Bakerian lecture.―On the statistical and thermodynamical relations of radiant energy

Abstract

It was surmised by a prominent school of thought in ancient times, it become absorbed into the mechanical philosophy of Newton, and it was at length established by the experiments and reasonings of Dalton and his contemporaries, that matter is not divisible without limit, but is constituted of an aggregate of discrete entities, all alike for the same homogeneous substance, and naturally extremely minute compared with our powers of direct perception. The smallest portion of matter which we can manipulate (at any rate until very recently) consists of a vast assemblage of molecules, of independent self-existing systems which exert dynamical influences on each other. The direct knowledge of matter that mankind can acquire is a knowledge of the average behaviour and relations of the crowd of molecules. The sentient intelligence with perceptions of space and time minute enough to examine the individual molecules, each of them -would probably appear as a cosmos in itself, influencing and influenced by others,—not unlike stars in a firmament. The observed laws of nature are thus laws of averages—are statistical relations. Yet they are for practical purposes exact. To illustrate this in a way that will presently be of use let us imagine a row of urns whose apertures are of different areas, and let us consider how N objects will be distributed at random among them, assuming that the chance of an object getting into an urn is proportional to the area of its aperture, and is otherwise indifferent as regards them all. If the number of objects is not very large in comparison with the number of urns, no direct law of numbers emerges in this random distribution: though by the doctrine of probabilities we may calculate definitely the relative numbers of times that the various distributions will occur in a vast total number of cases, and this will represent the chances of recurrence of these distributions, the most likely arrangements are those ranging close around the equable distribution, in which the contents of the urns are proportional to their apertures. Those far removed therefrom are much less likely. "When the number N is very great, a relatively small deviation from the equable distribution has an almost negligible chance of occurring. Equable distribution then assumes the aspect of a rigid law; nevertheless occasionally in an soon it will he widely departed from. The abstract laws governing the extent and distribution of the various kinds of deviations from the mean distribution constitute an important part of the theory of statistics, first explored and developed by J. Bernoulli.