44 Mr. J. J. E. Durack on Lenard Rays. 



Hence 



L ' mr r, — a 2 J 



If we suppose, as is very frequently done, that the radius 

 of the molecule and of the sphere of action are identical, 

 i. e. that actual contact takes place at a collision, the formula 

 for a p becomes 



where p is the radius of an ion. 



The experimental evidence available is not sufficient to test 

 the truth of this formula, but we can make a rough estimate 

 of p from the values of a p obtained by Professor Townsend 

 and myself. 



•4 \ 1+ 2ml0 17 H )/ V + 32ml0 18 pi' 



Taking the velocity giving Townsend a = 21 as 3 . 10 8 cm. 

 per sec, and the velocity in the case of the Lenard rays as 

 4 . 10 9 . 



From this we get p = 10~ u cm. 



From the values of ejm for cathode rays and for hydrogen 

 in electrolysis we know that m the mass of an ion is approx. 

 10~ 3 times the mass of an atom of hydrogen, and so if the 

 densities are equal the radius of an ion would be of the order 

 10~ 9 cm. ; but on Prof. Thomson's view of an atom, viz. that 

 it is made up of ions, the density of an atom would be much 

 less than the density of an ion ; hence 10~ 9 is too large for 

 the radius of the ion. 



Also we know that the radius of the ion must be greater 

 than 10 ~ 13 , for it has been shown by J. J. Thomson f, and 

 also by Searle J, that the inertia due to a moving charge e 

 on a sphere of radius p is 



2 e* 



when the velocity is small compared with that of light, 



* It was pointed out to me that this form A-f- — is the same as that 



deduced by Sutherland in calculating the influence of cohesion on the 

 free path (v. Meyer, Kinetic Theory of Gases, p. 425), and hence it is nut 

 necessary to assume any more than that the force is central. 



However, I have assumed less than this, having merely supposed a 

 charge could be induced on the molecule, that the force is central, and 

 the actual law of force follows from electrostatics ; moreover, we deduce 

 a definite form for a in terms of quantities which may be experimentally 

 determined, and thus we can test the theory. 



f J. J. Thomson, Rec. Researches, p. 21. 



X Searle, Phil. Mag. xliv. 1897. 



