appears never much exceeds the threshold distance.  Furthermore, there being no distinct line of demarcation between one and two, there must be many sensations which are just about as much like one as they are like two, and hence they must be lumped off with one or the other group.  To the mathematician one and two are far apart in the series because he has fractions in between, but we perceive only in terms of whole numbers; hence all sensations which might more accurately be represented by fractions must be classed with the nearest whole number.  A sensation is due to a combination of factors.  In case of the Vexirfehler one of these factors, viz., the stimulating object, is such as to suggest one, but some of the other conditions—­expectation, preceding sensation, perhaps blood pressure, etc.—­suggest two, so that the sensation as a whole suggests one-plus, if we may describe it that way, and hence the inference that the sensation was produced by two objects.

[2] Tawney, Guy A.:  ’Ueber die Wahrnehmung zweier Punkte mittelst des Tastsinnes mit Ruecksicht auf die Frage der Uebung und die Entstehung der Vexirfehler,’ Philos.  Stud., 1897, Bd.  XIII., S. 163.

   [3] See Nichols:  ‘Number and Space,’ p. 161.  Henri, V., and
   Tawney, G.:  Philos.  Stud., Bd.  XI., S. 400.

This, it seems to me, may account for the appearance of the Vexirfehler, but why should not the subject discover his error by studying the sensation more carefully?  He cannot attend to two things at once, nor can he attend to one thing continuously, even for a few seconds.  What we may call continuous attention is only a succession of attentive impulses.  If he could attend to the one object continuously and at the same time hunt for the other, I see no reason why he should not discover that there is only one.  But if he can have only one sensation at a time, then all he can do is to associate that particular sensation with some idea.  In the case before us he associates it with the idea of the number two.  He cannot conceive of two objects unless he conceives them as located in two different places.  Sometimes a person does find that the two objects of his perception are both in the same place, and when he does so he concludes at once that there is but one object.  At other times he cannot locate them so accurately, and he has no way of finding out the difference, and since he has associated the sensation with the idea of two he still continues to call it two.  If he is asked to locate the points on paper he fills out the figure just as he fills out the blind-spot, and he can draw them in just the same way that he can draw lines which he thinks he sees with the blind-spot, but which really he only infers.