the gaseous volume to be thus limited. This mechanical work is not performed when the expansion is prevented ; therefore less heat is absorbed by the gas during the elevation of its temperature. It has even been calculated, from the mechanical theory of heat, what the relation should be between the capacity of gases under constant pressure and the capacity under constant volume. According to Clausius, this theoretical relation is 1.67. Now, it appears that for elementary gases, such as hydrogen, oxygen, nitrogen, &c., this relation is smaller than that indicated by the theory (about 1·4). The explanation of this is, that these gases, which are diatomic, absorb a certain quantity of heat when they are heated under constant volume, not for the performance of external work, as there is no expansion, but to perform certain work in the molecule itself, which is formed of two atoms.

Now, Kundt and Warburg have shown that this internal work is not performed in the case of mercury vapour,' and that the relation between the specific heats of mercury vapour under constant pressure and under constant volume is the same as that indicated by theory. It is obvious that in this case there is no internal

Kundt and Warburg have calculated the relation of the two specific heats from the velocity of the propagation of sound in mercury vapour. The calculation was made from the length of a soundIn determining the length of a given sound-wave in the air and in mercury vapour, they found that the relation of the two specific heats of mercury vapour was

wave.

C

=e

= 1.67.

(Berichte der Deutschen

Chem. Gesellsch. zu Berlin, 1875, t. viii. p. 945. Pogg., Ann., t. clvii.

p. 353.)

work, because the molecule is only composed of a single

atom.

If similar experiments were undertaken for the vapours of sulphur, phosphorus, and arsenic, the result would doubtless be very different. Here the internal work should be considerable, and the relation between the specific heats under constant pressure and under constant volume would be still smaller than for the diatomic gases.

The distinction which it has been necessary to establish between the molecular constitution of the different elementary bodies in the gaseous state has now been explained, and the significance and value of the results given on p. 70 made intelligible.

VI.

The New System of Atomic Weights is in Harmony with the Law of Dulong and Petit.

There is not a single exception to the law of Dulong and Petit, as a glance at the following table will show. The second column of this table gives the specific heats of the elementary solid bodies mentioned in the first. The third column gives the atomic weights; the fourth, the product of the atomic weights multiplied by the specific heats. These products may be termed atomic heats, for they represent the quantities of heat absorbed by the atoms when their temperature is raised one degree. We see that these atomic heats are appreciably constant. This constitutes the great physical law discovered by Dulong and Petit.

The mean of the atomic heats of solid elementary bodies is 64, and the extreme limits within which these atomic heats vary are comprised within the numbers 5.5 and 6.9. The elements whose atomic heats are a little too low are certain metalloids of small atomic weight, such as boron, silicon, carbon, phosphorus, arsenic, sulphur, and selenium, to which must be added aluminium. Those whose atomic beat exceeds the average are certain metals, amongst which must be mentioned lithium, sodium, potassium, thallium, calcium, manganese, molybdenum, &c., to which we must. add iodine and bromine. But is it not a fact of some importance that while the atomic weights vary in the proportion of 1 to 30, and the specific heats in the proportion of 1 to 7, the products of these two quantities—that is to say, the atomic heats-only vary in the proportion of 1 to 1.2?

1

The variations of atomic heats may be attributed to various causes. In the first place, to errors of observation connected with the determination of atomic weights, and also with that of specific heats. Some of these determinations relate to bodies which have not yet been obtained in a state of perfect purity. On the other hand, as Regnault observes, the determination-and, we may add, the notion-of specific heats includes some uncertainties, for it includes several elements which we have not as yet been able to eliminate, especially the latent heat of dilatation, and a portion of the latent heat of fusion, which is gradually absorbed by bodies, as they frequently soften long before the tempera

Annales de Chimie et de Physique, 3a série, t. xxvi. p. 262, 1849.

All

ture which is regarded as their melting point is reached. Thus the heat applied to a solid body not only serves to raise its temperature-that is to say, to augment the vibratory energy of its molecules-but a portion, perhaps a considerable portion, of this heat is employed in performing the work of expansion, which work prepares the way for a change of state by diminishing the force of cohesion, by affecting the disaggregation of molecules, or by determining modifications of texture. these changes give rise to thermal phenomena, which are in some manner superposed, and the sum of which constitutes what is called specific heat. It is impossible to distinguish the part played by each of these elements in the phenomenon; but it is surely remarkable that, in spite of the complexity of the phenomena, so simple and so great a law should be evolved from them when formulated in the terms employed by Dulong and Petit. Doubtless it is not rigorously exact, but the different elements of which specific heat is composed obviously cannot act exactly in the same manner, either in different elements or in the same element at different temperatures; and yet these several influences enable us to estimate the variations to which specific heat is subject, and consequently the atomic heat of certain bodies according to the temperature. It is probable that for every element there are limits of temperature within which the specific heat is almost constant; experiment at least has proved it to be so in the case of certain metals, such as iron, copper, zinc, silver, antimony, mercury, platinum, lead, and bismuth, and it is to be noticed that the atomic heats of these metals approach