a Spherical Gaseous Nebula. 691 
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=St . . . (6), or p = p§t . . . (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(7—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 k ...... (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 intro- 
duced. Let p be the pressure and p the density, at any 
point P within a fluid, liquid or gaseous, homogeneous or 
heterogeneous, in equilibrium under the influence of mutual 
gravitation between its parts ; and let g be the gravitational 
attraction on a unit of mass at the position P. Let 
9P&=P (8). 
This means that H is the height to which homogeneous 
liquid, of uniform density p, ideally under the influence of 
uniform gravity equal to g, must stand in a vertical tube to 
give pressure at its foot equal to p. 
§ 8. The idea expressed by (8) is useful in connection with 
