Submerged Two-Dimensional Bodies 



which may be broadly construed as matters of opinion. Thus, there is very little 

 room for argument and I must restrict myself to comments of general nature. 



First, I submit that the author has presented a remarkable paper. It is not 

 every day that one can study what may be referred to as a classical problem 

 and be able to supply information not already available. This is exactly what he 

 has been able to do, however. Theoretical findings which are here presented 

 for the first time are of the greatest significance for the basic understanding of 

 the physical and mathematical features of the second-order wave theories. This 

 is particularly true when viewed against the background of experimental data 

 which are here indispensable. One can only imagine the author's feeling of re- 

 lief when measured data verified the large differences predicted between first- 

 order and second-order theories. It is comforting indeed to observe the close 

 correlation between second-order theory and experiments, although this leads 

 to the nagging question of convergence of the perturbation expansion of the ve- 

 locity potential. The less satisfactory agreement between experiments and 

 theory in the higher speed range may be due to the fact that the sources and 

 sinks are not suitable representation for the strut. I ask the author if he could 

 comment on this. 



It is stated in the paper that because the cylinder -wall condition is satisfied 

 only to the first order of approximation it can be argued that the second-order 

 theory presented here is not consistent. It is my opinion that for the depth of 

 submergence used by the author only higher than second-order resistance terms 

 will be influenced by the cylinder -wall conditions, provided the traced stream- 

 lines are made to form a closed body. This matter ought to be carefully inves- 

 tigated for at least one speed. 



I have a slight objection to referring to Eq. (30) as a Stokes wave. Within 

 the order of approximation the author is, of course, free to add a term of the 

 form 



— vS ^ COS 2v(x - t) 



and make it represent a higher order Stokes wave if it is preferable to do so. 

 To the order of approximation, however, it is not important whether the second- 

 order wave is a Stokes wave or not. 



In closing I wish to point out that the apparatus designed by the author will 

 be used at the University of Michigan for further studies into some of the areas 

 of continued research outlined by him. This work is being sponsored by the 

 David Taylor Model Basin. I wish therefore to thank the author for his direct 

 contribution to the education of new talent so vital to our profession. 



633 



