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 the two images, we may calculate the directions and paths of the luminous rays which form that fringe coming from each of the mirrors. Now in making this calculation, we find the following results:

(1.) The middle of the space comprised between the two luminous points is occupied by a band of colour formed by rays the lengths of whose paths from the luminous point to the eye are equal.

(2.) The first fringe on each side of this is formed by rays for which the difference of length is constant, and equal for instance to l.

(3.) The second coloured fringe arises from the rays having 2l for the difference of the distances they pass over.

(4.) In general for each fringe this difference is one of the terms of the series 0, l, 2l, 3l, 4l, &c.

(5.) The intermediate dark spaces are formed by rays for which the differences are $1⁄2l$, $3⁄2l$, $5⁄2l$, &c.

(6.) Lastly, the numerical value of l is exactly four times that of the length which Newton assigns to the fit for the particular kind of light considered.

The analogy between these laws and those of the rings is evident. The following is the explanation given of them in the system of undulations: the interval l is precisely equal to the length of a luminous wave, that is, to the distance of those points in the luminiferous ether, which, in the succession of the waves, are at the same moment in similar situations as to their motion. When the paths of two rays which interfere with one another differ exactly by half this quantity at the place where they cross, they bring together contrary motions of which the phases are exactly alike. Moreover the motions produced by these partial undulations take place almost along the same line, as the mutual inclination of the mirrors is supposed to be very small. Consequently the two motions destroy one another, the point of ether at which they meet remains at rest, and the eye receives no sensation of light. The same thing must occur at those points where the differences of the spaces passed over by the rays is $3⁄2l$, $5⁄2l$, or any