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.

Seventh. If the point of the compass is now put at H, and the pencil or
pen on the circle line F, the curve J can be drawn, so the latter curve
and the curve F will thus merge perfectly at the line I.

THE FOCAL POINTS.--The focal points can be selected at any arbitrary
point, between C and the line B, and the point H may be moved closer to
or farther away from the line A, and you will succeed in making the
ellipse correct, if you observe one thing, namely: The line I, which
must always run from H to E, and intersects the circle F, is the
starting or the ending point for the small curve F or the large circle
J.

[Illustration: _Fig. 115. Fig. 116. Fig. 117. Perspectives of Cubes_]

ISOMETRIC AND PERSPECTIVE.--A figure may be drawn so as to show an
isometric or a perspective view. Thus, a cube can be drawn so as to make
an isometric figure, as in Fig. 115, where the three sides are equal to
each other.

Isometric means a method of drawing any object in such a manner that the
height, length and breadth may be shown in the proportion they really
bear to each other. Fig. 115 has the sides not only equal to each other,
in appearance to the eye, but they have the same outlines and angles.

Contrast this figure with Figs. 116 and 117. In Fig. 116 two of the
sides are equal in angles and outline; and in Fig. 117 each side has a
different outline, and different angles. Nevertheless, all the cubes
are, in reality, of the same dimension.

THE PROTRACTOR.--This is a most useful tool for the draughtsman. It
enables the user to readily find any angle. Fig. 118 shows an approved
form of the tool for this purpose.

[Illustration: _Fig. 118. Protractor. Section Lining Me