a Spherical Gaseous Nebula. 
693 
§ 12. In the present paper we shall take as unit of mass 
the mass of a cubic kilometre of water at standard density 
(which is 10 9 metric tons) ; and we shall take its heaviness 
in mid-latitudes as unit of force. This means taking for g 
in (8) and (9), and in all future formulas, the ratio of gravity 
at the place under consideration to terrestrial gravity in 
mid-latitudes. Hence (remembering that in § 4 we have 
chosen for our unit temperature reckoned from absolute zero 
the temperature of melting ice, being equal to 273° Centi- 
grade above absolute zero) we see by (8) that S is simply 
the height in kilometres of the Homogeneous Atmosphere 
in mid-latitudes, at the freezing temperature. Thus, from 
known measurements of densities, we have the following- 
table * of values of S for several different gases : — 
Gas. S. 
Air 7*988 kilometres. 
Ammonia 13*414 
Argon 5*767 
Carbon dioxide . . . 5*232 
Carbon monoxide . . . 8*370 
Chlorine 3*297 
Helium 58-354 
Hydrogen 114*76 
Nitrogen 8*256 
Oxygen 7*233 
Sulphur dioxide . . . 3*709 
§ 13. Consider now convective equilibrium in any part 
of a wholly gaseous globe, or in any part of a fluid globe 
so near the boundary as to have density small enough to let 
it fulfil the gaseous laws. Let z be depth measured inwards 
from any convenient point of reference. The differential 
equation of fluid equilibrium is 
dp=gpdz (10). 
Now, if the equilibrium is convective, we have by (3) 
*~ l dt .... (11). 
' 
Using this, and (2), in (10), and dividing both member; 
find 
dt 
(12). 
by (-pV*- 1 , we 
dz k p' 
* If instead of taking- 10 9 tons as our unit of mass we take a gram, 
the numbers in this table must each ba multiplied by 10% and they will 
then be the values of S in centimetres instead of in kilometres. 
Phil. Mag. S. 6. Vol. 15. No. 90. June 1908. 3 A 
