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XL VI. On the Reflexion and Refraction of Light. 

 By Sir William Thomson *. 



1. /GREEN'S doctrine t of incompressible elastic solid with 

 vJ equal rigidity, but unequal densities, on the two 

 sides of an interface, to account for the reflexion and refrac- 

 tion of light, brings out, as is well known, for vibrations 

 perpendicular to the plane of incidence (§ 12 below), ex- 

 actly Fresnel's " sine-law : " and for vibrations in the plane 

 of incidence a formula which agrees with Fresnel's tangent- 

 law when the refractive index differs infinitely little from 

 unity ; — but which differs notably (enormously we may say) 

 from it, and from the results of observation, in all practical 

 cases : — in all cases, that is to say, in which the refractive 

 index differs sufficiently from unity to have become subject 

 of observation or measurement. 



2. Since the first publication of Oauchy's work on the 

 subject in 1830, and of Green's in 1837, many attempts have 

 been made by many workers to find a dynamical foundation 

 for Fresnel's laws of reflexion and refraction of light, but all 

 hitherto ineffectually. On resuming my own efforts since 

 the recent meeting of the British Association in Bath. I first 

 ascertained that an inviscid fluid permeating among pores of 

 an incompressible, but otherwise sponge-like, solid, does not 

 diminish, but on the contrary augments, the deviation from 

 Fresnel's law of reflexion for vibrations in the plane of 

 incidence. Having thus, after a great variety of previous 

 efforts which had been commenced in connexion with pre- 

 parations for my Baltimore Lectures of this time four years 

 ago, seemingly exhausted possibilities in respect to incom- 

 pressible elastic solid, without losing faith either in light or in 

 dynamics, and knowing that the condensational-rarefactional 

 wave disqualifies t any elastic solid of positive compressibility, 

 I saw that nothing was left but a solid of such negative com- 

 pressibility as should make the velocity of the condensational- 

 rarefactional wave zero. So I tried it and immediately found 

 that it, with other suppositions unaltered from Green's, exactly 

 fulfils Fresnel's " tangent-law " for vibrations in the plane of 

 incidence, and his " sine-law " for vibrations perpendicular to 

 the plane of incidence. I then noticed that homogeneous 

 air-less foam held from collapse by adhesion to a containing 



* Communicated by the Author. 



t Camb. Phil. Soc. Dec. 1837. Green's Collected Papers, pp. 246, 258, 

 267, 268. 



X Green's Collected Papers, p. 246. 



