ON THE COLOURS OF THICK PLATES.         193
the two diffractions. We may represent the phases of the four vibrations by 9 4- % + «, 0 + %, 6 4- o>, 0, respectively. Writing down for greater clearness the phases along with the symbols of the vibrations, we may express the resultant of the whole four vibrations by
Moreover, on account of the similarity of the two diffractions, the coefficients of the two vibrations J, J may be supposed equal to each other, and likewise those of the vibrations /', J '. It is true that the diffractions take place at different distances from the source of light, on account of the finite thickness of the glass, but the difference of distance compared with either of the absolute distances is a small quantity of the order t, which may be neglected. Hence the two resultants / + /', J+J' belong to a diffraction ring of the same kind, arid in fact differ in nothing but in phase ; the phase of the former exceeding that of the latter by %. Hence the two kinds of interference go on independently of each other. It is true that in the preceding reasoning we have considered only two interfering streams J, I', and that in calculations of diffraction we have to consider the resultant of an infinite number of streams. But the same reasoning would evidently hold good whatever were the number of streams /, J', I" ... with their correspondents J, J', J" ...
35. When an irregular powder, or anything of the kind, is used to scatter the light, no diffraction rings are visible, because a given point M in the plane of the rings would belong to a diffraction ring of one kind so far as one particle of dust was concerned, and to a diffraction ring of another kind so far as another such particle was concerned ; and therefore nothing is seen but the interference rings belonging to thick plates. But when lycopodium seed is used the lycopodium rings and the interference rings are seen together. The former are always arranged symmetrically around the image, as ought to be the case, since they depend only on the angle of diffraction, which is the same for all points of a circle described round L_3 as a centre. By this circumstance they are at once distinguished from the latter, the centre of which falls half way between the luminous point and its image. On scattering some lycopodium seed on a concave mirror, and placing a small flame near the centre of curvature, at such a distance laterally s. in.                                                                         13