grass like an ox. And this may properly suggest to our consideration, what is undeniably true, that there is hardly a greater blessing conferred on man than his natural wants. If he had wanted no more than the beasts, who can say how much more than they he would have attained? Does he associate, does he cultivate, does he build, does he navigate? The original impulse to all these lies in his wants. It proceeds from the necessities of his condition, and from the efforts of unsatisfied desire. Every want, not of a low kind, physical as well as moral, which the human breast feels, and which brutes do not feel and cannot feel, raises man by so much in the scale of existence, and is a clear proof and a direct instance of the favor of God toward his so much favored human offspring. If man had been so made as to have desired nothing, he would have wanted almost everything worth possessing.

But doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of man. By the exercise of this, he arrives at the knowledge of the properties of natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the true sublime of human acquisition. If any attainment deserve that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing world against world, and system against system. When we seek to accompany those who pursue their studies, at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat for light had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and proceeding

with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we say of man, in admiration of his physical structure, that "in form and moving he is express and admirable," it is here, and here without irreverence, we may exclaim, "In apprehension how like a god!" The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this, has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.

It has already been said, that the general and well-known agents usually regarded as the principal sources of mechanical powers, are gravity, acting on solid bodies, the fall of water, which is but gravity acting on fluids, air, heat, and animal strength. For the useful direction and application of the first four of these, that is, of all of them which belong to inanimate nature, some intermediate apparatus or contrivance becomes necessary, and this apparatus, whatever its form, is a machine. A machine is an invention for the application of motion, either by changing the direction of the moving power, or by rendering a body in motion capable of communicating a motion greater or less than its own to other bodies, or by enabling it to overcome a power of greater intensity or force than its own. And it is usually said that every machine, however apparently complex, is capable of being resolved into some one or more of those single machines, of which, according to one mode of description, there are six, and according to another three, called the mechanical powers. But because machinery, or all mechanical contrivance, is thus capable of resolution into a few elementary forms, it is not to be inferred that science, or art, or both together, though pressed with the utmost force of hu

man genius, and cultivated by the last degree of human assiduity, will ever exhaust the combinations into which these elementary forms may be thrown. An indefinite, though not an infinite, reach of invention may be expected; but indefinite, also, if not infinite, are the possible combinations of elementary principles. The field, then, is vast and unbounded. We know not to what yet unthought of heights the power of man over the agencies of nature may be carried. We only know that the last half-century has witnessed an amazingly accelerated progress in useful discoveries, and that, at the present moment, science and art are acting together with a new companionship, and with the most happy and striking results. The history of mechanical philosophy is, of itself, a very interesting subject, and will doubtless be treated in this place fully and methodically, by stated lecturers.

It is a part of the history of man, which, like that of his domestic habits and daily occupations, has been too unfrequently the subject of research; having been thrust aside by the more dazzling topics of war and political revolutions. We are not often conducted by historians within the houses or huts of our ancestors, as they were centuries ago, and made acquainted with their domestic utensils and domestic arrangements. We see too little both of the conveniences and inconveniences of their daily and ordinary life. There are, indeed, rich materials for interesting details on these particulars to be collected from the labors of Goguet and Beckmann, Henry and Turner; but still, a thorough and well written history of those inventions in the mechanic arts which are now commonly known, is a desideratum in literature.

Human sagacity, stimulated by human wants, seizes first on the nearest natural assistant. The power of his own arm is an early lesson among the studies of primitive man. This is animal strength; and from this he rises to the conception of employing, for his own use, the strength of other animals. A

stone, impelled by the power of his arm, he finds will produce a greater effect than the arm itself; this is a species of mechanical power. The effect results from a combination of the moving force with the gravity of a heavy body. The limb of a tree is a rude, but powerful instrument; it is a lever. And the mechanical powers being all discovered, like other natural qualities, by induction (I use the word as Bacon used it) or experience, and not by any reasoning a priori, their progress has kept pace with the general civilization and education of nations. The history of mechanical philosophy, while it strongly illustrates in its general results the force of the human mind, exhibits in its details most interesting pictures of ingenuity struggling with the conception of new combinations, and of deep, intense, and powerful thought, stretched to its utmost to find out or deduce the general principle from the indications of particular facts. We are now so far advanced beyond the age when the principal leading, important mathematical discoveries were made, and they have become so much matter of common knowledge, that it is not easy to feel their importance, or be justly sensible what an epoch in the history of science each constituted. The halffrantic exultation of Archimedes, when he had solved the problem respecting the crown of Hiero, was on an occasion and for a cause certainly well allowing very high joy. And so also was the duplication of the cube.

The altar of Apollo, at Athens, was a square block, or cube, and to double it, required the duplication of the cube. This was a process involving an unascertained mathematical principle. It was quite natural, therefore, that it should be a traditional story, that, by way of atoning for some affront to that god, the oracle commanded the Athenians to double his altar; an injunction, we know, which occupied the keen sagacity of the Greek geometricians for more than half a century, before they were able to obey it. It is to the great honor, however, of this inimitable people, the Greeks, a people whose genius

seems to have been equally fitted for the investigations of science and the works of imagination, that the immortal Euclid, centuries before our era, composed his Elements of Geometry; a work which, for two thousand years, has been, and still continues to be, a text-book, for instruction in that science.

A history of mechanical philosophy, however, would not begin with Greece. There is a wonder beyond Greece. Higher up in the annals of mankind, nearer, far nearer, to the origin of our race, out of all reach of letters, beyond the sources of tradition, beyond all history, except what remains in the monuments of her own art, stands Egypt, the mother of nations! Egypt! Thebes! the Labyrinth! the Pyramids! Who shall explain the mysteries which these names suggest? The Pyramids ! Who can inform us whether it was by mere numbers, and patience, and labor, aided perhaps by the simple lever, or if not, by what forgotten combination of powers, by what now unknown machines, mass was thus aggregated to mass, and quarry piled on quarry, till solid granite seemed to cover the earth and reach the skies.

The ancients discovered many things, but they left many things also to be discovered; and this, as a general truth, is what our posterity a thousand years hence will be able to say, doubtless, when we and our generation shall be recorded also among the ancients. For, indeed, God seems to have proposed his material universe as a standing, perpetual study to his intelligent creatures; where, ever learning, they can yet never learn all; and if that material universe shall last till man shall have discovered all that is now unknown, but which by the progressive improvement of his faculties he is capable of knowing, it will remain through a duration beyond human measurement, and beyond human comprehension.

The ancients knew nothing of our present system of arithmetical notation; nothing of algebra, and, of course, nothing