density increases. These results are difficult to reconcile with the density-law of absorption found by Lenard from the cathode rays, or with the results of the ionization method already considered. A further experimental examination of the whole question is very much to be desired.
86. Variation of the amount of radiation with the thickness of the layer of radiating material. The radiations
are sent out equally from all portions of the active mass, but the
ionization of the gas which is measured is due only to the radiations
which escape into the air. The depth from which the radiations
can reach the surface depends on the absorption of the radiation
by the active matter itself.
Let λ be the absorption constant of the homogeneous radiation by the active material. It can readily be shown that the intensity I of the rays issuing from a layer of active matter, of thickness d, is given by
I/I_{0} = 1 - e^{-λd},
where I_{0} is the intensity at the surface due to a very thick layer.
This equation has been confirmed experimentally by observing the current due to the β rays for different thicknesses of uranium oxide. In this case I = (1/2)I_{0} for a thickness of oxide corresponding to ·11 gr. per sq. cm. This gives a value of λ divided by density of 6·3. This is a value slightly greater than that observed for the absorption of the same rays in aluminium. Such a result shows clearly that the substance which gives rise to the β rays does not absorb them to a much greater extent than does ordinary matter of the same density.
The value of λ will vary, not only for the different active substances, but also for the different compounds of the same substance.
