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one of the extremities of the line of the apsides, or the greater axis of the ellipse, and a given part of this revolution; Kepler found, that these two times were always to each other as the whole of the area of the ellipsis to the area of the elliptical sector, comprised between the arc described by the planet and the radius vector drawn from each end of it to the Sun. The same proportion was also verified in the other planets; and it was afterward found, that it equally takes place in the revolution of the satellites round their primary planets. Thus it is become a fundamental principle of physical astronomy; and is commonly called the first law of Kepler, or the law of the proportionality of the areas to the times.

This important discovery led to another not less remarkable. Kepler suspected, that an analogy existed between the times of the revolutions of the planets and the dimensions of their orbits; and this he undertook to ascertain. Hence arose new calculations, the extent of which may be imagined, if we consider that Kepler was groping his way as it were in the dark but he was guided by genius, and succeeded in the search. The result of all his numerical calculations was, that the squares of the times of the complete revolutions of two planets were to each other, as the cubes of the transverse axes of the two ellipses described by the planet, or as the cubes of their mean distances from the Sun: another fundamental principle, verified in all the planets, and in all the satellites with respect to their primaries. This is called the second law of Kepler, or the law of the times relative to the mean distances.


Those who wish to know the origin and progress of Kepler's ideas on this subject may consult his work entitled, Astronomia nova.......cœlestis tradita cum Commentariis de Motibus Stella Martis, 1609. In this may be observed a lively imagination, fertile in resources, and in some places a kind of poetical enthusiasm, excited by the grandeur and interesting nature of the subject.

Though the two laws of Kepler form the base of all astronomical calculations of the motions of the planets, we shall nevertheless see hereafter, that slight modifications are requisite, to represent the alterations occasioned in the elliptical motion of a planet round the Sun, or of a satellite round it's primary, by the effect of the universal and reciprocal gravitation of all the heavenly bodies toward each other.

Astronomy made fresh progress by the help of the telescope, which was invented about the beginning of the seventeenth century, as I shall relate more particularly hereafter: a happy supplement to the imperfection of the naked eye in observing remote objects.

Galileo is one of the first, by whom this instrument was used. He began with attentively observing the Moon, on the surface of which he perceived various inequalities, some parts prominent, and others sunk and dark. Hence he inferred, that this satellite was interspersed with mountains, lakes, and rivers, and that it formed an opake body, similar to the Earth. In every part of the sky he discovered an immense number of small stars, invisible to the naked

naked eye. A false idea had been entertained of the spots in the Sun, which were considered as a sort of temporary scum. Galileo observed, that they adhered to the body of the Sun, and appeared and disappeared in consequence of a rotatory motion, by which that body is carried round. Copernicus had predicted, that at some future time Venus would be found to have phases nearly similar to those of the Moon; and Galileo proved the truth of his prediction. But what gave him the greatest pleasure and astonishment, was his gradual discovery, that Jupiter is surrounded by four satellites, which revolve round this planet as the Moon does round the Earth. He called them the Medicean stars, in gratitude for the marks of esteem and respect he had received from the house of Medici: but this appellation met with little success in the World, and the simple name of the satellites of Jupiter has prevailed.

The system of Copernicus, already so plausible, acquired a probability almost equivalent to demonstration, by the observations and reasonings of Galileo. Most of the objections made to this system were frivolous enough. It was said, for instance, that the Earth having the Moon for a satellite, it was not to be supposed, that the Earth itself was a satellite, or revolved round the Sun. To this Galileo gave an irrefragable answer, that Jupiter had four satellites, and notwithstanding revolved round the Sun, according to the observations and calculations of Tycho and he added, that, the Moon being a body similar to the Earth, there was no reason to suppose they might not both have similar motions in celestial

celestial space. But the strongest probability in favour of the copernican system, and that on which Galileo insisted the most, was the simple and natural explanation it gave of the stationary, direct, and retrograde appearances of the planets; while in this respect the system of Ptolemy, and even that of Tycho, exhibited a complication of motions, impossible to be reconciled with the laws of mechanics and sound philosophy.

Supported by all these considerations, Galileo had the courage, from the year 1615, openly to maintain the system of Copernicus. But this courage brought upon him the animadversions of the Inquisition, and he was obliged to retract, in order to avoid imprisonment. Twenty years afterward, imagining the truth to have become more mature, he declared himself anew, though in a more secret way, for this system, without which he saw clearly physical astronomy could not be supported. The Inquisition, by which he was constantly watched, now kept no measures with him he was obliged to appear before it's tribunal, and sentenced to pass the remainder of his days in a dungeon. At the expiration of a year, however, he was released from his imprisonment, on condition, that he should not again relapse, and that he should never quit the territory of Florence; where in fact he remained under the eye of the Inquisition, till the day of his death: a too notorious instance of the innumerable crimes, which an absurd and fanatic tribunal has committed against human reason, and which it has at length expiated in our days with ignominy.

In spite of the inquisitors, or of the passages in the Bible, which were incessantly brought forward as objections to the Earth's motion, the system of Copernicus continued to gain ground, and grow stronger every day. It ought not to be omitted however, that one difficulty was started, to which neither Copernicus nor Galileo could give a peremptory answer; but a complete solution of which they predicted would one day be found. This was, that, supposing the Earth arrived successively at the two extremities of one of the diameters of it's orbit, we ought to find a parallax or change of position in the stars; and this was not to be observed.

For more than a century astronomers made every exertion, to clear up this doubt: some perceived a very trifling parallax in the stars, while others found none; and others again, discovered motions directly contrary to those, which should have resulted from a parallax. The certain conclusion from all these uncertainties was, that the stars are placed at such distances from us, as may be considered as infinite with respect to the radius of the terrestrial orbit, though this radius is at least ninety five millions of miles. It will be seen hereafter, that this question was completely solved before the middle of the eighteenth century, so that now the doctrine of the Earth's motion is established on irrefragable evidence.

Italy was not the only country, where the use of the telescope contributed to the progress of astronomy. In 1631 Gassendi, a french philosopher, saw Mercury on the Sun's disk, which was the first obser


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