I need hardly say that here, and in all my other experiments, the subjects were kept as far as possible in complete ignorance of the object of the experiment.  This and the other recognized laboratory precautions were carefully observed throughout this work.  Four distances were used, 4, 8, 12 and 16 cm.  At frequent intervals throughout the tests the contact was made with only one of the points instead of four.  In this way there came to light again the interesting fact which we have already seen in the last section, which is of great significance for my theory—­that the end points are located differently when given alone than when they are presented simultaneously with the other points.  I give a graphic representation of the results obtained from a large number of judgments in Figs. 4, 5 and 6.  These experiments with filled spaces, like the earlier experiments, were made on the volar side of the forearm beginning near the wrist.  In each distance four points were used, equally distributed over the space.  The shaded curve, as in the previous figures, represents the results of the attempts to localize the points when all four were given simultaneously.  In the dotted curves, the end points were given alone.  The height of the curve at any place is determined by the number of times a point was located immediately underneath that particular part of the curve.  In Fig. 4 the curve which was determined by the localization of the four points when given simultaneously, shows by its shape how the points appear massed towards the center.  In Fig. 5 the curve AB shows, by its crests at A and B, that the end points tended to free themselves from the rest in the judgments.  But if the distance AB be taken to represent the average of the judgments upon the filled space 1, 2, 3, 4, it will be seen to be shorter than what may be regarded as the average of the judgments upon the corresponding open space, namely, the distance A’B’, determined by the localizations of the end points alone.  The comparative regularity of the curve indicates that the subject was unable to discriminate among the points of the filling with any degree of certainty.  The localizations were scattered quite uniformly along the line.  In these short distances the subject often judged four points as two, or even one.

[Illustration:  Fig. 5.]

[Illustration:  Fig. 6.]

Turning to Fig. 6, we notice that the tendency is now to locate the end points in the filled distance outside of the localization of these same points when given without the intermediate points.  It will also be seen from the irregularities in these two longer curves that there is now a clear-cut tendency to single out the individual points.  The fact that the curves here are again higher over point 4 simply signifies that at this, the wrist end, the failure to discover the presence of the points was less frequent than towards the elbow.  But this does not disturb the relation of the two series of