A very simple apparatus for describing an oval or ellipse may be constructed by any apprentice or school boy as follows: Procure a straight piece of wood about ¼ inch wide by 1/8 inch thick and 13 inches long. Beginning ½ inch from the end, bore a row of small holes only large enough for a darning needle to pass through and half an inch apart. Mark the first one (at A) 0, the third 1, the fifth 2, and so on to 12, so that the numbers represent the distance from O in inches. A small slit may be made in the end of the ruler or strip of wood near A, but a better plan is to attach a small clip on one side. [Illustration: ELLIPSE INSTRUMENT.] Next procure a strong piece of linen thread about four feet long; pass it through the eye of a coarse needle, wax and twist it until it forms a single cord. Pass the needle _upward_ through the hole marked 0, and tie a knot in the end of the thread to prevent its slipping through. The apparatus is now ready for immediate use. It only remains to set it to the size of the oval desired. Suppose it is required to describe an ellipse the longer diameter of which is 8 inches, and the distance between the foci 5 inches. Insert a pin or small tack loosely in the hole between 6 and 7, which is distant 6-½ inches from O. Pass the needle through hole 5, allowing the thread to pass around the tack or pin; draw it tightly and fasten it in the slit or clip at the end. Lay the apparatus on a smooth sheet of paper, place the point of a pencil at E, and keeping the string tight pass it around and describe the curve, just in the same manner as when the two ends of the string are fastened to the paper at the foci. The chief advantage claimed over the usual method is that it may be applied to metal and stone, where it is difficult to attach a string. On drawings it avoids the necessity of perforating the paper with pins. As the pencil point is liable to slip out of the loop formed by the string, it should have a nick cut or filed in one side, like a crochet needle. As the mechanic frequently wants to make an oval having a given width and length, but does not know what the distance between the foci must be to produce this effect, a few directions on this point may be useful: It is a fact well known to mathematicians that if the distance between the foci and the shorter diameter of an ellipse be made the sides of a right angled triangle, its hypothenuse will equal the greater diameter. Hence in order to find the distance between the foci, when the length and width of the ellipse are known, these two are squared and the lesser square subtracted from the greater, when the square root of the difference will be the quantity sought. For example, if it be required to describe an ellipse that shall have a length of 5 inches and a width of 3 inches, the distance between the foci will be found as follows: (5 x 5) - (3 x 3) = (4 x 4) or __ 25 - 9 = 16 and \/16 = 4.