﻿2S Dr. H. Stansfield and Mr. H. P. Walinsley on 



direction ON^ making the same angle with the normal on 

 the other side. 



The vector diagrams are symmetrical about the horizontal 

 axis, and the resultant amplitude vanishes for the cases where 

 the two ends meet as they cross this centre line. Fig. 2 

 shows how much larger the first secondary maximum will 

 be on the left side of this figure, where the aberration de- 

 creases the differences of phase, than on the right side, where 

 the aberration increases the phase differences and helps to 

 curl up the vector diagrams. 



The values of the amplitudes for a nineteen aperture 

 diffraction grating are represented in fig. 1, PI. III., curves 

 being drawn for the cases of zero, ^\, JA,, and |X aberrations. 

 About eighty points were calculated for each curve by adding 

 together the cosines of tlie phase-angles, four-figure values 

 being employed. The horizontal scale represents direction, 

 the normal to the centre of the wave-front being taken as 

 origin, and the length of the diagram being the angular 

 interval between the principal maxima. 



The corresponding intensity curves are represented in 

 fig. 2, PJ. III. These curves indicate the changes that 

 would be produced in the appearance of the diffraction 

 spectrum of a bright monochromatic source by varying 

 degrees of aberration. Commencing with zero aberration, 

 a few faint secondary maxima would be seen arranged 

 symmetrically about the principal maximum. The curve 

 drawn for ^X aberration shows that this degree is sufficient 

 to greatly increase the brightness of the secondaries on one 

 side of the line, and to practically wipe out those on the 

 other. With ^X aberration the secondaries on the right are 

 still further increased, and the principal maximum is reduced 

 to *74 of its original brightness. The |\ curve shows these 

 changes carried still further, the bright line having now 

 only about twice the intensity of the brightest secondary. 

 The bright line also shows a considerable extension on the 

 left, which would make it appear less sharp 'y defined on that 

 side than on the right, where it adjoins a bright secondary. 

 It will be seen that in this case five secondaries on the right 

 are brighter than the brightest of those on the left. 



In calculating these curves no account has been taken of 

 the variation with direction of the intensity of the light from 

 the individual apertures of the grating. The form of the 

 factor required to correct for this variation in the case of an 

 ideal echelon, that is when the width of the aperture is equal 

 to the grating interval, is represented by the dotted curve at 

 the top of fig. 2, PL III. 



