is nearly the same from year to year. And the same is the result when the deviations arise, not from mere accident, but from laws perfectly regular, though not contemplated in our investigation[33\3]. Thus the effects of the Moon's Parallax upon the Tides, sometimes operating one way and sometimes another, according to certain rules, are quite eliminated by taking the Means of a long series of observations; the excesses and defects neutralizing each other, so far as concerns the effect upon any law of the tides which we would investigate. [Note 33\3: Provided the argument of the law which we neglect have no coincidence with the argument of the law which we would determine.] 11. In order to obtain very great accuracy, very large masses of observations are often employed by philosophers, and the accuracy of the result increases with the multitude of observations. The immense collections of astronomical observations which have in this manner been employed in order to form and correct the Tables of the celestial motions are perhaps the most signal instances of the attempts to obtain {214} accuracy by this accumulation of observations. Delambre's Tables of the Sun are founded upon nearly 3000 observations; Burg's Tables of the Moon upon above 4000. But there are other instances hardly less remarkable. Mr. Lubbock's first investigations of the laws of the tides of London[34\3], included above 13,000 observations, extending through nineteen years; it being considered that this large number was necessary to remove the effects of accidental causes[35\3]. And the attempts to discover the laws of change in the barometer have led to the performance of labours of equal amount: Laplace and Bouvard examined this question by means of observations made at the Observatory of Paris, four times every day for eight years. [Note 34\3: _Phil. Trans._ 1831.] [Note 35\3: This period of nineteen years was also selected for a reason which is alluded to in a former note. It was thought that this period secured the inquirer from the errours which might be produced by the partial coincidence of the Arguments of different irregularities; for example, those due to the moon's Parallax and to the moon's Declination. It has since been found (_Phil. Tr._ 1838. _On the Determination of the Laws of the Tides from Short Series of Observations_), that with regard to Parallax at least, the Means of one year give sufficient accuracy.]