86 The Hon. J. W. Strutt on the Reflection of 



and for the bounding conditions, 



IT— ftp 1 



f% = i<%l f when ^ = °; .... (2) 



rc, w' are the rigidities ; D, D' the densities. 

 Assume 



£=f(ax + by + ct)+T?(—a3t: + by + ct), 



the coefficients 6 and c being necessarily the same for all three 

 waves, since their traces on the surface must move together. 

 Hence from (2) 



niaf'-a^n'aJlJ 

 and 



a n' 

 ¥' a~n 



fa nM 



J - + - 

 a, n 



or, since - = tan 0, — = tan 0,, 

 a 'a, ' 



tan ; n 1 



F __ tan ~n {% i 



/ 7 "~'tan0 / n" [ ' } 



tan n 



an equation giving the ratio of the reflected and incident vi- 

 brations. 



Case I. (Green's) n = n' : 



F Cpt0— CQt0 y 



sin (0,-0) 



/' cot + cot 0, 



sin(0, + 0) 



Case II. (MacCullagh's)D = D'. 





Since generally 





n n! a ' 









we have 





n' 1 sin 2 0, 





n ~ y?~~ sin 2 6 





and then (3) gives 





F_tan(0 — 6) 





/'~ tan (0,-1-0) 





