70 THE INTERFEROMETRY OF 



and the corresponding displacement of c parallel to itself, since </ = 9o, 

 t = s tan <p'/2=s = 2e sin 5/2. 



If = Q39 / , ^ = 5 = 2^X0.81 = 1.62^. Thus if = 0.25 cm., = 0.4 cm., and 

 since t is twice the width of the patches or strips sliding over each other, the 

 width of this strip would be 0.2 cm. 



It is the sliding of the pencil b along the edge of P' which introduces addi- 

 tional path-differences whenever P' is not symmetrical and its edge not par- 

 allel to the plane a a'. It is probable also that the same restrictions as to 

 the breadth and depth of efficient wave-fronts will apply here as before ; but 

 this should be specially investigated. The nearly circular outline of the locus 

 of fringes, when spectra are both reversed and inverted in 36, even though 

 homogeneous light is in question in the last case, clearly points in this direction. 



34. Range of displacement varying with orientation of reflector P'. The 



displacement e of the mirrors M and N slides the corresponding pencil b 

 or b', figure 43, along the edge of the reflecting prism P', and a reason for 

 the rotation of fringes is thus easily at hand. It does not at once appear why 

 the right or the left displacement (y) of P' should also produce a rotation of 

 fringes ; for here the pencils b and b' remain collinear and there is no sliding. 

 It must thus be remembered, however, that the fringes are ultimately ellip- 

 tic ; for the axis parallel to the Fraunhof er lines is conditioned by the obliquity 

 of rays in this plane only, whereas the axis in the direction of the length of 

 spectrum depends on dispersion. The motion y of P' displaces these ellipses 

 bodily through the spectrum. Hence the fringes first appear at any given 

 Fraunhof er line in the form of hair-like striations parallel to it. These 

 enlarge and rotate to a maximum normal to the Fraunhofer line. In fact, a 

 single interference line may now run from end to end of the spectrum. There- 

 after the fringes vanish in symmetrically the same manner and are last seen 

 as fine striations parallel to the Fraunhofer line. It is possible, therefore, 

 that the sliding of pencils which accompanies the e displacement accounts 

 for the difference of values of x = ze cos 5/2 and 2y. 



Before discussing this question further it seemed necessary to study the 

 effect of different orientations of P' relative to the b b' rays. One may note, 

 preliminarily, that a rotation of M and N on a horizontal axis parallel to 

 their faces, or of P' on a horizontal axis parallel to its edge, also rotates the 

 fringes; but it seems probable that these motions are virtually equivalent to 

 a displacement, y, of the edge of the prism. 



The fringes may be seen in all focal planes, at least the long line parallel 

 to the length of spectrum. The others may often be restored by rotating the 

 grating. The marked occurrence of fringes in the narrow longitudinal gap 

 between two spectra (overlapping just removed by the rotation of M and N 

 on a horizontal axis) can possibly be explained in this way. These fringes in 

 the dark space are very sharp and luminous and seen in the principal focal 

 plane with the Fraunhofer lines. But it will usually be found that on draw- 

 ing the ocular out the separated spectra will overlap at their edges again, 



