332 Mr Glazebrook, On the Reflexion [Feb. 9, 



Let (f> be the angle which the incident wave normal produced 

 makes with the positive part of the axis of x. 



Let 6 be the angle which the direction of vibration makes with 

 the axis of y. 



Let 0j, 6^, (f)', 6' have similar meanings for the other two waves, 

 then we have 



I = cos (f), 7)1 = 0, n = sin (^, 

 a = sin (^ sin 6, /3 = cos 0, \ — — cos cf) sin 6, 

 with similar equations for the others. 

 Also the equations 



become 

 therefore 



V~ V v 



sin (f) _ sin (j)^ _ sin (j)' 



V V V ' 



sin (f) = sin cf)^, 



<^^ = TT - </), 



and the surface conditions reduce to 



K sin (f) sind + k^ sin ^ sin 0^ = k sin cf)' sin (5), 



KCOS0 + /f^COS 0^ = K COS 0' (6), 



— K COS (j) sm0 + K^ COS ^ sin 0^ = — k cos 0' sin 0' . ... (7), 



K COS (^' sin ^' 



-73 B' ' 



Yr {k sin ^ + /^i sin 0^) —t^k' sin ^' 



+ K COS ^' 



\g 



Y^(«; COS (}) cos — K^ COS (^ cos ^J 



73' 



— ™ «' cos (^' cos 0' 



From (5) and (7) 



(8). 



. . .sm((/)-(^) 



AC, sm 0, = — K Sin tf -. — ,, , ,,. 

 1 ^ sm (9 + 9 ) 



, sin 2(^ 



sin (<^ + ^') 



/c' sin ^ = « sm 



..(9), 

 (10). 



B 



Jow 



5 = F V, -p = Fp = 7?p sin <^, 



