us suppose the bank of keys, as was actually the case in my first form
of apparatus, to consist of twelve separate reaction-mechanisms; and let
us suppose, further, the constant relation (problem) on the basis of
which the subject is required to react to be that of middleness. It is
evident that in successive trials or experiments the keys must be
presented to the subject in odd groups, the possibilities being groups
of 3, 5, 7, 9, or 11. If for a particular observation the experimenter
wishes to present the first three keys at the left end of the keyboard,
he pushes back the remaining nine keys so that they cannot be operated
and requires the subject to select from the group of three keys the one
which on being pressed causes a signal to appear. It is of course the
clearly understood task of the subject to learn to select the correct
key in the group on first trial. This becomes possible only as the
subject observes the relation of the key which produces the desired
effect to the other keys in the group. On the completion of a subject's
reaction to the group of three keys, a group of seven keys at the
opposite end of the keyboard may, for example, be presented. Similarly,
the subject is required to discover with the minimum number of trials
the correct reaction-mechanism. Thus, time after time, the experimenter
presents a different group of keys so that the subject in no two
successive trials is making use of the same portion of the keyboard. It
is therefore impossible for him to react to spatial relations in the
ordinary sense and manner, and unless he can perceive and appropriately
respond to the particular relation which constitutes the only constant
characteristic of the correct reaction-mechanism for a particular
problem, he cannot solve the problem, or at least cannot solve it
ideationally and on the basis of a small number of observations or
trials.

For the various infrahuman animals whose ideational behavior has been