pression or dilatation, or its elasticity of volume, whiJe B measures its resistance to distortion, or its rigidity. The equilibrium of the medium, it may be shewn, cannot be stable, unless both of these quantities are positive*. A Supplement to this paper supplying certain omissions, immediately follows it In the next paper, "On the Propagation of Light in Crystalline Media," the principle of Conservation of Work is again assumed as a starting-point and applied to a medium of any description. It is first assumed that the medium is symmetrical with respect to three planes at right angles to one another, by which supposition the twenty-one coefficients previously mentioned are reduced to nine. Fresnel's supposition, that the vibrations affecting the eye are accurately in front of the wave, is then introduced, and a complete explanation of the phenomena of polarization is shewn to follow, on the hypothesis that the vibrations constituting a plane-polarized ray are in the plane of polarization. The hypothesis adopted in the former paper—that these vibrations are perpendicular to the plane of polarization—is then resumed, and an explanation arrived at, by the aid of a subsidiary assumption—unfortunately not of the same simple character as those previously introduced—that for the three principal waves the wave-velocity depends on the direction of the disturbance only, and is independent of the position of the wave's front. The paper concludes by taking the case of a perfectly general medium, and it is shewn that Fresnel's supposition of the vibrations being accurately in the wave-front, gives rise to fourteen relations among the twenty-one coefficients, which virtually reduce the medium to one symmetrical with respect to three planes at right aDgles to one another. * In comparing Greeu'8 paper with the passage in Thomson and Tait's Natural Philosophy above referred to, it should be remarked that the A of the former is equal to the m - jn of the latter, and that R = n. This paper, read May 20, 1839, was his last production. Another, "On the Vibrations of Pendulums in Fluid Media," read before the Royal Society of Edinburgh, on Dec. 16, 1833, will be found at the end of this collection. The problem here considered is that of the motion of an inelastic fluid agitated by the small vibrations of a solid ellipsoid, moving parallel to itself. I have to express my thanks to the Council of the Cambridge Philosophical Society, and to that of the Royal Society of Edinburgh, for the permission to reproduce the papers published in their respective Transactions which "they have kindly given. N. M. FERRERS. GONVILLE AND CA1US COLLIOK, Dec. 1870. CONTENTS. ne, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism ... ... ... 1 Introductory Observations ... ... ... ... 9 General Preliminary Results... ... ... ... 19 Application of the preceding results to the Theory Application of the preliminary results to the Theory of Mag- netism ... ... ... ... ... ... ... 83 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 ... ... ... IBS On the Motion of Waves in a variable canal of small depth 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 On the Propagation of Light in crystallized Media ... ... 291 Researches on the Vibration of Pendulums in Fluid Media ... 313 |