538 HENRY A. ROWLAND 



This for very weak ghosts of the first, second, third, etc., order, 

 becomes 



The intensity of the ghosts of the first order varies as the square of 

 the order of the spectrum and as the square of the relative displace- 

 ment as compared with the grating space a . This is the same law as 

 we before found for other errors of ruling, and it is easy to prove that 

 it is general. Hence 



The effect of small errors of ruling is to produce diffused light around 

 the spectral lines. This diffused light is subtracted from the light of the 

 primary line, and its comparative amount varies as the square of the 

 relative error of ruling and the square of the order of the spectrum. 



Thus the effect of the periodic error is to dimmish the intensity of 

 the ordinary spectral lines (primary lines) from the intensity 1 to 

 t7 2 (fy" a i)j and surround it with a symmetrical system of lines called 

 ghosts, whose intensities are given above. 



When the ghosts are very near the primary line, as they nearly always 

 are in ordinary gratings ruled on a dividing engine with a large number 

 of teeth in the head of the screw, we shall have 



f- + A) + Jftai (f* j^} = IJfta^ nearly. 

 oaj \ baj 



Hence the total light is by a known theorem, 



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 

 concerned. 



For these reasons it is best to get defining power by using broad 

 gratings and a low order of spectra although the increased perfection of 

 the smaller gratings makes up for this defect 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, especi- 



