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TIIE PRINCIPLES OF BRIDGES.

TRACT I.

SECTION II.

OF THE ARCHES.

PROPOSITION I.

Let there be any number of linen ab, bc, cd, de, Sic. allin the same vertical plane, connected together and moveableabout the joints or angles a, b, c, d, e, f; the two extremepoints a and g being fixed: It is required to determine the pro-portion of the weights to be laid upon the angles b, c, d, Sic.so that the whole may remain in equilibria.

Solution. —From theseveral angles, havingdrawn the lines b b, cc,

D d, &c. perpendicularto the horizon ; aboutthem, as diagonals,constitute parallelo- A V-

grams such, that those sides of every two that are at the op-posite ends of the given lines, may be equal to each other ;viz, Laving made one parallelogram inn, take cp = Bn, andform the parallelogram pq; then take Dr = cq, and make theparallelogram rs; and take Er = da’, and form the parallelo-gram tv; and so on : Then the said vertical diagonals Bb, cc,d d, ep, &c, of those parallelograms, will be proportional tothe weiguts, as required.

Demonstration. —By the resolution of forces, each of theweights or forces nb, c c, d d, &c, in the diagonals of the pa-rallelograms, is equal to, and may be resolved into, twoforces, expressed by two adjacent sides of the parallelogram;viz. the force B b may be resolved into the two forces B??2, eh,