694 BELL SYSTEM TECHNICAL JOURNAL 



It looks as if (39) might be the Hmiting form of (40) — as if the 

 actual distribution-law might be obtained by avoiding the approxi- 

 mations whereby we came to the formula (39), as Planck's law of 

 distribution for oscillators was obtained by refraining from approxi- 

 mation. Such however is not the case. True, the second factor in 

 (39) is evidently the limiting form, for very high temperatures, of 

 the second factor in (40). But the first factor in (40) contains nothing 

 but the volume of the gas and some universal constants, while the 

 first factor in (39) contains the temperature and an apparently dis- 

 posable constant standing for the number of particles in the assemblage. 

 The former is not the limit of the latter. It will be noted also that 

 although I said that the volume of the elements of phase-space was 

 to be set equal to /r\ this assumption in no wise enters into the function 

 (39). Bose in fact found it necessary to upset the basis of the classical 

 statistics, in order to arrive at (40) instead of (39). 



The Bose Statistics 



The momentum-space of the photons is to be divided as heretofore 

 into equal compartments, and various distributions of the particles 

 among these are to be compared, in order that we may elect one of 

 them as "the most probable" and make a picture of the entropy of 

 the assemblage. But the manner of defining a distribution, the 

 manner of "counting the ways" in which it may be realized and 

 computing its "probability," is to be changed, and changed in a 

 most thoroughgoing and fundamental way. 



Start with any distribution of the particles, defined as heretofore: 

 defined that is, by saying that there are Nq of the particles in the 

 compartment 0, Ni in the compartment 1, and in general Ni in the 

 compartment /. 



Count the number of compartments containing no particle; call it 

 Zo. Count the number of compartments containing one particle 

 apiece; call it Zi. In general, let Z,; stand for the number of compart- 

 ments containing i particles apiece. Put down the values of all the 

 numbers Zi. 



Now change the terminology. Elect some neutral word, "arrange- 

 ment" say, to denote what we have heretofore denoted as a "distri- 

 bution," and use the latter word in the following new sense: a distri- 

 bution shall henceforth be described by stating the values of the 

 numbers Zo, Zi, Z2, • • • , Zi, • • • and the total energy of the assemblage.** 



* It is of course confusing thus to change the meanings of words, but in the long 

 run less confusing (I think) than to use some other word than distribution for the 

 concept always called by that name in the new statistics. 



