682 Prof. E. Rutherford an the 



through which the a particles are deflected in passing through 

 known thicknesses o£ different kinds of matter. 



A narrow pencil of homogeneous a. rays was used as a 

 source. After parsing through the scattering foil, the total 

 number of ol particles deflected through different angles 

 was directly measured. The angle for which the number of 

 scattered particles was a maximum was taken as the most 

 probable angle. The variation of the most probable angle 

 with thickness of matter was determined, but calculation from 

 these data is somewhat complicated by the variation' of 

 velocity of the « particles in their passage through the 

 scattering material. A consideration of the curve of distribu- 

 tion of the « particles given in the paper (loc. cit. p. 496) shows 

 that the angle through which half the particles are scattered 

 is about 20 per cent greater than the most probable angle. 



We have already seen that compound scattering may 

 become important when about half the particles are scattered 

 through a given angle, and it is difficult to disentangle in 

 such cases the relative effects due to the two kinds of 

 scattering. An approximate estimate can be made in the 

 following way : — From (§ 5) the relation between the 

 probabilities p x and p 2 for compound and single scattering 

 respectively is given by 



p 2 \ogp 1 =—'721. 



The probability q of the combined effects may as a first 

 approximation be taken as 



?=(Pi 2 +ft 2 ) 1/2 . 



If q = m 5, it follows that 



p : — '2 and p 2 = -46. 



We have seen that the probability p 2 of a single deflexion 

 greater than <£ is given by 



lh ^n.t.b°~cotm2. 

 Since in the experiments considered cj> is comparatively small 



\tTTnt~ mu z ' 



Geiger found that the most probable angle of scattering 

 of the a rays in passing through a thickness of gold equivalent 

 in stopping power to about -76 cm. of air was 1° 40'. The 

 angle </> through which half the a. particles are turned thus 

 corresponds to 2° nearly. 



$=•00017 cm. ; ?i = 6'07 X 10 22 ; 

 u (average value) = 1*8 x 10 9 . 

 E/m = 1-5 X 10 14 . E.S. units ; e=4*65 X lO" 10 . 



