261 
1907-8.] The Problem of a Spherical Gaseous Nebula. 
just over absolute zero ; that is to say, temperature and density would 
come to zero at the same height as we ideally rise through the air to the 
boundary of the atmosphere. Homer Lane’s problem gives us a corre- 
sponding law of zero density and zero temperature, at an absolutely defined 
spherical bounding surface (see § 27 below). In fact it is clear that if in 
Lane’s problem we first deal only with a region adjoining the spherical 
boundary, and having all its dimensions very small in comparison with the 
radius, we have the same problem of convective equilibrium as that which 
was dealt with in my letter to Joule. 
§ 3. According to the definition of “ convective equilibrium ” given in 
that letter, any fluid under the influence of gravity is said to be in 
convective equilibrium, if density and temperature are so distributed 
throughout the whole fluid mass that the surfaces of equal temperature 
and 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 contraction, 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 
Kankine. They may be written as follows, for the ideal case of a perfect 
gas : — 
p \ p) 
• • • a); 
• • ■ 
• • ■ (2); 
|(^ • • ■ 
• • • (3); 
where (£, p, p), (if, p, 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 
*=1-41; — j£— = *291 ; 3-44 . . . (4). 
