Crystalline Reflexion and Refraction. 

 and those of tj will be 



47 



tan0, cost, 



sint, 



(15) 



Let 



Z-\-A.X-\--B.y:=0, (16) 



be the equation of a plane passing through the directions of t^, t^ and t^. To 

 determine a and b, let the variables be eliminated from this equation by means 

 of (14) and (15) successively, and vie shall get the two equations of condition, 



, tan^j — Acosi, — Bsinfj^O, 



tan^^-J-Acos t, — B sint, =0 ; 



which, by addition and subtraction, give 



tan0,+tan0. 



(17) 



2sin«, 



tan 0, — tan ^3 

 2cost, 



(18) 



substituting, in these values, the expressions (13) for iaxiO^, tan^^, we have 



//COS( 



B=tan6'Xsm«^+ -^, ^- , 



A=tane^(cos<^— ^-5 L^); 



whence, by making 



we find 



tan K : 



B tant+tank- 



- =tan(t^+K). 



A 1 — Ian (jtan k 

 But if ;2:=0 in (16), we have 



for the equation of the right line in which the plane of the transversals in- 

 , tersects the plane of incidence. This right line, lying, like the refracted wave 



(19; 



(20) 

 (21) 

 (22) 





#"/ 



