690 Lor J Kelvin : The Problem of 
equal pressure, remain unchanged when currents are produced 
in it by any disturbing influence so gentle that changes of 
pressure due to inertia of the motions are negligible. The 
essence of convective equilibrium is that if a small spherical 
or cubic portion of the fluid in any position P is ideally 
enclosed in a sheath impermeable to heat, and expanded or 
contracted to the density of the fluid at any other place P', 
its temperature will be altered, by the expansion or con- 
traction, from the temperature which it had at P, to the 
actual temperature of the fluid at P ; . The formulas to 
express this condition were first given by Poisson. They 
are now generally known as the equations of adiabatic 
expansion or contraction, so named by Rankine. They may 
be written as follows, for the ideal case of a perfect gas : — 
K')* ^ 
HVr (2); 
£-©* (3); 
where (t, p,p), (t\ p f ,p') denote the temperatures, densities,- 
and pressures, at any two places in the fluid (temperatures 
being reckoned from absolute zero) ; and k denotes the ratio 
of the thermal capacity of the gas when kept at constant 
pressure to its thermal capacity at constant volume, which, 
according to a common usage, is for brevity called "the 
ratio of specific heats." For dry air, at any temperature, 
and at any density within the range of its approximate 
fulfilment of the gaseous laws, we have 
A =1-41; ^=-291; ^ = 3-44 . . (4). 
For monatomic gases we have 
5 jfe-l_2 k _5 ... 
For real gases, we learn from the Kinetic Theory of Gases, 
and by observation, that k may have any value between 
1 and If, but that it cannot have any value greater than 1§, 
or less than 1. 
§ 4. To specify fully the quality of any gas, so far as 
concerns our present purpose, we. need, besides k, the ratio 
of its specific heats, just one other numerical datum, the 
volume of a unit mass of it at unit temperature and unit 
