THE LIGHT-QUANTUM 37!ing all thermodynamic quantities he was interested in—but would not have given
him the answer he desired to derive.
However, let us leave aside for the moment what Planck did not do or what he
might have done and return to his unorthodox handling of Boltzmann's principle.
In his papers, Planck alluded to the inspiration he had received from Boltzmann's
statistical methods.* But in Boltzmann's case the question was to determine the
most probable way in which a fixed number of distinguishable gas molecules with
fixed total energy are distributed over cells in phase space. The corresponding
counting problem, discussed previously in Section 4b, has nothing to do with
Planck's counting of partitions of indistinguishable objects, the energy elements.
In fact, this new way of counting, which prefigures the Bose-Einstein counting of
a quarter century later, cannot be justified by any stretch of the classical imagi-
nation. Planck himself knew that and said so. Referring to Eq. 19.13, he wrote:
Experience will prove whether this hypothesis [my italics] is realized in nature.
[P7]**Thus the only justification for Planck's two desperate acts was that they gave him
what he wanted. His reasoning was mad, but his madness has that divine quality
that only the greatest transitional figures can bring to science. It cast Planck, con-
servative by inclination, into the role of a reluctant revolutionary. Deeply rooted
in nineteenth century thinking and prejudice, he made the first conceptual break
that has made twentieth century physics look so discontinuously different from
that of the preceding era. Although there have been other major innovations in
physics since December 1900, the world has not seen since a figure like Planck.
From 1859 to 1926, blackbody radiation remained a problem at the frontier of
theoretical physics, first in thermodynamics, then in electromagnetism, then in the
old quantum theory, and finally in quantum statistics. From the experimental
point of view, the right answer had been found by 1900. As Pringsheim put it in
a lecture given in 1903, 'Planck's equation is in such good agreement with exper-
iment that it can be considered, at least to high approximation, as the mathemat-
ical expression of Kirchhoff's function' [P8]. That statement still holds true. Sub-
sequent years saw only refinements of the early results.
The quality of the work by the experimental pioneers can best be illustrated by
the following numbers. In 1901 Planck obtained from the available data the value
h = 6.55 X 10~^27 erg-s for his constant [P9]. The modern value is 6.63 X 10~^27.
For the Boltzmann constant, he found k = 1.34 X 10~'^6 erg-K"^1 ; the present
best value is 1.38 X 10~^16. Using his value for k, he could determine Avogadro's
number N from the relation R = Nk, where R is the gas constant. Then from
Faraday's law for univalent electrolytes, F = Ne, he obtained the value e = 4.69
X 10^^10 esu [P7]. The present best value is 4.80 X 10~^10. At the time of Planck's
*In January 1905 and again in January 1906, Planck proposed Boltzmann for the Nobel prize.
**The interesting suggestion has been made that Planck may have been led to Eq. 19.13 by a math-
ematical formula in one of Boltzmann's papers [K4].