is actually supposed to distinguish between the ordinary 's' and the 'long s' at the end of the word, between 'äu' (with the Umlaut) and 'au' without it, and so on. Such, at all events, is the claim set forth for 'Hans's' miraculous intelligence. As a fact it is, of course, completely a matter of indifference to 'Hans' what the questions may be; they could with equal success be put in Greek or Sanskrit, so long as he can catch the right signal and stop pawing at the right time. And so again the gap between fact and fable is world-wide; and the assumption equally groundless that any measure of the human kind of reasoning intervenes to make possible the horse's replies.
Surely there is nothing in either of these performances, except the pretences of the showman, that in the least suggests the use of any of the powers that the developing child must first acquire to gain an actual knowledge of numbers and letters. And, if we look, we shall find many indications of the quite different processes that are really concerned. The best of these lies in the nature of the mistakes that are likely to occur. For 'Jim Key,' these take the form of selecting a neighboring letter—an 'x' for a 'y'—a kind of mistake which no mind that really was doing any spelling would be in the least tempted to commit; while 'Hans's' mistake consists in not seeing the signal quickly enough, and in pawing once too often or in anticipating through the getting ready of the signal, and stopping too soon, again a type of mistake that has no relation to the actual operation of those who calculate and read. So also the scope of the questions that these marvelous animals at once attack without preliminary training shows how unrelated is the finding of the answer to the consideration of the problem. If we add considerably to the difficulty of the problem that we set to a calculating child, we must be prepared to accustom its powers gradually to the increased difficulty and to take small steps repeatedly with much chance for mistake in the newer processes. But these calculating horses jump at once into fractions and square-roots, into propositions in geometry, and equations in algebra, when some enterprising questioner proposes them. This at all events is true for 'Hans's' master, who easily prepares the result; though in 'Jim Key's' case, one sometimes suspects that the calculating possibilities of the master are not immeasurably in advance of those of the horse.
And once more—it certainly seems strange that so exceptionally educated an animal should find no other occasion to exercise his remarkable powers, should not spontaneously exhibit some original evidences of his genius, that would distinguish him from the ordinary horse. We are even tempted to pity so talented an animal with no outlet for its vigorous mind, condemned to the monotonous round of oats and hay, varied only by the tit-bits of carrot and sugar which, however, seem to be appreciated as rewards of learning by these educated animals quite as keenly as by their untutored kind. It is also
