698 BELL SYSTEM TECHNICAL JOURNAL 



This assumption — let me remark in passing — takes a very elegant 

 form if we replace the compartments by the permitted energy-values, 

 and then the corpuscular picture by the wave picture; for then we have 

 a series of permitted wave-lengths, which are precisely those which 

 can form stationary waves in a cube of volume V. 

 So the new statistics leads to the distribution-law: 



P^^y^^^Tn^x"^- (52) 



Dividing out the factor V, we get the number of particles per unit 

 volume having energy-values between e and e + de, in an assemblage 

 having the most probable distribution at the temperature T. Multi- 

 plying this by €, we get the total energy per unit volume in the pos- 

 session of such particles. Identifying these particles with photons, 

 we observe that they have wave-lengths between chje and c/?/(e + dt), 

 frequencies between ejh and (e + de)/}2. Transforming then from 

 the variable e to the new variables X and v, we obtain distribution- 

 functions which give the density of radiant energy as functions of 

 wave-length and frequency. It turns out that these agree absolutely 

 with the observed distributions, except that they lack a factor 2. 

 This factor is at once imported, and is ascribed to the fact that light 

 is polarizable. So we arrive at the black body radiation-formula: 



p{p)di' = — ^,,^,r _ ^ (53) 



and the new statistics is justified by its success. 



It will be observed that the new statistics leads to a precise value 

 for the number of photons per unit volume, at any prescribed temper- 

 ature; whereas the old statistics led to nothing of the sort, but to a 

 formula which contained the number of atoms per unit volume as a 

 disposable constant. This corresponds to a profound physical differ- 

 ence between radiation-gas and material gases. When I state the 

 temperature and the volume of a box containing helium, I am not 

 giving data enough to fix the quantity of helium inside the box; 

 on the contrary, the quantity and the density of the helium in the 

 box can be varied ad libitum while the temperature and the volume 

 are held constant. But when I state the temperature and the volume 

 of an enclosure containing radiation, I am giving data sufiicient to 

 fix the amount of radiant energy and the number of quanta in the 

 enclosure absolutely. This is a fact of experience, and the new 

 statistics is evidently in accord with it. But if one were tempted to 



