﻿30 Dr. H. Stansfield and Mr. H. P. Walmsley on 



displacement is towards the side on which the aberration 

 decreases ihe phase differences in the vector diagrams, and 

 increases the intensities of the secondary maxima. The 

 secondary maxima near to a primary are shifted less than 

 those farther away, secondary maxima adjoining a primary 

 maximum on the side where the secondaries are strengthened 

 being displaced little more than the primary they adjoin. 



It follows from the first rule that the displacement of the 

 distant secondary maxima relative to the primary maxima is 

 about the same fraction, mentioned above, of the half-cycle 

 of the curve; the half -cycle being the interval between con- 

 secutive points where the zero aberration amplitude curve 

 cuts the horizontal axis. 



The displacements produced by various degrees of aber- 

 ration, in the secondaries whose importance h increased 

 by the aberration, are given in Table I., the position of any 

 secondary in the case of a continuous wave-front free from 

 aberration being taken as its standard position in finding 

 the displacement. The values have been obtained by reading 

 the positions of the maxima of amplitude curves drawn 

 through a number of calculated points, and the second figure 

 is in some cases only approximately correct. 



Table I. 



Displacements of Brightened Secondary Maxima relative 

 to the Primary Maximum. 



Aberration... 



1/4 X. 



1/2X. 



3/4 \. 



Standard 

 distances. 



Number of 

 apertures... 



33 



19 



33 



19 



33 



19 



1 



•00 

 •12 

 •16 

 •18 

 •19 

 •20 

 •21 



•01 

 •13 

 •18 

 •21 

 •22 

 •23 

 •24 



04 

 •22 

 •32 

 •38 

 •41 

 •42 

 ■43 



•04 

 •23 

 •35 

 •41 

 •44 

 •45 

 •46 



•09 

 •32 

 •46 

 •54 

 •60 

 •65 

 •67 



•10 

 •34 

 •50 

 •60 

 •66 

 •70 

 •73 



143 

 2-46 

 347 

 4-48 

 5-48 

 6-48 

 7-49 



2 



3 



4 



5 



6 



7 



1 

 P 33 



•35 



•63 



•69 



•93 -99 





The distance of a secondary from its primary may be found by adding the 

 value given for the displacement to the standard distance given in the last 

 column. The bottom line gives the absolute displacements of the primary 

 maxima. All the values are given in terms of the interval between successive 

 points of zero intensity in the absence of aberration. 



