Whenever, in the foregoing, we spoke of a certain degree of concentration which had to be attained, it is not to be understood that the same tension had to be maintained throughout the test, from the horse's first tap to his last. But rather, that it began with a low degree, and gradually increased as the final unit of the count was being approached. It may best be represented by a curve whose maximum represents that degree of tension which we have been discussing. The rise to this maximum which, when attained, was followed by a sudden fall, did not always occur in the same manner. Three types of curve may be distinguished, which were first discovered in purely empirical fashion, and later reproduced voluntarily for purposes of experimentation by diagramming before each test the intricate curve of the varying degrees which the intensity of concentration was to assume. The types may be described as follows:
I. Here the tension curve rises steadily from beginning to end. This type preponderates in the case of small numbers. Thus, when I asked the horse: "How much is 2 plus 4?", the tension increased slowly with every tap from the moment I began counting, until the final tap was reached, when it was again relaxed. Externally this relaxation is noticeable as a slight jerk.
II. In this case the curve does not rise at an equal rate, but rather more slowly at the beginning and later undergoes a sudden increase, or the tension increases immediately at the beginning, remains constant for some time and then ascends to the maximum. This curve is the rule in the case of large numbers and evidently means economy of physical energy, for experience soon taught that a steady increase in tension from the very beginning soon brought it to a level which cannot be long maintained and usually leads to a premature relaxation. In the case of very large numbers the alternation of the slight and the sudden increase may be repeated several times, and at times it may even sink below a level which has already been attained, thus making a wave-like curve.
III. The third type of curve shows a sudden jump between two units at a certain point in its course. This may occur in the case of both small and large numbers but only when the highest or first degree of concentration is employed (see page 91). Such a jump frequently occurs in the transition from the tap preceding the last to the last one which is being eagerly expected. Relaxation--with the upward jerk and raising of the head--here occurs at the normal time; Hans taps to the end with his right foot. Oftener still the "jump" described occurs while passing over to the number just before the last. The goal seems within reach and the mental tension relaxes, and with it the physical tension,--the head gives a slight jerk and Hans makes the back-step. Since, however, another tap is still awaited with some degree of tenseness and, since complete erection of the head does not follow immediately upon the jerk of the head, the horse gives another tap with the left foot. Thereupon occurs the complete relaxation of attention, and the assumption of the erect posture on the part of the questioner. That this is psychologically the clue which leads to the final tap, will readily appear from the following remarkable fact: I was able to bring about at will either the back-step with the right foot, or the additional extra tap with the left foot by concentrating the mind either upon the last unit or upon the one just preceding it. In either case the movement which served as stimulus to the horse followed naturally upon concentration on the number. I could of course also control the response by direct voluntary control of the movements involved. Hans thus solved for me the same ten problems first with the back-step, then with the extra final tap.