REFRACTION OF SOUND. 411 



Hence, when x = 0, we get 

 d(l) 



dx 



= a a cos {-^ + e) — a (i cos (\|/ + e). 



■^ = c a cos (x|r + e) + c /3 cos (v|/ + e,), 



-^ = — a' B sin \1/, 

 d X 



-y- = c B cos v// ; 



these substituted in the conditions {A), give 



a cos (■>// + e) - /3 COS (\/' + e,) = '- B sin v/^, 



a COS (>// + e) + /3 cos (x|/ + e^) = -^ B cos >// ; 



these expanded, give 



a cos e — /3 cos e, = 0, 



— a sin e + /3 sin e, = ^ jff, 



A „ 

 a cos e + /3 cos e, = — ' B, 



r- 'A 



a sin e + /3 sin e, = 0. 



Hence, we get, 



(10) 2asine = ^ -B, 



2 a COS e = -r B, 



2/3sine =- ^ .B, 



2/3cose,= ^^, 

 Vol.. VI. Part III. SG 



