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XXII
HERMANN VON HELMHOLTZ
ance that this borderland should be thoroughly explored, so
that we may not make the mistake of referring anything
which belongs to it to one or the other of the worlds which
it separates. When Helmholtz turned his attention to this
borderland it was not in a wholly uncultivated state; but he
found the richest fields in it lying fallow, and on either
side its limits were badly defined and hidden by a luxuriant
growth of error. He left it carefully defined and well
parcelled out, and much of it had been transformed into a
blooming garden.
His celebrated treatise On the Sensations of Tone is
known to a fairly wide circle of students. That which out-
side ourselves is a mere pulsing of the air becomes within our
minds a joyful harmony. What interests the physicist is the
air-pulsation, what interests the musician and the psychologist
is the harmony. The transition between the two is discovered
in the sensation which connects the definite physical process
with the definite mental process. What is there outside our-
selves which corresponds to the quality of the tones of musical
instruments, of human song, of vowels and consonants? What
corresponds to consonance and dissonance? Upon what does
the æsthetic opposition between the two depend? By what
ideas of order within us were those codes of music, the musical
scales, developed ? Not all the questions which are prompted
by a thirst for knowledge can be answered; but nearly all
the questions which Helmholtz had to leave open thirty years
ago remain unanswered to the present day. In his Physiological
Optics he discusses similar questions relating to sight. How
is it possible for vibrations of the ether to be transformed by
means of our eyes into purely mental processes which
apparently can have nothing in common with the former; and
whose relations nevertheless reflect with the greatest accuracy
the relations of external things? In the formation of mental
conceptions what part is played by the eye itself, by the form
of the images which it produces, by the nature of its colour-
sensations, accommodation, motion of the eyes, by the fact
that we possess two eyes? Is the manifold of these relations
sufficient to portray all conceivable manifolds of the external
world, to justify all manifolds of the internal world?
We see how closely these investigations are connected