366 Proceedings of Royal Society of Edinburgh. [sess. 
On the Reflexion and Refraction of Solitary Plane Waves 
at a Plane Interface between two Isotropic Elastic 
Mediums — Fluid, Solid, or Ether. By Lord Kelvin, 
G.C.Y.O. 
(Read December 19, 1898.) 
§ 1. “Elastic solid” includes fluid and ether; except conceiv- 
able dynamics * * * § of the mutual action across the interface of the 
two mediums. Maxwell’s electro-magnetic equations for a homo- 
geneous 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. J 
§ 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)]. Substituting 
according to D’Alembert’s principle, - p$, - pr), - p£ for X, Y, Z, 
and using as in a paper of mine § of date November 28, 1846, 
* See Math, and Phys. Papers , vol. iii., Art. xcix. (first published May 
1890), §§ 14-20, 21-28 ; and particularly §§ 44-47. Also Art. c. of same 
volume ; from Comptes Rendus for September 16, 1889, and Proc. Roy. Soc. 
Edin ., March 1890. 
t See Electricity and Magnetism, last four lines of § 616, last four lines 
of § 783, and equations (9) of § 784. 
+ Ibid., § 611, equations (1*). In these put C = 0, and take in connection 
with them equations (2) and (4) of § 616. Consider K and y 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. 
§ Camb. and Dublin Math. Jour., vol. ii. (1847). Republished as Art. 
xxvii. , vol. i. of Math, and Phys. Papers. 
