Highly Magnified Images. By J. W. Gordon. 



15 



refinements, he selects a case well, as lie supposed, within that 

 limit, and propounds it thus. Taking a median section of the paired 



Fig. 8. 



antipoints, as shown by the section lines in the figure, he first 

 draws their light intensity curves calculated by Sir George Airy's 

 formula, next he adds together the ordinates of the overlapping 

 parts of the curves, and so obtains the total light intensity curves 

 •■shown by broken lines in fig. 9.* When the distance between 



Fig. 9. 



the two centres = p or < p, the total curve will show, as in the 



first and second pairs of the figure, no more than one maximum, 



whereas the widely separated members of the third group will yield 



two maxima as shown. Hence Helmholtz concluded that a centre 



to centre distance = p would be too small for the representation of 



the .two adjacent points as separate objects. This rule would of 



1 *2 \ 

 course ^ive a limit of c = — =— in the case of a circular aperture 



2 sin u L 



if we write c for the centre to centre distance now under discussion, 



* The curves shown are actually reduced copies of Airy's Amplitude curve. The 

 resulting inaccuracy is not conspicuous, and will not, it is hoped, occasion the reader 

 any difficulty. 



