﻿Gyroscopic Iheory of Atoms and Molecules. 319 



Comparing this with the equation (3) we derive the relation 



w 



— — =p a constant (7) 



n 



Or v k = k-=ka:; ..... (8) 



where x replaces nijr n , and is proportional to the square root 

 of the frequency of the X-rays. The corpuscular ring theory 

 gives the approximate values for both n, the electrons per 

 ring, and r n , the radius of the ring, and hence values of x 

 proportional to the square root of the frequencies. Charting 

 these values points are obtained, as we pass across a series 

 of elements in the periodic table, which have some semblance 

 to the straight line series of Moseley. However, it is neces- 

 sary to restrict this to the Ka, series which applies to the 

 lighter elements, as the number of electrons corresponding 

 to Zr, the first of the La series, is too large to handle. The 

 best line to represent the Ka series when projected back to 

 the ordinal axis intersects at about three units instead of 

 unity as Moseley takes it, making 6 = 3 instead of b = l in 

 equation (1). iiydberg * makes this constant exactly 3 

 in his revision of the Moseley ordinals, and has in doing 

 this added 2 to each ordinal in the series of elements, 

 makim N for aluminium 15 instead of 13. In deriving 

 the spectra in this paper, Rydberg's interpretation of the 

 Moseley ordinals is used. 



The next process is to abandon the approximate values of 

 the radii r n obtained from considerations of equilibrium and 

 proceed to calculate thetn on the basis of Moseley's observa- 

 tions, assuming the points to lie exactly upon his Ka line or 

 series. In so doing, we are at liberty to distribute the elec- 

 trons in rings in any manner, but that particular arangement 

 lias been chosen which is demanded by the periodic system. 

 The resulting arrangement, therefore, contains an explanation 

 of both the periodic system of the elements and the X-ray 

 series of Moseley. 



In fig. 1, the line I represents the Ka series, the marks 

 upon it being the spectrum lines experimentally obtained, 

 but it begins at N = 3, and the abscissa are proportional 

 but not equal to the square root of the frequency, bemo- 



equal to x — ■—. The first point on the line at N = 15 and 



,s = 1*875 x 10 12 is found by taking Al to be the configuration 



27 = 3, 9, If), i he re being 27 electrons total with an outside 



* J. R. Rydberg-, Phil. Mag. July 1914, p. 147. 



