TESTING THE CHROMATIC ABERRATION. 163 



marginal points of the object. Since the refractions which they 

 undergo are, of course, symmetrical also, it would have been 

 sufficient to have made the construction on the one side and to 

 have added the image-points to the other at equal distances. For 

 more convenient comparison, two opposite cases have been placed 

 side, by side ; on the left the path of the rays when the objective 

 is chromatically over-corrected, and on the right when under-cor- 

 rected to the same extent. The apices of the violet cones of rays 

 are denoted on both sides by v, and those of the red by r ; 

 similarly, the corresponding points of the real image by v' and r'. 



It is now clear that the red pencils of light undergo, in the 

 field-lens, the same deviation on both sides, as they meet it also 

 at the same angle ; this obtains also with the violet pencils. The 

 focal points o and p of similarly indicated pencils therefore, of 

 necessity, lie in the axis. With regard to the position of the 

 real image-point v and /, it is clear that on the left /, and on the 

 right v', is nearer to the field-lens than the similarly indicated 

 image-point of the other side. The distance in the direction of 

 the axis is, however, necessarily less than that of the two rs or of 

 the two v's in our figure, therefore less than 6 '5 mm. Similarly, 

 it is clear that, with equal distance of the virtual objects v and r, 

 the violet image v' will be at somewhat less distance from the 

 field-lens than the red one r'. The real images on both sides must 

 therefore be situated as represented in the figure. 



The refraction in the eye-lens, as was above pointed out (Fig. 61 

 and the preceding), is dependent on its position. If the centre of 

 curvature of the refracting spherical surfaces lies between the focal 

 points o and p, the first refraction of both pencils takes place in 

 the opposite direction, and a relation may be produced, which will 

 lessen its divergence to any degree, or perfect parallelism may 

 possibly be effected ; the refraction in the opposite direction is not, 

 however, an indispensable condition. The fact that the red rays 

 meet the eye-lens at a greater distance from the centre than the 

 blue rays, and are therefore also more strongly refracted on account 

 of spherical aberration, is quite enough to. cancel these differences 

 of inclination, and might even reverse their direction. If we con- 

 sider that the differences in deviation due to this are the more 

 important the further the eye-lens is removed from the field-lens, 

 it becomes intelligible that a gradual increase of this distance will 

 at last bring the axes of the emergent pencils to convergence. In 



