state in a manner which would have consistent 

 meaning to all who would be involved in the work 

 or would use the results, and (e) the presentation 

 of data in a manner which would lend itself to a 

 maximum of usefulness. 



The work involved in this paper required sev- 

 eral years of patient, painstaking, and persistent 

 effort; and called for great vision and faith on the 

 part of the author. He not only has succeeded in 

 developing the necessary instruments and meth- 

 ods, but also has already used them on many 

 ships, and has applied the tools of statistics and 

 oceanography in collecting and presenting the 

 results. These much-needed accomplishments 

 are deserving of great credit to the author. Much 

 credit also is due to the several organizations 

 which nurtured this work, in particular to the 

 Society, the Navy, the Model Basin, and the 

 Coast Guard. 



With the advent of nuclear power for driving 

 surface ships, it is well that this paper gives us the 

 tools for defining and correcting the weaknesses 

 of huU designs, before they become handicaps 

 under nuclear speed requirements. 



Admiral Rickover has stressed this point in a 

 recent issue of Naval Institute Proceedings in the 

 following manner: "With nuclear power, the 

 Navy can go where it wants, when it wants, at 

 top speed without worrying about fuel economy." 



However, this highly desirable goal cannot be 

 attained unless the hull is also adequate as to its 

 seaworthiness characteristics. Thus, nuclear 

 power undoubtedly will bring greater emphasis 

 on these three questions: (a) How much of the 

 speed potential must be given up in medium and 

 heavy seas? (6) If the hull is inadequate, in what 

 way must its design be changed? (c) To what 

 extent do physiological and psychological factors 

 influence the decision to slow ships in heavy 

 seas? The answers to these questions are im- 

 portant for conventionally powered ships and be- 

 come even more so for those with nuclear drive. 



It is hoped that work in this jfield will be carried 

 forward vigorously; and particularly that the 

 problems of determining distribution patterns by 

 model testing, and of determining fully the in- 

 fluence of alternating stresses on hull structures 

 and the limitations as to heavy sea operation, 

 whether from stresses or motions, will be com- 

 pleted within the next few years. 



Dr. Julius Lieblein,^" Visitor: It is under- 

 stood that some comment has been raised con- 

 cerning a statement in the paper to the effect that 



820, David Taylo 



statistical tests of significance showed no signifi- 

 cant deviations in any of the more than one 

 hundred distributions tested. The argument 

 raised was that even with a significance level of 

 say, 95 per cent, about 5 per cent of the tests 

 should show significance even when none is pres- 

 ent. 



First, it may be noted that the statement of no- 

 significance cases may have been based upon 

 visual inspection in conjunction with calculation 

 of some values of "Chi-Square." This could 

 allow a few cases to be actually significant with- 

 out appearing so to the eye. 



Secondly, for the practical engineering pur- 

 poses intended, the postulated Rayleigh distribu- 

 tion seems amply supported by the data and past 

 experience. In fact, the quality of statistical 

 treatment is above that usually to be found in in- 

 vestigations of this character, and the issue of 

 combining numerous statistical tests is rarely, if 

 ever, raised — perhaps because the data seldom 

 allow calculations to be carried that far. More- 

 over, the too few significance cases might not be a 

 rare occurrence. It may be pointed out that ex- 

 tensive undertakings are often carried out on the 

 basis of conclusions obtained without detailed in- 

 vestigation of the results of significance tests. 



Prof. E. J. Gumbel,'' Visitor: Being a statis- 

 tician, I want to talk only about the statistical 

 aspects of this paper. The graphical way he 

 used the Rayleigh distribution is very able, be- 

 cause he reduces it to the exponential distribution. 

 This simplifies considerably the plotting, because 

 a semi-logarithmic paper can be used. 



The main point of his contribution is the state- 

 ment that "distribution of wave heights," and 

 many connected phenomena, "may well be ap- 

 proximated by the Rayleigh distributions, pro- 

 vided that environmental conditions are steady 

 and that the same variables will be reproduced by 

 a logarithmically normal distribution if the under- 

 lying environmental conditions are allowed to 

 vary over a wide spread." 



The first statement has a theoretical basis; 

 while the second statement is purely empirical. 

 This leads to the question how to prove that a con- 

 volution of Rayleigh distributions leads to a 

 logarithmic normal distribution. 



The logarithmic normal distribution is not 

 (as the author and bad textbooks claim) the nor- 

 mal distribution of the logarithm. In reality, 

 the probability function is an integral and the dis- 

 tributions are transformed as functions under an 

 integral. The incorrect statement, however, has 



" Columbia University, New York, N. Y. 



53 



