ME. CLEEK MAXWELL ON THE DYNAMICAL THEOEY OE GASES. 
87 
nical instability, or to any self-acting currents of air, and I was in some degree satisfied 
with it. But it is equally inconsistent with the second law of thermodynamics. In fact, 
if the temperature of any substance, when in thermic equilibrium, is a function of the 
height, that of any other substance must be the same function of the height. For if not, 
let equal columns of the two substances be enclosed in cylinders impermeable to heat, 
and put in thermal communication at the bottom. If, when in thermal equilibrium, the 
tops of the two columns are at different temperatures, an engine might be worked by 
taking heat from the hotter and giving it up to the cooler, and the refuse heat would 
circulate round the system till it was all converted into mechanical energy, which is in 
contradiction to the second law of thermodynamics. 
The result as now given is, that temperature in gases, when in thermal equili- 
brium, is independent of height, and it follows from what has been said that tempera- 
ture is independent of height in all other substances. 
If we accept this law of temperature as the actual one, and examine our assumptions, 
we shall find that unless § 4 =3| 2 .£ 2 , we should have obtained a different result. Now 
this equation is derived from the law of distribution of velocities to which we were led 
by independent considerations. We may therefore regard this law of temperature, if 
true, as in some measure a confirmation of the law of distribution of velocities.] 
Coefficient of Conductivity . 
If C is the coefficient of conductivity of the gas for heat, then the quantity of heat 
which passes through unit of area in unit of time measured as mechanical energy, is 
dee 6 A t A 2 ft) dx 
(148) 
by equation (147). 
Substituting for (3 its value in terms of y by equation (115), and for its value in 
terms of (x by equation (125), and calling _p 0 , g 0 , and 0 O the simultaneous pressure, density, 
and temperature of the standard gas, and s the specific gravity of the gas in question, 
we find 
C — ; 
149) 
_5 Pc l 
3(7-1) £(A) s 
For air we have 7=1-409, and at the temperature of melting ice, or 274 0, 6 C. 
above absolute zero, 91 8-6 feet per second, and at 16 0, 6 C., ^=0-0936 in foot- 
grain-second measure. Hence for air at 16 0, 6 C the conductivity for heat is 
C=1172 (150) 
That is to say, a horizontal stratum of air one foot thick, of which the upper surface is 
kept at 17° C., and the lower at 16° C., would in one second transmit through every 
square foot of horizontal surface a quantity of heat the mechanical energy of which is 
equal to that of 2344 grains moving at the rate of one foot per second. 
