The Helmholtz Theory of the Microscope. By J. W. Gordon. 405 



Let us then take the point 17! as an example and assume the 

 diffracted beam which focusses there to be reverted through the 

 instrument. Upon its arrival at the aperture A ... A it will rein- 

 force and exactly double the diffracted beam, which starts at that 

 aperture from the principal reverted beam, and, therefore, we can 

 ascertain the position of the diffracted image e x by working back 

 to the point in the object-plane which is conjugate to the point 17 x 

 in the image-plane. 



So far we have assumed an arbitrary position for the point 7} x 

 in the image-plane, but with the help of this result we can proceed 

 to determine it by calculation. For, if it is the image of the point 

 €1, its position is determined thereby. Now, the position of e x is 



Fig. 92. 



evidently determinable without any reference to the refracting 

 system B, for all the conditions upon which it depends are ascer- 

 tainable the instant that the aperture is passed by the outgoing 

 beam of light from e. Suppose then that instead of the refracting 

 system B and the image-plane ^ ... % we make use behind the 

 aperture of a spherical mirror b, as shown in fig. 92, having its 

 centre of curvature at e. Such a mirror will reflect the principal 

 beam to e, and the diffracted beam hot quite accurately to e lt If 

 we assume that for the first purpose it is to take the form of b sym- 

 metrical with reference to the optical axis of the principal beam, 

 and for the second purpose the form of c symmetrical to the axis 

 of the diffracted beam, we shall have the position of e x perfectly 

 defined. Then the point ^ must be conjugate to this point in the 

 optical system represented in fig. 91. 



