148 THE FINE ARTS. 
will intersect the transparent plane in the vanishing-point of the image of 
the parallel lines on the object. Vanishing-points determined by such 
imaginary lines in space are shown at p and s (fig. 40); at e (figs. 41, 42) ; 
and at P and D2 (jig. 45). If such a line in space intersect the trans- 
parent plane at right angles, the vanishing-point coincides with the point 
of sight (figs. 40,8; 41, e; 42,e; 45, P), and the horizontal line passing 
through this point is the horzzon of the image. If the line in space intersect 
the transparent plane at an angle of 45° or less and at the same time be 
horizontal, the point of intersection is called the point of distance of the 
image, and lies in the horizon at a distance (right or left) from the point of 
sight equal to the distance of the eye from the transparent plane (jig. 41d). 
If the line in space intersect the transparent plane at an angle of more than 
45°, the vanishing-point which marks the intersection is called the point of 
incidence ( fig. 45 D2). 
5. All cwrved lines, angles, and figures on an object, which lie in a plane 
whose extension would pass through the eye of the draughtsman, appear in 
the image as straight lines; the more or less curved appearance of curved 
lines, or broad appearance of angles and figures in the image, is in direct 
proportion to the distance at which the extension of their planes would pass 
over, under, or right or left from the eye of the draughtsman (pl. 20, jigs. 
8 and 9, the middle lines; jigs. 1, 2, and pl. 21, jigs. 6-11, the auxiliary 
lines through the eyes and points of the noses). 
The methods of determining these various points and the horizon in the 
plane of a picture can only be explained practically by elaborate deductions 
and with the assistance of models, and the instruction in these methods 
must be obtained from a teacher in a progressive course of lessons. 
Regarding their theory we offer the following remarks. 
The paper of the draughtsman, or the plane of the picture, represents the 
transparent plane itself, the frame of the former or its circumscription coin- 
ciding with the limits of the latter (pl. 19, jigs. 41-45, the rectangles circum- 
scribing the drawings). The lines of construction drawn on the plane of | 
the picture are partly those enumerated above, in part such as the draughts- 
man originally imagined drawn in space from his eye to points of the object 
or parallel to some of its lines, and which are, as it were, folded or flapped 
into the plane of the picture. The student of the art of drawing must 
acquire the faculty of imagining such constructive lines projecting into 
space before and behind the plane of the picture, in order to understand 
construction and to apply it. This accomplishment can only be attained 
by the study of perspective in models and by continued systematic lessons 
in drawing from nature. 
The same course of study is requisite to prepare and qualify the student 
for a due consideration of some points of particular importance in pictorial 
perspective, viz. the selection of the precise place for the transparent plane, 
and of the proper distance of the point of view from, as well as its position 
(line of sight) with respect to the transparent plane. 
Concerning the position of the transparent plane, the general rule, in 
ease a single angular body is to be drawn, is to place the plane vertically 
532 
