IN CRYSTALLIZED MEDIA. 331 



SECTION II. 



Investigation of the Motion of a System of Particles within a Crystal. 



1. We shall assume that the arrangement is an arrangement of 

 symmetry with respect to three planes mutually at right angles to each 

 other. 



Let their lines of intersection be taken as the axes of co-ordinates. 



X, y, X the co-ordinates of the particle under consideration in its po- 

 sition of rest. 



X -V u, y + /3, s + 7 its co-ordinates after the time t. 



X + Ix, y -vly, %-\-l% the co-ordinates of another particle whose dis- 

 tance from the former is /•. 



Then, by pursuing a process precisely analogous to that which 

 applies to non-crystallized media, {Trans. Camh. Phil. Soc. Vol. vi. Part i. 

 page 162.) supposing the particle in vibration, we have the following 

 equations of motion : 



^ = -2aS (- - ^) sm^^ -6/32^ sm^-/ 



-672-^j-sm^^, 



dt^ ^ W r^ J 2 r^ 2 



„ ^hll% . kip 



r- 2 ' 



f=-272(---^)sm^-6aS-^sm«-/ 



dt 



Vol. VI. Part II. Uu 



— 6/32-=— sm'— -i- 

 ^ r^ 2 



