30G PROFESSOR G. H. DARWIN ON THE STABILITY OF THE PEAR-SHAPED 
Meridian (?/ = 
0). 
Equator {x = 0). 
Z 1=. 
1, 
X 
= 0, 
Sn = 
+ 
•117. 
z = 
1, 
2/ = 0, 
Sn = 
-h -117. 
z = 
•96, 
X 
= -096, 
Sn = 
+ 
•068. 
Z 
•866, 
y= -216, 
Sn = 
+ -047. 
z = 
•83, 
X 
= -19, 
Sn = 
•012. 
Z = 
■5, 
y = ‘374, 
Sn = 
- -014. 
z = 
•48, 
X 
= -30, 
Sn = 
— 
•on. 
Z = 
0, 
y —• ’432, 
Sn = 
— -00 2. 
z = 
0, 
X 
= -345, 
Sfi = 
+ 
•001. 
Z — 
■5, 
y= -374, 
Sn = 
+ -003. 
z = 
- -48, 
X 
= -30, 
II 
60 
+ 
•010. 
Z = — 
CD 
CD 
00 
II 
lo 
1 — ' 
Sn = 
-h -017. 
Z — 
- -83, 
X 
= -19, 
Sn = 
— 
•007. 
Z = — 
1, 
2/ = 0, 
Sn = 
— -031. 
z = 
~ -96, 
X 
= -096, 
Sn = 
— 
•025. 
N.B.- 
-For z 
= ± *866, 
Sn is 
171 both 
z = 
“ 1, 
X 
= 0, 
Sn = 
— 
CO 
o 
cases jjositivc. 
These mimbers are set out graphically in the annexed figure. It will he noticed 
that whereas the protuberance at the positive end of the z axis is great, the 
B 
A 
deficiency at the negative end is almost filled up. We may describe the general 
effect by saying that the Jacobian ellipsoid is very little changed, excepting at one 
end of its longest axis, where it shoots forth a protuberance. 
Summary. 
If a mass of licpiid be rotating like a rigid body with uniform angular velocity, the 
determination of the figure of equilibrium may be treated as a statical problem, if 
the mass he subjected to a rotation potential. 
The energy, say W, lost in the concentration of a body from a condition of infinite 
dispersion is equal to the potential of the body in its final configuration at the 
