In 1822, however, Encke, then director of the Seeberg Observatory near Gotha, undertook to bring order out of the confusion of discordant, and discordantly interpreted observations. His combined result for both transits (1761 and 1769) was published in 1824,[752] and met universal acquiescence. The parallax of the sun thereby established was 8·5776", corresponding to a mean distance[753] of 95-1/4 million miles. Yet this abolition of doubt was far from being so satisfactory as it seemed. Serenity on the point lasted exactly thirty years. It was disturbed in 1854 by Hansen's announcement[754] that the observed motions of the moon could be drawn into accord with theory only on the terms of bringing the sun considerably nearer to us than he was supposed to be. Dr. Matthew Stewart, professor of mathematics in the University of Edinburgh, had made a futile attempt in 1763 to deduce the sun's distance from his disturbing power over our satellite.[755] Tobias Mayer of Göttingen, however, whose short career was fruitful of suggestions, struck out the right way to the same end; and Laplace, in the seventh book of the _Mécanique Céleste_,[756] gave a solar parallax derived from the lunar "parallactic inequality" substantially identical with that issuing from Encke's subsequent discussion of the eighteenth-century transits. Thus, two wholly independent methods--the trigonometrical, or method by survey, and the gravitational, or method by perturbation--seemed to corroborate each the upshot of the use of the other until the nineteenth century was well past its meridian. It is singular how often errors conspire to lead conviction astray. Hansen's note of alarm in 1854 was echoed by Leverrier in 1858.[757] He found that an apparent monthly oscillation of the sun which reflects a real monthly movement of the earth round its common centre of gravity with the moon, and which depends for its amount solely on the mass of the moon and the distance of the sun, required a diminution in the admitted value of that distance by fully four million miles. Three years later he pointed out that certain perplexing discrepancies between the observed and computed places both of Venus and Mars, would vanish on the adoption of a similar measure.[758] Moreover, a favourable opposition of Mars gave the opportunity in 1862 for fresh observations, which, separately worked out by Stone and Winnecke, agreed with all the newer investigations in fixing the great unit at slightly over 91 million miles. In Newcomb's hands they gave 92-1/2 million.[759] The accumulating evidence in favour of a large reduction in the sun's distance was just then reinforced by an auxiliary result of a totally different and unexpected kind.