1912] ON DEPARTURES FROM FRESNEL'S LAWS OF REFLEXION 97 and if % = 45°, 6= 22° 51'. We can thus deal with all kinds of reflexion from ^ = 90° down to nearly 18°, and this suffices for the purpose. The strip employed was of plate glass and was ground upon the back surface. The front reflecting face was treated for about 30s with hydrofluoric acid. It was now easy to trace the effects all the way from grazing incidence down to an incidence of 45° or less. The ray of equal index was in the yellow-green, as was apparent at once from the spectrum of the reflected light near grazing. There was a very dark band in this region, and total reflexion reaching nearly down to it from the blue end. The light was from a paraffin flame, at a distance of about two feet, seen edgeways. As grazing incidence is departed from, the flame continues at first to show a purple colour, and the spectrum shows a weakened, but not totally absent, green. As the angle of incidence % still further decreases, the reflected light weakens both in intensity and colour. When % = 45°, or thereabouts, the light was weak and the colour imperceptible. After two further treatments with hydrofluoric acid and immediate examination, the light seemed further diminished, but it remained bright enough to allow the absence of colour to be ascertained, especially when the lamp was temporarily brought nearer. An ordinary candle-flame at the same (2 feet) distance was easily visible. In order to allow the use of the stopper, the strip was removed from the bottle-prisrn when the observations were concluded, and it stood for four days exposed to the atmosphere. On re-examination it seemed that the reflexion at % = 45° had sensibly increased, a conclusion confirmed by a fresh treatment with hydrofluoric acid. It remains to consider the theoretical bearing of the two anomalies which manifest themselves (i) at the polarizing angle, and (ii) at other angles when both media have the same index, at any rate for a particular ray. Evidently the cause may lie in a skin due either to contamination or to the inevitable differences which must occur in the neighbourhood of the surface of a solid or fluid body. Such a skin would explain both anomalies and is certainly a part of the true explanation, but it remains doubtful whether it accounts for everything. Under these circumstances it seems worth while to inquire what would be the effect of less simple boundary conditions than those which lead to Fresnel's formulas. On the electromagnetic theory, if 9, &i are respectively the angles of incidence and refraction, the ratio of the reflected to the incident vibration is, for the two principal polarizations, tan fti/tan 6 — p/fr tan fli/tan 6 + p/fr..............................^ ' and 4-<ifi >0 /J-r»-n /3 IF I TF Lcin PI/Call (7 — JH/J\.i /T>\ tan0a/tan0+ w ' ...........................^ ' R. VI.buted to a not very thin superficial modification of the glass rendering it optically different from the interior.