Van Nostrand's eclectic engineering magazine . n of the tangent at any pointto the horizontal. Then as the arc A B (Fig. 7) may standfor any part of the curve counting fromthe horizontal point A towards one of thepoints of suspension, we have the followinggeneral equations from the triangle B F T jT2=p2-fH2 (1.) Tani px dpd X (2.) (p being = the load per unit of horizon-tal distance, A the origin of co-ordinates, A T= axis of X and A J = axis of y). From equations (1) and (2) we cansolve three problems. 1. Given the curve, and the load, to findT and H. 2. Given the curve, and T and H, to findP
Van Nostrand's eclectic engineering magazine . n of the tangent at any pointto the horizontal. Then as the arc A B (Fig. 7) may standfor any part of the curve counting fromthe horizontal point A towards one of thepoints of suspension, we have the followinggeneral equations from the triangle B F T jT2=p2-fH2 (1.) Tani px dpd X (2.) (p being = the load per unit of horizon-tal distance, A the origin of co-ordinates, A T= axis of X and A J = axis of y). From equations (1) and (2) we cansolve three problems. 1. Given the curve, and the load, to findT and H. 2. Given the curve, and T and H, to findP. 3. Given the load, and T and H, to findthe curve. For a full discussion of this case, seeEankines Civil Engineering. Such a distribution of the load as wehave discussed in the above case, is approxi-mated to in suspension bridges, and some-times in wood, iron, or steel arches, butnot usually in stone or brick ones. Case If. Let the load still be vertical,but distributed uniformly a^ong the curve. That is, divide the arc CAB (Fig. 8) Fig. into elements each of a unit in length; thenthe load on these elements is constantthroughout. It is easily seen that such aload is not, as in the last case, uniformalong the horizontal, for the basis of thelittle triangles of which the hypothenusesare now equal, diminish in extent as wego from A towards B or C. A chain of uni- 100 VAN NOSTRANDS ENGINEERING MAGAZINE. form material and cross-section and acted onby nothing but its own weight, is in thecondition described, and, as is well known,the curve assumed by it is the * commoncatenary. Let p = weight of a units length of thecord, then if p m = horizontal pull on theCord at A = H, m is called the modulus ofthe catenary^ and represents the length ofcord of the same kind as C B, the weightof which would equal the pull at A. Theweight onAB=P=^s when s = lengthof cord A B. Fig. 9.
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