EINSTEIN AND SPECIFIC HEATS 391It became clear rather soon, however, that even for solid elements the Dulong-
Petit rule is not as general as its propounders had thought. Amedeo Avogadro was
one of the first to remark on deviations in the case of carbon, but his measurements
were not very precise [Al]. Matters got more serious in 1840, when two Swiss
physicists, Auguste de la Rive and Francois Marcet, reported on studies of carbon.
In particular, they had obtained 'not without difficulty and expense' an amount
of diamond powder sufficient to experiment with, for which they found c ~ 1.4
[Rl]. At almost the same time, diamond was also being studied by Henri Victor
Regnault, who more than any other physicist contributed to the experimental
investigations of specific heats in the nineteenth century. His value: c = 1.8 [R2].
Regnault's conclusion about carbon was unequivocal: it is 'a complete exception
among the simple bodies: it does not satisfy the general law which [relates] specific
heats and atomic weights.' During the next twenty years, he continued his studies
of specific heats and found many more deviations from the general law, though
none as large as for diamond.
We now move to the 1870s, when Heinrich Friedrich Weber,** then in Berlin,
made the next advance. He began by re-analyzing the data of de la Rive and
Marcet and those of Regnault and came to the correct conclusion that the different
values for the specific heat of diamond found by these authors were not due to
systematic errors. However, the de la Rive-Marcet value referred to a tempera-
ture average from 3° to 14°C whereas Regnault's value was an average from 8°
to 98°C. Weber noted that both experiments could be correct if the specific heat
of carbon were to vary with temperature [Wl]! Tiny variations in specific heats
with temperature had long been known for some substances (for example, water)
[Nl]. In contrast, Weber raised the issue of a very strong temperature depen-
dence—a new and bold idea. His measurements for twelve different temperatures
between 0° and 200° C confirmed his conjecture: for diamond c varied by a factor
of 3 over this range. He wanted to continue his observations, but it was March
and, alas, there was no more snow for his ice calorimeter. He announced that he
would go on with his measurements 'as soon as meteorological circumstances per-
mit.' The next time we hear from Weber is in 1875, when he presented his beau-
tiful specific heat measurements for boron, silicon, graphite, and diamond, from
-100° to 1000°C [W2]. For the case of diamond, c varied by a factor of 15
between these limits.
By 1872, Weber had already made a conjecture which he confirmed in 1875:
at high T one gets close to the Dulong-Petit value. In Weber's words, 'The three
*In 1833 Avogadro obtained c =* 3 for carbon at room temperature. This value is too high. Since
it was accidentally just half the Dulong-Petit value, Avogadro incorrectly conjectured 'that one must
reduce the atom [i.e., the atomic weight] of sulfur and metals in general by [a factor of] one half
[Al].
**Weber was Einstein's teacher, whom we encountered in Chapter 3. Einstein's notebooks of
Weber's lectures are preserved. They do not indicate that as a student Einstein knew of Weber's
results.