96 ON DEPARTURES FROM FRESNEL'S LAWS OF REFLEXION [362 aperture at the top of the cell extended over the whole length. The general dimensions being the same as before, the body of the cell was formed by bending round a rectangular piece of tin-plate A (fig. 1) and securing the ends, to which the glass faces B were to be cemented, by enveloping copper wire. The plate G could then be removed for cleaning or polishing without breaking a joint. In emptying the cell it is necessary to employ a large funnel, as the liquid pours badly. The plate tried behaved much as the one just spoken of. In the reflected light, whether at moderate angles or nearly grazing, the yellow-green ray of equal index did not appear to be missing. A line or rather band of polish, by putty-powder applied with the finger, showed a great alteration. Near grazing there was now a dark band in the spectrum of the reflected light as formerly described, and the effect was intensified when the polish affected loth faces. In the transmitted light the spectrum was shorn of blue and green, the limit coming down as grazing is approached — a consequence of the total reflexion of certain rays which then sets in. But at incidences far removed from grazing the place of equal index in the spectrum of the reflected light showed little weakening. A few days' standing (after polishing) in the air did not appear to alter the behaviour materially. On the same plate other bands were treated with hydrofluoric acid — commercial acid dilated to one-third. This seemed more effective than the putty-powder. At about 15° off grazing, the spectrum of the reflected light still showed some weakening in the ray of equal index. In the cell with parallel faces it is not possible to reduce the angle of incidence (reckoned from the normal) sufficiently, a circumstance which led me to revert to the 60° bottle-prism. A strip of glass half an inch wide could be inserted through the neck, and this width suffices for the observation of the reflected light. But I experienced some trouble in finding the light until I had made a calculation of the angles concerned. Supposing the plane of the -reflecting surface to be parallel to the base of the prism, let us call the angle of incidence upon it %, and let 6, </> be the angles which the ray makes with the normal to the faces, externally and internally, measured in each case towards the refracting angle of the prism. Then sin 0). = sn The smallest % occurs when 9 = 90°, in which case ^ = 18° 10'. This value cannot be actually attained, since the emergence would be grazing. If % = 90°, giving grazing reflexion, 0 = - 48° 36'. Again, if 0 = 0, % = 60° ;to have manifested themselves; but they did not. The reflected image showed little deficiency in the yellow, although the incidence was nearly grazing, while at moderate angles it was fairly bright and without colour. This considerable departure from Fresnel's laws could only be attributed to a not very thin superficial modification of the glass rendering it optically different from the interior.