in Theory and Practice. 411 



Places. 



' 2ttN 



Intensities. 

 J 2 (6/*a a ). 



Designations. 

 Primary lines. 



^ =fl± ba-o 



Ji 2 (^i%)- 



Ghosts of 1st order. 



_l 2 *i 



J 2 2 (^i« 2 ). 



Ghosts of 2nd order. 



3^ 



&c. 



J 3 2 (V 1 a 3 ). 

 &c. 



Ghosts of 3rd order. 

 &c. 



Hence the light which would have gone into the primary 

 line now goes to making the ghosts, so that the total light in 

 the line and its ghosts is the same as in the original without 

 ghosts. 



The relative intensities of the ghosts as compared with the 

 primary line is 



J 2 (&//,%) 



This for very weak ghosts of the first, second, third, &c. 

 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 displacement 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 diminish the 

 intensity of the ordinary spectral lines (primary lines) from 

 the intensity I to Jo 2 ^/^), and surround it with a sym- 

 metrical 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- 



