Fig. 62.
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.
Fig. 63.—Anamorphosis.
Draw in outline any figure upon a piece of cardboard, and make a series of pin-holes along the most prominent lines of the drawing, taking care that they are pretty close together. Place the perforated card in a vertical position on a sheet of paper, so that the rays from a candle or lamp may fall, on the flat surface beneath. On looking at the luminous figure formed from the drawing, you will find that it is as much distorted as the lady’s head in [fig. 63], and that the lower you place the candle the greater will be the deformity. You may if you please, trace the luminous figure on the paper, and the result will appear distorted when looked at in the ordinary manner, but symmetrical when viewed from the point at which the flame of the candle was placed.
In the foregoing experiments we have spoken of the anamorphic drawings as being placed in a horizontal position, but they may be looked at just as well vertically, the card with the hole being in this instance horizontal. It is also not necessary that the point of sight (V, [fig. 63]) should be in the centre of the picture; it may be placed at one side or the other, care being taken to draw all the divisional lines so that they meet at this particular spot. A few experiments with a candle and a perforated figure will soon show the student how to accomplish this.
Anamorphoses by reflection may be prepared, if this principle is carried out, which appear a mass of confused lines until they are reflected in a cylindrical mirror. Formerly opticians were accustomed to construct anamorphoses which became symmetrical pictures when viewed in a conical mirror; but the fashion for such toys appears to have gone out. Such drawings were extremely difficult to make, and the mirrors, having to be ground and polished with great care, were very expensive.