MR, J. H. JEANS ON THE STABILITY OF A SPHERICAL NEBULA. 
5 
In general we shall denote the density by p, pressure by txt, temperature by T, 
toted potential by V, coefficient of conduction of heat by k, and the yas constant by X, 
the last of these being given by the equation 
trr = XT p .( 1 ). 
In the equilibrium configuration each of the quantities just defined is a function of 
r only. 
If c is any one of these quantities, we shall denote the 
Value of c in the equilibrium configuration, evaluated at x, y, 2 , by c 0 . 
„ „ displaced „ „ „ „ c 0 + c. 
,, ,, ,, ■>, ■>•> ■ 1 d - ■> y — t - y 1 • d~ C by ^0 d - ^ 1 • 
The quantities c 0 , c, <q are, of course, not independent. Since c 0 + c l is the same 
function of x -f- £ y y, 2 -f C, as is c 0 fi- c' of x, y, z, we have, as far as tlie first 
order of small quantities, 
c \) d~ — <0 d~ c d~ 
dc, 
c Z~0 
^ dx 
1 1 y 
+ 7J ¥ + ? 
hc 0 
dz’ 
or, since c v is a function of r only, 
clc n 
0 - c ' + u A 
§ 6. From the equation of continuity we have at once 
Pi — ~ Po A 
(3). 
Since X remains the same throughout the motion of any given element of the gas, 
J 
*i = 0..(4). 
Hence, from equation (1), 
a*u d~ ~~ *0 ( T o d- T i) (pu + Pi), 
giving as the value of vr, 
"i — *0 (T, Po -F I’upi) — \)po (d\ — AT 0 ) 
( 5 ). 
So long as we confine our attention to a single element of the gas, the coefficient of 
conduction of heat is proportional to the square root of the temperature, and is 
