expectation of results to be witnessed and enjoyed by the approaching
generations involves no postulate of human perfectibility, It finds
ample warrant in what has been accomplished under our eyes. A century
ago only Scotland and two or three of the American colonies could
be said to possess a system of common schools. From those feeble and
smouldering sparks what a flame has spread! The space it has covered
and the fructifying light and warmth it has produced may in some
measure be gauged by the newspaper press and the vast bulk of
popularized information in book-form created since then. This shows
the increase in the numerical ratio of readers to the aggregate of
population.

A difficulty exists in the provision of officers for this great
army of pupils. They cannot always be raised from the ranks. The
thoroughness of a teacher's knowledge is not acquired by the requisite
proportion. Normal schools demand more and more attention. But here we
arrive at a field of detail that would lead us far beyond the limit
of these articles. We pass naturally from the subject of education
to what is, in the narrower but most generally accepted sense of the
word--mental training--- its leading object of pursuit.

If, in the broader and truer meaning of education--that which assumes
the impalpable part of man to be something more than a sponge for
facts--- the slender phalanx of _the men who know_ will ever
remain, proportionally, a small band, it is at least certain that in
acquaintance with natural phenomena and their relations the masses
of the nineteenth century stand out from their forefathers as eminent
philosophers. Our age may be almost said to have created rather than
extended science, so mighty is the bulk of what it has added by the
side of what it found.

In mathematics, the branch which most nearly approaches pure reason,
least advance has been made. There was least room for it. Newton,
when, at quite a mature period of his career, Euclid was first brought
to his attention, laid the book down after a cursory glance with
the remark that it was only fit for children, its propositions being
self-evident. Yet to those truisms Newton added very little. His work
lay in their development and application. Laplace and Biot belong to
our own day; but their task, too, consisted in the employment of old
rules. The most effective tools of the mathematician are framed from
the Arab algebra and Napier's logarithms. The science itself