Periodic Wave Solutions For infinitely Deep Water Express- 
ed in Terms of Angular Wave Frequencies. 
ast 
Potential function 
-A 2 
O = Aa ue sin( 4 (x cos® + y sin@)- att ) (2.24) 
Free surface 
a2 3 
n= Acos(4—(x cos@ + y sine) — ut +6) (2.25) 
Pressure 
2 2 
D = pgAe 2/9 cos( 4 (x cos@ +y sin®@)-at+ 5)-gpz (2.26) 
Wave speed C=— (2.27) 
Wave length L= ae (2.28) 
A non periodic potential function results from integration 
over 4 and @. 
00 +1 
5 2 2 
O = if f eee et 2/9 sin( 4-(x cos + y sin@)-at +6 (u,0))dude 
-00 -TT 
(2529) 
PEAKE? itr 
= (ies 
