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