xing certain points
in the environment, it was possible to get approximately the same angle
repeatedly. The time from the third to the thirteenth tap was, in all
cases, taken by Prof. Stumpf by means of a stop-watch. The tests were
taken in the following order:

Grade of inclination: I VI II II IV V VI VII
Time for 10 taps: 5.2 4.6 5.0 5.0 4.8 4.8 4.6 4.4 sec.

From this series it will be seen that in the case of the same angle of
inclination (II and VI were repeated and III was omitted) the same rate
obtained in the tapping. In two other tests I constantly increased the
angle of inclination during the 15 taps, and Hans gradually increased
the rate of tapping accordingly.

In a second series I had the horse tap 14, five times. I myself took the
time of the taps up to 7 by means of the stop-watch, while Prof. Stumpf
took the time of the taps from 8 to 13. At 8 I suddenly bent forward a
little more and retained this position until tap 13. The results were as
follows:

Taps 2 to 7 (Pf.): 3.2 2.2-2.4 2.4 2.2-2.4 2.4 seconds.
" 8 to 13 (St.): 2.6 2.0 2.0 2.2 2.2 seconds.

Such good results, however, were possible only after a number of
preliminary practice tests had been made. The experiment was especially
difficult because the horse was often on the point of stopping in the
midst of a test. This was probably due to some unintentional movement
on my part. In such cases I could induce him to continue tapping only by
bending forward still more, but this effected also, as we have seen, an
increase in his rate of tapping. Such tests, of course, could not give
unambiguous results.

The rate of tapping was quite independent of my rate of counting. Thus,
if I counted aloud rapidly, but bent forward only very slightly, the
horse's tapping was slow and lagged behind my count. If I counted slowly
but bent far forward, Hans would tap rapidly and advance beyond my
count. Thus we see that his rate of tapping was in accordance with the
degree of inclination of my body and never in accordance with the rate
of my counting, i. e., it was quite independent of every sort of
auditory stimulation.

Direct observation and a comparison of the records of the time Hans
required in giving to his master responses involving small, medium and
large numbers, with the records of the time which he required to respond
to my questions when I bent only slightly, moderately or very far
forward,