GRATINGS IN THEORY AND PRACTICE 539 



ally 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: 



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



we may suppose that the ghosts corresponding to a i=~ will be visible 



a 50 



and those for - 1 = -^ very troublesome. The first error is a, = T Tnrinnnr 

 a 25 



in. and the second a^ = 5 0*0 o o in. Hence a periodic displacement of 

 one millionth of an inch will produce visible ghosts and one five hun- 

 dred thousandth of an inch will produce ghosts which are seen in the 

 second spectrum and are troublesome in the third. With very bright 

 spectra these might even be seen in the first spectrum. Indeed an over 

 exposed photographic plate would readily bring them out. 



When the error is very great, the primary line may be very faint or 

 disappear altogether, the ghosts to the number of twenty or fifty or 

 more being often more prominent than the original line. Thus, when 



bfia l = 2-405, 5-52, 8-65, etc. = 2*N -^ , 







the primary line disappears. When 



= 0, 3-83, 7-02, etc. = ZxN ^L , 



the ghosts of the first order will disappear. Indeed we can make any 

 ghost disappear by the proper amount of error. 

 Of course, in general 



r - 2 CM - 1) r j 



U n -- - t/ B _i /_> 



V 



Thus a table of ghosts can be formed readily and we may always tell 

 when the calculation is complete by taking the sum of the light and 

 finding unity. 



