﻿Changes in Diffraction Spectra. 31 



The \X aberration curve drawn in fig. 3, PL TIT., is 

 intended to show the relative displacement of the primary 

 and secondary maxima. The total difference of phase between 

 the centre and outside of the wave -front is taken as the 

 horizontal coordinate, 90° for the \\ aberration being sub- 

 tracted from N0, the difference of phase corresponding to 

 the direction in the absence of aberration. When the curves 

 for various degrees of aberration are plotted in this way the 

 distant secondaries are only slightly shifted by the aberra- 

 tion, their relative displacement being represented by the 

 movement of the principal maximum to the left. 



The values given by Lord Rayleigh* for a continuous 

 wave-front with \\ aberration are also plotted in fig. 3, 

 PI. Til., for comparison with the curves for finite numbers of 

 apertures. 



When aberration is present the effect of the number of 

 apertures on the position of the secondaries is increased. 

 Table I. shows the effect of changing the number of apertures 

 from nineteen to thirty-three. 



The displacements of the secondary maxima, brightened 

 by the aberration, away from the primary (given in Table I.) 

 may be emploved to determine the amount of aberration 

 present in a diffraction spectrum if a photograph showing a 

 few secondary maxima can be obtained. Fig. 3, PI. IV., is 

 reproduced from a photograph of the green mercury line 

 54G1 a, taken with the 33 aperture echelon we have employed, 

 which has been already described t. This photograph shows 

 secondary maxima on the right of the spectrum lines, and 

 six secondaries of the line 1 w r ere measured in the open 

 space between the lines 1 and 2. The distances of these 

 secondaries from their primary were divided by 1/33 of 

 the interval between successive repetitions of the primary 

 lines, and the amounts by which the values found exceeded 

 the standard distances for these secondaries are given below, 

 together with the }X displacements taken from Table 1. for 

 comparison. 



Photograph... *02 -25 -42 -52 -51 -58 

 |X, 33 -09 -32 -46 -54 -GO -65 



These numbers show that the aberration when the photo- 

 graph was taken was a little less than three-quarters of the 

 wave-length. 



It is also interesting to notice that the upper part of this 

 photograph, which was given a long exposure, shows signs 



* Lord Ravleiuh's Published Papers, vol. i. p. 430. 

 t Phil. Mag. [G] vol. xviii. p. 371 (1900). 



