near the knuckles and two toward the wrist and told him that was four.  As soon as he was sure he distinguished all of the points I stopped telling him and asked him to answer the number.  I had four subjects, and each one learned very soon to recognize the four contacts when three were given in the manner mentioned above.  I then repeated the same thing on the left hand, except that I did not tell him anything, but merely asked him to answer the number of contacts he felt.  In every case the idea of four was so firmly associated with that particular kind of a sensation that it was still called four when given on the hand which had not been trained.  I gave each subject a diagram of his hand and asked him to indicate the position of the points when three were given and when four were given.  This was done without difficulty.  Two subjects said they perceived the four contacts more distinctly than the three, and two said they perceived the three more distinctly than the four.

It seems very evident that the sensation produced by three contacts is no more complex when interpreted as four than when interpreted as three.  If that is true, then it must also be evident that the sensation produced by one contact is no more complex when interpreted as two than when interpreted as one.  The converse should also be true, that the sensation produced by two contacts is no less complex when interpreted as one than when interpreted as two.  Difference in number does not indicate difference in complexity.  The sensation of four is not made up of four sensations of one.  It is a unit as much as the sensation of one is.

There remains but one point to be elaborated.  If number is not a quality of objects, but is merely a matter of attitude of the subject, we should not expect to find a very clear-cut line of demarcation between the different numbers except with regard to those things which we constantly consider in terms of number.  Some of our associations are so firmly established and so uniform that we are likely to regard them as necessary.  It is not so with our associations of number and touch sensations.  We have there only a vague, general notion of what the sensation of one or two is, because usually it does not make much difference to us, yet some sensations are so well established in our minds that we call them one, two or four as the case may be without hesitation.  Other sensations are not so, and it is difficult to tell to which class they belong.  Just so it is easy to tell a pure yellow color from a pure orange, yet they shade into each other, so that it is impossible to tell where one leaves off and the other begins.  If we could speak of a one-two sensation as we speak of a yellow-orange color we might be better able to describe our sensations.  It would, indeed, be convenient if we could call a sensation which seems like one with a suggestion of two about it a two-one sensation, and one that seems nearly like two but yet suggests one a one-two sensation.  Since we