REVERSED AND NON-REVERSED SPECTRA. 



143 



fore, for the centers of ellipses in the spectrum fringes the equation heretofore 

 deduced, 



r x dp 



i = e\(iJL i) cos R 



> 

 cos R dXJ 



where AN is the displacement of the micrometer to restore the center of 

 fringes to their original position in wave-length X, when the angle of incidence 

 at the mirror is i, after a glass plate of thickness e and index of refraction /z 

 is introduced in one component beam, at an angle of incidence corresponding 

 to the angle of refraction R in the plate. This is equivalent to an equation 

 in terms of the coordinates N, if n = A-{-B/\ 2 is assumed, 



2N cos i = en cos R+2eB/\ 2 cos R 

 But for the colors of thin plates we may write 



n\ = 2en cos R 



where n is the order of the fringe. If the rays, as in the present experiment, 

 do not retrace their paths, the factor 2 is omitted, whence 



zN cos i = n\-\-2eB/\ 2 cos R 

 Let N and n vary together, i, R, X, e, B, n remaining constant. Then 



2 cos i-AN = X-An 

 Now let A(p be the angular breadth of a fringe in the telescope, so that 



In other words, the displacement A0 of the group of fringes is due to the 

 displacement of the individual fringes as usual; but as only those achromatic 

 fringes which coincide in micrometer value A./V with the centers of the elliptic 

 spectrum fringes are visible, the displacement of the group is actually seen 

 and thus determinable. It would not be so in case of sudden displacement 

 and homogeneous light. 



Finally, the relative sensitiveness of the measurement of the angle A a, 

 directly in terms of AAT and indirectly in terms of the displacement of achro- 

 matic fringes, must be presented. The given rough data in table 38 are as 

 close as they could be obtained from the small displacements entering. The 

 quantities to be compared are: A/V, the displacement of the micrometer; A or, 

 the corresponding rotation of the auxiliary mirror in the first method ; A<p, 

 the angle subtended by a single fringe in the telescope, and A0, the corre- 

 sponding angle of the displacement of the fringes in the telescope. A0 was 

 constant throughout and measured about 3 mm. in the ocular of a telescope 

 33 cm. long. 



TABLE 38. Values of AJV, A9, A<p, Aa. All angles in radians, A./V in cm. 



