RESERVED AND NON-REVERSED SPECTRA. 41 



For the angles in question the usual equations are given: 



sin 6' - sin i = X/> sin 0" + sin i = \/D 



so that 



which is thus not quite independent of X unless i is very small. It is obvious 

 that the optic paths of a+d and c-\-k are identical. Hence the path-differences 

 of the rays r, s are the same. If now the grating G' is shifted to G'\, over the 

 distance e f , the same path-length is cut off from both r and s, and hence the 

 fringes do not move. The locus or strip of fringes, however, is displaced in 

 wave-length, bodily, as shown in figure 25. 



The equation in n\, which may be written (<5, a differential symbol) 



n\ = hd( i/cos 0) 20 (X/D+sinf) 



suggests the phenomena to be expected both when X is constant and i varies 

 and when i is constant and X varies. The former require a wide, the latter 

 a narrow slit. 



Some time after, with an improved micrometer, not directly manipulated 

 by hand, I obtained the following data from a succession of 50 small fringes 

 (arc lamp) : 



?Xio 3 = 3.7 3.9 4.0 4.1 4.2 cm 

 SeXio 6 =74 78 80 81 84 cm. 



Again, from successions of 30 large fringes: 



eXio~ 3 = 2.6 2.6 2.4 cm. 

 10-^ = 87 87 79 cm. 



All of these are below the value computed for sodium light, from imperfect 

 adjustment. The march of values in the first series is probably incidental, 

 for I was not able to eliminate the effects of flexure in my improvised 

 apparatus. Again, the precise symmetry of the apparatus is not guaranteed. 



Simple as the method appears in figure 25, it is in practice quite difficult 

 to control. Fringes may be lost and thereafter hard to find again, and this 

 in spite of the large range of displacement. The cause was eventually located 

 in the circumstances under which the incident pencil L strikes the grating G. 

 If L shifts to right or to left the symmetrical rhombus of figure 25 will be 

 converted into a non-symmetric rectangle or into a figure as in figure 26. 

 If G and G', M and N were rigorously parallel this should not produce any 

 effect; but as they are not and as the surfaces are not optically flat (film 

 gratings) the effect is very marked and probably of the same nature as a 

 rotation of G' on an axis normal to its face. It requires but slight displace- 

 ment of L to right or left to make fringes in the yellow change to hair-lines 

 in the green or the red; or they may even be lost altogether. These fine 

 fringes may sometimes be enlarged, at other times made smaller, by adding 

 or thickening (rotation) the compensator. Naturally in all these cases the 

 overlapping spectra are perfect. The only method of finding the fringes 



