FIGURE OF EQUILIBRIUM OF A ROTATING MASS OF LIQUID. 
297 
It is easy to show from our analysis that for the deformation 
Oa - Sa) '#>2 + ; 
6)“ C- 
/TT/o n 
and that the corresponding expression with in place of holds good for the 
deformation 
Forestalling the results obtained below, it may be stated that for 
877=^' (/,)3 (- -01433 + -03959] ; 
and for /o'>S'/ 
hu {-00015 + -00002], 
Thus in both cases 8 77 is positive, and this shows that the Jacobian ellipsoid is also 
stable for the ellipsoidal deformations. The fact, that hE (the variation of my 
function of energy for constant angular velocity) is negative for the deformation *S7, 
illustrates the truth of AT. Poincare’s remark (‘Acta Alath.,’ 7, p. 365): “Si au 
contraire la rotation de la masse fluide etait determinee par celle d’un axe rigide 
(comme dans les experiences de Plateau par exemple), tout deplacement pi’oduirait 
line resistance passive et I’eHipsoide de Jacobi serait toujours instable.” 
I have in (32) written 
[b s] = 
+ 433 ,>,')’ - 
sin- /3 
4 cos /3 cos 7 
33 .' W ■ 
The following table then gives further stages in the work 
i. 
s. 
[i, s.] 
{BffICf. 
BeiCf. 
2 
0 
•00014032 
- -00022329 
- -12482 
0 
2 
•00000072 
+ -00000097 
- -08059 
4 
0 
•00009937 
•00020486 
•07705 
4 
2 
•00000276 
•00000231 
- -000506 
4 
4 
•00000001 
•00000001 
•0000019 
6 
0 
•00002835 
•00003118 
•01852 
6 
2 
• 00000403 
•00000256 
- -000278 
6 
4 
•00000002 
•00000001 
•00000034 
•00024190 --00022329 
•00027558 
+ -00024190 
213 [Ha-,y + 2Cd-4a-,= 
- -00050012 
— 
2 -i- -00001861 
1 
! 
i 
Ao — 
- -00022454 
i 
^ Cf ~ 
+-00001861 
Numerator. 
- -00020593 
2 Q 
VOL, CC.—A. 
