Forces of Attraction between Atoms and Molecules. 805 



But this law probably applies only to a region corresponding 

 to distances from the molecule of the order of the distances 

 of separation of the molecules of a liquid. The « particle, 

 on account of its great velocity and small mass in comparison 

 with that of the molecules of the matter through which it 

 passes, would approach a molecule very closely, and the law of 

 attraction relating to these small distances of approach of the 

 bodies might therefore be somewhat different from that given 

 ;ibove. Since the attraction undoubtedly increases very 

 greatly with the closeness of approach of the bodies, the 

 phenomenon would be regulated by the law holding at 

 closest approach. Let us suppose that the law of attraction 

 is 



- 3 2 y/m x .X y/m 2 , 



the only justification so far for making this assumption is that 

 it reduces the above equation to a simple form. We have 

 then 



Dividing the equation by v , and integrating we get 



\ . ajj 



V^-V^— 2 V'xi.5 vW(*i-#2> 



This equation states that an a. particle traverses the distance 

 (#!— # 2 ) in a gas during which its energy falls from 



— a *° — s~ 5 an d that this distance is inversely propor- 

 tional to the sum of the square roots of the atoms of a 

 molecule of the gas. 



Now Prof. Bragg and the writer* have carried out a set 

 of measurements on the range of the a particle in different 

 gases at the same pressure, and found it inversely propor- 

 tional to 2\/^2- Therefore, if the part of the energy 

 expended by the a particle due to its carrying a charge is 

 less than that expended in the way explained, the law found 

 by experiment is at once accounted for. There are various 

 reasons for believing that the energy expended on ionization 

 is less than that expended otherwise, as imparting kinetic 

 energy to the molecules it encounters, at any rate the loss of 

 energy by the a particle cannot be easily explained by ex- 

 penditure on ionization only. Thus the ionizations per unit 



* Phil. Mag. Sept. 1905, p. 318. 



