of the nose to the distance of two or three hundred yards. Beyond this it also becomes inappreciable, for the doubling of objects is only equal to the interocular distance. 3. By mathematical perspective. By diminution of the apparent size of known objects and the convergence of parallel lines we judge of distance with great accuracy and almost without limit. 4. By aërial perspective. Change of color and brightness of all objects, in proportion to the depth of air looked through, is still another mode of judging of distance, which, though far less accurate than the last, like it extends without limit. Estimates of distance, being judgments, are liable to error. Such errors are often called deceptions of sense, but they are not so. They are errors of judgment based upon true deliverances of sense. Size. The size of an unknown object is judged by its angular diameter, or the size of its retinal image FIG. 54. A multiplied by its estimated distance. For example, an image a, Fig. 54, occupies a certain space on the retina. Now, evidently, precisely the same image would be made by a small object at A, or a proportionally larger similar object at A', or a still larger similar one at A”. Therefore the estimated size of the object which produced the image will depend upon the distance we imagine the object to be from us, this distance being of course estimated by the different forms of perspective given above. Thus, estimates of size and distance are very closely related to each other, and an error in the one will involve an error in the other. If we misjudge the distance of an unknown object, we will to the same degree and in the same direction misjudge its size: if our estimate of distance be too great, our judgment of size will also and to the same extent be too great; if our estimate of distance be too small, so also will be our judgment of size. Contrarily, if we make a mistake as to the size of a known object-as, for example, if we mistake a boy for a man—we will also to the same extent misjudge the distance. Very many illustrations may be given of this general principle, but by far the most perfect are the experiments on combination of the regular figures given on pages 114 and 115. In combining by squinting, in proportion as the point of optic convergence, and therefore the imagined place of the pattern, becomes nearer and nearer, the figures of the pattern become smaller. On the other hand, when we combine beyond the plane of the pattern, so that the more distant point of optic convergence makes the imagined place of the pattern farther off than its real place, then the figures are magnified in the same proportion. So also stereoscopic scenes are larger or smaller than the actual picture, according as we combine beyond or on this side the plane of the picture. Illustrations like the above are most conclusive, because the relation of size and distance is seen to be mathematically proportioned; but many familiar illustrations may be given. 1. While intently regarding the paper on which I am writing, or the page which I am reading, a fly or gnat passes across the extreme margin of the field of view toward the open window. I mistake it for a large bird like a hawk flying at some distance in the open air. The reason is, that under these conditions we have no means of judging either of form or of distance; the size and distance of an object are therefore left wholly to the suggestions of the imagination. If we look around so as to see the form distinctly, and to bring binocular or other forms of perspective to bear on the subject, we quickly detect our error and correct our judgment. 2. Where there are no means of judging of distance, we can not estimate size, and different persons will estimate differently. Thus, the sun or moon seems to some persons the size of a saucer, to some that of a dinner-plate, and to some that of the head of a barrel. But under peculiar conditions we imagine them much larger. For example, a pine-tree stands on the western horizon about a mile distant. I am accustomed to judge of the size and distance of trees. This one seems to me at least 20 feet across the branches. The evening sun slowly descends and sets behind the tree. It fills and much more than fills its branches. Again, here in Berkeley, on a clear day, the Farallone Islands, 40 miles distant, are distinctly seen through the Golden Gate. I think no one would say that the larger one seems less than 100 feet across. At certain seasons in spring and autumn the sun sets behind the Farallones, and these islands are projected in clear outline as black spots on his disk. 3. Illustrations meet us on every side. In fog, objects look larger, because, through excess of aërial perspective, we overestimate distance. On the high Sierra, or the Colorado mountains, or anywhere on the high interior plateau, the clearness of the air and consequent distinctness of distant objects are such, that we imagine L objects to be rearer and therefore smaller than they really are. Form.-Outline form is a combination of directions of component radiants. In a ring of stars, the direction of each star is given immediately; the combination of these several directions gives the ring. This is so simple and immediate a judgment, that .it may almost be called a direct sense-perception. It is apparently a direct perception of the form of the retinal image. It is so sure and immediate that it is not liable to error; yet it is capable of analysis into simpler elements, as shown above. Solid form is a far more complex judgment, and therefore liable to error. We judge of solid form partly by binocular perspective and partly by shades of light. The roundness of a column is perceived partly by the greater optic convergence necessary to see distinctly the nearer central parts than the farther marginal parts, and partly by the shading of light on the different parts. The latter effect can be perfectly imitated by the painter, but not the former. Hence the illusion produced by the painter is most perfect at a distance where binocular perspective is very small, but is destroyed by near approach. Hence also the roundness of a painted column is most perfect when looking with one eye, but of a natural column when looking with two eyes. Gradation of Judgments.-Intensity, color, and direction of light are simple impressions which can not be further analyzed. Next come outline form and surface contents, which may indeed be analyzed into combination of directions, but yet the perception is so direct and so certain that it may well be called immediate. Next comes solid form, which, as we have seen, is a more complex judgment based on simple elements, and therefore may be deceived. Next come the closely related and still more complex judgments of size and distance, which are therefore still more liable to error. These latter judgments become more and more complex as the objects in the field of view become more numerous and more complex in form and varied in position; as, for example, the judgments of form, size, and distance of all the objects in an extended natural scene. All these seem to the uninstructed as immediate instinctive perceptions, and mistakes are supposed to be the result of deceptions of sense instead of errors of judgment, as they really are. Judgments like these, which are so quickly made that the process has largely dropped out of consciousness, I shall call visual judgments. But these higher and more complex visual judgments pass, by almost insensible degrees, into still higher and more complex intellectual judgments. Thus from simple sense-impressions we pass without break through the various grades of visual judgments to the lower intellectual judgments, and from these again through various grades of complexity to the highest efforts of the cultured mind. Now, as visual judgments seem to the uninstructed primary, immediate, and simple perceptions, so also among intellectual judgments many seem to those uninstructed in psychology and unskilled in mental analysis as primary, immediate, instinctive, or inpate, and therefore certain. But, as the study of visual phenomena teaches that these visual judgments are capable of analysis into simpler elements, and therefore liable to error, so also the study of psychology should teach us that many of the so-called instinctive judgments, primary intuitions, etc., may also be capable of analysis, |