Interference with Reflecting Gratings. 123 



The occurrences are in fact as follows : if, as in fig. 2, 

 i>Q (parallel white rays coming from L and U, R and R' 

 being reflected, D and D' diffracted rays for the normal n), 

 the grating g' must be in advance or forward of g. If now 

 the airspace e is reduced micrometrically, g' retreating, the 

 lines travel in a given direction (from left to right) through 

 the spectrum, while at the same time they grow continually 

 larger until for a minimum value of e still positive, they 

 vanish as a whole. The period of indistinctness before 

 •evanescence is not marked. 



On the other hand, if 6'>i, as in fig. 3, the grating // 

 must be to the rear of g and the airspace e is throughout 

 negative. If this is now decreased numerically the lines 

 travel through the spectrum in the opposite direction to the 

 preceding case, while at the same time they coarsen until 

 they vanish as a whole, as before. The grating g' is still 

 behind g when this occurs. 



Finally, if for any suitable value of e the grating g' is 

 moved in its own plane without rotation away from g, so as 

 to widen the crack at S between them, the fringes grow 

 continually finer until they pass beyond visibility, and vice 

 versa ; i. e. } as the crack at S is made smaller the lines 

 continually coarsen. 



5. Nature of the Evanescence. — The fact that the lines 

 vanish as a whole and almost suddenly after reaching their 

 maximum distance apart is very peculiar, as is also the fact 

 that they cannot be passed through infinite size or appear 

 symmetrically on both sides of this adjustment. To investi- 

 gate this case I provided both the collimator and the telescope 

 with slits so that the parts of the grating g and g from which 

 the interfering pencils come might be investigated. 



If a single vertical slit about 1 mm. wide is passed from 

 right to left towards the objective of the telescope, a black 

 line passes across the field of the spectrum, which line is 

 merely the image of the crack at S. Let the green rays, for 

 instance, come from the edge of both gratings g and g' , 

 whereas the red rays and the violet rays come from but a 

 single grating. Now when the space e is diminished, the 

 black band in the green gradually vanishes, and in its 

 place appear the coarsest fringes producible. When the 

 slit F is removed these coarse fringes disappear. The fringes 

 visible through the slit have, however, both an inferior and 

 superior limit in e and in angular size. When e is diminished 

 to zero they vanish and when e is sufficiently increased they 

 again vanish, though they now appear when the slit is either 

 removed or widened. From this it follows that the coarsest 



