MEMORIAL TO CLASSICAL STATISTICS 123 



energy and the entropy. This makes five altogether, and any two of the 

 five suffice to determine the state, — THE STATE, the uniform state, the 

 only one about which thermodynamics really knows or cares. When asked 

 about what I earlier called "a surging state", thermodynamics mutters 

 something to the effect that the entropy of such a state is smaller than that 

 of THE STATE, and then puts an end to the conversation by refusing to 

 commit itself further. Thermodynamics takes no cognizance of the molecu- 

 lar structure of matter. A gas might be a continuum, for all that it knows 

 or cares. 



Statistical mechanics talks about a mental image of the gas, in the form of 

 a flock of dots in the coordinate-space and another flock of dots in the mo- 

 mentum-space, or one may call them a single flock of dots in the /x-space. In 

 Boltzmann statistics, the "state" of this image is what I have been calhng 

 the "distribution". The most probable state of the image — to wit, the one 

 with the greatest number of inventories or complexions — is identified with 

 THE STATE of thermodynamics. All of the rest belong to the category of 

 which thermodynamics would say, that the entropy is smaller than it is for 

 THE STATE. But since according to S.M. they belong to a category for 

 which the probability is smaller than it is for THE STATE, one sees a con- 

 nection between entropy of the gas and probability of the image beginning 

 to take shape. 



Now it is time to make a formal introduction of the concepts of entropy 

 and temperature — the latter word having already sneaked into this article 

 two or three times in spite of all my efforts to keep it out. 



Formal Entrance of Entropy and Temperature 



For a substance, meaning now a gas, of a single kind, entropy and tempera- 

 ture are defined by the equation, 



dU = TdS - PdV (14) 



P stands for pressure, V for volume, and 5 for entropy. For energy I use 

 the symbol U already employed in that sense — but notice that formerly it 

 stood for the kinetic energy of the molecules! To use the same symbol in 

 both senses implies that the energy of the gas is entirely the kinetic energy 

 (of translatory motion) of the molecules. This identification turns out to be 

 valid for the "monatomic" gases, which are luckily numerous and well- 

 studied. To these we confine ourselves throughout this article. T stands 

 for the temperature called absolute; this being the only kind of temperature 

 which will ever figure in this article, the adjective henceforth is discarded. 

 Density was the fifth variable in my list given above, but volume is usually 

 preferred to it. To make them equally useful, the quantity of gas must be 

 stated; here it will be taken as one gramme-molecule. 



