8 DISPLACEMENT INTERFEROMETRY BY 



appropriately varied in accordance with the tests to be made on the plate g, 

 its shape, etc. Similarly, the set-screws h, h, h may be placed nearer together 

 or further apart in appropriate screw-sockets, and finally, the lever c may be 

 lengthened or shortened at pleasure. The pin e remains in permanent contact 

 with the plate g in consequence of a wide circular hole in the clip rr; or e may 

 clear rr, above or below it. 



If but one face of the plate g is to be tested, the system Ghrg must slide as a 

 whole, right and left, nearly parallel to the rays p, q. In such a case every- 

 thing will depend on the excellence of the slide carrying the system. I did 

 not attempt to make such arrangements, as I had no need of data of this kind ; 

 but the parts MM', AW, Fcmm', and Grg were nevertheless mounted on heavy 

 slides (lathe-bed fashion) for convenience in securing a variety of adjustments. 



In figure 3 the bar G has been reversed in position and the contact pin e 

 now passes through a circular hole in G, to be in contact with a lens g, for 

 instance, kept pressed to the tripod screws h, h, h in the same way as before. 

 The latter should in general be much closer together than the figure shows. 

 The instrument is now a spherometer. 



The experiments indicated that the mounting of the contact -pin e to the 

 extremity of the mirror mm' may be the occasion of annoyances ; for on sliding 

 g right and left, or even up and down, the mirror mm' is liable to be flexed. 

 In such a case the achromatic fringes rapidly lose sharpness, not to speak of 

 the errors involved. I endeavored to avoid this by keeping the pin e out of 

 contact with the plate g by a special lever (not shown) while g was being dis- 

 placed and to test a number of successive contacts thereafter; but it is best 

 (and I eventually did this) to mount e on a separate rigid cross-piece parallel 

 to mm' and firmly attached to c. In such a case no flexure of mm' can occur 

 and the contacts may also be repeated at pleasure. Before each reading the 

 bar G should be gently tapped. 



The achromatic fringes can be found only 

 through the spectrum fringes. This is not usu- 

 ally difficult, remembering that not only must 

 the slit-images in the spectrum be in contact 

 throughout, but the two beams must be locally 

 in contact on the mirror M'. Moreover, the 

 mirrors M' and N' must be equally thick and 

 the silvered faces all turned towards the auxil- 

 iary mirror mm'. 



2. Equations. If the mirrors At, M', etc., are set at an angle i, if the 

 deflection of the auxiliary mirror is 6, and if the breadth of the ray parallelo- 

 gram MM' or AW is b, we may write 



(i) 



where A./V is the displacement at the micrometer at M'. 



