waves, and yet they are forecasted to travel with classical 
group velocities, and refracted as if they were purely sinusoidal 
waves of one single period. 
The Sverdrup-lunk theory [1947, 1949a], as extended in part 
by Arthur [1948, 1949], depends on the validity of the assumption 
that two parameters, viz., the significant wave height and period, 
can adequately describe the sea surface at any time and any place. 
It will be shown that these parameters are not sufficient to 
characterize the sea surface and that the inadequacy of these 
parameters in part can explain the failure of the forecasting 
method to forecast the significant period as shown by Donn [1949], 
Isaacs and Saville [1949], and Pierson [1951p]. . 
Wave records at present are frequently obtained by recording 
the pressure as a function of time at the bottom as the wave 
passes overhead. The pressure records are then analyzed for the 
Significant period and significant pressure amplitude, and the 
Significant height and period at the free surface are computed 
from these values. It will be shown that this procedure is in- 
correct. 
The use of the significant period in problems in wave re- 
fraction is also a most doubtful procedure. A method will be 
developed in this paper which will be far more applicable to actual 
sea conditions than the present techniques. 
The overall plan of this paper is to start with the simple 
and proceed to the complex in the derivation of various models 
of waves on the sea surface. Models of the sea surface will finally 
be obtained which will prove to be adequate for a correct de- 
scription of the sea surface. 
- Cm 
