252 THE HORSE OF MR. VON OSTEN 



was first tapped and then the remainder of the number 

 added to the lo. Thus : " You are to add 9 and 5. How 

 much must you add to the 9 to have 10?" One tap. 

 " But now, you were to add not merely i, but 5 ; how 

 much have you still to add to the 10? " — Four taps. In 

 like manner, whenever the addends were below 20 or 30 

 and the sum above 20 or 30, Mr. von Osten would ask 

 for the 20 or 30 taps first. He thought that he was thus 

 giving his pupil an ever firmer grasp upon the principle 

 of the structure of our number system, in which all higher 

 numbers are constituted of tens and digits. For the 

 same reason he used at first, instead of the words ' eleven ' 

 and 'twelve' ('elf and ' zwolf ' in the German), ex- 

 pressions which in English might be rendered as ' one- 

 teen ' and ' two- teen ' (' einzehn ' and ' zweizehn ' in the 

 German) ; and only later, after the animal had seemingly 

 mastered the meaning in question, did Mr. von Osten re- 

 place them by the usual forms. 



All this was beautifully conceived and might perhaps 

 form the basis for the instruction of primitive races. 

 But it is of immediate interest for us only because it 

 enables us to better understand the origin of the con- 

 viction under which Mr. von Osten and his followers 

 labored. 



