been said; but we fail to appreciate the unevoked fund of intellect upon which he has additionally to draw.  The highest 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 without application is, like logic, a soul without a body.