however, new and decisive proof presented itself which destroyed all possible doubt. Before adverting to it, let us consider in a few words the reaction-time of the horse,--the time elapsing between the final sign of the questioner and the reaction of the horse (i. e., the back-step). Unfortunately this time cannot be directly determined. All that can be ascertained from our time-measurements, is the time intervening between the moment of the head-jerk and the moment in which the reaction of the horse is noted. (See page 51). This time averaged, for the 127 measurements, .45 seconds. If we stated the unavoidable error, (obtained on the basis of extended supplementary measurements which it is not necessary to consider here) as .15 seconds, and apply it to the value found above, we obtain .3 seconds as the probable reaction-time of the horse.[K] [Footnote K: See page 126 on the corresponding reaction-time in the case of man. Similar tests have been made in the case of animals in only one instance, and that for dogs, by E. W. Weyer.[5] But, as might have been expected, they did not yield any satisfactory results.] That the tapping--as well as all other movements of the horse--was nothing other than a reaction upon certain visual stimuli, was proved beyond a doubt by the fact that the voluntary execution of the head-jerk and of other movements--which we will describe in more detail later on,--brought about all the proper responses on the part of the horse. Thus, artificial synthesis became the test of the correctness of analytical observation. To elucidate; if the questioner retained the erect position he elicited no response from the horse, say what he would. If, however, he stooped over slightly, Hans would immediately begin to tap, whether or not he had been asked a question. It seems almost ridiculous that this should never have been noticed before, but it is easily understood, for as soon as the questioner gave the problem he bent forward--be it ever so slightly--in order to observe the horse's foot the more closely, for the foot was the horse's organ of speech. Hans would invariably begin to tap when I stooped to jot down some note I wished to make. Even to lower the head a little was sufficient to elicit a response, even though the body itself might remain completely erect. Of thirty tests made in this position, twenty-nine were successful. Hans would continue to tap until the questioner again resumed a completely erect posture. If, for instance, I stooped forward after having told the horse to tap 13, and if I purposely remained in this position until I had counted 20, he would, without any hesitation, tap 20. If I asked him to add 3 and 4, but did not move until 14 was reached, he would tap 14. Twenty-six such tests gave similar results.