1229 
second is the same he has used in the computation of a few coeffi- 
cients from the perturbative function. From my developments | 
deduce : 
0°R, m’ 
—+ — x .0.0728. 
00? es a’ 5 
0? OR : 
Neglecting ze by the side of er (this is allowed, the first term 
having mm’ as factor, the second not), the differential equation for 
aegis VR 48 
O07, taking account of the relation —--= + — , becomes : 
0A? de 
L200 oe 
2.89 —— Od = 0, 
dt? as 
or, taking account of the relation n?a’* = M + mm’ and neglecting 
the higher powers of mv: 
206 
ae en El og = 0, 
dt? M 
hence: 
06 = q sin (rt + ¥), 
q and y being the constants of integration and 
[= ! m! 
p= -+ 1.54 n Mm 
Thus, the stability of the solution 6 =O, d == const., F' == const. 
is evident and oscillations about these values are possible. In reality 
these oscillations are very considerable. Srruve derives the value 
36°.64 for the amplitude of the libration in @ (le. pg. 287). How- 
ever, the value of py is already a close approximation, as appears 
. . . . m' ~ 
from a comparison with observation: taking for u SAMTER’S *) value 
Te the above-mentioned formula for rv gives: r = 0°.542, while 
STRUVE gets (l.c. pg. 287): 0°.562. 
3. Starting from the solution tor e’ = 0, viz. 6 = 0, A= const, 
F==const…, I will construct the development of the solution in 
powers of e’. Putting 07, 0A, OT for the first-order terms in 6, -/, T, 
the differential equations for these quantities are: 
1) Die Masse des Saturnstrabanten Titan. Sitz. Ber. der K. Preussischen Akad. 
der Wissenschaften 1912, pg. 1058. 
