1. When the length of the wave is not greater than the depth of the
water, the velocity of the wave depends (sensibly) only on its length,
and is proportional to the square root of its length.
2. When the length of the wave is not less than a thousand times the
depth of the water, the velocity of the wave depends (sensibly) only
on the depth, and is proportional to the square root of the depth.
It is, in fact, the same as the velocity which a free body would
acquire by falling from rest under the action of gravity through a
height equal to half the depth of the water.
_Rollers_ are of the nature of a violent _ground swell_, and possibly
the worst of them may be due to the propagation of an earthquake wave.
They come with little notice, and rarely last long. All the small
islands in the Mid-Atlantic experience them, and they are frequent on
the African coast in the calm season. They are also not unknown in the
other oceans. In discussing the meteorology of the equatorial district
of the Atlantic, extending from lat. 20° to 10° S, Captain Toynbee
observes that "swells of the sea are not always caused by the
prevailing wind of the neighborhood. For instance, during the northern
winter and spring months, northwesterly swells abound. They are
sometimes long and heavy, and extend to the most southern limit of the
district. Again, during the southern winter and spring months,
southerly and southwesterly swells abound, extending at times to the
most northern limit of the district. They are frequently very heavy
and long."
The great _forced sea waves_, due to earthquakes, and generally to
subterranean and volcanic action, have been known to attain the
enormous height of 60 feet or more, and sweep to destruction whole
towns situated on the shores where they have broken--as for example
Lisbon and places on the west coast of America and in the island of
Java. Though so destructive when they come in toward the land, and
begin to feel the shelving sea bottom, it is not probable that, in the
open ocean, this wave would do more than appear as a long rolling
swell. It has, however, been observed that "a wave with a gentle front
has probably been produced by gentle rise or fall of a part of the sea
bottom, while a wave with a steep front has probably been due to a
somewhat sudden elevation or depression. Waves of complicated surface
form again would indicate violent oscillations of the bottom."
The altitude and volume of the great sea wave resulting from an
earthquake depend upon the suddenness and extent of the originating
disturbance and upon the depth of water at its origin. Its velocity of
translation at the surface of the sea varies with the depth of the sea
at any given point, and its form and dimensions depend upon this also,
as well as upon the sort of sea room it has to move in. In deep ocean
water, one of these waves may be so long and low as to pass under a
ship without being observed, but, as it approaches a sloping shore,
its advancing slope becomes steeper, and when the depth of water
becomes less than the altitude of the wave, it topples over, and comes
ashore as an enormous and overwhelming breaker.
Lastly, there is the _storm wave_--the result of the cyclone or
hurricane--and, perhaps, the greatest terror to seamen, for it almost
always appears in the character of a _heavy cross sea_, the period of
which is irregular and uncertain. The disturbance within the area of
the cyclone is not confined to the air, but extends also to the ocean,
producing first a rolling swell, which eventually culminates in a
tremendous pyramidal sea and a series of storm waves, the undulations
of which are propagated to an extraordinary distance, behind, before,
and on each side of the storm field.
Enough has now been said to show that whatever the character of the
waves encountered by the Umbria and Martello in July last, they were
in no sense "tidal," but, if approximating to the dimensions stated,
they were either due to storm or earthquake, or, possibly, to a
combination of both the last agents.
For those of our readers who may be interested in wave observations,
we conclude by introducing Prof. Stokes' summary of the method of
observing the phenomenon:
"_For a Ship at Sea._
"(1.) The apparent periodic time,[2] observed as if the ship
were at rest.
"(2.) The _true_ direction from which the waves come, also the
ship's _true_ course and speed per hour.
"(3.) A measure or estimate of the height of the waves.
"(4.) The depth of the sea if it is known, but, at any rate,
the position of the ship as near as possible, either by cross
bearings of land or any other method, so that the depth may be
got from charts or other sources.
"_For a Ship at Anchor._
"(1.) The periodic time.
"(2.) The true direction from which the waves come.
"(3.) A measure or estimate of the height of the waves.
"(4.) The depth of water where she is anchored."
[Footnote 2: The period of a wave is the interval of time which
elapses between the transits of two successive wave crests past a
stationary floating body, the wave crest being the highest line
along the ridge.]
It is the opinion of scientists that when the period of oscillation of
the ship and the period of the wave are nearly the same, the turning
over of the ship is an approximate consequence, and thus the wave to
such a ship would appear more formidable than to another ship with a
different period of oscillation.--_Nautical Magazine._
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