Minimum Wave Resistance for Dipole Distributions 117 
J. Kotik 
Dr. Weinblum has asked a question as regards an arithmetical error in Fig. 10. The pa- 
rameter € is defined as the average half-beam divided by the length, rather than the average 
beam. Perhaps this factor of 2 will accommodate Prof. Weinblum’s doubts. In reference to 
Dr. Weinblum’s descriptions of his work on the wave resistance of submerged boats, or of 
dipoles distributed on a submerged horizontal line segment, I have the following comment. 
It turns out that if one fixes the length and submergence of this horizontal line segment, 
distributes dipoles on it, and tries to minimize the wave resistance within the family of di- 
pole distributions having a fixed dipole moment (or approximately a fixed volume), one is led 
to an integral equation which has no solution. We cannot say at present my this apparently 
well-posed problem has no solution. 
S. Karp 
I would like to ask Prof. Timman whether the solution of the integral equations were 
Mathieu functions. 
R. Timman 
There is still a big gap between the mathematical approach to the problem of minimum 
resistance and the engineering point of view. With regard to the influence of viscosity, I am 
quite sure that the purely mathematical approach is not feasible. 
T. Inui (University of Tokyo) 
I should like to make some general remarks regarding future possible developments in 
our “practical” study of wavemaking resistance. 
Firstly, I wish to point out the necessity of improving our measuring techniques such as 
so-called stereophotography for recording the actual wavemaking phenomena which we can 
observe in our daily model basin work. Figure D2 is one example of such stereo slides. It 
is more than five years since I first tried to take a picture of model waves at the Tokyo Uni- 
versity Tank. 
Secondly, I should like to point out the special importance of coordination between 
theory and experiment in our study of wavemaking resistance. If we had no theoretical 
basis, we could not go any further in our study, even if we have succeeded in taking beauti- 
ful pictures of model waves. In this connection, Sir Thomas Havelock’s contribution in the 
field of wavemaking theory is most valuable. 
Thirdly and finally, I wish to mention our desire of having an international panel to 
make use of high speed computers for preparing many kinds of mathematical tables which 
may be valuable not only to our basic studies but also to our practical design work. 
