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in conic sections: the circle, ellipse, parabola and hyperbola.

The second law, fixing the equality of the spaces passed in equal times, by the lines joining the planets to the sun as these were carried round in their elliptio orbits, now became applicable to all bodies revolving about a fixed centre, in any curve, and according to

any law.

The third law, recognising the proportion between the squares of the periodic times and the cubes of the mean distances of the planets, was extended to the satellites, and to the comets; modified slightly in the case of the larger planets, by taking into account their masses or quantities of matter.

Here we close the era of research by observation. The mind has gained its last grand object. The era of physical astronomy dawns ; new and wonderful scenes open, and to the contemplation of these, wo shall soon invite your attention.

LECTURE V.

UNIVERSAL

GRAVITATION APPLIED TO THE EXPLANAT. ON

OF THE PHENOMENA OF THE SOLAR SYSTEM.

The progress of the mind, in its efforts to reach a satisfactory explanation of the movements of the heavenly bodies, previous to the discovery of universal gravitation, had been made independent of any guiding law.

The mind had been feeling its way slowly and laboriously, guiding its direction by attentively watching the celestial phenomena, and relying for its success exclusively on the accuracy and number of its observations. Each discovery made was isolated, and although it prepared the way for the succeeding ones, it did not in any sense involve them as necessary consequences. By the discovery of the great law of universal gravitation, a perfect and entire revolution had been made in the science of astronomy. A new department was

A now added, which, previous to the knowledge of this law, could have no existence. In this branch of astronomy, the process of investigation being inverted, the mind de scends from one great law to an examination of its consequences, tracing these in their modified and diversified influences to their final limits. Observation now employed to verify discovery, and not as the basis on which, and without which, discovery cannot be made,

The era of physical astronomy is, therefore, the great era in the history of the science. It involves the resolution of the most wonderful problems-it calls into use the most refined and powerful mathematical analysis, and demands the application of the most ingenious and delicate instruments in seeking for the data by means of which its theory may be rendered practically applicable to the problems of nature. The mechanical philosopher in his closet may construct his imaginary system. In its centre he locates a sun, containing a certain mass of matter.–At any convenient distance from this sun he locates a planet, whose weight he assumes. To this planet he gives an impulse, whose intensity and direction are assumed The moment these data are fixed, and the impulse given to the imaginary planet—no matter in what kind of an orbit it may dart away, whether circular, elliptical, parabolic, or hyperbolic—the laws of motion and gravitation asserting their empire, the planet is followed by the mathematician, with a certainty and accuracy defying all escape. He assigns its orbit in the heavens-the velocity of its movement—the period of its revolution. In short, in a single line, he writes out its history with perfect accuracy for a mil

lion years.

If, now, to this simple system of a great central sun and one solitary planet, the physical astronomer add a third body, a moon, to the planet, he assumes its weight, the intensity and direction of the impulsive force starting it in its career, and now his system becomes more complex. Strike the sun out of existence, fix the planet, and the process of binding the satellite in mathematical fetters is precisely similas tu that by which the movements of the planet were prescribed around the sun before the existence of the satellite. But now, with these three bodies the train of investigation becomes more intricate and involved While the planet alone circulated around the sun, such is the undeviating accuracy with which it will forever pursue its path around the sun, that if it were possible to hang up in space along its route golden rings, whose diameter would just permit the flying planet to pass, millions of revolutions will never mark the slightest change. The rings once passed and then fixed, will mark forever the pathway of the solitary planet. But the moment a moon is given to this flying world, in that instant its motion is changed-it is swayed from its original fixed orbit-it no longer passes through the golden rings, and although the physical astronomer may write out in his analytic symbols the future history of his planet and moon, these expressions are no longer marked with the simplicity which obtained in those which recorded the history of the single planet. While solitary, all changes were effected by the planet in one single revolution, and these were repeated in the same precise order in each successive revolution. Now, with the satellite added, there are changes introduced running through many revolutions, and requiring for their complete compensation vast periods of time. Indeed, the inquiry arises, whether this system of a central sun, with a planet and its satellite revolving about it, can be so constituted that the changes which the planet and its moon mutually produce on each other's movements, may not go on, constantly accumulating in the same direction until all features

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