﻿Gyroscopic Theory of Atoms and Molecules. 327 



I£ we consider that the mass which is subjected to this 

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

 in numerical values taking ?w = l*66 x 10 ~ 24 and other 

 quantities as above, 



n„ = -026xl0 15 ^ 



77 P =-018X10 15 J v j 



The wave-lengths o£ light corresponding to these vibrations 

 are 



\ a = 117000 x 10~ 8 cm., 1 



X p = 165000 xlO" 8 cm. ) * } 



The light spectrum of hydrogen is not to be attributed to 

 these two simple vibrations of the electron alone (ltf) and 

 (17), but rather to the disturbances to which they give rise 

 in the motion of the single electron in its orbit. 



It is remarkable that this calculated value of the frequency 

 of the electron perpendicular to the line joining centres 

 comes so close to the experimental value of the fundamental 

 constant in Balmer's series of hydrogen lines. The wave- 

 lengths in Balmer's series * of hydrogen lines are given by 

 the equation 



m 2 



\ = 3647-20xl0- 8 -f—, .... (20) 

 irr — 4 v 



m being a series of integers. 



If we express Balmer's series in terms of the frequency 

 instead of the wave-length, (20) may be written 



n = b+ SL (21) 



where 



b= ^^-jg-g. = -823 xlO 15 , and a= -46= -3'292x 10 lf 



It has been shown that this law of Balmer's can be 

 derived f from considerations of ordinary dynamics provided 

 there is a proper sort of gyroscopic connexion between the 

 two atoms. Let u and v be scalar functions of the time and 

 of the position of points in the two atoms respectively at an 



* J. S. Ames, Phil. Mag. vol. xxx. p. 55 (1890). 



t E. T. Whittaker, Proc. Roy. Soc. ser. A. vol. lxxxv. No. A 578, 

 Jane 9, 1911, p. 262. The importance of this demonstration warrants 

 repeating in full, as given in the original paper, since we have shown 

 that the values are obtainable from the hydrogen atom. 



