556 Sir E. Rutherford on Collision of 



a close collision differ considerably in magnitude and 

 probably in direction from those to be expected on the 

 simple theory. 



In order to throw light on the magnitudes involved, 

 consider the following case. Assume that for distances 

 greater than D between the centres of the colliding atoms, 

 the forces are given by the simple theory but for decreasing 

 distances the forces between the nuclei augment rapidly 

 according to other laws, and that all the collisions of closer 

 approach than D result in the production of a high-speed 

 H atom which for a particles of range about 7 cm. tends to 

 be projected approximately in the line of flight of the 

 cf. particles. 



Darwin (loc. cit.) has shown that the apsidal distance D 

 between an « particle and H atom is given on the simple 

 theory by 



D=^(l + sec0), 



where a= ■■-.,-( f- -^ ) = 9 21 x 10" 14 for a particles of 



V \m M/ l 



maximum range 7 cm., where is the angle of deflexion 

 of H atom and v the velocity of a particles from radium C. 

 In the same notation (§7) 



Vr 2 



Eliminating 6 from these two equations, p 2 = D I D — 2/x, -\ ). 



We have seen (§ 9) that for a particles of range about 

 7 cm. the value of ^> = 2*4xl0~ 13 . Substituting this value 

 of p and putting v = v we find the corresponding value of 

 D = o*5x 10~ 13 cm. It will be seen later that all collisions 

 for which D on the simple theory is greater than this value, 

 should give rise to H atoms of velocity too small for detec- 

 tion. We may consequently conclude that all collisions for 

 which D is equal or less than 3"5 x I0~ 13 cm. give rise to 

 a high-speed H atom. 



It is of interest to consider, on these assumptions, how the 

 number of H atoms should vary with the velocity of 

 the incident a particles. From tbe above equation, it is 



v 2 

 seen that ^> = when D = 2/jl~. Substituting the value 



D-3-5xl0- 13 , /*=9-27xlO- H , we find r /r=l'89. The 



