90 Mr. J. F. W. Herschel on the action of 
other similar bodies, and consequently that, even were its 
axes coincident, its tints, though perfectly regular, would 
still differ very sensibly from the colours of thin plates. This 
secondary cause of deviation ought to become sensible in 
plates cut so as to contain both axes, if examined at a per- 
pendicular incidence ; but I have not yet had an opportunity 
of making the trial. 
If we calculate on the numbers above given, it will soon 
appear that a perfect coincidence of all the colours in a single 
virtual pole is impossible. For this purpose we may employ 
our equation (i) which easily affords the following 
cos 2 (a -j- 0) = cos 2 a j i -}- Y~jr • tan 2 a . sin ( — 8 a ) J 
cos 2 a 
(cosM)* 
taking M an auxiliary angle such that 
tan M = >/ 2 . tan 2 a [ sin ( — 8 a ) 
whence the value of 0 or the position of the coincidence of 
any two coloured rays becomes known, the values of/,/ 7 , 
and — 8 a being given from the foregoing tables. If we 
unite the mean red with the mean green, these formulas give 
0 = — 11° 29', and if with the mean blue, 0 = — i4°8', of 
which the one falls short of, and the other exceeds the angle 
— 1 3 ° 1# given by observation. If we determine by inter- 
polation the values of l' and — 8 a, which give 0 = — 13V, 
we shall find very nearly 
^=34581 — 8 a — 3°37 7 — ^-f-i*2' = 4° 39' 
which correspond to a blue ray strongly inclining to green, 
and in the brightest part of the colour. Now it is evident 
that when a rigorous union of all the rays in the proportion 
in which they exist in white light, is impossible, that of the 
