66 
Mr. J. F. W. Herschel on the action of 
C. sin 2 (M k tf) -f- C'. sin 2 (M k'n) -f &c. (a) 
Now, suppose M to begin from zero, and to pass, by a va- 
riation either in the direction of the ray or thickness of the 
medium, or both, through all gradations of value, to infinity, 
or to its maximum, if not susceptible of infinite increase : then 
we see that for every value of M a certain peculiar tint will 
arise, and that, provided M commence at zero and continue 
increasing, the same succession of tints will invariably be 
developed in the same order. Consequently, if we fix upon 
any two tints in this scale of colour, or any two values of M, 
the same succession and the same number of alternations of 
colour must invariably intervene between them, however we 
pass from one to the other. 
In a crystal with two or more axes, the value of M for any 
ray C must of course be zero in the direction of the axis, and 
therefore if the same supposition of the independence of M 
on c be made, the same conclusions should follow ; namely, 
ist. that the extraordinary ray must always vanish in the 
pole, whatever be the thickness of the plate ; and 2dly, that 
the same succession and number of alternations of colour 
should intervene between the pole and any assigned unequi- 
vocal tint, such as black, or the pure brilliant green of the 
3d order of Newton’s scale. Both these conclusions are 
totally at variance with the facts above detailed, as to the 
developement of colour in the poles, and the situation in the 
order of the rings of what we have called the virtual poles. 
Hence we are necessitated either to give up the theory of 
alternate polarisation altogether, or to admit the dependence 
of the multiplier M on c, or on the nature of the ray. Let 
us see to what this will lead us. 
