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.

Different observers have found that subjects sometimes describe a
sensation as 'more than one, but less than two.' I had a subject who
habitually described this feeling as 'one and a half.' This does not
mean that he has one and a half sensations. That is obviously