On the Estimation of Ajperture. By Prof. E. Abhe. 419 



nor is it so in regard to the very essence of microscopical perform- 

 ance, the delineating power of objectives. This, however, does not 

 of course exclude the idea that there might be some other element 

 in the performance of the Microscope, which does not depend on 

 the aperture-equivalent, but rather depends on the angle of aperture 

 qua angle; and if such an element should be found, and should 

 prove to be of any practical importance for microscopical vision, the 

 angular aperture would also deserve attention. Down to more 

 recent times there has always been an opinion among some micro- 

 scopists in England that such an element exists — that there is 

 something in the operation of the Microscope, in regard to which 

 the wider range of obliquity of the admitted rays attendant upon 

 a wider aperture-angle, is an advantage. 



The question, whether there is such an x — which is called by 

 the names of " angular grip," " all-round vision," and similar 

 expressions — or whether there is not, can surely be settled at once 

 in a purely practical way. If it be not a mere outcome of imagina- 

 tion, it must be possible to demonstrate it in the Microscope with 

 actual preparations — in the same way as the increase of opening, or 

 the increase of light, or the increase of delineating power with the 

 greater aperture-equivalent can be shown. 



There is evidently ample range for doing this. The width of the 

 angular grip is certainly greater in a wide-angled dry lens than in an 

 objective 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 say monobromide of naphthaline 

 successively. If now the angles, qua angles, are effective in any 

 way, something must be lost, if we change the conditions of the 

 observation in the direction indicated above, and something must be 

 gained in the other direction, other circumstances being the same. 

 What is the benefit of the complete all-round vision of a dry lens of 

 170° aperture-angle against a moderate-angled immersion glass, 

 and what is lost by observing an object in balsam instead of air ? 



No microscopist has yet demonstrated this x. Of course, when 

 an object whose own refractive index is not much different from 

 1*5, is imbedded in balsam, the radiation of this object, and 

 particularly the intensity of the diffraction effect of its structure, 

 is changed, and may be totally obliterated ; and thus it may happen 

 that the observation of it becomes much more difficult, or the image 

 even entirely lost. But sueh a loss is at once recovered when we 

 substitute for the balsam a substance of much higher refractive 

 index, although the angle is now still more cut-down. 



The above considerations are sufficient for estabhshing the non- 

 existence of a peculiar operation of the angle qua angle in the 

 Microscope. The question may be settled, however, more ex- 

 haustively by tracing the suggestion back to its true origin. This 

 is certainly not to be found on any grounds of observation, but 



