TESTING THE SPHERICAL ABERRATION. 



153 



fog caused by the marginal rays incident on the surrounding 

 parts. If the screen is moved further to the left, in the position 

 / 2 , it cuts both the central cone and the aberrant peripheral rays 

 in a larger surface ; the image must consequently be dim, while 

 the fog increases in extent. If, on the other hand, the displace- 

 ment takes place in the opposite direction, the cross-section of 

 the solid cone of rays becomes at first smaller, attaining its 

 minimum in / 3 , where the peripheral rays intersect with the 

 image-forming rays, and consequently the fog disappears. The 

 screen is therefore illuminated in / 3 by a small sharply bounded 

 circle of light. Further to the right the latter again increases in 

 extent ; it retains, however, the same sharp outline, because the 

 peripheral rays are projected within it. In the neighbourhood of 

 / 4 even the marginal zone of the circle of light appears decidedly 

 brighter, because the aberrant rays here approach the upper surface 



FIG. 90. 



of the central cone ; it contrasts, therefore, still more decidedly 

 than before with the dark surroundings. 



The phenomena are precisely reversed when the spherical 

 aberration is under- corrected for the peripheral rays. In order to 

 apply the same construction to this case, let us suppose in the 

 above figure that the objective is at A I? instead of A B. The 

 path of the rays corresponds to the opposite aberration ; and the 

 same movement of the screen, which, as regards A B, was an 

 approximation, is now receding with regard to A B'. The pro- 

 jections of the united cones of rays remain obviously the same 

 in the different positions. 



If, therefore, the Microscope is focused on the illuminating 

 surface as accurately as possible, the approximation of the eye- 

 piece is accompanied, in an over-corrected instrument, with a 

 stronger appearance of fog; in an under-corrected one, by the 



