Scattering of a and /3 Particles by Matter. 675 



incidence of the rays is proportional to 



(1) cosec 4 <j>/2 or l/</> 4 if <f> be small ; 



(2) thickness of scattering material t provided this is 



small ; 



(3) magnitude of central charge N^ ; 



(4) and is inversely proportional to (mu 2 ) 2 , or to the 



fourth power of the velocity if m be constant. 



In these calculations, it is assumed that the a particles 

 scattered through a large angle suffer only one large deflexion. 

 For this to hold, it is essential that the thickness of the 

 scattering material should be so small that the chance of 

 a second encounter involving another large deflexion is very 

 small. If, for example, the probability of a single deflexion 

 (j) in passing through a thickness t is 1/1000, the probability 

 of two successive deflexions each of value <£ is 1/10 6 , and 

 is negligibly small. 



The angular distribution of the a particles scattered from 

 a thin metal sheet affords one of the simplest methods of 

 testing the general correctness of this theory of single 

 scattering. This has been done recently for a rays by 

 Dr. Geiger *, who found that the distribution for particles 

 deflected between 30° and 150° from a thin gold-foil was in 

 substantial agreement with the theory. A more detailed 

 account of these and other experiments to test the validity 

 of the theory will be published later. 



§ 4. Alteration of velocity in an atomic encounter. 



It has so far been assumed that an a or /3 particle does not 

 suffer an appreciable change of velocity as the result of a 

 single atomic encounter resulting in a large deflexion of the 

 particle. The effect of such an encounter in altering the 

 velocity of the particle can be calculated on certain assump- 

 tions. It is supposed that only two systems are involved, 

 viz., the swiftly moving particle and the atom which it 

 traverses supposed initially at rest. It is supposed that the 

 principle of conservation of momentum and of energy 

 applies, and that there is no appreciable loss of energy or 

 momentum by radiation. 



* Mauch. Lit. & Phil. Soc. 1010. 



