﻿Gyroscopic Theory of Atoms and Molecules. 321 



the L« series, which is represented by the line II in the 

 figure, begins at Zr with a line due to the outside ring, and 

 for a few of the elements in this region, which have lines in 

 each series in Moseley's table, the one is due to the first and 

 the other to the sixth ring of electrons. 



If this mode of explaining the observed X-ray spectra is 

 correct, it is conjectured that several other series of lines 

 between the Ka and the La exist. Of course a determination 

 of the spectra on this theory depends entirely upon the accurate 

 determination of the frequencies of nutation of the electrons 

 in their orbits — a most difficult problem — but the simple 

 assumption made above that v = k 2 n points to a distribution 

 of the electrons in good agreement with the corpuscular ring 

 theory. There is no doubt that the complete solution of 

 these frequencies of nutation is more complex than the 

 assumption made ; and even if this is one solution, it is not 

 surprising that Moseley has observed several other series of 

 varying intensity lying close to these principal series. 



A way of approximating to the absolute value of the 

 frequencies is by the use of Planck's constant. The energy 

 required to separate to a great distance an electron from the 

 unit of positive electricity may be taken as the minimum 

 energy change that ever takes place. If the electron starts 

 from the surface of the sphere of radius 5 = *735x 10" 12 cm. 

 as above determined, it is shown to be e 2 /2b. Equating this 

 to hs, where 5 is the frequency of revolution and h is 

 Planck's constant, we obtain 



hs = j b =15-5 xlO" 8 (9) 



where ^ = 4*77 x 10" 10 , and 7i=6'5 x 10" 27 . Hence for the 

 single electron atom, which on this theory is taken to 

 represent hydrogen, the frequency of revolution of the 

 electron is * 



. = 2-385 xlO 19 , | 

 and v- 25=4-770 xlO l9 J ' K } 



On the equilibrium theory, when there are two elec- 

 trons, they place themselves halfway from centre to circum- 

 ference of the positive sphere, and with only one electron 

 it would go to the centre, making the radius in the first 

 case *46 X ~ 12 cm., and in the second case zero. The suppo- 

 sition that the angular moment of momentum is constant for 

 all electrons and not zero, indicates that the true value 



* The letter v is reserved for the nutation frequencies and $ is 

 introduced for frequencies of revolution. 



Phil Mag. S. 6. Vol. 29. No. 170. Feb. 1915. V 



