In this sense, therefore, the Hipparchian theory was a real and indestructible truth, which was not rejected, and replaced by different truths, but adopted and incorporated into every succeeding astronomical theory; and which can never cease to be one of the most important and fundamental parts of our astronomical knowledge.

A moment's reflection will show that, in the events just spoken of, the introduction and establishment of the theory of epicycles, those characteristics were strictly exemplified, which we have asserted to be the conditions of every real advance in progressive science; namely, the application of distinct and appropriate ideas to a real series of facts. The distinctness of the geometrical conceptions which enabled Hipparchus to assign the orbits of the sun and moon, requires no illustration; and we have just explained how these ideas combined into a connected whole the various motions and.. places of those luminaries. To make this step in astronomy, required diligence and care exerted in collecting observations, mathematical clearness and steadiness of view exercised in seeing and showing that the theory was a successful analysis of the observations.

Sect. 3.-Discovery of the Precession of the

Equinoxes.

THE same qualities which we trace in the researches of Hipparchus already examined,—diligence in col

lecting observations, and clearness of idea in representing them,-appear also in other discoveries of his, which we must not pass unnoticed. The precession of the equinoxes, in particular, is one of the most important of these discoveries.

The circumstance here brought into notice was a change of longitude of the fixed stars. The longitudes of the heavenly bodies being measured from the point where the sun's annual path cuts the equator, will change if that path changes. Whether this happens, however, is not very easy to decide; for the sun's path among the stars is made out, not by merely looking at the heavens, but by a series of inferences from other observable facts. Hipparchus used for this purpose eclipses of the moon; for these, being exactly opposite to the sun, afford data in marking out his path. By comparing the eclipses of his own time with those observed at an earlier period by Timocharis, he found that the bright star, Spica Virginis, was six degrees from the equinoctial point in his own time, and had been eight degrees distant from the same point at an earlier epoch. The suspicion was thus suggested, that the longitudes of all the stars increase perpetually; but Hipparchus had too truly philosophical a spirit to take this for granted. He examined the places of Regulus, and those of other stars, as he had done those of Spica; and he found, in all these instances, a change of place which could

be explained by a certain alteration of position in the circles to which the stars are referred, which

alteration is described as the Precession of the

Equinoxes.

The distinctness with which Hipparchus conceived this change of relation in the heavens, is manifested by the question which, as we are told by Ptolemy, he examined and decided;-that this motion of the heavens takes place about the poles of the ecliptic and not of the equator. The care with which he collected this motion from the stars themselves, may be judged of from this, that having made his first observations for this purpose on Spica and Regulus, zodiacal stars, his first suspicion was that the stars of the zodiac alone changed their longitude. The idea of the nature of the motion, and the evidence of its existence, the two conditions of a discovery, were also fully brought into view. . The scale of the facts which Hipparchus was thus able to reduce to law, may be in some measure judged of, by recollecting that the precession, from his time to ours, has only carried the stars through one sign of the zodiac; and that, to complete one revolution of the sky by the motion thus discovered, would require a period of 25,000 years. Thus this discovery connected the various aspects of the heavens at the most remote periods of human history; and, accordingly, the novel and ingenious views which Newton published in his chronology, are founded on this single astronomical fact, of the precession of the equinoxes.

The two discoveries which have been described, the mode of constructing solar and lunar tables, and

the precession, were advances of the greatest importance in astronomy, not only in themselves, but in the new objects and undertakings which they suggested to astronomers. The one detected a constant law and order in the midst of perpetual change and apparent disorder; the other disclosed mutation and movement perpetually operating where everything had been supposed fixed and stationary. Such discoveries were well adapted to call up many questionings in the minds of speculative men; for, after this, nothing could be supposed constant till it had been ascertained to be so by close examination; and no apparent complexity or confusion could justify the philosopher in turning away in despair from the task of simplification. To answer the inquiries thus suggested, new methods of observing the facts were requisite, more exact and uniform than those hitherto employed. Moreover the discoveries which were made, and others which could not fail to follow in their train, led to many consequences, required to be reasoned upon, systematized, completed, enlarged. In short, the epoch of induction led, as we have stated that such epochs must always lead, to a period of developement, of verification, application, and extension.

CHAPTER IV.

SEQUEL TO THE INDUCTIVE EPOCH OF HIPPARCHUS.

Sect. 1.-Researches which verified the Theory.

THE discovery of the leading laws of the solar and lunar motions, and the detection of the precession, may be considered as the great positive steps in the Hipparchian astronomy;-the parent discoveries, from which many minor improvements proceeded. The task of preserving the collateral and consequent researches which now offered themselves,-of bringing the other parts of astronomy up to the level of its most improved portions,-was prosecuted by a succession of zealous observers and calculators, first, in the school of Alexandria, and afterwards in other parts of the world. We must notice the various labours of this series of astronomers; but we shall do so very briefly; for the ulterior developement of doctrines once established, is not so important an object of contemplation for our present purpose, as the first conception and proof of those fundamental truths on which systematic doctrines are founded. Yet periods of verification, as well as epochs of induction, deserve to be attended to; and they can