on, noticeably removed from this condition. The probability of the latter state of affairs is smaller, the further such a state is removed from thermal equilibrium, but it can be made as great as we please to assume the universe to be great. But there is necessary and sufficient probability that our earth as we know it is in its present state. By the second law (irreversible increase of entropy in natural processes) there is still greater probability that it tends to a final state of thermal equilibrium or death; and since the universe itself is so great, there is sufficient probability that other worlds than ours may deviate from thermal equilibrium. As a graphic exposition of this theory, which shows the vast scope of the second law of thermodynamics, a curve can be plotted with the variables H and the time as coordinates, to visualize what takes place in the universe. The H curve is shaped like a succession of inverted trees, the summits of which represent "the worlds where visible motion and life exist."[1] Physicists have found that the Maxwell-Boltzmann distribution of velocities is satisfactory for gases whose molecules move independently and at random; but when the molecules are supposed to be subject to one another's influence, it does not account for certain facts of nature such as the measured specific heats of gases or individual peculiarities of their spectra. In monatomic gases like argon, helium and mercury, the ratio of the specific heats will account for the three degrees of molecular freedom ascribed to them by the mathematical theory, but in the case of diatomic gases, like hydrogen or oxygen, the theory calls for six degrees of freedom, while experiment will account for only five. Boltzmann met these objections with frank or ironical admissions as to the ultimate inadequacy of all human hypotheses,[2] and although his theory is to some extent invalidated by facts like the above,[3] his subtle handling of molecular thermodynamics gives the physicist deeper insight into
- ↑ "Almost all these trees are extremely low, and have branches very nearly horizontal. Here H has nearly the minimum value. Only very few trees are higher, and have branches inclined to the axis of abscissa?, and the improbability of such a tree increases enormously with its height." Boltzmann, Nature, 1894-5, LI., 581.
- ↑ Neither the theory of Gases nor any other physical theory can be quite a congruent account of facts, and I can not hope with Mr. Burbury that Mr. Bryan will be able to deduce all the phenomena of spectroscopy from the electromagnetic theory of light. Certainly, therefore, Hertz is right when he says: 'The rigour of science requires that we distinguish well the undraped figure of Nature itself from the gay-coloured vesture with which we clothe it at our pleasure.' But I think the predilection for nudity would be carried too far if we were to forego every hypothesis. Only we must not demand too much from hypotheses." Boltzmann, Ibid., 413.
- ↑ The principal opponent of the Maxwell-Boltzmann partition of energies was Lord Kelvin in his "Nineteenth Century Clouds over the Dynamical Theory of Heat and Light." When asked what he had against it, he replied point-blank: "I don't think there is a single thing about it that is right" (Science, Jan. 3 r 1908, p. 6).
