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mum to the maximum, as deduced from the observations at Brest, and as determined by the theory of gravitation, there is an exact coincidence.
2. According to theory, the height of the tides, at their maximum, near the equinoxes, is to their height in similar circumstances at the solstices, nearly as the square of the radius to the square of the cosine of the declination of the sun at the solstice; and this is found to agree nearly with observation.
3. The influence of the moon on the tides increases as the cube of her parallax; and this agrees so well with observation, that the law might have been deduced from observation alone.
4. The retardation of the tides from one day to another, is but half as great at the syzigies as at the quadratures. This is the conclusion from theory; and it agrees well with observation, which makes the daily retardation of the tide 27′ in the one case, and 55′ in the other.
Many more examples of this agreement are mentioned; and it is highly satisfactory to find the genuine results of the theory of gravitation, when deduced with an attention to all the circumstances, and without any hypothetical simplification whatsoever, so fully confirmed in the instance that is nearest to us, and the most obvious to our senses.
Laplace has treated a subject connected with the tides, that, so far as we know, has not been touch
ed on by any author before him. This is the stability of the equilibrium of the sea. A fluid surrounding a solid nucleus, may either be so attracted to that nucleus, that, when any motion is communicated to it, it will oscillate backwards and forwards till its motion is destroyed by the resistance it meets with, when it will again settle into rest; or it may be in such a state, that when any motion is communicated to it, its vibrations may increase, and become of enormous magnitude. Whether the sea may not, by such means, have risen above the tops of the highest mountains, deserves to be considered; as that hypothesis, were it found to be consistent with the laws of nature, would serve to explain many of the phenomena of natural history. Laplace, with this view, has inquired into the nature of the equilibrium of the sea, or into the possibility of such vast undulations being propagated through it. The result is, that the equilibrium of the sea must be stable, and its oscillations continually tending to diminish, if the density of its waters be less than the mean density of the earth; and that its equilibrium does not admit of subversion, unless the mean density of the earth was equal to that of water, or less. As we know, from the experiments made on the attraction of mountains, as well as from other facts, that the sea is more than four times less dense than the materials which comthe solid nucleus of the globe are at a me
dium, the possibility of these great undulations is entirely excluded; and therefore, says Laplace, if, as cannot well be questioned, the sea has formerly covered continents that are now much elevated above its level, the cause must be sought for elsewhere than in the instability of its equilibrium.
With the questions of the figure of the earth, and of the flux and reflux of the sea, that of the precession of the equinoxes is closely connected; and Laplace has devoted his fifth book to the consideration of it. This motion, though slow, being always in the same direction, and therefore continually accumulating, had early been remarked, and was the first of the celestial appearances that suggested the idea of an annus magnus, one of those great astronomical periods by which so many days
years are circumscribed. As it affects the whole heavens, and as the changes it produces are spread out over the vast extent of 25,000 years, it has proved a valuable guide amid the darkness of antiquity, and has enabled the astronomer to steer his course with tolerable certainty, and here and there to discover a truth in the midst of the traditions and fables of the heroic ages.
Newton was the first who turned his thoughts to the physical cause of this appearance; and it required all the sagacity and penetration of that great man to discover this cause in the principle of universal gravitation. The effect of the forces of the
sun and moon on that excess of matter which surrounds the earth at the equator, must, as he has proved, produce a slow angular motion in the plane of the latter, and in a direction contrary to that of the earth's rotation. The accurate analysis of the complicated effect that was thus produced, was a work that surpassed the power, either of geometry or mechanics, at the time when Newton wrote; and his investigation, accordingly, was founded on assumptions that, though not destitute of probability, could not be shown to be perfectly conformable to truth; and it even involved a mechanical principle, which was taken up without due consideration. Nevertheless, the glory of having been first in the career, is not tarnished by a partial failure, and is a possession which the justice of posterity does not suffer Newton to share even with those who have since been more successful in their researches.
The first of these was D'Alembert. cellent mathematician gave a solution of this problem that has never been surpassed for accuracy and depth of reasoning, though it may have been, for simplicity and shortness. He employed the principle already ascribed to him of the equilibrium among the forces destroyed when any change of motion is produced; and it was by means of the equations that this proposition furnished, that he was enabled to proceed without the introduction of
hypothesis. Solutions of the same problem have since been given by several mathematicians, by Thomas Simpson, Frisi, Walmsley, &c. and many others; not, however, without some difference (such as the difficulty of the investigation) in the results they have obtained. Laplace has gone over the same ground, more that he might give unity and completeness to his work, than that he could expect to add much to the solution of D'Alembert. As he has proceeded in a more general manner than the latter, he has obtained some conclusions not included in this solution. He has shown, that the phenomena of the precession and nutation must be the same in the actual state of our terraqueous spheroid, as if the whole was a solid mass; and that this is true, whatever be the irregularity of the depth of the sea. He shows also, that currents in the sea, rivers, trade-winds, even earthquakes, can have no effect in altering the earth's rotation on its axis. The conclusions with regard to the constitution of the earth that are found to agree with the actual quantity of the precession of the equinoxes are, that the density of the earth increases from the circumference toward the centre; that it has the form of an ellipsoid of revolution, or, as we use to call it, of an elliptic spheroid; and that the compression of this spheroid at the poles is between the limits of and part of the radius of the equator.
The second part of Laplace's work has for its