[187] *Hugenii Cosmotheoros*, pp. 117, 118. Laplace’s *Système*, translated, vol. i. p. 67. Remarkable conjunctions of the planets may sometimes allow us to compare their periods of revolution, through great intervals of time, with much accuracy. Laplace in explaining the long inequality in the motions of Jupiter and Saturn, was assisted by a conjunction of these planets, observed at Cairo, towards the close of the eleventh century. Laplace calculated that such a conjunction must have happened on the 31st of October, A.D. 1087; and the discordance between the distances of the planets as recorded, and as assigned by theory, was less than one-fifth part of the apparent diameter of the sun. This difference being less than the probable error of the early record, the theory was confirmed as far as facts were available.[188] [188] Grant’s *History of Physical Astronomy*, p. 129. Ancient astronomers often showed the highest ingenuity in turning any opportunities of measurement which occurred to good account. Eratosthenes, as early as 250 B.C., happening to hear that the sun at Syene, in Upper Egypt, was visible at the summer solstice at the bottom of a well, proving that it was in the zenith, proposed to determine the dimensions of the earth, by measuring the length of the shadow of a rod at Alexandria on the same day of the year. He thus learnt in a rude manner the difference of latitude between Alexandria and Syene and finding it to be about one fiftieth part of the whole circumference, he ascertained the dimensions of the earth within about one sixth part of the truth. The use of wells in astronomical observation appears to have been occasionally practised in comparatively recent times as by Flamsteed in 1679.[189] The Alexandrian astronomers employed the moon as an instrument of measurement in several sagacious modes. When the moon is exactly half full, the moon, sun, and earth, are at the angles of a right-angled triangle. Aristarchus measured at such a time the moon’s elongation from the sun, which gave him the two other angles of the triangle, and enabled him to judge of the comparative distances of the moon and sun from the earth. His result, though very rude, was far more accurate than any notions previously entertained, and enabled him to form some estimate of the comparative magnitudes of the bodies. Eclipses of the moon were very useful to Hipparchus in ascertaining the longitude of the stars, which are invisible when the sun is above the horizon. For the moon when eclipsed must be 180° distant from the sun; hence it is only requisite to measure the distance of a fixed star in longitude from the eclipsed moon to obtain with ease its angular distance from the sun. [189] Baily’s *Account of Flamsteed*, p. lix.