res])ect to du not from 0 to od , but from 
a/" 
m 
flA to Qo . Thus the 
number which escape per second from unit area is 
iven by 
N 
Oui:. 
Hi 
pGO 
n 
— X 
' 77 ,/ 
. . . (5) 
^^ {km-rr) ^ 
= . 
^ IniTT 
. . (G), 
since k is connected Avith d, the absolute temperature, by the relation k = 
R being tlie gas constant lor a single corpuscle. The saturation current being equal 
to tlie quantity of electricity carried by the ions Avhich are shot olf from the surface 
in one second, is giAmn liy 
C = Ne8 = lieS a / -- 
V 27); 
I., lit) 
2?n7r 
(7), 
Avhere 8 is tlie area of the metal surface and e, as before, the charge on an ion. 
^ 3. Wlien the ions are removed by an external electric held as quickly as they ar 
