of course, that this dog counted
the exact number of days to know when to start to Guilford, but he
doubtless saw something to remind him of the past.

Sir John Lubbock once related before the British Association at Aberdeen
how cards bearing the ten numerals were arranged before a dog, and the
dog given a problem, such as to state the square root of nine, or of
sixteen, or the sum of two numbers. He would then point at each card in
succession, and the dog would bark when he came to the right one. The
dog never made a mistake. If this was not evidence of a mentality at
least approaching that of men, we do not know what to call it.

If there is any difference between an animal and a human mathematician,
it depends upon special training. The animal never has the same
opportunities to learn as the man. Many savages, for example, cannot
count beyond three or four. Sir John Lubbock gives an anecdote of Mr.
Galton, who compared the arithmetical knowledge of certain savages of
South Africa and a dog. The comparison proved to the advantage of the
dog.

There is no reason that a dog should not be taught arithmetic. And if
one wishes to do so, it might be well to begin by making the dog
distinguish one from two, allowing him to touch both once at the word
one, and twice at the word two. Then he might pass on to six or seven.
After he had progressed to ten, he might begin addition. At least the
experiment would be interesting and conducive to learning the truth.
Surely a knowledge of mathematics is no more wonderful than that of the
ordinary pointer dog's ability to distinguish different kinds of birds.
Certain of those wise dogs are trained to hunt only quail, while others
hunt several varieties of game.

It should be remembered that all degrees of arithmetical aptitude are
found in the human races, from the genius of a Newton and a Laplace to
the absolute inability of certain of the Hottentots to count to three.
These inequalities in the mathematical notions of different people
should make us very cautious about saying that animals cannot count and
have no sense of numbers. It is extremely probable that if we had a way
of choosing those animals with a special gift for arithmetic, they
would surprise us with their learning.

[Illustration: THE COYOTE CAN READILY DISTINGUISH WHETHER A HERD OF
SHEEP IS GUARDED BY ONE OR MORE DOGS, AND WILL PLAN HIS ATTACK
ACCORDINGLY.]

[Illustration: THE ZEBU, THE SACKED BULL OF INDIA, IN