262 
Mr Wilson , On the Hall Effect in Gases 
But i = Xne (k x -f- k 2 ) 
= Xe (h + k„) 
Therefore / = aeX (h + k 2 ) e A [“ 6 W<*‘ +h,z dz 
J 0 
2/3aee A f <&+**)« 
= - H l e2 ^ - 1 }- 
Hence 
J. = log 
IH 
HX 
O/O f ~9ft (^ 1 +^ 2 )® 1 ■) 
2/3ae\e 2 P - 1 ] 
• log » = ^ (*. + * 2 ) z + log -J x — — - . 
2/3 Wae{eV { *' + ^-l} 
Thus as we move across the tube log n increases uniformly 
with z. If n x is the value of n at z x and n 2 at z 2 , then 
log ~ = C (*i — *•)• 
•h 
where G = (*, + fc). 
Thus if and ft 2 denote the values of n at E and E' respec- 
?2 
tively we see that log — 1 increases proportionally to H. If tbere- 
n 2 
fore there were an appreciable charge on E or E' due to the 
negative ions diffusing more rapidly than the positive ions, as 
explained above, then the Hall effect could not have been found 
proportional to the magnetic field. 
Substituting the values of Z and X found experimentally in 
the formula 
Z = \HX{h-h), 
we get, since Z = ^ ^ _ 34.9 
2Z 
k 2 -k x = E ^ = 1-42 x IQ" 3 p - 1 ' 5 
This must be multiplied by 10 8 to get k 2 — k x in cms, per 
second, so that finally 
k 2 -k x = 1*42 x 10 5 p ~ 1>5 . 
