[Illustration: _Fig. 113. Drawing an Ellipse_]
MAKING ELLIPSES AND IRREGULAR CURVES.--This is the hardest thing to do with drawing tools. A properly constructed elliptical figure is difficult, principally, because two different sized curves are required, and the pen runs from one curve into the other. If the two curves meet at the wrong place, you may be sure you will have a distorted ellipse.
Follow the directions given in connection with Fig. 113, and it will give you a good idea of merging the two lines.
First. Draw a horizontal line, A, which is in the direction of the major axis of the ellipse--that is, the longest distance across. The narrow part of the ellipse is called the minor axis.
Second. Draw a perpendicular line, B, which we will call the center of the ellipse, where it crosses the line A. This point must not be confounded with the _focus_. In a circle the focus is the exact center of the ring, but there is no such thing in an ellipse. Instead, there are two focal points, called the _foci_, as you will see presently.
Third. Step off two points or marking places, as we shall term them, equidistant from the line B, and marked C, C. These marks will then represent the diameter of the ellipse across its major axis.
Fourth. We must now get the diameter of the minor axis, along the line B. This distance will depend on the perspective you have of the figure. If you look at a disk at an angle of about 30 degrees it will be half of the distance across the major axis.
So you may understand this examine Fig. 114. The first sketch shows the eye looking directly at the disk 1. In the second sketch the disk is at 30 degrees, and now the lines 2 2, from the eye, indicate that it is just half the width that it was when the lines 3 3 were projected. The marks D D, therefore, indicate the distance across the minor axis in Fig. 113.
[Illustration: _Fig. 114. Perspection in Angles_]
Fifth. We must now find the focal points of the ellipse. If the line A on each side of the cross line B is divided into four parts, the outer marks E may be used for the foci, and will be the places where the point of the compass, or bow pen, is to be placed.
Sixth. Describe a circle F, so it passes through the mark C, and move the point of the compass to the center of the ellipse, at the star, and describe a circle line G, from the mark C to the line B. This will give a centering point H. Then draw a line I from H to E, and extend it through the circle F.