80 F. CRISP ON THE INFLUENCE OF 



instrument on ordinary dioptric principles, that is, in the same way 

 in which they are formed in the telescope or a camera, and if any 

 microscopist were asked to describe the way in which a diatom or 

 other lined object is seen in the microscope, it would have been 

 in this manner that the explanation would, without hesitation, have 

 been given. It had never been suggested, prior to Professor Abbe, 

 that that (which may be termed the dioptric method) was at all 

 incorrect. 



One result of this view was that, in the manufacture of objectives, 

 very erroneous methods came to be adopted — methods that were 

 perfectly correct if the images were formed dioptrically, but entirely 

 inapplicable if that theory was unsound. 



The second error relates to angular aperture. 



Not long after achromatic object-glasses were first made, Dr. Gor- 

 ing found that the markings on particular objects, such as the scales 

 of the wings of insects, could not be seen by some object-glasses, 

 while with others, of equal magnifying power, they were clearly 

 visible. This led him to the important discovery that the resolving 

 power (or, as he termed it, the " penetrating" power) of an objec- 

 tive depended upon the extent of its angular aperture. 



One of the explanations given of the cause of this quality of the 

 objective was that, as by the larger aperture, rays of greater obliquity 

 were admitted, structural details became more plain, in the same way 

 that the inequalities on a white wall or a person's face are plainer 

 when the light falls upon them obliquely — casting shadows — than 

 they are by direct light. 



This theory has remained without alteration to the present day, 

 and some writers have exhibited the most praiseworthy efforts to 

 account for some of the anomalies that the theory did not satisfy, 

 much in the same way as the old astronomers who, when the motions 

 of a planet seemed to become erratic, did not throw over the theory 

 which they had adopted to account for the motions, but added 

 additional crystal spheres, until at last the whole thing was so mar- 

 vellously complicated that it is a wonder how any sane person could 

 have believed in it. 



I now come to the phenomena which show that a special and 

 important part of the functions of the microscope has been over- 

 looked, and that both the theories just referred to, that of the 

 dioptric formation of the image, and that of angular aperture are, 

 in the case of lined objects, erroneous ; the explanation, in fact, 



