HISTOLOGICAL ADVANTAGE OF HIGH POWEE 371 



easier to make a J-inch of 100 than a J with 100 ; the result is 

 that low powers with suitably wide apertures are costly. 



In the Zeiss apochromatic series of objectives the 24 mm. of -3 

 N.A. and 12 mm. of '65 N.A. may be considered as lenses of the 

 very highest order ; the relation of their aperture to their power is 

 such that everything which a keen and trained eye is capable of 

 taking cognisance of is resolved when the objective is yielding a 

 magnification equal to twelve times its initial power ; for this purpose 

 an objective must have 0'26 N.A. for each hundred diameters of 

 combined magnification. Under these conditions an object is seen in 

 the most perfect manner possible. In this connection Mr. Nelson 

 has suggested * that the term,V optical index ' should be added to 

 that of the numerical aperture. The optical index or O.I. is the 

 ratio of the numerical aperture ( X 1000) to the initial magnifying 

 power. Thus the numerical aperture of the Zeiss apochromatic 

 24 mm. is '3, and its initial power 1 0. Then its O.I. is \J = 30. The 

 O.I. of the 12 mm. apochromatic of '65 N.A. is 6 /V= 31. That of 

 the j- homogeneous immersion of 1'4 N.A. is J-|jp= 17. Compare 

 now these figures with an old water-immersion ^ of 1*1 N.A. VsV 

 = 2'0. The value of these figures will be apparent when we 

 remember that any lens used with a 10 power eye-piece must have 

 an O.I. of 26 to resolve all detail visible to a keen eye. 



The optical index therefore tells us that the -^ water-immersion 

 of I'l N.A. had a vast amount of empty magnifying power, while on 

 the other hand the 24 and 12 mm. will both stand a higher eye- 

 piece than 10 ; nay, even require it before the detail resolved by them 

 is made visible to the eye. It also shows that the ^ of 1*4 N.A. will 

 stand a higher eye-piece without arriving at an empty magnifying 

 power than the j^ef 1*4 N.A., whose O.I. is ll'O. 



As it is more difficult to put aperture into a lens than power, the 

 O.I. becomes also an index of the money value of a lens. Thus the 

 J mentioned above that had an initial magnifying power of 60 and 

 N.A. of '8 ought to be a cheaper lens than a true J with an initial 

 magnifying power of 40 and a N.A. of '9, their optical indices 

 being 13 and 22 respectively. The limit of combined power for best 

 definition with any objective of any given aperture may be found by 

 multiplying its N.A. by 400. Example : The limit of power for best 

 definition with a of '3 N.A. is 120 diameters. The converse rule 

 may be stated thus : The ideal N.A. for any objective whose initial 

 power is known can be found by multiplying its power by '025. 

 Example : The ideal N.A. for a | of power 20 is 20 x '025 = '5 N.A. 



It may be well for the student to prove this, which may be 

 readily done. 



Take a suitable object, such as a well-prepared proboscis of a 

 blow-fiy, and examine it under critical illumination with the 24 mm. 

 3 N.A. (= 1-inch) objective, and a 12 compensating eye-piece. 

 Note with close attention every particular of the image : the 

 resolution of the points of the minute hairs, the form of the edges of 

 the cut suctorial tubes, the extent of the surface taken into the 

 t field,' and the relation of all the parts to the whole. 



1 Journ. It. M. S. 1893, p. 12. 



B B 9. 



