28 USE OP PARALLELS TO SHIPWRIGHTS.

The properties of parallel lines are very often employ-ed to make another body or figure exactly equal to somegiven figure.

Let us suppose for example, that we had to make afigure abed, fig. 12, pi. 2, which should be exactly equalto ABCD, already made. Draw B6, Cc, Dd, equal andparallel to A a, and then draw the lines ab, be, cd, da;they will, necessarily, be equal and parallel to AB, BC,CD , DA, and the two figures will be equal.

This principle is applied both in civil and naval archi-tecture. —When it is necessary to make a piece of wood,stone, or iron, with a projection, which is to fit exactlyinto a hollow or cavity, the property of oarallei lines,just mentioned, is called into use. Let us suDnose, forexample, that, in the opening represented by ABCDEF,fig. 13, pi. 2, it is required to fit the piece of wood XY,it will be sufficient to draw the right lines, A a, B b, Cc,D d, Ee, Ff, from the points ABCDEF, equal and par.allel; then trace the line abedef, and shape XY accordingto this line.

These means are employed to make, with the help ofthin planks, the moulds or drafts of the principal parts orpieces out of which a ship is to be built according to somegiven plan. Shipwrights give the name of moulding tothis operation. By its accuracy, derived from the proper-ties of parallel lines, the vessel is constructed to a greatnicety, of the same form and shape as she was originallyplanned in the conception of the naval architect.

The solidity of the vessel also, depends on the precisionwith which the same process is applied, in adapting all thehollow and projecting pieces, such as those represented infig. 14, pi. 2, which are to fit into one another. As theyare closely fitted, the possibility of their moving one withinthe other, when the vessel is exposed to a heavy sea, islessened; and this movement or play, as it is called, is, aswe shall hereafter see, one of the most dangerous causes ofdestruction.

Method of vrojection.—Application of parallel lines to