﻿Gyroscopic Theory of Atoms and Molecules. 325 



the two hydrogen atoms which form the diatomic molecule, 

 including their distance apart, and the angle of latitude that 

 the line joining their centres makes with the planes of their 

 orbits. Although it is the average value of the forces when 

 taken over a long time that determines the stable position of 

 equilibrium of the two atoms forming the molecule, yet the 

 instantaneous values of the forces on the individual parts 

 of the atom varying during one revolution give rise to the 

 precessional motion which causes the light spectra. We 

 will now determine in absolute dimensions the distances 

 referred to, and then proceed to calculate for this simple 

 molecule the precessional period or frequency which gives 

 rise to the light spectrum of hydrogen. 



The Hydrogen Molecule. 



The mechanical force that two hydrogen atoms, having a 

 single electron each, exert upon one another when their axes 

 are parallel and in the same direction, may be derived from 

 equations (42) * and (44) of the former paper. They show 

 that two such atoms come to stable equilibrium with each 

 other when their axes are in the same straight line, the 

 revolution of the electrons being in the same direction, the 

 phase angle between them being zero, so that the line joining 

 the electrons is always parallel to the line joining the centres 

 of their orbits. When the distance between the centres of 

 the atoms is 



x =^l c ~ = -347x10-° cm (11) 



where c is the velocity of light and 5 the frequency of orbital 

 revolution of the electron obtained from Planck's constant 

 in (10), then it has been found that the atoms are in stable 

 equilibrium with each other. 



It is to be noticed that the distance between the two 

 hydrogen atoms is very small compared, for instance, with 

 the distance between a sodium and a chlorine atom in rock- 

 salt, which is 2*814 x 10~ 8 cm.; 81*2 times smaller, and yet 

 the same values of the fundamental constants s and i\ serve 

 to show that we get an equilibrium distance of this larger 

 order when the sodium and chlorine atoms are used. This 



* I11 giving- the coefficients B-2,2, B-i,2, &c, middle of page 70, Phil. 

 Mag. July 1913, a column of B's was omitted. The first column 



3 7 9 



should read Bo, 2 = 5 ; B4, 2 = 5B-2, 2 ; Be, 2 = % Bi, 2 ; Bs, 2=0 Be, a ; 



r>io,2= -r-Bs,2; Bi2,2 = - »m, 2 ; 13i4,2=-. Jt>i2,2. 



4 t'3 O 



