534 HENRY A. ROWLAND 



or N _ la 3 a 5 a , 



" ~cT J ~~c\~ > TT" *"*" 



2 y, 2 y, 2 y, 

 Thus when = 2, the 1st, 3d, etc., spectra will disappear, making 



y\ 



a grating of twice the number of lines to the cm. 



When =4, the 2d, 6th, 10th, etc., spectra disappear. When 



y\ 



= 6, the 3d, 9th, etc., spectra disappear. 



y\ 



The case in which = 4, as Lord Rayleigh has shown, would be very 



y\ 



useful as the second spectrum disappears leaving the red of the first 

 and the ultra violet of the third without contamination by the second. 

 In this case two lines are ruled and two left out. This would be easy 

 to do but the advantages would hardly pay for the trouble owing to 

 the following reasons: Suppose the machine was ruling 20,000 lines 

 to the inch. Leaving out two lines and ruling two would reduce the 

 dispersion down to a grating with 5000 lines to the inch. Again, the 

 above theory assumes that the grooves do not overlap. Now I believe 

 that in nearly, if not all, gratings with 20,000 lines to the inch the 

 whole surface is cut away and the grooves overlap. This would cause 

 the second spectrum to appear again after all our trouble. 



Let the grooves be nearly equidistant, one being slightly displaced. 



In this case y t = ? -j- v - 



, Ny, I 7TJV i:Nv . nN ff 



cos 2 TT S3 = [ oos-s- cos - sin -4- am - 



a \ 2 a % 



For the even spectra this is very nearly unity, but for the odd it 

 becomes 



Hence the grating has its principal spectra like a grating of space ^ 



but there are still the intermediate spectra due to the space a, and of 

 intensities depending on the squares of the order of spectrum, and the 

 squares of the relative displacement, a law which I shall show applies 

 to the effect of all errors of the ruling. 



This particular effect was brought to my attention by trying to use 

 a tangent screw on the head of my dividing engine to rule a grating 

 with say 28,872 lines to the inch, when a single tooth gave only 14,436 

 to the inch. However carefully I ground the tangent screw I never was 



