302 Transactions of the Society/. 



distinctly seen in an image of much lower amplification. We have 

 here an empty amplification, because there is nothing in the image 

 which requires so much power for distinct recognition. In the 

 first case (deficiency of power) the large aperture cannot show 

 more than a smaller one ; in the other case (deficiency of aperture), 

 the high amplification shows no more than a lower would do. 

 Consequently : — 



Wide apertuyes ivhen high ampUJieation is required ; low 

 or moderate apertures when low or moderate amplifications 

 are sufficient or cannot he overstepped. 



2. The utilization of a given aperture depends in principle on 

 the amplification of the ultimate image which is projected by the 

 entire Microscope to the observer's eye. Now one and the same 

 amplification may be obtained in very difiierent ways since it is the 

 resultant of three distinct elements, (a) focal length of the objective, 

 (b) focal length of the ocular, and (c) length of the tube. Any 

 definite number of diameters (say 1000) can be obtained with a low 

 power objective (say a 1-inch) as well, from a mere dioptrical 

 point of view, as with a higher power (say |-inch), by applying a 

 sufficiently deep eye-piece and a sufiicient length of the tube. It 

 is, however, well known that there is a great difierence in the optical 

 qualities of images which are produced under these different con- 

 ditions. Forcing a high amplification from a low-power objective 

 is always connected with a considerable loss of sharpness of defi- 

 nition of the image, owing to the magnification of the residuary 

 aberrations, which are inherent even in the most finished construc- 

 tions. It is, therefore, a well-established practical rule that a certain 

 amount of amplification requires a certain power of the objective — 

 higher amphfication a higher power (shorter focal length) — in 

 order to obtain the image under those favourable conditions which 

 are necessary for then- full eflfectiveness. This considered, the 

 inference of the foregoing paragraph may be expressed in these 

 terms : — 



Wide apertures with objectives of short focal length ; low 

 and moderate apertures with objectives of low and moderate 

 power. 



As a detailed discussion of this subject will be found in the 

 second part of this paper, it will be sufficient here to point out 

 some notable facts of experience by way of example only. 



"With objectives of say 1 inch, and ^ inch, focal length, the lower 

 and medium eye-pieces in use will yield 4()-80 and 80-160 dia- 

 meters only. In order to obtain 150 and 300 respectively, very 

 deep oculars (or an extra length of the tube) would be required. 

 So far now as such objectives are intended for the lower powers 

 mentioned above, an aperture of about 0*15 (18") in the case of 

 the 1-inch, and of • 3 (35^) in the case of the ^-inch, are at all 



