properly so as to observe what the
draughtsman wishes to express, look at Fig. 138, in which the three
diverging lines (A, B, C) are increased in thickness, and the cube
appears plainly. On the other hand, in Fig. 139, the thickening of the
lines (D, E, F) shows an entirely different structure.

[Illustration: _Fig. 137._]

[Illustration: _Fig. 138._]

[Illustration: _Fig. 139._]

It must be remembered, therefore, that to show raised surfaces the
general direction is to shade heavily the lower horizontal and the right
vertical lines. (See Fig. 133.)

HEAVY LINES.--But there is an exception to this rule. See two examples
(Fig. 140). Here two parallel lines appear close together to form the
edge nearest the eye. In such cases the second, or upper, line is
heaviest. On vertical lines, as in Fig. 141, the second line from the
right is heaviest. These examples show plain geometrical lines, and
those from Figs. 138 to 141, inclusive, are in perspective.

[Illustration: _Fig. 140._]

[Illustration: _Fig. 141._]

PERSPECTIVE.--A perspective is a most deceptive figure, and a cube, for
instance, may be drawn so that the various lines will differ in length,
and also be equidistant from each other. Or all the lines may be of the
same length and have the distances between them vary. Supposing we have
two cubes, one located above the other, separated, say, two feet or more
from each other. It is obvious that the lines of the two cubes will not
be the same to a camera, because, if they were photographed, they would
appear exactly as they are, so far as their positions are concerned, and
not as they appear. But the cubes do appear to the eye as having six
equal sides. The camera shows that they do not have six equal sides so
far as measurement is concerned. You will see, therefore, that the
position of the eye, relative to the cube, is what determines the angle,
or $the relative$ angles of all the lines.

[Illustration: _Fig. 142._]

[Illustration: _Fig. 143._]

A TRUE PERSPECTIVE OF A CUBE.--Fig. 142 shows a true perspective--that
is, it is true from the measurement standpoint. It is what is called an
_isometrical_ view, or a figure in which all the lines not only are of
equal length, but the parallel lines are all spaced apart the same
distances from each other.

ISOMETRIC CUBE.--I enclose this cube within a circle, as in Fig. 143. To
form this cube the circle (A) is drawn and bisected with a vertical line
(B). This f