( 542 ) 
dag 
Hat By ot Doga dn oa) Ac en Aa at 
ia 
where ( )' means that we have to take the quantity between brackets 
Lo 
as it was at the moment dh The function-solution of these 
equations may be represented by 
a, = Ci est dg = Cy est, 
If we substitute these expressions in the equations (1) and (2) 
and if we divide by et, we get: 
s 20 
C, (6 Ay He An + Ag) HOP Ar Hed; Ape "=O. 
nr J 
Cy (s° Bi + 8° By + Bo) + Cils Aa dsA; Ape V =0. 
from which we deduce: 
gi Ay teAsHA6 TST SB, Hs By + B, #3 
SS —— € ZT é 
Cy s? A, + 8? Ag + A3 s A, Hs A; + AG 
sto 
(Apt 6 Ast Ag)? — Art PAH) (6° By + 3B, +By)e V = 0. (3) 
As an exponential function is periodic, an infinite number of 
values of s will satisfy this equation, and the system will be able 
to vibrate with an infinite number of periods. 
The equations of motion, which GALITZIN used, instead of our 
equations (1) and (2) were: 
dt di 
) CL— CM = 0 
CTL Anarene dt? 
d'i 
yee by pe C' M = 0. 
Pee aA aa de 
From these he deduces instead of our equation (3) an equation 
of the following form: +) 
') Equation 7 P. 93, Loc. cit. The quantity z, which occurs there, is the quantity 
s of this formula. 
