674 Prof. E. Rutherford on th 



The probabilty m of entering an atom within a distance p 

 of its centre is given by 



m = 77 p 2 nt. 

 Chance dm of striking within radii p and p) + dp is given 



7T 



dm = 27rpnt . rfp = jntb 2 cot (£/2 cosec 2 <£ ; 2 rf<£, . (2) 



since cot <f>/2 = 2p/b. 



The value of dm gives the fraction of the total number of 

 particles which are deviated between the angles <f> and 

 <f) 4- d<j>. 



The fraction p of the total number of particles which are 

 deflected through an angle greater than <£ is given by 



p =z~ nth 2 cot 2 cj)/2 (3) 



The fraction p which is deflected between the angles <j>i 

 and cj> 2 is given by 



p = lntb*(cot*&-coV>&\ ... (4) 



It is convenient to express the equation (2) in another 

 form for comparison with experiment. In the case of the 

 a rays, the number of scintillations appearing on a constant 

 area of a zinc sulphide screen are counted for different 

 angles with the direction of incidence of the particles. 

 Let r = distance from point of incidence of a rays on 

 scattering material, then if Q be the total number of particles 

 falling on the scattering material, the number y of a particles 

 falling on unit area which are deflected through an angle </> 

 is given by 



_ Qdm nth 2 . Q . cosec 4 <j)/2 ,^ 



y ~~ 27T?- 2 sin $ . d<j> = 16? -" • ■ (5; 



2NeE 

 Since b = =-, we see from this equation that the 



number of a particles (scintillations) per unit area of zinc 

 sulphide screen at a given distance r from the point of 



