The history of the development of vectorial methods is told in Crowe (1994). Much has been written about the discovery of Neptune. The most comprehensive account is Grosser (1962) which also contains an extensive bibliography. Numerous articles are cited in the following pages of this book. The discovery of Neptune has been described in many books that have appeared since 1962, including Ronan (1967), Lyttleton (1968), Hoyt (1980), Baum and Sheehan (1997), and Standage (2000).

Bouvard was, in effect, attributing errors to previous distinguished astronomers an order of magnitude greater than any that had ever been found, and he seems to have realized that his solution was not built on solid foundations, since he wrote in the introduction to his tables:

I leave to the future the task of discovering whether the difficulty of reconciling the two systems results from the inaccuracy of the ancient observations, or whether it depends on some extraneous and unknown influence which may have acted on the planet.

Notwithstanding his dubious assumptions, which were the subject of serious criticism from fellow astronomers, Bouvard's new tables fit well with new observations of Uranus, but only for a few years.

When William Herschel died in 1822, the planet he had discovered over 40 years previously was still a source of great frustration. During the 1820s, the true heliocentric longitude of Uranus gradually got further and further ahead of the predicted position, with errors approaching 20" in 1825. Then, strangely, things started to improve and around 1829-30, the longitude of Uranus was pretty much as given by Bouvard's tables. This temporary respite was shortlived, though, and Uranus then began to fall behind its predicted position at an alarming rate; by 1832, the errors were nearly 30". What was going on? Many hypotheses for the strange behaviour of Uranus were suggested. Perhaps it was due to some resistance from the medium in which Uranus moved. Encke had used this same idea to attempt to explain the anomalous motion of a comet (comet Encke), the period of 3.3 years of which appeared to diminish by about

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2 2 h each cycle. But why would only some bodies be affected and not others? Other suggestions included the existence of an enormous, as yet undetected, satellite. Even ignoring the fact that one would have expected such a satellite to have been visible through a telescope, perturbations caused by such a body would have had a much shorter period than those observed. Another possibility was that the tables that had been constructed contained errors. It was impossible to produce error-free tables and Bouvard's were no exception. Mistakes were found, but they did not solve the problem.

A more serious candidate for the source of the errors was Newton's law of gravity itself. Maybe it needed modifying when the distances involved were as great as those that were relevant to the study of Uranus. While this could not be ruled out, most astronomers were not keen on the idea. Every time universal

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