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. Finally we will indicate the one true inner cause of the difficulty in getting the number 1 as a response. It is not easy to relax attention immediately after having just begun to concentrate. Relaxation, therefore, often occurs with a certain retardation, and the result is a belated jerk of the head.