of such exhibitions appeared furthermore, to depend
upon the close proximity of the trainer and the dog, whereas the
direction of the head (and even of the body) could very probably be
perceived at greater distances also. At least we learn from a reputable
source that in the hunt, dogs can perceive from the mere posture of
their master, what direction he intends to take.[58]

But a still more curious fact is this, that dogs, too, learn--evidently
spontaneously--to react to the minimal involuntary expressive movements
of their master. The first example mentioned in the literature on the
subject is that of an English bull-dog called Kepler, belonging to the
English astrophysicist, Sir William Huggins.[59] We are told that this
dog seemingly could solve the most difficult problems, such as
extracting square roots and the like. The numbers were indicated by
barking,--thus one bark was for one, two barks for two, etc. Every
correct solution was rewarded with a piece of cake. Huggins states
explicitly that he gave no signals voluntarily, but that he was
convinced that the dog could see from the questioner's face, when he
must cease barking, for he would never for an instant divert his gaze
during the process. Huggins was unable, however, to discover the nature
of the effective signs. This satisfactory, though still unproven,
explanation has been accepted by specialists, among them Sir John
Lubbock.[60] I, too, regard this dog as a predecessor of our Hans.

A similar case is reported by Mr. Hugo Kretschmer, a writer of Breslau,
in the "Schlesische Zeitung" of August 21, 1904. To him I am beholden
for a detailed written statement, which he has kindly permitted me to
use in this connection. The gentleman named, first trained his dog to
ring the table-bell, and this, by pressing the dog's paw upon the
bell-button. When the dog had learned to do this independently, his
master tried to teach him the rudiments of numbers, in such a way that
the animal was to give one ring of the bell for the number 1, two for 2,
etc. But these attempts failed utterly and had to be abandoned. But Mr.
Kretschmer had noticed that he was able to get the dog to ring any
number which he, Mr. Kretchmer, might decide upon. (Success was always
rewarded by a bit of bread and butter.) At first Mr. Kretschmer tried to
imagine vividly only the final number, but failed thereby to elicit
correct responses from the dog. But he did succeed when he tried making
a se