BOOK II.

CHAPTER I.

PROGRESS OF ASTRONOMY.

308. THE science of astronomy was cultivated very early, and many important observations and discoveries were made, yet no accurate inferences leading to the true system of the world were drawn from them, until a much later period. It is not surprising, that men deceived by appearances, occasioned by the rotation of the earth, should have been slow to believe the diurnal motion of the heavens to be an illusion; but the absurd consequence which the contrary hypothesis involves, convinced minds of a higher order, that the apparent could not be the true system of nature.

Many of the ancients were aware of the double motion of the earth; a system which Copernicus adopted, and confirmed by the comparison of a series of observations, that had been accumulating for ages; from these he inferred that the precession of the equinoxes might be attributed to a motion in the earth's axis. He ascertained the revolution of the planets round the sun, and determined the dimensions of their orbits, till then unknown. Although he proved these truths by evidence which has ultimately dissipated the erroneous theories resulting from the illusions of the senses, and overcame the objections which were opposed to them by ignorance of the laws of mechanics, this great philosopher, constrained by the prejudices of the times, only dared to publish the truths he had discovered, under the less objectionable name of hypotheses.

In the seventeenth century, Galileo, assisted by the discovery of the telescope, was the first who saw the magnificent system of Jupiter's satellites, which furnished a new analogy between the planets and the earth: he discovered the phases of Venus, by which he removed all doubts of the revolution of that planet round the sun. The bright spots which he saw in the moon beyond the line which separates the enlightened from the obscure part, showed the existence and height

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of its mountains. He observed the spots and rotation of the sun, and the singular appearances exhibited by the rings of Saturn; by which discoveries the rotation of the earth was confirmed: but if the rapid progress of mathematical science had not concurred to establish this essential truth, it would have been overwhelmed and stifled by fanatical zeal. The opinions of Galileo were denounced as heretical by the Inquisition, and he was ordered by the Church of Rome to retract them. At a late period he ventured to promulgate his discoveries, but in a different form, vindicating the system of Copernicus; but such was the force of superstition and prejudice, that he, who was alike an honour to his country, and to the human race, was again subjected to the mortification of being obliged to disavow what his transcendent genius had proved to be true. He died at Arcetri in the year 1642, the year in which Newton was born, carrying with him, says La Place, the regret of Europe, enlightened by his labours, and indignant at the judgment pronounced against him by an odious tribunal.

The truths discovered by Galileo could not fail to mortify the vanity of those who saw the earth, which they conceived to be the centre and primary object of creation, reduced to the rate of but a small planet in a system, which, however vast it may seem, forms but a point in the scale of the universe.

The force of reason by degrees made its way, and persecution ceased to be the consequence of stating physical truths, though many difficulties remained to impede its progress, and no ordinary share of moral courage was required to declare it: 'prejudice,' says an eminent author, 'bars up the gate of knowledge; but he who would learn, must despise the timidity that shrinks from wisdom, he must hate the tyranny of opinion that condemns its pursuit: wisdom is only to be obtained by the bold; prejudices must first be overcome, we must learn to scorn names, defy idle fears, and use the powers of nature to give us the mastery of nature. There are virtues in plants, in metals, even in woods, that to seek alarms the feeble, but to possess constitutes the mighty.'

About the end of the sixteenth, or the beginning of the seventeenth century, Tycho Brahe made a series of correct and numerous observations on the motion of the planets, which laid the foundation of the laws discovered by his pupil and assistant, Kepler,

Tycho Brahe, however, would not admit of the motion of the earth, because he could not conceive how a body detached from it could follow its motion: he was convinced that the earth was at rest, because a heavy body, falling from a great height, falls nearly at the foot of the vertical.

Kepler, one of those extraordinary men, who appear from time to time, to bring to light the great laws of nature, adopted sounder views. A lively imagination, which disposed him eagerly to search for first causes, tempered by a severity of judgment that made him dread being deceived, formed a character peculiarly fitted to investigate the unknown regions of science, and conducted him to the discovery of three of the most important laws in astronomy.

He directed his attention to the motions of Mars, whose orbit is one of the most eccentric in the planetary system, and as it approaches very near the earth in its oppositions, the inequalities of its motions are considerable; circumstances peculiarly favourable for the determination of their laws.

He found the orbit of Mars to be an ellipse, having the sun in one of its foci; and that the motion of the planet is such, that the radius vector drawn from its centre to the centre of the sun, describes equal areas in equal times. He extended these results to all the planets, and in the year 1626, published the Rudolphine Tables, memorable in the annals of astronomy, from being the first that were formed on the true laws of nature.

Kepler imagined that something corresponding to certain mysterious analogies, supposed by the Pythagoreans to exist in the laws of nature, might also be discovered between the mean distances of the planets, and their revolutions round the sun: after sixteen years spent in unavailing attempts, he at length found that the squares of the times of their sidereal revolutions are proportional to the cubes of the greater axes of their orbits; a very important law, which was afterwards found equally applicable to all the systems of the satellites. It was obvious to the comprehensive mind of Kepler, that motions so regular could only arise from some universal principle pervading the whole system. In his work De Stella Martis, he observes, that ' two insulated bodies would move towards one another like two magnets, describing spaces reciprocally as their masses. If the earth and moon were not held at the distance that separates them by some of the

force, they would come in contact, the moon describing distance, and the earth the remainder, supposing them to be equally dense.' ' If,' he continues, 'the earth ceased to attract the waters of the ocean, they would go to the moon by the attractive force of that body. The attraction of the moon, which extends to the earth, is the cause of the ebb and flow of the sea.' Thus Kepler's work, De Stella Martis, contains the first idea of a principle which Newton and his successors have fully developed.

The discoveries of Galileo on falling bodies, those of Huygens on Evolutes, and the centrifugal force, led to the theory of motion in curves. Kepler had determined the curves in which the planets move, and Hook was aware that planetary motion is the result of a force of projection combined with the attractive force of the sun.

Such was the state of astronomy when Newton, by his grand and comprehensive views, combined the whole, and connected the most distant parts of the solar system by one universal principle.

Having observed that the force of gravitation on the summits of the highest mountains is nearly the same as on the surface of the earth, Newton inferred, that its influence extended to the moon, and, combining with her force of projection, causes that satellite to describe an elliptical orbit round the earth. In order to verify this conjecture, it was necessary to know the law of the diminution of gravitation. Newton considered, that if terrestrial gravitation retained the moon in her orbit, the planets must be retained in theirs by their gravitation to the sun; and he proved this to be the case, by showing the areas to be proportional to the times: but it resulted from the constant ratio found by Kepler between the squares of the times of revolutions of the planets, and the cubes of the greater axes of their orbits, that their centrifugal force, and consequently their tendency to the sun, diminishes in the ratio of the squares of their distances from his centre. Thus the law of diminution was proved with regard to the planets, which led Newton to conjecture, that the same law of diminution takes place in terrestrial gravitation.

He extended the laws deduced by Galileo from his experiments on bodies falling at the surface of the earth, to the moon; and on these principles determined the space she would move through in a second of time, in her descent towards the earth, if acted upon by the earth's attraction alone. He had the satisfaction to find that the action of the earth on the moon is inversely as the square of the distance, thus proving the force which causes a stone to fall at the earth's surface, to be identical with that which retains the moon in her orbit.

Kepler having established the point that the planets move in ellipses, having the sun in one of their foci, Newton completed his theory, by showing that a projectile might move in any of the conic sections, if acted on by a force directed to the focus, and inversely as the square of the distance: he determined the conditions requisite to make the trajectory a circle, an ellipse, a parabola, or hyperbola. Hence he also concluded, that comets move round the sun by the same laws as the planets.

A comparison of the magnitude of the orbits of the satellites and the periods of their revolutions, with the same quantities relatively to the planets, made known to him the respective masses and densities of the sun and of planets accompanied by satellites, and the intensity of gravitation at their surfaces. He observed, that the satellites move round their planets nearly as they would have done, had the planets been at rest, whence he concluded that all these bodies obey the same law of gravitation towards the sun: he also concluded, from the equality of action and re-action, that the sun gravitates towards the planets, and the planets towards their satellites; and that the earth is attracted by all bodies which gravitate towards it. He afterwards extended this law to all the particles of matter, thus establishing the general principle, that each particle of matter attracts all other particles directly as its mass, and inversely as the square of its

distance.

These splendid discoveries were published by Newton in his Principia, a work which has been the admiration of mankind, and which will continue to be so while science is cultivated.

Referring to that stupendous effort of human genius, La Place, who perhaps only yields to Newton in priority of time, thus expresses himself in a letter to the writer of these pages:

'Je publie successivement les divers livres du cinquième volume qui doit terminer mon traité de Mécanique Céleste, et dans lequel je donne l'analyse historique des recherches des géomètres sur cette matière. Cela m'a fait relire avec une attention particulière l'ouvrage incomparable des Principes Mathématiques de la philosophie naturelle de Newton, qui contient le germe de toutes ces recherches. Plus