OBJECTS usually appear different in shape from what we know them to be. or, in other words, the appearance seems contrary to the facts which we know regarding these objects. We are aware, for instance, that a cube has six equal faces and that each of them is square. If we draw six squares, however, or a smaller number, combining them in any and every possible way, the final result will certainly not give us the same impression as the cube itself. We also know that the top of a right cylinder is a circle, yet it is seldom indeed that we see a cylinder in such a position that the top appears as a true circle. We think of it as a circle simply because we know it to be one; not because it seems really circular, for unless we look straight at the end of the cylinder it appears elliptical or even as a straight line.

So when we are in doubt as to how things should be drawn in order to have them look right, we not only study the things themselves but we also turn to the science of perspective which gives us principles that are helpful to us in drawing objects correctly, not as they actually are, but as they appear from the point from which they are viewed. Freehand perspective trains us especially in the application of these principles to the practical problems of free-hand sketching.

For the purpose of this book it seems desirable to discuss very briefly only a few of the more important of these principles. Nothing short of a complete volume could do justice to the subject, and as there are already many excellent works available it seems needless to duplicate here that which has already been so successfully and completely handled elsewhere. The reader who really desires to thoroughly master the subject should read some such hook as "Free-hand Perspective and Sketching" by Dora Miriam Norton, not forgetting, however, that the reading itself will do little good unless sketches are made to illustrate each point as the student goes along. And one should learn to be observing of the perspective appearance of objects all about him; if he is studying circles and ellipses, let him take notice of every circular arch, or clock face, or barrel, or other similar form which he sees.

Now fundamentally these principles which have to do with the appearance of things are few, and among them the following are perhaps the most important.

First, the apparent size of an object decreases in proportion to its distance from an imaginary plane which passes through the eye at right angles to the direction in which one is looking.

Second, a surface appears in its true shape only when parallel to this plane, or, in other words, when at right angles to the line of sight from eye to surface.

This first principle can be easily tested if one stands close to a window and looks straight through it; - an entire building in the distance will appear only a few inches in size on a single pane of glass. If there are several objects of equal size at varying distances from the eye it will be noticed that the nearest one appears to be the largest and the others seem smaller and smaller in proportion to their distance away.

By way of illustration of the second principle it will be easy for the student to demonstrate for himself that when a surface (take a circular end of a cylinder, for example) is not so placed as to be at right angles to the line of sight it appears smaller in one dimension because of being turned away, and the farther it is turned the smaller this dimension seems, until when turned so far as to cause the surface to coincide with the direction of sight it will appear simply as a line. This apparent change of shape is called foreshortening.

Now in order to give a working knowledge of the application of these principles in the quickest and most direct way we will discuss the appearance and methods of representation of a few typical geometric forms. Elsewhere we have explained that once the simple forms are understood it will not be difficult to do objects which are more complex, applying exactly the same principles.

The Horizon Line Or Eye Level

This is an imaginary horizontal line at the level of the eye. In object drawing or other small work, the latter term is the more commonly used; for buildings and outdoor work in general, the former is customary. The appearance of any object will vary according to whether it is at or above or below the eye level and to the right or in front or to the left of the spectator. To observe just what variation does take place in the appearance of objects as viewed from various points, it is advisable for the student before doing any drawing, to take simple things and to hold them in different positions, noticing just how they look when moved from place to place, nearer or farther from the eye and higher or lower in relation to the horizon line.

The Sphere

Take, for example, a sphere, or an apple or orange or some other object of spherical form. When held above the eye it appears as a circle, - below the eye and at the eye level its contour is practically the same. If it is a true sphere there will not be the slightest variation. If we take an apple, however, with the stem at the top, and hold it level but below the eye, not only is the stem visible but so is a portion of the surface beyond it. If we raise it until the top of the apple is at the height of the eye, still holding it level, the stem is still seen but none of the surface beyond is visible. A bit of the "blossom" below may now show. As we raise it above the eye the stem will gradually disappear as will a portion of the top surface, and as this is lost to view more of the lower part will become visible, so if it is held some distance above the eye we will see the entire "blossom" and the surface beyond. In other words, whereas a sphere remains the same in profile regardless of its position, we see different portions of its surface as it is moved up and down and the same is true if it is shifted to the right or to the left, or spun round and round. Sketch 1, Figure 8, illustrates this point. Study this and then draw several objects of spherical form placed in a variety of positions.