For the law of equipartition compare also the discussion at the meeting of the British Association (see 2).
In many of the papers cited so far deductions from the quantum
theory are compared with experimental facts. This is also done by:
F. Haber, Absorptionsspectra fester Körper und die Quantentheorie, Verhandlungen der Deutschen Physikalischen Gesellschaft, 13, p. 1117.
J. Franck und G. Hertz, Quantumhypothese und Ionisation, Ibid., 13, p. 967.
Attempts of giving a concrete physical idea of Planck's constant are made by:
A. Schidlof, Zur Aufklärung der universellen electrodynamischen Bedeutung der Planckschen Strahlungsconstanten , Ann. d. Phys. 35, p. 96.
D. A. Goldhammer, Ueber die Lichtquantenhypothese, Phys. Zeitschr., 13, p. 535.
J. J. Thomson, On the Structure of the Atom, Phil. Mag., 26, p. 792.
N. Bohr, On the Constitution of the Atom, Phil. Mag., 26, p. 1.
S. B. McLaren, The Magneton and Planck's Universal Constant, Phil. Mag., 26, p. 800.
The line of reasoning may be briefly stated thus: Find some quantity of the same dimension as , and then construct a model of an atom where this property plays an important part and can be made, by a simple hypothesis, to vary by finite amounts instead of continuously. The simplest of these is Bohr's, where is interpreted as angular momentum.
The logical reason for the quantum theory is found in the fact that the Rayleigh-Jeans radiation formula does not agree with experiment. Formerly Jeans attempted to reconcile theory and experiment by the assumption that the equilibrium of radiation and a black body observed and agreeing with Planck's law rather than his own, was only apparent, and that the true state of equilibrium which really corresponds to his law and the equipartition of energy among all variables, is so slowly reached that it is never actually observed. This standpoint, which was strongly objected to by authorities on the experimental side of the question (see, e.g., E. Pringsheim in 2), he has recently abandoned. H. Poincaré, in a profound mathematical investigation (H. Poincaré, Sur la Théorie des Quanta,
Journal de Physique (5), 2, p. 1, 1912) reached the conclusion that whatever the law of radiation may be, it must always, if the total radiation is assumed as finite, lead to a function presenting similar discontinuities as the one obtained from the hypothesis of quanta.
While most authorities have accepted the quantum theory for good (see J. H. Jeans and H. A. Lorentz in 2), a few still entertain
doubts as to the general validity of Poincaré's conclusion (see above C. Benedicks and R. A. Millikan 3). Others still reject the quantum theory on account of the fact that the experimental evidence in favor of Planck's law is not absolutely conclusive (see R. A. Millikan 3); among these is A. E. H. Love (2), who