ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 131 



unshaded parts iho wave-crests ; then the figure indicates the altered 

 conditions as compared with the first figure for the case in which, 

 corresponding to the different refractive indices of the two discs, the 

 portion of the light-wave which has traversed one of them is retarded hy 

 an uneven numher of half wave-lengths behind the other. It will be 

 seen at once that (//and gh in their action on B cancel each other, as do 

 also the other elementary strips, just as in the first case. Further, it 

 will be seen that this extinction takes place for every point of the line 

 independently of the distance g B, and that with an alteration in the 

 thickness of the fibre a periodic alternation between light and partial 

 darkness must take place. The case is different when we consider a 

 point which is not at right angles to the bounding surface, e. g. C, 

 fig. 33. The vis viva to be transferred from fh to C is neither 

 cancelled as in the second case, nor weakened in the same degree as in 

 the first case by the neighbouring elementary stripes, whose phase is 

 . shifted through a half wave-length, but it reaches C, so far as concerns 

 the portion f g, in its full extent, the action of ef and gh being added 

 with positive sign to that of fg, though each of the first is weakened to a 

 certain extent, it is true, by the slight action of d e and h L While there- 

 fore, the point B remains undisturbed, C receives an intensity of vibra- 

 tion, and a ray travels in the direction p C. This corresponds to the 

 first diffraction pencil, 



Supposing that the muscle disc m g f u were much smaller, and 

 extended from / only to a point, o (not shown in the figure), between e 

 and /, if this thin layer is to have any effect upon the microscopic image 

 it must, at least, contribute a diffracted pencil to the production of the 

 image. The smaller f o, the farther must C travel from C^ that the 

 difference of path between the portions of the wave/o and fg may attaiu 

 a half wave-length, and the larger, therefore, must be the angle made 

 by the diffraction pencil with the perpendicular n f. When/o is nearly 

 a half wave-length, then this angle is nearly a right angle, and we get 

 the law discovered by Helmholtz, that microscopic delineation ceases 

 when the detail to be observed diminishes to the size of a half wave- 

 length, presupposing an aperture of the Microscope of 180°. In this 

 case one, at least, of the pencils of light diffracted by the structural 

 element still enters into the microscopic image. 



If we consider the boundary of the disc more closely, it is clear 

 that there will be a similar interference upon the other side of / n. 

 Here also there will be a ray in the direction p x d- Now, the two 



rays p C and p x d have a difference of phase equal to -3-" Focusing, 



therefore, upon the point of intersection of these two rays, we shall see a 

 dark line under the upper surface of the fibre. If we focus the inter- 

 section of ]) C with the corresponding line r q from the other surface 

 of the disc, a bright band must be visible, as will also be the case 

 when the Microscope is focused on the point above the fibre in which 

 p, C x intersects the corresponding line (not shown) upon the other 

 side. 



The phenomena here described bear some relation, on the one hand, 

 to the interference phenomena of the so-called ' mixed scales ' discovered 

 by Young, which are explained by the retardation of a part of the light- 

 waves which traverse a medium of different refractive index from the 

 rest ; and, on the other hand, with the ' lamellar diffraction phenomena ' 



k 2 



