THE WAYS OF LIFE 257 



one movement of the head from left to right. Gently and 

 good-humouredly he taught them to associate a certain 

 sound or sight with a certain number, a certain sound or 

 sight with a certain object, or even operation. His educa- 

 tion was run on association lines. Very gradually he got 

 them, he thinks, to * understand ' addition, subtraction, 

 multiplication and division. In the course of time they 

 were able to deal with fractions and to extract square 

 roots and cube roots. Dr. Hartmann, of Koln, got a friend 

 to extract three cube roots and put the questions and 

 answers in separate envelopes. In the stable he opened 

 the first envelope and dictated, ' Cube root of 13,824 '. 

 In a few seconds came the answer, 24, which Hartmann 

 confirmed by opening the relevant envelope. The cube 

 root of 29,791 was stated to be 31. The cube root of 

 103,823 was given first as 57 and then, rightly, as 47. 



Professor Buttell-Keepen got a friend to put a number 

 of arithmetical questions in separate envelopes and the 

 answers in others. Neither he nor Krall knew what they 

 were. One was the square root of 3,364, and \/ 3,364 was 

 written on the board. Muhamed stamped 32 (wrong), 

 44 (wrong), then twice wrong, and then 58, which is right. 



Professor H. von. Buttel-Reepen relates a very interesting 

 experience. In September of last year he went one day, 

 with Professor Ziegler, to KralTs stables half an hour earlier 

 than had been arranged. In the yard they fell in with the 

 Shetland Pony ' Hansehen ', and resolved to make some 

 experiments in the owner's absence. They got out the 

 blackboard and the stamping-board, and without a word 



33 



Professor Ziegler wrote down the sum n. Hansehen 

 stood waiting before the stamping-board and at once 



