34 DISPLACEMENT INTERFEROMETRY BY 



and at right angles to its former position. Hence the normal displacement is 

 e = (b" b) sin 0/2 . The angle of incidence is i = 90 - (13/2 - a) . Thus the 

 path-difference here to be deducted is 2 e cos i or 



2 (6" -b) sin 0/2 . sin (0 ) = (&" 6) (cos a cos(0 a)) 

 and the total deduction from both sides is therefore 



(&" &) (cos a cos 5) + 2 (6 6') (cos a+cos a} 

 This expression when reduced gives for small a 



zba (cot a cot 0/sin 0) 



or more simply 



2ba cot 



It is practically as large as the total path-difference for reversed rays found 

 above. If, therefore, the two effects are opposite in sign, the path-difference 

 introduced by rotation would be zero, apart from the change of glass paths 

 and second-order effects which are relatively small. In fact, the experiments 

 show that the rotational effect, Aa, in case of reversed rays, is relatively 

 negligible as compared with the effect in case of rays not reversed. In other 

 words, if from the equation for direct rays 



ri\ = 2ba (i/sin 0+cot 0) 

 we deduct 



. . , . , / / \ a \ 

 2X-\-2e cos i-\-2e cos ^ = 2ba (i/sin 0-)-cot 0) 



the right-hand member vanishes to the second order of small quantities. 



18. Observations. Prism=prism method. In this case (fig. 19 below) a 

 sharp-angled prism at S, with its knife-edge vertical, cleaves the beam 

 of white light issuing from a collimator, reflecting the beams d and d' as 

 described in my earlier papers. The system should be leveled so that all 

 corresponding rays lie in a horizontal plane. By making the strips of light 

 on both mirrors m and n (figs. 13, 14) coincide horizontally and vertically 

 (using an auxiliary lens, if necessary) and then placing the prism P so that 

 the rays mP and nP all but escape at its edge, the adjustment may be com- 

 pleted by aid of the telescope at T. The two slit-images, which should be 

 equally bright, are made to coincide horizontally and vertically by the ad- 

 justment screws on m and n. If now the direct-vision spectroscope (prism 

 grating) is swiveled in front of the objective of T, fringes will usually appear 

 when the path-difference is annulled. For this purpose the prism P is placed 

 on a Fraunhofer micrometer with the screw in the direction mn. The spec- 

 trum fringes are as a rule easily found and are quite strong, but they can not 

 be centered in the field of view, for the occurrence of ellipses presupposes 

 the rigorous superposition of the two strips of light on the edge of the prism P, 

 which is not possible. The fringes, if too oblique, may be erected by a plate 

 compensator with a horizontal axis, or the prism P may be rotated on a 

 horizontal axis. Vertical spectrum fringes are not usually wanted in these 

 experiments, for they are to serve only as an essential aid to finding the 

 achromatic fringes. 



