ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
779 
(fig. 83) in the upper under-compensated lens S 15 the blue ray (punctuated 
in the figure) cuts the middle lens S 2 at a shorter distance from the axis 
than the yellow. Consequently by sufficient over-compensation of the 
middle lens, the blue and yellow rays on emergence from the front lens can 
be made to converge to the same point a. Then the angle of convergence u 
for both rays is the same, and therefore the difference of the magnification 
is removed. In seeking to apply this method, however, it was found 
that the chromatic difference of magnifi- 
cation is so connected with the chromatic Fro. 83. 
difference of the spherical aberration that ct 
a diminution of the one leads to an in- 
crease in the other. Tracing the path of 
a yellow and blue ray (very near to the 
axis) and the yellow and blue marginal ray 
from the eye-piece to the point of emer- 
gence from the front lens S (fig. 84), the 
two yellow rays do and do' and the blue 
circumpolar ray / o converge to the same 
point on the axis, when the system is 
spherically and chromatically corrected 
for this. On the other hand, the blue 
marginal ray f' o', in consequence of the 
chromatic difference of the spherical 
aberration, cuts the axis behind the point 
o (in o'). 
Now consider the system changed so 
that in the upper lens the dispersion of 
the crown glass is diminished, and that 
of the front lens increased, in both cases 
without change of refractive indices (for 
D). If this is done in such a way that 
the colour-aberration of the circumpolar 
ray is still removed, then the path of the 
two yellow rays suffers no change. On 
the other hand, the two blue rays, in con- 
sequence of the stronger over-compensation of the upper lens, cut the 
end face of the front lens at a greater distance from the axis than in 
the first system. By increasing the dispersion of the front lens, the 
blue circumpolar ray will cut the axis in the same point o as before, 
while the blue marginal ray, in consequence of the greater spherical 
aberration, cuts it in a point above o'. Accordingly, by sufficient over- 
compensation of the upper lens, the blue marginal ray can finally be 
also made to cut the axis in o. 
Thus in systems of three or four members of determined form and 
refraction the chromatic difference of the spherical aberration is reduced 
by chromatic over-compensation in the hinder members, accompanied by 
increased dispersion of the front lens. But, as seen from the figure, this 
must produce an increase of sin u, so that the diminution of the spherical 
aberration of the blue rays goes hand in hand with an increase of the 
chromatic difference of the magnification and vice versa. The method of 
under-compensation of the upper lens (fig. 83) is therefore not to be 
