which comes to consciousness only on, or shortly before, the completion of the eye-movement, nevertheless with positional values which correspond, remarkably enough, not to the later but to the earlier position and innervation of the eyes." Mach does not further attempt to explain the phenomenon.

It is brought up again by Lipps,10 who assumes that the streak ought to dart with the eyes and calls therefore the oppositely moving streak the 'falsely localized image.' For sake of brevity we may call this the 'false image.' The explanation of Lipps can be pieced together as follows (ibid., S. 64): "The explanation presupposes that sensations of eye-movements have nothing to do with the projection of retinal impressions into the visual field, that is, with the perception of the mutual relations as to direction and distance, of objects which are viewed simultaneously.... Undoubtedly, however, sensations of eye-movements, and of head-and body-movements as well, afford us a scale for measuring the displacements which our entire visual field and every point in it undergo within the surrounding totality of space, which we conceive of as fixed. We estimate according to the length of such movements, or at least we deduce therefrom, the distance through fixed space which our view by virtue of these movements has traversed.... They themselves are nothing for our consciousness but a series of purely intensive states. But in experience they can come to indicate distance traversed." Now in turning the eye from a luminous object, O, to some other fixation-point, P, the distance as simply contemplated is more or less subdivided or filled in by the objects which are seen to lie between O and P, or if no such objects are visible the distance is still felt to consist of an infinity of points; whereas the muscular innervation which is to carry the eye over this very distance is an undivided unit. But it is this which gives us our estimate of the arc we move through, and being thus uninterrupted it will appear shorter than the contemplated, much subdivided distance OP, just as a continuous line appears shorter than a broken line. "After such analogies, now, the movement of the eye from O to P, that is, the arc which I traverse, must be underestimated" (ibid., S. 67). There is thus a discrepancy between our two estimates of the distance OP. This discrepancy is felt during the movement, and can be harmonized only if we seem to see the two fixation-points move apart, until the arc between them, in terms of innervation-feeling, feels equal to the distance OP in terms of its visual subdivisions. Now either O and P can both seem to move apart from each other, or else one can seem fixed while the other moves. But the eye has for its goal P, which ought therefore to have a definite position. "P appears fixed because, as goal, I hold it fast in my thought" (loc. citat.). It must be O, therefore, which appears to move; that is, O must dart backward as the eye moves forward toward P. Thus Lipps explains the illusion.

Such an explanation involves many doubtful presuppositions, but if we were to grant to Lipps those, the following consideration would invalidate his account. Whether the feeling of innervation which he speaks of as being the underestimated factor is supposed to be a true innervation-feeling in the narrower sense, or a muscular sensation remembered from past movements, it would in the course of experience certainly come to be so closely associated with the corresponding objective distance as not to feel less than this. So far as an innervation-feeling might allow us to estimate distance, it could have no other meaning than to represent just that distance through which the innervation will move the organ in question. If OP is a distance and i is the feeling of such an innervation as will move the eye through that distance, it is inconceivable that i, if it represent any distance at all, should represent any other distance than just OP.

Cornelius11 brought up the matter a year later than Lipps. Cornelius criticises the unwarranted presuppositions of Lipps, and himself suggests that the falsely localized streak is due to a slight rebound which the eye, having overshot its intended goal, may make in the opposite direction to regain the mark. This would undoubtedly explain the phenomenon if such movements of rebound actually took place. Cornelius himself does not adduce any experiments to corroborate this account.

The writer, therefore, undertook to find out if such movements actually are made. The observations were made by watching the eyes of several subjects, who looked repeatedly from one fixation-point to another. Although sometimes such backward movements seemed indeed to be made, they were very rare and always very slight. Inasmuch as the 'false' streak is often one third as long as the distance moved through, a movement of rebound, such as Cornelius means, would have to be one third of the arc intended, and could therefore easily have been noticed. Furthermore, the researches of Lamansky,12 Guillery,13 Huey,14 Dodge and Cline,15 which are particularly concerned with the movements of the eyes, make no mention of such rebounds. Schwarz16 above all has made careful investigations on this very point, in which a screen was so placed between the observer and the luminous spot that it intervened between the pupil and the light, just before the end of the movement. Thus the retina was not stimulated during the latter part of its movement, just when Cornelius assumed the rebound to take place. This arrangement, however, did not in the least modify the appearance of the false streak.

This work of Schwarz certainly proves that the explanation of Cornelius is not correct. Schwarz found that the phenomenon takes place as well when the head moves and the eyes are fixed relatively to the head, as when the eyes alone move. He furthermore made this observation. Meaning by a the point of departure and by b the goal of either the eye-or the head-movement, movement, he says (ibid., S. 400-2): "While oftentimes the streak of the after-image extended uninterruptedly to the point b, or better seemed to proceed from this point,—as Lipps also reported—yet generally, under the experimental conditions which I have indicated, two streaks could be seen, separated by a dark space between; firstly the