The Abbe Diffract ion Theory. By J. W. Gordon. 331 



which they convey is propagated in what are sensibly rectilinear piths, 

 and this rectilinear propagation of light gives rise to sharply defined 

 boundaries between the lighted space and the shadow. The bounlary, 

 however, is not as simply rigorous as we conimoaly suppose. Careful 

 examination shows that it is transgressed by the shadows which 

 invade the lighted region, and by the light which in its turn makes 

 inroads upon the shadow. These boundary phenomena, confined 

 within limits too narrow to affect sensibly the common phenomena of 

 vision, have a very sensible effect upon the images formed by means 

 of shadows in various optical instruments, and pre-eminently in the 

 Microscope, where they give rise under high magnification to fringes, 

 intercostals, aud other such-like appearances which sometimes com- 

 pletely obscure the true image. Their investigation, although of 

 primary importance in the theory of the Microscope, aud presenting 

 in fact no serious difficulty, has been singularly neglected hitherto. 

 We have already seen how, by the simple expedient of observing by 

 an easy experiment the form of the autipoint, and then by an equally 

 easy construction developing a geometrical figure in which antipoiuts 

 replace the points of nature, it is possible to pass from an object on 

 the stage through an entire series of the varying appearances which 

 that object will take on when viewed through the Microscope. The 

 most complicated illusions exhibited by diatoms and such-like objects 

 can be investigated with equal success and no more difficulty, but I 

 do not propose to trespass on your time this evening with digressions 

 into that region. In bringing this long paper to a close I ask leave 

 only to add a few observations on the general considerations which 

 determine the shape and dimensions of the autipoint. 



We have, then, to consider how a segmental wave-front illuminates 

 a point which lies within its own geometrical shadow ; for, as has been 

 already mentioned, the reciprocal case of the imperfect lighting of the 

 illuminated area near the shadow boundary is of no consequence for 

 the present purpose. The light which thus p isses into the zone of 

 shadow is called diffracted light, and its propagation, like the formation 

 of the shadow itself, is due to the interference of successive waves with 

 one another's work. To this conception of interference of light we 

 rise by considering all the points upon a wave-front as so many 

 independent foci, sources of light from which the luminous impulse is 

 transmitted in all directions. These foci, however, are co-ordinated to 

 one another by a double law ; every one shines with exactly the same 

 brightness as every other one, and vibrates in exact synchronism with 

 every other one in the same wave-front. We may then estimate the 

 whole illuminating effect of the wave-front on any given point in front 

 of it by adding together the impulses which every part of the wave- 

 front would send to that point if it stood alone. For the case of a 

 focal point, such as p in fig. 87 which stands equidistant from all parts 

 of the segment, this addition is a very simple matter. All the several 

 impulses will arrive simultaneously and in equal phase, and the 



