Taking the phenomena of light to be due to periodic displacements in a rotational ether, we shall investigate the exact character of these displacements in the case of reflection from an isotropic transparent substance. Two wellknown vectors play the principal parts in any such optical discussion-the displacement of the medium and its curl; in the electro-magnetic theory the former is proportional to the magnetic force and the latter to the electric " displacement." To give precision to the

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... ussion we shall deal throughout with the displacement of the medium, there being no difficulty in dealing in a similar fashion with the curl. Let the displacement in the incident light be of unit amplitude and polarised in a plane making an angle 6 with the plane of incidence. It can be resolved into two components £ = cos 6 cos in the plane of incidence, and 7] = sin 0 cos pt perpendicular to this plane. The corresponding com ponents in the reflected beam are then given by the formulae f = -R'costfcos (p t-p')and = -R sin cos {p t-* [With reference to an oversight in his paper " On Metallic Reflexion," ' Roy. Soc. Proc.,' vol. 77, Jan., 1906, which has recently been pointed out privately by Mr. C. E. Hasse, Prof. Maclaurin writes that he had himself * observed it immediately on receipt of the printed paper, but that fortunately the blemish does not invalidate any of the results, beyond requiring a slight modification of the argument in one place. At the foot of p. 218, in quoting the formula E = /x_2(*gc£r from the previous paper, the first factor was left out. When it is inserted, the modulus of E is no longer large, and the following modification becomes necessary. We have If both the terms (E -1) \T-and (F -E) sin2 (f> are to be retained, we would require tw complex constants to specify the layer of transition, which the experimental knowledge would hardly be adequate to determine. When, however, < is small, the term (F -E) sin2 < fi will be negligible in comparison with (E -1) /i2; and even if < p is not small, the first term will not usually be more than one-tenth of the second, the modulus of the factor \j? in the latter being large. The neglect of the first term may therefore be expected to produce an error of about one-tenth in the estimated correction due to the layer of transition for large incidences, and practically no error at all for small incidences. This degree of approxima tion fortunately remains adequate, in relation to the exactness of the data utilised in the argument.] * Of course, if p were greater than p , this statement wuuld have to be reversed. Moreover, if we were dealing with the curl instead of the displacement, (Bp) would be interchanged with (B'p'), so that the component parallel to the plane of incidence would lag behind the other. + If we were dealing with the curl, instead of the displacement, the motion would be counter clockwise. 1907.] On Light Elliptically Polarised hy Reflexion. on July 20, 2018 http://rspa.royalsocietypublishing.org/ Downloaded from F ig. 17.-The continuous curve refers to realgar, the dotted curve to diamond.