IN CRYSTALLIZED MEDIA. 



hence P = C . cos 0, 

 Q = C . cos (j), 

 R = C . cos \p, 



C being some constant factor. 



Substituting these values in the equation 



we obtain C cos -r— + cos A -~t + cos x]/ — r-^ 

 V «^ ^ di' ^ dt' 1 



= - ^C (cos . a + cos (p . (i + cos >// . 7), 



which by making a cos + /3 cos (p + y cos x/^ = ^, 





a form which doe.s' not correspond to a vibration. 



The expression a cos 9 + fi cos 1^ + 7 cos \// is evidently the resolved 

 part of the disturbance parallel to the direction of transmission : it 

 follows therefore, that there is no vibration in the direction of trans- 

 mission, or in other words, that the vibration is entirely transversal, 

 a result to which I also arrived in a former Memoir. 



12. To determine the directions of vibration corresponding to the 

 values m - p of A. 



a — A = m + 2p - 3(m cos^ 9 +p sin^ 6) - (m — j)) 



= ^pcos'd - 3mcos^9 



= — 3(m - p) cos^ 9, 

 b — A = — 3 (m — p) cos^ <p, 



c — A = — 3{rn — p) cos'^ ^, 

 Vol. VI. Part II. Xx 



