Here is another verification of these results : if for the fourth index the mean value 1'42 is adopted, one works out that for an aluminium prism of 60°, the incidence giving the minimum deviation is 45° 19′, and that this deviation is 30° 38'; the observed deviation was 31° 10'. With the same incidence, the calculated deviation of the radiation, whose index is 167, is 57° 42'; the observed deviation was 56° 30′.

I now pass on to the determination of wave-lengths.

By means of the above-described arrangement for studying dispersion by the prism of 27° 15', refracted pencils are obtained, each of which is sensibly homogeneous. If we make the pencil we wish to study impinge on a second screen of wet cardboard, pierced with a slit 1'5 mm. wide, we can isolate a narrow portion of this pencil.

On the other hand, a piece of aluminium foil is fixed to the moving radial arm of a goniometer, so that its plane is normal to the arm; in this foil a slit is cut only o'07 mm. wide, and filled with phosphorescent calcium sulphide; the goniometer is arranged so that its

axis is exactly underneath the slit of the second wet cardboard. By turning the arm, the path of the pencil is exactly marked out, and one can verify that it is quite unique, and is accompanied by no lateral pencil, such as diffraction could eventually produce in the case of large wave-lengths.

A grating is then placed in front of the slit of the second wet cardboard (for instance, a Brunner grating of 200 lines per mm.). If, now, the emerging pencil is explored by turning the arm which bears the phosphorescent sulphide, the existence of a system of diffraction fringes is confirmed, just as with light, only these fringes are much closer together, and are sensibly equidistant. This already indicates that "N" rays have much shorter wave-lengths than luminous radiations.

The angular distance of the fringes, or what amounts to the same thing, the rotation of the arm corresponding to the passage of the phosphorescent slit from one luminous fringe to the next, is very small. It is therefore determined by the method of reflection, with the aid of a divided scale and telescope, a

plane-mirror being fixed to the arm. Moreover, one measures, not the distance between two consecutive fringes, but that between two symmetrical fringes of a high order-for example, that between the tenth fringe on the right, and the tenth fringe on the left. From these measures of angle, and from the number of lines per millimetre of the grating, the wave-length can be deduced by the known formula.

Each wave-length has been determined by three series of measures, effected with three gratings, having respectively 200, 100, and 50 lines per millimetre.

The following table exhibits the results of these measures :—

1.68 0'0146

0'0146

0'0176

1.85 0'0176 ΟΟΙΤΙ 0'0184

Being desirous of controlling these deter

minations by the use of a quite different method,

I had recourse to Newton's rings. These being produced, in yellow light, for instance, if one passes from one dark ring to the following, the variation of optical retardation in air is one wave-length of yellow light. If, now, with the same apparatus and the same incidence, rings are produced by means of "N" rays, and the number of these rings comprised between two dark rings in yellow light is counted, we shall obtain the number of times which the wavelength of "N" rays is contained in the wavelength of yellow light. This method, applied to rays of index 104, gave the values 00085 instead of 0.0081 found by the gratings; and for the index 185, the value o'017 instead of 00176. Though the ring method is inferior to the grating method, on account of the uncertainty attending the exact position of the dark rings in the experiment, an uncertainty which is due to the necessity of rendering these rings very wide, the concordance of the numbers obtained by the two methods constitutes a valuable control.

In the tables given above I have retained all the decimals occurring in the calculation of the

numbers deduced from observation. Although I cannot with certainty indicate the degree of approximation of the results, I believe, nevertheless, that the relative errors do not exceed 4 per cent.

The wave-lengths of "N" rays are much smaller than those of light. This is contrary to what I had imagined for a moment, and contrary to the determinations which M. Sagnac thought he had deduced from the position of the multiple images of a source, obtained with a quartz lens, images attributed by him to diffraction. I had previously observed that while polished mica lets "N" mica lets "N" rays pass, roughened mica stops them, and also that whereas polished glass reflects them regularly, ground glass diffuses them. These facts were already an indication that "N" rays could not have large wave-lengths. If we desire to study the transparency of a body, we must take care that the surface is well polished. Thus I had at first classed rock-salt amongst opaque substances, because the specimen I used, having been sawn from a large block, had remained unpolished; in reality, rock-salt is transparent.