412 



Transactions of the Society. 



Fig. 9t>. 



that these peripheral antipoints become distorted into a prolate 

 form with their long axes slightly more than twice the length of 

 their shorter axes. Then the points of these distorted antipoints 

 will overlap in the middle of the field, producing there an inter- 

 costal spot as shown. 



Now, this diagram shows very imperfectly what happens in the 

 Microscope when oblique beams, much mutilated by successive 



diaphragms, are admitted to the field of 

 the instrument. The assumption that the 

 long axes are double as long as the short 

 axes is by no means an extravagant assump- 

 tion since it implies only that one-half of an 

 oblique beam transmitted by the first aper- 

 ture has been intercepted by the second. 

 And here we have only four peripheral anti- 

 points shown out of the infinite number, 

 which would in fact find place upon the ring 

 in which these four are situated. It will 

 become evident upon consideration, that whenever the back lens 

 of an objective is completely filled by the wave-front transmitted by 

 the front lens from the central point of the field, that is to say, 

 if it presents no appearance of unoccupied aperture as seen from 

 along the axis of the instrument, it must cut down all the oblique 

 beams transmitted by the front lens, and cut them down in much 

 more than the simple proportion of their obliquity, if by this pro- 

 portion we understand the proportion between the angular aperture 



of the lens itself, and the inclination of the 

 axis of the oblique beam to the axis of the 

 instrument. In that case, therefore, we shall 

 have the various antipoints in successive 

 rings of the field of the instrument ; measur- 

 ing outward from the centre ; arranged some- 

 what as in the diagram (fig. 97). 



Here three excentric antipoints are shown, 

 and for greater clearness they are arranged 

 in different azimuths. It will of course 

 be understood that each represents a com- 

 plete ring of similar antipoints arranged about the centre of the 

 field at a central distance indicated by the letter a from c the 

 middle point of the field. The bounding circle indicates the dia- 

 phragm of the eye-piece, and it is assumed for the purpose of the 

 diagram, that the most excentric beam brought to a delineated 

 focus has had four-fifths of its full diameter cut off by the hinder 

 diaphragm of the objective. It will surprise nobody who considers 

 the state of the illumination produced in that way, that it should 

 render all clear definition of detail impossible. It may be that 

 even the largest antipoints here shown would give a well resolved 



Fig. 97. 



