658 Mr. R. D. Kleeman on Different Kinds of y Rays 
the plate. And since the primary and secondary rays possess 
the same properties of selective absorption, that group of 
secondary rays is best absorbed which corresponds to the 
best absorbed group of primary rays. Thus the group of 
secondary rays which is produced in a larger amount in a 
plate than the other groups, is best absorbed by the plate. 
Now, the experiments described in this paper show that the 
amount of secondary radiation from a thick plate corre- 
sponding to the group of primary 7 rays which is best 
absorbed, is small in comparison with the secondary rays 
corresponding to either of the other groups of primary rays. 
If the amount of secondary rays produced is proportional to 
the absorption of the primary rays, and the proportion 
absorbed of each group of secondary rays by the plate is the 
same multiple of the proportion absorbed by the plate of the 
corresponding group of primary rays, this would obviously 
not be the case. Let us therefore investigate this more 
closely. We will make the following assumptions and compare 
the conclusions that can be drawn from them with the results 
of experiment. Suppose that the coefficient of absorption of 
a group of secondary rays generated in a substance is for a 
distance dx in that substance n times that of the primary 
rays, and the coefficient of absorption of the tertiary rays 
n times that of the secondary, and so on. Suppose also that 
the fraction m of the energy absorbed of the primary rays in 
a distance dx is converted into secondary radiation, and the 
same fraction of the energy absorbed of the secondary radia- 
tion converted into tertiary radiation, and so on. Let us 
further suppose that n and m are the same for all substances. 
It will now be shown that on these assumptions the amount 
of secondary radiation from a plate corresponding to the 
group of primary rays which is best absorbed, would be 
greater than that corresponding to any other primary group. 
Let us consider the secondary radiation produced by two 
primary groups of rays which we will denote by A and B, 
where the group A is better absorbed than the group B. 
The amount of radiation from a given plate will not be 
altered if it be compressed to a less thickness, for the amount 
of radiation produced depends on the number of absorbing 
and radiating molecules only, and not on their distance of 
separation. Suppose then that a plate is compressed to such 
a thickness that the coefficient of absorption of the rays of 
group B (for a distance dx) is the same as that of the rays 
of group A in an uncompressed plate. Then it follows that 
the coefficients of absorption of the secondary rays, and rays 
of higher order, corresponding to group B in the compressed 
