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At once he set to work in a thorough and
systematic way. He first considered whether the discrepancies could be
due to errors in the tables or errors in the old observations. He
discussed them with minute care, and came to the conclusion that they
were not thus to be explained away. This part of the work he published
in November, 1845.
He then set to work to consider the perturbations produced by Jupiter
and Saturn to see whether they had been accurately allowed for, or
whether some minute improvements could be made sufficient to destroy the
irregularities. He introduced several fresh terms into these
calculations, but none of them of sufficient importance to do more than
partly explain the mysterious perturbations. He next examined the
various hypotheses that had been suggested to account for them. Were
they caused by a failure in the law of gravitation or by the presence of
a resisting medium? Were they due to some large but unseen satellite or
to a collision with some comet?
All these theories he examined and dismissed for various reasons.


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