254 THE POPULAR SCIENCE MONTHLY. 



and find the point where lie can pass a live hedge. This mechani- 

 cal 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 mathema- 

 ticians. 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 in- 

 tonations of the voice, the direction of the glance, and the gest- 

 ures. 



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 lan- 

 guage 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 regi- 

 ment, but we can calculate it rapidly, when we have noticed the 

 number in a line, the number of lines in a company, and the num- 

 ber 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 per- 

 forming 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 



