and find the point where he can pass a live hedge. This mechanical instinct is exercised spontaneously in him, by virtue of exact theorems of which he has no analytical consciousness, but which he applies with a precision that defies the ingenuity of mathematicians. Force, speed, mass, space, and time are calculated in an equation in which the means are closely adapted to the end, with a marvelous economy of efforts, and by the quickest if not always the shortest way.
In his relations with man, attentive to the will of his master, whose language he has learned to understand, partially at least, the dog comprehends whether he must go or come, run or stop. But he attends less to the phonetics of the words than to the intonations of the voice, the direction of the glance, and the gestures.
The horse knows whether he is to go to the right or left by the energetically pronounced interjections "gee" and "haw," but he measures the extent to which he must veer in either direction by the pull on the bridle, so much as to turn quite round if the pull is at once energetic and quick. If the strees is equal upon both sides, he stops abruptly on his haunches. He learns the language of the stable in a very short time, much less than it takes to train the horseman. But there is no notion of numbers in it, although the horse is very sensitive to musical rhythm.
We can not, at a glance, estimate the number of men in a regiment, but we can calculate it rapidly, when we have noticed the number in a line, the number of lines in a company, and the number of companies. We are still more incapable of distinguishing one hundred points in rows from ninety or one hundred and twenty, without dividing them into tens. But an animal, which has no faculty of numerical abstraction, or of unities of different orders, or of multiplication, would be absolutely incapable of performing this operation. When small numbers of concrete things are in question, however, the aptitude of animals to distinguish these numbers is evident, and is, moreover, indispensable to their existence. A wolf or a boar, which could not perceive how many dogs were attacking it, would not know how to defend itself; but, if it counts them, it is by means of the tactics by which it opposes them, and in which it follows geometrical rules; for if four dogs attack it, two on the right and two on the left, it retreats, facing them, so as not to be between them, but to hold them as much as possible in front and within reach of its tusks. But if the pack is too numerous, the animal becomes wild, loses a clear notion of the number of its adversaries, and bites at hazard the one which presses closest upon it. A man in a similar situation would do much the same.
Birds have at least a vague idea of the number of eggs in
