Rankine says, referring to the practical employment of these curves:—
“The ovals are figures suitable for vessels of low speed, it
being only necessary, in order to make them good water lines,
that the vertical disturbance should be small compared with the
vessel's draught of water. At higher speeds the sharper water
lines more distant from the oval become necessary. The water
lines generated by a circle, or ‘cyclogenous neoids,’ are the
‘leanest’ for a given proportion of length to breadth ; and as the
eccentricity increases the lines become ‘fuller.’ The lines
generated from a very much elongated oval approximate to a
straight middle body with more or less sharp ends. In short,
there is no form of water line that has been found to answer
in practice that cannot be imitated by means of oogenous
neoids.”
And further:—
“Inasmuch as all the water-line curves of a series, except the
primitive oval, are infinitely long, and have asymptotes, there
must necessarily be an abrupt change of motion at either end of
the limited portion of a curve which is used as a water line in
practice, and the question of the effect of such abrupt change
or discontinuity of motion is one which at present can be decided
by observation and experiment only. Now it appears from
observation and experiment that the effect of the discontinuity of
motion at the bow and stern of a vessel, which has an entrance
and run of ordinary sharpness and not convex, extends to a very
thin layer of water only; and that beyond a short distance from
the vessel's side the discontinuity ceases, through some slight
modification of the water lines, of which the mathematical theory
is not yet adequate to give an exact account.”
§ 78. Solids equivalent to Source and Sink Distribution.—In the light of present knowledge it would appear that the particular case of flow under discussion is merely one of an infinite number of possible systems in which sources and sinks of different strengths
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