If two exactly similar photographs are placed in a stereoscope, the fact that the eyes are not converged gives to the common picture an appearance of depth, notwithstanding the fact that corresponding points on the two retinæ are stimulated. If the two photographs have been taken, as they should be taken for this purpose, with a double camera, the disparity of the retinal images immensely enhances the impression of solidity.
It is impossible to exaggerate the dependence of sensation on judgment. At birth a child commences the long process of education which enables it to associate the sensations derived from its retinal images with the movements which place it in contact with things. It discovers that, when it is necessary to make the eyes converge, the object is near at hand. It also associates the voluntary action of contracting its ciliary muscle with nearness. Unconverged and unaccommodated eyes come to mean distance. So, too, do indistinctness due to absorption by the atmosphere, blueness due to the same cause, a small image on the retina. But there are obvious limits to its power of ascertaining the distance of an object, and therefore, conversely, of its power of estimating size. We have no idea of the size of the retinal image of the sun. Very few people would be prepared to believe that the angle which the sun subtends with the eye barely exceeds half a degree. (The first finger, viewed in profile, at arm’s length, covers one degree of arc.) A disc of paper of the right size, placed at the right distance, looks far too small to represent the sun. The most brilliant of orbs bulks larger than this in our minds. Everyone who for the first time looks at the sun through well-smoked glass, or, better, through a flat-sided vessel filled with ink and water, is astonished that it looks so small. Nor are we prepared to accept the evidence of a camera that the sun at the zenith does not produce a smaller image on the retina than the sun when rising above the horizon. Yet if a photographic plate is exposed to the rising sun, and again, without changing its focus, to the sun at the zenith, the two images are practically equal. There is a slight difference due to the greater refraction of rays passing tangentially through the atmosphere, but it is so slight as to bear no relation to the difference between our two judgments of size. When the sun is rising behind trees and houses, we compare it with objects which we know to be large and distant; yet it looks almost as large when rising out of the sea. One of the causes of the illusion is our conviction that the sky is flattened; and this, again, is due partly to its paler tint—its less substantial blueness—near the horizon, and partly to our impression that it is spread out over a flat earth. When the sun is in what we deem to be the more distant part of the vault of heaven, we judge it to be farther from us, and therefore larger than when it is above us. Yet the last word has not been said in explanation of a phenomenon which has been studied by mankind since the dawn of science. Helmholtz attributed the apparent greater distance, and consequent greater size, of the sun and moon when near the horizon to the indistinctness of their discs. When its image is so reflected from the zenith as to cause the moon to appear to rest upon the horizon, it does not, he said, increase in size. In answer to Helmholtz’s explanation, it may be objected that, when at midnight he brought the full moon down from the zenith, he did not bring with her the conditions of light and colour by which she is customarily surrounded when floating on the horizon. If, when watching the moon which has just risen, vast in diameter, out of the sea, one interposes between it and the eye a sheet of paper in which a small hole has been made, and looks at the moon with one eye through the hole, it instantly shrinks to the size which it appears to have at the zenith. It is not even necessary to blot out the whole of its trail of light on the sea. At the same time, it appears to retreat to a great distance. This shows how complicated are the associations upon which judgments of size and distance are based, and to how small an extent they are determined by the size of the image on the retina. This observation is most surprising if made one or two nights after full moon, when twilight is already dim at moon-rise.
Our estimate of the distance away from us of an object on the horizon is based upon the time and effort which experience tells us we should need to spend in reaching it. The untried appears shorter than the tried. Anyone who compares his feeling of the number of yards he would have to climb up a pole reaching to the zenith with his feeling of the number of steps he would need to take to reach the horizon will recognize that the horizon appears to him to be the farther away.
Fig. 36.—A Symmetrical Arch, divided by a Vertical Line, A,
which passes through its Apex.
In representing a solid object an artist conveys theidea that light is falling obliquely upon it. One side of the object, therefore, is more strongly illuminated than the other. By depth and gradation of shade he indicates the extent to which the thing projects forwards, if solid, or falls back, if hollow. He makes the margin of a ball hazy, in the expectation that the spectator will look at the spot nearest to him—an artifice which he may easily press too far, since the eyes wander restlessly over a flat surface. In representing distance he is dependent upon giving to the various objects in his picture sizes equivalent to the sizes of their images on the retina, making them brighter or paler and more or less distinct. Yet he cannot hope to simulate the convincing evidence of distance which is afforded by our sense of the degree of convergence of our eyes. Hence, as Francis Bacon pointed out, a picture appears more real when one eye is closed than when both are open. Its middle distance at once falls back.
Fig. 37.—Two Horizontal Lines of Equal Length—the One with Diverging,
the Other with Converging, Terminal Lines.