IN CRYSTALLIZED MEDIA. 327 



SECTION I. 



Remarks on M. FresneVs Theory. 



M. Fresnel in his Memoir on double refraction, p. 103, states the 

 principle, that "the elasticity put in play by luminous vibrations de- 

 pends solely on their direction and not on that of the waves." Of 

 this principle he demonstrates, in a very satisfactory manner, the 

 theoretic possibility, and there appears little room to doubt its truth. 

 Taking it for granted then, he proceeds (p. 106.) to an application of 

 it in the following manner. 



If we have two displacements corresponding to different waves, we 

 may consider each of them as belonging to a new wave, the front 

 of which is the plane passing through them, and shall, if we wish 

 to combine the two, have only to combine two vibrations in the 

 front of a common wave. Thus far, I think, there can be no ground 

 for the slightest objection. But the statement in p. 107 cannot, I 

 think, lay claim to the same degree of evidence as this. 



It would occupy too much space to give here the whole of this 

 statement. It will be quite sufficient to give an abstract of it, which 

 I copy from Professor Airy's Tracts, p. 343. 



" If the displacement of a particle considered in any direction be 

 resolved into three displacements in the directions of x, y, x, the va- 

 riations of force in those directions produced by the alteration of a 

 single particle (and consequently the force produced by the whole 

 system) are the same as if the displacements in those directions had 

 been made independently. From this it easily follows that the sum 

 of any number of displacements causes forces equal to the sum of 

 the forces corresponding to the separate displacements : and then any 

 number of undulations, produced by vibrations in different directions, 

 may coexist Avithout destroying each other." It will be seen that 

 this statement supposes the force put in play to depend only on the 



