468 Transactions of the Society. 



know very well that the most trustworthy power of a telescope 

 is not the highest power which the instrument will bear, but that 

 power which has a certain relation to the diameter of the objective. 

 If they use a higher amplification than about 40 per inch of the 

 diameter of the objective (i. e. 120 for a 3-inch, 400 for a 10-inch 

 objective) they begin to detect diameters of stars which have no 

 diameters. A very good 3-inch objective will, indeed, show more 

 under a power of 300 than of 100, apparently ; just the same as 

 with a very good wide-angled Microscope-lens in regard to 3000 

 and 1000 diameters. In fact, the 300 diameters of the 3-inch 

 will reveal, with somewhat bright fixed stars, very neat and distinct 

 disks which are invisible, or nearly invisible, under a power of 100. 

 But these disks disappear at once, when the amplification of 300 

 is obtained with an objective of 9 inches diameter.* Astronomers 

 are accustomed to apply much higher powers than 40 per inch for 

 various purposes ; but they do not apply them whenever they want 

 to recognize the true shape and magnitude of their objects. 



It is just the same in the Microscope. The greatest possible 

 approximation of the image to a true projection of the object is 

 not obtained by the highest powers, but by those powers which 

 are just capable of exhibiting to the eye the least dimensions of 

 real structure within the reach of any given aperture. 



I invite the particular attention of microscopists to this 

 subject, as it is in my opinion of great practical importance in 

 regard to the proper use of the Microscope. For my present 

 purpose I may confine myself to the statement that it does not 

 belong to the rational aim of microscopical optics to enhance the 

 amplification of the Microscope beyond those moderate figures 

 which are sufficient for utilizing the attainable apertures; the 

 rational aim is rather to obtain the best possible accomplishment 

 and the most favourable conditions, for the use of these moderate 

 amplifications. 



3. So much as to the proper relation of aperture and amplifica- 

 tion at the upper end of the scale of microscopical performance, 

 where the question is of the largest attainable apertures and 

 highest useful powers. In regard to the lower end of the scale, 

 the suggestions indicated by Tables I. and II. will require some 

 further remarks. 



So far as the principle is admitted on which the computation of 

 the tables has been based, we must consider the small apertures 

 assigned for the lower powers of the Microscope as sufficient, 



* The physical conditions of the phenomena in question are not the same in 

 the telescope and in the Microscope, but yet very similar. In both cases the 

 effects do not arise from deep oculars — as is often assumed — but depend only on 

 the relation of the total amplification of the instrument to the aperture. 



