DELINEATION OF THE FINE STRUCTURE OF OBJECTS. 233 



to a whole wave-length ( = \), is similar to the triangle a a' B, and 

 therefore B P: X = a B : a a ; 



7? 



w T hence B 1 



a a 



But a B is equal to the posterior focal length ^?* less the focal 

 /, that is, p* -f. Similarly, the distance a a, between the cor- 

 responding points of the aperture-images, is obtained by means of 

 sin a ./, as above explained. Since, then, for the first diffraction 



pencil sin a = T, if d denotes the distance of the lines in the 



Cij 



object, this formula becomes 



L f 



v*f d 



or, since f equals the magnifying power ra, B P = ra d t . 



t/ 



that is, the distance between the interference lines in the real 

 objective-image is ?ft-times the distance of the bright lines in the 

 object. This implies that the number of interference lines agrees 

 with those of the striae. 



The same action produces, of course, the diffraction image 

 formed at a", if it is combined with the direct one. On the other 

 hand, if the direct image be stopped off, and the two diffraction 

 images allowed to interfere (in the dark field of view), the de- 

 nominator a a in the above formula will be doubled, and the 

 distance of the lines therefore reduced to half. Similarly, by 

 means of suitable stops, a reduction of J, J, &c., of the actual 

 distances may be effected so far as additional diffraction images 

 come into play. The stria? will therefore appear in this case 

 three or four times as fine as they would be in an image true to 

 nature. In general, there is no difficulty in determining before- 

 hand the effect of interference, as soon as the number and position 

 of the diffraction images in the focal plane of the objective are 

 known. 



The method of stopping off the aperture-images in the upper 

 focal plane of the objective, the use of which for the study of 

 diffraction phenomena cannot be too much insisted upon, furnishes 

 unquestionable evidence of the production of the structure-image 

 through interference. As soon as the aperture-images due to 



