Page:Collected Physical Papers.djvu/82

62 index reading being now B. The difference of the two readings evidently gives twice the critical angle. The angle is repeated by clamping down the index and rotating the circle as a whole for total reflection in the direction of the upper arrow. The process may thus be repeated, the rotation of the platform in one direction being followed by the rotation of the circle in an opposite direction. There is thus produced at each operation a relative displacement of the index (in reference to the circle) through twice the critical angle. The value of i is by this means obtained with great accuracy, the errors due to eccentricity or defect in graduation being eliminated by repeating the angles n times where 2 ni is as near as possible equal to four right angles or any multiple of four right angles. If R be the difference between the first (zero) and the last readings, the critical angle $$i=\frac{R}{2n}$$. It is evident that by merely increasing n, the value of i could be obtained with any degree of accuracy, even with circles graduated only into degrees.

The index is fixed at the beginning against the zero of scale. It is therefore only necessary to take one final reading, and count the number of repetitions. A complete determination could thus be made in the course of a few minutes.

The air-film, as has been said before, should be placed in the vertical plane dividing the cylinder into two halves. This is more easily accomplished by suspending a metallic plate on knife edges, from V grooves cut at the ends of a diameter of the upper end of the cylinder. The plate remains vertical under the action of gravity. A central slit is cut in this plate; on opposite