. Carnegie Institution of Washington publication. THE AID OF THE ACHROMATIC FRINGES. 21 A-/VXIO" A0X io3 (AAVA0)Xio» 2-5 620 500 4-4 2-4 57« 4-2 3-6 850 4-2 3-9 870 4-5 The mean value AN/A6 = agrees with the theoretical value X/2 cos « = 6Xio~5 = quite as well as the observations warrant. Another interesting application of measurement by g g fringes is shown in figure 6. This is concerned with the distance apart, 13, of two objects S and S' ((3 par- allel to 6), both at a distance d from the observer. In passing from 5 to S' the angles at the base b are in- crem
. Carnegie Institution of Washington publication. THE AID OF THE ACHROMATIC FRINGES. 21 A-/VXIO" A0X io3 (AAVA0)Xio» 2-5 620 500 4-4 2-4 57« 4-2 3-6 850 4-2 3-9 870 4-5 The mean value AN/A6 = agrees with the theoretical value X/2 cos « = 6Xio~5 = quite as well as the observations warrant. Another interesting application of measurement by g g fringes is shown in figure 6. This is concerned with the distance apart, 13, of two objects S and S' ((3 par- allel to 6), both at a distance d from the observer. In passing from 5 to S' the angles at the base b are in- cremented by 8ff and decremented by dcr', where if 5 is very distant relatively to b. But 2 8a = 8s; whence 8a = 8ff and fi = d . 8s = d . 8a. Since 2 Aa = cos i/R = ri\/R, we obtain finally. if n fringes correspond to 8a, or the passage from -^L S to 5'. Thus in case of the spire above, where d = 7 X io4 cm. or mile, about 120 fringes were counted in passing from one side to the other of a conspicuous ledge of rock. Hence, since 2/^ = cm., = 7Xio4 i2oX6Xio - 9-4 -5 = 54 cm. 9. Ellipses and hyperbolas. — The occurrences of spectrum ellipses and of hyperbolas, the rotation of fringes, centering of ellipses, etc., may be suffi- ciently explained as follows. Let the equation (i) n \ = 2e/j. cos r refer to the horizontal axis, x, passing through the center of ellipses in the field of the ocular of the telescope. Here n is the order of a given dark fringe in wave-length X, e the thickness, n the index of refraction, and i and r the angles of incidence and refraction, all referring to the half-silver plate. There is no compensator. In the vertical direction in the spectrum the light is homogeneous in X and the equation would be at the center upward or downward wX = 2^^cos /3 . . (2), if a and /3 are here the angles of incidence and of refraction (vertical plane). Since the angle a at least is very small, we may consider as an approximation that these equations hold t
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