394 Transactions of the Society. 



The second of these conditions may be dismissed as being a mere 

 detail of manipulation. The illumination is so completely under the 

 operator's control, and so easily regulated, that the maker of the 

 objective does not need to take it into account. He may assume that 

 his lens will always be put to work under the best possible con- 

 ditions so far as illumination is concerned. 



The two remaining conditions are antagonistic the one to the other, 

 and to a certain extent mutually exclusive. A small antipoint is most 

 easily secured by giving a small radius of curvature to the wave-front at 

 the plane of the aperture. But a small radius of curvature behind the 

 objective implies a low magnifying power, and a low magnifying power 

 in its turn implies an image on a small scale. In fact, the radius of 

 curvature of the emergent wave-front as it passes out of the back lens 

 of the objective is always about 10 ins., a little more or less. This 

 may be taken to be a fixed quantity. There remains only the 

 expedient of expanding the wave-front as the last resource of the 

 Microscope maker for diminishing the antipoint, and so improving 

 the resolving power of his lens. The wide-angled objective is one 

 way, and a most excellent way, of accomplishing this object. The 

 wide angle fills and requires a back lens of comparatively large 

 diameter ; it also implies a shallow form of objective, with small axial 

 distance between the front and back lenses ; and this again implies 

 high magnifying power. Thus we get the two desiderata of large 

 scale and small antipoint combined. And this is the real cause of 

 success of wide-angled objectives. It is an accident, and a very 

 fortunate one, that Professor Abbe's theory should have pointed to this 

 form of construction ; for it mattered nothing to the practical result 

 upon what theory these objectives were constructed, provided they, 

 in fact, secured the broad wave-front and the large scale image. 



But that practical result is now secure, and if the Abbe theory 

 should continue to hold the field, it would in the future only obstruct 

 the further course of improvement. For it is manifest that the 

 simple wide-angled objective is not the only form which can yield 

 this combination. In fig. 93 is shown diagram- 

 Fig. 03- matically what I will venture to call a compound - 



angled objective. The beam of light enters the 

 front lens under a narrow angle, is expanded by 

 the negative lens seen in the middle of the ob- 

 jective, and emerges as a broad wave-front from a 

 back lens of high magnifying power. The objective 

 will possess many excellent properties when made. 

 As against the narrow-angled objective it will have 

 the excellence of superior denning, resolving, and 

 magnifying power. As compared with the wide-angled objective it 

 will be more manageable, for it will work at a greater distance from 

 the stage, and it will require a less oblique pencil of illuminating 



