﻿326 Dr. A. C. Crehore on the 



peculiarity of the hydrogen atom will later serve to explain 

 some of the compounds into which hydrogen enters. 



A small displacement in any direction whatever from this 

 position of equilibrium as origin gives rise to a restoring 

 force directed toward this origin. For small displacements 

 the restoring force is proportional to the displacement, giving 

 rise to harmonic vibrations about this point or origin. The 

 restoring force per unit of distance and per unit of mass along 

 the line joining centres of the atoms is 



4 e 2 8* 



F «=-w> < 12 > 



where a is the radius of the orbit of the electron and e its 

 charge, and ft the velocity of the electron divided by that of 

 light. If we equate this force to the mass times the accelera- 

 tion per unit of distance, we find the frequency of oscillation 

 in the direction of the line joining centres to be 



w= -3 r-r> • ( 13 > 



3*T" 



where m denotes the mass. 



The restoring force per unit of distance and mass along 

 any line perpendicular to the line joining centres is 



2 p 2 8 r ° 

 F p =-Ar e -^, (14) 



exactly one half the force in (12) along the line of centres. 

 The corresponding frequency of oscillation along the per- 

 pendicular line is, therefore, 



n p=2i • • (15) 



If we consider that the mass which is subjected to this 

 force is that of the single electron in the atom, we obtain in 

 numerical values taking £ = 4*77 x 10~ 10 ; a = *285 x 10" 12 ; 

 ?ft=-878xl0- 27 ; /3=27T5a/c; 5 = 2-385 x 10 19 ; c = 3xl0 10 T 



«.= 1-I2xl0» 1 



n p = -79xl0 15 J { ' 



The wave-lengths of light corresponding to these fre- 

 quencies are 



X n = 2680x 10~ 8 cm. along, 



At> = 3800 x 10~ 8 cm. perpendicula 



).. . (17) 



