struction and motion of pendulums, are neither few nor unimportant. For the purpose of counteracting the effects produced in the dimensions of the pendulum, by heat and cold, from which disorder and error necessarily arise, the contrivances of ingenious men have been numerous and successful. For the purpose, also, of regulating the curve in which this body shall move, various devices and calculations have been adopted. The principal of these improvements are, the Mercurial Pendulum, invented by GEORGE GRAHAM; the Gridiron Pendulum; that formed with a rod of baked and varmished wood; the contrivances, by means of a flexible rod, and other apparatus, to make the pendulum move in the curve of a cycloid; to say nothing of many other ingenious inventions to regulate the motions and to extend the application of this important instrument.

In that part of philosophy which relates to the structure and motion of machines, many great minds have been employed, in the course of the last age, and not without making some advances in this department of science.-M. AMONTONS, of the Royal Academy of Sciences at Paris, about the beginning of the century, very successfully developed some of the general laws of machinery. After him Mr. EMMERSON, of Great-Britain, a distinguished mathematician, investigated and systematized this subject, with still more practical care and accuracy. In 1735 the celebrated EuLER undertook to give a general and systematic view of machines, in order to found a complete theory, immediately conducive to the improvement of mechanics. In 1743 he published the first part of his theory, containing many new dynamical theorems of great importance. He afterwards

+ Comment. Petropólitani, tom. i.

prosecuted the subject further, and with so much success, as to excite deep regret that he had not continued his useful labours. Since the experiments and publications of EULER, many philosophers of inferior name have turned their attention to the same inquiry; but without laying the scientific world under the same obligations, by exhibiting original, or very interesting views of the subject. Among these it would be improper to pass, without respectful notice, the valuable services rendered to practical mechanics by Mr. SMEATON and Mr. BRAMAH, both of Great-Britain. The instances of the ingenious application of mecha nical principles to the construction of different machines, by which the last century is distinguished, are too numerous, and the authors of many of them too well known, to render a detailed view of them proper in this place.

HYDRAULICS.

In the principles and practice of this part of science great improvements have been made by the philosophers of the last age. To calculate upon sure and accurate grounds, the resistance and motion of dense fluids, so as to furnish a result which might be relied on by engineers, and other mechanics, was considered at the beginning of the century one of the most interesting and difficult problems in mechanical philosophy. NEWTON first endeavoured to reduce the laws of moving fluids to the precise form of mathematical calculation. In this, however, though he displayed great ingenuity, he was unsuccessful. His demonstrations, when tested by practice, were

.

d Comment. Petrop. tom. iii. and Mem. Acad. Berlin, 1747 and 1752.

found inaccurate and inapplicable. GUGLIELMINI, a celebrated Italian, succeeded him, assuming his principles, and aiming to attain the object in view by the same path. He also failed; his calcula tions turning out equally remote, from the truth with those of his illustrious predecessor. After GUGLIELMINI, Professor MICHELOTTI, of Turin, D. BERNOULLI, of Switzerland, and the Abbé BosSUT, of Paris, instituted many experiments, to ascertain the theory or mechanism of hydraulic motion. The last gentleman, in particular, conducted his experiments with great labour, care and perseverance, made a very important publication on the subject, and opened a path of inquiry in this field of science, so new, and in a manner so judicious, that he must always be considered as holding a high rank in the hydraulic history of the age in which he lived. After all, however, he left the subject very imperfectly explored. BosSUT was succeeded by his countryman, the Chevalier BUAT, who took up the inquiry where the Abbé had left it, prosecuted it with singular skill and assiduity, and formed a system much nearer to the truth than all who had gone before him.→→→ But distinguished as the Chevalier has justly ren dered himself, by his achievements in this branch of philosophy, he cannot be said so much to have discovered new principles, as to have classed and systematized, with great skill and ingenuity, the principles flowing from M. D'ALEMBERT'S unwearied experiments and calculations on this subject. Still the Hydraulique of BUAT may be considered the most ingenious, comprehensive and practical work, on the department of science of which it treats, to be found in any language. It furnishes most important information to the engineer; and enables him now to answer, with sufficient precision, many questions, in an

swer to which little but conjecture, and that too often most mischievously wide of the truth, could be offered before. In short, the general proposition, deduced from the Chevalier's numerous facts and experiments, respecting the motion of fluids, has been pronounced one of the most valuable results of modern inquiry.

Much light has been thrown, during the last century, on the doctrine of Tides. NEWTON: Was the first who gave a satisfactory explanation of this subject. But it has been remarked, that the wide steps taken by this philosopher, in his investigation, left ordinary minds frequently at a loss; and that many of his principles require very great mathematical knowledge to satisfy us of their truth. Accordingly the Academy of Sciences at Paris, soon after the death of the illustrious Briton, wishing to have this as well as some other parts of philosophy exhibited in a satisfactory, and, as far as could be, in a popular manner, published a prize question relative to the tides. This produced three excellent dissertations on the subject, by Mr. MACLAURIN, D. BERNOULLI, and EULER. Of these the work of BERNOULLI is considered the best, and is, perhaps, the most complete extant. And it is worthy of observation, that while he threw greater light than all who had gone before him on the subject which he immediately undertook to illustrate, he furnished

• See Encyclopædia. Art. Water Works.

f The Abbé BERNARDIN DE ST. PIERRE, in a late work, entitled Etudes de la Nature, rejects the Newtonian theory of Tides, and ascribes this class of phenomena to the liquefaction of the polar ice and snow. To this amiable writer the praise of ingenuity, and of possessing a happy talent of amusing and interesting his readers, cannot be denied. Neither can it be questioned that his work contains a considerable portion of sound and pleasing philosophy. But surely this and some other of his doctrines are utterly unworthy of a mind which had been conversant with the inquiries and the writings of the great practical philosophers of the eighteenth century.

G

an additional and most powerful argument in support of the Newtonian system.

The construction of Aqueducts has been rendered, by the labours of modern philosophers, more simple, easy, and precise. And, in consequence of these improvements, they have, within the last century, greatly increased in number. For the valuable experiments and discoveries which have been made on this subject, we are principally indebted to the great hydraulie philosophers on the continent of Europe, whose names were before mentioned. To those names may be added the distinguished experimenters and observers, on the same subject, DESAGULIERS, BELIDOR, DE PARCIEUX, and PERRONET, who successively laboured to deduce a system of doctrines from the numerous facts before them; and whose very mistakes, contributed to elucidate this obscure branch of science, which, however, is yet far from being fully understood.

Very great improvements have also been made, during the period in question, in the principles and construction of Water-Mills. The proper mode of adjusting forces, and calculating velocities, in this, as well as in almost every other branch of hydraulics, has long been considered among the most difficult problems in philosophy.-Mr. DESAGULIERS, early in the century, made a number of ex-periments on mills, and suggested some important improvements in their principles and construction. About the same time, M. BELIDOR, of France, M. BERNOULLI, and Mr. EMMERSON, of Britain, employed their great learning and talents on this subject, and made considerable progress in its illustration. These were followed by Mr. LAMBERT, of Berlin, Mr. ELVIUS, of Sweden, Professor KARSTNER, of Gottingen, M. DE PARCIEUX, before mentioned, and Messrs. SMEATON, BAR