1075 
if, as to its small vibrations, it obeys the laws of mechanics, secondly 
if it is restricted by Bonr’s condition. 
§ 2. Let the distance between the nuclei be 2a, the radius of the 
path of the electrons 7. The conditions that the nuclei are at rest 
and that the electrons circulate with the angular velocity @, are 
e 
Hse, 3? == (BOI) ve nn te a ee (2) 
Amr? 
For the case that no external forces act on the system, the equa- 
tions, which according to Desise hold for the forced vibrations, 
become those for the free vibrations of the system. If 7,, 9, 7, 
and 9, are polar coordinates for the two electrons in the plane of their 
path and z,, 2, their distances to that plane, X,, Y,, 4, X,, YZ, 
the components of the electrostatic attractions and repulsions, all with 
respect to a system of coordinates that also rotates with the angular 
velocity @, then these equations are for the first electron 
mr, —2mor, 3, — mor, = X, cos &, + Y, sind, 
mrd, + 2mor, = — X, sin 9, + Y, cos 9, 
m 2, =, 
For the second electron we find similar equations. If we introduce 
SDE an U A en ah 
then 0,, 9, fp, 2, and z, may be treated as small quantities, of 
whieh we need only take the first powers (this is not allowed for 
the deviations of 9, and #, themselves from the values they have 
in the stationary motion, because by a small change of the angular 
velocity 9, and &, may obtain great deviations). The equations 
then become 
nl 5 e? 2r 47?°— 2a? 1 Oo 
Jore ro) eS A 
Cam sr 1 (7 alt VY; Or err. | ! oa rn bev SL an 2 3 
VrPta VY ra? dr dr 
2 
ne 
IN 42 é e g 
ro 200, = — 
1 1 
5 m 8r? 
- 5 ; e? 2r 4r?— Za? 1 0, +0, 
0,—-2urd,—w’* (r+o,)= SS gers =a 
m Vrt Ha? Vr a? dr dr 
ae e p 
rd, + 200, = — — — 
2 2 2 
3 m 31° 
