1. When any object in space is being viewed, rays of light are reflected from all points of its visible surface, and enter the eye of the observer. These rays of light are called visual rays. They strike upon the sensitive membrane, called the retina, of the eye, and form an image. It is from this image that the observer receives his impression of the appearance of the object at which he is looking.

2. In Fig. 1, let the triangular card abc represent any object in space. The image of it on the retina of the observer's eye will be formed by the visual rays reflected from its surface. These rays form a pyramid or cone which has the observer's eye for its apex, and the object in space for its base.

3. If a transparent plane M, Fig. 2, be placed in such a position that it will intersect the cone of visual rays as shown, the intersection will be a projection of the object upon the plane M. It will be noticed that the projecting lines, or projectors, instead of being perpendicular to the plane, as is the ease in orthographic projection,* are the visual rays which all converge to a single point coincident with the observer's eye

* In orthographic projection an object is represented upon two planes at right angles to each other, by lines drawn perpendicular to these planes from all points on the edges or contour of the object. Such perpendicular lines intersecting the planes give figures which are called projections (orthographic) of the object.

4. Every point or line in the projection on the plane M will appear to the observer exactly to cover the corresponding point or line in the object. Thus the observer sees the point aP in the projection, apparently just coincident with the point a in the object. This must evidently be so, for both the points aP and a on the same visual ray. In the same way the line aPbP in the projection must appear to the observer to exactly cover the line ab in the object; and the projection, as a whole, must present to him exactly the same appearance as the object in space.

5. If the projection is supposed to be permanently fixed upon the plane, the object in space may be removed without affecting the image on the retina of the observer's eye, since the visual rays which were originally reflected from the surface of the object are now reflected from the projection on the plane M. In other words, this projection may be used as a substitute for the object in space, and when placed in proper relation to the eye of the observer, will convey to him an impression exactly similar to that which would be produced were he looking at the real object.

6. A projection such as that just described is known as a perspective projection of the object which it represents. The plane on which the perspective projection is made is called the Picture Plane. The position of the observer's eye is called the Station Point, or Point of Sight.

7. It will be seen that the perspective projection of any point in the object, is where the visual ray, through that point, pierces the picture plane.

8. A perspective projection may be defined as the representation, upon a plane surface, of the appearance of objects as seen from some given point of view.

9. Before beginning the study of the construction of the perspective projection, some consideration should be given to phenomena of perspective. One of the most important of these phenomena, and one which is the keynote to the whole science of perspective, has been noticed by everyone. It is the apparent diminution in the size of an object as the distance between the object and the eye increases. A railroad train moving over a long, straight track, furnishes a familiar example of this. As the train moves farther and farther away, its dimensions apparently become smaller and smaller, the details grow more and more indistinct, until the whole train appears like a black line crawling over the ground. It will be noticed also, that the speed of the train seems to diminish as it moves away, for the equal distances over which it will travel in a given time, seem less and less as they are taken farther and farther from the eye.

10. In the same way, if several objects having the same dimensions are situated at different distances from the eye, the nearest one appears to be the largest, and the others appear to be smaller and smaller as they are farther and farther away. Take, for illustration, a long, straight row of street-lamps. As one looks along the row, each succeeding lamp is apparently shorter and smaller than the one before. The reason for this can easily be explained. In estimating the size of any object, one most naturally compares it with some other object as a standard or unit. Now, as the observer compares the lamp-posts, one with another, the result will be something as follows (see Fig. 3). If he is looking at the top of No. 1, along the line ba, the top of No. 2 is invisible. It is apparently below the top of No. 1, for, in order to see No. 2, he has to lower his eye until he is looking in the direction baP He now sees the top of No. 2, but the top of No. 1 seems some distance above, and he naturally concludes that No. - appears shorter than No. 1. As the observer looks at the top of No. 2, No. 3 is still invisible, and, in order to see it, he has to lower his eye still farther. Comparing the bottoms of the posts, he finds the same apparent diminution in size as the distance of the posts from his eve increases. The length of the second post appears only equal to the distance mn as measured on the first post, while the length of the third post appears only equal to the distance 08 as measured on post No. 1.

11. In the same way that the'lamp-posts appear to diminish in size as they recede from the eye, the parallel lines (a, a1, a2, etc., and c, c1, c2, etc.) which run along the tops and bottoms of the posts appear to converge as they recede, for the distance between these lines seems less and less as it is taken farther and farther away. At infinity the distance between the lines becomes zero, and the lines appear to meet in a single point. This point is called the vanishing point of the lines.