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viii occasional notes, I have pointed out interesting and important geometrical truths, illustrated by the problems.

It is much to be regretted that a large majority of the youth of this country leave school utterly unacquainted with the useful and beautiful truths of algebra and geometry. For them, save a little arithmetic, the noble sciences of the mathematics do not exist. They are sent into the world without that mental training, derived from exercise in the exact definitions, problems, rules of mathematics; without that valuable training of hand and eye, imparted by the careful construction of geometrical figures; unable to work a common question in mensuration; unable to understand a simple algebraic formula; and hence, incapable of comprehending elementary truths in important departments of science and art. They are quite deficient in that early foundation on which to rear an after structure of scientific education or technical knowledge; and, from want of a little rudimentary instruction, are unfit to rise above the lowest grades of work in the mechanical arts.

These radical defects in the education of so many of our youth are owing mainly to four causes:—