1074 
If, further, we put 
EH 0; = 0, 0, —0,=8, a, + 3, =u, Ai Gj 2,—2,=9, 
and use the equations (2) we obtain 
5 ‘ y3—s . 
a — 20 ru — w* a = ———— Wa 
48//3—1) ee 
ru 20 a=—=0 
ef 5 15/8 
B — 20 rp — w’ 8 = — Un wp 
(BVB —1) 
(4) 
Peony SNS rop \ 
Pas AE 
ec 5 
RTE ( 
3 34 
re Ay cee PR een Won (0) 
4 (8 W83—1) 
From this we shall deduce the six principal modes of vibration 
of the system. We suppose that all quantities contain the time only 
in the factor et, by which the differential equations (8)—(6) become 
ordinary linear equations which we shall indicate in the same order 
with (3’)—(6’). The determinants of the systems (8’) and (4’) and 
the equations (5’) and (6’) give us then the six values of 7. From 
the obtained equations (3’) and (4’) we calculate for each value 
of n the complex ratios between ru and «, rg and 8 and then 
know the form of vibration. So we obtain 
(A) from equations (6) the mode of vibration (A) in which both 
electrons execute linear vibrations along the Z-axis, in such a way 
that they always have the same and opposite deviations ; the frequency 
U PA Ok 
(B) from equation (5) the mode of vibration (B), in which they 
always have equal deviations in the same sense parallel to the 
Z-axis with the frequency nz = 0,556 w. 
(C) from the equations (3) mc =O and ng, = + 1,47 w. To ng, 
belongs a mode of vibration c, in which both electrons are dis- 
placed over the circle in the same sense; to which disturbance the 
system is of course indifferent. To ne, belongs a vibration C,, in 
which both electrons describe equal and congruent ellipses of the 
same position, but in such a way that the radii vectors are always 
oppositely directed : = = 20,64 7. 
nL 
(D) from the equations (4) finally np, = + 1,41 2m. In this mode the 
electrons describe equal and congruent ellipses of the same position 
