458 APPENDIX 



is nearly right and 7 is a possible fourth root for a number ending 

 in i, but it must have been a mere shot, whoever is responsible for 

 it, for it is followed by 16, which is hopeless, and then by 19, 

 where the terminal is, for the first time, right. Shots are then 

 made at the first figure, which is got at the third try. Compare 

 the very next sum : 



7 + 8 + 3 + ii + 5 = 25, 33, 34. 



Here we have an operation which seems rather more consequent. 

 The approximations are successive. The first figure is probably 

 influenced by the terminal 5. The second shot brings us very 

 nearly right. 



One of the most suggestive cases is recorded by Monsieur 

 Claparede (Archives^ XII., p. 289), \/99225 = 315. For this 

 Muhamed gives the following answers: 134, 155, 113, 135, 153, 

 235, 134, 175, 325, 215. Monsieur Claparede rightly notes that 

 the digits group themselves about 315. Two digits are right 

 in every shot, and in several cases all three digits. Anyone 

 applying our test, knowing only that someone had given these 

 solutions without knowing who it was, would say that that 

 someone had got a notion of the digits constituting the number, 

 but no notion whatever of the operation by which the number is 

 obtained. 



With these results we may associate the tendency to answer 

 wrong questions, which we have already noted. If, without 

 knowing it was a horse, we learnt that the answer 56 was given 

 to one sum when it belonged to a previous one for which the 

 answers propounded had been hopelessly wrong, we should infer 

 that the person who did that sum had somehow got the number 

 56 implanted in his mind and that it came out on the wrong 

 occasion. The previous sum might have set in motion the 

 train of association destined to call it forth, but it had worked too 

 slowly and come up at a moment when quite another figure was 

 required. On the whole, on these considerations we seem war- 

 ranted in drawing at least one negative conclusion. The horses 

 do not work sums of any complexity as arithmeticians. They 

 arrive at their results by some other method. Whatever that 

 may be, this method involves a great deal of guessing and groping, 

 and the same appears to be true of the words attributed to the 

 horses. Dr. zur Strassen gives as his opinion 1 that the horses 

 produce senseless words at first, and that then when their 

 rappings give some sense, which their modes of spelling render 

 easy, they seem suddenly to know what they mean to say ; indeed, 

 the formation of words is no test, for the operation of signs is 



1 Tierseele, Heft III. p. 265. 



