The Relation of Aperture and Power. By Prof. E. Ahhe. 301 



widest apertures hitherto obtained will not afford complete or 

 strictly true images, but will show these objects more or less 

 incomplete or modified. This general principle holds good in 

 regard to objects of every kind, regular or irregular, isolated 

 particles or composite structui-es, because the physical conditions of 

 microscopical delineation are always the same. 



The obvious inference from this principle is that the widest 

 possible apertures must be used for the observation of objects or 

 structures of very minute dimensions, low and moderate apertures 

 for relatively large objects. 



It may perhaps be said that the objects of microscopical research 

 do not justify such a distinction of large and minute, since the 

 works of natui'e are always elaborated to the minutest details, all 

 coarse objects being composed of smaller elements, and these of 

 still smaller ones, etc. This is quite true in regard to the objects 

 considered as natural things, but not as objects of scientific 

 research. The interest of research is not always directed to the 

 ultimate elements, but is as often confined to the consideration of 

 the coarser parts, and in such cases the observer is not only allowed 

 but sometimes compelled, to disregard everything which is not con- 

 nected with the scientific aim of his investigation. To observe 

 every object in nature throughout, from alpha to omega, is the 

 privilege of dilettante microscopy only, which has no distinct aim. 

 There are many lines of the most valuable scientific research (e. g, 

 the greatest part of all morphological investigations) which have 

 not to deal with very minute things. This kmd of work can be 

 completely done with low or moderate apertures. 



To recommend the application of wide-angled objectives for 

 every branch of microscopy, as has been, in fact, done by excited 

 wide-aperturists, is no more to be supported than it would be to 

 recommend the use of a magnifier to a painter for inspecting the 

 tree which he proposes to delineate. 



According to what has just been said, the only benefit of 

 greater apertui'e is that it is capable of delineating minuter things. 

 Now minute dimensions require high amplifications in order that 

 they may be enlarged to a visual angle sufficient for distinct vision. 

 Low figures of amplification cannot render visible (at least not 

 distinctly visible) details which are beyond a certain limit of 

 minuteness. Even if they are dehneated by the Microscope they 

 would remain hidden to the eye for want of sufficient visual angle. 

 It follows therefore that wide apertures will not be utilized unless 

 at the same time there is a hnear amplification of the image, at 

 least sufficient for exhibiting to the eye the smallest dimensions 

 which are within the reach of such an aperture. On the other 

 hand, a high amplification will be useless if we have small aper- 

 tures which delineate details of dimensions only capable of being 



