e been noticed before, but it is easily understood, for as soon
as the questioner gave the problem he bent forward--be it ever so
slightly--in order to observe the horse's foot the more closely, for the
foot was the horse's organ of speech. Hans would invariably begin to tap
when I stooped to jot down some note I wished to make. Even to lower the
head a little was sufficient to elicit a response, even though the body
itself might remain completely erect. Of thirty tests made in this
position, twenty-nine were successful. Hans would continue to tap until
the questioner again resumed a completely erect posture. If, for
instance, I stooped forward after having told the horse to tap 13, and
if I purposely remained in this position until I had counted 20, he
would, without any hesitation, tap 20. If I asked him to add 3 and 4,
but did not move until 14 was reached, he would tap 14. Twenty-six such
tests gave similar results.

The reaction of the horse upon such a signal for stopping showed slight
modifications according to the time which elapsed between the last tap
and the signal for stopping. These modifications, which had hitherto
been paraded as expressions of the horse's psychical power may be
illustrated by the following schematic figures (Figures 1-4). In all of
them the dotted line _c-d_ represents the ground level; _d_ shows where
the horse's right forefoot was located before he began tapping; _a_ and
_c_, respectively, indicate the place to which the foot is lowered
during the process of tapping. The unbroken line gives the direction of
the back-step.

If Hans, having raised his foot from _a_ to _b_--preparatory to
tapping,--receives the signal at or just before the moment he lowers the
foot, he immediately swings it in a wide circle from _c_ back to its
original position at _d_, (Fig. 1). As a matter of fact _a_ and _c_
coincide, but are juxtaposed in the diagram for the sake of schematic
utility. This was the usual form of the back-step.

[Illustration: FIG. 1.]

If the signal for stopping is given a little after the last tap (Fig.
2), i. e., at the time that the foot is already being raised for another
tap, then the back-step occurs as _a-b-d_. The horse thus gives, at the
moment it receives the signal for stopping, a changed impulse to the
moving foot. The curve, therefore, has a kink at _b_, and the back-step
occurs with seeming hesitancy,--Hans appears not quite certain of his
result.

[Illustration: FI