foot, just as a teacher tries to aid a pupil in learning to
write by guiding his hand. He repeated this exercise so often that
finally the single tap was made. And always the right foot was insisted
upon. Bread and carrots were the constant rewards.

Two of the pins were now set up and the command given: "Raise the
foot!--One, two!" Mr. von Osten again aided the establishment of the
proper association by using his hand as before. At the same time the two
pins were pointed out, and the order was always without exception from
left to right. Gradually it became unnecessary to touch the foot or to
point to the pins, and instead the question was introduced: "How many
are there?", in order that the horse should become accustomed to these
words as an invitation to give the taps when he saw the wooden pins
before him.

Then three pins were taken and the words "one, two, three" were spoken,
and so on. In naming a number the preceding ones were always named along
with it, in order that the normal order might thus be learned at the
same time. Later the number alone, without the preceding ones, sufficed
to elicit the proper number of taps. The last word of the series thus
becomes characteristic of the series as a whole. It differs from all the
others, and thus becomes the sign for the whole series of numbers thus
named, each of which arises as a memory image at the proper place in the
series and is accompanied by a tap of the foot. Thus, Mr. von Osten at
any rate had accounted to himself for his success.

But Hans was not to acquire merely this relatively mechanical process of
counting (hardly to be called counting), but he was to acquire also some
meaning content for the number terms. For this purpose everything
depended upon the concept "and". Only he who can grasp its meaning will
be able to understand a number. 2 is 1 _and_ 1, 3 is 2 _and_ 1. Mr. von
Osten had someone hold a large cloth before the horse, where the wooden
pins usually were placed. He then had the cloth taken up and he would
pronounce emphatically the word "and". After this had been done a number
of times, he put up two of the pins and obscured them by the cloth. The
cloth was again raised and the word "and" pronounced. Then Hans, as a
result of his previous instruction (so Mr. von Osten thought) would give
two taps at sight of the pins. The thing was repeated with three pins,
then with one, and so on, and the horse would always execute the proper
number of tap