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On the Reflexion and Refraction of Solitary Plane Waves at a Plane Interface between two Isotropic Elastic Mediums—Fluid, Solid, or Ether
Published online by Cambridge University Press: 15 September 2014
Extract
§ 1. “Elastic solid” includes fluid and ether; except conceivable dynamics of the mutual action across the interface of the two mediums. Maxwell's electro-magnetic equations for a homogeneous non-conductor of electricity are identical with the equations of motion of an incompressible elastic solid, or with the equations expressing the rotational components of the motion of an elastic solid compressible or incompressible; but not so their application to a heterogeneous non-conductor or to the interface between two homogeneous non-conductors.
§ 2. The equations of equilibrium of a homogeneous elastic solid, under the influence of forces X, Y, Z, per unit volume, acting at any point (x, y, z) of the substance are given in Stokes' classical paper “On the Theories of the Internal Friction of Fluids in Motion, and of the Equilibrium and Motion of Elastic Solids,” p. 115, vol. i. of his Mathematical Papers; also in Thomson and Tait's Natural Philosophy [§ 698 (5) (6)].
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- Copyright © Royal Society of Edinburgh 1899
References
page 366 note * See Math. and Phys. Papers, vol. iii., Art. xcix. (first published May 1890), §§ 14–20, 21–28Google Scholar; and particularly §§ 44–47. Also Art. c. of same volume; from Comptes Rendus for September 16, 1889, and Proc. Roy. Soc. Edin., March 1890.
page 366 note † See Electricity and Magnetism, last four lines of § 616, last four lines of § 783, and equations (9) of § 784.
page 366 note ‡ Ibid., § 611, equations (1*). In these put C = 0, and take in connection with them equations (2) and (4) of § 616. Consider K and μ as different functions of x, y, z; consider particularly uniform values for each of these quantities on one side of an interface, and different uniform values on the other side of an interface between two different non-conductors, each homogeneous.
page 366 note § Camb. and Dublin Math. Jour., vol. ii. (1847)Google Scholar. Republished as Art. xxvii., vol. i. of Math. and Phys. Papers.
page 368 note * Camb. Phil. Trans., November 26, 1849. Republished in vol. ii. of his Math. Papers.
page 369 note * “On the Reflection and Refraction of Light at the common Surface of two Non-Crystallized Media,” Math. Papers, p. 258. Also Trans. Camb. Phil. Soc., 1838.
page 370 note * See Glazebrook's, “Report on Optical Theories” to British Association, 1885Google Scholar.
page 372 note * Green's, Math. Papers, p. 253Google Scholar.
page 373 note * The force-conditions for this case are as follows:—
Normal component force equated for upper and lower mediums,
,;
and tangential forces equated,
,.
page 374 note * In that paper B, A, and ζ denote respectively the n, the k+⅛n, and the p of the present paper.
page 374 note † See first footnote to § 1.
page 376 note * Phil. Mag., 1871, 2nd half year.
page 376 note † See * of § 1.
page 376 note ‡ Dynamical Theory of Diffraction. See footnote § 5.
page 376 note § See footnote § 14.