302 THE AMERICAN MONTHLY [Oct 



made a most careful and profoundly scientific enquiry into 

 the matter, and found that there was no basis whatever 

 for such an assertion. No, it had formed on wrong con- 

 ceptions, and wonderfully did he expose and demolish the 

 theory in a manner too long to enter upon here in a short 

 article of this nature. The angle is that formed in the ob 

 jective. 



To put the matter in quite another way, perfect defi- 

 nition is wholly and absolutely dependent not upon the 

 obliquity of the rays to the object, as before believed,but 

 in truth upon the obliquity they bear to the axis of the 

 microscope. To repeat then,, to increase the aperture of 

 the objective is found to be the means for improvement 

 of definition. But Prof. Abbe went further into the mat- 

 ter and found that increased aperture seemed to admit "a 

 something'" more than the true dioptric image, and this 

 "something" he ultimately discovered by a series oil ele- 

 gantly and well-contrived experiments to be nothing more 

 or less than the diffraction rays which proceeded from the 

 object itself. Pressing the subject to its logical conclu- 

 sion, he found that the more of these rays that were ad- 

 mitted to the optical combination, i. e., the greater the 

 numerical apeture of the objective, the more the similar- 

 ity that would exist between the object and its image. 



We are now in a position to reply to our question, and 

 the reply is simply this : — The higher the defining power 

 of the objective, the greater is its numerical aperture 

 (usually written thus "N. A."), and as the definition de- 

 pends on the greatness of this aperture, so it directly 

 follows, that the higher the power used the better the fi- 

 nal result. Seeing that achromatics, especially the higher 

 power ones, cannot without greater difficulty be made 

 with such high numerical aperture as those built on the 

 apochromatic system, so the former cannot on this ground 

 — if on no other — be expected to give the results that the 

 new system affords ; still, on the other hand, it must not 



