392 THE QUANTUM THEORYcurious exceptions [C, B, Si] to the Dulong-Petit law which were until now a
cause for despair have been eliminated: the Dulong-Petit law for the specific heats
of solid elements has become an unexceptional rigorous law' [W2]. This is, of
course, not quite true, but it was distinct progress. The experimental points on
page 390 are Weber's points of 1875.*
In 1872, not only Weber, but also a second physicist, made the conjecture that
the Dulong-Petit value c ~ 6 would be reached by carbon at high temperatures:
James Dewar. His road to the carbon problem was altogether different: for rea-
sons having to do with solar temperatures, Dewar became interested in the boiling
point of carbon. This led him to high-temperature experiments, from which he
concluded [Dl] that the mean specific heat of carbon between 0° and 2000°C
equals about 5 and that 'the true specific heat [per gram] at 2000°C must be at
least 0.5, so that at this temperature carbon would agree with the law of Dulong
and Petit.'**
Dewar's most important contribution to our subject deals with very low tem-
peratures. He had liquefied hydrogen in 1898. In 1905 he reported on the first
specific heat measurements in the newly opened temperature region. It will come
as no surprise that diamond was among the first substances he chose to study. For
this case, he found the very low average value c ~ 0.05 in the interval from 20
to 85 K. 'An almost endless field of research in the determination of specific heats
is now opened,' Dewar remarked in this paper [D2]. His work is included in a
detailed compilation by Alfred Wigand [W3] of the literature on the specific heats
of solid elements that appeared in the same issue of the Annalen der Physik as
Einstein's first paper on the quantum theory of specific heats. We are therefore
up to date in regard to the experimental developments preceding Einstein's work.
The theoretical interpretation of the Dulong-Petit rule is due to Boltzmann. In
1866 he grappled unsuccessfully with this problem [B2]. It took another ten years
before he recognized that this rule can be understood with the help of the equi-
partition theorem of classical statistical mechanics. The simplest version of that
theorem had been known since 1860: the average kinetic energy equals £772 for
each degree of freedom.! In 1871 Boltzmann showed that the average kinetic
energy equals the average potential energy for a system of particles each one of
which oscillates under the influence of external harmonic forces [B4]. In 1876 he
applied these results to a three-dimensional lattice [B5]. This gave him an average
energy 3RT ^ 6 cal/mol. Hence cv, the specific heat at constant volume, equals
* By the end of the nineteenth century, it was clear that the decrease in c with temperature occurs
far more generally than just for C, B, and Si [Bl].
** There followed a controversy about priorities between Weber and Dewar, but only a very mild
one by nineteenth century standards. In any event, there is no question that the issues were settled
only by Weber's detailed measurements in 1875.
fThis result (phrased somewhat differently) is due to John James Waterston and Maxwell [Ml].
For the curious story of Waterston's contribution, see [B3].