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1912] ON DEPARTURES FROM FRESNEL'S LAWS OF REFLEXION
drops are allowed to dry on, the effect is usually bad. Sometimes it is possible to shake the drops away sufficiently. After a successful operation of this sort wiping with an ordinarily clean cloth usually increases the minimum reflexion, and of course a touch with the finger, however prepared, is much worse. As the result of numerous trials I got the impression that the reflexion could not be reduced below a certain standard which left the flame still easily visible. Rotation of the diamond surface in its own plane seemed to be without effect.
During the last few months I have resumed these observations, using the same diamonds, but with such additions to the apparatus as are necessary for obtaining measures of the residual reflexion. Besides the polarizing nicol, there is required a quarter-wave mica plate and an analysing nicol, to be traversed successively by the light after reflexion, as described in my former papers. The analysing nicol is set alternately at angles /3 = ± 45°. At each of these angles extinction may be obtained by a suitable rotation of the polarizing nicol; and the observation consists in determining the angle a' — a between the two positions. Jamin's k, representing the ratio of reflected amplitudes for the two principal planes when light incident at the angle tan-I /j, is polarized at 45° to these planes, is equal to tan •£ (a! — a). The sign of a' — a is reversed when the mica is rotated through a right angle, and the absolute sign of k must be found independently.
Wiped with an ordinarily clean cloth, the diamond gave at first a — a = 2°'3. By various treatments this angle could be much reduced. There was no difficulty in getting down to 1°. On the whole the best results were obtained when the surface was finally wiped, or rather pressed repeatedly, upon sheet asbestos which had been ignited a few minutes earlier in the blowpipe flame; but they were not very consistent. The lowest reading was 00<4; and we may, I think, conclude that with a clean surface a — a would not exceed 00>5. No more than in the case of glass, did the effect seem sensitive to moisture, no appreciable difference being observable when chemically dried air played upon the surface. It is impossible to attain absolute certainty, but my impression is that the angle cannot be reduced much further. So long as it exceeds a few tenths of a degree, the paraffin flame is quite adequate as a source of light.
If we take for diamond a — a = 30', we get
k = tan £• (a! - a) = '0044.
Jamin's value for k is -019, corresponding more nearly with what I found for a merely wiped surface.
Similar observations have been made upon the face of a small dispersing prism which has been in my possession some 45 years. When first examined, it gave a' — a = 9°, or thereabouts. Treatment with rouge on a piece ofof a Welsbach mantle suffices; but, as was to be expected, the utilization of the whole number (ten)