BEGINNING THE TUITION 87 



she knows, therefore, that the difference between 

 these numbers of raps has some meaning. I then 

 began to count to her on my fingers at first from one 

 to five and then back, finally taking the numbers 

 irregularly and then holding up as many fingers as 

 composed the number in question. To my surprise 

 the dog was quiet and attentive, and I therefore soon 

 continued to count up to ten. In order to enforce 

 this lesson more I placed a row of small lumps of sugar 

 in front of her, counting them as I did so for it seemed 

 to me that these might draw her attention more to 

 the numbers. And I also rewarded her from time to 

 time with a little bit for having sat so still. Then, 

 holding up four fingers, I ventured with the question : 

 " How many fingers do I show ? Rap out the 

 number I " And to my Joy she rapped " 4 ! " Yet, 

 thinking this might have been accidental, I held up 

 five and said : " Rap out this number i " and taking 

 hold of her paw this time in order to make her tap her 

 answer on the palm of my hand. After this I ceased 

 my questions, for it seemed impossible that she should 

 have comprehended so readily, but I went on just 

 repeating the numbers to her. On the following day 

 I also only counted, and then began questioning again, 

 for I could not understand why she refused to look at 

 my hands any more, and was continually yawning. 

 Therefore, without holding out my hands, I asked her : 

 " How many make six ? " At which she gave six 

 raps. I could hardly believe it, so I asked her : 

 " four ? " and she replied with four raps. I asked for 

 five, and she answered correctly. I was now confident 

 that she did understand ; but what mystified me was 

 the celerity with which her answers were given, for 

 allowing even that she had understood, this swiftness 

 seemed incomprehensible, and I decided to form no 



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