12 

 He \ J 



and we obtain easily that, if p^ds/dxp, 



^ 3 1^ \ «/ jmv, 



Now, provided that \xpds is small, this quantity is very nearly 

 equal to A'N, the total deflection of the ray. 



But this integral 



He 



c'^iai I 8\^\ He 



_ He 4a2 



mv^ ' 7 ' 



and this quantity is very small, since it is only slightly 

 greater than A N. 



Finally then we have that 



A'N/AN = 8/7. 



It is easily found that if we had supposed the a particle 

 to spend its energy uniformly along its path, we should have 

 obtained the result :— A 'N/ AN = 4/3. 



It will thus be clear that, on any reasonable hypothesis 

 as to the particular law of diminution of velocity, the actual 

 path of the particle differs very little from a circle. In the 

 extreme case which I have considered, the small deviation 

 therefrom at the end of the path is small compared to the 

 widths of the images in M. BecquereFs photograph. If the 

 particle ceases to ionise whilst its velocity is still great, as 

 has been shown by Professor Rutherford, the variation is still 

 less. 



Let us now consider the circumstances of M. Becquerel's 

 experiment. 



As a first approximation, suppose the widths of the 

 groove containing the radium salt and of the slit to be 

 negligible. 



If no magnetic field is acting, all the a particles move in 

 the vertical line O N. The range of the particles from RaC 

 is very nearly 7*0 cm. : from which it follows that the number 



