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hours, 16 minutes. As to Mercury, it's smallness and proximity to the Sum prevent us from discovering, whether it have any rotatory motion; but no doubt in this it resembles the other planets.

The fixed stars, which are Suns similar to our own, and round which planets and comets probably revolve as in our system, have likewise, according to all ap→ pearance, rotatory motions. Besides, the axis of ro tation of a star may change it's position in the heavens, either by the attraction and disposition of the planets with which it is surrounded, or by the attraction of some large comets belonging to the neighbouring systems. These hypotheses, which are very admissible, serve to explain, why we sometimes perceive certain stars appear or disappear, and why some vary in their magnitude and lustre. When a star presents to us the plane of it's equator, we see it of a circular figure, and with it's greatest brightness, as if it were perfectly spherical. But if a star be con siderably flattened, and the plane of it's equator become inclined with respect to us, it will diminish in size and lustre; and may even disappear entirely from our sight, when, exhibiting to us it's edge, we no longer receive from it a sufficient quantity of light to be perceptible. By a contrary movement of the plane of their equator we may be enabled to see new stars, which will afterward disappear, as they return to their former state. Such was the great star seen in the constellation of Cassiopeia in 1572.

The motion, by which the planets revolve about their axes, does not follow the same laws, as that by which they are carried round the Sun. The latter i

hore slow, in proportion as the planet is farther disi tant from the Sun: while Jupiter and Saturn, whichd are more remote than Venus, the Earth, or Mars, re-, volve round their axes in a much shorter period than these planets. Yet these two motions may be produced by one and the same cause. It is sufficient, that the planets should not have been originally projected through space by forces, the directions of which passed through their centres of gravity, or the centres of their mass. For on this hypothesis a planet receives two motions, one of rotation round it's axis, the other of revolution round a centre: the velocity of the latter is independant of the direction of the force with respect to it's centre of gravity, and would always be the same with the same force; but the planet will turn round it's axis with the more quickness, in proportion as the direction of the force passes farther from it's centre of gravity. Thus a cannon ball, issuing from a gun, has a rotatory motion, when the force resulting from the impulse of the powder, the friction, and some shocks against the sides of the orifice, does not pass through it's centre of gravity, which must generally be the case.

For this explanation of the double motion of the planets we are indebted to John Bernoulli; and I cannot take leave of this great geometrician, without rendering him farther homage. I have not concealed some weaknesses, by which he paid tribute to hunan nature; but posterity now sees in him only the man of genius, and the worthy rival of his brother James. No doubt the reader expects me here to draw a comparison between them; and accordingly

I shall

I shall give this parallel in few words, agreeably, I believe, to the opinion generally received among geometricians.

Extent, strength, and profundity characterize the genius of James Bernoulli: in John we find more flexibility, and that turn of mind which applies, indifferently to all objects. The former published a greater number of truly original works, which belong exclusively to himself; as the theory of spiral lines, the problem of the elastic curve, that of isoperimeters, which occupies so great a place in the history of geometry, the principle from which was afterward derived the solution of problems in dynamics, the treatise de Arte Conjectandi, &c. The latter was fond of uncommon and curious questions in every branch of mathematics: he had a peculiar art of proposing and resolving new problems: whatever object was offered to his investigation, he entered into it with extreme readiness, and never treated any one without placing it in the most perspicuous light, and making some important discovery in it. To conclude, James Bernoulli became what he was of himself, and died at the age of fifty: John was initiated into mathematics by his brother, and lived fourscore years? In this he had immense advantage: for if all the faculties of the human mind be enfeebled by age, this loss is compensated in the mathematical sciences, which are the fruits of study and reasoning, by the mass of knowledge acquired; and by a long practice in geometrical methods, which enables us to discern that which is most proper for the solution of a problem; so that we are often saved many useless attempts, and the

powers

powers of the mind are less exhausted. All things considered, I compare James Bernoulli to Newton, John to Leibnitz.

I now resume the explanation of the great phenomena of nature by the principle of attraction. Of this number is the alternate motion of the ebb and flow of the sea.

Every person knows, that in large and deep seas the waters alternately rise and fall in about the space of six hours; so that in twenty-four hours there are two tides, each consisting of an ebb and flood. The strength of the flood pushes back the water of rivers, which run into the sea; and during the ebb they resume their ordinary course. It is only in the ocean, that the flux and reflux are very perceptible: they are scarcely, if at all, to be observed in lakes, gulfs, rivers, and in general all bodies of water of little extent compared with the ocean. Sometimes, however, the water in mediterranean seas, being forced into narrow places, exhibit ebbing and flowing motions. Such are perceptible at the entrance of the gulf of Venice, for example; though they are very trifling, or scarcely observable, on the greater part of the coasts of the Mediterranean.

The Cartesians pretended, that the waters of the sea rose in consequence of a pressure, which the Moon, when in the meridian, exerted on the portion of the atmosphere placed between it and the sea; and that they afterward fell by their own weight, when the Moon went down. But for such a pressure to take place, it is necessary that the atmosphere beneath the Moon should have something to prevent

it from extending in all directions; otherwise the Moon will only take the place of a volume of air equal to it's own bulk, and leave the waters of the sea in the same state as they were.

At present there is no doubt, that, gravitation be ing reciprocal between all the bodies in the universe, the ebbing and flowing of the sea are produced by the attractions of the Sun and Moon, combined with the daily rotation of the Earth about it's axis. When the Moon is in the meridian, it attracts the waters of the sea, which consist of corpuscles detached from the rest of the globe; and it likewise attracts the whole mass of the Earth, which must be considered as uniting entirely in the centre. Now, as the waters are nearer the Moon than the centre of the Earth is, they are attracted more than the centre, and conse, quently they must tend to leave the Earth, if the expres sion may be allowed, and rise. Thus a flood is produced. On the contrary, in the point diametrically opposite, or at the antipodes of this place, the waters, being more remote, are less attracted than the centre of the Earth, and consequently they must also recede from this centre, or rise; which produces another flood. Thus, in both these places, the motion of flood is occasioned by the difference between the Moon's attractive force at the centre of the Earth and at the surface of the waters, and must occur at the same time at each extremity of the Earth's diameter in a line with the Moon. As to the ebb, this takes place, when, the Moon having left the meridian, it's force of attraction diminishes, and allows the natural weight of the waters to depress them.

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