484 
If « and B, and thus eo, and o, are solved from (I) and (IJ), 
eqq. (10) and (11) give 3, and 9, 
It appears from equations (I1)—(IV) that we get 4 stable modes 
of vibration; the unstable vibration D, and the indifferent one C,, 
which Miss v. LeevweN gave (l. ce. p. 1074) have disappeared. 
sesides some of the frequencies have changed a little. 
Helium: 
EE TT Pe (1) 
Ere PS, Ee EN 
VEB ONO rn nae ee 
dl PZ OY. en. 150 3 
(N.B. In the He-atom the plane of the orbit of the electrons can 
turn freely about the nucleus; hence the d-motion is here not a true 
vibration). 
Note. 
As the coordinates wp, and vp, do not appear themselves in 7’, we 
might, in deducing the equations of motion, treat them as cyclic 
coordinates, eliminating ur, (=w + 9) by means of 
h 
_ 2amr;? 
and forming the kinetic potential according to Rourn and Hermuoutz. 
eo 
4’ 
This method of eliminating the w; is used by L. Föppr in an invest- 
igation on the stability of Boxr’s model’). If we applied it here, 
the term 
pt (WW) 
TR ER 
would remain in V, so that we should be obliged to omit it 
altogether, whereas in the calculation given above its influence is 
annihilated by the forces Q, and Q,. 
B. Forced vibrations. — Dispersion formula. 
The course of the following calculation is for the greater part the 
same as that followed by DeBije *). 
We will make use of two systems of coordinates: One system 
is invariably attached to the molecule, the axis of z is laid along 
the line which joins the nuclei; the axis of « along the line which 
joins the electrons; the axis of y perpendicularly to the latter in 
ly Phys. Z..S.215 (1914), S707. 
2) Sitz. Ber. Bayr. Akad. 1915, S. 1. 
