ME. J. H. JEANS ON THE STABILITY OF A SPHERICAL NEBULA. 
11 
dV 
dr 
p dr 
— ^ (C - BT) 
p dr v 7 
»(” + i) F 
(29). 
ipp(MpB+C,C) = ~ + 
k j d 
r* [ dr 
o dC' 
V ~ dr 
— n (n + 1) C 
d 
+ K 7r 
'_C\ JT 
2T/rfr 
k^TJ 1 
rfr j r dr \ dr ) 
4 dA _ n(n + 1) - 2 
r dr “ /' 2 
The boundary-equations found in § 9 reduce to the following:— 
(i) [C - BT], =I?1 = 0. 
= 0.(33), 
-'■=«o 
(iii) Equations similar to (33) at r — Pi^.(34), 
(iv) (A) r=Ro = 0, when n is different from unity, or a more complex equation in the 
case of n = 1.(35). 
(ii) C, =no = 0 or 
clC 
dr 
§ 12. From the manner in which the analysis has been conducted, it will be clear 
that every principal vibration must either be one of the class just investigated, or 
else a vibration such that u, A, and T vanish everywhere. 
For the latter class of vibration there are no forces of restitution. Thus the 
frequency of vibration is zero, and the motion consists of the flow of the gas in closed 
circuits, this flow being entirely tangential, and the gas behaving like an incom¬ 
pressible fluid. Obviously these steady currents are of no importance in connection 
with the question of stability or instability. 
Discussion of the Frequency Equation. 
§ 13. Returning to the class of vibrations in which u, A, and T do not all vanish, 
we have seen that the frequency equation is found by the elimination of F, A, B, and 
C from equations (28) to (35). Now q> on ly enters into three of these equations : 
namely (31), in which it enters through the factor ip, and (29) and (30), in which it 
enters through the factor — p~ or (ip) 2 . Regarding ip, A, B, C, and F as unknowns, 
it will be seen that the coefficients which occur in equations (28) to (35) are all real. 
The four volume equations enable us to determine A, B, C, and F except for certain 
