REFLECTED AT THE SURFACE OF A CRYSTAL. 39 



as Mr M'CULLAGH had previously done.* We have to add that Mr M'CULLAGH, 

 whose investigations had previously rested on equations assumed from analogy, 

 has recently taken up the mechanical solution of the problem of crystalline re- 

 flexion.f 



Such is a very brief outline of the present state of theory on this branch of 

 Physical Optics. From the extreme difficulty attendant even on the conception 

 of pressure as applied to transversal vibrations, it has appeared to the author de- 

 sirable to reduce all theory ultimately to the action of force. Having been once 

 irresistibly led to the belief that the Newtonian Law \ is the true law of molecular 

 action, he has not hesitated to adopt it in all other cases. 



SECTION I. DETERMINATION OF THE EQUATIONS OF CONDITION AT THE COMMON 



SURFACE OF TWO MEDIA. 



To understand fully the following process, it is desirable that the reader 

 should examine our preceding Memoir On Fresnets Formulae, in vol. xiii. We 

 may remark, that the hypotheses are, 1. That the vibrations are transversal and 

 perpendicular to the plane of polarization. 2. That at the surface a portion of 

 the motion is changed in form. 3. That the vibrations are isochronous. 4. That 

 the action of one medium on a particle at rest is the same as that of any other 

 which may supply its place. The difference between different media is sufficiently 

 defined by means of the different directions which a ray of light takes in passing 

 into them. 



To determine the values of the disturbances without and within the crystal. 

 Let YOZ (see next page) be a portion of the surface of the crystal, OX the normal 

 to the surface at the point of incidence under consideration ; and let OX, OY, 02 

 be respectively the axes of x, y, and z : x being measured downwards. Conceive 

 a sphere to be described about the point 0, and let I be the point In which the 

 incident pencil corresponding with the point cuts its surface. 



Let also T, T' be the points in which the normals to two refracted waves 

 passing through and produced backwards cut the same surface ; these points 

 will lie all in the plane XOY. 



The vibration of the incident pencil may be resolved into two parts, one in 

 the plane XOY, and the other perpendicular to it ; call these I and F respectively. 

 Let A be the position of the axis as referred to the sphere : i. e. let OA be parallel 

 to the direction of the axis of the crystal : then the vibration of one wave will be 



* Phil. Mag., vol. x. p. 382, &c. Trans, of the Royal Irish Ac., vol. xiii, p. 71, See also 

 Comptes Rendus, vol. viii. pp. 961, 964. 



t Proceedings of the Royal Irish Ac., Dec. 91 1839, p. 375. 

 I Trans, of the Camb. Phil. Soc., vol. vi. p. 178. 



