His educational methods also differ materially from Von Osten's. It was a strange thing, but deep down in the rather queer, cross-grained soul of the old enthusiast there had grown up gradually a sort of hatred for his four-legged pupil. He felt the stallion's proud and nervous will resisting his with an obstinacy which he qualified as diabolical. They stood up to each other like two enemies: and the lessons almost assumed the form of a tragic and secret struggle in which the animal's soul rebelled against man's domination. Krall, on the other hand, adores his pupils; and this atmosphere of affection has in a manner of speaking humanized them. There are no longer those sudden movements of wild panic which reveal the ancestral dread of man in the quietest and best-trained horse. He talks to them long and tenderly, as a father might talk to his children; and we have the strange feeling that they listen to all that he says and understand it. If they appear not to grasp an explanation or a demonstration, he will begin it all over again, analyze it, paraphrase it ten times in succession, with the patience of a mother. And so their progress has been incomparably swifter and more astounding than that of old Hans. Within a fortnight of the first lesson Mohammed did simple little addition and subtraction sums quite correctly. He had learnt to distinguish the tens from the units, striking the latter with his right foot and the former with his left. He knew the meaning of the symbols plus and minus. Four days later, he was beginning multiplication and division. In four months' time, he knew how to extract square and cubic roots; and, soon after, he learnt to spell and read by means of the conventional alphabet devised by Krall. This alphabet, at the first glance, seems rather complicated. For that matter, it is only a makeshift; but how could one find anything better? The unfortunate horse, who is almost voiceless, has only one way in which to express himself: a clumsy hoof, which was not created to put thought into words. It became necessary, therefore, to contrive, as in table-turning, a special alphabet, in which each letter is designated by a certain number of blows struck by the right foot and the left. Here is the copy handed to visitors at Elberfeld to enable them to follow the horse's operations: -- 1 2 3 4 5 6 10 E N R S M C 20 A H L T A: CH 30 I D G W J SCH 40 O B F K O: -- 50 U V Z P U: -- 60 EI AU EU X Q -- To mark the letter E, for instance, the stallion will strike one blow with his left foot and one with his right; for the letter L, two blows with his left foot and three with his right; and so on. The horses have this alphabet so deeply imprinted in their memory that, practically speaking, they never make a mistake; and they strike their hoofs so quickly, one after the other, that at first one has some difficulty in following them.