National Republican., 1883-04-27
THE DEEP SEA WAVE.
Interesting Paper by Naval Constructor
Gatewood Read Before the Naval In
atttute.

Interesting Paper by Naval Constructor
GRtewood Read Before the Naval In
stitute.
Assistant Naval Constructor Richard Gate
wood, U. s. N, read highly interesting
paper on "The Theory of the Deep Sea
Wavo" before the Washington branch of the
Naval institute last night. The paper in its
entirety is far too technical for popular fa-
vor, the greater portion being taken up with
abstruse mathematical reasoning. The OBJ
ject of the paper was to treat of tho rolling
of ships He commenced by saying: The
mathematical theory Of the rolling of ships
in a seaway is now so we'll established in all
its main features as not to admit of doubt as
to its principal deductions affecting the meth
DDS Of obtaining desirable qualities in ships.
Here however, the disagreeable fact obtrudes
itself that all ships and especially war ships,
are in their qualities only compromises, the
prominence of the individual qualities aimed
at depending on the circumstances Of their
design"
Mr.. Gatewood then defined the funda-
mental conditions of fluid motion. The first
of these known as the condition of continuity
expresses the fact that the mass of each ele-
mentary volume fixed in space within the
fluid is constant. The second is the condi-
tion Of dynamical equilibrium, viz: That in
fluids the effective forces acting on each par
ticle to produce acceleration is the resultant
of its weight and the pressure Of the sur
rounding frictionless fluid.
The mathematical expressions Of these two
conditions are essentially difiereutial, and
admit of an infinite number of solutions. In
each particular case thero are, in addition,
what may be called the boundary conditions,
such as the form and position, or the state Of
pressure, or other popularity of the bound
aries capable Of affecting the adjacent fluid
motion.
If, in the mathematical study of particular
cases of fluid motion, functional motion be
found satisfying the necessary conditions of
continuity and dynamical equilibrium and
the particular boundary conditions, then its
physical Interpretation must denote q posi-
BILE scheme of fluid motion, the identity of
which with the particular observed motion
can be tested experimentally by observation
of the physical conformation, and of the
"dynamical structure" or qualities of the
motion at different points, and further inn
portant check may bo applied by the con.
formity of the mathematical motion with the
necessary conditions of formation of the OBJ
served motion from the fluid in its initial
condition by observed forces.
1t is by one or more of these tests that GER
tain refnements have been imposed upon the
mathematical theories of such comparatively
well-known motions as the solitary wave of
Mr.. Gatewood then defined the functions of
steady and unsteady motion, wave motion in
perfect fluids, defined "chopping sea-" and
examined the conditions of the running wave
of pure oscillation. The latter must involve
for the individual particles, oval paths, or
orbits, the mathematical expression of which
in each case of motion must fulfill the condi-
tions of continuity, dynamical equilibrium,
boundary, and formation. The physical limi-
tations which these conditions imply were
examined. The boundary conditions are, in
general, the depth and conformation of the
bottom and the state of pressure on the upper
surface of the fluid.
The conditions of formation generally in
volve some estimate of the perfectness of the
actual fluid, tho initial condition as to 'mole-
cular rotation, "a somewhat complex quality,
involving sliding over one another Of sue
cessive layers, grinding action, so to speak
or, in other words, an initial current Of We
locity varying with the depth below the sur
face-and somo particular conception of the
action of wind on water.
A fairly good idea of the physical nature of
molecular rotation" may be obtained by
considering small sphere anywhere in tho
fluid to become suddenly solidifed and re-
moved from the remaining fluid, when, if the
sphere retains only a motion Of translation
which may vanish-the fluid motion is said
TO be irrotational." If, however, rotation
tion is rotational." Such motion evidently
requires for its generation force equivalent
to internal friction, and hence cannot be gem
Grated or destroyed in perfect fluid by natu-
raj forces. Thus if fluid motion is once irro-
rational it is always 30. We have then Us n
consequence that no wave motion involving
molecular rotation can be generated by natu.
raj forces from a perfect fluid at rest land
therefore irrotational), and this is one of tho
tests which the conditions offormation imply.
Further reasoning was applied to find
mathematical theory of motion fulfilling the
first three conditions after which the qualities
Of the motion were developed and the complex
conditions of formation applied to discover
the initial circumstances necessary for gen.
Grafton of such motion He concluded with
From all these considerations it does not
seem probable that truly trochoidal wave is
ever formed except in accidental cases, and
yet the notifications rendered necessary by
the above, though important in character are
not 80 important in extent. In general it
may be said that there seems to be marked
tendency for waves once formed to work down
into the trochoidal form aud characteristics"