CONTENTS PAGE An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism ... ... ... 1 Preface ... ... ... ... ... ... 3 General Preliminary Results ... ... Application of the preceding results to the Theory of Electricity ... ... ... ... ... Application of the preliminary results to the Theory of Mag- Mathematical Investigations concerning the Laws of the Equi- librium of Fluids analogous to the Electric Fluid, with other similar researches ... ... ... ... ... 117 On the Determination of the Exterior and Interior Attractions of Ellipsoids of Variable Densities On the Motion of Waves in a variable canal of small depth and width ... ... ... ... ... ... ... 223 On the Reflexion and Refraction of Sound ... ... ... 231 On the Laws of the Reflexion and Refraction of Light at the common surface of two non-crystallized Media ... ... 243 Note on the Motion of Waves in Canals ... ... ... 271 Supplement to a Memoir on the Reflexion and Refraction of Light ... ... ... ... ... ... ... 281 On the Propagation of Light in crystallized Media ... ... 291 Researches on the Vibration of Pendulums in Fluid Media ... 313 ERRATA. Page 23, line 11, for there read these. 25, for dzdy read dydz. dī dū » 22, after co-ordinates, insert of. 19, for e(. - ) =< (2 - ) read « (1 - 1) =< (2-1). 13, for Sustav read Shop 4 from bottom, before a potential insert of. . Ư(2) . U (1) for gitt read ng 20, for 9% read god. for sin o' read sin 0. 18, for U(0) read U(1), 24, for I read of the , , 19, for these read thus. 24, for sin a', read sin w'. AN ESSAY ON THE APPLICATION OF MATHEMATICAL ANALYSIS TO THE THEORIES OF ELECTRICITY AND MAGNETISM.* * Published at Nottingham, in 1828. PREFACE. AFTER I had composed the following Essay, I naturally felt anxious to become acquainted with what had been effected by former writers on the same subject, and, had it been practicable, I should have been glad to have given, in this place, an historical sketch of its progress; my limited sources of information, however, will by no means permit me to do so; but probably I may here be allowed to make one or two observations on the few works which have fallen in my way, more particularly as an opportunity will thus offer itself, of noticing an excellent paper, presented to the Royal Society by one of the most illustrious members of that learned body, which appears to have attracted little attention, but which, on examination, will be found not unworthy the man who was able to lay the foundations of pneumatic chymistry, and to discover that water, far from being according to the opinions then received, an elementary substance, was a compound of two of the most important gases in nature. It is almost needless to say the author just alluded to is the celebrated CAVENDISH, who, having confined himself to such simple methods, as may readily be understood by any one possessed of an elementary knowledge of geometry and fluxions, has rendered his paper accessible to a great number of readers; and although, from subsequent remarks, he appears dissatisfied with an hypothesis which enabled him to draw soine important conclusions, it will readily be perceived, on an attentive perusal of his paper, that a trifting alteration will suffice to render the whole perfectly legitimate*. • In order to make this quite clear, let us select one of CAVENDISH’s propositions, the twentieth for instance, and examine with some attention the method |