96 The Hon. J. W. Strutt on the Reflection of 



but the form of <p so determined is different from Cauchy's, and 

 leads to a more complicated solution. On the whole I cannot 

 see that Cauchy's theory of reflection has any claim to be consi- 

 dered dynamical, although his formula? are, beyond doubt, very 

 good empirical representations of the facts. 



I now come to the modification of Green's theory proposed by 

 Haughton. If M were an arbitrary constant instead of a defi- 

 nite function of fju, there would be but little difference between 

 the two sets of formulae ; for the factor sin 6 would not vary 

 greatly in the neighbourhood of the polarizing angle, where 

 alone the correction to FresnePs original expression is sensible. 

 So far as the question has been treated experimentally, the ba- 

 lance of evidence seems to be rather against than. for the factor 

 sin 6. I have already remarked that Haughton's reasons for con- 

 sidering M as an independent constant cannot be sustained, but 

 at the same time I think that others of considerable force may 

 be given. 



In a supplement to his memoir <f On the Reflection of Light"*, 

 Green says : — " Should the radius of the sphere of sensible action 

 of the molecular forces bear any finite ratio to \, the length of a 

 wave of light, as some philosophers have supposed in order to 

 explain the phenomena of dispersion, instead of an abrupt ter- 

 mination of our two media we should have a continuous though 

 rapid change of state of the setherial medium in the immediate 

 vicinity of their surface of separation. And I have here endea- 

 voured to show by probable reasoning that the effect of such a 

 change would be to diminish greatly the quantity of light re- 

 flected at the polarizing angle, even for highly refractive sub- 

 stances, supposing the light polarized perpendicular to the plane 

 of incidence." The contrast between this view and that of 

 Lorenz is remarkable. 



Referring to equation (9), we see that when n' = n, it reduces to 



Reasoning from the analogy of elastic solids, we found 



m(«' 2 + Z> 2 ) : m'(a/ 2 + & 2 ) = D : D'. . (11) 



Now although the transition between the two media is so sudden 

 that the principal waves of transverse vibrations are affected 

 nearly in the same way as if it were instantaneous, yet we may 

 readily imagine that the case is different for the surface-waves, 

 whose existence is almost confined to the layer of variable den- 

 sity. It is probable that the ratio of m(a ,2 + Z> 2 ) :m l (aj 2 + b' 2 ), 

 instead of being equal to 1 : y?, approaches much more nearly to 



* Cambridge Trans. 1839, or Green's works. 



