﻿Changes in Di fraction Spectra. 29 



In the case of a wire grating, referred to later on p. 33, 

 the maximum of the dotted curve always coincides with the 

 central principal maximum, but in the echelon case the 

 relative position of the curves is not fixed, and any desired 

 part of the spectrum may be moved into the position where 

 the single aperture curve has its maximum, by a slight 

 rotation of the echelon. 



Position of the Secondary Maxima in the absence 

 of Aberration. 



If in plotting zero aberration amplitude curves the hori- 

 zontal scale of direction is N0, where N is the number of 

 apertures in the grating and 6 half the phase difference 

 between successive vectors for the given direction, then what- 

 ever the number of apertures in the gratings the curves will 

 all cut the horizontal axis at the same points. 



On plotting the zero aberration curves sin N0/N sin 6 for 

 gratings of nineteen and thirty- three apertures in this way 

 it was found that these curves coincided very closely with 

 one another, and with the sin N0/N0 curve drawn to represent 

 the case of a continuous wave-front or a grating with an 

 infinite number of apertures. 



As the curves agree so closely, we may say that for 

 diffraction gratings with nineteen or more apertures and free 

 from aberration, the relative intensity of the first three or 

 four secondary maximum on either side of principal maxima 

 and their distances from the principal maxima, expressed in 

 terms of the interval between consecutive points where the 

 intensity vanishes, are practically independent of the number 

 of apertures in the grating. 



In fig. 3, PI. III., the sin N#/N# curve has been drawn, 

 and it was found impossible to draw the zero aberration 

 curves for nineteen and thirty-three apertures because they 

 so nearly coincided with it. 



Changes in the Position of Primary and Secondary 

 Maxima produced by Aberration. 



An examination of the curves of fig. 1, PI. III., leads 

 to the following rough rules for the displacements of the 

 maxima: — A cubic aberration of the wave-front leaving a 

 diffraction grating displaces the secondaries farthest from 

 a primary maximum by approximately the same fraction of 

 a complete cycle of the amplitude curve that the aberration 

 between the centre and the outside of the wave-front is of 

 the wave-length, and shifts the primary maxima through 

 rather more than hall; this distance in the same direction. The 



