and 



9 \\)y . d \\i, 



= 



8r ax 



\ 9r ax / 



Therefore, the potential \\i satisfies the conditions [55] and [56] with a 

 fractional error of order R. 



REFERENCES 



1. Barakat, Richard, "A Sumnnary of the Theoretical Analysis of a 

 Vertical Cylinder in a Regular and an Irregular Seaway, " Reference No. 

 57-41, Woods Hole Oceanographic Institution (Jul 1957), Unpublished 

 Manuscript. 



2. Wehausen, J.V., "Surface Waves," Handbuch der Physik, Springer 

 Verlag, Section 13 (1961). 



3. Lighthill, M.J. , "Mathematics and Aeronautics," Journal of the 

 Royal Aeronautical Society, Vol. 64, No. 595 (Jul I960), pp. 375-394. 



4. Newman, J.N. , "A Linearized Theory for the Motions of a Thin 

 Ship in Regular Waves," Journal of Ship Research, Vol. 5, No. 1 (1961). 



27 



