The Relation of Aperture and Power. By Prof. E. Able. 307 



tion of successive layers, unless the preparation is exceedingly 

 thin.* 



So far as the necessity of obtaining a certain amount of amplifi- 

 cation in an efficacious manner requires a certain aperture, the 

 above-mentioned restrictions and difficulties in the proj)er manage- 

 ment of the objectives cannot be avoided. But all restrictions in 

 regard to the objects, and all the trouble taken in the adjustment 

 of the objectives, is quite for nothing when the same result can be 

 obtained with a lower aperture. If for the sake of convenience the 

 precautions required in the use of wide-angled lenses should be 

 disregarded in working with the lower powers of wide aperture, 

 the performance of such lenses is always worse than that of much 

 narrower apertures under the same amplification. The best wide- 

 angled system, if not carefully adjusted when in use, is not better 

 than a had low-angled lens, for the tolerably sharp image, which 

 could be still obtained through the central part of the aperture 

 alone (even under the imperfect state of correction) is disturbed 

 by the coarse dissipation of light from the ineffective marginal parts 

 of the aperture. 



The amateur who likes the Microscope for his amusement may 

 not much object to some extra trouble connected with the use of 



* The reduction of this sensibility in somewhat large apertures is one of the 

 great practical advantages of the immersioo-metliod. The extreme increase of 

 that sensibility which is met with when the aperture of dry lenses approaches 

 the maximal value of a for air (1 N.A.), is in my opinion a strong objection to 

 the construction of such lenses with greater apertures than 0' 80-0' 85. Not only 

 in this case must the working distance be reduced to an intolerably small 

 amount in order to obtain proper correction, but the preservation of that correction 

 in the practical use of the systems is almost impossible, notwitlistanding the 

 correction-collar, whilst at all events the very slight benefit of optical performance 

 is not worth speaking of in comparison to the large increase obtained with the 

 immersion-method under so much more favourable conditions. 



I need scarcely point out here that the claim of a special insensibility of 

 certain lenses in regard to differences of the cover-glass (as has been sometimes 

 made) is, to say the least, either great thoughtlessness or simple self-delusion, 

 just as are similar claims of special penetration in favour of certain objectives. 

 The aberrations in question, as well as the dissipation-circles from difference of 

 focus, originate outi-ide the Microscope. The particular construction of the 

 objective cannot possibly therefore influence their amount in a cone of rays of 

 given aperture, and the degree in which both become visible in the ultimate image 

 of the Microscope must be strictly determined by the same elements which 

 determine the visibility of any real object of given dimensions at the same plane 

 of focus. There is no room left, therefore, for special properties of ditierent 

 constructions. 



^ It is, however, true that an apparent insensibility, as well as an apparent 

 depth of focus, is sometimes found, viz. in badly corrected objectives. When a 

 syfetem has no distinct focus at all, it is quite evident that the dissipation-circles 

 arisiug from different thicknesses of the cover-glass, and from the difference of 

 focus of different levels, may become much greater before the deterioration of the 

 indistinct image becomes visible. Well-corrected objectives must be sensitive in 

 both respects in strict accordance with their aperture so far as one and the same 

 system of construction (dry or immersion) is in question. 



