Ming-Shun Chang 
probability distributions really represent the sea behaviour, and to 
this end, Iurge Miss Chang to explain, if possible, the double dip in 
the curves. After long meditation on the subject I have succeeded 
only in convincing myself that I do not understand the plot and am in 
somewhat of a dilemma as to whether the explanation underlying the 
double dip is a physical or a statistical inaccuracy. At all events, 
the orderly presentation is a pleasant reward for the reader who seeks 
insight into this fascinating subject of how to describe the wind-driven 
sea and leaves him with a stimulating thought for further work. From 
a single Paper written by a young lady one cannot possibly ask for 
more, 
REPLY TO DISCUSSION 
Ming-Shun Chang 
Naval Shtp Research and Development Center 
Bethesda, Maryland, U.S.A. 
My thanks to Dr. Cummins and Dr, Saint-Denis for their kind 
comments, 
On the question of how well the linear supposition of the direc- 
tional waves can be applied to the ship applications, I do not yet know 
the answer. This is one of the reasons for doing the directional waves 
experiment in the basin. 
The cosine power law spreading in the wave directions has 
been observed by a few experimental studies suchas SWOP and the 
floating buoy of N.I.O. However, these data were taken with respect 
to wind generated waves. For a large percent of the time, the waves 
in the ocean are a combination of swell and wind waves ; thus, one 
should not expect this power law to hold in general. The Atlantic hind- 
cast data could give a preliminary picture on this subject. 
As to Dr. Saint-Denis' comment on the use of two parameter 
spectral formulation, I certainly agree that it is dependent on the types 
of problems one is studying. I do not believe it will be very good for 
studying optimum design and its associated problems because the 
shifting period may introduce a large error in probability at the large 
response end, 
About Dr. Saint-Denis' question on the probability diagram 
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