constant volume. Hence the ratios for other gases could easily be calculated from the known value of the ratio for any one gas if their specific heats at constant volume were known.

But the specific heat at constant volume is with much greater difficulty accessible to observation and measurement than the specific heat at constant pressure. On this ground no direct determinations of the former have been made.' But their values may be calculated from the measured values of the latter by means of the law just given, which is expressed by the last formula. Since this formula and law are strictly exact only for perfect gases, the calculation can indeed be admitted without hesitation only for such gases as have no cohesion and strictly obey Boyle's law. For other gases and vapours this calculation can only supply numbers which, at most, can claim to be approximately correct estimations.

Still more doubtful becomes the interpretation of this theoretical calculation if it is necessary to employ values of the density which are not actually observed but are theoretically deduced on the assumption of Boyle's and GayLussac's laws or of Avogadro's law.

Finally, as a further cause that makes the values so calculated uncertain, must be added the circumstance observed by Regnault, E. Wiedemann,3 Winkelmann,1 and Wüllner,5 that the specific heat of many gases and vapours is variable in a high degree with the temperature. This is especially the case, according to an observation made by F. Weber, with those compounds which contain carbon.

1

With these reservations the values of the specific heat

[Dr. Joly's direct determinations by means of his steam-calorimeter must not be ignored. See Phil. Trans. clxxxii. 1891, p. 73; clxxxv. 1894, pp. 943, 961.-TR.]

2 Mém. de l'Acad. de Paris, xxvi.

3 Habilitationsschrift, Leipzig 1875; Pogg. Ann. clvii. 1876, p. 1.

Pogg. Ann. clix. 1876, p. 177.

Wied. Ann. iv. 1878, p. 321.

Hohenheimer Programm, Stuttgart 1874, p. 82; Pogg. Ann. cliv. 1875,

p. 580.

y, which I have borrowed from a table calculated by Clausius' from Regnault's observations and displayed in the annexed table, are to be taken; and the values of the ratios in the last three columns, which I have deduced from them, must be similarly judged.

In addition to the values of the ratio of the kinetic energy K of the molecules to the whole heat-energy H, this table also contains, like the former one, the values of the ratios of the mean energy & of all the n atoms of a molecule and of the mean value e for a single atom to the energy

Ann. Chem. Pharm. cxviii. 1861, p. 106; Abhandl. ü. Wärmetheorie, 1. Abth. 1864, p. 296; 2nd ed. 1876, p. 62; 3rd ed. 1887, p. 62.

K

of translatory motion E of the molecule. The values of this last ratio, which are placed in the last column, are in nearly all cases less than 1, and, indeed, are in general less than . The number of exceptions, including perhaps ethyl ether1 and possibly seven chlorine compounds, is so small that we shall be inclined to consider the rule, that in gases with polyatomic molecules the mean energy of an atom is smaller than the translatory energy of a molecule, to be a veritable law of nature, which, like Boyle's and the other laws of gases, admits exceptions under certain circumstances.

The possible grounds for such exceptions will appear from the following considerations.

57. Dissociation and Disgregation

By our theory and by experiment, so far as the theory has up to the present been confirmed by observation, the molecular energy E consists only in that of the linear toand-fro motion of the molecules, that is, in kinetic energy, or, in the older nomenclature, in vis viva. We may not, however, assert this of the energy & of the atoms nor of the mean energy of a single atom. For the atoms do not move freely like the molecules, which in the gaseous state exert no cohesion towards each other, but they are bound to each other by chemical affinity, and are, consequently, constrained to a certain extent in their motion. The energy of the atoms, therefore, does not consist, as that of the molecules, entirely in kinetic energy, but also in the potential energy of the affinity which holds the atoms together; the magnitude is the sum of the amounts of both kinds of energy which are present within the molecule, or, according to Leibniz's terminology, it is the sum of the vis viva and vis mortua of the components of the molecule. In the same way the mean energy e of an atom is made up of its kinetic energy and its share of the potential energy of the chemical forces of affinity.

From this it first of all follows that we are not entitled to infer the magnitude of the speed of the atoms from the Refer also to the table of § 55.

calculated values of e as we were able to deduce the speed of translatory motion of the molecules from the molecular energy E. It would rather be allowable to estimate the strength of chemical affinity from the atomic energy e.

But from what has been said regarding the character of the atomic energy we further draw this as a necessary conclusion, that an atom cannot, like a molecule, attain any speed we choose. A great speed exceeding a certain limit would be able to tear the atom from its combination with the others, and such a freed atom would then move on in straight lines free from external forces like an independent molecule, and its energy, therefore, which till then formed a part of the atomic energy, would go to increase the molecular energy E. Herein lies an evident ground for the view that the mean energy e of an atom must be smaller than the average energy E of translatory motion of the molecules.

That an atom can be actually loosened from the molecular combination by an increase in its speed cannot be doubted; to this testifies the fact of dissociation, that is, the phenomenon that chemical combinations can be broken up by a rise of temperature, and, therefore, by an increase in the energy of the molecules and of the atoms. With a moderate amount of heat this breaking up of molecules into single atoms does not in general occur; but among a great number of molecules there will always be some which become split up into their components in consequence either of extraordinary high speed or of collision under exceptionally favourable circumstances.

This view, first put forward by Clausius, is applicable not only to gases but also to liquids. From measurements on the conductivity of water made by F. Kohlrausch and A. Heydweiller' it may with great probability be assumed that even the purest water contains traces of uncombined oxygen and hydrogen.

Analogously to this partially occurring dissociation we should expect a partial chemical combination to result when two gases are mixed together at a temperature below that Sitzungsber. d. Berl. Akad. 1894, p. 295.

of normal combination or combustion. This presumption is confirmed by H. B. Dixon's observations on mixtures of oxygen and hydrogen.

Before a complete breaking up of a compound molecule occurs the addition of heat produces a loosening of the bonds of the atoms in the molecule. In this process, which with Clausius we may term disgregation, the heat acts in two ways it increases the kinetic energy of the atoms and overcomes a part of their affinity. The sum of both actions requires the expenditure of energy, which we will denote by the letter e.

Disgregation becomes dissociation, i.e. the molecules break up into their atoms, when the energy of the atomic motion is able to overcome the remaining part of the affinity.

For this to be produced the energy of motion must be at least equal in magnitude to the total amount of the energy of chemical affinity. The value therefore of the atomic energy which is attained at the temperature of commencement of complete dissociation is the mechanical measure of the maximum energy to which the chemical affinity of an atom is capable of giving rise.

58. Dependence of the Specific Heats on
Temperature

The foregoing discussions show that the molecular and atomic energies are by no means magnitudes of the same kind. Now that we know this, it seems doubtful if both kinds of energy will increase in equal measure when the temperature rises. Hitherto we have assumed this, since the theory had given the law that the kinetic energy of the molecules bears a constant ratio to the total energy contained in a gas. The proof of this law, however, rests on the assumption, which is not in general true, that the specific heat of gases at constant volume is independent of the temperature.

We cannot well test by direct observation of the specific heat at constant volume whether this assumption is

1 Nature, xxxii. 1885, p. 535.