Saturation Currents in Ionization. 653 
We thus get 
7? 2 geR a ee 0 do}, : ’ s q fo) 
and ra ( a Y 
“dy Peosmroe (ff, 0 
4) -EF{0-Doe loon ajo 
where y=y, at v=. 
The solution of (10) is, if oe JL 
2 
i {(1- “) cosh wx + cosh pl \ 
eat fh A\ 
2 (1 — 2 cosh pl 
where 
¢ | sh 
Y1 1( | aeons =) —4-+4 00s ‘’ i 
(i- ; ) cosh pol 
ap 
35 2 2 
ee 0 Teo2 ne t-s) 
4g/yl 
je Xe y 
Using these values in (9) we get 
5 20\2 % 3 
1 J cosh pl— oars | 
C= 2gel jul ae . oy) i enee Re (12) 
The a is given by | 
Uy) ae 1 
ane n i cosh ux + cosh ul \? dx. (13) 
2 21? Joo Jeosh pl 7 
The integration can be completed by means of ‘elliptic 
functions, but net m a form very suitable for numerical 
purposes. 
We may note in (12) that 2qge/ is the value of the satura- 
tion current on the simple theory. We shall denote by / the 
function 
1 aa pol— a-y 
cosh pl 
oe: : 
and shall first take — as very small. The following numerical 
table indicates the ceneral character of the functions. They 
Phil. Mag. S. 6. Vol. 8. No. 47. Nov. 1904. 2 ZL | 
