the planets; and he applied himself to the determination of their courses through the heavens their respective arrangement, and their distances from the Earth, with more accuracy than had hitherto been obtained.

If we consult appearances, the Earth seems to occupy the centre of the universe, and all the motions in the heavens to be made around it. Pythagoras, however, opposed this idea: he placed the Earth among the planets, and made it revolve round the Sun with the rest of them. Aristarchus of Samos afterward embraced the opinion of Pythagoras, and supported it by powerful arguments. But the prejudice in favour of the immobility of the Earth was too deeply rooted, and too agreeable to the testimony of the senses, easily to give place to a truth, which the force of genius might rather be said to have divined, than to have proved, or rendered comprehensible to the vulgar. Ptolemy embraced the common opinion. He supposed that the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn, revolved at different distances round the immovable Earth, in the order in which they are here given. All his explanations of the motions of the planets rested on this hypothesis, to which his authority as an astronomer ensured a universal reception, and which has descended to posterity under the name of the Ptolemaic system.

As soon as he began to make the application of his system, the apparent motion of the planets with regard to the Earth presented difficulties, which he could neither elude nor surmount, but by new and

very embarrassing hypotheses. It has already been observed, that the planets Mercury, Venus, Mars, Jupiter, and Saturn, sometimes appear to move directly forward with respect to us, sometimes backward, and sometimes to be stationary. To account for all these appearances, Ptolemy supposed, that each particular planet describes in space a small cit cle, which he called a deferent; and that all these circles, carrying each it's planet with it, described other concentric or eccentric circles round the Earth. The motion of the planet round it's deferent circle being combined with the motion of this deferent round the Earth, a compound motion is produced, which explains the successive aspects of the planets with regard to the Earth. But it But it may be imagined, that such a complication of motion, and of real or optical appearances, must form a chaos difficult to unravel. Every person is acquainted with the witticism of Alphonsus x, king of Castile, surnamed the astronomer. Though he believed in this mechanism of the heavenly bodies, the perplexity he observed in it led him to say: if God had summoned me to his council, when he created the World, I would have advised him better.' This speech was considered at that time as impious, because it was supposed, no doubt, that Ptolemy had assisted at the council of the Creator.

The progress of the stars in longitude, which was discovered by Hipparchus, was adopted and confirmed by Ptolemy, who only thought it necessary to diminish it a little. According to Hipparchus, this progress, or the consequent retrogression of the equi

noctial points, amounted to two degrees in a hundred and fifty years, or forty eight seconds of a degree in a year; which is somewhat below the truth. Ptolemy reduced it to one degree in a hundred years, or thirty-six seconds annually, which is still farther from the true quantity. From this errour arose a perceptible increase in the duration of the year, which Ptolemy assigned from a comparison of the observations of his time with those of Hipparchus : he made it 365 days, 5 hours, 55 minutes, which was upward of six minutes too much.

In his other investigations of the theory of the Sun and Moon he was more fortunate. Hipparchus had noticed the eccentricities of the orbits of these two bodies: Ptolemy demonstrated the same truths by different means. He made likewise a very important discovery, which was wholly his own: he remarked that noted inequality in the motion of the Moon, which is familiar to us at present by the name of evection. It was known in general, that the velocity of the Moon in it's orbit is not always the same; and that it increases or diminishes, in proportion as the diameter of this satellite appears to increase or diminish: it was known too, that the greatest and least velocities take place at the extre mities of the line of the apses of the lunar orbit: but astronomers had gone no farther than this. Ptolemy observed, that the absolute quantities of these two extreme velocities varied from one revolution to another; and that the more remote the Sun was from the line of the apses of the Moon, the greater in proportion was the difference between these two

velocities. Hence he concluded, that the first inequality of the Moon, that which depends on the eccentricity of it's orbit, is itself subject to an annual inequality, dependant on the position of the line of the apses of the lunar orbit with respect to the Sun. Modern observations have fully demonstrated the truth of this theory; and they have likewise made known a great many other inequalities in the motion of the Moon, which will be mentioned when I speak of the progress of astronomy in modern times.

Beside the Almagest, of which a succinct account has been given, there exists another great work of Ptolemy's, his Geography, in which he determines the situation of places by their latitude and longitude according to the method of Hipparchus. If Ptolemy have made many mistakes in the situation of the towns and countries of which he has spoken, it must be remembered, that geography is the work of time; that, at the period when Ptolemy lived, only a small portion of the old World was clearly known; and that even at present, when the knowledge of astronomy is without comparison more widely diffused, the situation of a multitude of places in both hemispheres is not accurately ascertained. It must not be omitted too, that this work contains the first principles of the ingenious theory of projections now employed in the construction of maps.

Some books, in which judiciary astrology is treated of and explained, are published under Ptolemy's name: but learned critics have shown, that he was not their author; no doubt, therefore, some impostors endeavoured to shelter their pernicious.

reveries

reveries under so great an authority. Thus much is certain, neither the Geography nor Almagest, the two greatest works of Ptolemy, contains the least vestige of it.

Ptolemy had the ambition, like Archimedes, to transmit the remembrance of his labours to posterity by a public monument. In a fragment, which Bouillaud published in 1668, Olympiodorus and Theodorus, two astronomers of Mytilene, relate that Ptolemy had put up in the temple of Serapis at Canopus an inscription engraved on marble, in which the hypotheses of his astronomical system were explained; such as the duration of the year, the eccentricities of the solar and lunar orbits, the dimensions of the epicycles of the planets, &c.

If men of greater genius than Ptolemy have existed, at least no man ever collected a greater body of profound knowledge, or more truly conducive to the progress of astronomy, considering the age in which he lived.

From Ptolemy to the time of the arabs no astronomer of the first order can be reckoned among the greeks, except perhaps Theon of Alexandria [A. ð. 395], of whom we have a learned commentary on the Almagest.

Among the different applications that have been made of astronomy to common use, gnomonics, or the science of dialling, much occupied the ancient astronomers and indeed it merited all their attention, by it's universal utility at that time in pointing out the hours of the day for civil purposes. At present it is not necessary, either in the country or in K 2 cities,