of the original orbits of both may be destroyed, both worlds being finally precipitated on the sun, or driven farther and farther from this luminary, until they are lost in infinite space. This inquiry, in a more extended form, will be examined hereafter. We proceed to build up our imaginary system. Thus far we have regarded our planet and its satellite as mere material heavy points. In case we give to them magnitude and rotation on an axis, the velocity of rotation will determine the figure of the planet and of its satellite. These figures will deviate from the exact spherical form, and this change of figure will sensibly affect the stability of the axis of rotation, and will introduce a series of subordinate movements, each of which must become the subject of research; and to write out the future history of the system, these minute and concealed changes must likewise receive their mathematical expression. Having thus thoroughly mastered all the phenomena of this system of three bodies, the astronomer now adds another planet, whose mass is assumed, together with the direction and intensity of its primitive impulse.' Its orbit is now computed, subject to the greatly predominant influence of the sun, but sensibly affected by the quantity of matter in the old planet and its satellite, which prevents it from forming a fixed and unchangeable orbit in space. Again he is obliged to return to an examination of his first planet and its moon, for these again break away from their previous routes, and in consequence of the action of the second planet, assume new orbits, and are subjected to periodical fluctuations, which demand critical examination, and without a knowledge of which no truthful history of the planetary system can be written. To the second planet let us now add several satellites, each of which has its mass assigned, and the direction and intensity of the impulsive force by which they are projected in their orbits. Here, then, is a subordinate system demanding a complete examination. The satellites mutually affect each other's motions, and each is subjected to the influence of the primitive planet and its moon. Again does the physical astronomer review his entire investigation. The addition of these satellites to his second planet has introduced changes in all the previous bodies of the system, which must now be computed, to keep up with the growing complexity. This task is at last accomplished. All the changes are accurately represented. Analysis has mastered the system, and the history of its changes are written out for hundreds and thousands of years. A third planet, with its satellite, is now added. This new subordinate system is discussed, and its op eration on all the previous planets and satellites computed, and after incredible pains, the astronomer once more masters the entire group, and follows them all with unerring precision, through cycles of changes comprehending thousands or even millions of years. Thus does the difficulty of grasping the system increase in a high ratio by the addition of every new planet and satellite, till finally the last one is placed in its orbit, and the system is complete, so far as planets and satellites are concerned. Through this complicated system now cause thousands of comets to move in eccentric orbits, coming in from every quarter of the heavens, plunging downwards towards the sun sweeping with incredible velocity around this centras luminary, and receding into space to vast distances, either to be lost forever, or to return after long peri ods to revisit our system. These wandering bodies must be traced and tracked, their orbits fixed, their periods determined, their influence on the planets and satellites, and that exerted by these on the comets, must be computed and determined; then, and not till then, does the physical astronomer reach to a full knowledge of this now almost infinitely complex system. In this imaginary problem it will be observed that certain quantities were invariably assumed before the discussion could proceed. The mass of the sun—the mass of each planet and satellite—the intensity and direction of the primitive impulse given to each planet and satellite-these quantities are supposed to be known. If, now, the astronomer has actually accomplished the resolution of the imaginary problem, and has obtained analytic expressions which write out and reveal the future history of his assumed planets and satellites, as they revolve around his assumed sun, if in these expressions he should substitute the actual quantities which exist in the solar system for those assumed, his expressions would then give the history of the solar system for coming ages and by reverse action would reveal its past history with equal certainty. Before we can, therefore, bring the power of analy sis to bear on the resolution of the grand problem of nature, we must interrogate the heavens, and obtain the absolute weight of our sun, of each planet, and of every satellite. Next we require the intensity In case and direction of the impulsive force which projected each planet and satellite in its orbit, and which would have fixed forever the magnitude and position of that orbit, in case no disturbing causes had operated to modify the action of the primitive impulse. Having thus attempted to exhibit, at a single view, the general outlines of the great problem of the solar system, we propose now to return to the examination of a system composed of three bodies; and to fix our ideas, we assume the sun, earth, and moon. the earth existed alone, the elliptic orbit described in its first revolution around the sun would remain unchanged forever, and having pursued it, and marked its changes of velocity in the different parts of its orbit for a single revolution, this would be repeated for millions of years. But let us now give to the earth its satellite, the moon, and setting out from its perihelion, or nearest distance from the sun, let us endeavor to follow these two bodies as they sweep together through space, and mark particularly the effect produced on the moon's orbit by the disturbing influence of the sun. To give to the problem greater simplicity, let us conceive the plane of the moon's orbit to coincide with the earth's. The law of gravitation which gives to every attracting body a power over the attracted one, gravity increasing as the distance decreases, it will be perceived that when the earth and moon are nearest to the sun, whatever in. fluence the sun possesses to embarrass or disturb the motions of the moon about the earth, will here be exercised with the greatest effect. But since the sun is exterior to the moon's orbit, its tendency will be to draw the moon away from the earth, and cause het to describe around her primary a larger orbit, in a longer period of revolution than would have been employed in case no sun existed, and the moon was given up to the exclusive control of the earth. Starting the planet on its annual journey, as it recedes from the sun in passing from its nearest to its most remote distance, or from perihelion to aphelion the moon is gradually removed from the disturbing influence of the sun; it is subjected more exclusively to the earth's attraction; its distance from the earth grows less, and the periodic time becomes shorter. These changes continue in the same order until the earth reaches its aphelion. There the moon's orbit is a minimum, and its motion is swiftest. In passing from the aphelion to the perihelion, the earth is con stantly approaching the sun, and as the sun's influence on the moon increases as its distance diminishes, its orbit will now expand by slow degrees, and the periodic time will diminish until on reaching the perihelion, in case the figure of the earth's orbit remains unchanged, the moon's periodic time will be restored to its primitive value, and all the effects resulting from the elliptic figure of the earth's orbit will have been entirely effaced. Thus far we have directed our attention exclusively to the changes in the distance of the moon and its periodic time. But the moon's orbit is elliptical, as well as the earth's, and it is manifest that the sun's influence will operate to change not only the magnitude of this orbit, but will in like manner produce a change in the position of the moon's perigee, or nearest point of distance from the earth. If the earth were stationary, and the moon revolved around it, passing |