PREFACE

xiii

we are now accustomed to use the word art, all things feelable,
 all things which stir our emotions, come under the term
of art, in the sense of the subject-matter of the @sthetic
faculty. So that we are shut up to this—that the business
of education is, in the first place, to provide the young with
the means and the habit of observation ; and, secondly, to
supply the subject-matter of knowledge either in the shape
of science or of art, or of both combined.
Now, it is a very vemarkable fact—but it is true of most
things in this world—that there is hardly anything onesided,
 or of one nature ; and it is not immediately obvious
what of the things that interest us may be vegarded as pure
science, and what may be regarded as puve art. It
may be that theve ave some peculiarly constituted persons
who, before they have advanced far into the depths of
geometry, find artistic beauty about it; but, taking the
generality of mankind, I think it may be said that, when
they begin to learn mathematics, their whole souls ave absorbed
 in tracing the connection between the premisses and
the conclusion, and that to them geometry is puve science.
So I think it may be said that mechanics and osteology are
pure science. On the other hand, melody in music is pure
art. You cannot veason about it ; there is no proposition
involved inil. So, again, in the pictorial art, an arabesque,
or a “harmony in grey,’ touches none but the @sthetic
Jaculty. But a great mathematician, and even many persons
 who are not great mathematicians, will tell you that
they derive immense pleasure from geometrical yeasonings.
Everybody knows mathematicians speak of solutions and
problems as « elegant,” and they tell you that a certain mass
of mystic symbols is * beautiful, quite lovely”. Well, you
do not see it. They do see it, because the intellectual process,
the process of comprehending the reasons symbolized by these
figures and these signs, confers upon them a sort of pleasure,
such as an artist has in visual symmetry. Take a science
of which I may speak with move confidence, and which is