REVERSED AND NON-REVERSED SPECTRA. 83 



will be visible within a certain range of path-difference. If one spectrum 

 shrinks longitudinally on the other, the strip carrying fringes rapidly dimin- 

 ishes in breadth; but interference is still marked near the transverse line of 

 coincident wave-lengths. If one spectrum is reversed with reference to the 

 other on a transverse axis, the interferences are reduced to a single nearly 

 linear strip coincident with the line of symmetry. The width of this strip 

 is independent of the dispersion of the system. It depends on the breadth of 

 colored region which contributes rays to the strip in question. Hence, if, 

 beginning with both ends of the spectrum, rays are cut off except those very 

 near the line of symmetry, the linear phenomenon rapidly increases in size 

 until all light is extinguished. This is what one would expect from the 

 theory of the diffraction of wave-fronts broad or slender, with the generaliza- 

 tion as to the rotation of fringes to which I have already referred. 



The association of the two diffractions is well illustrated by the experiments 

 with inverted spectra. Here the edge of the reflecting prism is horizontal 

 and normal to the interfering beams. When this edge is moved normal to 

 itself, path-difference only is introduced. To compensate a plate 0.434 cm. 

 thick the motion should be about 0.243 c* 11 - The displacement found was 

 27 = 0.247 cm., the difference being referable to insufficiently accurate dis- 

 persive constants. When either of the opaque mirrors moves, the correspond- 

 ing beam slides along the edge of the prism and the displacement 2^ = 0.370 

 cm. of mirror was found, corresponding to the path-difference x = 2e cos 5/2 = 

 0.282 cm. About 14 per cent more path-difference is thus needed with sliding 

 (x) than without (27). 



If now the reflecting prism is turned 90, so that the edge is vertical, the 

 corresponding beams slide normally to or from the edge of the prism when 

 the opaque mirrors are moved. The corresponding data were then found to 

 be 27 = 0.250 cm., # = 0.235 crfi - Here about 6 per cent less path-difference 

 is needed with sliding (x) than without (27). The smaller effect in the latter 

 case is to be expected, since the two corresponding rays slide toward each 

 other in the same plane and can not pass through each other. In the former 

 case they pass in marked degree across or through each other and must there- 

 fore essentially contribute to the rotation of fringes. But the sign of the 

 effect is precisely the opposite to what one would expect. Investigations such 

 as these and the corresponding question of the width of strip carrying inter- 

 ference fringes in case of crossed rays call for apparatus with better optical 

 plate, or for more rigorous instrumental adjustment than I have been able 

 to utilize in the present papers. It is best, therefore, to waive them for the 

 present, however interesting the theoretical results with which they are 

 associated.* 



* I have since treated the outstanding difficulties of the text rigorously and the results 

 will be given in a future report. 



