262 
Proceedings of the Royal Society of Edinburgh. [Sess. 
For monatomic gases we have 
7 5. k-l 2. k 5 /KX 
k ~3’ k ~ 5 3 k- 1“2 * ' 
For real gases, we learn from the Kinetic Theory of Gases, and by 
observation, that h may have any value between 1 and If, but that it 
cannot have any value greater than If, 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 pressure. This, which we shall denote by S, is commonly called 
the specific volume; and its reciprocal, 1/S, we shall call the specific density 
(D) of the gas. In terms of this notation, the Boyle and Charles gaseous 
laws are expressed by either of the equations 
pv = $t . . . (6), or p = pSt (6'); 
where p, v, p, denote respectively the pressure, the volume of unit mass, and 
the density of the gas at temperature t, reckoned from absolute zero. Our 
unit of temperature throughout the present paper will be 273° C. Thus 
the Centigrade temperature corresponding to t in our notation is 273(£ — 1). 
§ 5. In virtue of § 4, what is expressed by (1), (2), (3), equivalent as 
they are to two equations, may now, for working purposes, be expressed 
much more conveniently by the single formula (6), together with the 
following equation — 
P = Ap* (7); 
where A denotes what we may call the Adiabatic Constant, which is what 
the pressure would be, in adiabatic convective equilibrium, at unit density, 
if the fluid could be gaseous at so great a density as that. 
§ 6. Looking to (6), remark that p being pressure per unit of area, the 
dimensions of pv are L -2 x L 3 or L, if we express force in terms of an 
arbitrary unit, as in § 10 below ; therefore S, though we call it specific 
volume, is a length. It is in fact, as we see by (9) below, equal to the 
height of the homogeneous atmosphere at unit temperature, in a place for 
which the heaviness of a unit mass is the force which we call unity in the 
reckoning of p. 
§ 7. In the definition of what is commonly called the “ height of the 
homogeneous atmosphere,” and denoted by H, an idea very convenient for 
our present purpose is introduced. Let p be the pressure and p the density, 
at any point P within a fluid, liquid or gaseous, homogeneous or hetero- 
