﻿Gyroscopic Theory of Atoms and Molecules. 331 



be reached when the number of electrons is so great that the 

 outside ring, which grows at a greater rate, equals in 

 diameter the positive electricity, which point should occur 

 somewhere near the element uranium. Self-radioactivity is 

 attributed to the fact that when near this limit the outside 

 ring of electrons is most unstable; and comparatively slight 

 forces may drive an electron outside the positive electricity, 

 where the law of force changes allowing it to escape, thus 

 breaking up the figure and requiring readjustment. The 

 self-radioactive elements should, according to this, occur at 

 the latter end of the periodic system, as they do. 



4. There is assumed to be no radiation of energy from an 

 atom when the electrons describe circular orbits in the steady 

 state. A disturbance of this state may give rise to rapid 

 nutations of the electrons both natural and forced, accounting 

 for the X-rays. In the single electron or hydrogen atom 

 the natural nutation frequency is twice the frequency of 

 orbital revolution. The orbital frequency is determined from 

 Planck's constant together with the size of the hydrogen 

 atom to be 5 = 2*385 X 10 19 , and the characteristic X-ray 

 frequency for hydrogen should, therefore, be twice this 

 value. 



5. When there is more than one electron in the same 

 orbit the natural nutation frequencies are not easily obtained 

 from analogy with gyroscopic equations, and an assump- 

 tion is made that these frequencies are (v = k 2 n) propor- 

 tional to the number of electrons per ring. Upon this 

 assumption, together with the grouping of electrons in rings 

 to represent the periodic table of the elements, a tentative 

 distribution of electrons is given, which would account for 

 the Ka and La, series of X-ray spectra of Moseley. 



G. The comparatively low frequencies of light are attri- 

 buted to the precessional frequencies of the electrons in their 

 orbits. A calculation of the simplest case, that of the single 

 electron atom, is made to determine the frequency that the 

 one atom in the hydrogen diatomic molecule causes in the 

 other atom. The hydrogen molecule is first determined 

 definitely, including the distance between the two atoms and 

 the angle that their two axes make with the line joining- 

 centres. This distance is 1220 times the radius of the orbit 

 of the electron in the atom, equal to "347 x 10~ 9 cm., and the 

 angle is 0°. The frequency of vibration of the electron in a 

 direction perpendicular to the line joining centres agree- 

 well with the principal constant in the equation expressing 

 Balmer's hydrogen series. It has been shown by Whittaker 

 that if there are certain terms in the differential equations 



