and the carpenter
who are employed on odd jobs employ it no less for their work than
the mechanician, the engineer, and the architect. The lady's maid
who arranges a new dress requires it for the same reason as the
decorator employed on a palace, or the agent who lays out great
estates. Strategists, artists of all denominations, physicists who
contrive new experiments, and in short all who do not follow routine,
have need of it. The pleasure its use can afford is immense. I have
many correspondents who say that the delight of recalling beautiful
scenery and great works of art is the highest that they know; they
carry whole picture galleries in their minds. Our bookish and wordy
education tends to repress this valuable gift of nature. A faculty
that is of importance in all technical and artistic occupations,
that gives accuracy to our perceptions, and justness to our
generalisations, is starved by lazy disuse, instead of being
cultivated judiciously in such a way as will on the whole bring the
best return. I believe that a serious study of the best method of
developing and utilising this faculty, without prejudice to the
practice of abstract thought in symbols, is one of the many pressing
desiderata in the yet unformed science of education.

NUMBER-FORMS.

Persons who are imaginative almost invariably think of _numerals_ in
some form of visual imagery. If the idea of _six_ occurs to them,
the word "six" does not sound in their mental ear, but the figure 6
in a written or printed form rises before their mental eye. The
clearness of the images of numerals, and the number of them that can
be mentally viewed at the same time, differs greatly in different
persons. The most common case is to see only two or three figures at
once, and in a position too vague to admit of definition. There are
a few persons in whom the visualising faculty is so low that they
can mentally see neither numerals nor anything else; and again there
are a few in whom it is so high as to give rise to hallucinations.
Those who are able to visualise a numeral with a distinctness
comparable to reality, and to behold it as if it were before their
eyes, and not in some sort of dreamland, will define the direction in
which it seems to lie, and the distance at which it appears to be.
If they were looking at a ship on the horizon at the moment that the
figure 6 happened to present itself to their minds, they could say
whether the image lay to the left