11. In the same way that the lamp-posts appear to diminish in size as they recede from the •eye, the parallel lines (a, a„ a„ etc., and c, c„ c„ etc.) which run along the tops and bot toms of the posts appear to converge as they recede, for the dis tance between these lines seems less and less as it is taken farther and farther away. At infinity the distance between the lines be comes zero, and the lines appear to meet in a single point. This point is called the vanishing point of the lines.
12. If any Abject, as, for illustration, a cube, is studied, it will be seen that the lines which form its edges may be separated into groups according to their different direc tions; all lines having• the same direction form ing -one group, and ap parently converging to a common vanishing point. Each group of parallel lines is called a system, and each line an element of the sys tem. For example, in Fig. 4, A, and A, belong to one group or system ; B, B,, and to another ; and C, and C,, to a third. Each systein has its own vanishing point, towards which all the elements of that system appear to converge. This phenomenon is well illustrated in the parallel lines of a railroad track, or by the horizontal lines which form the courses of a stone wall.
13. As all lines whicli belong to the same system appear to meet at the vanishing point of their system, it follows that if the eye is placed so as to look directly along any line of a system, that line will be seen endwise, and appear as a point exactly covering the vanishing point of the system to which it belongs.
If, for illustration, the eye glances directly along one of the horizontal lines formed by the courses of a stone wall, this line will be seen as a point, and all the other horizontal lines in the wall will apparently converge towards the point. In other words, the line along which the eye is looking appears to cover the van ishing point of the system to which it belongs. Thus, the vanish ing point of any system of lines must lie on that element of the system which enters the observer's eye, and must be at an infinite distance from, the observer. Therefore, to find the vanishing point of any system of lines, imagine one of its elements to enter the observer's eye. This element is called the visual element of the system, and may often be a purely imaginary line indicating simply the direction in which the vanishing lies. The van
ishing point will always be found on this visual element and at an infinite distance from the observer.
14. To further illustrate 1his point, suppose an observe'r to be viewing the objects in space represented in Fig. 5. He desires to find the vanishing point for the system of lines parallel to the oblique line ab which forms one edge of the roof plane abed. There are two lines in the roof that belong to this system, namely: ab and do If he imagines an element of the system to enter his eye, and looks directly along this element, he will be look ing in a direction exactly parallel to the line ab, and he will be looking directly at the vanishing point of the system (§ 13). This visual element along which he is looking is a purely imaginary line parallel to ab and do. All lines in the object belonging to this system will appear to converge towards a point situated on the line, along which he is looking, and at an infinite distance from him.
This phenomenon is of great importance, and is the founda tion of most of the operations in making a perspective drawing.
15. The word " vanish " as used in perspective always im plies a recession. Thus, a line that vanishes • upward, slopes up ward as it recedes from the observer ; a line that vanishes to the right, slopes to the right as it recedes from the observer.
16. It follows from paragraphs 13 and 14 that any system of lines that vanishes upward, will have its vanishing point above the observer's eye. Similarly, any system vanishing downward, will have its vanishing point below the observer's eye ; any sys tem vanishing to the right, will have its vanishing point to the right of the observer's eye ; and 'any system vanishing to the left, will have its vanishing point to the left of the observer's eye. Any system of horizontal lines will have its vanishing point on a level with the observer's eye, and a systeth of vertical lines will have its vanishing point vertically in line with the observer's eye.
17. All planes that are parallel .to one another are said to belong to the same system, each plane being called an element of the system.