The combined length of the two lines drawn from any point on the ellipse to the two foci must always be the same and equal to the length of the major axis. This is readily seen with the two pins and string. ([Fig. 71].)
Fig. 71. Drawing the ellipse with string and pins
The pencil point as it traverses the ellipse represents any point, and the string remains the same length. Where it is required to draw an ellipse of definite size, say two by three, it becomes necessary to find the foci before the string can be used, and as it requires considerable skill to get the string the exact length, Ralph showed the boy another way, called the trammel method. ([Fig. 72].)
Suppose the problem is to construct an ellipse 6 inches × 21⁄2 inches. First draw the two lines a b and c d at right angles, intersecting at the exact centre. Take a straight piece of paper, lay it along a b with one end at a. Make a dot on the edge of the paper where the lines cross, and mark it x. Next, lay the same strip of paper along c d, with the original end at c, and again mark a point where the lines cross. Mark this point y. At any position of this strip of paper when the points x and y touch the two axes a b and c d, the end of the paper strip will be on the ellipse. By shifting this paper trammel and keeping the two points on the axes a series of points may be made at the end of the paper. Connecting this by a pencil line will complete the ellipse. This is a very simple method and a very accurate one.
Fig. 72. The trammel method