152 RATE OF EMISSION OF ENERGY [CH. 
greater proportion of the radiation is absorbed by the radio-active 
substance itself. This is seen to be the case when it 1s recalled 
that the @ radiation of thorium or radium is reduced to half 
value after passing through a thickness of about 0:0005 cm. of 
aluminium. Taking into consideration the great density of the 
radio-active substances, it is probable that most of the radiation 
which escapes into the air is due to a thin skin of the powder not 
much more than ‘0001 cm. in thickness. 
An estimate, however, of the relative rate of emission of 
energy by the a and @ rays from a thick layer of material can be 
made in the following way :—For simplicity suppose a thick layer 
of radio-active substance spread uniformly over a large plane area. 
There seems to be no doubt that the radiations are emitted 
uniformly from each portion of the mass; consequently the 
radiation, which produces the ionizing action in the gas above 
the radio-active layer, is the sum total of all the radiation which 
reaches the surface of the layer. 
Let 2X, be the average coefficient of absorption of the a rays in 
the radio-active substance itself and o the specific gravity of the 
substance. Let H, be the total energy radiated per sec. per unit 
mass of the substance when the absorption of the rays in the 
substance itself is disregarded. The energy per sec. radiated to 
the upper surface by a thickness da of a layer of unit area at a 
distance « from the surface is given by 
4 hice “da. 
The total energy W, per unit area radiated to the surface per 
sec. by a thickness d is given by 
E,o Lio 
wie 1 SGN) a es 
Ten TAINO ORG 
if A,d 1s large. 
In a similar way it may be shown that the energy W, of the 
ee 
8 rays reaching the surface is given by W.= De 
where /, and 2), 
