The Relation of Aperture and Poiver. By Prof. Abbe. 465 



hand, we shall have an empty amplification, which does not improve 

 the representation of the objects, if the power should go much 

 beyond the maximum figure. 



The salient fact suggested by the two tables is the relatively 

 low figures of amplification which are sufficient for very wide — in 

 particular for the widest — apertures ; and, conversely, the small 

 apertures which are sufficient for the low powers of the Microscope. 

 I do not, of course, intend to assert that, under particular cir- 

 cumstances and for particular purposes, much higher figures of 

 amplification than are shown in the tables may not be very useful 

 or even necessary ; as, for instance, for counting, measuring, draw- 

 ing, &c. What I wish to convey is, that in the present state of the 

 Microscope they are not required and are not even advantageous, 

 for research, i. e. for the proper recognition of the objects. A 

 visual angle, for the minutest elements of a microscopical image, 

 of 2', or at all events of 4' (which is about the eighth part of the 

 moon's apparent diameter), is certainly quite sufficient for distinct 

 observation. If indications of shape or arrangement should be 

 found in the image, which are too minute for the powers given 

 above, they must be at any rate of minuter dimensions than the 

 values of 8 assigned by the first table. Indications of that kind — 

 if such there be — have no true relation to the objects, but are 

 attributes of the image only — mere optical phenomena, dependent 

 upon the limitation of the delineating pencils by the lens-opening. 



Apart from all theory and experimental demonstration in sup- 

 port of the principles in question, the practical experience of micro- 

 scopists has sufficiently established that there is a limit to the 

 performance of the Microscope, and one depending on the aperture 

 of the objectives in the manner pointed out above. No kind of 

 microscopical object can possibly afford in any respect more 

 favourable conditions for the recognition of minutest details than 

 those very expressive (and at the same time very simple and 

 regular) structures of the silica skeleton of diatoms. But even with 

 this kind of object not one trustworthy observation is on record in 

 favour of the assumption that any given aperture, be it either * 3 or 

 1 ' 40, could reach a finer detail than is assigned by the table above, 

 whilst there are many indubitable proofs that these theoretical limits 

 may be as closely reached as can be expected, having regard to the 

 difficulty of a strict determination of the actual circumstances of 

 observation. 



The low figures of amplification suggested above, even for the 

 widest attainable apertures — low in face of the views of many 

 microscopists — are an unavoidable inference from the principle 

 under consideration. In support of this inference I may, however, 

 appeal to the evidence of many experienced naturalists who have 

 done valuable work in lines of research dealing with the most 



Ser. 2.— Vol. II. 2 I 



