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the piles for the foundation of a bridge, in boring cannon of the largest calibre, raising the ponderous anchor from the bottom of the ocean, working the complicated steam engine with the greatest effect, or investigating the motions of the celestial bodies.

II. Pneumatics relates to the nature and properties of the air of this thin, compressible, dilatable and transparent fluid, few properties are known without the assistance of mechanics and geometry. Its elastic force, pressure, and weight have been discovered by experiments. The knowledge of these properties has led to many others equally surprising and useful, such as the gradual decrease of the density of the air in proportion to the distance from the surface of the earth, its various kinds, its essential service in the support of life, and the altitude of the atmosphere, which surrounds the globe.

III. The science of Hydrostatics, in its most extensive sense, teaches the pressure, equilibrium, and motion of fluids. To it belongs whatever relates to the resistance of fluids, with the art of weighing bodies, such as metals, minerals, &c. in water, in order to ascertain their specific gravity. It is of great use to mankind in the arts of life. To the sciences of pneumatics and hydrostatics we owe the pump, the fire engine, canals, aqueducts, &c.

IV. Optics is that science which treats of the nature and properties of light, and the various phenomena of vision. It is divided into catoptrics and dioptrics; the former of which treats of reflected, and the latter of refracted light; and they combine to instruct mankind in the management of this subtile fluid for the useful purposes of life. Upon the principles of optics are formed those

glasses, which assist the short-sighted, and remedy the infirmity of age, with respect to vision. This useful branch of science likewise supplies the defects of the naked eye, by the application of microscopes to examine the most minute, and of telescopes to survey the most distant bodies.

V. Of all the sciences, to which geometry imparts the solidity of its principles, and the clearness of its proofs the most beautiful and the most sublime is astronomy. This is perhaps the most exact and most definite part of natural philosophy; for it rectifies the errors of sight, with respect to the apparent motions of the planets: explains the just dimensions, relative distances, due order, and exact proportions of the spherical bodies, which compose the solar system. Nor is it even confined to these great objects of nature, since it opens the stupendous prospect of other suns, and other systems of planets, scattered over the boundless regions of space, and moving in obedience to their respective laws. It marks out their particular places, assigns their various names, and classes all the systems of worlds in their respective constellations. The calculations of astronomy prove the certainty of the future phenomena of the heavenly bodies; the various phases of the moon; the places of the planets; the point of time when the sun and moon will be immersed in the partial, or the total darkness of an eclipse. These sublime truths are established upon such evidence, and the calculations upon which they proceed are marked with such accuracy, as incontestably to prove the solid basis upon which this most wonderful of the sciences is founded.

Navigation, which depends entirely for the certainty of its principles upon astronomy and geometry, is so noble an art, to which mankind owe so many advan

tages, that on this account these sciences ought to be particularly studied, and merit the greatest encouragement, especially in a nation indebted to it for its riches security, and glory. And not only does the ordinary art of navigation in the direction of the course of vessels depend upon mathematics, but whatever improvements are made in ship building.

Mathematical studies have been held in honour, and cultivated with diligence, wherever polite learning has flourished. The remaining works of Archimedes attest the profundity of his genius; and the wonderful and destructive effects related of his burning glasses, when Syracuse was besieged by the Romans, are confirmed by modern experiments. By the Grecian philosophers in general these studies were regarded as forming an essential part of a liberal education. They were taught to the eminent scholars of Pythagoras. Plato allayed the warmth of a poetical fancy by these pursuits, and denied admittance into his school to those who were not conversant with geometry. He earnestly recommended arithmetic, geometry, and astronomy as excellent preparatives to all other studies, and as more immediately useful to those who were intended for the public offices of the state. Aristotle illustrated the rules of his logic and the precepts of his ethics by arithmetical and geometrical proportions. At the time when the elegant arts were gaining ground in Rome, Cæsar found his most agreeable relaxation from the tumults of war, and the business of a camp, in reforming the callendar, and tracing amid the stillness of the night the courses of the planets, as they revolved in the clear hemispheres of Egypt and Gaul. The decline of science marked the continuance of the dark ages; during

which theology consisted in absurd dogmas and gross superstition, and confused and unintelligible systems dishonoured the name of philosophy*.

CHAPTER III.

THE SUBJECT CONTINUED.

THE detail of those who, in modern times, have followed mathematical studies with ardour, and united useful discoveries to scientific researches, constitutes the history of some of the greatest efforts of the human mind.

Nicholas Copernicus was born at Thorn, a city of Prussia, in 1473. Dissatisfied with the reigning system of Ptolemy, who placed the earth in the centre of the universe, he revived the very ancient opinion which had been taught by Pythagoras nineteen centuries before in the schools of Magna Græcia. He derived his information respecting the astronomical doctrines of the great philosopher of Samos from the academical questions of Cicero, and the works of Plutarch, as he acknowledged in the dedication of his works to Pope Paul the third. Copernicus maintained that the sun was placed in the centre of the universe, and that Mercury, Venus, the Earth, Mars, Jupiter, and Saturn

The preceding account of mathematics is very concise and defective. The reader must examine the best mathematical books in the list at the end of this volume.

revolving each upon its axis, move round the sun from west to east. The different revolutions of these six planets are proportioned to their respective distances from the sun, and the circles which they describe cut the ecliptic in different points.* The earth completes its revolution in the space of a year, in a circle which includes the orbit of Venus, and is included by the orbit of Mars. It has another revolution upon its axis in twenty- -four hours, and by this movement the distinctions of day and night are produced. The moon, an inferior planet, attendant on the earth, moves round it in an elliptic orbit, and revolves upon her own axis exactly in the time she goes round the earth. The heavens which form the spacious fields of ether are immoveable, and the stars are fixed in them at an immense distance from the sunf.—Such is the Copernican system, the glory of modern philosophy, and the basis of the subsequent observations of astronomers.

Kepler, born at Weil, in Saxony, in 1571, was the friend of Tycho Brahe, and the associate of his astronomical studies. He has rendered his name illustrious in the annals of science by developing the laws which regulate the motions of the planets. Assisted by the observations of the Danish philosopher, he made the following discoveries. I. That the six primary planets move round the sun not in circles, but in ellipses, having the sun in one of the foci. II. That the planets describe round the sun equal areas in equal times. III. That the squares of the periodical times, in which the planets revolve round the sun, are, as the cubes of their mean distances from him. This discovery is

* The planets revolve 1ound the sun in elliptical orbits or paths.

+ This is erroneous