MR, J. H. JEANS ON THE STABILITY OF A SPHERICAL NEBULA. 
13 
Thus vibrations for which y = 0, if they exist, must satisfy equations (32) to (36), 
and also equations (29) and (30), in which p is put equal to zero, and equation (28). 
The case of n = 0 will be considered later (§ 28). Excluding this for the present, 
we find that putting p = 0 in (30) leads to 
F - 0 . .. 
... (37). 
Equation (29) now reduces to 
B (1 y 4- X q- (C — BT) = 0 . . . . 
dr dr 
DO 
or, replacing — by its value XTp, 
b4,(x t ) + x|c=o .... 
. . . . (39). 
Equation (28) becomes 
Y — X (C — BT) — — y = 0 . . . 
. . . . (40), 
and the elimination of C — BT from this equation and (38) leads to the equation 
l/p V = - (A y + Bp 
dr \ dr ' 
\ 1 f/w 
p dr 
Substituting for Y from equation (27), this becomes 
4,r r|V,, A'i + P> p)r"*"-dr + 
(41). 
( 2 n + 1 )r»+! L j b „ v 
47T?- n 
"l / c 
A (p - tr,,) r n+z 
>=Ro 
nM — \ 
(2)1 +1) [J r 
§ 15. With a view to transforming this equation, let us consider the equation 
4-7T f f' t ,o 7 , T r 1 . 4c7T) ,n 
| Jr w+3 dr + K 0 1 + 
(42). 
(2 n + 1) r n+1 [ J 
(2a + 1) 
h dr + K,) = L (43). 
1 
in which J and L are any functions of r, and K 0 , K 1 are constants. If we multiply 
by r n+l , and differentiate with respect to r, we obtain, after some simplification, 
+ =|(Lr-T . 
• • (44), 
while by multiplying (43) by r " and differentiating, we obtain in a similar way 
d 
- m : 
YhA 1 Jr ” +2 dr + K 
di 
7 (Lr - ") . . . . 
(45). 
