points made by Lamb [1932] concerning the propagation of gravity 
waves in infinitely deep water, are illustrated in these two con- 
crete exact solutions which have been presented. Two quotations 
from Lamb follow which illustrate this point. 
"It has often been noticed that when an isolated 
group of waves, of sensibly the same length, is advancing 
over relatively deep water, the velocity of the group as 
a whole is less than that of the individual waves com- 
posing it. If attention be fixed on a particular wave, 
it is seen to advance through the group, gradually dying 
out as it approaches the front, whilst its former place 
in the group is occupied in succession by other waves which 
have come forward from the rear." 
“Hence in the case of an isolated group the supply 
of energy is sufficient only if the group advance with 
half the velocity of the individual waves." 
Note also that the solutions obtained in this paper give 
some information which is not described by Lamb [1932]. For ex- 
ample the solution for the finite wave group gives information 
about how the amplitude dies down and how the apparent wave periods 
change with time. The solution for the finite wave train gives 
information about how the ends of the train are modulated. 
Comments 
The finite wave train is an interesting study. It still 
has infinitely long crests, and it is still unrealistic in that 
respect. However, properly interpreted and modified it will be 
a building block in the formulation of the more realistic models. 
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