The following year, he was elected as a Fellow of the Royal Society. As Brown's work progressed, he gradually evolved a plan to create a completely new lunar theory. This was eventually published as a series of papers in the Memoirs of the Royal Astronomical Society between 1897 and 1908. In 1907, he was appointed Professor of Mathematics at Yale University, with which he secured an agreement for funding the massive task of calculating detailed tables of the Moon's motion, based on his lunar theory. After a period of 12 years and a cost of over $34,000, Brown's magnum opus, Tables of the Motion of the Moon, was published in 1919. Discrepancies between theory and observation Brown's objective had been to produce an accurate ephemeris of the Moon, based purely on gravitational theory. For the 'main problem' of the Earth-Moon-Sun system, he calculated terms in longitude and latitude down to an uncertainty of 0.001 arcseconds. He also included perturbations due to the other planets (principally Jupiter and Venus) and also accounted for the more difficult problem of the non-spherical nature of the Earth and Moon. Observations showed that Brown's tables were indeed superior to those of Hansen, which had been in use since 1857, but there was still a large unexplained fluctuation in the Moon's mean longitude of the order of 10 arcseconds. A 'great empirical term', of magnitude 10.71 arcseconds and period 257 years, was introduced to eliminate this as far as possible. Given the precision of Brown's calculations, it must have come as a great disappointment to have to introduce this arbitrary adjustment. It had been discovered by Edmond Halley over two centuries previously that the Moon's motion appeared to be gradually speeding up. This 'secular acceleration' could not be explained by gravitational theory alone, and it had been suggested by Simon Newcomb that it was in fact due to a gradual deceleration of the Earth's rate of rotation, due to friction generated by the tides. The implication of this was that it was not the Moon that was speeding up – it was time (as measured in terms of Earth's increasingly long day) that appeared to be slowing down. Brown devoted much study to this problem and proposed it should be attacked observationally, using lunar occultations to map the Moon's path more precisely. He also reasoned that, if the discrepancies were caused by variations in the Earth's