第50章 SPACIAL IDEAS(8)

19. Similar differences in the estimation of distances can be demonstrated for the normal eye. Although the ocular muscles are so arranged that their movements in various directions require about the same amount of exertion, still, this is not exactly so. The reasons are apparently closely connected with the adaptation of the eye to its functions. The neighboring objects of our immediate environment, on which the lines of regard must be converged, are the ones most often looked it. For this reason, the muscles of the eye have so adapted themselves that the movements for the convergence of the lines of regard are the easiest, particularly those directed downwards as compared with other possible movements of convergence. This general facilitation of convergence has been acquired by the addition of special auxiliary and compensatory muscles (superior and inferior oblique) to the muscles that move the eye upwards and downwards (superior and inferior recti). As a result of the greater complexity of muscular activity thus necessary for the upward and downward movements of the eyes, the exertion is greater in these directions than towards the two sides, where only the internal and external recti act. The relative case of downward movements of convergence shows itself partly in the differences in the intensity of sensations accom- [p. 123] panying the movements, as already remarked (p. 121), and partly in the fact that downward convergence is involuntarily too great and upward too small. There are certain constant optical illusions depending on the direction of the object in the field of vision, which correspond to these differences in the motor mechanism. They are of two kinds: illusions of direction, and those of magnitude.

Both eyes are subject to an illusion as to the Direction of vertical lines in the field of vision . Such a line whose upper end is inclined 1 o -- 3 o outward, appears vertical, and one really vertical, seems inclined inward. Since the illusion is in opposite directions for the two eyes, it disappears in binocular vision. it can obviously be explained by the fact just noted, that the downward movements of the eyes are connected with an involuntary increase, and the upward movements with a decrease, in the convergence. This deflection of the movement from the vertical is not noticed, but we refer it to the object as a deflection in the opposite direction. An equally regular illusion in magnitude appears when we compare distances extending in different directions in the field of vision. This, too, is very probably to be referred to the asymmetry in the arrangement of the muscles which arises from the adaptation of the eye to the ordinary position of objects in space. A vertical straight line is judged on the average 1/6 too long as compared with an equal horizontal line. A square, accordingly, appears as a rectangle whose base is shorter than its sides, and a square drawn by the eye is always too low. This illusion is explained when we remember that, as a result of the highly developed tendency to convergence, the muscular activity for upward and downward movements is much more complex than for inward [p. 124] and outward movements.

The consequence is the same as in the case of partially paralyzed eyes, distances in the direction of the more difficult movement appear greater.

19a. Besides this difference between vertical and horizontal distances, which is most noticeable because it is so large, there are less marked differences between upward and downward, as well as between outward and inward distances. The upper half of a vertical line is overestimated on the average by 1/16 Of its length, and the outer half of a horizontal line by 1/40. The first way be due to a slight asymmetry in the arrangement of the upper and lower muscles, or it may be due to the involuntary convergence of the lines of regard in downward movement, or, finally, to a combination of both influences. The effect of convergence is due to the fact that it corresponds to an approach of the object, so that we are generally inclined to see the lower half of the line nearer. In accordance with certain conditions of association to be described later (§ 16, 9), when the angle of vision remains constant, whatever is judged as nearer is judged to be smaller, so that the lower half of a line seems shorter than the upper. This explanation by the perspective can not be applied to the greater illusion in the overestimation of vertical as compared with horizontal lines, for if it were applicable, the illusion would at most be about equal to that found in the comparison of the two halves of a vertical line, while in reality it is approximately three times as great. The fact that this greater illusion appears only when straight distances are compared, not in the case of objects bounded by curved lines, is also a proof against the explanation by perspective.

A circle, for example, does not appear as an ellipse with a longer vertical axis, but as a real circle. The slight overestimation of the outer half of a horizontal line is also due most probably to the asymmetrical activity of the muscles, which arises from the relative ease of convergence-movements.