Vassilopoulos and Mandel 



attempted to reinterprete the above theory in the second part was solely due to 

 the difficulties explained in the previous paragraph. To Dr. Kaplan who has, we 

 believe, in the past, offered explanations for the "erroneous time differentiation," 

 the situation is very clear; to an outsider who attempts to trace back and forth 

 the use of Galilean and non- Galilean coordinate systems in the derivation of the 

 coefficients, the situation is not that clear. With the assistance of Professor 

 Abkowitz, we developed the new approach with the hope that it would yield iden- 

 tical results to the Korvin approach. We did not get identical results, but we 

 did clarify several of the coefficients. With the additional corrections and ex- 

 planations offered by Professor Abkowitz, the situation may be summarized as 

 follows: 



If the added mass distribution for a given ship form is zero at the ends, 

 then the new and Korvin-Kroukovsky approaches differ in two coefficients only, 

 C and E. If the above assumption is not fulfilled, then they differ in four coeffi- 

 cients, namely, e, B, c, and E. We would point out that for several kinds of 

 ships the added mass at the stern is not zero, for example, destroyers, the 

 latest aircraft carriers or even trawlers. Hence, added mass end-effects may 

 be responsible for discrepancies between theory and experiment for these kinds 

 of ships. Furthermore, the new approach as extended by Professor Abkowitz 

 always satisfied the equalities indicated by the more sophisticated hydrodynamic 

 analyses of Newman- Timman, whereas the Korvin-Kroukovsky approach does 

 not. Finally, we believe that the new excitation term will be numerically as 

 adequate as the Jacobs one, due to the small speed dependency. 



The authors wish to express their sincere thanks to all discussers. In this 

 case it is not a cliche to say that each and every one of them made a significant 

 contribution to the content of this paper. 



406 



