(a) The questioner computes correctly but does not move at the proper moment. Nearly all the errors which had been accredited to the horse, were of this kind.

A part of these errors had the appearance of being significant, that is, they might be interpreted as a misapprehension of the question. If, for instance, instead of a sum only one of the quantities was given, or, if instead of a product only one of the factors was given, it might be interpreted that the horse simply wished to repeat the problem. Thus, Mr. von Osten in response to the question: "How much is 3 times 5?", twice in succession received the answer, "3", and upon my question, "How much is 3 plus 4?" he answered, "3", and to "How much is 2 times 6?" he tapped 6, and to "What is one-fourth of 36?" 4. In part (certainly in the second and third example cited) an individual quantity or factor had been emphasized in the consciousness of the questioner (cf. [page 105]) and in part the reactions were due to chance. Thus, when Mr. Hahn asked the question: "What is one-half of 10?", he received the following responses: 2 and 10, and then 17 and 3. To this class belong also, the tests made by the Commission of September and reported in [Supplement III. (See page 255)].

Other errors, even though they may not have appeared to be significant, might yet have been characterized as mistakes due to speed; as when, e. g., Hans made an error of one unit—and sometimes, though less frequently, of two units—too much or too little in his response. One might be led to believe that Hans had not made an error of calculation but merely of counting in the process of giving his result, which always had to be done by the cumbersome method of tapping. As a matter of fact, the trouble lay in the wrong degree of concentration on the part of the questioner: In errors of +1, tension was too slight, in those of -1, it was too great (see [page 91]). This comes out clearly in a comparison of the two more extensive series which I took in the case of Mr. Schillings. During the first series, he was well disposed, and was able to concentrate effectively, while during the second, he was nervous and easily diverted. This difference in intensity of concentration in the case of the two series is attested, not only subjectively by Mr. Schillings's introspective statement, but may be measured objectively by means of the number of final taps which the horse gave with his left foot during these two series. We saw ([page 94]) that these final taps were always a sign of intense concentration and, as a matter of fact, one-half of the horse's responses to Mr. Schillings during the first series were made in this way; whereas, in the second series, only one-third were of this sort. (I, myself, was never able to get, without conscious control, a greater number of this type of response.) We may therefore say that, in the first series we had a high degree of tension, or concentration, whereas, in the second series, we had a low degree. The errors distribute themselves over the two series as follows:

+1+2-1-2
Series I(31 tests)
Correct responses: 87%
Incorrect ":0%0%13%0%
Series II(40 tests)
Correct responses: 40%
Incorrect ":40%8%2.5%0%(and 9.5%
other kinds of errors.)

We find in Series I no "+1" errors, but only "-1" errors; in series II, on the other hand, the errors are almost exclusively of the "+1" category, equaling the number of correct responses, and there is only one "-1" error. A series obtained in the case of Mr. von Osten is almost as satisfactory an illustration. When he first began to take part in tests in which the procedure was the one we characterized as "without knowledge" and had to note their complete failure, he was thrown into such confusion that the responses in the case of procedure with knowledge were also incorrect. The errors there were always +1, (whereas those in the case of procedure with knowledge, which were due to quite different causes, were very great and inconstant.) The number of +1 errors obtained on this occasion comprises one-fourth of all the plus errors which were ever obtained in the case of Mr. von Osten during the entire course of these experiments. Finally, I would mention two examples of my own. In the course of my very first attempts with Hans I obtained, as I said on [page 89], three responses in a total of five which exceeded the correct result by 1. This I would explain by the fact that although I employed a high degree of concentration, I nevertheless was somewhat skeptical. The result was a certain deficiency in the degree of concentration. A second example which I would cite is taken from the period in which I had already discovered the cue to Hans's reactions and goes to show that I was then still able to eliminate the influence of this knowledge and to work ingenuously. To the question, "How much is 9 less 1?" I, momentarily indisposed, received the answer 10, and then six times in succession the answer "9", and finally the correct response, "8".

Errors of another kind—the not infrequent offenses against the very elements of counting and the fundamental arithmetical processes—were regarded in part as intentional jokes and by an authority in pedagogy as a "sign of independence and stubbornness which might also be called humor". Hans emphatically asserted that 2+2 was 3 or he would answer questions given in immediate succession as follows: "How many eyes have

you?"—2. "How many ears?"—2. "How many tails?"—2. These errors, as a matter of fact, evince neither wit nor humor, but prove incontrovertibly that Hans had not even mastered the fundamentals.

Many of the errors baffle every charitable attempt at interpretation. These gave the horse the reputation of capriciousness and unreliability. If Hans designated the tone "e" as the seventeenth, or "g" as the eleventh, or when he called Friday the 35th day of the week or believed 50 pfennige to be worth only 48, the cause for these responses lay either in the insufficient degree of tension on the part of the questioner (as in the first three examples) or in the extravagant expenditure of the same (as in the last case). If, therefore, the horse at times would "hopelessly flounder" which would seem to be indicated by tapping now with the right and now with the left foot, then as a matter of fact, this form of reaction came about as was described on [page 61], with this difference that there we had to do with voluntary controlled movements on the part of the questioner, whereas here, they are the result of an unsuitable degree of tension which expressed itself in frequent and disconcerting jerks. Besides the answer 3, this so-called floundering was the only reaction the average person could obtain from the horse in the absence of Mr. von Osten and Mr. Schillings. It would however occur also in the case of these gentlemen and would be received by them with resentment when in truth it was Hans's greatest feat, for he showed his extremely keen reaction upon every movement of the questioner. To this group belong also the errors in the case of higher numbers, the sole cause of which lay in the difficulty with which tension could be maintained and the body kept motionless for so long a period. These errors occurred in accordance with a certain law. If, for instance, a certain test repeatedly evoked incorrect responses, the questioner would gradually increase the duration of tension and would thus come a little nearer to the desired goal with every test. In this way, Mr. von Osten desiring 30 as an answer obtained consecutively the responses, 25, 28, 30; and I, myself, for the answer 20, received consecutively the responses 10, 18, 20 (see also the laboratory tests, [page 105]). Sometimes too, the questioner would flag in his efforts before the goal was reached. Thus in one of my first tests, I received for the answer 11 the following responses: 1, 4, 5, 7, 4. I was unable to get beyond 7. In other instances, the horse responded first with too few and then with too many taps. The correct response therefore could only be obtained after an appreciable amount of gauging of tension, as in target practice there must be a gauging of distance. (See [page 92]). In this way Mr. von Osten obtained for 10 the responses 8, 8, 11, 10, and Mr. Schillings for 17, received 9, 16, 19, 18, 18, 14, 9, 9, and finally, after some efforts, 17 taps. Thus there was a rise from 9 to 19, then a fall back to 9 and after eight tests the correct response. As long as we attempt to explain this fact as error on the part of the horse, so long will it remain inexplicable, but the moment we regard it from the point of view of the psychology of the tension of expectation, it becomes perfectly plain.

The same holds true for the curious predilection which Hans appeared to have for the numbers from 2 to 4, especially for 3 (see [page 68]). As a matter of fact the cause of this lies in nothing other than the inadequate concentration of attention on the part of the questioner and less often in an extravagant expenditure of concentration, which explodes immediately after the first tap on the part of Hans (as in the case of my first tests); but usually the cause lay in a complete lack of concentration, though the same result may be produced by various causes. It is usually after 2 to 4 taps of the horse's foot that the questioner, who does not concentrate, makes his first move which naturally puts an end to the tapping on the part of the horse. As a rule this jerk follows immediately upon the second tap. (On the other hand, relaxation of attention is very difficult upon the first tap. See [page 95]). The questioner, however, would expect further tapping and therefore would not bring his body back to a completely erect position and the result would be a 3, the last unit of which would be given by the final tap with the left foot. Here we also obtained light as to the answers which Hans gave in those tests in which the method was that of "procedure without knowledge". These responses had nothing to do with the problem, for neither the horse nor any one else knew the solution. But in the horse's responses the degree of tension of the questioner's concentration was faithfully mirrored. An experimenter who was as skillful in concentrating as Mr. von Osten, obtained—almost without exception—very high numbers, whereas one whose concentration was slight would receive in response to nearly all questions the answers 2, 3 or 4. Thus, the Count zu Castell received in response to seventeen questions the answer 2, three times, the answer 3, six times, and the answer 4, four times, two answers being accidentally correct.