Light from Transparent Matter. 87 



If we assume the complete accuracy of FresnePs expressions, 

 either case agrees with observation; only, if n = n f , light vi- 

 brates normally to the plane of polarization ; while if D = I)', the 

 vibrations are parallel to that plane. But we know that FresneFs 

 tangent-formula is not accurate, and that there is in general no 

 angle of complete polarization, so that already the presumption 

 is in favour of Case 1 ; but I would not lay much stress upon 

 this, as the phenomena investigated by Jamin are of a secondary 

 character, and might be due to the action of disturbing causes. 



Case III. We may suppose that n and D both vary. Here we 

 should obtain something between FresneFs two expressions, 

 which could hardly be reconciled with observation, unless one 

 variation were very subordinate to the other. Other considera- 

 tions seem to exclude this case ; for if n and D both vary, there 

 is nothing to prevent their varying proportionally, so as to 

 leave the wave- velocity unchanged, or fi=l. The transmitted 

 wave would then not be turned, although there would be a finite 

 reflection. Nothing of this kind is known in nature, whichever 

 way the light may be polarized. But the most satisfactory argu- 

 ment against the joint variation is derived from the theory of the 

 diffraction of light from very small particles, whose diameter does 

 not exceed a small fraction of the wave-length. Hitherto there 

 has been no theoretical difficulty. Case I. is only a trans- 

 lation into analysis of the reasoning of Frcsnel, and Case II. of 

 the reasoning of MacCullagh. But when we pass on to the con- 

 sideration of the problem when the vibrations are in the plane 

 of incidence, our footing is no longer so sure. However close 

 the analogy may be between the phenomena of light and the 

 transverse vibrations of an elastic solid, one cannot but feel that 

 it may not extend to those motions which are independent of 

 rigidity, and of which in the case of the aether we have no direct 

 knowledge. Still, in the absence of all others, we cannot do 

 better than follow the guide which has already served us so well. 



Since the displacement is entirely in the plane of incidence, 

 f=0, and £, rj are independent of,?. The equations to be satis- 

 fied in the interior of the first medium are*. 



dt* ~ y dx \dx "*" dy)^ 7 dy\dy dx)' 



where 



dyJ ' dy \dy 

 ' y dy\.dx ' dy) ' dx\dy 



J dy\dx dy) 7 dx\dy dx) } 



(4) 



o m + n 9 n 

 * See Green, or Thomson and Tait, p. 530. 



