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true place and an apparent place, as astronomers say, on account of parallax. For it seems incredible that the species or rays of the celestial bodies can pass through the immense interval between them and us in an instant, or that they do not even require some considerable portion of time.'
As great discoveries generally lead to a variety of conclusions, the aberration of light affords a direct proof of the motion of the earth in its orbit; and its rotation is proved by the theory of falling bodies, since the centrifugal force it induces retards the oscillations of the pendulum in going from the pole to the equator. Thus a high degree of scientific knowledge has been requisite to dispel the errors of the senses.
The little that is known of the theories of the satellites of Saturn and Uranus is, in all respects, similar to that of Jupiter. The great compression of Saturn occasions its satellites to move nearly in the plane of its equator. Of the situation of the equator of Uranus we know nothing, nor of his compression; but the orbits of his satellites are nearly perpendicular to the plane of the ecliptic, and by analogy they ought to be in the plane of his equator.
Our constant companion, the moon, next claims our attention. Several circumstances concur to render her motions the most interesting, and at the same time the most difficult to investigate of all the bodies of our system. In the solar system, planet troubles planet, but in the lunar theory the sun is the great disturbing cause; his vast dis
tance being compensated by his enormous magnitude, so that the motions of the moon are more irregular than those of the planets; and, on account of the great ellipticity of her orbit, and the size of the sun, the approximations to her motions are tedious and difficult beyond what those unaccustomed to such investigations could imagine. Among the innumerable periodic inequalities to which the moon's motion in longitude is liable, the most remarkable are the Evection, the Variation, and the annual Equation. The forces producing the evection diminish the eccentricity of the lunar orbit in conjunction and opposition, and augment it in quadrature. The period of this inequality is less than thirty-two days. Were the increase and diminution always the same, the evection would only depend upon the distance of the moon from the sun; but its absolute value also varies with her distance from the perigee of her orbit. Ancient astronomers, who observed the moon solely with a view to the prediction of eclipses, which can only happen in conjunction and opposition, where the eccentricity is diminished by the evection, assigned too small value to the elipticity of her orbit. The variation, which is at its maximum when the moon is 45° distant from the sun, vanishes when that distance amounts to a quadrant, and also when the moon is in conjunction and opposition; consequently, that inequality never could have been discovered from the eclipses; its period is half a lunar month. The annual equation arises from the moon's motion being accelerated when that of the earth is retarded, and vice versa-for, when the earth is in its perihelion, the lunar orbit is enlarged by the action of the sun; therefore, the moon requires more time to perform her revolution. But, as the earth approaches its aphelion,
the moon's orbit contracts, and less time is necessary to accomplish her motion,-its period, consequently, depends upon the time of the year. In the eclipses the annual equation combines with the equation of the centre of the terrestrial orbit, so that ancient astronomers imagined the earth's orbit to have a greater eccentricity than modern astronomers assign to it.
The planets disturb the motion of the moon both directly and indirectly; because their action on the earth alters its relative position with regard to the sun and moon, and occasions inequalities in the moon's motion, which are more considerable than those arising from their direct action: for the same reason the moon, by disturbing the earth, indirectly disturbs her own motion. Neither the eccentricity of the lunar orbit, nor its mean inclination to the plane of the ecliptic, have experienced any changes from secular inequalities; for although the mean action of the sun on the moon depends upon the inclination of the lunar orbit to the ecliptic, and that the position of the ecliptic is subject to a secular inequality, yet analysis shows that it does not occasion a secular variation in the inclination of the lunar orbit because the action of the sun constantly brings the moon's orbit to the same inclination on the ecliptic. The mean motion, the nodes, and the perigee, however, subject to very remarkable variation.
From an eclipse observed by the Chaldeans at Babylon, on the 19th of March, seven hundred and twenty-one years before the Christian era, the place of the moon is known from that of the sun at the instant of opposition, whence her mean longitude may be found; but the comparison of this mean longitude with another mean longitude, computed back for the instance of the eclipse from
modern observations, shows that the moon performs her revolution round the earth more rapidly and in a shorter time now, than she did formerly; and that the acceleration in her mean motion has been increasing from age to age as the square of the time: all ancient and intermediate eclipses confirm this result. As the mean motions of the planets have no secular inequalities, this seemed to be an unaccountable anomaly. It was at one time attributed to the resistance of an etherial medium pervading space, and at another to the successive transmission of the gravitating force; but as La Place proved that neither of these causes, even if they exist, have any influence on the motions of the lunar perigee or nodes, they could not affect the mean motion; a variation in the mean motion from such causes being inseparably connected with variations in the motions of the perigee and nodes. That great mathematician, in studying the theory of Jupiter's satellites, perceived that the secular variation in the elements of Jupiter's orbit, from the action of the planets, occasions corresponding changes in the motions of the satellites, which led him to suspect that the acceleration in the mean motion of the moon might be connected with the secular variation in the eccentricity of the terrestrial orbit; and analysis has proved that he assigned the true cause of the acceleration.
If the eccentricity of the earth's orbit were invariable, the moon would be exposed to a variable disturbance from the action of the sun, in consequence of the earth's annual revolution; it would however be periodic, since it would be the same as often as the sun, the earth, and the moon returned to the same relative positions: but on account of the slow and incessant diminution in the eccentricity of
the terrestrial orbit, the revolution of our planet is per formed at different distances from the sun every year. The position of the moon with regard to the sun undergoes a corresponding change: so that the mean action of the sun on the moon varies from one century to another, and occasions the secular increase in the moon's velocity called the Acceleration, a name peculiarly appropriate in the present age, and which will continue to be so for a vast number of ages to come; because, as long as the earth's eccentricity diminishes, the moon's mean motion will be accelerated, but when the eccentricity has passed its minimum, and begins to increase, the mean motion will be retarded from age to age. At present the secular acceleration is about 11".209, but its effect on the moon's place increases as the square of the time. It is remarkable that the action of the planets thus reflected by the sun to the moon is much more sensible than their direct action, either on the earth or moon. The secular diminution in the eccentricity, which has not altered the equation of the centre of the sun by eight minutes since the earliest recorded eclipses, has produced a variation of about 1° 48' in the moon's longitude, and of 7° 12′ in her mean anomaly.
The action of the sun occasions a rapid but variable motion in the nodes and perigee of the lunar orbit. Though the nodes recede during the greater part of the moon's revolution, and advance during the smaller, they perform their sidereal revolution in 6793.37953 days; and the perigee accomplishes a revolution in 3232.56731 days, than nine years, noth withstanding its mo
retrograde and sometimes direct; but ce between the disturbing energy of