96 ROYAL SOCIETY OF CANADA 
Case IJ.— With an absorbing substance between the thorium hy- 
droxide and the testing vessel. 
If a tube containing an absorbing substance is placed between the 
thorium tube and the testing vessel, we can investigate mathematically 
the effect on the ionization current in the testing vessel, if we adopt 
certain assumptions concerning the absorption. 
It is natural to suppose that the absorption of the emanation is 
proportioned. 
(1) to the number of emanation atoms passing per second. 
(2) inversely to the velocity of the air current carrying the eman- 
ation, 
(3) to the absorptive power of the absorbing substance, and for 
the present. ; 
(4) to the amount, that is, volume, of the absorbing substance 
through which the emanation passes. 
Consider an element of the absorbing substance, with its plane per- 
pendicular to the direction of the tube, and of length dx, fig. 6. There 
are two causes for the diminution of the number of emanation atoms 
in passing through it, (1) the natural decay of the emanation, (2) the 
absorption. 
Let 7 = the length of tube filled by the absorbent, 
N, = the number of emanation atoms entering the absorbent 
per second, 
N, = the number of free emanation atoms leaving the absorbent 
per second, 
n = the number of emanation atoms passing through the 
element per second, 
dn = the total change in the number of emanation atoms which 
pass through the element per sec., 
A, = the total cross-sectional area of the interstices of the 
absorbent, 
A, = the total cross-sectional area of the particles of the absor- 
bent, 7.e., the cross sectional area of the tube minus the 
total cross-sectional area of the interstices of the absor- 
bent, 
s = the coefficient of absorption. s will depend upon the 
capability of the substance to absorb, or, on its absorptive 
power ; it will have a definite value for every material, 
and in the majority of cases, viz., the non-absorbing sub- 
stances, will be zero. 
