278 Mr Kleeman, The Unstable Nature of the Ion in a Gas. - | 
_ velocity of the positive clusters per second. Hence 
§(d—2) 
S=khe ” =k, Az*, 
15 8 
where A=e 2 and z=e”., 
Let r’ be the number of negative ions produced by collision 
in the layer of gas between the plate and the parallel plane at 
a distance #, and r the number of positive ions produced by 
collision between this plane and the gauze. Let c denote the 
current crossing the plane which gives rise to further ionisation 
by collision. Then we have 
c=k,1—Az)+r+r’. 
The number of ions dr generated between the two planes at 
distances « and x+dz is given by the equation 
—dr=[{k,(1—Az*)+7r} B+r'a] da. 
Substituting for r’ from the foregoing equation we obtain 
dr z 
da + (B~ 0) 7 =(B— @) ha (Az —1)—ca. 
Multiplying by e®®” and integrating we obtain 
8 
k, (8 — a) An a 
7 tena ae 
re@—2)% — — fp,e(B—a)e 4 +(...(4), 
where C is an arbitrary constant. The value of the constant is 
obtained from the condition that »=0 when #=1, which gives 
) 
— feath,(B—a)\ , ., ke(B-a) Anes 
Vy, 2 oom 
From one of the foregoing equations we have c=k,(1—A)+7, 
when «=0, where 7 is given by equation (4), and hence on sub- 
stituting for 7 we obtain 
B —ae8b—) \ = kn; 2 . 
o ( Ee SENe eave (e@- 94 See ew (5). 
The total current c; is given by 
