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of Edinburgh, Session 1867 - 68 . 
ful to be able to place the lenses and prism in such a way as to 
bring the rays of all colours to their foci at approximately the same 
distance from the prism. 
We shall first examine the effect of tbe prism in changing the 
convergency or divergency of the pencils passing through it, and 
then that of the lens, so that by combining the prism and the lens 
we may cause their defects to disappear. 
When a pencil of light is refracted through a plane surface, its 
convergency or divergency is less in that medium which has the 
greatest refractive index ; and this change is greater as the angle 
of incidence is greater, and also as the index of refraction is 
greater. 
When the pencil passes through a prism its convergency or 
divergency will be diminished as it enters, and will be increased 
when it emerges, and the emergent pencil will be more or less con- 
vergent or divergent than the incident one, according as the angle 
of emergence is greater or less than that of incidence. This effect 
will increase with the difference of these angles and with the 
refractive index. 
When the angle of incidence is equal to that of emergence the 
convergence of the pencil is unaltered, but since the more refran- 
gible rays have the greatest angle of emergence, their convergency 
or divergency will be greater than that of the less refrangible 
rays. 
This effect will be increased by making the angle of incidence 
less, and that of emergence greater; and it will be diminished by 
increasing the angle of incidence, that is, by turning the prism 
round its edge towards the slit. If the angle of the prism is not 
too great, the convergency or divergency of all the pencils may be 
made the same (approximately) by turning the prism in this way. 
This correction, however, diminishes the separation of the colours. 
It is inapplicable to a prism of large angle, and it takes no account 
of the chromatic aberration of the lens. By altering the arrange- 
ment, the lens may be made to correct the prism. The effect of a 
convex lens is to increase the convergency, and to diminish the diver- 
gency, of every pencil ; but the change is greatest on the most refran- 
gible rays. The prism, except when its base is very much turned 
towards the slit, makes the highly refrangible rays more convergent 
