20 THE HORSE OF MR. VON OSTEN 



the playing cards were indicated by taps. In the case of 

 playing cards one tap meant " ace," two taps " king," 

 three " queen," etc. 



Let us turn now to some of his specific accomplish- 

 ments. He had, apparently, completely mastered the 

 cardinal numbers from i to loo and the ordinals to lo, at 

 least. Upon request he would count objects of all sorts, 

 the persons present, even to distinctions of sex. Then 

 hats, umbrellas, and eyeglasses. Even the mechanical 

 activity of tapping seemed to reveal a measure of in- 

 telligence. Small numbers were given with a, slow 

 tapping of the right foot. With larger numbers he 

 would increase his speed, and would often tap very 

 rapidly right from the start, so that one might have 

 gained the impression that knowing that he had a large 

 number to tap, he desired to hasten the monotonous 

 activity. After the final tap, he would return his right 

 foot — which he used in his counting — to its original 

 position, or he would make the final count with a very 

 energetic tap of the left foot, — to underscore it, as it 

 were. " Zero " was expressed by a shake of the head. 



But Hans could not only count, he could also solve 

 problems in arithmetic. The four fundamental pro- 

 cesses were entirely familiar to him. Common fractions 

 he changed to decimals, and vice versa; he could solve 

 problems in mensuration — and all with such ease that it 

 was difficult to follow him if one had become somewhat 

 rusty in these branches. The following problems are 

 illustrations of the kind he solved.* " How much is f 

 plus J^ ? " Answer : A- (In the case of all fractions Hans 

 would first tap the numerator, then the denominator; in 



* All examples mentioned are cited from extant works of various 

 observers. 



