472 Transactions of the Society. 



dent beam always utilized the full area of the objective. In point 

 of fact, a system of a = 0*2 (23°) applied with a power of 106 

 diameters will not show any want of light under that condition, even 

 with dull daylight. The deficiency which, under all circumstances, 

 is found in the use of high powers (notwithstanding correspondingly 

 wider apertures) has no other cause but that we are not allowed to 

 apply illuminating pencils as large as the full aperture of the Micro- 

 scope. With the exception of some particular cases, the utilization 

 of wide apertures in observing delicate objects will always require 

 such narrower incident beams of light (generally of no greater angle 

 than 30-40° in air) as utilize directly a small portion of the aperture- 

 area only ; the effect of the wider aperture being to collect those 

 rays which are dissipated to large angles by the structural elements 

 of the objects. The actual brightness of the image which is ob- 

 tained under these circumstances is of course much less than it 

 would be if an illuminating pencil equal to the full aperture could 

 be employed. The proper effect of low apertures is, it is true, much 

 less dependent upon the reduction of the illuminating beams. 

 Nevertheless, such reduction — by means of diaphragms below the 

 preparations — is an important benefit in many observations. For 

 that purpose it is of practical importance that the aperture should 

 be greater than would be required for the brightness of the image 

 under full illumination. If twice the value of a assigned by 

 Table II. is admitted for the several powers, these powers will still 

 afford sufficient light, even if incident pencils of half the aperture 

 only are used for illumination, and three-quarters of the clear 

 area therefore is left for the utilization of dissipated rays. 



4. We have now all necessary data for defining, at any rate in 

 outline, a rational standard for the ratio between aperture and 

 power in regard to the entire Microscope, i. e. the amplification of 

 the ultimate image (without considering at present the participation 

 of objective and ocular). 



(1.) So far as those apertures are in question which cannot at the 

 present time be overstepped, the aim must be to obtain the most 

 perfect performance for those powers which are just sufficient for 

 the full utilization of the delineating capacities of these apertures. 

 The figures of N assigned by Table I. may thus indicate the par- 

 ticular aims for the various kinds of lenses — dry, water-immersion, 

 homogeneous-immersion — in regard to those values of a which must 

 be considered as the practical limits for these various systems 

 (i.e. about 0*95 for the dry, X'25 for the water-immersion, and 

 1*45 for the homogeneous-immersion systems respectively). For 

 the full development of every system a reasonable latitude for 

 further increase of power, beyond the limits of strictly useful powers, 

 must, however, be left. 



