154 PROCEEDINGS OF THE AMERICAN ACADEMY. 



not opposed to any facts, but is capable of explaining many facts besides 

 those which we have already discussed. On the other hand, this assump- 

 tion seems entirely irreconcilable with one of the accepted principles of 

 the kinetic theory, but it is directly deducible from this theory if the 

 latter is modified in the way which will now be proposed. 



In the kinetic theory of gases there are two quantities of fundamental 

 importance : one is the kinetic energy of a molecule, and is represented 

 by ^mu^, where m is the mass, and u the velocity of the molecule ; the 

 other is that which has been called thermal pressure, and is proportional 

 to tnu X n, the product of mu. the momentum of the molecule and 7i, the 

 number of molecules whose centres of gravity pass in one second through 

 unit area. In the perfect gas n is proportional to u ; the kinetic energy 

 and the thermal pressure in a perfect gas are proportional to each other 

 and to mw'^. In substances, however, which deviate from the condition 

 of a perfect gas the kinetic energy will still be proportional to mu^, but 

 (mu) n will be proportional to mu^ only when n is proportional to m, 

 and this will be the case only when the molecules behave on collision 

 as perfectly elastic mathematical particles, that is, when there is no 

 correction corresponding to the quantity b of van der Waals. 



In the kinetic theory of gases the temperature is shown to be measured 

 by mu^, and in every attempt hitherto to extend this theory to less sim- 

 ple conditions of matter the fundamental assumption has been that the 

 kinetic energy of progression of the molecule is proportional to the 

 absolute temperature. I now propose to reject this assumption entirely, 

 and to substitute the assumption that the temperature is in all cases 

 measured by the quantity {run) n or by the thermal pressure ; more ex- 

 plicitly, instead of assuming that the kinetic energy of a molecule of any 

 substance is the same as if it were a perfect gas, while the quantity 

 {mu)n may vary in any way, it will now be assumed that (mu) n in any 

 substance is the same as it would be if the substance should behave as a 

 perfect gas and that at one temperature the average kinetic energy of 

 progression of the molecule may vary. 



This proposition appears less revolutionary if it is borne in mind that 

 in the only case in which the kinetic theory is entirely satisfactory, 

 namely, the perfect gas, the two assumptions become identical, and, 

 therefore, the change in no way affects the previous kinetic explanation 

 of all the phenomena of gases. The only other application of the kinetic 

 theory that has met with any degree of success, the equation of van 

 der Waals, will be discussed later in its relation to this new kinetic 

 conception. 



