Let us consider first the simplest case, where two points c and b are presented, lying at different depths, and connected by a straight line. A change in the fixation from a to b is always accompanied by a change in convergence, and brings about, first, the passage through a continuous series of retinal local signs corresponding to the line ab, and, secondly, a sensation of movement, [alp], corresponding to the difference in convergence between these two points. This gives us here, too, the elements of a spacial fusion. The [p. 134] product of this fusion is, however, peculiar in kind; it differs in both its components, in the successive series of local signs and in the concomitant sensations of movement, from the fusions that arise when a line in the field of vision is passed over (p. 128). In the latter case the changes in local signs and sensations of movement are alike for both eyes, while in changing the point of fixation from far to near or the reverse they are opposite in the two eyes. For when the right eye a rotation towards the left convergence gives it will produce a rotation towards the right in the left eye, and vice versa. The same must also hold for the movement of the retinal images: when the image of the point as it leaves the point of fixation, moves towards the right in the right eye, it moves towards the left in the left eye, and vice versa. The first takes place when the eyes turn from a nearer to a more distant point, the latter, when they move in the opposite direction.
Such fusions arising from movements of convergence have, so far as their qualitative and intensive components are concerned, a composition analogous to that on which the arrangement of the elements in the field of vision with regard to one another depends; but the special way in which these elements are united is entirely different in the two cases.
28. Thus, the fusions between local signs and sensations of convergence form a system of complex local signs which is analogous to that deduced above (p. 130), but still peculiar in its composition. This system, differing in composition from the system of local signs in the field of vision, is supplementary to the latter in that it adds to the reciprocal relation between the objective elements a relation between the ideating subject and these elements. The relation to the subject divides into two ideational elements, characterized by peculiar sensational elements: the idea of direction and [p. 135] that of distance. Both refer primarily to the point of orientation in the head of the ideating subject, and are then secondarily applied to the relations of external objects in regard to one another. Thus, we come to assign to two points which lie at different distances along the line of orientation a direction and distance in relation to each other. All such ideas of spacial distance referring to various positions along the line of orientation, when taken together, are called ideas of depth, or when they are also ideas of particular single objects ideas of three dimensions.
29. An idea of depth arising in the way described varies according to objective and subjective conditions. The determination of the absolute distance of an isolated point in the field of vision, is always very uncertain.
Even, the determination of the relative distance between two points a and b lying at different depths is generally certain only under the condition assumed above, that they are connected by a line along which the points of fixation for the two eyes can move in changing the convergence from a to b . We may call such lines which connect different points in space with one another lines of fixation. The principle may then be formulated: points in space are apprehended in their true relations only when they are connected by lines of fixation, along which the point of fixation may move. This principle is explicable on the ground that the condition of a regularly connected change in the local signs of the retina and in the accompanying sensations of convergence, that is, the condition for the rise of ideas of depth as we found before (p. 133), is obviously fulfilled only when impressions are presented which can arouse the appropriate local signs.
30. When the condition mentioned is not fulfilled, there arises either an imperfect and indefinite idea of the different relative distances of the two points from the subject, or else [p. 136] the two points seem to the equally distant -- a phenomenon which can appear only when one of the points is rigidly fixated. Under the latter condition still another charge, always arises in the idea; only the fixated point is seen as single, the other as double. The same thing happens while looking at objects when they are not connected with the binocular fixation-point by means of lines of fixation. Double images that arise in this way are uncrossed -- i.e., the right belongs to the right eye, the left to the left eye -- when the crossed fixated point is nearer than the observed object and crossed when the point is beyond the object.
Binocular localization in depth and binocular double images are, accordingly, phenomena directly interrelated; where the former is indefinite and imperfect, we have double images, and where, on the other hand, the latter are absent, the, localization in depth is definite and exact. The two phenomena stand in such a relation to the line of fixation that, when it is present, localization is aided and double images removed. Still, this rule is not without exception, for when a point is ridgidly fixated with both eyes, double images arise easily in spite of any lines of fixation that may be present. This is explained by the necessary conditions, for both of depth as mentioned above (p. 133).