All the experiments we have described afford great interest to the student; they can easily be performed by those of our readers who are particularly interested in these little-known subjects. Any one may construct the greater part of the appliances we have enumerated, and others can be obtained at an optician’s. The discs in particular are extensively manufactured, and with great success. FOOTNOTES: [10] _Traité de Physique_, Paris 1874. [11] _Traité d’optique Physiologique._ French translation by MM. Javal and Klein. CHAPTER XI. OPTICAL ILLUSIONS—ZOLLNER’S DESIGNS—THE THAUMATROPE—PHENOKISTOSCOPE—THE ZOOTROPE—THE PRAXINOSCOPE—THE DAZZLING TOP. We shall now continue the subject by describing some illusions more curious still—those of _ocular estimation_. These illusions depend rather on the particular properties of the figures we examine, and the greater part of these phenomena may be placed in that category whose law we have just formulated: _the differences clearly perceived appear greater than the differences equal to them, but perceived with greater difficulty_. Thus a line —— when divided appears greater than when not divided; the direct perception of the parts makes us notice the number of the sub-divisions, the size of which is more perceptible than when the parts are not clearly marked off. Thus, in fig. 115, we imagine the length _ab_ equals _bc_, although _ab_ is in reality longer than _bc_. In an experiment consisting of dividing a line into two equal parts, the right eye tends to increase the half on the right, and the left eye to enlarge that on the left. To arrive at an exact estimate, we turn over the paper and find the exact centre. [Illustration: Fig. 115.] [Illustration: Fig. 116.] Illusions of this kind become more striking when the distances to be compared run in different directions. If we look at A and B (fig. 116), which are perfect squares, A appears greater in length than width, whilst B, on the contrary, appears to have greater width than length. The case is the same with angles. On looking at fig. 117, angles 1, 2, 3, 4 are straight, and should appear so when examined. But 1 and 2 appear pointed, and 3 and 4 obtuse. The illusion is still greater if we look at the figure with the right eye. If, on the contrary, we turn it, so that 2 and 3 are at the bottom, 1 and 2 will appear greatly pointed to the left eye. The divided angles always appear relatively greater than they would appear without divisions. The same illusion is presented in a number of examples in the course of daily life. An empty room appears smaller than a furnished room, and a wall covered with paperhangings appears larger than a bare wall. It is a well-known source of amusement to present someone in company with a hat, and request him to mark on the wall its supposed height from the ground. The height generally indicated will be a size and a half too large.