CHAPTER VI. 



THE DISPLACEMENT INTERFEROMETRY OF SMALL ANGLES AND OF LONG 

 DISTANCES. COMPLEMENTARY FRINGES. 



67. Parallel rays retracing their path. The following method was devised 

 with a view to the micrometric measurement of angles. It will be used else- 

 where in connection with an electrometer for reading microvolts. An inter- 

 ference method of a different kind for measuring small angles was developed 

 some time since and used at length in connection with the deviation of the 

 horizontal pendulum.* Again, the 

 electrometer was treated in different 

 wayst by the aid of the interferom- 

 eter. The present method, however, 

 will differ from all of these. In figure 

 88, L is a horizontal beam of white 

 light from a collimator after passing 

 through the auxiliary clear plate P 

 (to be used preliminarily for paral- 

 lelizing the mirrors of the system 

 in a way presently to be shown), 

 the beam is reflected at a and 6 by the half -silver plates H \ and Hi respect- 

 ively, to the wide opaque mirror in. The rays now retrace their paths 

 or nearly so, to be in turn transmitted at a and b by the half-silvers 

 Hi and H 2 . These transmitted pencils similarly impinge on the opaque mir- 

 ror M and the half-silver H 3 at c and d respectively, and pass thence (the ray 

 from c being transmitted) into the telescope at T. The direct-vision grating 

 prism g may be swiveled in place or removed at pleasure. 



To bring the system of four mirrors into complete parallelism is here of 

 considerable importance if the spectrum fringes or the achromatic phenomenon 

 are to be adequately large for measurement. The presence of the common 

 mirror m, however, suggests the procedure. When the clear plate P is in 

 place, the rays ae and bf on returning are also again reflected at a and b toward 

 L and may be clearly seen in a telescope at p. Hence if m is the standard 

 plane and nearly vertical, the mirrors Hi and H z will be parallel when the 

 slit images seen at p coincide horizontally and vertically, while H\,H%, and m 

 will have their common normal plane in the diagram. In the same way the 

 mirrors M and H 3 may be parallelized with their common normal plane in 

 the diagram. Again, the return rays aL and bL may be projected on the 

 objective of the collimator, or on a small screen near it, by correspondingly 

 focusing the collimator. The two sharp slit images are put in coincidence 



* Carnegie Inst. Wash. Pub. No. 229, 19 et seq., 1915. 

 130 



f Ibid., 67 et seq. 



