1315 
Consequently for the outer surface we have 
C'—A' 
5, =} M'd?” = 2Q, Pi de) 
hue BA 4 nk (7) 
ce rye oe 
Putting now 
— 1 
&, = 6,—72?,; 
so that ¢, is the mean ee a of the meridians, we find 
a es Gy; 
4 be, (5) 
5. We now put 
B do B dp g dD 
N=. ee ees, GR ee 
oO dp yv dp D dp 
From the definition of D we find easily 
A 
¢=—3,1——}. 
D 
If now the assumption is made that the density never increases 
A 
from the centre outwards '), we have always 1 ee 0, or 
Gs 
We now differentiate the equations (6). If the whole mass rotates 
as one solid body, then Do is constant. Also Dx is a constant. We 
1 +- 5 et Eee ') 
er en ky REG 
P 
64 a(S, 1)=0. 
8° oD (6—1) = 3 (8° S—p* Ao). 
We have thus 
te ee eee . 
If for B'S we write [4 1p (3°95) dB, and integrate by parts, we find 
; A 
Li) 
dh 
1) It is not necessary to suppose that, for all values of B, es” If is suffi- 
Pp ie 
; Mey B 8" ki 
cient if fr — dB <0 and |B aa, d3< 0. 
i. dp zg dp 
0 0 
87 
Proceedings Royal Acad. Amsterdam. Vol. XVII. 
