114 
Proceedings of Royal Society of Edinburgh, [feb. 21, 
artificially all through its volume, currents not considerably dis- 
turbing the static distribution of pressure and density will bring it 
approximately to what I have called convective equilibrium * of 
temperature, that is to say, the condition in which the temperature 
in any part P is the same as that which any other part of the gas 
would acquire if enclosed in an impermeable cylinder with piston, 
and dilated or expanded to the same density as P. The natural 
stirring produced in a great free fluid mass like the Sun’s, by the 
cooling at the surface, must, I believe, maintain a somewhat close 
approximation to convective equilibrium throughout the whole mass. 
The known relations between temperature, pressure, and density for 
the ideal “ perfect gas,” when condensed or allowed to expand in a 
cylinder and piston of material impermeable to heat, are f 
( 8 ), 
( 9 ); 
where k denotes the ratio of the thermal capacity of the gas, 
pressure constant, to its thermal capacity, volume constant, which 
is approximately equal to U41 or 1*40 (we shall take it 1’4) for all 
gases, and all temperatures, densities, and pressures • and T denotes 
the temperature corresponding to unit density in the particular 
gaseous mass under consideration. 
Using (8) to eliminate p from (7) we find 
</r|_ dr J HT/c ' * 
which, if we put p l ~' = u . 
1/(*-1) = k . . . 
( 10 ), 
( 11 ), 
( 12 ), 
and / HT& 
( 13 ), 
takes the remarkably simple form 
d 2 u u K 
dx 2 ic 4 
(14). 
* See “On the Convective Equilibrium of Temperature in the Atmo- 
sphere,” Manchester Phil. Soc., vol. ii. , 3rd series, 1861 ; and vol. iii. of 
Collected Papers. 
t See my Collected Mathematical and Physical Papers, vol. i. art. xlviif. 
note 3. 
