The reaction of the horse upon such a signal for stopping showed slight modifications according to the time which elapsed between the last tap and the signal for stopping. These modifications, which had hitherto been paraded as expressions of the horse's psychical power may be illustrated by the following schematic figures (Figures 1-4). In all of them the dotted line _c-d_ represents the ground level; _d_ shows where the horse's right forefoot was located before he began tapping; _a_ and _c_, respectively, indicate the place to which the foot is lowered during the process of tapping. The unbroken line gives the direction of the back-step. If Hans, having raised his foot from _a_ to _b_--preparatory to tapping,--receives the signal at or just before the moment he lowers the foot, he immediately swings it in a wide circle from _c_ back to its original position at _d_, (Fig. 1). As a matter of fact _a_ and _c_ coincide, but are juxtaposed in the diagram for the sake of schematic utility. This was the usual form of the back-step. [Illustration: FIG. 1.] If the signal for stopping is given a little after the last tap (Fig. 2), i. e., at the time that the foot is already being raised for another tap, then the back-step occurs as _a-b-d_. The horse thus gives, at the moment it receives the signal for stopping, a changed impulse to the moving foot. The curve, therefore, has a kink at _b_, and the back-step occurs with seeming hesitancy,--Hans appears not quite certain of his result. [Illustration: FIG. 2.] If the signal be given somewhat later still (Fig. 3), i. e., when the foot is being lowered to complete a tap, Hans is still able to put on the brakes--as it were--and draw back his foot before it reaches the ground. The whole process gives the impression that the horse was just about to make a "mistake" of one unit, but at the last moment had bethought himself of the correct answer. [Illustration: FIG. 3.] Finally, if the signal be deferred still longer, it becomes impossible to prevent the extra tap. The back-step again has the same form as in figure 1; Hans has made a "mistake" in his answer by one unit too many. Conversely, if the head-jerk of the questioner occurs too soon; i. e., at the moment the horse has raised his foot for the final tap to the height _b_, (Fig. 4), then the tap is not completed,--but the foot, without touching the ground, makes the curve _b c_{2} d_, back to its original position. Hans has again made a "mistake" in his answer,--this time by one unit too few. [Illustration: FIG. 4.] All these variations go to show one thing: Hans never knows in advance which tap is to be the final one. These variations in his reactions occurred often without having been intended by the questioner. But to bring them about at will required skill, on account of the shortness of the time involved in the reaction.