to the Firft Volume, 589

refponding rife of the head of the gate to 3,3,th inches, or half the whole rife of the gate’s head, at any given angle within the quadrant: and the rife in the head afterwards will be, as the co-fine of any given angle formed by the gate with its line of equilibrium in defcribing the complement of that angle, is to the length of the gate, or radius, fo will be the correfponding rife of the head of the gate to the remaining 37, inches, which co-/ixe of the angle formed by the gate, with the line of equilibrium, is equal to the fine of the complementary angle, or angle of the gate’s progrefs, from a radius at right angles to, or equi-diftant from, the lines of reft and equilibrium, in performing its fupplementary courfe. Thus it appears, that though the rife of the gate at the head in the firft 90°, or half of its femi- circular courfe, be 3,7, inches, yet in the firft and laft22° 30’ of its courfe, it will rife only r-fourth ofan inch, or exactly.%-ths and°°. ths ofa 24th in each refpectively; and rejecting the greater fractions, the rife of the gate’s head, and correfponding velocity of the gate’s fall in equal eighth parts of its femicircular courfe, is nearly in proportion to the numbers 6, 16, 26, 32, and then inverfely 32, 26, 16&6.*

And in further illuftration of the above principles, a“ reprefentation is given of the horizontal fe@ion of two hooks for a right-handed gate, Opening one way, brought into one plane of obfervation; the upper hook, the lower hook, the line of fafiening, the line of reft, and the line of equilibrium. The diameter of the hooks+3ths of an inch, which is the proper fize fora common gate. The horizontal diftance of the lines falling from the two hooks being 2 or 14. inch, is the meafure adapted to hinges which are forty inches afunder, In ad- jufting the hinges, it is neceflary that the upper thimble fhould incline+ inch from its centre towards the hanging poft, and that the lower thimble fhould be{crewed into the heel of the gate+ inch out of the firaight line, inclining in the oppofite direction, that is, from inftead of towards the hanging poft, both thimbles together making a variation of the ,*, inch; and to correfpond with this variation, the upper hook fhould meafure, from the centre of the pin to the fhouldering, about half the thicknefs of the heel of the gate, as the inch inclination of the upper thimble will allow fufficiently for the gate hanging clear of the poft. The lower hook mutt be -*- inch longer than the upper hook, and muft be driven into the gate-poft 14 inch out of the perpendicular line of the perforated parts of the gate-pofi, in which the hooks are to be received, asthe lower thimble mutt alfo exceed the upper thimble in length 12 inch, fuppofing the gate to be a right-angled parallelogram, or at leatt the rail and heel to be at right angles with each other; elfe the lower thimbles muft be extended by a wafher to make up the deficiency, which, however, will not at all

* Parker’s Effay on Gates,