crystallized bodies on homogeneous light • 6g 
degree of proportional intensity for the production of a white 
image, provided we suppose 
which, since k, k ' , a, $ a, are constant elements, cp, q>' determinate 
functions of 0, and 6'= Q -J- 2 a, suffices to determine Q. 
If we suppose C and C' to represent the extreme red and 
violet rays, it is evident that the coincidence of the extra- 
ordinary pencils of the same order for these two extremes, 
will ensure that of the intermediate ones, at least very nearly. 
It would do so precisely, were the value of 8 a for any inter- 
mediate ray, such a function of k as would result from mak- 
ing 6 constant in the preceding equation, because the two 
laws, that of the dispersion of the axes, and that of the magni- 
tude of the rings of different colours, would then act in exact 
opposition to each other throughout their whole extent. It 
is, in fact, a case precisely analogous to that of the compound 
achromatic prism, where if the law of dispersion in the one 
medium were identical with that in the other, a perfectly 
colourless pencil would emerge, and when these laws differ, 
the coincidence of the red and violet rays ensures an approxi- 
mate coincidence of all the rest. Should these laws however 
differ very considerably, an uncorrected colour will appear 
at the point so determined, and a nearer approximation will 
be obtained by uniting two of the more powerful intermediate 
rays, such as for instance the mean red and the blue, or 
limit of the green and blue. 
This then is the origin of the virtual poles or points be- 
yond or between the axes where the tint rises to a white of 
the first order, more or less feeble, or even to an absolute 
black ; and we may now see the reason why the tints in 
