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date of the poems, thus confirming other evidence, and establishing Homer's character for accuracy.1

(4) The orientation of Egyptian temples and Druidical stones is such that possibly they were so placed as to assist in the observation of the heliacal rising2 of certain stars. If the star were known, this would give an approximate date. Up to the present the results of these investigations are far from being conclusive.

Ptolemy (130 A.d.) wrote the Suntaxis, or Almagest, which includes a cyclopaedia of astronomy, containing a summary of knowledge at that date. We have no evidence beyond his own statement that he was a practical observer. He theorised on the planetary motions, and held that the earth is fixed in the centre of the universe. He adopted the excentric and equant of Hipparchus to explain the unequal motions of the sun and moon. He adopted the epicycles and deferents which had been used by Apollonius and others to explain the retrograde motions of the planets. We, who know that the earth revolves round the sun once in a year, can understand that the apparent motion of a planet is only its motion

1 See Pearson in the Camb. Phil. Soc. Proc, vol. iv., pt. ii., p. 93, on whose authority the above statements are made.

2 See p. 8 for definition.

relative to the earth. If, then, we suppose the earth fixed and the sun to revolve round it once a year, and the planets each in its own period, it is only necessary to impose upon each of these an additional annual motion to enable us to represent truly the apparent motions. This way of looking at the apparent motions shows why each planet, when nearest to the earth, seems to move for a time in a retrograde direction. The attempts of Ptolemy and others of his time to explain the retrograde motion in this way were only approximate. Let us suppose each planet to have a bar with one end centered at the earth. If at the other end of the bar one end of a shorter bar is pivotted, having the planet at its other end, then the planet is given an annual motion in the secondary circle (the epicycle), whose centre revolves round the earth on the primary circle (the deferent), at a uniform rate round the excentric. Ptolemy supposed the centres of the epicycles of Mercury and Venus to be on a bar passing through the sun, and to be between the earth and the sun. The centres of the epicycles of Mars, Jupiter, and Saturn were supposed to be further away than the sun. Mercury and Venus were supposed to revolve in their epicycles in their own periodic times and in the deferent round the earth in a year. The major planets were supposed to revolve in the deferent round the earth in their own periodic times, and in their epicycles once in a year.

It did not occur to Ptolemy to place the centres of the epicycles of Mercury and Venus at the sun, and to extend the same system to the major planets. Something of this sort had been proposed by the Egyptians (we are told by Cicero and others), and was accepted by Tycho Brahe; and was as true a representation of the relative motions in the solar system as when we suppose the sun to be fixed and the earth to revolve.

The cumbrous system advocated by Ptolemy answered its purpose, enabling him to predict astronomical events approximately. He improved the lunar theory considerably, and discovered minor inequalities which could be allowed for by the addition of new epicycles, We may look upon these epicycles of Apollonius, and the excentric of Hipparchus, as the responses of these astronomers to the demand of Plato for uniform circular motions. Their use became more and more confirmed, until the seventeenth century, when the accurate observations of Tycho Brahe enabled Kepler to abolish these purely geometrical makeshifts, and to substitute a system in which the sun became physically its controller.

4. The Reign Of Epicycles From Ptolemy To Copernicus.

After Ptolemy had published his book there seemed to be nothing more to do for the solar system except to go on observing and finding more and more accurate values for the constants involved — viz., the periods of revolution, the diameter of the deferent,1 and its ratio to that of the epicycle,3 the distance of the excentric3 from the centre of the deferent, and the position of the line of apses,4 besides the inclination and position of the plane of the planet's orbit. The only object ever aimed at in those days was to prepare tables for predicting the places of the planets. It was not a mechanical problem; there was no notion of a governing law of forces.

From this time onwards all interest in astronomy seemed, in Europe at least, to sink to a low ebb. When the Caliph Omar, in the middle of the seventh century, burnt the library of Alexandria, which had been the centre of intellectual progress, that centre migrated to Baghdad, and the Arabs became the leaders of science and philosophy. In astronomy they made careful observations. In the middle of the ninth century Albategnius, a Syrian prince,

1 For definition see p. 28.

* Ibid.'

* For definition see p. 23.
4 Ibid.

improved the value of excentricity of the sun's orbit, observed the motion of the moon's apse, and thought he detected a smaller progression of the sun's apse. His tables were much more accurate than Ptolemy's. Abul Wefa, in the tenth century, seems to have discovered the moon's "variation." Meanwhile the Moors were leaders of science in the west, and Arzachel of Toledo improved the solar tables very much. Ulugh Begh, grandson of the great Tamerlane the Tartar, built a fine observatory at Samarcand in the fifteenth century, and made a great catalogue of stars, the first since the time of Hipparchus.

At the close of the fifteenth century King Alphonso of Spain employed computers to produce the Alphonsine Tables (1488 A.d.), Purbach translated Ptolemy's book, and observations were carried out in Germany by Miiller, known as Regiomontanus, and Waltherus.

Nicolai Copernicus, a Sclav, was born in 1473 at Thorn, in Polish Prussia. He studied at Cracow and in Italy. He was a priest, and settled at Frauenberg. He did not undertake continuous observations, but devoted himself to simplifying the planetary systems and devising means for more accurately predicting the positions of the sun, moon, and planets. He had no idea of framing a solar system on a dynamical basis. His great object was to increase the

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