of the spectrometer by a camera with a lens of long focus (176 cm.). Figs. II, III, and IV reproduce three photographs taken at three different angles of incidence, the reflecting strips in this case being 0.754 cm. wide and 1.446 cm. apart. In all the figures, the central fringe of the pattern is indicated by a small cross x. The asymmetry of the luminosity curve will be evident on comparing the brightness of the corresponding bands on either side of the central fringe; for instance, the second band on the right and the second band on the left in figs. II and III, or the first band on the right and the first band on the left in fig. IV.

The positions of the interference minima in the pattern are given by the formula of the usual type

where =(a+b) (sin i—sin 0)/λ, a being the width of each of the apertures, b their distance apart, and i, 0, λ having their usual significance. To test whether the formula holds good at the oblique incidences used, the negatives were measured under a travelling microscope. In photograph I, the distances between the successive interference minima were determined to find whether the relations

sin 01-sin 0,= sin 02-sin 03 = sin 03 - sin 04, &c., indicated by the formula were valid. The results are shown in Table I.

For photographs II, III, and IV, the actual values of for the interference minima were calculated from the known constants a, b, i, λ and compared with the observed values. These are shown in Tables II., III., and IV.

The Asymmetry of the Illumination-Curves.

As remarked above, there is a very marked difference in the luminosity of the corresponding bands on either side of the central fringe of the pattern due to the reflecting surface of two elements. Similar effects are also noticeable when the reflecting surface consists of three elements. Figs. V and VI in the Plate reproduce two photographs obtained with a reflecting surface consisting of three elements. The difference between the intensities of the 2nd principal maximum on either side of the central one is very evident in the reproductions and might be made out even in respect of the secondary maxima on either side. This asymmetry demands an explanation. As is shown by the measurements given in Tables I. to IV., the positions of the minima of illumination are in good agreement with those calculated from the formula of the usual type, which are obtained on the assumption that each of the elements into which the reflecting surface may be divided diffracts light strictly in proportion to its area, and that the phase and intensity of the disturbance incident on the surface are the same as when the waves travel undisturbed. Further, the intensities at the points of minimum illumination are shown by observation and by the photographs to be zero, in agreement with the results indicated by these formula. On the other hand, the difference in the intensity at corresponding points of the pattern on either side of the central fringe remains unexplained according to such formulæ unless regarded as an obliquity effect.

A series of comparisons of the intensities of corresponding bands on the two sides of the pattern has been made for the cases in which the reflecting surface consists of one, two, and three reflecting elements respectively, for various angles of incidence. For this purpose, I have used a rotatingsector photometer of the Abney type supplied by Messrs. Adam Hilger, in which the free disk, which can be adjusted by handle while in rotation, is smaller in radius than the fixed disk. The sectors when in rotation thus present two annuli of different intensities, the ratio of which can be adjusted at pleasure by moving the handle of the instrument. The disk of the photometer is placed at the focal plane of the observing telescope, so that the diffraction pattern can be seen through it with an eyepiece, the fringes on the brighter side being observed through the inner annulus of the disk, and those on the fainter side through the outer annulus. To enable the intensities at corresponding points on the two sides of the pattern to be compared, a screen with two vertical slits is interposed immediately in front of the photometric disk so as to cut off everything except the regions under observation, which are then adjusted to equality of brightness by moving the handle of the photometer. Several readings can be taken in succession and their average struck. The diffraction angles and ' of the two bands under comparison may then be measured under a micrometer eyepiece. Tables V., VI., and VII. show the observed ratios of the illumination and those calculated on the assumption that the formula for illumination includes a factor proportional to the square of the cosine of the obliquity. It is seen that the agreement is good except when the ratio is so large that it cannot be measured accurately, owing to the near approach of the fainter band towards the direct image of the slit.

TABLE V.

Single Reflecting Surface, width 0.90 cm.

Ratio of intensity of the first band on the right and
the first band on the left.

1. The unsymmetrical interference fringes of the light obliquely diffracted by two parallel reflecting surfaces in the same plane have been observed and photographed.

2. The illumination curve in the diffraction pattern (of the Fraunhofer class) due to an obliquely-held reflecting surface (which may consist of two or more separate parts in the same plane), is found to be markedly asymmetrical, corresponding points on either side of the central fringe being of very different intensities. As the positions of the points of minimum (i. e. zero) illumination are found to be in close agreement with those given by the formula of the usual type, the asymmetry of the illumination curve may be explained as due to the varying obliquity at different points in the diffraction pattern. Measurements of the ratio of the