4f6 Mr. J. F. W. Herschel on the action of 
directions in which a ray may penetrate their substance with- 
out separation into distinct pencils, has proved the fallacy of 
any such generalization, and rendered it necessary to enter 
on a far more extensive scale of investigation. 
There are two methods which may be pursued in obser- 
vations on double refraction and polarisation, the one direct, 
the other indirect. The former turns on immediate observ- 
ations of the angular deviation of the extraordinary pencil, 
and is, of course, only applicable when the forces which act 
exclusively on the rays composing it are sufficiently intense 
to cause a sensible separation of the two pencils. There 
exist, however, a multitude of crystals in which the force of 
double refraction is so feeble as to produce scarcely any, or 
at most a very inconsiderable deviation of the extraordinary 
ray, and in which, consequently, the laws of double refrac- 
tion could neither be investigated nor verified, without having 
recourse to some artificial means of magnifying the quantity 
to be observed ; a thing easy enough in theory, but requiring, 
in practice, the. greatest nicety on the part of the observer, 
and in many cases altogether impracticable, from the phy- 
sical constitution of the crystals themselves. The indirect 
method depends on the discovery of Arago, scarcely inferior 
in intrinsic importance to that of Malus, of the separation of 
a polarised ray into complementary portions by the action of 
a crystallized lamina. It was reserved, however, for the 
genius of M. Biot, to trace this striking phenomenon to its 
ultimate causes, in the action of crystals on the differently 
coloured rays, and to develope, in a simple and elegant theory, 
the successive gradations by which the polarisation of a ray 
in its passage through a doubly refracting crystal is performed; 
