January 18, 1918] 



SCIENCE 



61 



Planck endeavored to find a mathematical 

 compromise which should reduce to Wien's 

 formula when XT was small and to that of 

 Rayleigh when XT was great. In this way" 

 he was led to the celebrated formula which 

 has proved to be of such unexpected im- 

 portance in the development of theoretical 

 physics. In its original publication, how- 

 ever, the formula was otherwise deduced." 

 Planck had previouslj' calculated the en- 

 tropy of a system of linear resonators and 

 believed that he had proved "Wien's formula 

 to be a necessary consequence of the sec- 

 ond law." To obtain the new formula (by 

 a process similar to that of Boltzmann in 

 the kinetic theory of gases), he found it 

 necessary to assume that energy was ab- 

 sorbed and radiated discontinuously. To 

 satisfy Wien's displacement law these dis- 

 crete energy quanta must be proportional 

 to the frequency of the radiation, and thus 

 the constant, h, came into existence. 



The process was not very convincing and 

 I suppose that, if nothing else had come of 

 it, Planck's result would have been re- 

 garded as an empirical formula for which a 

 satisfactory theoretical basis was lacking. 

 But there were other puzzles which were, 

 at nearly the same time, troubling the 

 minds of physicists. One was the curious 

 relation between X-rays of a certain hard- 

 ness and the speed of the secondary elec- 

 trons which they caused to be emitted from 

 a metal. "We all remember how Bragg was 

 led by these difficulties to support a cor- 

 puscular theory of X-rays. The same diffi- 

 culties existed in the case of photo-elec- 

 trons and the ultra-violet light which liber- 

 ated them. Einstein also proposed a 

 quasi-corpuscular theory in which, how- 

 ever, instead of actual corpuscles, he sub- 

 stituted light-quanta whose energy was 



" Planck, " Warmestrahlung, " Ite Aufl., p. 219. 



li Planck, Ann. d. Phys., 4, p. 553 (1901). 



IS Jnn. d. Phys., 1, p. 118 (1900). 



equal to Planck's hv. It was not difficult to 

 show, as Lorentz did, that Einstein's 

 quanta were quite irreconcilable with the 

 phenomena of diffraction ; but the fact re- 

 mains that the quantitative predictions of 

 his theorj' have been verified in the ease of 

 both X-raj-s and light, in the latter in- 

 stance with great accuracy by Professor 

 Millikan and his pupils. 



Time permits only the barest mention of 

 Debye's daring application of Planck's 

 formula to the elastic vibrations of solid 

 bodies, his calculations of their specific 

 heats upon this basis, and the remarkable 

 agreement of the calculated values with 

 the experimental results of Nernst and his 

 collaborators. I must be equally brief in 

 referring to Bohr's theory of line spectra 

 in which the form of the Balmer progres- 

 sion is undoubtedly introduced in the as- 

 sumptions; but the numerical value of 

 Rydberg's constant is accurately calculated 

 from the mass and charge of the electron and 

 the inevitable h. In all these applications 

 the same characteristics are observable : the 

 fundamental ideas are not clear and pre- 

 cise, except arithmetically; if we try to 

 make them so, we encounter apparently in- 

 superable contradictions with some of the 

 most firmly established experimental facts; 

 the deductions from the premises do not 

 follow inevitably, but must be helped out 

 by special hypotheses in each different ap- 

 plication ; but numerical relations of sur- 

 prising exactness are obtained, and an ac- 

 count is given of whole classes of phenom- 

 ena which seem to be quite beyond the 

 scope of the "classical" methods of twenty 

 yeai'S ago. "We do not know whether 

 Planck's constant is an atom of Hamilton- 

 ian action, or of angular momentum, or of 

 something quite different from either; but 

 we can not doubt that it is a physical con- 

 stant comparable in importance with the 



