replaced by propyl or by isopropyl, the third as ethyl hydrate in which one atom of hydrogen is replaced by ethyl, and another by methyl, and lastly, the fourth as ethyl hydrate in which three atoms of hydrogen are replaced by three methyl groups; this last alcohol corresponding to the trimethylacetic acid of Boutlerow. This point of view is expressed in the following formula:

The secondary amyl alcohols are three in number, viz.

These secondary amyl alcohols can be regarded as derivatives of methyl alcohol in which two atoms of hydrogen are replaced either by propyl and methyl, or by isopropyl and methyl, or by two ethyl groups.

We thus have the simplified formulæ :—

Lastly, a tertiary amyl alcohol is known : it is the body which I have described under the name of amylene hydrate. It contains two methyl and one ethyl groups.

We have given all these formulæ in order to show with what facility the theory of atomicity foretells, limits, and interprets the most complicated cases of isomerism. The principles here developed may be applied to many other examples.

NOTE IV.

THE ACTION OF HEAT UPON GASES.

We have pointed out in the text the manner of action of heat upon the molecules of a solid body. We think it useful to follow up this point by analysing the case of a gaseous body. We know that the heat absorbed by gases produces different effects, whether we heat it under constant pressure or under constant volume. In the first case

(i.) It increases the external work corresponding to dilatation and to the pressure supported by the gas;

(ii.) It increases the energy of the progressive rectilinear molecular motion;

(iii.) It increases the energy of the atomic motion, and performs certain work within the molecule when the molecule is composed of many atoms.

In the second case, when the gas is heated under con

stant volume, the first effect is nil. The second and the third are produced, but nothing proves that the internal work is the same under constant pressure and under constant volume. This work disappears in the case of monatomic gases, such as mercury vapour (p. 121). It should increase with the number of atoms in the molecule.

The total energy of a gaseous molecule is composed of the energy of the progressive molecule motion and of the atomic energy (Kinetic and Potential). Clausius admits that a relation exists between the total energy H and the energy of the progressive motion к, and he expresses this relation by the following equation :—

H 2 1

=

K 3 k-1'

k being the ratio of the specific heats

(p. 122). In the case

of mercury vapour н=K, k=1·666. In the case of polyatomic gases, the values of k become smaller, for the gases H2, O2, and N2 falling between 1.395 and 1·413. These values decrease as the number of atoms in the gaseous molecule increase.

The absolute zero would correspond to the cessation of the molecular and atomic motions. The temperatures of a gas increase proportionately with the kinetic energy of its molecules; or again, since the masses remain constant, with the squares of the molecular velocities. The heat contained in a gaseous mass is represented by the sum of the kinetic energies of its molecules.

INDEX.