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 which undulations of the same nature arrive together or separate. If the periods of these returns are very rapid, a third sound is heard, the tone of which maybe calculated à priori from the epochs of coincidence; but if these happen so seldom as to be heard distinctly, and counted, the effect is a series of beats which succeed each other more or less rapidly. The mixture of two rays, which arrive together at the eye, under proper circumstances, produces an effect of the same kind, which Grimaldi remarked long ago, but of which Dr. Young first showed the numerous applications. The neatest way of exhibiting this phænomenon is the following, which is due to M. Fresnel.

A beam of sun-light, reflected into a fixed direction by a heliostat, is introduced into a darkened room; it is transmitted through a very powerful lens, which collects it almost into a single point at its focus. The rays diverging from thence form a cone of light within which there are placed, at the distance of two or three yards, two metallic mirrors inclined to each other at a very small angle, so that they receive the rays almost under the same angle; the observer places himself at a certain distance, so as to observe the reflexion of the luminous point in both the mirrors. There are thus seen two images separated by an angular interval which depends on the inclination of the two mirrors, their distances from the radiating point, and the place of the observer; but besides these, which is the essential point of the phænomenon, there may be seen, by the help of a strong magnifying lens, between the places of the two images, a series of luminous coloured fringes parallel to each other, and perpendicular to the line joining the images; if the incident light is simple, the fringes are of the colour of that light, and separated by dark intervals. Their direction depends solely on those of the mirrors, and not at all on any influence of the edges of those mirrors, as each of them may be turned round in its own plane without producing the slightest alteration in the phænomenon.

Let us confine our attention, for the sake of greater simplicity, to the case in which the incident light is homogeneous; this case may be easily exhibited in practice by observing the fringes through a coloured glass which will transmit only the rays of a particular tint. In this case if we select any one of the brilliant fringes formed