'ANGLE' AS SUCH OF NO VALUE 6 1 



microscope was determined by the geometrically traceable relations 

 of the refracted rays of light. 



A prolonged course of able and exhaustive experiments con- 

 ducted by Abbe showed that, whilst the old view held good in 

 certain cases capable of definite verification, yet that the vast 

 majority of objects, and especially those with which the highest 

 qualities of an objective are called into operation, the production of 

 the microscopic image is wholly and absolutely dependent, not upon 

 the obliquity of the rays to the object, as it had been so long and so 

 stoutly maintained, but upon their obliquity to the axis of the micro- 



Such coarse objects as require only a few degrees of aperture 

 to disclose them are dependent on ' shadow effects ; ' but when 

 extremely minute and delicate structures are to be disclosed small 

 apertures are absolutely useless, and mere increase of obliquity of 

 pencil as such is powerless to alter the result. It can be effected 

 only by increased numerical aperture, showing that the greater 

 obliquity of the rays incident on, or remitted from, the object is not, 

 and cannot be, of itself an element in the superior optical perform- 

 ance of greater aperture. If it were so, all the results of increased 

 aperture would be secured by inclining the object to the axis of the 

 microscope ; but it may be readily tested that when a given object 

 cannot be 'resolved,' or its structure delineated, by an objective with 

 an aperture of 80 in the ordinary position, but can be resolved in 

 the ordinary position by an objective with an aperture of 90, no 

 inclination of the object to the axis of the instrument will enable the 

 objective of 80 to do the work easily done by one of 90. This 

 may be tested by any one possessing the instruments. 



As a matter of fact, this so-called but imaginary * angular grip ' 

 is greater in a wide-angled dry lens than in one of 90 balsam-angle, 

 and it is certainly cut down more and more when with one and the 

 same objective preparations are observed in water, balsam, and 

 cedar oil successively. If now the angles qua angles are effective 

 in any way, something must be lost by change of angle in this direc- 

 tion, and something ought to be gained by change in the reverse 

 direction, other conditions remaining the same. It is needless to 

 say that all experience and the entire course of proof and reasoning 

 given above are diametrically opposed to such conclusions. 



Similarly it will be manifest that the conception that ' solid 

 vision ' or perspective effect in a microscopic image is one of the 

 consequences of oblique * angular ' illumination is equally invalid. 

 It assumes that the different perspective views of a preparation 

 examined with the microscope, which correspond to the different 

 obliquities, produce the same effects as if they were seen separately 

 by different eyes, as in the case with the binocular microscope. In 

 reality, whenever we have the advantage of solid vision, owing to a 

 different perspective projection of different images, in the microscope 

 or otherwise, this is solely because the different images are seen by 

 different eyes. In microscopic vision there is no difference of pro- 

 jection connected with different obliquities ; in the binocular micro- 

 scope there is a diversity of images which are depicted by pencils of 



