42 THE INTERFEROMETRY OF 



after the parts are symmetrically placed relatively to the light is to move L 

 successively and gradually toward one side or the other and to test each 

 case with compensators i to 2 mm. thick, placed in the b or b' pencils. It 

 would be advisable to place the slit on a right-and-left micrometer. When 

 found, however, the fringes, if reasonably treated, are very persistent, strong, 

 and easily enlarged. 



Finally, the fore-and-aft motion of G' must produce a bodily shift of 

 fringes, while the strip as a whole is displaced in mean wave-length; for 

 figure 25 shows at once that if G' were displaced to G'\, the X rays bb' would 

 lose their coincidence in T, while that property would now be possessed by 

 the X' rays, dd'. If G' is on a fore-and-aft micrometer, therefore, one might 

 suppose a second method of interferometry to be available in which symmetry 

 is retained throughout and (since the angle at which the rays bb' meet is 

 5 = 20) subject to the equation 



n\ = ze' cos 5/2 = ze r cos 6 



where e' is the displacement corresponding to n fringes passing in wave- 

 length X. 



This equation, however, is inapplicable, as already explained, because the 

 pencils bb' are not reflected, but diffracted into T. In the symmetrical appa- 

 ratus, therefore, no perceptible motion of fringes is produced by the fore-and- 

 aft motion of G', because in all cases the rays bb' meet the grating with a 

 constant phase-difference. If the phases are identical they remain so while 

 G' is displaced. The strip of fringes as a whole, however, is slowly though 

 imperceptibly displaced through the spectrum, without accentuated motion 

 of the fringes within the strip. This inference was tested by placing G' on 

 a fore-and-aft micrometer. Large displacements of the screw (fractions of 

 a centimeter) shifted the strip from color to color as specified. A micrometric 

 displacement of G', however, was unaccompanied by any appreciable dis- 

 placement of fringes. On the other hand, any flexure of the supports of G' 

 at once produced a marked displacement of fringes, while from mere microm- 

 eter displacement no measurement could be obtained. 



Equation (i) is of interest in interferometry, in view of the very long 

 ranges of displacement available. For such purposes gratings of lower dis- 

 persion (preferably ruled gratings or else prisms) should be used, to obtain 

 greater luminous intensity in the spectrum. Of course, the gratings G and G' 

 may have different constants, but in such a case GNG'M will no longer be 

 a rhombus. Since for constant X the ray-lengths in figure 25 are constant 

 for all positions of G parallel to G', M parallel to N, large path-difference may 

 conveniently be introduced by compensators. If a thin sheet of mica is moved 

 in either the b or b' pencils, there is a lively skirmish of fringes, but they do 

 not change size appreciably. A glass plate 5 mm. or more thick placed in 

 both rays b and b' and rotated produces the same results, but the fringes move 

 more slowly. A plate 2.8 mm. thick, with strong fringes horizontal in the 

 yellow, if placed in the b f pencil produces hair-lines inclined toward the left 

 in the red; if placed in the b pencil, hair-lines inclined to the left in the green, 



