its deviation from its former course requires for its determination a much more complicated rule, which cannot be understood or even stated without a pretty intimate knowledge of geometry. Now, rock-crystal and Iceland spar differ from glass in a very remarkable circumstance. They affect naturally certain regular figures, not being found in shapeless lumps, but in determinate geometrical forms; and they are susceptible of being cleft or split much easier in certain directions than in others--they have a _grain_ which glass has not. When other substances having this peculiarity (and which are called _crystallized_ substances) were examined, they were all, or by far the greater part, found to possess this singular property of _double refraction_; and it was very natural to conclude, therefore, that the same thing took place in all of them, viz. that of the two rays, into which any beam of light falling on the surface of such a substance was split, or of the two images of an object seen through it, _one_ only was turned aside out of its _plane_ and _extraordinarily_ refracted, while the other followed the _ordinary_ rule. Accordingly this was supposed to be the case; and not only so, but from some trials and measurements purposely made by a philosopher of great eminence, it was considered to be a fact sufficiently established by experiment. (23.) Perhaps we might have remained long under this impression, for the measurements are delicate, and the subject very difficult. But it has lately been demonstrated by an eminent French philosopher and mathematician, M. Fresnel, that, granting certain _principles_ or postulates, all the phenomena of double refraction, including perhaps the greatest variety of facts that have ever yet been arranged under one general head, may be satisfactorily explained and deduced from them by strict mathematical calculation; and _that_, when applied to the cases first mentioned, these principles give a satisfactory account of the _want_ of the extraordinary image; _that_ when applied to such cases as those of rock-crystal or Iceland spar, they also give a correct account of both the images, and agree in their conclusions with the rules before ascertained for them: but so far from coinciding with that part of the previous statement, which would make these conclusions extend to all crystallised substances, M. Fresnel’s principles lead to a conclusion quite opposite, and point to a _fact_ which had never been observed, viz. that in by far the greater number of crystallized substances which possess the property of double refraction, _neither_ of the images follows the ordinary law, but both undergo a deviation from their original plane. Now this had never been observed to be the case in any previous trial, and all opinion was against it. But when put to the test of experiment in a great variety of new and ingenious methods, it was found to be fully verified; and to complete