in which the double overbar signifies that spatial as well as temporal 

 average is to be taken. 



In the present context use of equations CA-19) and (A-23) in 

 conjunction with Lorentz' principle yields: 



i|^dA(i0pf^ lulU^dt)^ 



,1 dA {^ [ p f, toh U^ dt} , (A-403 



A 1^ TJq b 



wh 



ich leads to a determination of f, in terms of known quantities. 



As an illustration we take a progressive wave in a constant depth 

 of water, h = h , and equation (A-40) may be written: 



^ f U U 



+ 



in which U is given by equations (A-26) and (A-29) corresponding to 

 the surface profile given by equation (A-36) , i.e., 



"" 6o/l-if, 

 b 



-k.x 

 U e ^ cos(ojt -k X + (j) 3 , - (A-42) 



in which <^, is given by equation (A-35) and 

 gk a 



Oj/ 1 + f, 



12 



