Upon a second piece of paper draw the figure shown in fig. 63 in the following manner. Draw the horizontal line _a b_ equal to A B (fig. 62), and divide it into the same number of parts. Through the centre draw a perpendicular line to V, and cross it by a line _e d_ parallel to _a b_. Lastly, draw V S horizontal to _e d_. The length of the two lines _e_ V and S V is quite arbitrary, but the longer you make the former in proportion to the latter the greater will be the distortion of the drawing. Now draw the lines V 1, V 2, V 3, and V 4, and join S to _a_. Wherever S _a_ crosses the divisions 1, 2, _e_, 3, 4, and _b_, draw a horizontal line, parallel of course with _a b_. You will thus have a trapezium _a b c d_ divided into as many spaces as the square A B C D in fig. 62, and it now remains to fill them in with similar portions of the figure. Thus, for instance, the nose is in the fourth vertical division, starting from the left, and in the third and fourth counting from the top; in order, therefore, to make it occupy so lengthened a space it must be considerably distorted by the pencil. It will be readily seen also that the more numerous the spaces into which the square is divided, the easier it will be to draw the distorted picture. It is by this means that the _anamorphosis_ shown in fig. 63 has been drawn. The next thing to do is to find the point of view from which we can see the figure in its natural proportions. This will be found to be at a distance above the point V equal to the line V S. In order to complete the experiment it is simply necessary to place the distorted picture in a horizontal position, and fix a piece of cardboard vertically at the point V. If a hole be punched in it at a distance from V equal to S, and the drawing be looked at through it, the whole of the parts will fall into symmetry immediately. The experiment may be tried first with fig. 63, the hole being made rather large, and the eye placed at a distance of from 3 to 4 inches. It would be difficult, without having recourse to geometrical formulæ, to explain how it happens that by placing the eye at a particular point the distorted lines of the drawing become symmetrical; but perhaps a mechanical demonstration will help to make this difficult subject a little plainer. [Illustration: FIG. 63.—Anamorphosis. ]