1082 
If in the motion considered the total energy of the system is a 
minimum with respect to all those disturbances of the system in 
which the moment of momentum of each of the electrons remains 
unchanged, the system will be stable. It must be remarked, however 
that, both for his hypothetie atoms and e.g. for the hydrogen- 
molecule Bonr examines only disturbances, which consist in an 
increase or a decrease of the radius of the circle on which the 
electrons continue circulating uniformly and in which the moment 
of momentum keeps the same value as in the undisturbed motion. 
Such a disturbance, however, is no longer possible now, for in 
the case of uniform rotation the values of r, (=r,) and those of 
9, =d) and a may be deduced from equations similar to (2); 
if besides we give the value of the moment, the value of 7, will be 
determined. The electrons cannot therefore describe a larger or a 
smaller circle with the same value of the moment of momentum as 
in the undisturbed motion. 
For the atoms, i.e. for systems with one nucleus, about which 
electrons circulate in a circle, L. FOppL*) has investigated disturb- 
ances of a more general kind. We shall now apply his mode of 
reasoning to the hydrogen molecule. Thus we have to take the 
sum of the kinetic energy 7 and the potential energy P viz. 
mn ic . . . 
P + =e rd dr DH 
-_ 
a 
Has aa 
Vr,24+1r,? — 2r,r, cos (,—9,)+ (z,—2,)” 
e? e? e? 
ta)? Vrt) Vr +@, +0) 
Replacing 9, and 9, by the values found from 
h : h 
<3 ae axe ie a 
Pe TPE DE 
mt Qa 
and expanding in powers of the small quantities that determine the 
deviations from the stationary motion, we obtain : 
; ji (3/3 —1 — Mm. B B Ss 
Pat BE + 5 (es Tri@as ey, ay) 
| a BY Ble tes) = gi mast +(21 V3 Loy te = (@: +02)" 
r 32r? 16 167? 32r? 8r? 
or 
1) L. Förpr: Ueber die Stabilität des Bour’schen Atommodelles. Phys. Zeitschr, 
XV, 1914, p. 707. 
