264 
Proceedings of the Royal Society of Edinburgh. [Sess. 
speak of 73 pounds per square inch (which might be 73 pounds of lead, or 
of iron, or of stone) we mean a force. If we call the pressure on the boiler 
of a ship 73 pounds per square inch, we mean a somewhat greater pressure 
when the ship is in middle or northern latitudes than when she is on the 
equator ; though the difference is, for pressures on safety-valves, practically 
negligible, being for example three-tenths per cent, between the equator 
and the latitude of Glasgow or Edinburgh. 
§ 12. In the present paper we shall take as our 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 our 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° Centigrade 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 
13414 
Argon 
5767 
„ 
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 
yy 
§ 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). 
* If instead of taking 10 9 tons as our unit of mass we take a gram, the numbers in this 
table must each be multiplied by 10 5 , and they will then be the values of S in centimetres 
instead of in kilometres. 
