Let ab and cd (Fig. 406) be the given axes. Place the trammel so that a line passing through the centre of the grooves would coincide with the axes; make the distance from the pencil e to the nut f equal to half cd; also, from the pencil e to the nut g equal to half a b; letting the pins under the nuts slide in the grooves, move the trammel eg in the direction cbd; then the pencil at e will describe the required ellipse.

A trammel may be constructed thus: take two straight strips of board, and make a groove on their face, in the centre of their width; join them together, in the middle of their length, at right angles to one another; as is seen at Fig, 406. A rod is then to be prepared, having two movable nuts made of wood, with a mortise through them of the size of the rod, and pins under them large enough to fill the grooves. Make a hole at one end of the rod, in which to place a pencil. In the absence of a regular trammel a temporary one may be made, which, for any short job, will answer every purpose. Fasten two straight-edges at right angles to one another. Lay them so as to coincide with the axes of the proposed ellipse, having the angular point at the centre. Then, in a rod having a hole for the pencil at one end, place two brad-awls at the distances described at Art, 549. While the pencil is moved in the direction of the curve, keep the brad-awls hard against the straight-edges, as directed for using the trammel-rod, and one quarter of the ellipse will be drawn. Then, by shifting the straightedges, the other three quarters in succession may be drawn. If the required ellipse be not too large, a carpenters'-square may be made use of, in place of the straight-edges.

549 The Axes Being Given To Describe An Ellipsis W 583

Fig. 406.

An improved method of constructing the trammel is as follows: make the sides of the grooves bevelling from the face of the stuff, or dove-tailing instead of square. Prepare two slips of wood, each about two inches long, which shall be of a shape to just fill the groove when slipped in at the end. These, instead of pins, are to be attached one to each of the movable nuts with a screw, loose enough for the nut to move freely about the screw as an axis. The advantage of this contrivance is, in preventing the nuts from slipping out of their places during the operation of describing the curve.