180 
PROFESSOR KOPP OjS t THE SPECIFIC HEAT OF SOLID BODIES. 
the true specific heat (for constant volume), also the heat of expansion. As specific 
heat we can indeed only take the sum of the heats necessary for heating and for expan- 
sion. But it is not yet proved that the products of the first, quantity (the specific heat 
for constant volume) and the atomic weights would agree better than the atomic heats 
now do ; it is only a supposition, and even the very contrary may be possible with 
individual substances. Temperature has an influence on the specific heat of solid bodies, 
and to a different extent with different bodies. Even in this respect, also, all means are 
wanting by which the different temperatures at which bodies are really comparable can 
be known, and a comparison made of their atomic heats. The utmost possible is to 
determine the specific heat at such a distance from the melting-point that latent heat of 
softening can have no influence. It is impossible to say with certainty whether the 
atomic heats of bodies compared at other temperatures than those which are nearly 
identical (ranging about 90° on each side of 10°) will show a closer agreement. It is not 
probable. Changes in the specific heat of solid bodies, so long as they are unaffected by 
heat of softening, are small in comparison with the differences which the atomic heats of 
individual elements show. And it is well worth consideration that individual elements 
(phosphorus and sulphur, e.g.) at temperatures relatively near their melting-points, 
have not materially greater specific heats than other elements (iron and platinum, 
for example) at temperatures relatively distant from their melting-points, but, on the con- 
trary, considerably smaller. As regards the influence of density on the specific heat, it is 
undoubtedly certain that the latter may somewhat vary with the former ; but it is equally 
so that, in all cases in which substances of undoubted purity were examined and the 
sources of error mentioned (§91) excluded, this variation is too inconsiderable to give an 
adequate explanation of the differences of the atomic heats found for the various solid 
elements. 
I need not here revert to the considerations developed in §§ 90 and 91, as to how far 
a difference in the physical condition of a solid substance exercises an essential influence 
on its specific heat ; for whatever view may be held in reference to this influence, and 
generally in reference to the circumstances which alter the specific heat of a substance, 
and therewith the atomic heat, this is certain, that there are individual elements whose 
atomic heat is distinctly and decidedly different from that of most other elements. 
Such elements are, from § 82, first of all boron, carbon, and silicium. 
The decision of the question whether these elements really form exceptions to Dulong 
and Petit’s law presupposes, besides a knowledge of their specific heat, a knowledge of 
their atomic weight also. There can be no exceptions to Dulorg and Petit’s law, if, 
regardless of anything which may be in opposition to it, the principle is held to, that the 
atomic weights of the elements must be so taken as to agree with this law. As a trial 
whether this law is universally applicable, the atomic weights ought rather to be taken as 
established in another manner. It may be confessed that the determination of the true 
atomic weights by chemical and physico-chemical investigations and considerations is 
still uncertain, and many questions are still unanswered the settlement of which may 
influence that determination. But there seems now to be no more trustworthy basis 
