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boldly cut the knot, by pronouncing the acceleration as impossible, and without any foundation in fact. Others admitted the fact, but finding it impossible to account for it on the hypothesis of gravitation, conceived the idea that the moon was moving in some ethereal fluid capable of resisting its motion, and producing a diminution in its periodic time of revolution. That acceleration should be the effect of resistance, may seem to some very strange, but a little reflection will render the subject clear. In case the moon's orbitual motion is resisted, then the centrifugal force, which depends on the velocity, becomes diminished, and the central power of the earth draws the moon closer to itself, decreases the magnitude of its orbit, and in like manner reduces the time of accomplishing one revolution about the earth.
Finding no better solution of the mystery, and being obliged to acknowledge the fact that the mean motion of the moon was becoming swifter and swifter, from the action of a resisting medium, there was no escape from the final consequences; and it was by some believed that the elements of decay existed, that the doom of the system was fixed, and although thousands, possibly millions, of years might roll away before the fatal day, yet it must come, slowly, but surely as the march of time. Such was the condition of the problem when Laplace gave the powers of his giant intellect to the resolution of this mysterious subject. The consequences involved gave to it an unspeakable interest, and the world waited with keen anxiety to learn the result of the investigations of this great geometer. Long and difficult was the struggle -slow and laborious the task of devising and tracing
out the secret causes of this inscrutable phenomenon. The planets are weighed and poised against the earth, their effects computed on its orbit, the final re sult of these effects determined, and the reflex influence on the moon's motion computed with the most extraordinary precision. Under the searching exanination of Laplace's potent analysis, nature is conquered, the mystery is resolved, the law of gravitation is vindicated—the system is stable, and shall endure through periods whose limits God alone, and not man, shall prescribe.
Follow me in a simple explanation of this most remarkable discovery. It has already bee 1 stated, that in case the earth's orbit could remain unchanged, that the mean period of the moon, as derived from a thousand of its revolutions, would be constant, and would endure without the slightest change for millions of years. But this permanency of the earth’s orbit does not exist.-Laplace discovered that under the joint action of all the planets, the figure of the earth's orbit was slowly changing ; that while its longer axis remained invariable, that its shape was gradually be. coming more and more nearly circular. At the end of a vast period, its ellipticity would be destroyed, and the earth would sweep around the sun in an orbit precisely circular. Attaining this limit, a reversed action commences—the elliptic form is resumed by slow degrees—the eccentricity increases from age to age_until, at the end of millions of years, a second . limit is reached. The motion is again reversed—the orbit again opens out, approaches its circular form, and thus vibrates backwards and forwards in millions
of years, like some mighty pendulum beating tho slowly ebbing seconds of eternity!
But do you demand how this change in the figure of the earth's orbit can affect the moon's mean motion? The explanation is easy. Were it possible to seize the earth and hurl it to an infinite distance from the sun, its satellite, now released from the disturbing influence of this great central mass, would yield itself up implicitly to the earth's control. It would be drawn closer to its centre of motion, and its orbit being thus diminished, its periodic time would be shorter, or its motion would be accelerated or made swifter than it now is. This is an exaggerated hypothesis, to render more clear the effect produced by removing the earth farther from the sun. Now the change from the elliptical to the circular form, which has been progressing for thousands of years, in the earth's orbit, is, so far as it goes, carrying the earth at each revolution a little farther from the sun, releasing in this way the moon, by slow degrees, from the disturbing influence of that body; giving to the earth a more exclusive control over the movements of its satellite, and thus increasing the velocity of the moon in its orbit from age to age. But will this acceleration ever reach a limit ? Never, until the earth's orbit becomes an exact circle, at the end of millions of years. Then, indeed, does the process change. At every succeeding revolution of the earth in its orbit, its ellipticity returns—its distance from the sun diminishes—the moon is again subjected more and more to the action of the sun, is drawn farther and farther from the earth, and its periodic time slowly increases. Thus is acceleration changed in to retardation, and at
the end of one of these mighty cycles, consisting of millions of years, an exact compensation is effected and the moon's motion having gone through all its changes, once more resumes its original value.
I can never contemplate this wonderful revolution without feelings of profound admiration. Such is the extreme slowness of this change in the moon's mear. motion, that in the period of three thousand years she has got only four of her diameters in advance of the position she would have occupied in case no change whatever had been going on. Here, then, is a cycle of changes extending backward to its least limit millions of years, and extending forward to its greatest limit tens of millions of years, detected and measured by man, the existence of whose race on our globe has scarcely been an infinitesimal portion of the vast period required for the full accomplishment of this entire series of changes.
May it not, then, be truly said, that man is in some sense immortal, even here on earth. What is time to him, who embraces changes in swiftly revolving worlds, requiring countless ages for their completion, within the limits of an expression so condensed that it may be written in a single line? Does he not live in the past and in the future, as absolutely as in the present ? Indeed, the present is nothing—it is the past and future which make up existence.
In the example of the moon's acceleration just ex. plained, we must not fail to notice a most remarkable fact. It is this:--The slow change in the figure of the earth's orbit, occasioned by the joint action of all the planets, and upon which depends the acceleration of the moon's mean motion, is so disguised, that but for its reflex influence on the moon, the probability is it would have escaped detection for thousands of years. The direct effect is almost insensible, but being indirectly propagated to the moon, it is displayed in a greatly exaggerated manner-is in this
— way detected, and finally, after incredible pains, traced to its origin, and demonstrates in the most beautiful manner the prevalence of the great law of universal gravitation.
Since the general adoption of this law, the human mind has been, in not a few instances, disposed to abandon its universality, and seek for a solution of some intricate problem, by which it was perplexed, in some change or modification of the law ; but in no instance has the effort to fly from the law been successful. No matter how long and intricate the examination, how far the mind might be carried from this great law, in the end it must come back and acknowledge its universal empire over our entire system.
It has already been remarked, that one of the effects of the sun's disturbing influence exerted on the moon, was to occasion a change in the position of its perigee, causing it to complete an entire revolution in the heavens in about nine years. The theory of gravitation gave a very satisfactory account of this phenomenon generally; but when Sir Isaac Newton undertook the theoretic computation of the rapidity with which the moon's perigee should move, he found, to his astonishment, that no more than one half of the observed motion of the perigee was obtained from theory. In other language, in case the law of gravi tation be true, Newton found that the moon's perigeu