681 Prof. E. Rutherford on the 



scattering are thus identical in general form, but differ by a 

 numerical constant. It is thus clear that the main relations 

 on the theory of compound scattering of Sir J. J. Thomson, 

 which were verified experimentally by Crowther, hold equally 

 well on the theory of single scattering. 



For example, if t m be the thickness for which half the 

 particles are scattered through an angle (f>, Crowther showed 



9 



Yfill 



that (/>/ */t m and also ^r • Vt m were constants for a given 



material when <j> was fixed. These relations hold also on the 

 theory of single scattering. Notwithstanding this apparent 

 similarity in form, the two theories are fundamentally 

 different. In one case, the effects observed are due to 

 cumulative effects of small deflexions, while in the other 

 the large deflexions are supposed to result from a single 

 encounter. The distribution of scattered particles is entirely 

 different on the two theories when the probability of deflexion 

 greater than </> is small. 



We have already seen that the distribution of scattered 

 a particles at various angles has been found by Geiger to be 

 in substantial agreement with the theory of single scattering, 

 but cannot be explained on the theory of compound scat- 

 tering alone. Since there is every reason to believe that 

 the laws of scattering of a and /3 particles are very similar, 

 the law of distribution of scattered j3 particles should be the 

 same as for a particles for small thicknesses of matter. 

 Since the value of 7nu 2 /E for the /3 particles is in most cases 

 much smaller than the corresponding value for the a. par- 

 ticles, the chance of large single deflexions for j3 particles in 

 passing through a given thickness of matter is much greater 

 than for a particles. Since on the theory of single scattering 

 the fraction of the number of particles which are deflected 

 through a given angle is proportional to Id, where t is the 

 thickness supposed small and k a constant, the number of 

 particles which are undeflected through this angle is propor- 

 tional to 1 — Jet. From considerations based on the theory of 

 compound scattering, Sir J. J. Thomson deduced that the 

 probability of deflexion less than (/> is proportional to 1 — e~^ 1 

 where fi is a constant for any given value of d>. 



The correctness of this latter formula was tested by Crowther 

 by measuring electrically the fraction J/I of the scattered 

 /3 particles which passed through a circular opening sub- 

 tending an angle of '66° with the scattering material. If 



I/I^l -«-**, 



the value of I should decrease very slowly at first with 



