"B. Report on the Dog Heinz
"A second dog, by name Heinz, who came into the possession of Mr. Justice Leser in Mannheim, has proved himself to be an excellent arithmetician, and this without ever having been worried with instruction. In the same way as Rolf he gives two raps for 'yes' and three for 'no,' while four express that he is 'tired.'
"Mr. Justice Leser reports:
"If I ask Heinz whether he will do arithmetic he invariably raps "2," even though sometimes accompanying his assent with a yawn. I am generally obliged to hold out the prospect of some reward as an inducement to do his sums. I should have preferred his rapping against some article one could hold in one's hand, or that he could be induced to "rap out" on a board setting forth the numbers, and which might be placed on the floor before him; but to neither of these alternatives will he agree, having since his earliest youth learnt to rap in the same way as Rolf does. He will, however, not only rap for me, but for any person he knows well, solving such problems as: 3 + 4 - 6, or √121 + 3, or 14/2 + 4, or 32, and he seldom makes a mistake, even when the sum he may be asked merely resembles the form of arithmetic he has learnt. But he generally gives up after two or three sums and is generally distracted. He can read the figures too, and generally gives a correct solution to sums which have been written down for him and which I myself have not read. Like Rolf, he only looks at the paper sideways. He reads very reluctantly. His memory is excellent; especially quick is he at recognizing those persons again who have at any time had to do with him.'
"When I was in Mannheim on 22 March, 1916, Mr. Justice Leser was kind enough to show me the dog. I put some problems to it verbally and was able to satisfy myself as to its abilities in the matter of arithmetic. Of those then put by me I still call to mind the following: '24 ÷ 3 - 3?' Answer: '5,' and '√10,000 - 87?' Answer: '13.'[9 ]
"C. Report on the Dog Harras
"The third dog, Harras, came into the possession of Fräulein Eva Hoffmann, of Schloss Berwartstein, near Bergzabern, and was instructed by her in spelling and arithmetic with excellent results. This lady sends the following report:
"'From the very beginning his gift for arithmetic was quite remarkable. It was enough to give him an idea of how to reckon, explaining to him the different forms of arithmetic, for the dog to learn to give the right answers to easy sums immediately.
"'Fractions, decimals, cubes and the easier forms of equation, have been set him by a stranger. With some coaching he was also able to master textual problems in this way, giving eager and glad response in the form of "yes" and "no" when it came to questioning him as to his having understood or not understood—liked or not liked the subject. He usually did his sums with evident pleasure and with amazing celerity. Spelling gave him more trouble. He could not even remember an alphabet he had himself put together, and one I invented for him he only memorized after going over it many times. He took no pleasure in putting words together and got tired very soon. Some of his original remarks are that he recognized Sunday by the "dress" I had on; also that he had dreamt of a "cow" (this after having seen one when we were out walking), and so on.