a ae 
ON WAVES. 449 
be distinctly seen moving in opposite directions ; if they be of 
nearly equal dimensions a very singular appearance results. 
When the crests coincide, the ordinates of the compound wave 
surface become the same ordinates of the elementary waves, 
and their difference when the crest of the one is in the cavity of 
the other ; so that the sea is alternately in the forms represented 
in ec and d, fig. 2, Plate II. 
When these two systems of waves are compounded with a 
third system arising from some other breeze, or by a third sy- 
stem resulting from the reflection of a bold coast, the third series 
combines with the two former in the manner represented in 
fig. 3, with an appearance of still less regularity, and so on for 
any number of parallel systems. 
It is manifest that if these parallel systems be compounded 
with transverse systems, making any angle with the first, we 
shall have a compound system of surfaces of double curvature 
so complex in its structure as to represent the phenomena of the 
most troubled sea. On all occasions where the sea was ob-- 
served, there were found two or more such systems of coexistent 
waves. 
The phenomena of the waves at the surface of the sea appear 
to coincide very well with the hypothesis, that when a wave 
agitates the fluid only to a small depth it may be considered as 
formed in a shallow canal of that depth ; for it may be observed 
_ that a short wave of a given height is always more pointed than 
a longer wave of the same height, and also that whenever a wave 
reaches the limit of the cycloidal form it breaks. 
Whenever the height of a wave exceeds the limit of the cy- 
cloidal form due to its depth, the wave, after having become 
cusped or pointed, passes into the nodated form of unstable 
equilibrium and is broken. See figs. 4 and 5. 
Whenever a wave of a higher order coincides with the ridge 
of one of an inferior order, its curvature at the crest will be a 
maximum, and it may break, although it would not have broken 
on any other part of the wave. See figs. 4and 5, Pl. II. From 
this cause a large wave frequently exhibits the appearance of a 
breaking wave, although its own figure has not approached the 
limits of equilibrium ; but in that case it is not the large wave 
which is breaking, but the smaller one on its summit, whose 
curvature is then increased by the amount of the curvature of 
the greater wave at the crest. 
Waves break on the shore when they reach the point where 
the depth of the fluid becomes nearly equal to the height of the 
wave above the fluid. When at a distance from the shore they 
may be observed long and low, see fig. 6; as they approach the 
VOL. VI. 1837. 2G 
