its centre. The latter part of this affirmation we should have in these days little difficulty in admitting, but the inference deduced was rather extraordinary. "So much the more then," said Aristotle, "will the whole earth rest in the centre, and that which receives all heavy bodies falling on it, remain immoveable by its own weight." To this he adds an argument still more fanciful. "All simple motion must be rectilinear or circular; to a centre, from a centre, or round a centre. It suits earth and water, which are heavy bodies, to tend downwards; air, and fire, which are light, to rise upwards: it seems reasonable to give these four elements rectilinear motion, but to the celestial bodies, a circular motion." It must be confessed that the objections urged by Ptolemy, though sufficiently trivial, were a little more rational. This latter author objected to the diurnal revolution of the earth, that from its extreme rapidity it would overcome the force of gravity, and everything on the earth's surface be scattered and dissipated into space. The reply of Copernicus is not completely satisfactory; he might have said that such effects would not necessarily take place, unless the velocity of rotation were sufficiently great to counteract the force of gravity: but he replied, in a style too consonant to that of his adversaries, that the motion was natural and not violent; that natural motions have not the same effects as violent ones; the latter tending to dissolution, the former to conservation*. He adds, however, much more reasonably, that if Ptolemy's argument be worth anything, it will apply with still greater force to the celestial sphere, which must revolve with a velocity infinitely greater, and consequently be exposed in an infinitely greater degree to this dispersion. Why, then, do we hesitate," he exclaims, "to give to the earth the mobility suitable to its form, rather than that the universe, whose bounds we do not and cannot know, should revolve? why should we not confess that the diurnal revolution is apparent only in the heavens and real in the earth? Thus Eneas in Virgil exclaims

Provehimur portu, terræque urbesque recedunt. Since while the ship glides tranquilly along, all external objects appear to the sailors to move in proportion as their vessel moves, and they alone and what is with them, seem to be at

Revol. i. S.

rest." It were to be wished that Copernicus had always contented himself with reasoning as soundly; but we have seen that he frequently combats the Aristotelians with arguments frivolous and futile as their own objections. The most illustrious sages have shown that on some weak point they were as fallible as their brethren, and Copernicus has not avoided paying this tribute to mortal nature. But we must not class with such errors his speculations on the existence of several centres of gravity in the universe. The Aristotelians, observing that heavy bodies on the earth's surface tended to its centre, hastily concluded that this point was the centre of gravity of the universe. But this, Copernicus remarks, is very doubtful. Gravity, according to him, is nothing but the tendency of parts to draw together and coalesce in the form of a globe*. "Now it is probable that such a tendency exists in the sun, moon, and other heavenly bodies; but this does not hinder them from describing their respective orbits. If, then, the earth have other motions, these must be the same as we appear to observe in other bodies; and if we change the solar orbit into a terrestrial one, the risings and settings of the signs and fixed stars, in the evening and morning, will appear the same: the retrogradations, and precessions of the planets will be no longer their real motions, but appearances borrowed from that of the earth: the sun, lastly, will be in the centre of the universe, as the order in which these phenomena succeed each other, and the harmony of the whole world, sufficiently show."

After having combated the opinions of preceding philosophers, with regard to the immobility of the earth, Copernicus proceeds to explain his own system; which placed the sun in the centre of the world, the planets revolving round it in the following order, beginning with the nearest: Mercury, Venus, the Earth, Mars, Jupiter, and Saturn. The Moon revolved in a circle, which had the Earth for its centre, and consequently participated in the annual motion of that body. As the Copernican system is now explained in all treatises on astronomy, we shall not enter into details respecting it, but shall merely notice one or two circumstances connected with it, which are not so generally known. Ever since the time of Aristotle it had been

Revol, j. 9.

The doctrines of Copernicus found, at first, few partizans; but these were all men of great scientific merit, and among the first astronomers of their day. Such were Rhæticus, who has written a commentary on the Revolutions, and to whom we owe the valuable Opus Palatinum *, and Erasmus Rheinold, author of the Prutenic Tables, which may be considered as an amelioration of those of Copernicus, and which enjoyed for some time considerable reputation. The commentary of Rhæticus informs us of a curious fact; that it was the observation of the orbit of Mars, and of the very great difference between his apparent diameters at different times, which first led Copernicus to embrace the system of the Pythagoreans; we shall see that the same planet led Kepler to the discovery of one of the most important facts connected with our system. Rheinold is remarkable, as having taught that the orbit of Mercury was elliptic; and in his theory of the moon he made her epicycle to revolve on an elliptic orbit, thereby partially anticipating the great discovery of Kepler, to which we have just alluded. To Rheinold and Rhæticus we may add the names of Rothmann, astronomer to the Landgrave of Hesse, and Mæstlin, the instructor of Kepler. The Landgrave of Hesse is a remarkable instance of a sovereign prince animated with such an ardour for science, that for many years !he devoted himself to assiduous observation, and produced a catalogue of the fixed stars, which was enabled to bear a comparison with that of Tycho Brahé. He was assisted by Rothmann, just mentioned, and Justus Byrgius, a mathematician of considerable eminence, and well versed in the construction of astronomical instruments. Mæstlin, one of the few partisans in those days of the system of Copernicus, is known, not merely as the preceptor of the illustrious Kepler, but as having been the first to explain the real cause of the light seen on that part of the moon's disk which is not directly illuminated by the sun. The opinion previously entertained upon that subject had been, that this was produced by a proper light be longing to the moon itself +; but Mæstlin attributed it, and with reason, to the reflection of the solar light from the

An extremely extensive table of sines, tan gents, &c.

+ Others said that it was produced by the light of Venus. V. Life of Galileo, p. 34.

illuminated part of the earth's surface. This explanation is so simple and so natural, that it has been universally admitted by astronomers ever since. It is said, however, that the celebrated painter, Lionardo da Vinci, had made this remark before Mæstlin*.

The middle of the sixteenth century was rendered memorable by the publication of the immortal work of Copernicus; the close of it was adorned by the labours of Tycho Brahé. The former had passed his life in meditation on the sublimest truths of astronomy, the latter devoted his time and fortune to diligent observation of the heavens. He was rewarded by a number of brilliant discoveries, which have secured for him a fame equal to that of his most distinguished predecessors. Fortunately for science, he found a protector in Frederic, king of Denmark, who granted him the island of Huene in the Baltic, and assisted him in building a splendid observatory, furnished with instruments superior to any that had yet been constructed. Here he continued for twenty years; and in that time collected a mass of observations, which were of the greatest use to succeeding astronomers, as well as to himself, in the reformation of the sciences. But, at the death of Frederic, the enemies of Tycho induced the minister Walchendorp, to withdraw the donations of the late king, and the assistance he had been in the habit of receiving. These, and other circumstances, induced the illustrious astronomer to withdraw in disgust into Germany, where he met with Kepler, who, of all men in Europe at that time, was perhaps the best able to make a good use of his extensive and valuable observations.

We have seen that the Greeks, in comparing the position of the fixed stars with that of the sun, made use of the moon; they determined in the day-time the distance of these two bodies, and at night the difference of position between the moon and a given fixed star. The rapid proper motion of the moon made this method very inaccurate: Tycho improved it materially by substituting for the moon the planet Venus, whose proper motion is at once much smaller and more uniform, and from its great brightness is frequently visible for some

time while the sun is yet above the horizon. Having once determined in this way the places of a few principal fixed stars, the others were referred to them by measuring their angular distances to two fixed stars, one to the east, and one to the west, and by determining their meridian altitudes. It was easy from these data, to calculate the right ascensions; and, as the meridian observation gave the declination, to determine the longitudes and latitudes. It appears that Walther was the author of the method of determining a star's place by observing its distances to other known fixed stars. These contrivances would have been unnecessary had astronomers possessed any means of measuring time accurately. The Greeks used for this purpose water-clocks, which were necessarily very imperfect: Tycho had substituted for water, mercury, and this not answering, he had made several attempts, as Walther and the Landgrave of Hesse had done before him, to measure time by means of clocks moved with wheels, but had not been able to construct any which gave satisfaction. This difficulty was not surmounted before the time of Huyghens. Tycho was, however, enabled to form a catalogue of the fixed stars, surpassing considerably in accuracy those of Ptolemy and the Arabs. Indeed, he flattered himself that the errors never exceeded a minute; but in this he seems to pretend to a greater degree of accuracy than his instruments were susceptible of.

Hitherto astronomers had always determined the latitude of the place, where they made their observations, by observing the zenith distances of the sun, at the summer and winter solstices. Half the sum of these quantities was the latitude required. Tycho invented another method, much more convenient, as the latitude could by it be found in twelve hours instead of six months, during which it was necessary to wait in the old method. He observed the zenith distances of some circumpolar star on the meridian when above and below the pole: half the sum of these was the colatitude of the place. On comparing the latitude thus found with that determined by observations of the solstices, he found a difference of four minutes, which he rightly imputed to the effects of refraction. This led him to form from observation a table of refractions, which though necessarily imperfect secures for him the glory of having been the first

who introduced this important correction. He made the horizontal refraction 34', which agrees very well with modern determinations; but he was mistaken in supposing that refraction does not exist above 45° of altitude. This mistake in observation led him to another in theory. In the beginning he had formed a just conception of the causes of refraction; he attributed it to a difference in density between the atmosphere and the ethereal matter which he supposed to pervade the planetary regions. On this subject he had a warm discussion with Rothmann, who attributed refraction to vapours arising from the earth, and rendering more dense the lower regions of the atmosphere. The argument of Rothmann against the theory of the Danish astronomer was indeed irrefragable, had the facts been as admitted on both sides. If refraction were owing to the causes assigned by Tycho, he contended that it would extend to the zenith; and though Tycho at one time admitted that this might be sot, he seems ultimately to have been convinced of the contrary, as in the Progymnasmata The adopts the explanation of Rothmann.

The year 1572 is memorable in the annals of astronomy for the appearance of a new star of extraordinary brilliancy in the constellation Cassiopeia. It appeared on a sudden with a light greater than that of any of the fixed stars, or even Jupiter, and nearly equal to that of Venus when brightest. But it did not long shine with this degree of splendour: it was first seen by Tycho on the 11th of November, and by the month of January, its light was less than that of Jupiter; in February and March it was comparable to the fixed stars of the first magnitude; during April and May to those of the second, and so it went on diminishing till it finally disappeared in March 1574. A phenomenon so extraordinary could not fail to fix the attention of all astronomers. It furnished Tycho Brahé with matter for a considerable treatise, in which he has compared and discussed the various observations made on it in different parts of Europe. From all of these it evidently resulted that the star in question had no sensible parallax, and consequently was infinitely beyond the planetary regions. It has been said that this phenomenon, rare as it is, was not altogether unprecedented in

V. Epist. Astron. p. 81. † Epist. Astron. P. 108. De Stellà, nová. p. 91.

the history of the world. Pliny narrates that a similar circumstance suggested to Hipparchus the idea of forming a catalogue of the fixed stars. The fact is certainly possible; but if it be true, it seems singular that the star should not be mentioned in the catalogue of that astronomer. Some authors have quoted on this subject the tradition with regard to the constellation of the Pleiades; which are said to have been originally seven in number, whereas six only are usually perceived by the naked eye; but this, even if well established, would merely prove a diminution in brightness of one of the stars forming that constellation.

Tycho was too good an astronomer to admit the pretended inequality in the precession of the equinoxes, which had been introduced into the tables of Alphonso and Copernicus. This invention of a barbarous age was now finally discarded; nor would it have stood so long, were it not for the undeserved confidence some astronomers placed in the position of the fixed stars as given by Ptolemy. But Tycho and his correspondent Rothmann were satisfied that Ptolemy had only borrowed the catalogue of Hipparchus, reducing it to his own times, by the value he assigned to Precession *; an opinion which has generally been adopted by succeeding philosophers. In comparing the positions given by Hipparchus, with those of his own catalogue of the fixed stars, Tycho Brahé was led to the important discovery that the inclination of the earth's equator to the plane of the ecliptic is not constant, but subject to a very slow diminution. As the diminution in question is very gradual, the existence of it was for a long time disputed; but modern observations have established it beyond dispute, and La Grange has shown that it is a consequence of the theory of universal gravitation.

We have seen that Ptolemy attributed to the moon two inequalities, the one depending on the excentricity of her orbit, the other on the position of the line of the apsides with regard to that of the syzigies. Tycho discovered a third, called the variation: this is greatest in the octants, that is to say, at 45° of elongation from the sun (at which time it amounts to more than 40'), while the evection discovered by Ptolemy is greatest in the quadratures. This discovery was an important improvement in the lunar theory; it is not the only one that we owe to the Epist. Astron. p. 87.

same illustrious author. Hipparchus had shown that the lunar orbit was inclined to the ecliptic at an angle of nearly 5; but Tycho proved that this inclination is not constant, it varies nearly 20'; it is at its maximum when the moon is in quadratures, and at its minimum when in syzigies*. The third discovery of Tycho on this subject was that the motion of the lunar nodes, is not, as had been supposed, uniform, but variable, at one time appearing to advance, at another to retrograde.

It has been shown that the Chaldæans, according to Apollonius Myndius, believed comets to be hodies of the same nature as the planets; and this opinion is warmly embraced by Seneca. But it never seems to have enjoyed much favour among astronomers before the latter part of the fifteenth century. The best philosophers entertained the most inadequate ideas upon this point, believing them to be not merely sublunary bodies, but even within the terrestrial atmosphere, and to these false notions they added others still more absurd about the generation of these bodies in the upper regions of the air. Tycho was the first to overthrow these prejudices; and his labours on this point form one of his most solid titles to glory. Having observed carefully the comet of the year 1577 through the whole visible part of its orbit, he established beyond a doubt, that it had no sensible parallax; whence he deduced two conclusions of great importance, and quite fatal to the established theories on the subject. The first, that comets move far beyond the orbit of the moon; the second that the heavens are not formed, as was then supposed, of solid transparent spheres, since they are traversed by comets in every direction. The Aristotelians were reluctant to concede two points so opposed to their doctrines; and Tycho was violently attacked upon this subject by a Scotchman named Craig ; but his adversaries, totally unable to meet his reasons, had recourse to personalities, which could not shake the facts laid down by the Danish astronomer. The debate was renewed in the time of Kepler, but the question was decided in the minds of all really scientific men by the discussion of Tycho.

It being once established that the cometary orbits were of a magnitude comparable to those of the planets, the

The inequality of the inclination depends also on the position of the moon's nodes; but this Tycho does not seem to have perceived,