The London, Edinburgh and Dublin philosophical magazine and journal of science . and .-. PR = PQ*/\; and therefore that the whole system of fringes is moved late-rally by the same fraction of the width of a fringe as s is of X. Motion of the Earth and JEther. 21 Now this can be true only if the images are symmetrical withrespect to L, or if each wave-front is absolutely uniform incharacter. But in dealing with wave-fronts of light in con-nexion with interference we must be careful to conjoin theeffects of parts only of identical origin, as, for instance, that*of C with that of E, or that of 0
The London, Edinburgh and Dublin philosophical magazine and journal of science . and .-. PR = PQ*/\; and therefore that the whole system of fringes is moved late-rally by the same fraction of the width of a fringe as s is of X. Motion of the Earth and JEther. 21 Now this can be true only if the images are symmetrical withrespect to L, or if each wave-front is absolutely uniform incharacter. But in dealing with wave-fronts of light in con-nexion with interference we must be careful to conjoin theeffects of parts only of identical origin, as, for instance, that*of C with that of E, or that of 0 with that of 07 or that of Lin CD with that of L in EF. But in the actual experiments it is practically impossible tosecure that the two images intersect in a point that corre-sponds to itself as L does. In general we must assume thatthe two images CD and EF intersect under the conditionsrepresented in the next diagram (fig. 3), where 0 in EF andCK in CD are images of the same point in the original wave-front. Let 00 = c ; then if T is any point at distance x from 0 Fi°\ in EF, the corresponding point U in CD is at distancec + x from 0. Let us bisect FOD by AB, and find thevalue of x which determines a pair of corresponding pointsso that they are equidistant from a point whose polar coordi-nates relative to 0 and OB are r and 0. Denote the anodeFOB by a ; then the equality of PT and PU gives r2 + x2-2rxcos(6 + *) = r2+(c + x)2-2r(c + x)cos{0-u), (1) .*. 2x(c — 2r sin 6 sin a) — 2rc cos [6 — a) + c2 = 0 ;and treating a as a small angle 2x(c — 2rot sin 6) — 2rc cos 6 — 2rca sin 6 f cl = 0 r cos 6 by q, and r sin 0 by p, and then 2x(c — 2pa) +c(c—2pa) —2cg = 0. ... (2)In this equation first suppose that c — 2px = 0,then either c = 0 or ^ = 0. If c happens to be zero, then 28 Mr. W. Sutherland on the Relative either p = 0 or « = 0. The case of p=-§ is of no interest, andwith c = 0, a = 0 we have the case of absolutely coincidentimages with n
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
