432 C. Barns — Interference of Reversed Spectra. 



and the details are not yet clear in my mind. Thus in fig. 12, 

 if G' is oblique at an angle $, as at g\ path excess on the right 

 in the case <?/ becomes path deficiency in case g/. Hence 

 also a rotation, <£, of the grating around a vertical axis has the 

 same effect as a fore and aft motion along the normal axis. 



Returning to fig. 12 and the positions G/ or G„' of the grat- 

 ing, there is clearly path difference not only virtually for the 

 rays distributed in the vertical plane, but also for those dis- 

 tributed in the horizontal plane, because the pencils (b,b f ; c,c') 

 are separated and in case of a wide slit and oblique incidence 

 reach the focal plane or lens or mirror obliquely. The result 

 must therefore, in case of a wide slit, be a set of fringes due to 

 pencils of parallel rays obliquely to the grating. The central 

 region a of the grating G' is found on inspection to be yellow 

 in the position G', red in the position G/, and green in the 

 position 6V 



. From this point of view the vertical fringes for the cases bb' 

 or cc' are Fresnellian interferences, superimposed on whatever 

 phase difference arrives at these points. If c is the effective 

 width at the concave grating it may be shown that for 

 c = 1-6 cm., X = 6 X 10- 5 cm., dO = 3*7 X 10' 5 , or about 8" of 

 arc. 



The corresponding deviation d0 D equivalent to d\ D of the 

 JD^D^ lines would be (if the grating space is D = 173 X 10~" cm. 

 = 20°, nearly the normal deviations for yellow light), 



d0 D = 3-7 X 10- 4 . 



or, in this special case, there would be ten hair lines to the 

 D X D^ space. As c is smaller or larger, there would be more or 

 less lines. This is about the actual state of the case as 

 observed. Finally if c is very small, the fringes are large. 



To resume the evidence thus far obtained we may therefore 

 assert that in the case of homogeneous light and a wide slit, or 

 the absence of a slit, the field would either be bright or dark, 

 as a whole. There is a single enormous horizontal fringe in 

 the field. Hence the pronounced flickering with half wave 

 length displacements of any part of the apparatus. With the 

 slit narrowed until the Fraunhofer lines are seen sharply, the 

 linear phenomenon in question appears. This may become 

 ladder-like ; but it always remains very narrow (1/3 X D X D^) 

 when the rulings of the two gratings are not quite parallel. 



Furthermore the linear phenomena sometimes shows a 

 behavior that suggests probable relations to the Fresnellian 

 interferences, produced however not within the telescope (for 



