they had distinctly the experience that the distance was widening.  In these experiments I used five sorts of motion, quick and heavy, quick and light, slow and heavy, slow and light, and interrupted.  I made no attempt to determine either the exact amount of pressure or the exact rate.  I aimed simply at securing pronounced extremes.  The slow rate was approximately 3, and the fast approximately 15 cm. per second.

   [7] ‘Zeitsinn,’ Tuebingen, 1858.

   [8] Fechner, G. Th., ‘Elem. d.  Psychophysik,’ Leipzig, 1889; 2. 
   Theil, S. 328.

I have already said that these filled spaces were invariably overestimated and that the slower the movement, the greater, in general, is the overestimation.  In addition to the facts just stated I found also, what Hall and Donaldson[9] discovered, that an increase in the pressure of a moving point diminishes the apparent distance.

   [9] Hall, G. St., and Donaldson, H.H., ’Motor Sensations on the
   Skin,’ Mind, 1885, X., p. 557.

Nichols,[10] however, says that heavy movements seem longer and light ones shorter.

   [10] Op. citat., p. 98.

V.

There are several important matters which might properly have been mentioned in an earlier part of this paper, in connection with the experiments to which they relate, but which I have designedly omitted, in order not to disturb the continuity in the development of the central object of the research.  The first of these is the question of the influence of visualization on the judgments of cutaneous distances.  This is in many ways a most important question, and confronts one who is making studies in tactual space everywhere.  The reader may have already noticed that I have said but little about the factor of visualization in any of my experiments, and may have regarded it as a serious omission.  It might be offered as a criticism of my work that the fact that I found the tactual illusions to exist in the same sense as the optical illusions was perhaps due to the failure to exclude visualization.  All of the subjects declare that they were unable to shut out the influence of visualizing entirely.  Some of the subjects who were very good visualizers found the habit especially insistent.  I think, however, that not even in these latter cases does this factor at all vitiate my conclusions.

It will be remembered that the experiments up to this time fall into two groups, first, those in which the judgments on the cutaneous distances were reached by direct comparisons of the sensations themselves; and secondly, those in which the sensations were first localized and then the judgment of the distance read from these localizations.  Visualizing, therefore, entered very differently into the two groups.  In the first instance all of the judgments were made with the eyes closed, while all of the localizations were made with the eyes open.  I was uncertain