days which it contains; but the day can be subdivided into hours only by artificial means; and the mechanical skill of the ancients did not enable them to attain any considerable accuracy in the measure of such portions of time; though clepsydras and similar instruments were used by astronomers. The equality of days could only be proved, therefore, by the consequences of such a supposition; and in this manner it appears to have been assumed, as the fact really is, that the apparent revolution of the stars is accurately uniform, never becoming either quicker or slower. It followed as a consequence of this, that the solar days (or rather the nycthemers, compounded of a night and a day,) would be unequal, in consequence of the sun's unequal motion, thus giving rise to what we now call the Equation of Time,-the interval by which the time, as marked on a dial, is before or after the time, as indicated by the accurate time-pieces which modern skill can produce. This inequality was fully taken account of by the ancient astronomers; and they thus in fact assumed the equality of the sidereal days.

Sect. 2.-Researches which did not verify the

Theory.

SOME of the researches of Hipparchus and his followers fell upon the weak parts of his theory; and if the observations had been sufficiently exact, must have led to its being corrected or rejected.

Among these we may notice the researches. which were made concerning the Parallax of the heavenly bodies, that is, their apparent displacement by the alteration of position of the observer from one part of the earth's surface to the other. This subject is treated of at length by Ptolemy; and there can be no doubt that it was well examined by Hipparchus, who invented a parallatic instrument for that purpose. The idea of parallax, as a geometrical possibility, was indeed too obvious to be overlooked by geometers at any time; and when the doctrine of the sphere was established, it must have appeared strange to the student, that every place on the earth's surface might alike be considered as the center of the celestial motions. But if this was true with respect to the motions of the fixed stars, was it also true with regard to those of the sun and moon? The displacement of the sun by parallax is so small that the best observers among the ancients could never be sure of its existence; but with respect to the moon, the case is different. She may be displaced by this cause to the amount of twice her own breadth, a quantity easily noticed by the rudest process of instrumental observation. The law of the displacement thus produced is easily obtained by theory, the globular form of the earth being supposed known; but the amount of the displacement depends upon the distance of the moon from the earth, and requires at least one good observation

to determine it. Ptolemy has given a table of the effects of parallax, calculated according to the apparent altitude of the moon, assuming certain supposed distances; these distances, however, do not follow the real law of the moon's distances, in consequence of their being founded upon the Hypothesis of the Eccentric and Epicycle.

In fact this Hypothesis, though a very close representation of the truth, so far as the positions of the luminaries are concerned, fails altogether when we apply it to their distances. The radius of the epicycle, or the eccentricity of the eccentric, are determined so as to satisfy the observations of the apparent motions of the bodies: but, inasmuch as the hypothetical motions are different altogether from the real motions, the Hypothesis does not, at the same time, satisfy the observations of the distances of the bodies, if we are able to make any such observations.

Parallax is one method by which the distances of the moon, at different times, may be compared ; her Apparent Diameters afford another method. Neither of these modes, however, is easily capable of such accuracy as to overturn at once the Hypothesis of epicycles; and, accordingly, the Hypothesis continued to be entertained in spite of such measures; the measures being, indeed, in some degree falsified in consequence of the reigning opinion. In fact, however, the imperfection of the methods of measuring parallax and magnitude, which were P

VOL. I.

in use at this period, was such, their results could not lead to any degree of conviction deserving to be set in opposition to a theory which was so satisfactory with regard to the more certain observations.

The Eccentricity, or the Radius of the Epicycle, which would satisfy the inequality of the motions of the moon, would, in fact, double the inequality of the distances. The Eccentricity of the moon's orbit is determined by Ptolemy as of the radius of the orbit; but its real amount is only half as great; this difference is a necessary consequence of the supposition of uniform circular motions, on which the Epicyclic Hypothesis proceeds.

We see, therefore, that this part of the Hipparchian theory carries in itself the germ of its own destruction. As soon as the art of celestial measurement was so far perfected, that astronomers could be sure of the apparent diameter of the moon within or of the whole, the inconsistency of the theory with itself would become manifest. We shall see, hereafter, the way in which this inconsistency operated; in reality, a very long period elapsed before the methods of observing were sufficiently good to bring it clearly into view.

Sect. 3.-Methods of Observation of the Greek Astronomers.

We must now say a word concerning the Methods above spoken of. Since one of the most important

tasks of a period of verification is to ascertain with accuracy the magnitude of the quantities which enter, as elements, into the theory which occupies men during the period; the improvement of instruments, and the methods of observing and experimenting, are principal features in such periods. We shall, therefore, mention some of the facts which bear upon this point.

The estimation of distances among the stars by the eye, is an extremely inexact process. In some of the ancient observations, however, this appears to have been the method employed: and stars are described as being a cubit or two cubits from other stars. We We may form some notion of the scale of this kind of measurement, from what Cleomedes remarks, that the sun appears to be about a foot broad; an opinion which he confutes at length.

A method of determining the positions of the stars, susceptible of a little more exactness than the former, is the use of alineations, already noticed in speaking of Hipparchus's catalogue. Thus, a straight line passing through two stars of the Great Bear passes also through the pole-star: this is, indeed, even now a method usually employed to enable us readily to fix on the pole-star; and the two stars, ẞ and a of Ursa Major, are hence often called "the pointers."

But nothing like accurate measurements of any portions of the sky were obtained, till astronomers

* Del. A. A. i. 222.