Non-Linear Shtp Wave Theory 
description of the naive small Froude number? Is it an adjective, or 
should it correctly be an adverb, meaning ''naively small'' ? But how 
is anything naively small in the modern interpretation of the word 
“naave" 2 
My second question is, would he care to hazard a guess as 
to how at very low speeds the wave-making resistance varies? Does 
it vary as the fourth power of the speed or does it vary as the sixth 
power of the speed? Could he just give an answer to that, because in 
a further paper to be discussed this afternoon this point will proba- 
bly arise? 
REPLY TO DISCUSSION 
Gedeon Dagan 
Technion Hatfa, and Hydronauttics Ltd 
Rechovoth, Israel 
Regarding the Kutta-Joukovsky condition, I have stated in 
the paper that Iam not really interested in solving problems of two- 
dimensional flow, but only in using the two-dimensional computations 
as an instrument for understanding and opening the way for the more 
complex solution of three-dimensional ship problems. Since in the 
latter case only the thickness effect is generally taken into account, 
I did not consider the circulation. I agree that if one really wants to 
solve the problem of the hydrofoil (but I do not see the usefulness for 
small Froude numbers), the Kutta-Joukovsky condition has to be 
taken into consideration. 
The paper of Dr.Salvesen has been amply quotedin the present 
work. I believe that my main contribution is the solution of the second 
paradox, and not its discovery. 
The term 'naive'' as applied to a perturbation expansion has 
been borrowed from the applied mathematics literature. The word 
is used in the sense that one expands in an apparently natural way in 
a power series, without observing the nonuniformity of the expansion. 
Since the present work is concerned with two-dimensional 
flow, no attempt has been made to correlate the resistance curve to 
the power of the Froude number. 
1737 
