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.

   [10] Lipps, Th., Zeitschrift f.  Psychologie u.  Physiologie der
   Sinnesorgane, 1890, I., S. 60-74.

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