single semi-cylinder of the given substance; the electric ray was refracted from the denser medium into air, and at the critical angle of incidence it underwent total reflection. The experiment was repeated with two semi-cylinders separated by a parallel air-space. With light waves an extremely thin air-film is effective in producing total reflection. But a question might arise whether waves a hundred thousand times as long would be totally reflected by films of air, and, if so, it would be interesting to find out the minimum thickness of air-space which would be effective in producing this result. This point was raised by Professor Lodge, at the discussion on my paper "On a Complete Apparatus for the Study of the Properties of Electric Waves," read before the Liverpool meeting of the British Association last year. I have for some time past been engaged in an investigation on this subject. The factors which are likely to determine the effective thickness of air-space for total reflection are: (1) the index of refraction of the refracting substance; (2) the angle of incidence; (3) the wave-length of the incident electric radiation. In the following investigation, I have studied the influence of the angle of incidence and of the wave-length in modifying the thickness of the effective air-space. The refracting substance used was glass.
I. Influence of the Angle of Incidence.
The great experimental difficulty in these investigations lies in the fact, that there is at present no receiver for electric radiation which is very sensitive, and at the same time strictly metrical in its indications. This difficulty is further complicated by the fact that the intensity of the electric radiation cannot be maintained absolutely constant. For these reasons, it is extremely difficult to compare the results obtained from different sets of observations. Attempts have been made in the following experiments to remove, to a certain extent, some of these difficulties.
Two semi-cylinders of glass, with a radius of 12·5 cm., were placed on the spectrometer circle. The plane faces were separated by a parallel air-space. The radiator was placed at the principal focus of one of the semi-cylinders; the rays emerged into the air-space as a parallel beam, and were focussed by the second semi-cylinder on the receiver placed opposite the radiator. Electric radiation was produced by oscillatory discharge between two small circular plates 1·2 cm. in diameter and an interposed platinum ball 0·97 cm. in diameter.
The two semi-cylinders were separated by an air-space 2 cm. in thickness; this thickness was found to be more than sufficient for total reflection. The critical angle for glass I found to be 29°. I commenced my experiments with an angle of incidence of 30°
