have not seen them, I am not guilty of any undue appropriation, and no injury can be done to the cause I wish to promote, by detailing again such beautiful and admirable contrivances.'- -p. 291-293.

We again most strongly recommend this little unpretending volume to the attention of every lover of nature, and more particularly of our country readers. It will induce them, we are sure, to examine more closely than they have been accustomed to do, into the objects of animated nature, and such examination will prove one of the most innocent and the most satisfactory sources of gratification and amusement. The knowledge thus to be obtained will elevate their minds from the creature to the Creator, and enable them with heart-felt rapture to exclaim with our sublime poet,

These are thy glorious works, Parent of Good,

Almighty! Thine this universal frame

Thus wondrous fair!

The enjoyment and satisfaction which our author has through life derived from these sources, are thus stated in his closing paragraph, with which we must also conclude.

'And now I think I have pretty well run over my diary, the humble record of the birds, the reptiles, the plants, and inanimate things around me. They who have had the patience to read these my notes, will probably be surprised that I could take the trouble to register such accounts of such things; and I might think so too, did I not know how much occupation and healthful recreation the seeking out these trifles have afforded me, rendering, besides, all my rural rambles full of enjoyment and interest: companions and intimates were found in every hedge, on every bank, whose connexions I knew something of, and whose individual habits had become familiar by association; and thus this narrative of my contemporaries was formed. Few of us perhaps, in reviewing our by-gone days, could the hours return again, but would wish many of them differently disposed of, and more profitably employed: but I gratefully say, that portion of my own passed in the contémplation of the works of nature is the part which I most approve; which has been most conducive to my happiness; and, perhaps from the sensations excited by the wisdom and benevolence perceived, not wholly unprofitable to a final state. . If, in my

profound ignorance, I received such gratification and pleasure,-what would have been my enjoyment and satisfaction, "if the secrets of the Most High had been with me, and by His light I had walked through darkness"?'-p. 395.

VOL. XXXIX. NO, LXXVIII.

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ART. VI.-An Elementary Treatise of Mechanical Philosophy, written for the Use of the Undergraduate Students of the University of Dublin. By Bartholomew Lloyd, D.D., Professor of Natural Philosophy in the University. 2 vols. Dublin. 1828. IT T is a fact deserving of notice, and one which may tend to throw some light on the rise and progress of invention, that the ancients had made considerable advances in practical mechanics, long before they were acquainted with the theoretic principles of the instruments they employed. Vitruvius describes many which had been in use for a considerable time before he wrote, some of which are those in common use at the present day. But although the necessities of life had led to the invention of engines destined to aid the strength of man, a long time elapsed before mechanical philosophy assumed the attitude of a sciArchimedes was the first who attempted an explanation of the laws of equilibrium in machines. In his work, De Æquiponderantibus, he demonstrates the theory of the lever by a process of reasoning which, from its simplicity and strictness, has been deemed worthy of a place in elementary works of the present day. Thus was laid the foundation of the doctrine of statics. Observing that the pressure on the point of support in the lever was the same as if the two weights had been immediately applied there, he was led to the composition of parallel forces, and thereby to establish the existence of a point in every body or system of bodies, which may be considered as the point of application of the weights of its several parts. This point is now well known by the name of the centre of gravity.

But it is not by such discoveries as these only that we are to estimate the advances made by Archimedes in the hitherto unexplored regions of mechanical philosophy. He, moreover, displayed the resources of a powerful mind, in combining these simple instruments, and thereby forming compound machines of wonderful power and efficacy, but of which, at the present day, we know nothing, except their almost miraculous effects, as described by Plutarch, in his account of the siege of Syracuse. These applications of science, however, were far less prized by their author than the abstract speculations of geometry; a science which received from his hands a greater impulse than it has owed to any other individual, from its origin to the present day. To this great man we are, moreover, indebted for the discovery of the fundamental laws of the equilibrium of fluids. The treatise in which his researches on this subject have come down

*This work has reached us only in the Latin translation, entitled De Humido Insidentibus.

to

to us, and in which he considers the conditions of equilibrium of a solid body floating on a liquid, is built upon the principle adopted at present as the basis of hydrostatical science; namely, that each particle of a fluid mass in equilibrio is pressed equally in all directions. The solution of the famous problem of the crown, proposed by the king of Syracuse, is generally supposed by mathematicians to have been derived by him from the following proposition, contained in this treatise ;-that two bodies equal in volume suffer equal losses of weight when immersed in the same fluid, both being heavier than the fluid in which they are immersed.' The hydraulic machine, known by the name of Archimedes' screw, is said to have been discovered by him (according to Diodorus Siculus) during his travels in Egypt; and to have been employed for the purpose of carrying off the waters, after the inundations of the Nile. But Vitruvius, a contemporary of Diodorus, has not mentioned this among his discoveries.

From the time of Archimedes, a long period elapsed, during which little advance was made in mechanical philosophy. Ctesibius and Hero, mathematicians of Alexandria, who lived about 120 years before the Christian era, and Pappus Alexandrinus, in the fourth century, pursued the inquiries of Archimedes connected with the equilibrium of machines; and the two former were the first who analysed their various combinations, and reduced them to five simple elements, which they called duvaμeis, or Powers, a name which they have retained to the present day. Still, however, the theory of the mechanic powers remained imperfect, the successors of Archimedes finding themselves unable to determine the laws of their equilibrium, except in those cases only which can be readily reduced to the principle of the lever. Thus, though the basis of the fabric was somewhat polished and reduced to symmetry, little was added to the superstructure, and the science of mechanics made no acquisition of any importance until the close of the sixteenth century.

Stevinus, a Flemish engineer, appears to have been the first who demonstrated the conditions of equilibrium of a body resting on an inclined plane. His solution of this important problem appeared in the year 1585. From the theory of the inclined plane, he deduced the general conditions of equilibrium among three forces acting on a point; and proved that these forces, when in equilibrio, are proportional to the sides of a triangle drawn parallel to their directions. He did not seem, however, to have felt the importance or fruitfulness of this principle, which he rather inferred as a corollary, than demonstrated as a fundamental truth.

The science of hydrostatics is also indebted to Stevin for some important additions. He was the first to show that the pressure

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of

of a fluid on the bottom of any vessel is altogether independent of its figure, and proportional to the product of the area of the base by the perpendicular height of the fluid.

The name of Galileo is the next which offers itself to our view, in contemplating the progress of physical science. This celebrated philosopher was born at Pisa, in the year 1564, and devoted himself, at an early age, to the study of mathematics and natural philosophy. In the year 1592, he published a short treatise, entitled Della Scienza Mecanica, which he reduced to a single principle; namely, that equal forces are required to raise two weights to heights reciprocally proportional to those weights; from which it was easy to conclude that, in all machines in equilibrio, the power and the resistance are reciprocally proportional to the spaces which they tend to describe in the same time. This principle (it is obvious) is a limited case of the principle of virtual velocities, which was afterwards employed as the basis of the whole doctrine of equilibrium. But the fame of this author, and the benefits which he has conferred on mechanical science, do not rest here. Before his time, scarce anything was known of the second great division of mechanical philosophy, the theory of motion. The notions of the ancients on this subject were confused and absurd in the extreme. What, indeed, could be expected from the investigations of the disciples of Aristotle, who assumed, as the point d'appui of their reasonings on this head, the celebrated definition of motion given by their master: the act of a being in power, so far forth as in power'? But we need not go so far back as the age of the Stagyrite for evidence of the ignorance which prevailed upon this branch of natural philosophy. The knowledge of the fundamental laws by which motion is governed was the result of a much later period and more matured philosophy; and while these remained unknown, no advance could be made in the doctrine of motion. So far from holding that there was an universal tendency in body to preserve its state of rest or uniform rectilineal motion, the predecessors of Galileo believed that all terrestrial bodies has a natural tendency to fall to the earth, or ascend from it until they reached their former position; while they endued the celestial bodies with the distinct and far different disposition to revolve in circular orbits. It would not be difficult to trace the ignorance of the ancients on these fundamental facts to their unacquaintance with the spirit of the inductive philosophy. The laws of motion have no necessary connexion with axiomatic truth, and are not, therefore, to be attained by any process of à priori reasoning, however refined. They are but the general expression of facts, which can be arrived at only by an attentive examination of the phenomena which nature presents to our view, and a scrupulous generalization of their laws.

It

It is somewhat remarkable that, although in the investigations of Galileo on the subject of motion, the inertia of matter, or the indisposition of body to alter its state of rest or uniform rectilineal motion, is tacitly assumed throughout, yet this 'fundamental principle is nowhere formally stated in the writings of this philosopher. The first distinct enunciation of the laws of motion is found in the writings of Descartes. The French philosopher, however, regards the inertia of matter as a real force inherent in bodies, and exerted by them in order to preserve their state; and this erroneous view of the first law of motion has led him into some inaccuracies in its application. Many years elapsed before the second law of motion, which states the proportionality of the force to the motion produced, was universally received as a law of nature. Leibnitz was the first to dispute the truth of the Cartesian law, and to assign a different measure of force, which he estimated by the square of the velocity produced, and thus gave rise to a controversy the most remarkable that the history of demonstrative science affords. Among the disputants on either side were ranged the most illustrious mathematicians which Europe then produced. The writers of Germany, Italy, and Holland, declared for the Leibnitzian measure of force; those of England supported the old doctrine; while the mathematical strength of France was divided between the two opinions. Voltaire engaged in the controversy, and in a Memoir presented to the Academy of Sciences in 1741, ably contended that the dispute was merely verbal. In the list of the disputants, we find, too, the name of Madame de Châtelet, a name which the excellent translations and commentary on the Principia of Newton, by this distinguished authoress, will always preserve from oblivion.

But to return to the period from which we have been insensibly led. The science of dynamics, it has been already observed, remained altogether unexplored until the time of Galileo; and it is to the judicious combination of experiment and mathematical reasoning, adopted by this philosopher, that we are to attribute its birth. At the early age of nineteen, while engaged in his studies at the University, he began his experiments on falling bodies, and soon discovered that all bodies descend from the same height in the same time, if the resistance of the air be abstracted; and by observing the vibration of the lamps in the Cathedral of Pisa, he was led to the important discovery of the isochronism of the pendulum. Setting out from this principle of the equal acceleration of heavy bodies, he deduced, by mathematical reasoning, the general laws of motion uniformly accelerated, and applied them to the motion of bodies falling freely by the force of gravity, and to the descent on inclined planes; and having found the

results