88 The Hon. J. W. Strut* on the Reflection of 



Putting, with Green, 



dx dy 



we find 



d(j> dty 

 dy dx' 



(5) 



(6) 



_ JdJ± d*$\ ■ 

 dP~~ y \dx* + dy*)' 



dP 7 W dy 9 )'. 



Two similar equations apply to the lower medium. 

 The boundary conditions are 



(m + n)-? +( m —n)-r =(mf + n') -$± -f (m'—n 1 ) -% 

 dx v ' dy v ; tf # v ' ay 



Wz/ dx)~ \dy dx)' 



of which the first pair express the continuity of displacement, 

 and the second the continuity of stress. Assume 





> upper medium ; 



<l>-<j> l € i(a/ * +bl ' +et) , J 



, lower medium. 



The coefficient of t must be the same for all the waves on account 

 of the periodicity, and b must be the same because the traces of 

 all the waves on the plane of separation x=0 must move together. 

 The constants yjr 1 , >jr n , ... are complex. From (6) we get the 

 following relations, 



c*= 7 V + b*) = 7 ?(a* + b*) =g*{a<* + 6 2 ) = ^ 2 («/ 2 + £ 2 ). 

 Since g and g t are indefinitely great, 



a« + 6 8 =0, «/ 2 + A 2 =0; (7) 



whence we obtain 



a! = ib, a\—^ib 



if the upper medium correspond to the positive x. Equations 

 (7) express the incompressibility of the aether in the two media, 



