The Belation of A][>erture and Power. By Frof. E. Abbe, 811 



been derived, triple systems of moderate working distance must be 

 supposed down to apertures of about • 3, and du'plex systems for 

 all the lower ones which are considered here. The medium aper- 

 tures, if realized with two lenses only, and the lower ones, if 

 realized with single lenses, would show considerably smaller figures 

 of V than are given above. On the other hand, triple systems with 

 apertures much below ' 3 do not afford any perceptible increase 

 of the admissible super-amplification — a fact which is well accounted 

 for by the theory of the aberrations. 



So far as the basis of my reasoning is admitted as valid, the 

 table given above will exhibit the proper ratio of aperture to focal 

 length in an ideal series of dry objectives of increasing apertures, 

 traced out in strict conformity to the principle that every objective 

 should yield, under the best ^possible conditions, such a total amplifi- 

 cation as is just sufficient for fully exhausting the delineating power 

 of its aperture — wherein " best possible conditions " means that no 

 higher super-amplification, by tube and ocular combined, should be 

 required than that which will just raise the dioptrical defects of the 

 image up to the threshold of vision. 



It is not my opinion that the standard series thus obtained 

 should always be strictly adhered to in the practical construction of 

 objectives. It is rather advanced here as a theoretical guide which 

 will give a general direction in designing systems on a rational 

 basis, but does not prohibit any deviation from that standard, 

 provided it be justified by this or that practical consideration. 



Deviations in the direction of diminished aperture (or increased 

 power) need not be discussed here, since at present no tendency of 

 that kind is met with, except in Microscopes of quite an inferior 

 class. The only question which deserves consideration is therefore. 

 What latitude may be properly admitted for deviations from the 

 standard proportion in the direction of increased apertures (or 

 diminished objective-powers) ? 



The case here is somewhat different from that discussed above 

 in the consideration of the proper utihzation of the maximum aper- 

 ture of any kind of system. For the angles which come into con- 

 sideration now, being more or less within the attainable maximum, 

 aperture is no longer difficult to attain. A surplus being easily 

 obtained, may be sacrificed without hesitation, whenever such a 

 benefit may be expected therefrom as is not counterbalanced by 

 greater disadvantages. The question will therefore come to merely 

 practical grounds : how far a surplus of aperture may afford a real 

 (not only illusory) advantage, and what is the balance between 

 these advantages and disadvantages which are perhaps attendant 

 upon the increase ? 



As has been pointed out before (Vol. II. 1882, p. 469), there is 

 a reasonable consideration which will recommend in some cases, 



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