REVERSED AND NON-REVERSED SPECTRA. 43 



etc. In contrast with this, the shift from red to green, if produced without 

 compensator by the displacement of M, shows scarcely any change of fringes, 

 either as to size or inclination. 



To change the size of fringes it is necessary to rotate the grating G' (rela- 

 tively to G] on a horizontal axis normal to itself. They then both rotate 

 and grow larger, attaining the maximum of size when the fringes are vertical. 

 Fringes quite large and black, which are naturally much more sensitive to 

 compensators, may be obtained in this way; but the fringes are still easily con- 

 trolled by hand. Limitations of the incident light in breadth, or simultaneous 

 rotation of M and N, produced no marked effects. 



Fringes may also be enlarged on moving the collimator with slit micro- 

 metrically right or left, as already stated, though this must be done with 

 caution, as the effects are often surprisingly abrupt; for when the system 

 is not quite symmetric displacements on G will be equivalent to accentuated 

 displacement on G', owing to the reflections. The reflected rays soon cease 

 to intersect and the displacement on M and N is invariably large. Further- 

 more, by the insertion of compensators (glass plates i to 2 mm. thick) in 

 the b or b' pencils, either directly or differentially, larger or smaller fringes 

 may be obtained. 



It is now of interest to return to the equation referring to the displacement 

 of G', normal to itself, and to consider the resolving power of the system ; for 

 the latter bears a close analogy to the experiments made in a preceding 

 paper (Carnegie Inst. Wash. Pub. 249, Chap. V, 1916) on the remarkable 

 behavior of crossed rays. If G' is displaced to G'\ over a distance e' = dh (see 

 fig. 25, where h is the distance apart of G and G r ), the rays X' meeting in T 

 will now be in the same condition as were originally the rays X. In other 

 words, e\ and e\ have become coincident at G', If we assume that the same 

 type of fringe results in these cases, and if X' X = dX, 6 0' = dd (for the 

 passage of bb' into dd' is in the direction from red to violet), 



(2) dd=dh sin 6 cos 6/h, nearly 



Since X =D sin 6 and d\= D cos 6 dd, this may be changed to 



(3) d\/\ = dh(i-\ 2 /D*)/h 



when D is the grating constant. This is the expression used heretofore. 



In general it is to be noted that the present method, apart from any prac- 

 tical outcome, is of great interest as to the data it will furnish of the width 

 of the strip of spectrum carrying interference fringes under any given con- 

 ditions. For here the spectra are not reversed or inverted and the latitude 

 of interference of diffraction throughout X is much broader than in case of 

 reversed spectra. But for this purpose films will not suffice and rigid refracting 

 systems must be devised. 



20. The same, continued. Homogeneous light. Dissimilar gratings. To 



show the close relation of the present experiments with one reflection to the 



