a Particles with Light Atoms. 505 



cube of the distance, we can also work out the orbits and show 

 that the dependence of v on angle disagrees with experiment. 

 For simplicity we shall suppose the nucleus immovable. In 

 polar coordinates the motion is given by : — 



rW=pY and > + r ?08 = V 3 - -^ , 

 where the force is proportional to — . 



j£ P = u we have 



&)'+*=■ 



£-.*-!. 



p n ~ 1 V 2 

 The deflexion <f> must therefore be a function of p w_1 V 2 or 



2 



inverting p = Y M_1 /(^). The number of scintillations seen 



on a screen is proportional to .,,, -, and, as far as it 

 r r sin 909 4 



concerns the velocity, this is proportional to V »-k 



Thus only if n = 2 can v be proportional to ^ 



When ?z = 3 the orbit can be worked out completely and 

 we find 



\/( 1+ pW' 



from which we derive that z; is proportional to 

 ^^cosec 6 — j _ 



v - t*{-t)r 



The ratio of the numbers at 30° and 150° for this law is 51. 

 For the inverse square law it is 194. For a comparison of 10° 

 and 90° the inverse cube gives 525 and the inverse square 4330. 



6. We may calculate an upper limit to the size of atomic 

 nuclei from the distance of closest approach between the 

 a particle and nucleus. By (5) the apsidal distance is 



and for any fairly strong deflexion of the a particle sec 6 is 

 practically 1, so that we may take the distance as 



