Observations and Measurements of Ocean Waves 65 



to determine the integral (III. 21) it is dissolved into a partial sum of cor- 

 responding terms, so that 



Q 

 7](t) = lim ^ C0S[<7 ill+1 t + d(a 2n + 1 )]Y{h 2 (<J.2„ + 1 )[<J2n + 2—O2nV>. (111.23) 



J 2n+2 °2n 



O.T„—CO 



For practical purposes it is not necessary to subdivide the interval into too 

 small parts. A satisfactory approximation will also be obtained by a sufficiently 

 large but finite frequency band. This new kind of representation of the sea 

 motion corresponds much better to natural conditions than those used 

 formerly. Towards a practical application only the first steps have been made; 

 Pierson has also extended this method to short-wave sea motion, but final 

 results are still missing (see Roll, 1957). 



