in medium 

 mnp ; 



in medium 

 m'n'p*. 



96 Oa the Reflexion and Refraction of Elastic Waves. 



III. Condensational- Rare factional Wave at the Interface 

 of two Elastic Solids. 



The solution is of the form 



The equations of motion give the relations 



(m + n)(c 2 + l)= p&) 2 = ?2(7 2 +l) ^ 



(m'+w')(c' 2 + l)=p'G) 2 =n / (7' 2 + l) i 



- The conditions to be satisfied at the surface (^?=0) are 

 identical with those for the incident distortional wave, and 

 lead to the equations 



Bj+ cY= B' + c'A' 



ryB x + X= -7 / B / + A' 



2-Vb'+-( 7 ' 2 -1)A' ! 



(10 



•2 7 B l +(7 2 -l)X 



(2') 



( 7 2 _ i) b, - 2cY = - (y /2 - 1) B' - 



2 -c'A' 



where X = A + Ai and Y = A— A 1# 



By taking the difference of the products of the first and 

 third and of the second and fourth of these, and by suitable 

 substitution according to (1'), we get the energy equation in 

 the form 



cpA?-cpA 1 a = ypB 1 2 + c'p'A.' 2 + v'p'B' 2 ; . . (3') 



IV. Condensational-Raref actional Wave at the Interface of an 

 Elastic Solid and a Fluid ; incident in the Solid. 



Here again we must drop the second boundary condition ; 

 and, as in case No. II., are led to the simplified equations, 



Bx+ cY= c'A.' "] 



-2 7 B 1 + r7 2 -l)X= £'( 7 2 + l)A' |>; 



whence 



( 7 2_1)B X - 2cY = 







J 



(*') 



(5') 



