48 
ME. J. H. JEANS ON THE STABILITY OF A SPHEEICAL NEBULA. 
Over the part of the nebula which is in adiabatic equilibrium, the relation between 
density and pressure is 
~ = cp y , 
where c is a constant, so that the equations of equilibrium become 
7 _o dp dV 
C VP lx = * ’ &c -’ 
and are therefore equivalent to the single equation 
r' = v - v 0 , 
7-1 
where V 0 is the potential of the outer boundary of the nebula. This takes the form 
\r \t _ cr /Po / \ -i i / i \ Fi p i (y ~~ i)( r y — -) (p\ p r i 
+ (y - 1) Pj P. + ■ ■ 
Pij 
or, 
- v » + + ■ ■ ■ = { 1 + ( 7 ~T~ - (£ 
It is obvious that equation (124) again gives the general form of solution, and that, 
as far as cr, the equations are (cf equations 121, 123) 
e « - v 0 = JZl .( 131 ), 
<h = cypj-' (^) (132), 
* = \2 + i - J [fj] .(133), 
_ cy (y - 2) ! [a\ Y , 0 . 
~ 6 .( lo4 ^- 
Writing k for ey/V _ \ we see that equations (132) and (133) may be written 
o-i = 
Po$i 
Pu^i | 1 /.) \ 
^2 — „ + f (2 — y) 
O 
(135). 
(133). 
