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in question, for gravity draws the particle to the centre of the earth, while the centrifugal force urges it from the axis in a plane perpendicular to that axis The direction of these two forces is inclined under an angle which is nothing at the equator, and increases from the equator to the poles. But the effect produced by the centrifugal force may always be obtained by the joint action of two forces, the one directed to the centre of the earth, the other tangent to the earth's surface. Substituting these two forces for the centrifugal force, we perceive that the partial force directed towards the earth’s centre is destroyed by gravitation, while the tangential force exerts its full power to move the particle towards the equator of the earth.

This being understood, it is manifest that as particles are coming constantly from both poles towards the equator, that a change of figure in the earth must be effected. It becomes protuberant at the equator, and is flattened at the poles.

The question now arises, whether there be any limit to this change of figure. In case the velocity of rotation continues undiminished, is there not reason to fear that the earth will grow more and more protuberant at the equator, heaping up the matter higher and higher, till the figure of the earth be destroyed, and its surface rendered uninhabitable? Theory has answered this important question; and it has been fully demonstrated that the figure of the earth cannot pass a limit, which it has even now actually attained, and its present form will not change, from the action of the centrifugal force, in millions of years. А condition of equilibrium has been attained, and all further change is at an end. Indeed, if we examine carefully the subject, we may readily perceive, from the nature of the forces, and the conditions of the problem, that such a result might have been anticipated. As the earth grows more protuberant, change ing from the spherical form, the particles must be heaved up the side of this elevated ridge which belts the earth around the equatorial regions, and finally the resistance they meet from the elevation they are obliged to overcome, is quite equal to the moving force, and the two destroy each other. This point attained, equilibrium ensues, and further change becomes impossible.

Such is the beautiful order of nature, such the admirable arrangement for stability and perpetuity, every where manifested, that the thought constantly comes to the mind that divine wisdom alone could have framed so admirable a system.

But the question may here arise, is this a mere theoretic result? Has observation confirmed the theoretic figure? I answer that observations, the most numerous and diversified, have all united their harmonious testimony to the truth of these beautiful results. In executing exact measures of the degrees of a meridian passing through the poles round the earth, the length of the degree is found to increase from the equator towards the poles, showing that the curvature is more flattened as we recede from the equator. But a more delicate proof is found in the vibrations of the pendulum. A pendulum of a given length will vibrate with a velocity precisely proportioned to the intensity of the force of gravity which operates on it. But the intensity of gravity decreases

as the square

of the distance from the centre increases Bo that it is manifest that the force of gravity is less at the equator than at the poles, in case the surface at the equator is farther from the centre than at the poles, which is the fact asserted by theory.

This being understood, we are prepared to determine the exact figure of the earth, by transporting a pendulum of given length from the equator to different latitudes north and south. The number of vibrations in one hour being accurately counted at the equator, as we recede north or south, will determine with certainty whether we are approaching to, or going farther from the earth's centre. These experiments have actually been performed, and with the most satisfactory results. The number of vibrations in an hour increases the farther we go north or south, and in a ratio giving the strongest confirmation to the truth of the earth's figure derived from the theoretio investigations—each combining to show that the polar diameter of the earth is but 7,898 miles, while the equatorial diameter is 7,924 miles, producing a sort of ridge or belt around the equatorial regions rising about thirteen miles above the general spherical surface described about the polar axis as a diameter.

More than two thousand years have passed away since a discovery was made, showing that the sun's path among the fixed stars was slowly changing.The point at which it crossed the equatorial line, and which for ages had been regarded as fixed, was finally detected to have a slow retrograde motion, producing the precession of the equinoxes. The fact was received but, no depth of penetration, no stretch of intellectual vigor could divine the cause of this inexplicable change. Another fact was revealed about the same time. It was found by attentive examination, that the north pole of the heavens, the point in which the prolongation of the earth’s axis pierces the celestial sphere, was actually changing, by slow degrees, its place among the fixed stars. The bright star which, in former ages, had marked the place of the pole, and whose circle of diurnal revolution was scarcely to be perceived from its smallness, as centuries slowly glided by, was increasing its distance from the pole, gradually describing around it a circle of greater radius. An attentive examination of the stars near the pole soon demonstrated the fact that it was an actual motion of the pole, and not of the stars in its neighborhood.

Now, incredible as this statement may appear, modern science has traced these phenomena, the revolution of the equinoctial point, and the movement of the north pole of the heavens, to a common origin, and has demonstrated, in the clearest manner, that they are both consequences of the spheroidal figure of the earth, which we have just examined. It is not my design to enter into an elaborate investigation of this wonderful subject, but, in accordance with the plan already announced, I cannot leave you with a mere announcement of a truth so startling, without some effort to explain how this may be. The subject is difficult, but favored by your close attention, I do not despair of rendering it approximately intelligible.

Let us conceive the earth's axis to be a solid bar of iron driven through the centre of the earth, coming out at the poles, and extending indefinitely towards the sphere of the fixed stars. Now turn this

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axis up until it stands perpendicular to the plane of the orbit in which the earth revolves around the sun. Then do the equator and ecliptic exactly coincide, and if the fixed stars are at a distance nearly infinite, the point in which the earth’s axis prolonged pierces the heavens will appear stationary, so far as the revolution of the earth in its orbit is concerned. Now if this iron axle could be grasped by some giant hand, and drawn away from its upright or perpendicular position, the solid earth would turn with it, and the equator, ceasing to coincide with the ecliptic or plane of the earth's orbit, comes to be inclined to it, under an angle precisely equal to the angle through which the axis has been inclined. It is thus seen that no change can be wrought on the position of the axis, that does not involve a corresponding change in the whole earth, and especially in the plane of the equator, which must ever remain perpendicular to the axis in all its positions.

The reverse of this proposition is equally manifest. If the solid earth be seized at the equator, and be turned up or down, the axis will participate in this movement, and its change will exhibit itself in the changed position of the point in which it meets the celestial sphere. One step more, and the difficulty is surmounted.Conceive a flat wheel of wood floating on still water. Through its centre pass an axle which stands perpendicular to the surface of the wheel and water. So long as the wheel floats level, the axle stands erect, but in case the north half of the wheel is tilted down under the water, the south half at the same time rising out of the water, the axis will tilt towards the north. Bring the wheel again to its level position. Now

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