78 Mr. J. F. W. Herschel on the action of 
will lead to some very remarkable consequences, requires us 
to know the form of the function *|/ and the values of k, k'. We 
will begin with the former, and in this investigation the first 
step is to determine the general equation of the isochromatic 
lines. In order to this, we must separate in all cases the law of 
the tint from that of its intensity. The latter depends entirely 
on the greater or less facility which the emergent ray finds in 
penetrating the prism of Iceland spar employed for its analysis, 
and will not enter into the present investigation. When we 
examine a crystallized plate in a convenient graduated appa- 
ratus, between tourmaline plates crossed at right angles, turn- 
ing it slowly round between them in its own plane, the form 
of the coloured bands, if illuminated with homogeneous light, 
will remain perfectly unchanged during the rotation, but the 
two black hyperbolic branches passing through the poles, 
will obliterate in succession every part of their periphery ; 
and the space over which the darkness extends, as well as 
the degree of illumination of what remains visible, varying 
at every instant, give rise to so great a variety of appearances, 
that some little attention is required to recognize this perfect 
identity of figure. When the tourmaline next the eye is 
made to revolve, the crystallized plate remaining fixed, the 
complicated changes which take place, are perfectly recon- 
cilable with the superposition of the primary on its comple- 
mentary set of rings, the relative intensities of the two sets 
at any point being regulated by laws we have no occasion to 
consider at present, but the figure of the isochromatic lines, 
where visible, remains absolutely unchanged by any rotation 
in this part of the apparatus. 
To form a first hypothesis on the nature of the function 
