GRATINGS IN THEORY AND PRACTICE 535 



able to entirely eliminate the intermediate spectra due to 14,436 lines, 

 and make a pure spectrum due to 28,872 lines to the inch, although I 

 could nearly succeed. 



EXAMPLE 3. ONE GROOVE IN m MISPLACED 



Let the space a contain m grooves equidistant except one which is 

 displaced a distance v. The displacement is now proportional to 



Multiplying this by itself with i in place of -+- i, and adding the 

 factors in the intensity, we have the whole expression for the intensity. 

 One of the terms entering the expression will be 



sm 



sin^ sin** 

 2m 2 



Now the first two terms have finite values only around the points 



_^= rw^Vrr, where mN is a whole number. But 2p m -\- 1 is also a 

 2 



whole number, and hence the last term is zero at these points. Hence 

 the term vanishes and leaves the intensity, omitting the groove factor, 



baa . . ba 



sin ~ sin* - 



2 in 2 



The first term gives the principal spectra as due to a grating space 

 of and number of lines nm as if the grating were perfect. The last 



term gives entirely new spectra due to the grating space, a, and with 

 lines of breadth due to a grating of n lines and intensities equal to 



Hence, when the tangent screw is used on my machine for 14,436 

 lines to the inch, there will still be present weak spectra due to the 

 14,436 spacing although I should rule say 400 lines to the mm. This 

 I have practically observed also. 



The same law holds as before that the relative intensity in these 



