صور الصفحة
PDF
النشر الإلكتروني

365 24655 days for the true length of the solar year. This is in excess of the truth by 6 minutes and 13 seconds only; since, according to Laplace, the tropical year was then 4.2 seconds shorter than in the present age. This investigation of Hipparchus led him to suggest an improvement in the calendar by leaving out one of the intercalated days (of every fourth year) at the end of every three hundred years.

Ptolemy informs us that Hipparchus found, from observation, that the interval of time from the vernal equinox to the summer solstice was equal to 94 days, and from the latter to the autumnal equinox there were 924 days; from which it follows that the summer half of the year consisted of 187 days, and the winter half of 178 days. "To explain these differences, Hipparchus supposed the sun to move uniformly in a circular orbit; but, instead of placing the earth in the centre of it, he supposed it removed the twenty-fourth part of the radius, and fixed the apogee in the sixth degree of Gemini. From these data he formed the first solar tables to be found in the history of astronomy.

After establishing the theory of the motions of the sun, Hipparchus applied himself to an investigation of the lunar theory. The theory of the moon's motions is by far more difficult than that of the sun; indeed, more labour has been expended on the lunar theory alone than on that of all the other celestial bodies together. Hipparchus availed himself of the registers of the ancient eclipses, and probably of many direct observations of the phases of the moon, as these latter would afford many useful approximations to the lunar elements. By comparing the ancient observations with those of his own time, he found the mean synodical revolution of the moon equal to 29.5297 days, and the mean sidereal revolution equal to 27.3214 days. He also found that the line of apsides completed a revolution in 3229.3 days, and the line of nodes in 6806.6 days. These numbers are close approximations to the truth; especially shall we consider them so when we remember the difficulties which Hipparchus had to encounter in determining them. By comparing these results with those deduced from the most accurate observations of modern times, it is proved that the moon's mean motion has been accelerated since the days of Hipparchus, and the theory of gravitation con

*"System of the World," vol. i., p. 268. ¡

firms the result, giving numbers that agree almost precisely with those found from observation.

To find the variation of the apparent diameter of the moon, he again had recourse to lunar eclipses. In this way it was found that the moon's apparent diameter in perigee exceeded that in apogee by 2'10", the true value being about double this. As soon as it was discovered that the magnitude of the earth bore a definite relation to the distance of the sun and moon, it must have been perceived that the apparent places of these bodies would be affected by the position which the observer occupies on the surface of the first body. This change of apparent place was denominated parallax, and Ptolemy informs us that Hipparchus not only understood the nature of the element, but he was in possession of rules for computing its amount. He called the horizontal parallax of the moon 57', and that of the sun 3', according to the determination of the sun's distance by Aristarchus.

After having revised and improved the lunar theory, Hipparchus turned his attention to the planets. In most of the ancient systems of astronomy, the earth was considered as a quiescent body in the centre of the universe with the celestial bodies revolving around it. The first and nearest was the moon, then Mercury, Venus, the sun, Mars, Jupiter, and Saturn; after which came the sphere of the fixed stars. Hipparchus found the time occupied by a synodical revolution of each of the planets, or the interval between two successive conjunctions with the sun, as follows: Mercury, 115 875 days; Venus, 583.95 days; Mars, 779 68 days; Jupiter, 398 89 days; Saturn, 378 09 days. The sidereal revolutions were as follows: Mercury, Venus, and the sun, each a year; Mars, 1·88 years; Jupiter, 11.86 years; Saturn, 29-03 years. These numbers are approximately correct, except the sidereal periods of Mercury and Venus.

In concluding this sketch of the labours of Hipparchus, we may add, that besides his invention or improvement of trigonometry and the calculation of tables to facilitate astronomical calculations, the improvement of the theories of the sun, moon, and planets, and the correction of the tables of their movements, he must have applied himself for many years to the observations of the heavenly bodies, so as to leave behind him numerous correct data for the improvement of those theories to which he had devoted the powers of his gifted mind. He died about the year 125 B. C.

Between the times of Hipparchus and Ptolemy, a space of about three hundred years, there flourished no astronomers of any particular note; or such as added any thing of importance to what was already known. Ptolemy was born at Ptolemais in Egypt, about the year 100 of our era. He laboured to extend and perfect what Hipparchus had begun. The results of all his labours are embodied in his great work, the Almagest, which is a complete treatise on the science of astronomy. In the first book of this work, Ptolemy gives the result of his researches on the obliquity of the ecliptic. His method was to observe the zenith distances of the sun on the days of the summer and the winter solstices, which gave him the double obliquity equal to about 47° 42′ 30′′, half of which is 23° 51′ 15′′. His method of ascertaining the length of the tropical year, was the same as that practised by Hipparchus, and he found a result coinciding with that of the last-named astronomer. This exact coincidence has given rise to a suspicion, since several different comparisons give the same result, that his observations are not real. That he was not a very accurate observer seems probable from the fact that he made the latitude of Alexandria, the scene of his labours, a quarter of a degree too small. Ptolemy does not seem to have improved the solar theory of Hipparchus.

In the fourth book of the Almagest, Ptolemy investigates the theory of the moon's motions. Hipparchus had determined the eccentricity of the moon's orbit, or the radius of the epicycle in his theory, the maximum equations of her centre, and the place of her apogees. The equations of the moon's centre, or the principal inequality, as it was also called, was found by a comparison of the mean place of that body with her true place at the time of an eclipse; and Hipparchus seems to have concluded that the same correction applied in any situation with respect to the sun; but we are indebted to Ptolemy for the discovery of the fact that it is only applicable when she is in syzygy. This inequality is known as the evection. He constructed an instrument, by means of which the positions of the moon could be observed in other parts of her orbit than in syzygy, and he "found that they sometimes agreed, but were more frequently at variance with the calculated places; the greatest amount of error always taking place at quadrature and vanishing altogether

*Narrion, pp. 256-7.

at syzygy. What must, however, have been a source of great perplexity to Ptolemy, when he attempted to investigate the law of this new irregularity, was to find that it did not return in any quadrature-in some quadratures it totally disappeared, and in others amounted to 2° 39′, which was its maximum value."* These changes are owing to the fact, that the evection is proportional to the sum of twice the mean angular distance of the sun from the moon, diminished by the mean angular distance of the moon from the perigee.

To represent this new inequality, Ptolemy caused the moon, in his theory, to move on the circumference of an epicycle whose centre was moved on the circumference of an eccentric circle whose centre was carried in a retrograde order on the circumference of another circle whose centre was the centre of the earth. One of the erroneous notions of the ancients, was that, because circular motion is the most simple and natural, it was necessarily that of the heavenly bodies. After being retarded for some time in his progress by the same notion, Kepler finally overthrew it, and established the elliptic theory. Although Ptolemy's theory might be made to represent approximately the principal inequalities of the moon's motion, yet it never could explain the variation in distance; and could he have measured with his instruments the change in the apparent diameter of the moon as it revolves around the earth, it would have shown him that his theory was entirely at variance with nature, since the diameter varies inversely as the distance.

In the planetary theory there was no question in reference to the positions of Mars, Jupiter, and Saturn with respect to the earth and sun, but Mercury and Venus, owing to the peculiarity of their apparent motions, gave the ancients no little difficulty. There were three opinions respecting them. The hypothesis of the first class placed them between the sun and the earth, Mercury being nearest to the latter; the second placed them beyond the sun; and lastly, the Egyptians, more sagacious than the others, made them move round the sun according to nature. Ptolemy adopted the first hypothesis. Had he followed the Egyptians, the simplicity which it would have introduced into his theory might have led him to the discovery of the true system of the world. Every new discovery of irregularities in the motion of the

*Godfray's Lunar Theory, p. 105.

celestial bodies added new difficulties to the theory; and instead of being confirmed by the progress of the science, it grew more and more complicated; and this alone should have convinced the ancients that their system was not that of nature. "But in considering it," says Laplace, "as a method of adapting the celestial motions to calculation, this first attempt of the human understanding toward an object so very complicated, does great honour to the sagacity of its author."

In preparing his catalogue of stars, Ptolemy has been accused of copying that of Hipparchus, and allowing for the motion of the equinoxes in the interval. In determining the motion of the equinoctial points, he arrived at a result agreeing with that of Hipparchus. But Laplace* shows that the erroneous determination was owing to the error then existing in the observed length of the tropical year. "The astronomical edifice raised by Ptolemy, subsisted nearly fourteen centuries, and now that it is entirely destroyed, his Almagest, considered as a depository of ancient observations, is one of the most precious monuments of antiquity." Ptolemy rendered great service to geography by collecting all the known longitudes and latitudes of different places, and by laying the foundation of projections for the construction of geographical charts. He composed a treatise on optics, which has been preserved. In this work he explains the influence of astronomical refractions. He also wrote treatises on chronology, music, gnomonics, and mechanics.

His

Megale Syntaxis was translated by the Arabs into their language, and called by them the Almagest. In the thirteenth century it was translated from Arabic into Latin, under the auspices of the emperor Frederick the Second. This step was attended with the most beneficial consequences to the study of astronomy, for the work could now be read by most persons of learning.

ART. VIII.-1. Articles of Impeachment against the President of the United States for High Crimes and Misdemeanors.

2. Speeches of Managers and of Counsel for Defence and other documents. May, 1868.

No party is so strong that it can afford to be rash in important actions. Five hundred persons more than one

System of the World, vol. ii., pp. 278-9.

« السابقةمتابعة »