182 Lord Kelvin on the Reflexion 



and so denotes the propagational velocity of the distortional 

 waves ; and A, B, C are arbitrary constants subject to the 

 relation 



«A + /3B + 7C = (16). 



§ 7. To suit the case of solitary waves we shall suppose the 

 arbitrary function f(t) to have any arbitrarily given value for 

 all values of t from to t, and to be zero for all negative 

 values of t and all positive values greater than t. Thus t is 

 what we may call the transit-time of the wave, that is, the 

 time it takes to pass any fixed plane parallel to its front ; or 

 the time during which any point of the medium is moved by 

 it. The thicknesses, or, as we shall sometimes say, the wave* 

 lengths, of the two kinds of waves are ur and vr respectively, 

 being for the same transit-times directly as the propagational 

 velocities. 



§ 8. And now for cur problem of reflexion and refraction. 

 At present we need not occupy ourselves with the case of 

 purely distortional waves with vibratory motions perpendicular 

 to the plane of the incident, reflected, and refracted rays. It 

 was fully solved by Green * with an arbitrary function to 

 express the character of the motion (including therefore the 

 case of a solitary wave or of an infinite procession of simple 

 harmonic waves). He showed that it gave precisely the 

 " sine law " which Fresnel had found for the reflexion and 

 refraction of waves " polarized in the plane of incidence." 

 The same law has been found for light, regarded as electro- 

 magnetic waves of one of the two orthogonal polarizations, 

 by von Helmholtz, H. A. Lorenz, J. J. Thomson, Fitz Gerald, 

 and Rayleigh f . None of them has quite dared to say that 

 the physical action represented by his formulas for this case is 

 a to-and-fro motion of the ether perpendicular to the plane of 

 incidence, reflexion, and refraction ; nor has any one, so far 

 as I know, absolutely determined whether it is the lines of 

 electric force or of magnetic force that are perpendicular 

 to that plane in the case of light polarized by reflexion at the 

 surface of a transparent medium. For the action, whatever 

 its rjhysical character may be, which takes place perpendicular 

 to that plane, they all seem to prefer " electric displacement/' 

 of which the only conceivable meaning is motion of electricity 

 to and fro perpendicular to the plane. If they had declared, 

 or even suggested, definitely this motion of ether, they would 



* " On the Reflexion and Refraction of Light at the common Surface 

 of two Non-Crystallized Media/' Math. Papers, p. 258. Also Trans. 

 Caruo. Phil. Soc. 1838. 



t Sde Glazebrook's Rsport " on Optical Theories " to British Asso- 

 ciation, 1885. 



