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, proved that the increased rapidity in tapping in the case of large numbers, which many regarded as an evidence of high intelligence, (see [page 20]), was, as a matter of fact, brought about in the way described. The two series (in each of which the time measured was for 10 taps) are quite in accord. The horse did not tap faster because he had been given a large number by Mr. von Osten, but because the latter had bent farther forward.
From all this it readily appears why it was possible to cause Hans to increase his rate of tapping but not to decrease it. To do the latter would involve a decrease in the angle of inclination of the body. This would necessitate the erection of the body. As we have seen, this was the signal to which Hans reacted by ceasing to tap. And as a matter of fact we never knew the horse to decrease his rate of tapping in the course of any single test, except in the case of very large numbers, and then it was probably due to fatigue. Mr. von Osten insisted that Hans often slowed down toward the end of a test, "in order to obviate mistakes", but all the tests in which he tried to demonstrate this to us, were unsuccessful. In spite of all exhortation, Hans would tap either uniformly or somewhat more rapidly as soon as his master—in all probability unconsciously—bent somewhat lower. Only once was such a test successful. Mr. von Osten—upon our request—asked the horse to give a certain large number. In this instance the decrease in the rate of tapping was due to fatigue and had nothing whatever to do with the desire on the part of the horse to avoid error.
Furthermore, Mr. Hahn, who had visited Hans twenty times and had made careful notes of his observations, corroborated my statement when he said that he himself never noted the decrease in rate mentioned. Contrary statements may perhaps be due to the fact that the tense state of expectancy on the part of the observer made the interval between the last taps appear subjectively somewhat longer.
So much for the technique of the tapping. Now a word about the numbers which Hans tapped. (I refer only to the results obtained in series which involved no volitional control). The number 1 was very difficult to get. Hans usually tapped 2 instead. Thus even in the case of Mr. von Osten he responded five times with 2, and only in the sixth test did he react correctly. As far as other questioners were concerned, 1 was seldom ever obtained, except in the case of Mr. Schillings and myself. The numbers 2, 3 and 4, on the other hand, were very easily obtained and, above all, 3 seldom failed. 3 seemed to be the horse's favorite number and was very frequently given instead of other numbers. Thus, one-sixth of all the horse's incorrect responses which were given to me were in terms of the number 3. The numbers 5 and 6 were a little more difficult to obtain and above 10 the difficulty increased rapidly. Indeed, I never saw Hans respond with a number exceeding 20 to any questioner, Mr. Schillings and Mr. von Osten excepted. I saw the nine vain attempts of Count zu Castell to get the number 15, and Count Matuschka's eight unsuccessful attempts to obtain the number 16 as a response. But even with Mr. von Osten and Mr. Schillings such failures were not infrequent. Thus, Mr. von Osten tried five consecutive times to obtain the number 24. I myself did not fare any better at first. But the following table shows what practice can do. If we compare the percentage of correct responses (involving the numbers 1 to 7—for which alone I have sufficient material, viz., 80 to 100 cases), obtained in the first half of our tests, with that of the second half, we get the following:
| For Number: | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| In first half of tests: | 49, | 92, | 89, | 86, | 74, | 62, | 53% |
| " second " " : | 92, | 95, | 92, | 98, | 97, | 86, | 96% |
From this we see how hard it was at first to get the number 1 and that failure was as frequent as success, and how much easier it was on the other hand to get the numbers 2 and 3 (and which, therefore, do not show any great improvement in the second half of the tests). Beyond the 3 the percentage of correct responses decreased and the number 7 stood at the same level as the number 1. In the second half of the tests, all these differences disappeared and errors were infrequent and seldom exceeded +1 or -1. These results of practice are not to be accredited to the horse, but to the experimenter, who was at first quite unskilled. This difference in results does not appear in the case of Mr. von Osten, for his initial practice had been had many years previous. The values obtained in his case were very constant throughout our experimentation and generally showed something like 90% of correct responses. To be sure, in his case also, the number 1 was somewhat unfavorable, (79% were correct responses). But the percentages obtained in his case showed no improvement whatever throughout our experimentation. We need scarcely add that with the voluntary control of the giving of the signs, in the case at least of such small numbers as are here discussed, no errors, whatever, occurred.