January 24, 1913] 



SCIENCE 



121 



sorbed or emitted by atomic or sub-atomic 

 oscillators. Let us glance in succession at 

 these various atomistic theories and inquire, 

 first, what are the experimental facts which 

 have called these five different types of as- 

 sumption into being. 



1. The first and least concentrated form, 

 namely, that of Planck," grew out of the 

 fact that we had two radiation formulas, 

 (1) that of Rayleigh,' and (2) that of 

 Wien,® the first of which fitted the experi- 

 mental facts for long wave-lengths (for 

 which, indeed, it was alone suggested), 

 while the second fitted the experimental 

 curve at the other end of the spectrum only, 

 although it was originally hoped that it 

 would give the correct distribution of 

 energy throughout the spectrum. Wien's 

 general formula had been deduced from 

 his displacement equation — an equation 

 which rests only on thermodynamic rea- 

 soning and the proved facts of radiation 

 pressure — with the aid of two additional 

 assumptions, namely, (1) that the veloci- 

 ties of gas molecules follow the Maxwell 

 distribution law; and (2) that the fre- 

 quency of the vibrations sent out from a 

 given molecule depends only on the tem- 

 perature. Since this equation failed at 

 long wave-lengths, and yet contained no 

 more particular assumptions than those just 

 mentioned, and since the first of these as- 

 sumptions is one which we have the best of 

 grounds for making, there was nothing to 

 do but to modify the last one. Planck 

 modified it in such a way as to obtain an 

 equation that would go over into Rayleigh 's 

 equation at long wave-lengths, and into 

 Wien's at short wave-lengths. I do not 

 mean to imply that this sort of crass em- 

 piricism is all that there is behind Planck's 



' ' ' Vorlesungen iiber die Theorie des Warmes- 

 trahlung, ' ' 1906, and ' ' Acht Vorlesungen, ' ' etc., 

 1910. 



' Eayleigh, Fhil. Mag., 49, p. 539. 



'Wien, Wied. Ann., 58, p. 662, 1896. 



equation. It is fair to point out, however, 

 that this was the experimental situation 

 which guided him in his search for a new 

 radiation formula. His own argument is, 

 in brief, somewhat as follows: 



Boltzmann's identification of the con- 

 cept of entropy in thermodynamics with 

 the concept of probability in statistical me- 

 chanics, a step which Planck calls the 

 ' ' emancipation of the entropy concept from 

 the limitations of man's experimental skill, 

 and the elevation of the second law to a real 

 principle," carries with it as a necessity 

 not only the atomistic conception of mat- 

 ter, but also some sort of an atomistic con- 

 ception of radiant energy. For the as- 

 signing of an exact numerical value to the 

 probability of a given physical condition 

 can be accomplished only by considering 

 that condition as dependent on a finite 

 member of equally likely possibilities or 

 complexions. The greater the number of 

 these complexions, the greater the value of 

 the probability. For example, in the 

 throwing of two dice, there are three 

 equally likely complexions with which a 

 throw of four dots can be realized, namely, 

 a 3 with the first die and a 1 with the sec- 

 ond, a 1 with the first and a 3 with the sec- 

 ond, and a 2 with each. On the other hand, 

 a throw of 2 dots can be realized through 

 but one complexion, namely, a one with 

 each. The probability, then, of a four-dot 

 throw is just 3 times that of a two-dot 

 throw. Now when the entropy of a phys- 

 ical condition is made to depend in this 

 way on the probability of its occurrence, 

 we see at once that entropy tends toward a 

 maximum simply because a change to a new 

 state will not take place unless that new 

 state has a greater probability than the 

 old one. But, says Planck, there is no way 

 of making the appearance of a given phys- 

 ical condition in a system depend in this 

 way upon a definite, countable number of 



