GRATINGS IN THEORY AND PRACTICE 



537 



CASE I. SINGLE PERIODIC ERROR 

 In this case only a and a^ exist. We have the formula 



Hence the expression for the intensity becomes 



sn n 



sin n 



Mo e l } 



+ etc. 



2 



J 



As n is large, this represents various very narrow spectral lines whose 

 light does not overlap and thus the different terms are independent of 

 each other. Indeed in obtaining this expression the products of quan- 

 tities have been neglected for this reason because one or the other is 

 zero at all points. These lines are all alike in relative distribution 

 of light and their intensities and positions are given by the following 

 table : 



Places. Intensities. Designations. 



Primary line 



Ghosts of 1st order. 

 Ghosts of 2d order. 



Ghosts of 3d order, 

 etc. etc. etc. 



= I* 



= ;*-E- 1 J.'QwJ 



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 



