E. M, NELSON ON BINOCULARS. 57 



that the difference between " perspective " and " parallactic dis- 

 placement " becomes infinitely small and altogether quite imper- 

 ceptible to the eye. However keen in detecting errors of per- 

 spective an artist's eye might be, he would not be able in a thin 

 object to distingnish between "parallactic displacement" and 

 " perspective " with only 8° of displacement, in spite of the 

 methods of drawing being so widely different. Now Prof. 

 Abbe is perfectly right in saying that there can be no such a 

 thing as perspective in the microscope image, and that the 

 difference between the images seen with the right and left half 

 of the objective is caused by parallactic displacement. The 

 difference is, however, only one of name, because we must 

 remember that the depth of vision in the microscope is very 

 small (smaller than is allowed by Abbe) ; therefore, however 

 thick the object may be, the thickness you can see does not 

 amount to much, and no one could possibly distinguish between 

 such images, whether drawn in perspective or in parallactic 

 displacement (see dotted lines, Figs. 8 and 9). 



Carpenter, it is true, uses the words " perspective projection '' 

 loosely.* He calls the pictures of the truncated pyramids 

 " perspective projections " when they are nothing of the kind, 

 and he uses it in the same loose way in dealing with the micro- 

 scopical image. 



The truncated pyramids, of course, ought to be " perspective 

 projections " whereas they are drawn by " parallactic displace- 

 ment," and the microscope image is a "parallactic displace- 

 ment," though Carpenter calls it a "perspective projection." 

 Abbe, on the other hand, unduly accentuates the difference 

 between the microscopic and macroscopic images, so that a 

 wholly false impression is conveyed by his paper. After 

 rhetorical statements such as " the microscope image is a thing 

 sui generis;" "peculiar property of microscopic vision is in 

 strong contrast to the method of ordinary vision;" "elements 

 of an object are no longer depicted as solid objects seen by the 

 naked eye ; " "an essential geometrical difference between 



* The words " perspective projection " occur in Carpenter's (5tli edition, 

 1875) article " Stereoscopic Binocular," pp. 57-73) six times in connection 

 ■v\ith ordinary vision, and once with microscopic vision. The sole passage in 

 connection with microscopic vision is " pictures .... sufficiently dissimilar 

 in their perspective projections to give when combined in the microscope a 

 suflBcient but unexaggerated stereoscopic relief." 



