Briefly stated, the most important points upon which this discussion hinges are thus the following:  We have shown—­

1.  That the introduction of either a local difference or a difference of intensity in the tactual stimulations limiting an interval has, in general, the effect of causing the interval to appear longer than it otherwise would appear.

2.  That the apparent exceptions to the above rule are, (a) that the increase of the local difference in the first interval, the stimulated areas remaining unchanged, produces a slight decrease in the subjective lengthening of the interval, and (b) that in certain cases a difference in intensity of the stimulations limiting the second interval apparently causes the interval to seem shorter than it otherwise would.

3.  That the ‘constant error’ of time judgment is dependent upon the intensity of the stimulations employed, although the three stimulations limiting the two intervals remain of equal intensity.

To harmonize these results we have found it necessary to assume: 

    1.  That the length of a time interval is perceived as the
    amount of change in the sensation-complex corresponding to
    that interval.

2.  That the so-called ‘constant error’ of time estimation is determined by two mutually opposing factors, of which the first is the loss of time occasioned by the change of attitude at the division between the two intervals, and the second is the diminishing effect of perspective.

It is evident, however, that this last assumption applies only to the conditions under which the results were obtained, namely, the comparison of two intervals marked off by three brief stimulations.

* * * * *

PERCEPTION OF NUMBER THROUGH TOUCH.

BY J. FRANKLIN MESSENGER.

The investigation which I am now reporting began as a study of the fusion of touch sensations when more than two contacts were possible.  As the work proceeded new questions came up and the inquiry broadened so much that it seemed more appropriate to call it a study in the perception of number.

The experiments are intended to have reference chiefly to three questions:  the space-threshold, fusion of touch sensations, and the perception of number.  I shall deny the validity of a threshold, and deny that there is fusion, and then offer a theory which attempts to explain the phenomena connected with the determination of a threshold and the problem of fusion and diffusion of touch sensations.