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excentricity of the moon's orbit to be the same now as in the earliest ages of astronomy.
(576.) The movements of the perihelia, and varia. tions of excentricity of the planetary orbits, are interlaced and complicated together in the same manner and nearly by the same laws as the variations of their nodes and inclinations. Each acts upon every other, and every such mutual action generates its own peculiar period of compensation; and every such period, in pursuance of the principle of art. 526., is thence propagated throughout the system. Thus arise cycles upon cycles, of whose compound duration some notion may be formed, when we consider what is the length of one such period in the case of the two principal planets — Jupiter and Saturn. Neglecting the action of the rest, the effect of their mutual attraction would be to produce a variation in the excentricity of Saturn's orbit, from 0.08409, its maximum, to 0.01345, its minimum value; while that of Jupiter would vary between the narrower limits, 0.06036 and 0·02606: the greatest excentricity of Jupiter corresponding to the least of Saturn, and vice versa. The period in which these changes are gone through, would be 70414 years. After this example, it will be easily conceived that many millions of years will require to elapse before a complete fulfilment of the joint cycle which shall restore the whole system to its original state as far as the excentricities of its orbits are concerned.
(577.) The place of the perihelion of a planet's orbit is of little consequence to its well-being ; but its excentricity is most important, as upon this (the axes of the orbits being permanent) depends the mean temperature of its surface, and the extreme variations to which its seasons may be liable. For it may be easily shown that the mean annual amount of light and heat received by a planet from the sun is, cæteris paribus, as the minor axis of the ellipse described by it. * Any variation, therefore, in the ex.
* “On the Astronomical Causes which may influence Geological Phænomena."- Geol. Trans. 1832.
centrity by changing the minor axis, will alter the mean temperature of the surface. How such a change will also influence the extremes of temperature appears from art. 315. Now, it may naturally be enquired whether, in the vast cycle above spoken of, in which, at some period or other, conspiring changes may accu. mulate on the orbit of one planet from several quarters, it may not happen that the excentricity of any one planet -as the earth — may become exorbitantly great, so as to subvert those relations which render it habitable to man, or to give rise to great changes, at least, in the physical comfort of his state. To this the researches of geometers have enabled us to answer in the negative. A relation has been demonstrated by Lagrange between the masses, axes of the orbits, and excentricities of each planet, similar to what we have already stated with respect to their inclinations, viz. that if the mass of each planet be multiplied by the square root of the axis of its orbit, and the product by the square of its excentricity, the sum of all such products throughout the system is invariable ; and as, in point of fact, this sum is extremely small, so it will always remain. Now, since the axes of the orbits are liable to no secular changes, this is equivalent to saying that no one orbit shall increase its excentricity, unless at the expense of a common fund, the whole amount of which is, and must for ever remain, extremely minute. *
(578.) We have hinted, in our last art. but one, at perturbations produced in the lunar orbit by the protuberant matter of the earth's equator. The attraction of a sphere is the same as if all its matter were condensed into a point in its center; but that is not the case with a spheroid. The attraction of such a mass is neither exactly directed to its center, nor does it exactly
* There is nothing in this relation, however, taken per s?, to secure the smaller planets - Mercury, Mars, Juno, Ceres, &c. - from a catastrophe, could they accumulate on themselves, or any one of them, the whole amount of this excentricity fund. But that can never be : Jupiter and Saturn will always retain the lion's share of it. A similar remark applies to the inclination fund of art 515. These funds, be it observed, can never get into debt. Every term of them is essentially positive.
follow the law of the inverse squares of the distances. Hence will arise a series of perturbations, extremely small in amount, but still perceptible, in the lunar motions ; by which the node and the apogee will be affected. A more remarkable consequence of this cause, however, is a small nutation of the lunar orbit, exactly analogous to that which the moon causes in the plane of the earth's equator, by its action on the same elliptic protuberance. And, in general, it may be observed, that in the systems of planets which have satellites, the elliptic figure of the primary has a tendency to bring the orbits of the satellites to coincide with its equator, a tendency which, though small in the case of the earth, yet in that of Jupiter, whose ellipticity is very considerable, and of Saturn especially, where the ellipticity of the body is reinforced by the attraction of the rings, becomes predominant over every external and internal cause of disturbance, and produces and maintains an almost exact coincidence of the planes in question. Such, at least, is the case with the nearer satellites. The more distant are comparatively less affected by this cause, the difference of attractions between a sphere and spheroid diminishing with great rapidity as the distance increases. Thus, while the orbits of all the six interior satellites of Saturn lie almost exactly in the plane of the ring and equator of the planet, that of the external satellite, whose distance from Saturn is between sixty and seventy diameters of the planet, is inclined to that plane considerably. On the other hand, this considerable distance, while it permits the satellite to retain its actual inclination, prevents (by parity of reasoning) the ring and equator of the planet from being perceptibly disturbed by its attraction, or being subjected to any appreciable movements analogous to our nutation and precession. If such exist, they must be much slower than those of the earth; the mass of this satellite (though the largest of its system) being, as far as can be judged by its apparent size, a much smaller fraction of that of Saturn than the moon is of the earth; while the solar precession, by reason of the immense distance of the sun, must be quite inappreciable.
(579.) It is by means of the perturbations of the planets, as ascertained by observation, and compared with theory, that we arrive at a knowledge of the masses of those planets, which, having no satellites, offer no other hold upon them for this purpose. Every planet produces an amount of perturbation in the motions of every other, proportioned to its mass, and to the degree of advantage or purchase which its situation in the system gives it over their movements. The latter is a subject of exact calculation; the former is unknown, otherwise than by observation of its effects. In the determination, however, of the masses of the planets by this means, theory lends the greatest assistance to observation, by pointing out the combinations most favour. able for eliciting this knowledge from the confused mass of superposed inequalities which affect every observed place of a planet; by pointing out the laws of each inequality in its periodical rise and decay; and by showing how every particular inequality depends for its magnitude on the mass producing it. It is thus that the mass of Jupiter itself (employed by Laplace in his investigations, and interwoven with all the planetary tables) has of late been ascertained, by observ. ations of the derangements produced by it in the motions of the ultra-zodiacal planets, to have been insufficiently determined, or rather considerably mistaken, by relying too much on observations of its satellites, made long ago by Pound and others, with inadequate instrumental means. The same conclusion has been arrived at, and nearly the same mass obtained, by means of the pertur. bations produced by Jupiter on Encke's comet. The error was one of great importance; the mass of Jupiter being by far the most influential element in the planetary system, after that of the sun. It is satisfactory, then, to have ascertained, -as by his observations Professor Airy. is understood to have recently done, — the cause of the error; to have traced it up to its source, in insufficien
micrometric measurements of the greatest elongations of the satellites; and to have found it disappear when measures taken with more care, and with infinitely superior instruments, are substituted for those before employed.
(580.) In the same way that the perturbations of the planets lead us to a knowledge of their masses, as compared with that of the sun, so the perturbations of the satellites of Jupiter have led, and those of Saturn's attendants will, no doubt, hereafter lead, to a knowledge of the proportion their masses bear to their respective primaries. The system of Jupiter's satellites has been elaborately treated by Laplace; and it is from his theory, compared with innumerable observations of their eclipses, that the masses assigned to them in art. 463. have been fixed. Few results of theory are more surprising, than to see these minute atoms weighed in the same balance which we have applied to the ponderous mass of the sun, which exceeds the least of them in the enormous proportion of 65000000 to 1.
OF SIDEREAL ASTRONOMY.
OF THE STARS GENERALLY. THEIR DISTRIBUTION INTO CLASSES
ACCORDING TO THEIR APPARENT MAGNITUDES. -THEIR DISTRIBUTION OVER THE HEAVENS. — OF THE MILKY WAY. ANNUAL PARALLAX, REAL DISTANCES, PROBABLE DIMENSIONS, AND NATURE OF THE STARS. VARIABLL STARS. — TEMPORARY STARS. —OF DOUBLE STARS. —THEIR REVOLUTION ABOUT EACH OTHER IN ELLIPTIC ORBITS. -EXTENSION OF THE LAW OF GRAVITY TO SUCH SYSTEMS. OF COLOURED STARS. PROPER MOTION OF THE SUN AND STARS. -SYSTEMATIC ABERRATION AND PARALLAX. - OF COMPOUND SIDEREAL SYSTEMS. -CLUSTERS OF STARS. OF NEBULÆ. NEBULOUS STARS. ANNULAR AND PLANETARY NEBULÆ. ZODIACAL LIGHT,
(581.) BESIDES the bodies we have described in the foregoing chapters, the heavens present us with an in