;1 16 Mr. Herschel on the Action of [Feb. 



'The discovery, by Dr. Brewster, of crystals possessing two axes 

 of double reirection, or two directions in which a ray may pene- 

 trate their substance without 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 observations 

 on double refraction and polarisation, the one direct, the other 

 indirect. The former turns on immediate observations of the 

 .{angular deviation of the extraordmary 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 separa- 

 tion 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 refraction could neither be investigated nor verified, 

 ^vithout 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 

 physical 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 pola- 

 rised ray into complimentary portions by the action of a crystal- 

 lized 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 grada- 

 tions by which the polarisation of a ray in its passage through a 

 doubly refracting crystal is performed ; while, on the other hand, 

 the splendid phenomena of the polarised rings, which we owe to 

 Dr. Brewster, have established the connection of the tints so 

 polarised with the force producing the deviation of the extraor- 

 dinary pencil, and shown the legitimacy of conclusions respect- 

 ing the intensity of the latter, drawn from observations on the 

 former. 



This indirect mode of observation, which consists in noticing 

 the gradations of colour for different positions and thicknesses 

 of the crystal, possesses three capital advantages. The first is 

 its extreme sensibility, which enables us to detect the existence, 

 and measure precisely the intensity of forces, far too feeble to 

 produce any measurable deviation of the extraordinary pencil. 

 It, in fact, affords the rare combination of an almost indefinite 

 enlargement of our scale of measurement, with a possibility of 

 applying it precisely to the object measured, arising from the 

 distinctness of all its parts. Another, no less precious, is the 

 leading us by mere ocular inspection to the laws of very compli- 

 .cated phenomena, and enabling us to form, and mould, as it 

 'Were, our analytical formula), not on a laborious, and sometimes 



