588 Additions and Correéhions

be where it approaches neareft to the ground; and from thence being moved half a circle to the right or left,. it will there attain its greateft elevation, and fupport itfelf, or, with a very flight affiftance, may be fupported in equilibrio. When agate isin its line of reft, or in its oppofite line of equilibrium, the two hooks by which it is fafpended, and the centre of the gate’s gravitation, will bein the fame vertical plane with each other; which may be eafily underftood by obferving a common gate, whofe hinges are put on inany manner, however awkward or perverfe. And when the hooks are in one perpendicular line, it can admit no doubt but that they muft always be in the fame vertical plane with the centre of the gate’s gravitation, be- canfe they will be fo with any third given point whatfoever. Thefe principles are alfo applicable toa common fwing gate, which has two or more pivots or hooks at the lower hinge, when the pofition of either one of the lower pivots is confidered

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with refpect to the upper hook*.” In explanation of thefe principles, a figure is given which is fuppofed“ the outline of a gate nine feet two inches long, from the fore part of its head to its upper point of fufpenfion, reprefented in the line of reft, as well as in the oppofite line of equilibrium; fhowing the velocity with which the gate is made to fall, from an elevation of fix inches gained at the head in attaining its line of equilibrium, eftimated from the line of reft_ by means of the pofition of the two hooks, and the proportionate extra length of the lower thimble+.” And it is con- tended that“ the line of faftening fhould be 22° 30’, or 1-fixteenth part of a circle, fhoit of cr within the line of reft, and confequently the correfponding line of equi- librium will alfo be 22° 30° fhort of the greateft extent of the gate’s opening}.” But in order‘‘ to prevent the gate being left unfhut, it is advifed that a fhort poft fhould be placed at about half the diftance between the road to be paffed and the fence ad- joining the hanging poft, that is 22° 30 within the line of equilibrium; fo that the gate{hould not open from its line of faftening more than about 135°, which will an- {wer every purpofe; and the hinges muft be fo adjutted that the gate fhall be perfectly upright at its line of faftening§.” It is ftated that a gate, fufpended in this manner, cannot be left open,(excepting in high winds) but will fhut of itfelf, though not with an uniformly accelerated motion, as might be fuppofed; its velocity being rather increafed as it paffes the middle part of its femicircular courfe, and retarded again as it approaches its line of reft, coinciding with the proportionate rife of the bead, allowing only for fuch acceleration as muft be acquired while the gate, in fall- ing with a continued motion, recedes more and more from the line of equilibrium. As the verfed fine of the angle formed by the gate with its line of reft, is to the length of the gate 110 inches, which is the made radius, fo will be the cor-

* Parker's Efflay on Gates,+ Ibid.+ Ibid,§ Ibid.