MATHEMATICAL PAPERS OF THE LATE GEORGE GREEN, FELLOW OF GONYILLE AND CAIUS COLLEGE, CAMBRIDGE. EDITED BY N. M. FERRERS, M.A., FELLOW AND TUTOR OF GONYILLE AND CAIUS COLLEGE. Hontion: MACMILLAN AND CO. 1871. [All Rights reserved.,] PREFACE. Having been requested by the Master and Fellows of Gonville and Caius College to superintend an edition of the mathematical writings of the late George Green, I have fulfilled the task to the best of my ability. The publication may be opportune at present, as several of the subjects with which they are directly or indirectly concerned, have recently been introduced into the course of mathematical study at Cambridge. They have also an interest as being the work of an almost entirely self-taught mathematical genius. George Green was born at Sneinton, near Nottingham, in 1793. He commenced residence at Gonville and Caius College, in October, 1833, and in January, 1837, took his degree of Bachelor of Arts as Fourth Wrangler. It is hardly necessary to say that this position, distinguished as it was, most inadequately represented his mathematical power. He laboured under the double disadvantage of advanced age, and of inability to submit entirely to the course of systematic training needed for the highest places in the Tripos. He was elected to a fellowship of his College in 1839, but did not long enjoy this position, as he died in 1841. The contents of the following pages will sufficiently shew the heavy loss which the scientific world sustained by his premature death. A slight sketch of the papers comprised in this volume may not be uninteresting. The first paper, which is also the longest and perhaps the most important, was published by subscription at Nottingham in 1828. It was in this paper that the term potential was first introduced to denote the result obtained by adding together the masses of all the particles of a system, each divided by its distance from a given point. In this essay, which is divided into three parts, the properties of this function are first considered, and they are then applied, in the second and third parts, to the theories of magnetism and electricity respectively. The full analysis of this essay which the author has given in his Preface, renders any detailed description in this place unnecessary. In connexion with this essay, the corresponding portions of Thomson and Tait's Natural Philosophy should be studied, especially Appendix A. to Chap. I., and Arts. 482 —550, inclusive. The next paper, "On the Laws of the Equilibrium of Fluids analogous to the Electric Fluid," was laid before the Cambridge Philosophical Society by Sir Edward Ffrench Bromhead, in 1832. The law of repulsion of the particles of the supposedfluid here considered is taken to be inversely proportional to the nth power of the distance. This paper, though displaying great analytical power, is perhaps rather curious than practically interesting ; and a similar remark applies to that which succeeds it, "On the determination of the attractions of Ellipsoids of variable Densities," which, like its predecessor, was communicated to the Cambridge Philosophical Society by Sir E. F. Bromhead. Space of n dimensions is here considered, and the surfaces of the attracting bodies are supposed to be repre |