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Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly, Lalande, Delambre, Meyer, Hansen, Burchardt, Binet, Damoiseau, Plana, Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier, Adams, and others of later date. By passing over these important developments it is possible to trace some of the steps in the crowning triumph of the Newtonian theory, by which the planet Neptune was added to the known members of the solar system by the independent researches of Professor J. C. Adams and of M. Le Verrier, in 1846. It will be best to introduce this subject by relating how the eighteenth century increased the number of known planets, which was then only six, including the earth. On March 13th, 1781, Sir William Herschel was, as usual, engaged on examining some small stars, and, noticing that one of them appeared to be larger than the fixed stars, suspected that it might be a comet. To test this he increased his magnifying power from 227 to 460 and 932, finding that, unlike the fixed stars near it, its definition was impaired and its size increased. This convinced him that the object was a comet, and he was not surprised to find on succeeding nights that the position was changed, the motion being in the ecliptic. He gave the observations of five weeks to the Royal Society without a suspicion that the object was a new planet. For a long time people could not compute a satisfactory orbit for the supposed comet, because it seemed to be near the perihelion, and no comet had ever been observed with a perihelion distance from the sun greater than four times the earth's distance. Lexell was the first to suspect that this was a new planet eighteen times as far from the sun as the earth is. In January, 1783, Laplace published the elliptic elements. The discoverer of a planet has a right to name it, so Herschel called it'Georgium Sidus, after the king. But Lalande urged the adoption of the name Herschel. Bode suggested Uranus, and this was adopted. The new planet was found to rank in size next to Jupiter and Saturn, being 4.3 times the diameter of the earth. In 1787 Herschel discovered two satellites, both revolving in nearly the same plane, inclined 80° to the ecliptic, and the motion of both was retrograde. In 1772, before Herschel's discovery, Bode' had discovered a curious arbitrary law of planetary distances. Opposite each planet's name write the figure 4; and, in succession, add the * Bode's law, or something like it, had already been

foreshadowed by Kepler and others, especially Titius (see Monatliche Correspondenz, vol. vii., p. 72).

numbers o, 3, 6, 12, 24, 48, 96, etc., to the 4, always doubling the last numbers. You then get the planetary distances.

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All the five planets, and the earth, fitted this rule, except that there was a blank between Mars and Jupiter. When Uranus was discovered, also fitting the rule, the conclusion was irresistible that there is probably a planet between Mars and Jupiter. An association of twenty-four astronomers was now formed in Germany to search for the planet. Almost immediately afterwards the planet was discovered, not by any member of the association, but by Piazzi, when engaged upon his great catalogue of stars. On January 1st, 1801, he observed a star which had changed its place the next night. Its motion was retrograde till January 11th, direct after the 13th. Piazzi fell ill before he had enough observations for computing the orbit with certainty, and the planet disappeared in the sun's rays. Gauss published an approxi

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mate ephemeris of probable positions when the planet should emerge from the sun's light. There was an exciting hunt, and on December 31st (the day before its birthday) De Zach captured the truant, and Piazzi christened it Ceres. The mean distance from the sun was found to be 2.767, agreeing with the 2.8 glven by Bode's law. Its orbit was found to be inclined over Io° to the ecliptic, and its diameter was only 161 miles. On March 28th, 1802, Olbers discovered a new seventh magnitude star, which turned out to be a planet resembling Ceres. It was called Pallas. Gauss found its orbit to be inclind 35° to the ecliptic, and to cut the orbit of Ceres; whence Olbers considered that these might be fragments of a broken-up planet. He then commenced a search for other fragments. In 1804 Harding discovered Juno, and in 1807 Olbers found Vesta. The next one was not discovered until 1845, from which date asteroids, or minor planets (as these small planets are called), have been found almost every year. They now number about 700. It is impossible to give any idea of the interest with which the first additions since prehistoric times to the planetary system were received. All of those who showered congratulations upon the discoverers regarded these discoveries in the light of rewards for patient and continuous labours, the very highest rewards that could be desired. And yet there remained still the most brilliant triumph of all, the addition of another planet like Uranus, before it had ever been seen, when the analysis of Adams and Le Verrier gave a final proof of the powers of Newton's great law to explain any planetary irregularity. After Sir William Herschel discovered Uranus, in 1781, it was found that astronomers had observed it on many previous occasions, mistaking it for a fixed star of the sixth or seventh magnitude. Altogether, nineteen observations of Uranus's position, from the time of Flamsteed, in 1690, had been recorded. In 1790 Delambre, using all these observations, prepared tables for computing its position. These worked well enough for a time, but at last the differences between the calculated and observed longitudes of the planet became serious. In 1821 Bouvard undertook a revision of the tables, but found it impossible to reconcile all the observations of 130 years (the period of revolution of Uranus is eighty-four years). So he deliberately rejected the old ones, expressing the opinion that the discrepancies might depend upon “some foreign and unperceived cause which may have been acting upon the planet.” In a few years the errors even of these tables became intolerable. In 1835 the error of longitude was 30"; in 1838,

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50"; in 1841, 7 o'; and, by comparing the errors

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