This remark can, however, be valid only so far as the question concerns the phenomena which are conditioned by heat alone. By this is only intended to be meant that addition of heat can bring about no other motions than those named. But that other kinds of motion can be produced in the molecules and atoms of gas by other causes is shown by the spectra of incandescent gases. The motions inside a molecule, which are perceptible as light, are easily brought about by electrical or chemical forces. But simple heating in gases does not cause them to radiate red or white light like solids or liquids. Hot gases, of course, send out both dark and luminous radiation; but the radiation which they emit, purely in consequence of their being heated, is very much less than that which comes from gases in combustion; and under all circumstances gases radiate heat in much less degree than solids or liquids. With this remarkable fact the results of the kinetic theory agree most excellently.' It is not for all diatomic gases that the value of the ratio of the specific heats is independent of the temperature and equal to 14; for many of these gases it is smaller and is variable with the temperature. This fact can be interpreted in two ways. In the first place, the constant h, which expresses the ratio of the energy spent on internal work to the energy of translation, need not be equal to 0 for these gases; and if it is greater than zero, the ratio of C to c is less than 1.4. Another, though not essentially different, possible explanation might be found in the assumption that the number of degrees of freedom is not 5, but 6. There is, indeed, a sixth kind of movability if we drop the assumption that the two atoms of the molecule must remain at an invariable distance from each other. With the value h = 0, the ratio would approach the value C 1 R. v. Helmholtz, Licht- und Wärmestrahlung verbrennender Gase, 1890, p. 64. as from the table in § 55 we see is really the case for some gases. For gases whose molecules contain three or more atoms the number of degrees of freedom q is to be taken still greater, since the structure of such a molecule cannot be imagined to be that of a figure of revolution. The position of such a figure as a triangle or tetrahedron is not completely determined when only the position of its centroid and the direction of one axis are given; there are thus more elements required for its determination. If, therefore, we assume to be greater than 5 or 6, the ratio of C to c becomes smaller, and with increasing approaches more and more the limit 1, as observation also teaches. This theory therefore gives a satisfactory account of all the principal circumstances. In spite of this we cannot think that by it the question has been exhaustively treated. For there is a weighty objection to this theory, which H. T. Eddy has pointed out. Since the bonds of the atoms by which they are bound together in the molecule allow of neither perfect freedom nor perfect fastness, it does not seem admissible simply to count the kinds of movability; the degrees of freedom cannot be introduced as all of equal value, but must be brought into the calculation differently weighted. An atom in a molecule has not the same degree of freedom of its motions as the centroid of the molecule, and a limited freedom must not be counted as a perfectly unlimited freedom. As we shall easily see, this objection amounts to the same thing as the opinion already mentioned in § 56, that the energy of the limited motion of an atom cannot be equal to the energy of a molecule, but must be smaller-an opinion which in the first edition of this book was shown to be in accordance with experiment. On these grounds, at the Aberdeen meeting of the British Association in 1885, a great number of prominent investigators denied, or at least threw doubt upon, the validity of Scient. Proc. Ohio Mech. Inst. 1883, p. 42; Journ. Franklin Inst. [3] lxxxv. pp. 339, 409; Ohio Mech. Inst. 1883, p. 82. Boltzmann's proposition of the equal distribution of energy among the different degrees of freedom. The objection which had been raised against this theorem by Crum Brown was supported by Liveing, Lord Kelvin, J. J. Thomson, Hicks, and Osborne Reynolds.1 1 Nature, xxxii. 1885, pp. 352, 533. L |