Popular Scientific Recreations in Natural Philosphy, Astronomy, Geology, Chemistry, etc., etc., etc. Gaston Tissandier

intensity is evidently constant through the extent of each layer; nevertheless every strip appears darker at the edge touching a more transparent layer, and lighter at the edge in contact with a thicker layer. The dull tints of China ink, superposed in layers, will produce a similar effect. The phenomena are produced by means of rotative discs of most beautiful and delicate gradations of colour. Let us give the sectors of the disc the form represented by fig. 114, and make them black and white; and when in rotation we shall see a series of concentric rings of a shade that becomes darker and darker towards the centre. The angular surface of the dark portions is constant in each of these rings. The intensity, therefore, of each ring is uniform during rapid rotation; it is only between one ring and another that the intensity varies. Each ring also appears lighter on its inner side when it borders on a darker ring, and darker on its outer side when in contact with a lighter ring. If the differences of intensity in the rings are very slight, one can scarcely judge sometimes if the inner rings are darker than the outer; the eye is only struck by the periodical alternations of light and shade presented by the edges of the rings. If, instead of white and black, we take two different colours, each ring will present two colours on its two edges, although the colour of the rest of the ring will be uniform. Each of the constituent colours presents itself with more intensity on that edge of the ring which borders on another ring containing a smaller quantity of the colour. Thus, if we mix blue and yellow, and the blue predominates in the exterior and the yellow in the interior, every ring will appear yellow at its outer, and blue at its inner edge; and if the colours present together very slight differences, we may fall into the illusion which causes the differences really existing between the colours of the different rings to disappear, leaving instead, on a uniformly coloured background, the contrasting blue and yellow of the edges of the rings. It is very characteristic that in these cases we do not see the mixed colours, but seem to see the constituent colours separately, one beside the other, and one through the other.

      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.

      

CHAPTER XI.

       Table of Contents

      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.

      Fig. 115.

      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.

      We will relate an experience described by Bravais: “When at sea,” he says, “at a certain distance from a coast which presents many inequalities, if we attempt to draw the coastline as it presents itself to the eye, we shall find on verification that the horizontal dimensions have been correctly sketched at a certain scale, while all the vertical angular objects have been represented on a scale twice as large. This illusion, which is sure to occur in estimates of this kind, can be demonstrated by numerous observations.”

      M. Helmholtz has also indicated several optical illusions.

      Fig. 117.

      Fig. 118.

      Fig. 119.

      If we examine fig. 118, the continuation of the line a does not appear to be d—which it is in reality—but f, which is a little lower. This illusion is still more striking when we make the figure on a smaller scale (fig. 119), as at B, where the two fine lines are in continuation with each other, but do not appear to be so, and at C, where they appear so, but are not in reality. If we draw the figures as at A (fig. 118), leaving out the line d, and look at them from a gradually increasing distance, so that they appear to diminish, it will be found that the further off the figure is placed, the more it seems necessary to lower the line f to make it appear a continuation of a. These effects are produced by irradiation; they can also be produced by black lines on a white foundation. Near the point of the two acute angles, the circles of diffusion of the two black lines touch and mutually reinforce each other; consequently the retinal image of the narrow line presents its maximum of darkness nearest to the broad line, and appears to deviate on that side. In figures of this kind, however, executed on a larger scale, as in fig. 118, irradiation can scarcely be the only cause of illusion. We will continue our exposition as a means of finding an explanation. In fig. 120, A and B present some examples pointed out by Hering; the straight, parallel lines, a b, and c d, appear to bend outwards at A, and inwards at B. But the most striking example is that represented by fig. 121, published by Zollner.

      The vertical black strips of this figure are parallel with each other, but they appear convergent and divergent, and seem constantly turned out of a vertical position into a direction inverse to that of the oblique lines which divide them. The separate halves of the oblique lines are displaced respectively, like the narrow lines in fig. 119. If the figure is turned so that the broad vertical lines present an inclination of 45° to the horizon, the convergence appears even more remarkable, whilst we notice less the apparent deviation of the halves of the small lines, which are then horizontal and vertical. The direction of the vertical and horizontal lines is less modified than that of the oblique lines. We may look upon these latter illusions as fresh examples of the aforesaid rule, according to which acute angles clearly defined, but of small size, appear, as a rule, relatively larger