68 
Mr. J. F. W. Herschel on the action of 
axes of double refraction to differ in the same crystal for 
the differently coloured rays. We must now show that this 
supposition is sufficient to represent the phenomena cor- 
rectly. 
The symmetry of the rings and total evanescence of colour 
in the principal section at an azimuth zero, requires that the 
axes of all the different colours shall be symmetrically ar- 
ranged, on either side of a fixed line (which may be called 
the optic axis) in this plane, or in one perpendicular to it. At 
present we need only consider the former case. Let a repre- 
sent the angular distance of the axis for any one standard 
species of ray C (the extreme red, for instance) from this 
line, a $a, the same distance for any other ray. Then 
the distance of the transmitted ray C, from the axes of rays 
of that colour being 9, 9', the corresponding distances from 
their respective axes for rays of any other colour C' emerging 
in the same direction will be 9 — £ a and 9' + Sa -f- S<p f 
$ q> being the difference ( = <p' — <p) of the angles of refrac- 
tion, corresponding to the same incidence, for the colours 
C, C'. The positive values of 9 here reckon outwards from 
the pole ; £ a is negative for crystals of the second class, 
and d'cp is negative or positive according as C or C' is the less 
refrangible colour. 
Let us for a moment consider rays of only these two 
colours. The portion of the extraordinary pencil due to them 
will be 
sin E (^ ^ (0» Q')’ 7r )+ C'. s ^ n ” a + 7r )‘ 
The rays of these colours of the same order in their respective 
series of rings will therefore coincide, and that in the proper 
