216 Mr. J. C. Maxwell on the Dynamical Theory of Gases. 



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 equilibrium, is independent of height, and it follows 

 from what has been said that temperature 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 J 4 =3f 2 • f 2 , 

 we should have obtained a different result. Now this equation 

 is derived from the law cf 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 



^ dx~Qk x K 2 pW dx K } 



by equation (147). 



Substituting for j3 its value in terms of 7 by equation (115), 

 and for k ± its value in terms of \x by equation (125), and calling 

 p Q , p , and O the simultaneous pressure, density, and tempera- 

 ture of the standard gas, and s the specific gravity of the gas in 

 question, we find 



0==* Al* (149) 



For air we have 7= 1*409, and, at the temperature of melting ice, 



or 274°'6C. above absolute zero, a/£ = 918-6 feet per second, 



and at 16° # 6 C, ^ = 0*0936 in foot-grain-second measure. Hence 

 for air at 16°*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 



