therefore, to separate itself from it, but it is retained by its gravity, which this tendency diminishes. Twelve hours afterwards, this particle is opposite to the Sun, which attracts it less forcibly than it does the centre of the Earth; the surface of the terrestrial globe therefore tends to separate itself from it, but the gravity of the particles retains it. This force is therefore diminished also in this case by the solar attraction. But since the distance of the Sun is very great, compared with the radius of the Earth, it is easy to see that the diminution of gravity in each case is very nearly the same. A simple decomposition of the action of the Sun upon the particles of the ocean, is sufficient to shew, that in any position of this body, relatively to these particles, its action in disturbing their equilibrium, becomes the same after twelve hours. And it may be established as a general principle in mechanics, that the state of a system of bodies, in which the primitive conditions of

motion have disappeared by the resistances it meets with, is periodic, like the forces which solicit it. The state of the ocean should therefore be the same at each interval of half a-day, so that the tide should ebb and flow in this interval.

The law according to which the water rises and falls, may be thus determined. Let us conceive a vertical circle, whose circumference represents half a day, and whose diameter is equal to the whole tide, or the difference between the height of high and low water, and let the arcs of this circumference, reckoning from the lowest point, express the time elapsed since low water, the versed sines of these arcs will express the heights of the water, corresponding to these times. Thus, the ocean in rising, covers in equal times, equal arcs of this circumference. This law is exactly observed in the middle of the ocean, which is free on every side, but in our harbours, local circumstances produce some deviations. The sea employs rather a longer time to fall than to rise,

which difference at Brest amounts to about * 10 minutes.

The greater the extent of the surface of the water, the more perceptible are the phenomena of the tides. In a fluid mass, the impressions which a fluid particle receives, are communicated to the whole. It is thus that the action of the Sun, which is insensible on an insulated particle, produces on the ocean such remarkable effects. Let us imagine, at the bottom of the sea, a curved canal, terminated at one of its extremities by a vertical tube, rising above the surface of the water, and which, if prolonged, would pass through the centre of the Sun.

The water will rise in this tube by the direct action of the Sun, which diminishes the gravity of its particles, and particularly by the pressure of the particles enclosed in the canal, which all make an effort to unite themselves beneath the Sun. The elevation of the water in the tube

* 14/27".

above the natural level of the sea, is the integral of all these infinitely small efforts. If the length of this canal is increased, this integral also becomes greater, because it extends over a larger space, and because there will be a greater difference in the quantity and direction of the forces, by which the extreme particles are sollicited.

By this example we see the influence which the extent of the sea has upon the phenomena of the tides, and the reason why they are insensible in the very small seas, as the Euxine and the Caspian. The magnitude of the tides depends also much on local circumstances. The oscillations of the ocean, when confined in a narrow channel, may become extremely great, and these may be augmented by the reflection of the waters from the opposite shore. It is thus, that the tides, very small in the South Sea islands, are very considerable in our harbours.

If the ocean covered a spheroid of revolution, and experienced no resistance to its motion, the instant of high water would

be that of the passage of the Sun over the superior or inferior meridian; but it is not thus in nature; local circumstances produce great variations in the times of high water, even in harbours that are very near each other. To have a just idea of these variations, we may suppose a large canal communicating with the sea, and extending into the land; it is evident that the undulations which take place at its entrance, will be propagated successively through its whole length, so that the figure of its surface will be formed by the undulations of large waves in motion, which will be incessantly renewed, and will describe the whole length of the interval of half-a day. These waves will produce at every point of the canal, a flux and reflux, which will follow the preceding laws, but the hours of the flowing will be retarded, in proportion as the points are further from the entrance of the canal. What we have here said of a canal, may be applied to rivers whose surfaces rise and fall by similar waves, notwithstanding the contrary motion These waves are observed

of their waves.