TABLE XIII.
| Observer | Const. Err. | Av. Dev. | Mean Var. | Rotation. |
|---|---|---|---|---|
| F (20) | +130.50 | 130.50 | 3.20 | 20° |
| " | +115.50 | 115.50 | 1.10 | 50° |
| J (20) | +443.10 | 443.10 | 9.47 | 45° |
These experiments were carried on in the presence of the definitely figured visual field of the lighted room, and the observers were conscious of taking these permanent features into account as correctives in making their judgments. Before proceeding, this defect was remedied as far as possible by enclosing the apparatus of experimentation, including the observer, between two walls of black fabric. Nothing was to be seen but these two walls, and the inclined plane which terminated the observer's view. The position of the screen remained constant at an inclination of 45°. The upper bounding lines of the enclosing walls, on the contrary, were adjusted in three different relations to the plane of the gravity horizon. In the first arrangement these lines were horizontal; in the second the ends next to the observer were depressed five degrees; while in the final arrangement these ends were elevated through a like angular distance.
The inclined position of the screen was of course observed by every reactor, but of the changes in the enclosing walls no subject was informed, and none discerned them on any occasion. Each observer was questioned as to alterations in the experimental conditions after the use of each arrangement, and at the close of the whole series inquiry was made of each as to the planes of the upper boundaries of the walls. On various occasions, but not customarily, the observer was aware of a change of some kind in the whole set of conditions, but the particular feature altered was not suspected. The results for all three arrangements are given in the following table; of the sections of this table the third is incomplete, full results having been reached in the cases of only three observers:
TABLE XV.
| Ascending Planes. | Descending Planes. | |||||
|---|---|---|---|---|---|---|
| Observer | Const. Err. | Av. Dev. | M. Var. | Const. Err. | Av. Dev. | M. V. |
| C (50) | - 8.02 | 11.82 | 9.47 | - 48.14 | 48.14 | 9.52 |
| F (50) | + 78.88 | 78.88 | 2.89 | + 25.54 | 25.54 | 1.98 |
| G (50) | - 22.56 | 24.64 | 6.58 | -101.20 | 101.20 | 7.39 |
| H (50) | - 83.84 | 83.84 | 11.78 | -230.20 | 230.20 | 11.88 |
| J (50) | +315.64 | 315.64 | 18.16 | +120.12 | 120.12 | 9.01 |
| Average: | + 55.96 | 102.96 | 9.78 | -44.98 | 104.84 | 7.96 |
| Horizontal Planes. | |||
|---|---|---|---|
| Observer | Const. Err. | Av. Dev. | Mean Var. |
| C (50) | - 27.86 | 27.86 | 9.58 |
| G (50) | - 73.84 | 73.84 | 7.59 |
| J (50) | +243.72 | 243.72 | 18.52 |
For every individual observer, the position of the disc on the screen has been affected by each change in the direction of these visible lines. In every case, also, its location when these boundaries lay in a horizontal plane was intermediate between the other two. The importance of such relations in the objects of the visual field as factors in our ordinary determination of the subjective horizon is made evident by these experimental results. They become construction lines having assumed permanence in the world of visual-motor experience. The conception of unchanging spatial relations in the fundamental lines of perspective vision receives constant reinforcement from the facts of daily experience. The influence of the above-described changes in experimental conditions is mediated through their effect upon the location of the focus of the limiting and perspective lines of vision. As the plane of the upper boundaries of the enclosing walls was elevated and depressed the intersection of the two systems of lines was correspondingly raised and lowered, and in dependence upon the location of this imaginary point the determination of the position of the white disc was made, and the plane of perspective positively or negatively rotated.
Why such perspective lines should enter into the process of judgment it is not difficult to infer. The plane of perspective for human beings is characteristically horizontal, in consequence of the distribution of important objects within the field of visual perception. Roughly, the belt of the earth's horizon contains the loci of all human perspective planes. Both natural and artificial arrangements of lines converge there. The systems of visual objects on the earth and in the sky are there broken sharply off in virtue of their practically vast differences in quality and significance for the observer. The latter perspective probably never extends downward illusorily to points on the earth's surface; and the former system of objects is carried continuously upward to skyey points only on relatively rare occasions, as when one mistakes clouds for mountains or the upper edge of a fog-belt on the horizon for the rim of sea and sky. The point of convergence of the fundamental lines of perspective thus becomes assimilated with the idea of the visual horizon, as that concept has fused with the notion of a subjective horizon. There can be little doubt that the disposition of such lines enters constantly into our bodily orientation in space along with sensations arising from the general body position and from those organs more specially concerned with the static sense.
Upon the misinterpretation of such objective planes depends the illusion of underestimation of the height or incline of a hill one is breasting, and of the converse overestimation of one seen across a descending slope or intervening valley. The latter illusion is especially striking, and in driving over forest roads (in which case the correction of a wider range of view is excluded) the stretch of level ground at the foot of a hill one is descending is constantly mistaken for an opposing rise. This illusion is put into picturesque words by Stevenson when he describes the world, seen from the summit of a mountain upon which one stands, as rising about him on every side as toward the rim of a great cup. The fitness of the image may be proved by climbing the nearest hill. In all such cases a reconstruction of the sensory data of judgment takes place, in which the most significant factor is the plane determined by the positions of the observing eye and the perspective focus. In these judgments of spatial relationship, as they follow one another from moment to moment, this plane becomes a temporary subjective horizon, and according as it is positively or negatively rotated do corresponding illusions of perception appear.