450 SEVENTH REPORT—1837. 
shallow part of the shore they gradually assume the greater curva- 
ture due to the increased ratio of height to depth ; the form at last 
becomes cusped and perfectly cycloidal, the equilibrium of the 
summit ceases, and the particles of water on the extreme ridge of 
the wave, abandoned to the force of gravity, and aggregated in 
spherical drops by this cohesion, present to the eye the white foam- 
ing crest by which breakers are distinguished. Waves of great 
height are thus broken on the beach at a greater distance from 
the shore than such as are smaller. 
The depth of water may be judged of by the form and height 
of the waves. See fig. 7, Plate II. Where a wave of a given height 
can exist, suppose a wave of five feet, the water must have a 
depth below the surface of at least five feet, and wherever in a 
calm day waves are broken, the depth of the water is equal to 
their height above its surface. 
It must be observed that the existence of a strong wind will 
often destroy the equilibrium of the ridge of a wave, independent 
of depth or of the equilibrium of its proper form. When the 
curvature of the ridge of the wave becomes considerable, and 
it approaches the cusped form, the direct incidence of the 
wind upon the surface of the ridge will derange the equili- 
brium of the thin and slender column presented by the top of it 
before it reaches the limits of undisturbed equilibrium. Hence 
the phenomenon well known to sailors, that a very strong wind 
will blow the sea down, in other words, that it will blow off the 
ridges of the highest waves, and keep them from attaining the 
height they afterwards reach wien the gale has subsided. The 
highest seas are thus generated by the continuance of a strong 
gale in one direction rather than by the sudden and short im- 
pulse of a hurricane ; for in the former case the wind only breaks 
the summits of the smaller waves as they rise to the top of the 
larger ones, so as to add the mass of the smaller to the crest of 
the larger waves, without injuring the equilibrium of the latter ; 
these continual additions increase the magnitude of these great 
waves, while the force of the gale is not sufficiently great to de- 
range their equilibrium. The waves in these circumstances go 
on increasing in magnitude. 
The phenomena of waves breaking on the shore were observed 
principally on a very fine smooth beach of sand, having a slope 
towards the sea of 1* in 50°; so perfectly plane and level was it 
at the time when the observations were made, that a single wave 
a mile in breadth might be observed advancing to the shore, so 
perfectly parallel to the edge of the water that the whole wave 
rose, became cusped, and broke at the same instant ; a line of 
graduated rods was fixed in the water at different depths from 
