perfectly similar group of retinal impressions on the same nervous elements.

The implications of Listing's law are still more important in relation to our present subject. It follows from this law that when the moving eye traces a line immediately in front of it, it necessarily receives the image of the line on the same series of retinal elements or the same retinal meridian.* That is to say,

the nervous elements excited by any two successive impressions of the lines will for the greater part be the same, only a few of the old elements being dropped and new ones taken up. Consequently any deviation from a perfectly rectilinear direction in the line would (so far as this is appreciated through retinal sensibility) at once make itself felt through this intrusion of a new nervous element falling outside the meridian. It follows then, that, so far as the eye appreciates form through retinal sensibility alone, it will be much better able to estimate the straightness of a line which lies immediately in front of it than of those situated elsewhere.

Observation bears out this conclusion. When we want to tell very nicely whether a line is straight, we half instinctively bring it exactly in front of the eye so that its centre coincides with the principal point of fixation, and then let the eye wander up and down it. In this case the appreciation of rectilinear form is very delicate.+

Another consequence of Listing's law is that when the eye (the head being supposed to be fixed) moves from the primary position over the field in different directions, certain fixed lines. in the field will necessarily be pictured on the same retinal meridian. This applies to all parallel lines lying in the central portions of the field. It would seem to follow that so far as retinal sensibility is involved there will be an advantage in appreciating the direction of parallel rather than of any other lines in these regions. Further, one may deduce from this law

Strictly speaking this holds true of all lines, straight or curved, which cover or could be projected on any one of the great circles of the concave field which intersect at the principal point of fixation' immediately in front of the eye.

†This is true even when the eye is at rest. This would be explained by the supposition that the elements of one and the same meridian (in the central regions of the retina) have their discriminative sensibility sharpened by the exercise involved in these habitual and critical movements. Of this more hereafter.

·

This is true of all lines whose projections on the concave field correspond to circles which intersect at the occipital point'-an imaginary point supposed to be situated behind the head, and answering to the principal point of fixation-and which at this point of intersection touch one and the same meridian of the field.

that it will be much easier to measure the length of two parallel lines than of two diverging lines, since in the former case the successive images may be made to fall on exactly the same series of retinal elements.

These conclusions, again, are fully corroborated by observation. The eye is able to detect very slight deviations from a parallel direction in pairs of lines when these lie opposite the eye in the central regions of the field. Again, it detects inequalities between lines much more easily when they are parallel than when they have different directions. Once more, the magnitudes of angles with parallel pairs of lines are compared much more exactly than those of angles contained by non-parallel pairs of lines.

One further consequence deserves to be mentioned. We are able to appreciate form to some extent in indirect vision. It might be conjectured from what has gone before that the relations of points and lines implied in the forms of objects thus viewed will be better appreciated when they are so situated that their images may successively be received on the same retinal elements. This seems to be so far borne out that with the eye at rest we can pretty accurately appreciate the inequality of two parallel lines in the central field, though the comparative measurement of two lines having unlike directions is liable to be far from exact.

The most striking fact, however, in this indirect visual appreciation illustrative of the law of movement now discussed is the following. When the eye moves from its primary position to a point far out in the peripheral region of the field a really vertical or horizontal line is no longer imaged on the same retinal meridian as lines of the same direction in the central regions. How then, it may be asked, does the eye at rest regard such lines in these outlying portions of the field? Curiously enough, under these circumstances it estimates form in relation to the impression which would be made on the central area of the retina if the eye were moved to the object. Thus a line actually vertical appears in indirect vision inclined and vice versa. As soon as the eye fixates the line the illusion disappears. This fact is of great interest as pointing to the secondary or derivative character of the eye's indirect appreciation of form.

I have hitherto assumed with Helmholtz that in these appreciations of form and magnitude the discriminative sensibility of the sensory elements of the retina takes part. At the same time it is to be observed that in all cases of successive comparison in direct vision the sensibility connected with the eye's movements may be the ground of judgment as well. Thus, in comparing the length of two parallel lines it may be

SO.

said that the perception rests on the motor or muscular feelings which accompany the eye's movements along each of the lines. In truth there are facts which seem to prove that this is actually E. Hering has in a recent work, Die Lehre vom Binocularen Sehen, attempted to show that within certain limits in the centre of the field a movement along a line is carried out from first to last by the same muscles; further that under these circumstances the muscles employed work in the same ratio of intensity from the beginning to the end; and finally that owing to the particular arrangements of the muscular apparatus all parallel movements within these limits are effected by the same muscles pulling in the same ratio of force. These facts, if fully established, are of the first consequence for the understanding of the eye's appreciation of form. They would serve to explain its peculiar delicacy in the estimation of straight lines, and in the comparison of the directions of parallel lines (and so of the magnitude of angles contained by parallel pairs of lines), solely on the ground of muscular sensibility.

There seems, then, to be two equally good ways of explaining these facts. Since movement accompanies nearly all our perceptions of the direction and magnitude of lines, we may suppose that muscular sensibility commonly takes part in these judgments. At the same time it is certain that some of these judgments are carried out by means of simultaneous impressions, the eye being at rest and fixating the centre of the line. Thus the differential sensibility of the nervous elements is a fact which must be accepted and accounted for.

Yet though this sensibility must be supposed to enter into our judgments of relative position and magnitude, it by no means follows that it is superior in delicacy to the motor feelings. Wundt argues on the contrary that the finest discriminations of magnitude are only possible by help of ocular movement. According to the experiments of Volkmann and Fechner, the eye's discriminative appreciation of linear magnitude follows within certain limits the latter's psychophysical law. That is to say, the minimum difference perceived is a pretty constant fraction of the length of line compared.* Below a particular limit, however, this relation no longer holds good. Wundt argues very ingeniously that this threshold' is imposed not by the area of the retinal elements, but by the limits of discriminative motor sensibility.

Wundt considers that the influence of the motor feelings (which he calls 'feelings of innervation') on the visual appre

This fact does not tell, so far as I can see, in favour of either sensibility, since Fechner's law is known to apply both to the intensive and the extensive magnitude of sensations.

ciation of form and magnitude is illustrated in many of the well-known optical illusions respecting relative direction and size. These he seeks systematically to refer to peculiarities in the process of innervation involved, and its attendant feeling. Thus it is known that we over-estimate vertical magnitude relatively to horizontal. This arises, says Wundt, from the fact that horizontal movements are executed by a single pair of muscles (rectus externus and internus), whereas vertical movements involve two pairs (rectus superior and inferior and the two obliqui) which oppose one another in a certain measure. Hence a greater muscular strain, and so a greater feeling of innervation, in the latter than in the former instance. Similarly the error made in over-estimating magnitude in the upper as contrasted with the lower regions of the field, and in the outer as compared with the inner regions, is referred to differences in the degrees of innervation involved.+

While Wundt thus emphasises the influence of the feelings of movement in monocular appreciation, Helmholtz calls attention to the effects of past experience. Thus he would explain our disposition to over-rate the magnitude of the vertical direction relatively to that of the horizontal by the fact that by far the largest number of forms compared in daily life coincide with the plane of the ground, and consequently have their upper portion further from the eye than their under, so that the vertical is foreshortened. Owing to this prevailing experience we acquire the habit of interpreting the vertical dimension as larger than it directly appears.S

The co-operation of ideation or of imagination based on experience, is illustrated still more distinctly in the fillingin of the lacuna in the visual field answering to the blind spot in the retina. Volkmann has called attention to the fact that when the lacuna falls on the printed page of a book, we fancy at first that we see letters within the limits of the lacuna.

Wundt holds that rolling about the axis is prevented by an antagonistic action of the combining muscles (e.g. the superior rectus and obliquus).

† He thinks that since in transverse section the upper muscle exceeds the under in calibre, and the inner the outer, a smaller degree of innervation is required. Wundt's attempt to reduce all the well-known cases of illusory measurements (including Zöllner's pattern) to special moments in the feeling of innervation is ingenious though somewhat forced. On the other hand, Helmholtz's explanations hardly seem more satisfactory. The reason for this prevailing mode of viewing forms is to be found later on.

§ Another fact differently interpreted by these two observers is that a line drawn precisely vertical to a given horizontal line appears to be slightly inclined. The meaning of this will be best discussed later.

The illusion disappears with a concentrated effort of attention. The phenomena of the blind spot show incontestably that our visual perception of space-relations is to some extent a process of inference or of imaginative construction out of remembered elements of previous experiences. We fill the gap in the field with ideal impressions, which the eye would receive were it to fixate this particular region.

Let us now pass to another aspect of our visual intuition of space. So far I have spoken of relative direction only, or the position of points in relation to one another. It is a different question what determines the eye's judgment of the absolute direction of objects in the field, i.e., their position relatively to one fixed starting point. This standard of direction is clearly our own position in space. When we refer an object to the left or right of the whole field over which our moving eye wanders, we assign it a position relatively to that of our own body.

This absolute direction is known in monocular vision when the position of the axis of vision (principal axis) is known. The several parts of the total field over which the eye travels (the head being supposed to be fixed) are all projected in different directions. As soon as we know the absolute direction of any one of these successive lesser fields we are able to fix the direction of any particular object in this region in relation to this fixed direction as centre. Accordingly what we have to find is the eye's means of determining the absolute direction of any given partial field, in other words, any given centre of fixation.

Our perception of direction depends, as abundant observation shows, in part on the motor feelings of the eye. In every movement of the organ upwards or downwards, to the right or to the left, and so on, some peculiar shade of motor feeling arises. Moreover each of these modes of feeling varies with the range of the movement executed. The different feelings attending these varieties of movement are the ground of our projecting impressions in this or that direction.

That the motor feelings do thus serve as the ground of judgment is proved, as Helmholtz says, by the simple experiment of closing one eye and pressing the other inwards with the finger. The result of this is that objects appear to move inwards too. The explanation of the phenomenon is that since in this case there is a transference of the retinal picture to new elements without any consciously executed ocular rotation, we ignore the passive movement of the eye-ball and infer that objects have shifted their position in the opposite direction to that of the retinal image.