Note 19 — Chapter XXIV

The following statement of Lord Dundonald's "axiom" accompanied the model which was submitted to the Admiralty:—"It is universally admitted that a sharp bow and a clear run contribute to the speed of vessels; but what the consecutive lines ought to be, in order to constitute a perfect bow, or what those to form the run, no builder has yet exemplified by uniformity of practice, or theoretically defined. Ship-delineators profess the art as a mystery, and arbitrary forms are assumed as the result of science. These lines ought to be, by an axiom, founded on a law imposed by Infinite Wisdom for the perfect guidance of inanimate matter. Projectiles, thrown obliquely, take their flight in convex parabolic curves, wherein resistance is overcome by a minimum of force; and elastic surfaces obey the converse of that law in opposing certain external influences. It is a property of conic sections that a straight line, centred in the apex, and caused to circumscribe the surface of the cone, will apply itself continuously to all consecutive parabolic curves. Hence curves similar to the flight of projectiles, and to those formed by the flection of elastic surfaces, may be described on a large scale simply by causing a straight line or beam to revolve as on the axis of a cone, in contact with a parabolic or elliptical section. Thus a consecutive series of convex parabolic or elliptical curves may be substituted in ship-building for hollow fantastical lines. The benefits from which application are, increased velocity, capacity, strength, buoyancy, facility of steering, ease in hard seas, and exemption from breaking or 'hogging.'" Diagrams and explanations thereof accompanied this concise statement of the principle.