Mathematical and Physical Papers

Abstract

EVERY one interested in the study of physics of the more profound kind will welcome this collection of essays by the celebrated natural philosopher, so many of which, hitherto scattered throughout various periodicals, difficult to gather together, or even wholly inaccessible to readers out of the reach of large public libraries, are yet of decisive importance for those chapters of the science to which they refer. With the two volumes now before us, in conjunction with the late publication, “Reprint of Papers on Electrostatics and Magnetism,” the collection is now completed down to the date of February, 1856. Vol. II. contains, besides, all that the author has written on the Transatlantic Telegraphs, which, according to the strict order of time, might have been looked for in later volumes. The first volume begins with a series of essays, for the most part of a mathematical nature, ranging from the year 1841 to 1850. So far as these essays relate to physical problems, their - chief interest turns on the difficulties connected with the analytic method. These difficulties were, however, even at that early period, treated by the youthful author with great skill, and under comprehensive points of view. The problems are, in part, geometrical and mechanical, referring to lines of curvature, systems of orthogonal surfaces, principal axes of a rigid body, &c. Most of them, however, deal with the integration of the differential equations, on which is based the doctrine of thermal conductivity and potential functions. The latter, as is well known, form the mathematical foundation of a large number of chapters in physics—the doctrine of gravitation, of electrostatical distribution, of magnetic induction, of stationary currents of heat, of electricity and of ponderable fluids. By treating all these problems collaterally and rendering concretely in some what in others appears in the highest degree abstract, the author has succeeded in overcoming the greatest difficulties, and we can only recommend every student of mathematical physics to follow his example. A field particularly favourable for the exercise of his powers was opened up to Sir W. Thomson by the phenomena, newly discovered by Faraday, in diamagnetic and weakly magnetic bodies, crystalline as well as uncrystalline. These our author rapidly and easily succeeded in arranging under comprehensive points of view. One great merit in the scientific method of Sir William Thomson consists in the fact that, following the example set by Faraday, he avoids as far as possible hypotheses on unknown subjects, and by his mathematical treatment of problems endeavours to express the law simply of observable processes. By this circumscription of his field the analogy between the different processes of nature is brought out much more distinctly than would be the case were it complicated by widely-diverging ideas respecting the unknown interior mechanism of the phenomena.

Mathematical and Physical Papers.

By Sir William Thomson. Vols. I. and II. (Cambridge University Press. 1882, 1884.)