the spirit of a philosophical enquirer into some of the actual relations of the system of the world. He advocated the Pythagorean or solar system. One of the most serious objections brought against it was, that if the earth were in motion, a fixed star seen from one point in the earth's orbit would be referred by us to a point in the heavens different from that to which it would be referred when we are at the opposite point, but that, in fact, no such difference is observed. The reply of Aristarchus evinced a correct conception of the magnitude of the celestial spaces: he alleged that the whole orbit of the earth is a mere point in comparison with the distance of the fixed stars. This would, of course, render such difference in apparent position (called parallax) so small as to be quite insensible to the nicest observations.

He also suggested an ingenious mode of obtaining the relative distances of the sun and moon from the earth. When the moon is exactly half way between new and full, it requires but a moment's consideration to perceive, that the three bodies form a triangle which has a right angle at the moon. In this case, therefore, if we measure the angle subtended between the moon and the sun, the ratio of their distances from the earth is simply (in modern language) that of the cosine of that angle to radius. His determination, though but roughly obtained, served to give much more accurate notions of these distances than had as yet been entertained. He also endeavoured to estimate the magnitudes of the two luminaries.

The name of Eratosthenes, another Alexandrian astronomer, has been rendered ever memorable from his attempt, the first ever made, to estimate the actual magnitude of the globe on which we live. That the figure of the earth was of a spherical kind had been long before held in the schools of Greece; and there were so many obvious arguments in favour of the belief, that it must have become evident as soon as men began to reason at all on the subject. We have no ground to suppose

that any actual attempt was made to measure the earth's magnitude before the time of Eratosthenes. Aristotle, indeed, mentions that mathematicians had assigned the circumference of the earth as 40,000 stadia. But no grounds for this are assigned; and it seems that various conjectural ideas on the subject were prevalent. The principle on which Eratosthenes proceeded was the very same which has been adopted by the modern astronomers, and in theory is perfectly exact and satisfactory. Observations of the meridian altitude of the heavenly bodies made at two stations under the same meridian will give the difference of latitude of those stations. If, then, the distance between them be actually measured, we shall obviously have the length of a degree of latitude in terms of the measure employed; and thence the length of the whole circumference of the globe. Hence, again, we can calculate (to any degree of approximation) its diameter, and again its mass or solid content.

When, however, Eratosthenes proceeded to reduce this idea to practice, so loose were the determinations of the data (contenting himself with a mere guess at the distance of the two stations), that the result would be of no value even were it not lost to us from our ignorance of the length of the stadium by which he reckons. His observations were made by means of the shadow of a gnomon; and by this method he has also recorded observations of the solstices, which agree remarkably well with what the values should have been at that date upon the modern theory of the diminution of obliquity according to the principles of gravitation. He died B. c. 194.

Hipparchus.

Hipparchus, perhaps the most distinguished ornament of the Alexandrian observatory, flourished about B. c. 150, and has been called the father of astronomy. Unfortunately all his works, except one of trifling importance, have been lost. We learn, however, the particulars of

his researches from Ptolemy. From his existing work it has been elicited that he was in possession of the principles of spherical trigonometry, of which we find no traces in any previous Greek author. Delambre consi

ders him as the inventor of that science; and if so, this alone would entitle him to the highest degree of praise; both in an abstract point of view, and since without this auxiliary science astronomy could not advance a step.

Hipparchus not only gave a more accurate determination of the length of the solar year than had been previously done, but investigated with particular care the inequality in the sun's motion, which had, in a general way, been long before noticed. The most ordinary observations of the solstices and equinoxes sufficed to show that the sun took a longer time in passing through the northern than through the southern half of the ecliptic. Hipparchus determined the former to be 187 days, and the latter 1781. To account for the increased velocity of the sun's motion during this latter half of his course, Hipparchus imagined the theory of the sun's apparent orbit still circular, but the earth not in its centre. This would give a plausible explanation of the apparent difference of motion. He pursued also similar observations with regard to the moon, and constructed a similar theory of her orbit; observing, also, its slight inclination to the plane of the ecliptic.

With regard to Hipparchus's theory of the solar orbit above mentioned, and to the views of the planetary system generally adopted in the school of Alexandria, considerable difference of opinion is found between different historians. By some it is contended that the primary principles at least of the theory afterwards adopted by Ptolemy were introduced in the age of which we are now treating. It may not, therefore, be improper here to give a cursory sketch of its nature.

As soon as the actual apparent motions of the planets were tolerably well known by observation, it of course became an object of interest and importance to form some scheme by which their real nature might be best repre

sented. The simplest and most natural, that of an uniform motion round the earth, was soon disproved, when it was noticed that the motion at some periods became slower, the planet at length stationary, and then for a time retrograde; again stationary; and after that progressive: all this recurring at certain periods, which were known from observation.

The original suggestion of a mode of solving the difficulty, and representing these apparently complex motions on a simple hypothesis, has been ascribed to Apollonius. He conceived, that in the circumference of a circle, having the earth for its centre, there moved the centre of another circle, in the circumference of which the planet revolved. The first was called the deferent, the second the epicycle, and the motion in each was supposed uniform. The motion of the centre of the epicycle in the circumference of the deferent was towards the east, that of the planet in the epicycle towards the west. In this way the observed changes from direct to retrograde motion, with intermediate stationary points, were readily explained, and the ratios of the radii necessary to account for the observed extent of these changes were also calculated.

Thus an object which was then considered of great importance to astronomy was accomplished, viz. the production of a variable motion, or one which was continually changing both its rate and its direction, from two uniform circular motions, each of which preserved always the same quantity and the same direction.

The theory framed by Hipparchus to represent the inequality of the sun's motion (of which we have already: spoken) has been represented by some authors as involving this principle of epicycles; and as consisting in an epicycle of small radius, in which the sun revolved with the same angular velocity, but in an opposite direction 10 that with which the centre of the epicycle moved in the deferent. We feel, however, little interest in entering upon such a question: it was necessary to refer to it, and to the general subject of the theory of the epi

cycles, on account of the celebrity they afterwards acquired, as we shall see in the sequel.

He also made the first attempt to estimate the distances of the sun and moon. His calculation was founded on measures of their apparent diameters, and of the diameter of the earth's shadow at the moon's orbit; which was derived from the time occupied by the moon in passing through it in an eclipse.*

The most important, perhaps, of all the services rendered to astronomy by Hipparchus was the formation of a catalogue of the fixed stars; an enumeration, that is, of all the principal stars referred to their actual positions in latitude and longitude. Indeed nothing but such an examination can ratify their claim to the title of fixed bodies. This was obviously a work requiring immense assiduity as well as precision. But its chief value is in being an exact representation of the state of the heavens at a particular epoch. It is the comparison of an ancient catalogue with one made from observations of the present day, which gives the value to both sets of observations. It is by this comparison that we learn whether, in the course of ages, the actual configuration of the stars has undergone any change; and by this means alone that we can decide whether the fixed stars are what they are assumed to be, points actually fixed as standards of measurement, to which we can refer the places of the obviously varying bodies of our system; and by measuring from which, as fixed points, we can estimate their motions, and deduce with accuracy the laws which govern them. Hence the values of catalogues of different ages. If these ancient astronomers had enjoyed the instrumental means of making their catalogues as perfect as ours, there are numerous questions of the highest interest in astronomy which might now have received their solution, but which, under existing circumstances, must wait for ages to come, perhaps, before they can be decided. There are many of the smaller variations which require the accumulation of Libes Hist. de Phys. i. 68.