806 Transactions of the Society. 



increased aberration attendant upon a relatively thicker air-space 

 in front of the system. Considering the medium-power objectives 

 as they are generally (and properly) made with the view to a 

 convenient working distance, I cannot admit of a higher number 

 for the critical v than 5 to 6, even for apertures down to about 

 0*40 (47°). If the aperture is reduced below this, the increase of 

 V becomes decidedly more rapid, in so far that for • 15-0 • 20 N. A. 

 (17°-23^), 8 to 10 appears to me to be the correct super- amplifica- 

 tion which very good objectives will bear without a perceptible loss 

 of definition (under the condition, of course, that the total powers 

 obtained thereby are not empty powers in regard to the delineating 

 capacity of the aperture in question). 



Similar indications for still lower apertures would be of very 

 subordinate interest ; and, besides that, they could not be given on 

 the basis of reasoning established here, which depends on the con- 

 dition of a constant visual angle of the inherent dissipation of the 

 rays for different distances of the objective-image. This condition 

 (as has been observed) holds good with sufficient approximation 

 only as long as that distance^ — the length of the microscope-tube 

 practically — is not too small a multiple of the focal length of the 

 objective ; this is not fulfilled, under ordinary circumstances, with 

 the very low-power systems which would come in question for 

 apertures of only a few degrees. 



4. The values of v assigned above for different kinds of objectives 

 express, in my opinion, the conditions of the test ^possible per- 

 formance of the Microscope under present circumstances. 1 by 

 no means contend, however, that ninch higher super-amplifications 

 might not still be very useful ; but if it cannot be denied that 

 with the objectives which are made at this date, a letter image is 

 obtained under a four-fold, or six-fold, super-amplification than can 

 be obtained under a higher figure, it is absolutely certain that the 

 lower powers ought to be used, when the utmost attainable degree 

 of perfection is required. It is quite immaterial for that conclusion, 

 whether the loss of sharpness (" definition ") attendant upon higher 

 values of v, may be deemed small or great, and whether it may 

 become obvious with all preparations or with a few only. If there 

 is a loss, however small, and if only one kind of object is found with 

 which it can be perceived, this alone will be suflicient to prove the 

 advantage of the lower numbers ; for there cannot be a reasonable 

 doubt, that even the slightest difference in the perfection of the 

 microscopic image may become a matter of decisive importance in 

 critical cases of difiicult research. 



The conclusion from the foregoing experimental facts must 

 therefore be : — 



In order to obtain the best possible conditions for the utilization 



