132 Mr. L. Simons on the Beta-Ray Emission froi 

 the K a frequency of the elements as 



and also 



^=(p-4) (N - 1)2n ' 



%=(J-^)(N-7-4)< 



where N is the atomic number of the element and n the- 

 fundamental frequency of line spectra ( = 109720 x velocity 

 of light). These formulae give the K a frequency of .-.rsenic 

 equals the L,, frequency of lead. The result is approximately 

 the same as Chapman's. 



Reference to the curves in fig. 7 (PI. III.) will show that 

 this result is applicable not only to X-ray emission but 

 analogously to /3-ray emission. This is clearer in the dotted 

 curves, the distribution in speeds 'of the electrons about an 

 arsenic screen being similar lo that about a lead serf eh. 



There are appearances, too, that the effect is carried on 

 through the range of the elements. 



An attempt to detect groups of /3-partieles possessing sub- 

 speeds and to determine the numerical relations between 

 them. (Figs. 8 and 9, PI. III.) 



The range of the /3-particles and the law of absorption 

 that they follow are matters of some obscurity. Whiddington 

 set himself to determine whether the range was proportional 

 to E or E 2 , where E is the energy of the particle. 

 W. Wilson's * results give E 32 for the rays from radioactive 

 substances. J. J. Thomson f and Bohr ± have both deduced 

 complex formulae involving E 2 as one of their terms. The 

 difficulty arises from the impossibility of determining the 

 diminution in energy along the complex path of the /3-ray. 

 Wilson showed that only a complex distribution of velocities 

 amongst the /3-rays from radioactive substances would give 

 rise to an exponential law of absorption, whilst Sadler stated 

 that his slow-moving homogeneous /S-rays were absorbed 

 according to an exponential law. 



In a previous paper § I deduced tentatively a result based 

 upon an exponential law of absorption. The major speed ^ 



* Proc. Roy. Soc. A. lxxxiv. p. 141 (1910). 



t ' Conduction of Electricity tkrorgh Gases/ p. 381 (1906). 



X Phil. Mag-, ser. 6, vol. xxv. p. 28 (1913). 



§ Loc. cit. 



