7.-, THE DYNAMICAL THEORY OF OASES. 



which is inconsistent with the second law of thermodynamics. I wrote to 

 Profewor Sir W. Thomson about this result, and the difficulty I had met with, 

 but presently discovered one of my mistakes, and arrived at the conclusion 

 that the temperature would increase with the height. This does not lead to 

 mechanical 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 thermo- 

 dynamics. 



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 f = 3* . *, 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 there- 

 fore 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 me- 

 chanical energy, is 



by equation (147). 



