116 THE AMERICAN MONTHLY [July 



Prof. Abbe's early contention as to " different origins " 

 of different parts of the image. Many of us have written 

 of this as an "error," now "recanted," which strictly is 

 true; but there is this broad practical sense in which it 

 also is true. 



And we are unable to use either kind of image or of 

 illumination absolutely pure, if we desired to do so. The 

 narrowest pencil we can practically use will not give us 

 absolutely plane waves alone ; there will be some amount 

 of heterogeneity in the pencil, which in some little 

 degree serves to correct our image. And the widest 

 cones we can use, or even ground glass, do not prevent 

 greater or less approach to the character of plane-waves, 

 as the rays travel farther from the lamp ; and these by 

 their interference tend to intensify the image. We have 

 to play off and adjust one against the other. In so far 

 as we may regard every elementary or excessively small 

 cone or pencil of rays from the condenser as an indi- 

 vidual beam of plane waves (which no doubt is the case 

 in some degree), in passing through the object it originates 

 two or more pencils from the same point. These being 

 necessarily in the same phase or phase-relation, so far as 

 they exist must interfere at the focus, and thus intensify 

 the image. On the other hand, the numerous such ele- 

 mentary pencils comsrising a wide cone, are in many dis- 

 cordant phases and transversals, and this very hetero- 

 geneity tends to correct the contours in the image, as 

 above. We thus understand why, in really critical 

 work, a large cone from a good condenser usually gives 

 us the best results ; but why it may be impossible, even 

 with a perfect objective, to use a cone of light which 

 will fill its aperture completely. It may be necessary^ 

 to intensify the image, while using as much heteroge- 

 neous light as we can, to use only pencils each of which 

 throws out another diffracted pencil grasped by the 

 aperture, so as to intensify, or correct it. But this 



