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 1¾
2 1½ 1¼

2½ 1 2¼
2½ 1½ 2