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.

In the shop this distance may be found experimentally by laying a foot
rule on a square so that one end of the former will touch the figure
marking the lesser diameter on the latter, and then bringing the figure
on the rule that represents the greater diameter to the edge of the
square; the figure on the square at this point is the distance sought.
Unfortunately they rarely represent whole numbers. We present herewith a
table giving the width to the eighth of an inch for several different
ovals when the length and distance between foci are given.

Length. Distance between foci. Width.
Inches. Inches. Inches.

2 1 13/4
2 11/2 11/4

21/2 1 21/4
21/2 11/2 2
21/2 2 11/2

3 1 11/2
3 11/2 2-7/8
3 2 2-5/8
3 21/2 21/4

31/2 1 3-3/8
31/2 11/2 3-1/8