20 Dr. N. Bohr : Theory of Decrease of Velocity of 



This relation is of the same form as the one deduced by 

 Sir J. J. Thomson, and shown by Whiddington to hold 

 approximately for cathode-rays (see p. 10). For still greater 

 velocities, corresponding to the fastest /3-rays, the form of 

 the relation between V and x will be altered on account of the 

 rapid increase in the mass of the particles if their velocity 

 is very near to the velocity of" light (see later, p. 29). 



For smaller values of the velocities of the particles the 

 logarithmic term will be of material influence on the relation 

 between V and x, the effect being of the sense as to diminish 

 the power of V on the right side of the equation (5). This is 

 in agreement with experiments on a- rays. 



If we assume that the number of electrons in an atom is 

 proportional to the atomic weight, and if we consider that 

 the atoms of elements of increasing atomic weight contain 

 electrons of increasing frequency, we see immediately that 

 the formula (4) accounts for some of the principal features of 

 the absorption of a-rays by different elements. It accounts 

 for the fact that the absorption for equal weight of matter 

 per square centimetre decreases for elements of increasing 

 atomic weight *. It accounts further for the fact that the 

 relative absorption for different elements varies with the 

 velocity of the a-rays, the absorption for the heavier elements 

 being comparatively greater for greater velocities of the raysf. 



For a closer numerical comparison between the theory 

 and the experiments we must, however, observe that in the 

 deduction of the formula (4) we have made use of some 

 assumptions about the magnitude of the frequency and 

 velocity of the electrons which may not be satisfied with all 

 the electrons in the atoms considered, for the velocities of 

 the particles in question. These assumptions are : — 



(1) That the frequency n is small compared with Y/X; 



(2) That the velocity t of the electrons in their undisturbed 



orbits is small compared with the velocity of the 

 particles ; 



(3) That the linear dimensions p of the orbits in question 



Y 

 are small compared with — (see p. 16). 



As regarding the order of magnitude t and p are 

 connected by the relation T = wp,we see that condition 

 (2) is fulfilled at the same time as (3). The calcula- 

 tions involves still the assumption, 



(4) that the displacement of the electrons caused by the 



* W. II. Bragg and R. Kleeman, Phil. Mag. x. p. 318*(190o). 

 t T. S. Taylor, Phil. Mag. xviii. p. 604 (1909). 



