10 Transactions of the Society. 



aperture, reading N.A. for S.A., by those to whom this last men- 

 tioned form of expression is familiar. 



In plate III. fig. 6 you have a photograph of Pleurosigma aiigu- 

 latum, of the familiar type, obtained with wide-angled lenses. Since 

 it is familiar I need not enlarge upon its features. You will recognise 

 the " white " dot growing up within the " black," which is a feature 

 •commonly employed as a test of the resolving power of a lens of 

 N.A = 1 '3. My lens of N.A. = 1 is, of course, quite incapable of 

 yielding this picture, unless its effective aperture is increased by a 

 central stop. The stop used to produce this particular image has, 

 as you will see from the picture of the liamsden disk, a semi- 

 aperture of • 2 /. But the observed effect cannot be attributed to 

 tliis stop alone. The suppression of much of the refracted light, by 

 interference due to diffraction, has the same effect on the image as 

 a very large stop. In fact, the refracted light which escapes sup- 

 pression in this way, all lies either in tlie narrow prolate central 

 beam, or in the six divided beams wliich lie in an annulus around 

 the margin of the liamsden disk. This annulus has, in fact, a 

 semi-aperture of 1*7/, which is equivalent for the purpose of image 

 formation to a N.A. of 1 • 7. The semi-aperture of the central Ijeam 

 is 0'8/in the longer direction, and 0*45 /in the shorter. It will, 

 of course, be obvious that the diameter of the mean zone of an 

 annulus is greater than that of the mean zone of the circle which 

 forms its outer boundary by a quantity equal to the diameter of 

 the circle whicli forms its inner boundary. Thus, if we stop out 

 tlie centre of a circular beam of light by means of a circular stop, 

 we increase the angular value of what is left by a quantity equal 

 to the angular value of the stop itself It is tlms possible to 

 increase the numerical aperture of any given lens up to a limit 

 which is equal to twice the aperture of the lens unstopped. 



While pointing out the fact that we can, in this indirect way, 

 increase numerical aperture, I desire to guard myself against being 

 supposed to suggest that the mere increase of this function accounts 

 for all the improvements which the stop introduces into the per- 

 formance of the lens. The stop does much more than that. It 

 reduces to a minimum the errors due to residual spherical aberra- 

 tion — a matter, if 1 mistake not, greatly more important than mere 

 increase of angle. But it does also what is more important still, 

 more important than the diminution of the spherical and diffraction 

 eiTors taken together, that is to say, it gives us the means of so 

 balancing the refracted and unrefracted light emitted bv the 

 object as to be able to render salient those features which we wish 

 to observe. This is why an annular lens, tried and found wanting 

 in the telescope, where it would be quite effective so far as mere 

 corrections are concerned, proves to be of high value in the Micro- 

 scope. You cannot voluntarily vary the lighting of the moon. If 

 jou want to measure the height of Tycho, you must wait for the 



