RBPORT ON PHYSICAL OPTICS. 383 



any particle displaced from its position of rest, the resultant of 

 the elastic forces which resist the displacement will not, in 

 general, act in the direction of that displacement (as in the case 

 of a medium uniformly elastic), and therefore will not drive the 

 displaced particle directly back to its position of equilibrium. 

 Fresnel has shown, however, that there are three directions at 

 right angles to each other, in any of which, if the particles are 

 displaced, the elastic forces do act in the direction of the dis- 

 placement whatever be the nature or laws of the molecular ac- 

 tion ; and the only assumption which he makes is — that these 

 three directions arc parallel all throughout the crystal*. These 

 directions Fresnel denominates axes of elasticity/. He conceives 

 that they ought also to be axes of symmetry with respect to the 

 crystalline form ; but observes that M. Mitscherlich has noticed 

 some crystals in which this does not hold f. If on each of these 

 axes, and on every line diverging from the same origin, portions 

 be taken which are as tlie square roots of the elastic forces in 

 their direction, the locus of the extremities of these portions will 

 be a surface which Fresnel calls the surface of elasticity . This 

 surface determines the velocity of propagation of the wave, when 

 the direction of its vibrations is given. For the velocity of un- 

 dulatory propagation in an elastic medium, being as the square 

 root of the elastic force, must be represented by the radius-vector 

 of the surface of elasticity in the direction of the vibrations. 



Now let us conceive a plane wave advancing within the crystal. 

 By the principle of transversal vibrations the movements of the 

 ethereal molecules are all parallel to the wave. But the motion 

 of each displaced particle is resisted by the elastic force of the 

 medium, and that force is, in general, oblique to the direction of 

 the displacement. Fresnel shows, however, that the displace- 

 ment may be resolved in two directions in the plane of the wave, 

 such that the elastic force called into action by each component 

 will be the resultant of two forces, one of which acts in the di- 

 rection of the displacement itself, while the other is normal to 

 the wave. The latter, by the principle of transversal vibrations, 

 can produce no effect ^ and the former will give rise to a wave 

 propagated with a constant velocity. These two directions, he 



* This will be the case, if the homologous lines of the groups of particles are 

 all parallel ; an arrangement at once the simplest and most natural, and which 

 appears to be observed in most crystallized bodies. Fresnel admits, however, 

 the possibility of other regular arrangements; and he conceives that the pheno- 

 mena of circular polarization in rock crystal oblige us to suppose that its mole- 

 cules are arranged according to some less simple law. 



t See Bulletin de la Societe Philomathique, March 1824. 



