68 THE YOUNG 
four lines of equal length, united to each 
other at right angles. 
A parallogram is composed of four 
straight lines, the opposite sides being 
parallel and equal ; but the adjacent sides 
maybe unequal. Place several of these 
in conjunction and study their positions, 
etc. (Fig. 2). 
A superficies is a surface of any form. 
A cube is a solid body having six equal 
square sides, and all its angles right an- 
gles. A model of one should be procured 
by the student ; as the laws of perspec- 
tive can be simplified by observing the 
different angles produced by every change 
of its position in relation to the eye. 
The cube being placed before the eye 
will illustrate this perfectly, as the top 
and sides, although square, do not appear 
to be so, and the i)urpose of drawing is to 
D 
z 
B 
Fig. 3. 
represent objects as they are seen. In the 
cube (Fig. 3), the top, w^hich in nature is 
square, is represented by a figure nar- 
rower than it is long, and with two acute 
and two obtuse angles. 
Lines converge w^hen they are inclined 
toward each other, and if extended in this 
direction they will meet at some point. 
To prove the form that a square assumes, 
place the image of one in a perpendicu- 
lar position with one end retreating from 
the eye—the end removed will appear 
shorter, and in the horizontal will appear 
to converge to some point. 
Let us construct a cube with these 
ideas distinctly before us, and without 
the actual knowledge of perspective we 
SCIENTIST. 
can train the hand and the eye to do 
much. 
Fix the perpendicular a b, of any 
length, and as the eye is to look down on 
the cube, draw c a, foreshortened, or less 
than A B, which is the only line seen of 
its real length. Next draw c d shorter 
than A B, (but longer than c a), because it 
is more distant ; again join d b. Here we 
have the square a, b, d, c in perspective 
Now determine the slope of a e, which 
being more foreshortened than c a, will 
slope more and be shorter. Again, e f 
being more distant than c d, will also be 
shorter. Join b f. Fix on the point g, sc 
that G E shall be shorter than c a, and g c 
shorter than a e, being more distant: 
then the line g h being most distant, will 
be the shortest perpendicular, and joined 
with D and f, we will have the figure 
complete. 
We will now observe that the figure a, 
c, G, E, the top of the cube, is narrower 
than B, D, H, F the base, because it is more 
on a level with the eye, and we see less of 
its natural form. Thus we have now 
learned that although lines are of equal 
length in nature, in drawing they should 
be made smaller according to their dis- 
tance. Angles are also modified and obey 
a similar law. This important exercise 
should be practiced by an indefinite num- 
ber of examples, changing the i)osition of 
the cube in relation to the eye; for the 
diagrams so constructed are the bases on 
which we fill in the varied forms from na- 
ture. 
In the construction of a diagram for prac- 
tical purposes, we must be able to divide 
and subdivide its sides into propcrtionate 
parts. Take the following example (Fig. 4). 
In drawing a building we construct the 
side A, B, D, c, then a, b, f, e. Now if we 
want to divide either of these sides into 
any given number of equal parts, divide a 
B, and c, D, into the given number, join 
the corresponding points, and draw a 
diagonal from a to d. The points of in. 
tersection will give the positions for the 
perpendicular and proportionate divisions. 
In these may be described arches or win- 
dows in perspective'. 
By a well grounded practice in exercises 
which almost any object may suggest, the 
