340 Mr KELLAND, ON THE TRANSMISSION OF LIGHT 



which values substituted in (1) give 



(cos' 9 cos= (p - cos' cos' <^) Q= (cos- 9 cos (p cos^^- cos' 9 cos (p cos v//) R, 

 an identical equation independently of Q and E: and the other equa- 

 tions give 



- 3 {m -}}) cos' 9.P=3{m -p) cos cos ^ . Q + 3 {m -p) cos cos y\,E, 



which is satisfied by making either cos = 



or P cos + Q cos (^ + ^ cos ^ = 0, 



and the former is evidently impossible, wherefore the latter equation 

 must be satisfied: and it is the only equation in P, Q, E. 



Suppose now tlie direction of motion of the particle to make 

 ano-les X, V, Z with the axes of x, y, x, then the displacement A is 



A=a C0sX+/3 cos V+y COS Z: 

 Pa + Ql3 + Ey 



but it is also 



C 



P ^ Q ^ E „ 



:. j^ =cos X, -^ =^*^s ^' T ^^°® ^' 



and from the above equation 



COS X COS + cos F COS (/) + cos Z cos x|/ = ; 



which shews that the directions of displacement, and of transmission 

 are at right angles with each other, and since this is the only con- 

 dition which exists amongst the quantities P, Q, E, the displacement 

 may be in any direction in the plane perpendicular to the direction 

 of transmission, and it is propagated with a velocity equal in all 

 directions. 



13. We will now return to our equations, and suppose the me- 

 dium symmetrical with respect to each of the axes respectively, but 

 not absolutely a medium of symmetry : suppose, for instance, that in 

 passing from the plane of xy the distance between two consecutive 



