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 which is produced in this way, and we are thrown back upon astronomical observations for the determination of the total acceleration.

For this purpose modern observations are of little value, because the Moon's motion is subject to unexplained fluctuations, from which it is impossible to disentangle the effect of the acceleration. But this objection does not apply to ancient observations. The effect of an acceleration on the Moon's position is proportional to the square of the time during which the acceleration has been operating. But there is no reason to suppose that the fluctuations had a greater effect in ancient than in modern times. When, therefore, we deal with ancient observations, the fluctuations become negligible as compared with the acceleration, and, if the observations are good enough, a comparison of ancient with modern observations ought to give us the acceleration of the Moon. Dr. Brown, however, is of opinion that in tables designed for present-day use it is unnecessary to make any addition to that part of, the acceleration which can be computed from gravitational theory, and has preferred to use the gravitational acceleration only, endeavouring to compensate the neglect of the rest of the acceleration by artificial changes in terms which can be determined by observation only. In my opinion the compensation is inadequate, and I venture to predict that the Moon will, subject to fluctuations, move further and further in advance of her computed position as time goes on.

The first suggestion of an acceleration of the Moon's motion was made by an alumnus of this University, Edmund Halley, afterwards Savilian Professor of Geometry, after whom this lecture is named, and that shall be my excuse for detaining you a little on the subject. Halley's announcement that he believed that