4d2 Astronomical and Nauiical Collections, 



of the next bright stripe on either side, the middle points 

 of the other stripes will correspond to the differences 2 d, 

 3d, 4df 5d, 6 d, and so forth ; while the middle points 

 of the dark stripes, from the jfirst to the most remote, corre- 

 spond successively to differences in the routes, expressed by 

 id, f rf, ^d, |c?, and so forth. 



Hence it follows, that the union of the rays produces the 

 maximum of light, when the difference of the paths, which 

 ihey have described, amounts to 0, d, 2d, 3d, 4:d, 5 d, 

 and so forth ; and that, on the contrary, they neutralise 

 each other, and produce darkness only, when this difference 

 is equal to ^, ^d, ^d, |^, %d, ^d, and so forth. Such 

 is the general law of the periodical influences which the rays 

 of light exert on each other. 



When the two luminous pencils are of equal intensity, as 

 in the experiment just described, the middle of the dark 

 stripes exhibits a total absence of light, at least in the fringes 

 of the first and second, and even of the third order, if the 

 light employed is sufficiently homogeneous; but, as it is never 

 completely so, it happens that the inequality of brightness 

 of the dark and light stripes, which is so prominent in the 

 first fringes, diminishes gradually as we go further from the 

 middle, and at a certain distance becomes insensible. The 

 reason is easily understood ; the light employed, however 

 simple it may have been rendered, either by decomposition 

 in a prism, or by its passage through a coloured glass, is 

 always composed of heterogeneous rays, of which the colour 

 and the physical properties differ but very little, although 

 the period of interference has not precisely the same length: 

 hence it arises, that the dark and bright stripes, of which 

 the situation depends on the period, are not separated by 

 precisely the same intervals. In truth, the breadths of the 

 fringes, produced by the heterogeneous rays, differ so much 

 the less, as the light employed approaches the more to per- 

 fect homogeneity ; but however small this difference may be, 

 it may be imagined, that, when repeated a great number of 

 times, it will at last produce such a difference in the situa- 

 tion of the fringes, that the dark stripes of some of them 

 will coincide with the bright stripes of others ; so that at a 



