﻿348 Prof. W. M. Hicks on certain Assumptions in the 



It is not to be expected that the numerical values of the 

 constants fju, a. on this special theory should accord with any 

 determined by experiment, but they should be of a suitable 

 order of magnitude and general character. It may be 

 interesting to test this. The expressions for the constants- 

 //,, a may be written 



8 ( ,15/3/ 3*-*A ,1 2 



where 



, _ (27r) 4 m 



4/< 

 and 



<x 3?r 



^ = (2,)%Ve ( z^ ) = 8 . 9(Z _^ )( ^^ )ioiv 



/9_Z-*x 2 

 /* " 2n 2 h\2 k-sic) 7 ' 



If p be measured in wave number instead of frequency, 

 the a must be multiplied by the velocity of light. Then 



uc 6-12 /9 Z-£ 



/9 &-k \ 

 \2 k-sj 



/jl n" \4 /c — Sk 



Here r denotes the radius of the internal ring in cm., Z the 

 atomic number of the element, k the number of external 

 electrons, and s k depends on the mutual action of the external 

 electrons on one of them. For Li, Z = ll, & = 3, s/ >; = , 577, 

 and 



2-2/. 4-5 



10 



16, 



In actual cases, for wave numbers of about p = 10 5 , poLc/ji 

 lies between about *9 and *01. Hence the second equation 

 requires r< 10~ 7 ' 5 > 10 -8 ' 5 . Since fi<l, the first equation 

 requires r to be about 10 -8 , but as the second term in the 

 bracket is determined by an approximation it must be a 

 small fraction, whence r < 10 -8 ' 5 . The fact that both give 

 values of the same order of magnitude, even if they cannot 

 exactly agree, and not far from what might be expected for 

 an 8-electron ring, is certainly satisfactory. 



2. It is deduced that the different types of sequences 

 correspond to azimuthal numbers n — 1, 2, 3, 4, the different 



orders of the same type to radial quanta n' = 0, 1, These 



are then co-ordinated with the s, p, d, f types because it is 

 stated that these types have their lowest orders respectively 

 of 1, 2, 3, 4. It is difficult to see how this statement has 

 been arrived at, as it is quite incorrect. For the sake of 



