Eggers 



This agrees with Dr. Eggers' results given by Eqs. (25), (26), and (27) ex- 

 cept that his integral containing s( 2) js replaced by the integral above with the 

 integrand 



^x - -g-^x *xy ■ 



It is not immediately clear that these integrals are equal, although this may be 

 true. If they are not identical, the difference should be 0(e), provided neither 

 of us has made an error. In any case, the formula above seems to be well 

 founded, perhaps easier to evaluate than the other by using asymptotic expres- 

 sions as Xp ^a, and to lend itself to Dr. Eggers' later analysis. However, Dr. 

 Eggers evidently has special insights into this problem as a result of his expe- 

 rience with the computation, and I would appreciate his clarifying further the 

 reasons for choosing his method for computing P.. 



Finally, I should like to express my pleasure in learning that my paper at 

 the Ann Arbor symposium has played some part in the genesis of Dr. Eggers' 

 interesting work. 



DISCUSSION 



B. Yim 

 Hydronautics, Inc. 

 Laurel, Maryland 



I respect Dr. Eggers' courage of committing himself in such a complicated 

 and difficult task of evaluating the second-order wave resistance due to a finite- 

 draft ship. It is so complicated that I would even be glad at this stage to see 

 just the partial numerical results, for example, those related to the higher or- 

 der free surface effect or to the ship bottom effect. In the formulation of the 

 second-order theory I think he very nicely combined the line integral with the 

 ship surface integral. However, he omitted the influence on the potential due to 

 the change of ship singularity domain caused by wave height, namely, the change 

 of the wet area of a ship surface. This was considered by Wehausen (3) and 

 Sisov (4) as another line integral on the free surface. However, as long as we 

 consider a Green's function defined under the mean free surface, it is meaning- 

 less to put a ship singularity over the mean free surface so that the free surface 

 condition is satisfied on the mean free surface. Thus, it is not easy to deal with 

 this problem in a conventional way. 



Recently I considered this (Hydronautics, Incorporated, Technical Report 

 503-1, "Higher Order Wave Theory for Slender Ships," 1966) with a distorted 

 coordinate system (^,17,^, x=^, 7=77, z = i+ f(x,y), and f(x,y) = free surface 

 wave height, so that C = in (^",77, l,) space corresponds exactly to the free 



674 



