thar. its outer. On the night of Nov. 11, 1850, however, Mr. G. B Bond, of the Harvard Observatory (Cambridge, U. S.,) using the great Fraunhofer equatorial of that institution, became aware of a line of demarcation between these two portions so definite, and an extension inwards of the dusky border to such an extent (one fifth, by measurement, of the joint breadth of the two old rings,) as to justify him in considering it as a newly-discovered ring. On the nights of the 25th and 29th of the same month, and without knowledge of Mr. Bond's observations, Mr. Dawes, at his observatory at Wateringbury, by the aid of an exquisite achromatic by Merz, of 6 inches aperture, observed the very same fact, and even more distinctly, so as to be sure of a decidedly darker interval between the old and new rings, and even to subdivide the latter into two of unequal degrees of obscurity, separated by a line more obscure than either.]

(523.) Of Uranus we see nothing but a small round uniformly illuminated disc, without rings, belts, or discernible spots. Its apparent diameter is about 4", from which it never varies much, owing to the smallness of our orbit in comparison of its own. Its real diameter is about 35,000 miles, and its bulk 82 times that of the earth. It is attended by satellites-four at least, probably five or six-whose orbits (as will be seen in the next chapter) offer remarkable peculiarities.

(524.) The discovery of Neptune is so recent, and its situation in the ecliptic at present so little favourable for seeing it with perfect distinctness, that nothing very positive can be stated as to its physical appearance. To two observers it has afforded strong suspicion of being surrounded with a ring very highly inclined. And from the observations of Mr. Lassell, M. Otto Struve, and Mr. Bond, it appears to be attended certainly by one, and very probably by two satellites-though the existence of the second can hardly yet be considered as quite demonstrated.

(525.) If the immense distance of Neptune precludes all hope of coming at much knowledge of its physical state, the minuteness of the ultra-zodiacal planets is no less a bar into any inquiry into theirs. One of them, Pallas, has been said to have somewhat of a nebulous or hazy appearance, indicative of an extensive and vaporous atmosphere, little repressed and condensed by the inadequate gravity of so small a mass. It is probable, however, that the appearance in question has originated in some imperfection in the telescope employed or other temporary causes of illusion. In Vesta and Pallas only have sensible discs been hitherto observed, and those only with very high magnifying powers. Vesta was once seen by Schroeter with the naked eye. No doubt the most remarkable of their peculiarities must lie in this condition of their state. A

man placed on one of them would spring with ease 60 feet high, and sustain no greater shock in his descent than he does on the earth from leaping a yard. On such planets giants might exist; and those enormous animals, which on earth require the buoyant power of water to counteract their weight, might there be denizens of the land. But of such speculations there is no end.

(526.) We shall close this chapter with an illustration calculated to convey to the minds of our readers a general impression of the relative magnitudes and distances of the parts of our system. Choose any well levelled field or bowling-green. On it place a globe, two feet in diameter; this will represent the Sun; Mercury will be represented by a grain of mustard seed, on the circumference of a circle 164 feet in diameter for its orbit; Venus a pea, on a circle 284 feet in diameter; the Earth also a pea, on a circle of 430 feet; Mars a rather large pin's head, on a circle of 654 feet; Juno, Ceres, Vesta, and Pallas, grains of sand, in orbits of from 1000 to 1200 feet; Jupiter a moderate-sized orange, in a circle nearly half a mile across, Saturn a small orange, on a circle of four-fifths of a mile; Uranus a full-sized cherry, or small plum, upon the circumference of a circle more than a mile and a half, and Neptune a good-sized plum on a circle about two miles and a half in diameter. As to getting correct notions on this subject by drawing circles on paper, or, still worse, from those very childish toys called orreries, it is out of the question. To imitate the motions of the planets, in the above-mentioned orbits, Mercury must describe its own diameter in 41 seconds; Venus in 4m 14s; the Earth, in 7 minutes; Mars, in 4 48; Jupiter, 2 56; Saturn, in 35 13; Uranus, in 2 16; and Neptune in 3 30.

CHAPTER X.

OF THE SATELLITES.

OF THE MOON, AS A SATELLITE OF THE EARTH. — GENERAL PROXIMITY OF SATELLITES TO THEIR PRIMARIES, AND CONSEQUENT SUBORDINATION OF THEIR MOTIONS. MASSES OF THE PRIMARIES CONCLUDED FROM THE PERIODS OF THEIR SATELLITES. MAINTENANCE OF KEPLER'S LAWS IN THE SECONDARY SYSTEMS. OF JUPITER'S SATELTHEIR ECLIPSES, ETC. VELOCITY OF LIGHT DISCOVERED SATELLITES OF SATURN

LITES.

BY THEIR MEANS.

- OF URANUS -OF

NEPTUNE.

(527.) In the annual circuit of the earth about the sun, it is constantly attended by its satellite, the moon, which revolves round it, or rather both round their common centre of gravity; while this centre, strictly speaking, and not either of the two bodies thus connected, moves in an elliptic orbit, undisturbed by their mutual action, just as the centre of gravity of a large and small stone tied together and flung into the air describes a parabola as if it were a real material substance under the earth's attraction, while the stones circulate round it or round each other, as we choose to conceive the matter.

(528.) If we trace, therefore, the real curve actually described by either the moon's or the earth's centres, in virtue of this compound motion, it will appear to be, not an exact ellipse, but an undulated curve, like that represented in the figure to article 324, only that the number of undulations in a whole revolution is but 13, and their actual deviation from the general ellipse, which serves them as a central line, is comparatively very much smaller-so much so, indeed, that every part of the curve described by either the earth or moon is concave towards the sun. The excursions of the earth on either side of the ellipse, indeed, are so very small as to be hardly appreciable. In fact, the centre of gravity of the earth and moon lies always within the surface of the earth, so that the monthly orbit described by the earth's centre about the common centre of gravity is comprehended within a space less than the size of the earth itself. The effect is, nevertheless, sensible, in producing an appa

rent monthly displacement of the sun in longitude, of a parallactic kind, which is called the menstrual equation; whose greatest amount is, however, less than the sun's horizontal parallax, or than 8.6′′.

(529.) The moon, as we have seen, is about 60 radii of the earth distant from the centre of the latter. Its proximity, therefore, to its centre of attraction, thus estimated, is much greater than that of the planets to the sun; of which Mercury, the nearest, is 84, and Uranus 2026 solar radii from its centre. It is owing to this proximity that the moon remains attached to the earth as a satellite. Were it much farther, the feebleness of its gravity towards the earth would be inadequate to produce that alternate acceleration and retardation in its motion about the sun, which divests it of the character of an independent planet, and keeps its movements subordinate to those of the earth. The one would outrun, or be left behind the other, in their revolutions round the sun (by reason of Kepler's third law,) according to the relative dimensions of their heliocentric orbits, after which the whole influence of the earth would be confined to producing some considerable periodical disturbance in the moon's motion, as it passed or was passed by it in each synodical revolution.

(530.) At the distance at which the moon really is from us, its gravity towards the earth is actually less than towards the sun. That this is the case, appears sufficiently from what we have already stated, that the moon's real path, even when between the earth and sun, is concave towards the latter. But it will appear still more clearly if, from the known periodic times' in which the earth completes its annual and the moon its monthly orbit, and from the dimensions of those orbits, we calculate the amount of deflection, in either, from their tangents, in equal very minute portions of time, as one second. These are the versed sines of the arcs described in that time in the two orbits, and these are the measures of the acting forces which produce those deflections. If we execute the numerical calculation in the case before us, we shall find 2.233 1 for the proportion in which the intensity of the force which retains the earth in its orbit round the sun actually exceeds that by which the moon is retained in its orbit about the earth.

R and r radii of two orbits (supposed circular,) P and p the periodic times; then the arcs in question (A and a) are to each other as to ; and since the versed sines are as the squares of the arcs directly and the radii inversely, these are to each other R

as

case.

R T
P p1

T

; and in this ratio are the forces acting on the revolving bodies in either

(531.) Now the sun is 399 times more remote from the earth than the moon is. And, as gravity increases as the squares of the distances decrease, it must follow that at equal distances, the intensity of solar would exceed that of terrestrial gravity in the above proportion, augmented in the further ratio of the square of 400 to 1; that is, in the proportion of 355000 to 1; and therefore, if we grant that the intensity of the gravi tating energy is commensurate with the mass or inertia of the attracting body, we are compelled to admit the mass of the earth to be no more of that of the sun.

than 3000

(532.) The argument is, in fact, nothing more than a recapitulation of what has been adduced in Chap. VIII. (art. 448.) But it is here reintroduced, in order to show how the mass of a planet which is attended by one or more satellites can be as it were weighed against the sun, provided we have learned from observation the dimensions of the orbits described by the planet about the sun, and by the satellites about the planet, and also the periods in which these orbits are respectively described. It is by this method that the masses of Jupiter, Saturn, Uranus, and Neptune have been ascertained. (See Synoptic Table.)

(533.) Jupiter, as already stated, is attended by four satellites, Saturn by seven; Uranus, certainly by four, and perhaps by six; and Neptune by two or more. These, with their respective primaries (as the central planets are called,) form in each case miniature systems entirely analogous, in the general laws by which their motions are governed, to the great system in which the sun acts the part of the primary, and the planets of its satellites. In each of these systems the laws of Kepler are obeyed, in the sense, that is to say, in which they are obeyed in the planetary system approximately, and without prejudice to the effects of mutual perturbation, of extraneous interference, if any, and of that small but not imperceptible correction which arises from the elliptic form of the central body. Their orbits are circles or ellipses of very moderate excentricity, the primary occupying one focus. very nearly proportional to the times; and the squares of the periodical times of all the satellites belonging to each planet are in proportion to each other as the cubes of their distances. The tables at the end of the volume exhibit a synoptic view of the distances and periods in these several systems, so far as they are at present known; and to all of them it will be observed that the same remark respecting their proximity to their primaries holds good, as in the case of the moon, with a similar reason for such close connection.

About this they describe areas

(534.) Of these systems, however, the only one which has been studied