but the idea of two would not persist through a series of any length.  He would call it two when two points very close together were used.  I could bring the knobs within two or three millimeters of each other and he would report two, but when only one point was used he would find out after a very few stimulations were given that it was only one.  After I had given up the attempt I told him what I had been trying to do and he gave what seems to me a very satisfactory explanation of his own case.  He says the early sensations keep coming up in his mind, and when he feels like calling a sensation two he remembers how the first sensation felt and sees that this one is not like that, and hence he calls it one.  I pass now to a brief discussion of what these experiments suggest.

It has long been known that two points near together on the skin are often perceived as one.  It has been held that in order to be felt as two they must be far enough apart to have a spatial character, and hence the distance necessary for two points to be perceived has been called the ‘space-threshold.’  This threshold is usually determined either by the method of minimal changes or by the method of right and wrong cases.

If, in determining a threshold by the method of minimal changes—­on the back of the hand, for example, we assume that we can begin the ascending series and find that two are perceived as one always until the distance of twenty millimeters is reached, and that in the descending series two are perceived as two until the distance of ten millimeters is reached, we might then say that the threshold is somewhere between ten and twenty millimeters.  But if the results were always the same and always as simple as this, still we could not say that there is any probability in regard to the answer which would be received if two contacts 12, 15, or 18 millimeters apart were given by themselves.  All we should know is that if they form part of an ascending series the answer will be ‘one,’ if part of a descending series ‘two.’

The method of right and wrong cases is also subject to serious objections.  There is no lower limit, for no matter how close together two points are they are often called two.  If there is any upper limit at all, it is so great that it is entirely useless.  It might be argued that by this method a distance could be found at which a given percentage of answers would be correct.  This is quite true, but of what value is it?  It enables one to obtain what one arbitrarily calls a threshold, but it can go no further than that.  When the experiment changes the conditions change.  The space may remain the same, but it is only one of the elements which assist in forming the judgment, and its importance is very much overestimated when it is made the basis for determining the threshold.