﻿Absorption and Scattering of the a Rays. 



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and the equation be solved for a, a value is given several 

 times greater than 10 ~ 8 . Thus here as for hydrogen a has 

 a value greater than that given by the kinetic theory, and 

 this may probably be set down to the inaccuracy of meaning 

 of a in the case of a very small number of electrons in 

 the atom. 



From the table it appears that as the atomic weight grows 

 a becomes less and is very small for a heavy substance. This 

 is rather surprising, but it does not seem unreasonable that a 

 small cluster of a large number of electrons should exert 

 elastic forces at as great a distance as a larger cluster 

 composed of a smaller number. There is no great difference 

 which should enable us to distinguish whether the distri- 

 bution of electrons through the volume of the atom or that 

 over its surface gives values most in agreement with the 

 results of experiment. 



The fact that stopping power depends on both n and or 

 prevents the deduction of any simple relation from Bragg's 

 law of stopping power *. Table I. suggests that n is pro- 

 portional to the atomic weight A, and if this is supposed 

 accurately true it is possible to find a relation for a ; but it 

 is not very intelligible because it contains the velocity, and 

 it was only by neglecting the variation due to velocity that 

 Bragg propounded his law. The " atomic stopping power 3y 

 of Bragg is, from (8), proportional to n'{\og (l + w f ) — f( w ')} 

 and this is proportional to V A. Then approximately log?// 

 varies as 1/ v'A, or making the velocity constant 



log or' + const, cc 1/ \/A, 



which is the form that Bragg's law takes on the present 

 theory. 



The analysis of this paper is not sufficient to give a 

 complete figure of the Bragg ionization curve. In the 

 earlier part of the range the ionization is proportional to 

 the mean rate of loss of energy of the a rays. But the 

 interesting part of the curve is the end, and here measure- 

 ment of loss of energy is useless, because the dominant factor 

 is the straggling of the rays, and the problem of this 

 straggling has not been discussed. In his investigation on 

 the connexion between ionization and absorption, Geiger 

 points out that the ionization is inversely proportional to the 

 velocity of tho rays. On the present hypothesis this is 

 accidental. If the ionization is proportional to the rate of 



* W. II. Biag-g, he. cit. 

 Phil. Mag. S. G. Yol. 23. No. 138. June 1912. 3 



