Fig. 54.—How to draw an Ellipse.
We must first take another lesson in drawing, and the appliances I want you to use for the purpose are very simple. You must have a smooth board and some tacks or drawing-pins, besides paper, pencil, and twine.
Fig. 55.—Specimens of Ellipses.
We first lay a sheet of paper on the board, and then put in two tacks through the paper and into the board. It does not much matter where we put them in. Next we take a piece of twine and tie the two ends together so as to form a loop, which we pass round the two tacks ([Fig. 54]). In the loop I place the pencil, and then you see I move it round, taking care to keep the twine stretched. Thus I produce a pretty curve, which we call the ellipse. I must ask all of you to practise this experiment. Try with different lengths of string, and try using different distances between the tacks. Here are some sketches of two shapes of ellipse and a parabola ([Fig. 55]). Elliptic curves can be made almost circles by putting the two tacks close together, or they can be made very long in comparison with their width. They are all pretty and graceful figures, and are often useful for ornamental work. The ellipse is a pretty shape for beds of flowers in a grass-plot.
The importance of the ellipse to astronomers is greater than that of any other geometrical figure. In fact, all the planets, as they perform their long and unceasing journeys round the sun, move in ellipses; and though it is true that these ellipses are very nearly circles, yet the difference is quite appreciable.
It is also important to observe that the sun is not in the centre of the ellipse which the planet describes. The sun is nearer to one end than to the other. And the actual position of the sun must be particularly noted. Suppose that some mighty giant were preparing to draw an exact path for the earth, or for Mars, of course he would want to have millions of miles of string for producing a big enough curve, and one of the nails that he used would have to be driven right into the sun. The following is the astronomer’s more accurate method of stating the facts. He calls each of the points represented by the tacks around which the string is looped a focus of the ellipse; the two points together are said to be the foci; and as the planet is describing its orbit, the position of the sun will lie exactly at one of the foci.
The ellipse is a curve that nature is very fond of reproducing. From an electric light, a brilliant beam will diverge. If you hold a globe in the beam, and let the shadow fall on a sheet of paper, it forms an ellipse. If you hold the sheet squarely, the shadow is a circle; but as you incline it, you obtain a beautiful oval, and by gradually altering the position, you can get a greatly elongated curve. Indeed, you can thus produce an ellipse of almost any form. The electric light is not indispensable for this purpose; any ordinary bright lamp with a small flame will answer, and by taking different sized balls and putting them in various positions, you can make many ellipses, great and small.