54 Transactions of the Society. 



eye-piece has less effect with it in magnifying every imperfection 

 of the image. 



It might be rash to predict what is the utmost pencil that may 

 be brought together to form the picture in the Microscope, but 

 the object-glasses of our best artists are now constructed expressly 

 with a view to this, and considering the greatly increasing difficulty, 

 as the angle is further enlarged, of obtaining the essential state of 

 true correction while the definition even on the most favourable 

 objects does not increase correspondingly, I am induced to believe 

 that it cannot be carried with advantage much further than it has 

 been. The finest vision I have yet seen has been with a pencil of 

 about 80°, and even supposing 100° collected as exactly, which we 

 can hardly anticipate, we should not have advanced beyond a 

 separation of 0' 000014 in. 



To express the magnifying-power of the compound Microscope, 

 we may first take that of the object-glass, which is inversely as 

 its front focal distance (d) to that of distinct sight, usually called 



10 in., or -^,* and this is increased, in the ratio of the diameter (a) 



of the object-glass, to that of the pencil entering the eye as in the 

 telescope (p. 45) ; so that if as before we take the latter pencil as 

 0*02 in., we should have for the magnifying-power, with any 

 object-glass that will reach the utmost definition of an object 



placed in the most favourable circumstances, —r • t^-?^^ = — i — , oi" 



cl yj'Ol d 



500 times the aperture divided by the focal length. 



This rule may be applied to the range of microscopical power 



in general, but there may be no disadvantage to definition with 



somewhat greater enlargement if the light is sufficient and the 



instrument fi-ue ; and, indeed, some details of transparent objects 



viewed by strong illumination with object-glasses of large pencil 



and short focus, seem more satisfactorily made out with rather 



750 a 

 higher amplification ; to raise it, however, to — -^ — , which allows 



a power of 750 for a pencil of 60° and for 80° barely lOOO-linear, 

 will, I believe, more than provide for such cases ; and it is always 

 found that to go much beyond wliat is necessary for distinctness 

 tends to produce the contrary, so that (except for measurements, 

 or other ])urposes than definition) sucli enlargements as 2000 or 

 3000 which have been assigned to Microscopes must be worse 

 than useless. 



There is another mode of considering defining-power which, 



* Note by A.E.C. — Having forestalled Abbe as to numerical aperture, it will be 

 seen tbat J. J. Lister bere anticipates tbat novel way of apportioning the total 

 magnification whieb first became generally known as an Abbe innovation when 

 the apochromatic objectives were issued in the eighties I 



