The Helmholtz Theory of the Microscope. By J. W. Gordon. 413 



picture if all the antipoints in the picture were of the same size 

 and shape. But with graduated antipoints arranged in a geometrical 

 pattern, the background pattern of the mere blank field becomes so 

 complicated and obtrusive that resolution of anything but strongly 

 contrasted features is rendered thereby impossible. 



This difficulty is not unknown to microscopists. The necessary 

 limitation of the working aperture has been observed, notably by 

 Mr. E. M. Nelson, who has recently made a communication to your 

 Society upon the subject (R.M.S. Journal^ vol. for 1901, p. 242). 

 But it has not as yet, I think, received its explanation. For the 

 benefit of Fellows and visitors this evening who may desire to test 

 the explanation here proposed by an actual observation, there is 

 arranged among the exhibits a piece of apparatus upon the plan 

 of arranging a shutter within the tube of the Microscope just 

 behind the objective, so that it can be very gradually introduced 

 into the path of the beam and caused to cut down first the 

 excentric and ultimately the central pencils unsymmetrically. As 

 it is introduced a vague shadow, which denotes the advance of the 

 invading distorted antipoints from the shutter side of the field, will 

 be seen travelling across the object, and in this pernicious shadow, 

 so tender as itself to be barely visible, all the delicate details of the 

 picture will be seen to dissolve away. 



It thus appears, that for fine resolution two conditions are 

 essential, a wide angle to secure a small type of antipoint, and 

 a clear course to secure the uniformity of the antipoint of that 

 type throughout the field of the instrument. 



The first of these conditions is secured by a wide angle for the 

 beam which forms the image, an object which can be attained in 

 various ways. But as a wide angle behind the objective involves 

 loss of magnifying power, this condition is only consistent with 

 high magnification on the further condition that the front of the 

 objective has an angle commensurably wide. That is to say, it is- 

 attained by high numerical aperture, the virtue of which has been 

 fully recognised, perhaps even somewhat over-estimated, for many 

 years. 



But the second of these conditions, that is to say, the clear- 

 course and consequently uniform antipoint, is very little under- 

 stood and at the present moment only dimly recognised at all as 

 a condition of the best performance.^ It must even be admitted 

 that Helmholtz himself does not draw attention to it, and appa- 

 rently did not consider the point. He assumed that all the anti- 

 points with which he was concerned were of one size and form' 

 and worked out his conclusions accordingly. The practical import- 

 ance of this point is, however, at the present day too great to be' 

 now passed over in silence. In order, however, to resume the 

 thread of Helmholtz' paper, I will defer to a later paragraph the 

 further discussion of this theme. 



Aug. 19th, 1903 2 e 



