Apparent Diminution in Size.—The complete theory of perspective can be developed from a single basic phenomenon; viz., the apparent decrease in size of an object as it recedes from the eye. A railway train moving over a straight track furnishes an example. As the train becomes more distant its dimensions apparently become smaller. Its speed also seems to diminish, for the space over which it travels in a given time appears to be shorter and shorter as it is taken farther and farther away. Plate I., fig. 8, is another example, showing posts of equal height and with equidistant spaces between.
The reason for the apparent diminution in size is readily under stood from fig. 4. The size of any object is estimated by corn paring it with some standard. As the observer looks along the line ba at the top of the first post, the top of the second post is in visible. It is apparently below the top of No. r, and in order to see it he must lower his direction of sight until he looks along bd.
He now sees the top of No. 2, but No. 3 is still invisible and in order to see No. 3 he must lower his gaze still further until he looks along bf. Considering the bottoms of the posts he finds the same apparent shrinkage. Compared with No. r, No. 2 seems to have a length only equal to km, No. 3 only equal to op, and so on. The posts thus appear relatively smaller and smaller as they are taken farther and farther from the eye. If the line of posts could be extended an infinite distance, the last post would evidently appear incalculably small or of zero length.
Similarly the two parallel lines, adf and ceg, running respectively along the tops and bottoms of the posts must, owing to the apparent decrease in the lengths of the posts, appear to approach one another as they recede. Could they be of infinite length they would evidently appear to meet in a point at an infinite distance from the observer. This imaginary point which parallel lines seem to approach is called a vanishing point. Plate I., fig. 3, shows a perspective of the interior of an aqueduct in which the parallel lines of the stone courses can easily be imagined to meet in a vanishing point.
Systems of Lines.—If any object bounded by planes, e.g., a cube is examined, its edges can be grouped into several series or systems of parallel lines. Each system will have its particular vanishing point. In
fig. 5 there are three such series, one appar ently converging or vanishing toward the right, one toward the left, and a vertical system. It is important to be able to locate the imaginary vanishing point of any sys tem of lines. This can always be done by looking along one of the lines or elements of the system. Whatever the position of the • observer, every element of a given system appears to converge towards the vanish ing point of that system and, if extended indefinitely, to meet the vanishing point. Hence if the observer looks along any element, he will be looking directly at the vanishing point of the system. The line along which he sights will be seen endwise, as a point, exactly covering the vanishing point toward which all other elements of the system will appear to converge. Thus, an observer might sight directly along one of the course lines in Plate I., fig. 3, and discover the vanishing point for the other course lines directly in front of his eye.
This principle is further illustrated by the model shown in Plate I., fig. r, which consists of a series of rods representing straight lines and arranged in a parallel system. Let the observer look directly along any one of the rods, as the one at the lower left corner. This rod will appear as a dot, and apparently cover the imaginary infinitely distant vanishing point of the system. All the other rods or elements will appear to converge toward the vanishing point which the observer has located. Again if he sights along the centre rod, Plate I., fig. 4, he will see it as a dot covering the imaginary vanishing point towards which the other elements of the system appear to converge. Let him choose which rod he will the result will evidently be the same. The line along which the observer sights is called the visual element of the system. Plate I., fig. 9, shows the use of this method to locate the vanishing point of the horizontal lines in the view that are parallel to the curbing. The observer sights along the fence rail which being parallel to the curb leads his gaze to the desired van ishing point. All other horizontal lines in the view belonging to this system seem to converge towards the infinitely distant vanishing point covered by the fence rail.