APPENDIX 453 



It may be remarked here that experiments in the extraction of 

 roots, of which Herr Krall is particularly fond, are in reality very 

 unsuitable as tests of arithmetical power. Roots can be very rapidly 

 guessed by anyone who has once got the trick, and fifth roots, 

 which sound the hardest, are in reality the easiest of all because 

 the terminal digit is always the same, and unless we run into three 

 figures, only one of them remains to be guessed. On the whole, 

 the loophole experiments add very little to our knowledge. We 

 pass to cases in which Krall is altogether absent. Doctors Sarasin 

 and Brunies give an account l of experiments made when Krall was 

 away, the groom coming in only when the horse declined to 

 answer, except in the case of blind Berto, who is apparently 

 unmanageable without him. Experiments with Zarif failed com- 

 pletely. The pony Hanschen read 23 correctly after certain 

 failures, failed to add 2 and 3, asked to count 63 gave successively 

 53, 33, 63 ; for 4 x 5 gave 45 and then 54. Having thus 

 disgraced himself he was energetically smacked and set the sum 

 of 25 X 5, which, after two failures, he gave correctly: 125. 

 There followed a series of trials with Muhamed, which 

 included some failures in very simple operations, e.g., 4+6 and 

 6x6. But Muhamed extracted v^ 22 5 correctly after one failure, 

 ^5625 correctly after two failures, and ^/23 13441 correctly after 

 four failures. He then tapped the name of Albert the groom, 

 thus : A 1 p b a i d. Asked which letter is wrong he says the 

 sixth, which should be r. R is, in fact, given by thirteen taps and 

 i by thirty -one, so that Muhamed's error is excusable. Shown a 

 book and asked what it is, he taps b u, and then after accidental 

 interruption, g. 



There followed some experiments with Berto, but as the groom 

 was present in these they need not be regarded. 



Monsieur Bohn's successes with Muhamed in the absence of 

 Krall have already been referred to. It may be added that when 

 he proposed to the horse an addition, he got a result which' he 

 thought was mistaken until he saw that he was himself responsible 

 for the error, having made the vertical sign of the plus so faint 

 that Muhamed had taken it for a minus and carried out a sub- 

 traction, which was worked correctly. 



Monsieur Claparede's results under similar conditions were 

 hardly so favourable. On his first visit Krall wrote up the follow- 

 ing sum on the blackboard and then left the room : 



Muhamed, says Monsieur Claparede, threw a glance at the board 

 and instantly replied 115, which is wrong. Krall then called to 



1 Tierseele, Heft I. p. 184. 



