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PROJECTION—SHIP-BUILDING,

figure of curved lines, or of measuring curved lines bythem.

Let any curved line, MABCDN, fig. 15, pi. 2, begiven; it is transferred to a principal right line or axis,m, n, by means of a succession of other parallel right linesA a, B5, Cc, Dd, &c. In general the latter are drawnat equal distances from one another.

Application to drawing curve lines :—The advantage ofthis geometrical property is, that it permits us to writeand calculate, if this mode of expression be allowable, theform of the least regular curves. We have an example ofthis in ship-building.

The fleetness with which a vessel moves through thewater, depends, other things being equal, on the form ofher bottom or part beneath the water, which meets resist-ance from the fluid. It is necessaiy that the surface ofthis part should be closely connected. and smooth at everypoint, offering, whatever may be the plan of the architect,no sudden irregularities in any direction. To plan andconstruct a ship the most rigorous and exact geometricalprinciples are accordingly adopted ; and parallel and per-pendicular lines are in this case generally had recourse to.

xiiVery vessel has its right, or starboard side, preciselythe same as its left, or larboard side; or both sides, thougheach is a very irregular curve, have exactly the same formand dimensions, and are equal and similar throughout.To represent them a horizontal line is drawn, MN, fig. 16,pi. 2, which reaches from the stern-post to the stem. Onthis right line, divided into equal parts, MA, AB, BC,perpendiculars are erected ; and on them are marked thepoints which indicate the extreme breadth of the ship orthe situation of the water lines.

It is supposed that the floating vessel, without leaningeither to one side or the other, sinks gradually down,and the line formed by the water on her surface, as shesinks, is marked at every foot or other convenient dis-tance. These lines are called water lines, and on their6uioothness, if I may so speak, or their gradual continuity,