[footnote] *If, according to Burckhardt's determination, the Moon's radius be 0.2725 and its volume 1/49.00th, its density will be 0.5596, or nearly five ninths. Compare, also, Wilh. Beer and H. Madler, 'der Mond', 2, 10, and Madler, 'Ast.', 157. The material contents of the Moon are, according to Hansen, nearly 1/34th (and ädler 1/40.6th) that of the Earth, and its mass equal to 1/87.73d that of the Earth. In the largest of Jupiter's moons, the third, the relations of volume to the central body are 1/15370th, and of mass 1/11300th. On the polar flattening of Uranus, see Schum, 'Astron. Nachr.', 1844, No. 493.
While the density of the Moon is five ninths less than that of the Earth, it would appear, if we may sufficiently depend upon the determinations of their magnitudes and masses, that the second of Jupiter's moons is actually denser than that great planet itself. Among the fourteen satellites that have been investigated with any degree of certainty, the system of the seven satellites of Saturn presents an instance of the greatest possible contrast, both in absolute magnitude and in distance from the central body. The sixth of these satellites is probably not much smaller than Mars, while our moon has a diameter which does not amount to more than half that of the latter planet. With respect to volume, the two outer, the sixth and seventh of Saturn's satellites, approach the nearest to the third and brightest of Jupiter's moons. The two innermost of these satellites belong perhaps, together with the remote moons of Uranus to the smallest cosmical bodies of our solar system, being only made visible under favorable circumstances by the most powerful instruments. They were first discovered by the forty-foot telescope of William Herschel in 1789, and were seen again by John Herschel at the Cape of Good Hope, by Vico at Rome, and by Lamont at Munich. Determinations of the 'true' diameter of satellites, made by the measurement of the apparent size of their small disks, are subjected to many optical difficulties; but numerical astronomy, whose task it is to predetermine by calculation the motions of the heavenly bodies as they will appear when viewed from the Earth, is directed almost p 97 exclusively to motion and mass, and but little to volume. The absolute distance of a satellite from its central body is greatest in the case of the outermost or seventh satellite of Saturn, its distance from the body round which it revolves amounting to more than two millions of miles, or ten times as great a distance as that of our moon from the Earth. In the case of Jupiter we find that the outermost or fourth attendant moon is only 1,040,000 miles from that planet, while the distance between Uranus and its sixth satellite (if the latter really exist) amounts to as much as 1,360,000 miles. If we compare, in each of these subordinate systems, the volume of the satellite, we discover the existence of entirely new numerical relations. The distances of the outermost satellites of Uranus, Saturn, and Jupiter are when expressed in semi-diameters of the main planets, as 91, 64, and 27. The outermost satellite of Saturn appears, therefore, to be removed only about one fifteenth further from the center of that planet than our moon is from the Earth. The first or innermost of Saturn's satellites is nearer to its central body than any other of the secondary planets, and presents, moreover, the only instance of a period of revolution of less than twenty-four hours. Its distance from the center of Saturn may, according to Mädler and Wilhelm Beer, be expressed as 2.47 semi-diameters of that planet, or as 80,088 miles. Its distance from the surface of the main planet is therefore 47,480 miles, and from the outer-most edge of the ring only 4916 miles. The traveler may form to himself an estimate of the smallness of this amount by remembering the statement of an enterprising navigator, Captain Beechey, that he had in three years passed over 72,800 miles. If, instead of absolute distances, we take the semi-diameters of the principal planets, we shall find that even the first or nearest of the moons of Jupiter (which is 26,000 miles further removed from the center of that planet than our moon is from that of the Earth) is only six semi-diameters of Jupiter from its center, while our moon is removed from us fully 60 1/3d semi-diameters of the Earth.
In the subordinate systems of satellites, we find that the same laws of gravitation which regulate the revolutions of the principal planets round the Sun likewise govern the mutual relations existing between these planets among one another and with reference to their attendant satellites. The twelve moons of Saturn, Jupiter, and the Earth all most like the primary planets from west to east, and in elliptic orbits, deviating p 98 but little from circles. It is only in the case of one moon, and perhaps in that of the first and innermost of the satellites of Saturn (0.068), that we discover an eccentricity greater than that of Jupiter; according to the very exact observations of Bessel, the eccentricity of the sixth of Saturn's satellites (0.029) exceeds that of the Earth. On the extremest limits of the planetary system, where, at a distance nineteen times greater than that of our Earth, the centripetal force of the Sun is greatly diminished, the satellites of Uranus (which most striking contrasts from the facts observed with regard to other secondary planets. Instead, as in all other satellites, of having their orbits but slightly inclined toward the ecliptic and (not excepting even Saturn's ring, which may be regarded as a fusion of agglomerated satellites) moving from west to east, the satellites of Uranus are almost perpendicular to the ecliptic, and move retrogressively from east to west, as Sir John Herschel has proved by observations continued during many years. If the primary and secondary planets have been formed by the condensation of rotating rings of solar and planetary atmospheric vapor, there must have existed singular causes of retardation or impediment in the vaporous rings revolving round Uranus, by which, under the relations with which we are unacquainted, the revolution of the second and fourth of its satellites was made to assume a direction opposite to that of the rotation of the central planet.
It seems highly probable that the period of rotation of 'all' secondary planets is equal to that of their revolution round the main planet, and therefore that they always present to the latter the same side. Inequalities, occasioned by sight variations in the revolution, give rise to fluctuations of from 6 degrees to 8 degrees, or to an apparent libration in longitude as well as in latitude. Thus, in the case of our moon, we sometimes observe more than the half of its surface, the eastern and northern edges being more visible at one time, and the western or southern at another. By means of this libration* we are enabled to see the annular mountain Malapert (which occasionally conceals the Moon's south pole), the arctic landscape round the crater of Gioja, and the large gray plane near Endymion which exceeds in superficial extent the 'Mare Vaporum'.
[footnote] *Beer and Madler, op. cit., 185, s.208, and § 347, s. 332; and ix their 'Phys. Kenntniss der himml. Korper', s. 4 und 69, Tab. 1 (Physical History of the Heavenly Bodies).
Three sevenths of the Moon's surface are entirely p 99 concealed from our observation, and must always remain so, unless new and unexpected disturbing causes come into play. These cosmical relations involuntarily remind us of nearly similar conditions in the intellectual world, where, in the domain of deep research into the mysteries and the primeval creative forces of nature, there are regions similarly turned away from us, and apparently unattainable, of which only a narrow margin has revealed itself, for thousands of years, to the human mind, appearing, from time to time, either glimmering in true or delusive light. We have hitherto considered the primary planets, their satellites, and the concentric rings which belong to one, at least, of the outermost planets, as products of tangential force, and as closely connected together by mutual attraction; it therefore now only remains for us to speak of the unnumbered host of 'comets' which constitute a portion of the cosmical bodies revolving in independent orbits round the Sun. If we assume an equable distribution of their orbits, and the limits of their perihelia, or greatest proximities to the Sun, and the possibility of their remaining invisible to the inhabitants of the Earth, and base our estimates on the rules of the calculus of probabilities, we shall obtain as the result an amount of myriads perfectly astonishing. Kepler, with his usual animation of expression, said that there were more comets in the regions of space than fishes in the depths of the ocean. As yet, however, there are scarcely one hundred and fifty whose paths have been calculated, if we may assume at six or seven hundred the number of comets whose appearance and passage through known constellations have been ascertained by more or less precise observations. While the so-called classical nations of the West, the Greeks and Romans, although they may occasionally have indicated the position in which a comet first appeared, never afford any information regarding its apparent path, the copious literature of the Chinese (who observed nature carefully, and recorded with accuracy what they saw) contains circumstantial notices of the constellations through which each comet was observed to pass. These notices go back to more than five hundred years before the Christian era, and many of them are still found to be of value in astronomical observations.*
[footnote] *The first comets of whose orbits we have any knowledge, and which were calculated from Chinese observations, are those of 240 (under Gordian II.), 539 (under Justinian), 565, 568, 574, 837, 1337, and 1385. See John Russell Hind, in Schum., 'Astron. Nachr.', 1843, No. 498. While the comet of 837 (which, according to Du Sejour, continued during twenty-four hours within a distance of 2,000,000 miles from the Earth) terrified Louis I. of France to that degree that he busied himself in building churches and founding monastic establishments, in the hope of appeasing the evils threatened by its appearance, the Chinese astronomers made observations on the path of this cosmical body, whose tail extended over a space of 60 degrees, appearing sometimes single and sometimes multiple. The first comet that has been calculated solely from European observations was that of 1456, known as Halley's comet, from the belief long, but erroneously, entertained that the period when it was first observed by that astronomer was its first and only well-attested appearance. See Arago, in the 'Annuaire', 1836, p. 204, and Langier, 'Comptes Rendus des Seances de l'Acad.', 1843, t. xvi., 1006.
p 100 Although comets have a smaller mass than any other cosmical bodies — being, according to our present knowledge, probably not equal to 1/5000th part of the Earth's mass — yet they occupy the largest space, as their tails in several instances extend over many millions of miles. The cone of luminous vapor which radiates from them has been found, in some cases (as in 1680 and 1811), to equal the length of the Earth's distance from the Sun, forming a line that intersects both the orbits of Venus and Mercury. It is even probable that the vapor of the tails of comets mingled with our atmosphere in the years 1819 and 1823.
Comets exhibit such diversities of form, which appear rather to appertain to the individual than the class, that a description of one of these "wandering light-clouds," as they were already called by Xenophanes and Theon of Alexandria, contemporaries of Pappus, can only be applied with caution to another. The faintest telescopic comets are generally devoid of visible tails, and resemble Herschel's nebulous stars. They appear like circular nebulae of faintly-glimmering vapor, with the light concentrted toward the middle. This is the most simple type; but it can not, however, be regarded as rudimentary, since it might equally be the type of an older cosmical body, exhausted by exhalation. In the larger comets we may distinguish both the so-called "head" or "nucleus," and the single or multiple tail, which is characteristically denominated by the Chinese astronomers "the brush" ('sui'). The nucleus generally presents no definite outline, although, in a few rare cases, it appears like a star of the first or second magnitude, and has even been seen in bright sunshine;* as, p 101 for instance, in the large comets of 1402, 1532, 1577, 1744, and 1843.
[footnote] *Arago, 'Annuaire', 1832, p. 209, 211. The phenomenon of the tail of a comet being visible in bright sunshine, which is recorded of the comet of 1402, occurred again in the case of the large comet of 1843, whose nucleus and tail were seen in North America on the 28th of February (according to the testimony of J. G. Clarke, of Portland, state of Maine), between 1 and 3 o'clock in the afternoon.(a) The distance of the very dense nucleus from the sun's light admitted of being measured with much exactness. The nucleus and tail appeared like a very pure white cloud, a darker space intervening between the tail and the nucleus. ('Amer. Journ. of Science', vol. xiv., No. 1, p. 229.)