traced out in the very order and succession of creation. Science is itself but a development of the laws of creation, so far as man has been able to discover and develop them. Creation is its cradle, and every new discovery but a new testimony to the order, beauty, and harmony which dwell forever in the works of God.

This deduction of science from the order and system of the universe, as exhibited to man, by the right use of reason, proves clearly for what end and purpose it is to be used in education. We have first the strengthening of reason by this exercise of its powers. Next we have the recognition of order and method, in the pursuit of any design, or object, as it is illustrated in all the works of creation. Next we have the knowledge of fixed, eternal truth, as the basis of all created things. Then we have demonstrated the superior power of the spirit, by its faculty of abstraction, in taking the principles or laws from the material objects and laying them before the mind in an independent condition. Finally, we find the higher power of creating a language of signs, which shall express their relations, and convey them from mind to mind, in a state of abstraction and independence. Thus we have the science of physics, the science of metaphysics, and the science of a logic in language and signs, which expresses, explains, and connects, and communicates the laws deduced from the system of creation.*

* The recent work of Professor Davies, on the "Logic of Mathematics," supplies a desideratum, which has long existed, in reference

The IDEA of SCIENCE, then, is, in its general and complete sense, the idea of the constitution; properties and laws of all created things, whether of matter or mind, as developed and expressed from the works of creation by the reason of man. There are three corollaries consequent upon this idea of science: 1st, That it is the best exercise to improve the reason to the highest point. 2dly, That as the works of God are found to be perfect, this development of them gives the most complete idea we can have of form, order, beauty, and harmony. 3dly, That as the works of creation are exhaustless, and the spirit of man immortal, science affords an exhaustless field for the investigations, the improvement, the strengthening, and enlargement of the human mind. For science is not, in this idea of it, limited to the science of matter, nor to the science of mind, nor to the discoveries of man, independent of Revelation. In one word, it is true science, and not science "falsely so called," that I have here defined. It is that law, of which Hooker said, "No less can be acknowledged than that her seat is the bosom of God; her voice the harmony of the world."

to the connection of the physical and metaphysical sciences. That work is, so far as I know, original; and it will be found as useful as it is novel. The connections of the various branches of physical science, and of the whole with metaphysics and logic, constitute now an open field of inquiry.

CHAPTER VI.

THE UTILITY OF MATHEMATICS.

"I have mentioned mathematics as a way to settle in the mind an habit of reasoning closely, and in train; not that I think it necessary that all men should be deep mathematicians, but that having got the way of reasoning, which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they have occasion."-Locke on the Human Understanding.

To the scholar and lover of knowledge, the sciences are a harmonious brotherhood; a golden circle, which he would fracture with scarcely less reluctance than he would pluck from the heavenly system one of its glorious planets. He may look upon another with a longer and steadier gaze, or to him another light may be purer and brighter; but he will recollect that the illumination of the mind, like that of the firmament, is made up of many lights, each shining in its own sphere, and each, as it rolls on, casting its rays over that intellectual pathway in which he moves to his immortal destiny.

While, however, each one of the sciences may thus claim its own excellence and its peculiar prerogatives, I shall consider only those which, in a direct way, strengthen the reasoning powers, or aid the manifestation and development of the human mind in a very remarkable manner.

Mathematics belong to this class, and have, at all

times, constituted a portion of a liberal education. Indeed, arithmetic, a very important branch of mathematics, is so necessary to the business calculations of the world, as never to be omitted in any course of instruction, however slight. This, therefore, no theorist, wild as he may be, will ever neglect. But all the elementary parts of mathematics are equally useful, as a means of education, though not as universally necessary to the wants of mankind. And I lay it down as a fundamental principle, that this science is so accessory to the received methods of human reasoning; is the foundation of so many arts and sciences, and so interwoven with the various operations of society, that its study cannot be wholly omitted in the schools, without destroying nearly all that is solid and valuable in education.

Indeed, I cannot conceive of any such thing as an education, in a fair sense, without mathematics. Words, literature, and a certain species of metaphysics, may be acquired without any direct study of mathematics; but how can any accurate ideas of any thing in nature be obtained without just notions of form, measure, magnitude, and quantity?

What are the objects of intellectual education? I suppose them to be twofold: First, the discipline of the mind. Second, the attainment of such knowledge as may be of practical use in after life.

I shall now proceed to ascertain the real value of mathematics as a means of education, comparing its uses and results in reference to human improvement.

THE KINDS OF MATHEMATICS.

Mathematics, in its extended sense, comprehends more than that of which we now speak. It is both pure and applied: pure, as respects its elementary branches―algebra, geometry, etc.; applied, as regards those sciences, mechanical philosophy, astronomy, and others dependent upon the former. The pure mathematics are commonly understood by that term, and in this sense I now understand it.

To improve the reason, as well as the heart, is the peculiar care of that branch of education whose object is the discipline of the mind. To do this, indeed, and to secure the ultimate object of that improvement, happiness was the end of those various systems of philosophy, which, under glorious names and beautiful forms, have from time to time fastened the attention of mankind. But those systems have successively sunk; the reason of verbal philosophy has crumbled to pieces, while that of demonstration, based upon experiment, has strengthened and increased; and with it knowledge has enlarged its bounds, as the successive circles in the water increase from the centre of motion.

To measure the influence of mathematics as an intellectual power in producing these results, would be to analyze the whole machinery of civilized society. But without doing that, we may yet go far enough into mental history to prove this science, either as a part of education or of knowledge, the most power