PROFESSOR. KOPP ON THE SPECIFIC HEAT OF SOLID BODIES. 
179 
phosphorus was found to be considerably greater at higher temperatures than that of red 
phosphorus, but not at low ones (compare § 82), that the specific heat of amorphous 
cane-sugar was found to be decidedly greater than that of crystallized (§ 78), and, ac- 
cording to Regnault’s opinion, also that the specific heat of amorphous selenium between 
80° and 18° was found much greater ( = 0103) than that of the crystalline, while for 
lower temperatures there was no difference in the specific heats of the two substances 
(§ 82). 2. That in heating one modification its transition into the other is induced, 
and the heat liberated in this transition makes the numbers for the specific heat in- 
correct; in § 33 I have discussed the probability that this circumstance, in Regnault’s 
first experiments with sulphur, gave the specific heat much too high, and it is possible 
that it was also perceptible in the above-mentioned experiments with amorphous sele- 
nium. 3. That in immersing heated porous bodies in the water of the calorimeter heat 
becomes free (compare § 19) ; I consider this as the reason why Regnault found the 
specific heat of the more porous forms of carbon so much greater than that of the more 
compact (compare § 36) ; and Regnault himself sees in this the reason why he found 
the specific heat of the feebly ignited and porous oxides of nickel and of iron greater 
than that of the same oxides after stronger heating (compare § 85). 
From the importance of this subject for the considerations to be afterwards adduced, 
I have here had to discuss more fully what differences are real and what are only appa- 
rent in the numbers found for the specific heat of one and the same substance. Even if 
the apparent differences are often considerable, their importance diminishes, if allowance 
is made for the foreign influence which may have prevailed. In many cases, on the 
other hand, a body in totally different modifications has almost exactly the same 
specific heat if these foreign influences are excluded. It may, then, be said that, from 
our present knowledge, one and the same body may exhibit small differences with cer- 
tain physical circumstances (temperature, different degree of density), but never so great 
that they may be taken as an explanation why a body decidedly and undoubtedly forms 
an exception to a regularity which might have perhaps been expected for it — provided 
that the determination of the specific heat, according to which the body in question 
forms an exception, is trustworthy, and kept free from foreign influences. 
92. Among the regularities in the atomic heat of solid bodies, that found by Dulong 
and Petit for the elements stands foremost. A glance at the atomic heats of the so- 
called elements collated in § 82, shows that for by far the greater number the atomic 
heats are in fact approximately equal. But the differences in the atomic heats, even of 
those elements which are usually regarded as coming under Dulong and Petit’s law, 
are often very considerable, even when the comparison is limited to those which are 
most easily obtained in a pure state, and even if numbers are taken for the specific heats 
which give the most closely agreeing atomic heats. Regnault * sought an explanation 
of the differences of the atomic heats of the elements in the circumstance that the latter 
could not be investigated in comparable conditions of temperature and density ; further^ 
that the numbers for the specific heat, as determined for solid bodies, contain, besides 
* Annal. de Chim. et de Phys. [2] vol. lxxiii. p. 66, and [3] vol. xlvi. p. 257. 
