TESTING THE SPHERICAL ABERRATION. 155 



placement of the screen in the direction of/ x to wards / 4 , influences 

 the distinctness of the image less than the opposite displacement, 

 as all the focal points of the peripheral rays, and consequently 

 the images corresponding to them, lie to the right of f v "between 

 p and p. A displacement in this direction corresponds, in an 

 under-corrected objective, to an approximation, and in an over- 

 corrected one to a withdrawal of the object. If the objective is so 

 constructed that the marginal rays of the cone of light, up to a 

 certain minimum of inclination, are the image-forming ones, while 

 the central rays aberr towards the one or the other side (Fig. 91), 

 then, of course, the rule stated by these writers is applicable. 

 This, however, is only one of the various combinations imaginable ; 

 and even if it frequently occurred, which we doubt, it should not 

 be accepted without further investigation. We must not therefore 

 take the slower or quicker disappearance of the minute image on 

 raising or lowering the focus as a criterion of over- or under- 

 correction, except in so far as its applicability has been otherwise 

 demonstrated. 



In the path of the rays delineated in Fig. 91, the position of 

 the screen (or of the eye-piece setting) to the plane /j/p in which 

 the objective-image is formed, necessarily involves a slight fog, 

 due to the central rays; but this disappears immediately on a 

 slight displacement to the right or left. It is immaterial whether 

 the objective is supposed to be in A B or A B' \ the circle of 

 light, which is projected upon the screen by different focal 

 adjustment, appears clearly denned in either case. Spherical 

 aberration, therefore, is exhibited only in the plane of the image 

 as fog, which does not appreciably alter on the withdrawal of 

 the diaphragm that limits the aperture of the whole effective cone. 



If to the image-forming peripheral rays others are added which, 

 like the central ones, are affected with aberration, the phenomena 

 become more complicated. By the effect which the marginal rays 

 produce with higher or lower focal adjustment, they are seen 'to be 

 over- or under-corrected, whether the central rays aberr in the 

 same or in opposite directions. In this case it is necessary to 

 diminish or to withdraw the diaphragm until the bluish fog suffers 

 no further alteration with a medium adjustment, and totally 

 vanishes with a lower or higher adjustment. The residual traces 

 of aberration must therefore proceed from the central rays ; and 

 the above-mentioned criterion of under- and over-correction, that 



