The Able Diffraction Theory. By J. W. Gordon. 393 



The last of these influences, that is to say, the complicating effect 

 of the reinforcement of the outlying parts of the antipoints by over- 

 lapping has been briefly considered in the notice given to intercostals ; 

 and it is not possible, in a paper of the general character of this one, 

 to do fuller justice to it. But it is obvious that this overlapping 

 results from the contiguity of distinct luminous details in the image. 

 If the centres of two antipoints are juxtaposed, the overlapping of 

 their peripheral parts does not in general give rise to patterns ; but 

 when the centres are separated by a dark field, that dark field may, 

 and in some circumstances does, serve as the background upon which 

 the overlapping peripheral parts of the antipoints become visible. A 

 third case may be proposed, that, namely, in which the two centres 

 are so widely separated that the outlying members cannot overlap. 

 But in that case the third influence — that which we are now consider- 

 ing — would not come into play. The appearance of the antipoint 

 in such a case would be determined only by the shape and dimensions 

 of the wave-front and the amplitude of its oscillations. This last 

 consideration shows that the scale of the image has much to do with 

 the resolution of its details. Any feature which bulks large enough 

 to dwarf the details of the antipoint will be clearly defined ; but, on 

 the other hand, any feature which is so small that its appearance is 

 liable to be materially affected by the pattern of the antipoint by 

 means of which it is portrayed, will be liable to be seriously obscured 

 by the prominence which overlapping gives to the subordinate parts 

 of the antipoint. 



There is still another circumstance connected with the scale of the 

 image to which it is worth while to advert, although it does not 

 immediately grow out of the considerations so far advanced. The eye 

 itself, like every other optical instrument, constructs its image, not 

 of true points, but of antipoints. Any detail, however well defined in 

 the instrumental image, will be lost in the visible image if its projec- 

 tion on the retina is not sufficiently large to be clearly depicted by 

 means of the retinal antipoint. It is for this reason that a mere 

 reduction of scale by shortening the tube-length of the Microscope 

 will cause a loss of the finest detail. Such a shortening does not in 

 any way impair the resolution in the instrumental image ; it may 

 even improve that resolution. But a point is reached at which the 

 antipoint produced by the human iris is too coarse for the true 

 delineation of the minutest detail, and then, of course, defective 

 resolution occurs in the eye. 



We are now able to lay down the instrumental conditions of good 

 resolution in general terms : — 



1. — The emitted wave-front must produce a very small antipoint. 



2. — The image must be sufficiently, but only just sufficiently, 

 illuminated for good definition. 



3. — The scale of the image must be sufficiently large. 



