1887.] Sir W. Thomson on the Equilibrium of Gas. 
113 
pressure, p the density, and t the temperature from absolute zero, 
we have, by Boyle and Charles’s laws, 
p = Hpt ( 4 ); 
where t denotes absolute (thermodynamic*) temperature, with 0° 
C. taken as unit ; and H denotes what is commonly, in technical 
language, called “ the height of the homogeneous atmosphere ” at 
0° C. For dry common air, according to Regnault’s determination 
of density, 
H = 7 ‘985 kilometres (4'). 
Let /3 be the gravitational coefficient proper to the units chosen ; 
so that fimm /D 2 is the force between m, m' at distance D. The 
earth’s mean density being 5 ’6, and radius 6370 kilometres, we 
have 
g-. 6370. 5*6/2 = 1; and therefore 4 tt/?= 1/11890 .... (5). 
Let now they), p, t of (4) be the pressure, density, and tempera- 
ture at distance r from the centre of a spherical shell containing gas 
in gross-dynamic f equilibrium. We have, by elementary hydro- 
statics 
whence 
dr 
• • ( 6 )> 
• • ( 7 ), 
where M denotes the whole quantity of matter within raidius a from 
the centre ; which may be a nucleus and gas, or may be all gas. 
If the gas is enclosed in a rigid spherical shell, impermeable to 
heat, and left to itself for a sufficiently long time, it settles into the 
condition of gross-thermal equilibrium, by “ conduction of heat,” till 
the temperature becomes uniform throughout. But if it were stirred 
* The notation of the text is related to temperature Centigrade on the 
thermodynamic principle (which is approximately temperature Centigrade by 
the air-thermometer), as follows : — 
1 
273 
(temperature Centigrade + 273) ; 
see my Collected Mathematical and Physical Papers, vol. i. arts, xxxix. and 
xlviii. part vi. §§ 99, 100; and article “Heat,” §§ 35-38 and 47-67, Encyc. 
Brit., and vol. iii. (soon to be published) of Collected Papers. 
t Not in molecular equilibrium of course ; and not in gross-thermal equi- 
librium, except in the case of t uniform throughout the gas. 
VOL. XIV. 16/9/87 
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