44 DISPLACEMENT INTERFEROMETRY BY 



when the micrometer mirror moves. Moreover, quite a narrow silt is pref- 

 erable, so that all the light reflected by the prism is that diffracted by the slit 

 and issuing in parallel rays from the objective. Any further light escapes 

 interference and blurs the fringes. The adjustment is not easy, as has 

 been shown in the earlier papers. It is necessary that the two rays mp 

 and np pass through the same vertical at p and additionally enter the tele- 

 scope at T in parallel. When this is the case and the path-difference is 

 annulled, the fringes are very black on the yellowish background of the spec- 

 trum near the D lines. In proportion as the rays separate into pT and qT, 

 the fringes become fainter and finally vanish. Near p, however, they may 

 be seen until they vanish at either elongation from smallness. Another 

 reason for this marked tendency to vanish is the fact that the slit -images 

 are mirror-images of each other. Hence if the slit -images are widened, even 

 when the strips of light seen at p coincide, there can only be a narrow vertical 

 region of actual coincidence of light of like origin. It follows, moreover, 

 that the achromatic fringes proper can not be produced with white light by 

 this method, though it is possible to produce the linear phenomenon with 

 white light when the ellipses are vertically centered. The experiment, 

 which is at first very difficult, will presently be treated. Movable fringes are 

 sometimes seen on the white slit-images. 



When first obtained the spectrum fringes are usually very fine parallel 

 lines. To bring the center of ellipses into the center of the field a plate- 

 glass compensator, capable of rotation on a horizontal axis, should be placed 

 either in the ray d or b, or on the other side, as the case may be. When the 

 compensator is set at the proper angle very dense black ellipses may be brought 

 into the center of the field by the micrometer screw or by the rotation of the 

 system Pn, figure 23. In fact, on using both of these displacements in a con- 

 trary sense (i. e., annulling the effect of slight displacements of the microm- 

 eter by a corresponding counter-displacement of rotation), the two beams 

 may be made to pass through p together and without path-difference. In 

 this case the ellipses are very strong. If both the mirrors at n and P are 

 displaced contrariwise but parallel to themselves this may also be done. 

 There is no such difficulty with the method of reversed rays. 



The following measurements were made as a rough test of the equations 

 given above. The constants of the apparatus were (fig. 4) 

 ^ = 62.3 cm. p = Pp=io.6 cm. 18 = 71.3 7 = 27.1 6 = 20 cm. 



the prism angle therefore being about 18.7 and the divergence of rays from 

 it 37.4. A much sharper prism than this would have been desirable, so the 

 d could have been larger, but none was at hand. The angle of incidence 

 here is (/3+7)/2 = 49.2. Hence 



2AWXQ.653 



- = 20 (o-947+0. 455) = 28. 



The procedure for the test of the equation consisted in establishing the 

 ellipses with the micrometer at n (reading N) , rotating the rail over a small 



