462 Transactions of the Society. 



Hence every aperture is fully utilized when the amplification 

 of the entire Microscope is sufficient for a distinct and convenient 

 observation of details corresponding to the value of S. Lower 

 amplifications would not exhaust the aperture, because indications 

 of real structure which exist in the image, would remain hidden 

 from the eye. Higher amplifications, on the other hand, will not 

 promote the recognition of the objects, because all the indications 

 of minuter scale which they might perhaps display, do not exist 

 in the objects, but belong to the image only — they are simply 

 modifications of the image due to the aperture in use. Such higher 

 powers would therefore afford nothing more than an exaggeration 

 of those features of the image which are not conformable to the 

 real nature of the object. 



We have now therefore reduced the problem under consider- 

 ation to the single question : What amplification is necessary and 

 sufficient in order to display the 8 of every aperture, under that 

 visual angle which is required for distinct vision ? 



The facts of observation which are within the reach of every 

 microscopist, afford all necessary data for an approximate determi- 

 nation of this amplification. The striation of an ordinary specimen 

 of PI. angulatum becomes visible to a very sharp-sighted eye under 

 an amplification of 150 diameters. As the closeness of the lines 

 is about 0'5 fju (50,000 to the inch) they are thus recognized 

 under a visual angle not much exceeding 1' of arc. But distinct 

 and convenient observation for an average eye will in any case 

 require a much higher power ; how much higher, will of course 

 vary with different individuals. I am, however, sure to leave 

 sufficient latitude for personal diversities in assigning 300 and 

 600 diameters as the limits of useful amplification for details of 

 these dimensions. In observing the diatom, no one, I presume, 

 will deny the advantage of increasing the power if it is below 

 300 ; and on the other hand, no one will admit any further 

 advantage in going beyond 600, provided the observation is made 

 with an aperture not exceeding - 6, which shows the striae, but 

 nothing more* 



It may be inferred from this example, in accordance with 

 many similar facts, that satisfactory observation requires that the 

 smallest detail of the microscopical image shall be displayed under 

 a visual angle of not less than 2' and not more than 4', approxi- 

 mately ; angles which correspond very nearly to the amplifications 

 300 and 600 for dimensions of " 5 [i. 



This admitted, we obtain at once the number of diameters which 

 are required for properly utilizing any given aperture. If a 

 dimension 8 is to be displayed under a visual angle of v minutes of 



* Much higher powers may of course be utilized in the observation of 

 PL angulatum with objectives of wide aperture. Iu this case, however, the image 

 contains indications of form upon the markings of much minuter dimensions. 



