THE ART OF DRAWING. 147 
line, filled up with exact imitations of the colors of the object and their 
delicate shades, and placed in the precise position of the imagined trans- 
parent plane, will convey to the eye from the old point of view the 
impression of seeing the object itself, though it be entirely covered by 
the picture or taken away. 
The pupil in the art of drawing must by practice acquire the faculty of 
beholding all visible objects before which he assumes a fixed point of view 
as if they were already drawn on a transparent plane; and conversely, of 
imagining a natural drawing as a transparent plane behind which the 
objects of the drawing appear as if existing in reality. Both these accom- 
plishments must be aimed at from the very beginning of instruction in 
drawing, in order to insure a thorough understanding on the part of the 
pupil. ? 
When we view various natural objects as if seen through a transparent 
plane, and fixed upon it as described, we can by mere ocular perception 
recognise the following laws, which are also susceptible of mathematical 
demonstration. 
1. Lines, angles, and figures of solid bodies (2. ¢. of objects of threefold 
extension in space), parallel to the transparent plane, preserve wm the 
image their real position and form, or, more explicitly, such lines 
retain their real durection ; such angles their real size; and such figures 
their real form and position. All lines, angles, and figures not parallel to 
the transparent plane exhibit in the image an altered direction and position. 
This will be more clearly understood after a comparison (p/. 19, figs. 48, 44) 
of the perspective niches in the backgrounds with those on the sides; and 
(jig. 45) of the facade in the centre of the background and of its details 
with the perspective forms of the similar fronts on the left side in the fore- 
ground ; and finally of the front and side faces of a perspective drawing of 
a double cross (jig. 40). 
2. Lines and figures on a body, or the body itself, appear smaller on the 
transparent plane 7 proportion to their increased distance behind the same. 
This perspective reduction is illustrated (pl. 19, jig. 40) by the different 
appearance of the projecting and receding lines, squares, and cubes, which 
in reality are all alike; and is still more prominent (fig. 45) in the perspec- 
tive forms of the buildings in the background as compared with those of 
the foreground, whose real dimensions are equal; as well as in the divisions 
of the floors (figs. 41, 42), which in reality are of the same size. 
8. All lines on a body parallel to each other, but not to the transparent 
plane, from which they recede either at right angles or obliquely, converge 
in the image to one point, the vanishing point, if sufficiently extended. 
Thus all the lines converging to the point s (jig. 40) are in reality parallel 
to each other, receding at right angles from the transparent plane. The 
same is the case with the lines converging in the point P (jig. 45), whilst 
those converging in D2, being parallel to each other, recede obliquely from 
the transparent plane. 
5. A line im space drawn from the eye of the draughtsman towards the 
transparent plane, and parallel to a number of parallel lines on the object, 
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