320 SUMMARY OF CURRENT RESEARCHES RELATING TO 



It was shown tliat both theory and experiment may be applied to 

 prove that the mere angular extension of the pencils — -obliquity qua 

 obliquity — so far from being of importance, is absolutely indifferent; 

 that the greater obliquity of the rays incident on or emitted from the 

 object is not and cannot be of itself an element of the optical per- 

 formance of greater aperture. If it were, the necessary consequence 

 would be that the same increase of optical performance which is obtained 

 by a greater aperture, must be equally obtained with a lesser aperture, 

 by inclining the object to the axis of the Microscope. Now this is of 

 course so in regard to the shadow effects of coarse elements which are 

 plainly seen by aperture angles of a few degrees. But this is not the 

 performance for which we require aperture ; the only essential practical 

 function of increased aperture is to afford vision of minute elements or 

 structures which are not seen by small-angled pencils. When, how- 

 ever, we have objects which are not resolved by direct light and in 

 the ordinary position by an aperture of say 80^, but are readily resolved 

 under the same circumstances by an aperture of 90°, they are not re- 

 solved with the 80°, even if we incline the preparation to any angle, 

 though a few degrees of inclination would give the same increase of 

 obliquity as regards tbe object which the increase of aperture gave. 



The experimental consideration was seen to be supported by 

 theory. Whenever the linear dimensions of objects are reduced to 

 small multiples of the wave-lengths, all shadow and similar effects 

 must cease. The reason is similar to that which shows why objects 

 of not more than a few feet in diameter do not give a sensible acoustic 

 shadow behind them, but only those whose dimensions are large mul- 

 tiples of the sound-waves. The waves of both sound and light pass 

 round an obstacle which is not much greater than their length. 



The supposed advantage of " angular grip " is also sometimes 

 based on the contention that the increase in obliquity obtained by 

 wide angles produces an effect of " solidity." This idea of solidity 

 obviously arises from the supposition that the different perspective 

 views of a preparation which correspond to the different obliquities 

 produce the same result as if they were seen separately by different 

 eyes, as is the case in the binocular Microscope, In reality the 

 various views are united on one and the same retina, and as the 

 image is nevertheless perfectly delineated, the idea of solidity must 

 be erroneous. 



The true effects of obliquity are proved by Professor Abbe's 

 experiments (which every microscopist can try for himself without 

 any apparatus costing more than a few shillings), to depend not on 

 the angles but on the numerical equivalents of these angles (n sin m), 

 and thus an obliquity of 41° in balsam must have the same effect as 

 an obliquity of 90° in air. 



If the angular aperturist is still not satisfied that there can be 

 no virtue in mere obliquity qua obliquity, then it is of course for Mm 

 to bring forward the grounds, whether theoretical or experimental, by 

 which he establishes the virtue of the obliquity — that the large air- 

 pencil of 180°, carrying with it demonstrably no greater quantity of 

 light, and equally demonstrably no more resolving power than the 



