32 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



(identical plates) in front and rear, so that the grating, etc., may be seen. A 

 convex mirror if placed at g reflects a beam of light, showing the pendulum to 

 be nearly stationary during the day, in spite of the surrounding city. The 

 slow normal variations were not greater than 5 mm. on a radius of 13 meters, 

 corresponding therefore to about 40 seconds of arc. The corresponding change 

 of inclination relative to the plumb-line would be less than one one-hundredth 

 of this, depending on the period given to the horizontal pendulum. 



The mass of the pendulum was 720 grams, that of the grating holder orig- 

 inally 475 grams, and that of the grating, etc., about 55 grams, making a total 

 of 1,250 grams; but these masses are to be much modified in the future. The 

 center of gravity, at G, with the grating in place, was originally about 80 cm. 

 from the axis AB. 



The grating at g moves between the two opaque mirrors, usually called M 

 and N, of the displacement interferometer, in the way shown in my earlier 

 work on interferometry. 



But these mirrors M and N must in the present case be identically concave, 

 silvered on their front faces, and at a distance equal to their common radius 

 of curvature from the center of the ruled face of the grating. This center is 

 illuminated by the impinging beam of light from the collimator, and the re- 

 turned beams, reflected from M and N, must pass through the same area of 

 illumination. In such a case the reflection at M and N is always normal to 

 those surfaces and the rotation of the grating does not interfere with the defi- 

 nition of the ellipses of the interference pattern. For any other distance of M 

 and N, except these radii of curvature, the spectra in the telescope will cease 

 to coincide horizontally on rotating the grating and the ellipses would at once 

 vanish. On the other hand, the displacement of the grating in arc at the end 

 of the arm of the horizontal pendulum is registered in amount by the shifting of 

 the ellipses in the interfering spectra. This displacement includes, of course 

 (as a small correction), the additional thickness of glass introduced by the 

 rotation of the grating. The displacement in question is the arc, which, when 

 referred to the axis of the horizontal pendulum, measures its angular devia- 

 tion resulting from the inclination of the earth's surface relatively to the 

 plumb-line. 



It is convenient to exhibit the details of the instrument (figs. 20 and 21) in 

 separate parts for convenience in drawing, these being superimposed in 

 practice. 



Fig. 20 shows the attachment of the two opaque mirrors M and N of the 

 interferometer to the pier P. Here abed is an ordinary framework of % -inch 

 gas-pipe. The end a is firmly plastered into the pier, b rises at a slight angle, 

 cd being horizontal and parallel to the pencil of light from the slit, while g 

 shows the position of the grating on the horizontal pendulum in fig. 19. The 

 arm b lies below the case in that figure and is free from it. Each of the mir- 

 rors M and N is on plane dot slot adjustments, and M is provided with a 

 Fraunhofer micrometer suggested in the figure. Both M and TV can be rotated 

 around horizontal and vertical axes for adjustment, the former M being pro- 



