448 SEVENTH REPORT—1837. 
The summit of the wave is round and flat so long as its height 
bears only a small ratio to its length in the direction of its 
motion ; but as the height increases the summit of the wave be- 
comes more and more acuminated, and the limit to which the 
height of a wave approaches, but which it never appears to ex- 
ceed, is nearly a third part of its length. If the wave belong to 
the cycloidal family, and if its length being constant the height 
vary with the generating radius, the rolling circle continuing the 
same, we shall have a series of lines accurately representing 
the form of the waves. See Plate II. fig. 1. Now it is manifest 
that when the describing radius of the wave becomes greater than 
the radius of the rolling circle, the curve ceases to have a form 
of possible equilibrium, and that portion which falls down from 
the top.of the wave constitutes the white crest which we observe 
on the summits of the largest waves, when they are said to break. 
There is generally much confusion in the appearance of an 
agitated sea. The waves do not appear regular in their forms, 
their intervals, or their velocities. Sometimes a wave seems to 
stand still or even to retrograde, and frequently after the eye 
has traced a wave for a considerable time it suddenly disappears 
altogether. Close attention will however discover some method 
in this irregularity. 
The surface of the sea is seldom covered with only one series 
of successive waves. Every breeze that ruffles the surface of 
the sea generates a series of waves that move in the direction of 
the motion of the wind. These waves do not subside with the 
breeze which raised them, but continue their oscillations until 
the adhesion of the water or the resistance of the shore has dif- 
fused the elevated fluid uniformly over the surface. In the mean 
time a second breeze springs up in another direction, and new 
waves rise to its pressure and follow its direction ; they mingle 
with those of the former wind without becoming mixed with 
them. Two distinct series of waves are now coexistent, and 
give rise to more complex phenomena. A third gale arises, and 
a new class of waves intersect and overlap the two former, 
while the long low swell—the residue and telegraph of some 
distant storm—rolls across the whole, and to the untutored eye 
leaves nothing to be looked on but a chaos of tumultuous, troubled 
waters. The seeming chaos is however to be analyzed by pa- 
tient attention: by ascending the mast of the ship, or standing 
on an elevated rock on the shore, much of this apparent confu- 
sion may be dispelled; and by attention to the phenomena of 
coexistent oscillations every thing may be understood. 
When a breeze has been blowing for some time in one di- 
rection, and the wind has shifted round into the opposite one 
and blown with nearly equal force, the two sets of waves may 
