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. [Illustration: Fig. 117.] [Illustration: Fig. 118.] [Illustration: 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.