[BOYLE] TEMPERATURE AND VELOCITY OF GAS CURRENT 97 
The time for the air charged with emanation to pass through the 
À, da dia! PL 
small element = dt = —*—. The diminution in the number of emana- 
4 
tion atoms which pass through per second owing to the natural decay of 
À : : A, dx 
the emanation while passing through the element = An .dt = An — a 
a q 

With the above assumptions, the diminution by the absorbent within 
sn. A dx 
the element = Hence we can write, 
— On 

vu An . da: a sn As eg 
q q 
the minus sign being used because n is decreased. Writing this as 
dx, 

dn in A 26 + S 4 
i q 
and integrating between the limits MN, and N,, we have 
Ve aD AA tsa 1e hdl 
Ny o 
-A A, + s A,)l 

From this it follows that V, = Me q * Denoting the 
actual volume of the absorbent, viz, A, J, by V,, and the intersticial 
AV, eV 
volume, viz., A, 1, by V, it follows that VW, = M e 7. e;. 
Hence, the effect of the absorbing substance is to decrease by an ex- 
-sV; 
ponential factor, eq ,the number of emanation atoms which would leave 
the tube if the substance were non-absorbing. If we denote, as in 
case I, by V the total free volume between the thorium hydroxide and 
the testing vessel, and use for the oiher quantities, the same notation as 
heretofore, it is easily deduced that the ionization current (/;) in the 
testing vessel is given by 
-AV sh" -A W 
ts = K N e q ne q 1 = q Sro000e 008. (3), 
and, corresponding to (2), Case I, 7, will be a maximum when 
AV + sV, 
— LE" eee ee ER ET ET (4). 
log ( AVE r.) 
Sec. III., 1907. 7. 
