THE ANALYTICAL THEORY OF HEAT BY JOSEPH FOURIER. TRANSLATED, WITH NOTES, BY ALEXANDER FREEMAN, M.A., FELLOW OF ST JOHN'S COLLEGE, CAMBRIDGE. EDITED FOR THE SYNDICS OF THE UNIVERSITY PRESS. Cambridge: AT THE UNIVERSITY PRESS. LONDON: CAMBRIDGE WAREHOUSE, 17, PATERNOSTER ROW. CAMBRIDGE: DEIGHTON, BELL, AND CO. LEIPZIG: F. A. BROCKHAUS. 1878 [All Rights reserved.] PREFACE. IN preparing this version in English of Fourier's celebrated treatise on Heat, the translator has followed faithfully the French original. He has, however, appended brief foot-notes, in which will be found references to other writings of Fourier and modern authors on the subject these are distinguished by the initials A. F. The notes marked R. L. E. are taken from pencil memoranda on the margin of a copy of the work that formerly belonged to the late Robert Leslie Ellis, Fellow of Trinity College, and is now in the possession of St John's College. It was the translator's hope to have been able to prefix to this treatise a Memoir of Fourier's life with some account of his writings; unforeseen circumstances have however prevented its completion in time to appear with the present work. 7 1. Object of the theoretical researches 2-10. Different examples, ring, cube, sphere, infinite prism; the variable temperature at any point whatever is a function of the coordinates and of the time. The quantity of heat, which during unit of time crosses a given surface in the interior of the solid, is also a function of the time elapsed, and of quantities which determine the form and position of the surface. The object of the theory is to discover these 11. The three specific elements which must be observed, are the capacity, the conducibility proper or permeability, and the external conducibility or penetrability. The coefficients which express them may be regarded at 12. First statement of the problem of the terrestrial temperatures 13-15. Conditions necessary to applications of the theory. Object of the 16-21. The rays of heat which escape from the same point of a surface 1 Each paragraph of the Table indicates the matter treated of in the articles |