drawn at random from a population actually with 

 the probability density function being tested could 

 differ by chance by as much as it does from the 

 theoretical distribution, one can argue that charac- 

 terizing the data as in Table 3 by terms such as 

 "fair fit" or "very good fit" is not justifiable. One 

 can only state that the hypothesis that the data 

 were drawn from the theoretical population being 

 tested cannot be rejected at the 5 per cent signifi- 

 cance level. It is odd that in one hundred such 

 tests of ship motion or hull stresses no discrep- 

 ancies at the 5 or 1 per cent level were found. 

 One should expect to reject the hypothesis at the 

 5 per cent level about 5 times in 100 trials and 

 once at the 1 per cent level (despite the fact that 

 it is true). 



Recently Cartwright and RydilP' have found 

 that the Rayleigh distribution did not fit certain 

 ship-motion records and wave records which they 

 were studying due to the fact that the spectrum 

 was not a narrow band. They give a more refined 

 formula which fits the data better. 



Dr. J. H. Chadwick, Associate Member: It has 

 been said often that the main object of scientific 

 research is to discover and explain regularities in 

 the data. In this sense the paper is certainly a 

 contribution to marine science as well as to marine 

 engineering — for what could be more regular than 

 a straight line? This paper will be, I am sure, 

 another important landmark on the trail recently 

 blazed by St. Denis and Pierson in the paper they 

 presented before this Society in 1953. Where 

 St. Denis and Pierson emphasized theory and fre- 

 quency distribution (power spectrum), the present 

 author emphasizes fact and amplitude distribu- 

 tion. Taken singly or together, these papers 

 offer us an infinitely more reahstic view of ocean 

 waves and ship motions than we have had hereto- 

 fore. 



The two papers are closely related and comple- 

 ment each other in a natural way. I have to 

 violently disagree with my friend Dr. Pierson, 

 however, when he argues that Jasper's results are 

 based on his linear model assumptions. The 

 author's results are largely factual, and it is a 

 fundamental principle of science that theories are 

 based on assumptions, while facts are based on 

 measurements. In support of this view may I 

 quote the epigram that appeared at the head of 

 the original St. Denis-Pierson paper (15) : 

 "Mathematics can never tell us what is; only 

 what would be if." (Poincare). It is true that 

 some of the author's results can be explained 

 (i.e., predicted) in terms of the linear model 

 assumptions; which is to say that his facts so far 

 tend to confirm the. St. Denis-Pierson theory. 



Nevertheless, theories are not facts, and never 

 the twain shall meet. 



Both of these papers have as a central theme, 

 the notion that waves and wave-induced ship mo- 

 tions are stochastic processes; i.e., essentially 

 random in nature. Actually, this is something 

 that marine science has recognized implicitly for a 

 long, long time, but we have stood shivering on the 

 verge of an idea, unwilling to plunge into the seem- 

 ingly infinite mathematical complexities of the 

 statistical approach, until Messrs. St. Denis and 

 Pierson came along to push us in. A surprising 

 number of us survived this immersion. To the 

 few that have felt themselves going down for the 

 third time, the author now throws a life-ring. 



Mr. St. Denis, in another paper on ship mo- 

 tions, once quoted Lord Rayleigh as saying: "The 

 basic law of the seaway is the apparent lack of any 

 law." It is pleasantly ironic that one basic law 

 of the seaway, discovered during the evolution 

 of these new theories, is that peak amplitudes over 

 the short term tend to fall on a Rayleigh distribu- 

 tion, a fact not known in Rayleigh's lifetime. This 

 little joke of fate tells the whole story. The basic 

 law of the seaway is randomness, but randomness 

 itself obeys statistical laws, some of them as 

 simple as straight lines. 



The author stresses engineering applications, 

 and the point is well taken. Since the present 

 models are vastly more realistic than the old single- 

 sine-wave models they also have a much greater 

 potential value to the engineer. The amplitude- 

 distribution data presented in the paper are par- 

 ticularly important with respect to the economic 

 side of design. 



In the collection of his data, the author has used 

 a technique the importance of which cannot be 

 overemphasized ; namely, the collection of data at 

 predetermined times. This technique provides 

 objective data with the minimum intervention of 

 theory, and hence provides the best possible test 

 of theory. In its application, this technique has 

 certain consequences: It tends to call for a long- 

 term, low-level effort; it requires automatic re- 

 corders; and it uses a minimum of shipboard per- 

 sonnel. At the other extreme we have the grand 

 expedition approach, using short-term, high-level 

 efforts, subjective recording and a maximum of 

 shipboard personnel. History has shown that 

 the expedition approach is an extraordinarily in- 

 efficient method of collecting data about wave- 

 induced ship motions. The San Francisco and 

 Ocean Vulcan expeditions are cases in point, par- 

 ticularly the former. It is to be hoped that in the 

 near future we will see the same type of recording 

 technique used by the author for amplitudes ap- 

 plied also to power spectra and cross spectra. 



50 



