328 Prof. Rutherford and Mr. Grier on Deviable 



For simplicity let us suppose a thick layer of radioactive 

 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, radiation 

 which produces the ionizing actions in the gas above the 

 radioactive layer is the sum total of all the radiation which 

 reaches the surface of the layer. Let X t be the average 

 coefficient of absorption of the rays in the radioactive sub- 

 stance, and <j the specific gravity of the substance. Let E x 

 be the total energy radiated per sec. per unit mass of the 

 substance where the absorption of the rays in the substance 

 itself is disregarded. The energy per sec. radiated to the 

 surface by a thickness dx of a layer of unit area distant x 

 from the surface is given by 



±R x ae- Xx dx. 



In a similar way it may be shown that the energy W 2 

 radiated per sec. by the /3-rays for a very thick layer is 

 given by 



2 2\ 2 



where E 2 is the total rate of emission of energy of unit 

 mass disregarding absorption, and \ 2 the coefficient of absorp- 

 tion of rays in the substance. Therefore 



W x _ E1X2 

 W 2 ~E 2 A? 



or 



Ei_ A1W1 



E 2 X 2 W 2 • 



It is difficult to determine X x and A 2 directly for the radio- 

 active substance itself ; but it is probable that the ratio is 

 not widely different from the ratio of the absorption-coefficients 

 for another substance like aluminium, which has been directly 

 determined. This follows from the general result that the 

 absorptions of a- and /3-radiations in any substance are approxi- 

 mately proportional to the density of the substance. 



^~ is the ratio of the number of ions produced by the a- 



to those produced by the /3-rays, and can be determined in 

 the way already explained for a thin layer. 



TT 



The ratio ^ has been determined for uranium from the 



following experimental data. A thick layer of uranium oxide 



