412 Prof. Henry A. Rowland on Gratings 



engine with a large number of teeth in the head of the screw, 

 we shall have 



J l 2 ba 1 ( f i+ ^ + J 1 2 ba 1 (^fi- ^\ = 2J 1 2 ba 1 p nearly. 



Hence the total light is by a known theorem, 



J 2 + 2[J 1 2 + J 2 2 + &c.] = l. 



Thus, in all gratings, the intensity of the ghosts as well as 

 the diffused light increases rapidly with the order of the 

 spectrum. This is often marked in gratings showing too 

 much crystalline structure. For the ruling brings out the 

 structure and causes local difference of ruling which is 

 equivalent to error of ruling as far as diffused light is con- 

 cerned. 



For these reasons it is best to get denning power by using 

 broad gratings and a low order of spectra, although the 

 increased perfection of the smaller gratings makes up for this 

 effect in some respects. 



There is seldom advantage in making both the angle of 

 incidence and diffraction more than 45°, but if the angle of 

 incidence is 0, the other angle may be 60°, or even 70°, as in 

 concave gratings. Both theory and practice agree in these 

 statements. 



Ghosts are particularly objectionable in photographic 

 plates, especially when they are exposed very long. In this 

 case ghosts may be brought out which would be scarcely 

 visible to the eye. 



As a special case, take the following numerical results : — 



N = 1. 2. 3. 



a, _ 1_ vl J_ 111 1 1_ 1 



a n 25' 50' 100" 25' 50' 100' 25' 50' 100" 



, 



K) 2 4> 



_L J— JL i_ _L Hi_ 



252' 1008' 16' 63' 252' V 28' 102* 



In a grating with 20,000 lines to the inch, using the third 

 spectrum, we may suppose that the ghosts corresponding to 



— = tt\ ^iU De visible and those for — = ^ very trouble- 



a 50 a 2o J 



