888 Profs. Trowbridge and Wood on Groove-Form . 



wave-fronts reflected from the oblique edges of the grooves. 

 As Lord Rayleigh has pointed out, this method holds only 

 when the width of* the groove considerably exceeds the wave- 

 length of the light. 



In the present case, with our closest ruling, the groove- 

 width was 1*5 times the wave-length of our longest waves, 

 and it appears probable that in this case we are very near, 

 if not beyond the point, at which we may safely employ the 

 Fresnel treatment. 



In continuing the work it is our intention to employ 

 waves of continually increasing wave-length, until the 

 point is reached at which the spectra disappear entirely, 

 whi.h will give us the complete experimental solution of 

 each case. 



In the ease of the echelette grating the conditions are 

 quite different from tho>e which obtain in the case of the 

 gratings usually considered, which act by opacity. For a 

 wire grating, or a reflecting grating made by ruling black 

 lines on ;i reflecting surface, the spectra of even order fall 

 out when the widths of the operative and inoperative elements 

 are equal. In tint ease of the echelette grating, practically 

 the whole surface is operative, and if we place the eye, or 

 better the objective of a microscope (focussed upon the 

 grooves in the direction of a spectrum) we see a uniform 

 blaze of light illuminating the entire surface. This means 

 that the widths of the reflected elements of the wave-front 

 are twice as wide as in the ease of a grating of the opaque 

 type having the same constant. 



Now in a grating of this type the spectra of even order 

 disappear when a = b, as a result of the circumstance that in 

 the directions of these spectra each diffracted wave front is 

 self destructive, i. e. these directions are the directions of 

 Fraunhofer's minima of the first class, namely such as will 

 make the path difference between the disturbances coming 

 from the two edges of each reflecting element equal to the 

 w r ave-length of light. In the case of the reflecting grating 

 with its opaque strips, if we widen the reflecting strips and 

 narrow the opaque ones, keeping the constant the same, the 

 direction of the first class minima will move in towards the 

 first order spectra, which will disappear when the opaque 

 strips become infinitely narrow. The same thing, however, 

 holds for all the other spectra, for as we widen the reflecting 

 strip the first class minima draw closer together, coinciding 

 with the spectra of the second class (grating spectra) in the 

 limiting case of opaque lines infinitely n irrovv. Jf, however, 

 we narrow the reflecting strips, keeping the grating space 



