812 Dr. Norman Campbell on 



scattering and absorption of the charged particles in the 

 primary rays which arises from their interaction with the 

 electrons of the atoms through which they pass. The 

 electrons of the atoms take np energy from the rays ; if this 

 energy is sufficient they break free from the atom and appear 

 as 8 rays. On the assumption that the forces holding the 

 electron to the atom may be neglected in calculating the 

 action between the electron and the rays, the following- 

 relations are deduced between T, the kinetic energy of a 

 (3 ray, e its charge, a the distance of the undisturbed electron 

 from the asymptote of the path of the ray, Q the energy 

 given by the ray to the electron, and 26 the angle through 

 which the ray is deflected : — 



Q=— 4— • • (1), sin^=— J—. . . (2> 



±+~T 2 1+-,T 2 



If the ray is an a ray, supposed to act as a point charge 2e r 

 then it can be shown that, so far as communication of 

 energy to the electrons is concerned, it behaves in exactly 

 the same manner as a/3 ray travelling with a speed twice 

 that of the a rav. 



Ionization is supposed to occur if Q>W , when W is 

 the energy necessary to ionize an atom. If it be assumed 

 that, while the ray passes through unit thickness, the number 

 of collisions in which a has a value lying between a and 

 a + da is 2miada, where n is the number of electrons in unit 

 volume of the substance, formula? can be deduced for the 

 scattering of the rays and the amount of ionization caused by 

 them which agree with experiment when very fast j3 rays are 

 considered. 



From (1) together with this assumption it can be proved 

 readily that the ratio of the number of electrons acquiring at 

 a single collision an energy greater than W + W T0 the 

 number so acquiring an energy greater than Wo, is 



T-W-Wp Wo m 



rv_- T _ Wo 'W + W *'/'■" W 



The latter number is the whole number of 8 rays, the former 

 may be plausibly identified with the number of 8 rays 

 originally liberated with an energy greater than W. Hence, 

 if T is very great compared with W (and it is only in this case 

 that the theory is likely to be valid), the proportion of the- 



W 



8 rays liberated with an energy greater than W is ^p — -I'.— , & 

 J &J & )\ +\\ 



quantity which is independent of T. Hence the theory is in 



