ought to require eighteen years to perform its revolution in the heavens, while observation showed that the revolution was actually performed in one half of this period. This great philosopher exhausted all his skill and power in the vain effort to overcome this difficulty. He died, leaving the problem unresolved, bequeathing it to his successors, as a research worthy of their utmost efforts.

Astronomers did not fail to recognize the high claims of this investigation. Gravitation was once more endangered. The most elaborate computations were made, and the results obtained by Newton were so invariably verified by each successive computer, that it seemed utterly impossible to avoid the conclusion; they were absolutely accurate, and that the theory of gravitation must be modified in its application to this peculiar phenomenon. At length the problem was taken up by the distinguished astronomer Clairaut. After repeating, in the most accurate manner, the extensive computations of his predecessors, reaching invariably the same results, he finally abandoned the law of gravitation in despair, pronounced it incapable of explaining the phenomenon, and undertook to frame a theory which should be in accordance with the facts.

This startling declaration of Clairaut excited the greatest interest. An abandonment of the theory of gravitation was nothing less than returning once more to the original chaos which had reigned in the planetary worlds, and of commencing again the resolution of the great problem which it had long been hoped was entirely within the grasp of the human intellect. In this dilemma, when the physical astrono

mer had abandoned the law of gravitation in despair and the legitimate defenders of the theory were mute an advocate arose where one was least to be ex pected. Buffon, the eminent naturalist and metaphysician, boldly attacked the new theory of Clairaut pronounced it impossible, and defended the law of gravitation by a train of general reasoning, which the astronomer felt almost disposed to treat with ridicule. What should a naturalist know of such matters? was rather contemptuously asked by the astronomer. It is true he knew but little, yet his attack on Clairaut had the effect to induce the now irritated astronomer to return to his computations, with a view to overwhelm his adversary. He now determined to rest satisfied with nothing short of absolute perfection.— A certain series which had been reached by every computer, and the value of whose terms had been regarded as decreasing by a certain law, until they finally became inappreciable, from their extreme minuteness, and therefore might, without sensible error, be rejected, was found, on a more careful examination, to undergo a most remarkable change in its character. It was true that the value of its terms did decrease till they became exceedingly small; but so far from becoming absolutely nothing, on reaching a certain value, the decrease became changed into increase the sum of the series expressing the velocity of the moon's perigee was in this way actually doubled, and Clairaut found, to his inexpressible astonishment, that the investigation which had been commenced with the intention of forever destroying the universality of the law of gravitation, resulted in

his own defeat, and in the perfect and triumphant establishment of this great law.

Thus far, in our examinations of the moon and earth, we have regarded their orbits as lying in the same plane, an hypothesis which greatly simplifies the complexity of their motions. This, however, is not the case of nature. The moon revolves in an orbit whose plane is inclined under an angle of about four degrees to the plane of the ecliptic. During half of its journey, it lies above the plane of the earth's orbit, while the remaining part of its route is performed below the ecliptic. Thus does the moon, at each revolution, pass through the ecliptic at two points, called the nodes, which points, being joined by a straight line, gives us the intersection of the plane of the moon's orbit with that of the earth. This line of intersection, called the line of the nodes, but for the disturbing influence of external causes, would re main fixed in the heavens. But we know it to be constantly fluctuating, and in the end performing an entire revolution. The exact amount of this change has been made the subject of accurate examination, and the law of its movement has been found to result precisely from the law of gravitation. Not only is the line of intersection of the plane of the moon's orbit with that of the earth constantly changing, but theory, as well as observation, has ascertained that a series of changes are equally progressing in the angles of inclination of these two planes. The limits are narrow, but the oscillations are unceasing complicating more and more the relative motions of these two remarkable bodies.

In the physical examination of the revolution of

the planetary orbs by the application of the law of gravitation, the general features of the investigation are greatly simplified by the fact that the planets and satellites may be regarded as spherical bodies, and may in general be treated as though their entire mass were condensed into a material heavy point, situated at their centre. While this statement is true in its broader application to the theory of planetary perturbations, or even in the theory of the sun's action on the planets, especially the more distant ones, it is by no means to be admitted, when we come to a critical examination of the figures of the planets, and the influence exerted by these figures on their near satellites.

In case the earth had been created an exact sphere, and had been projected in its orbit without any rotation on an axis, then would its globular figure have remained without sensible change. But as it revolves swiftly on its axis, the laws of motion and gravitation come in to modify the figure of the earth, and to change it from an exact spherical figure to one which is flattened at the poles and protuberant at the equator. Newton's sagacity detected this result as a necessary consequence of the action of gravitation, and he actually computed the figure of the earth from theory, long before any observation or measurement had created a suspicion that its form was other than spherical. The truly wonderful train of consequences flowing from the spheroidal form of the earth gives to this subject a high interest, and demands as close an examination of its principal features as the nature of our investigations will permit.

Give to the earth, then, an exactly spherical form

and a diameter of 8000 miles, with a rotation on an axis once in twenty-four hours, and let us critically examine the consequences. A particle of matter

situated on the equator is 4,000 miles from the earth's axis, and since it passes over the circumference of a circle whose radius is 4,000 miles, it will move with a velocity of about one thousand miles an hour. As we recede from the equator towards the poles, either north or south, the particles revolve at the extremities of radii constantly growing shorter and shorter, until finally at the exact pole there is no motion whatever. But in every revolving body, a centrifugal force is generated a tendency or disposition to fly from the axis of rotation in a plane perpendicular to this axis.

Such is the power of this centrifugal force, that if it were possible to make the earth rotate seventeen times in twenty-fours, instead of once, bodies at the equator would be lifted up by the centrifugal force, and the attraction of gravitation would be counterpoised, if not absolutely overcome. The force of gravity exerts its power in directions passing nearly through the centre of the earth, while the centrifugal force is always exerted in a direction perpendicular to the axis of rotation. The consequence is manifest, that these two forces cannot counterpoise each other, except in their action on particles situated on the equator of the revolving body. Let us consider the condition of a particle situated any where between the equator and the pole, and free to move under the joint action of these two forces.

In order that such a particle may be held in equili brium, the two forces must act on the same straight line, and in opposite directions. This is not the case