gates into a mass whose greatest dimension lies in the plane of the orbit, both tendencies will conspire to produce rotation in that plane. placed on the table with its ends meeting, will make a ring shaped like the hoop of a barrel-a ring whose thickness in the line of its diameter is very small, but whose width in a direction perpendicular On referring to the facts, we find them, to its diameter is considerable. Suppose, as far as can be judged without exact now, that in place of an orange, which is mathematical investigation, quite in hara spheroid of very slight oblateness, we mony with this view. Considering the take a spheroid of very great oblateness, enormous circumference of Uranus' orbit, having a shape somewhat like that of a and his comparatively small mass, we may lens of small convexity. If from the edge conclude that the ring from which he reor equator of this lens-shaped spheroid, a sulted was comparatively slender, and ring of moderate size were cut off, it therofore a hoop-shaped one: especially would be unlike the previous one in this if the nebulous mass was at that time less respect, that its greatest thickness would oblate, which is highly probable. Hence, be in the line of its diameter, and not in a a plane of rotation nearly perpendicular line at right angles to its diameter: it to his orbit, and a direction of rotation would be a ring shaped somewhat like a having no reference to his orbitual movequoit, only far more slender. That is to ment. Saturn has a mass seven times as say, according to the oblateness of a ro- great, and an orbit of less than half the tating spheroid, the detached ring may diameter; whence it follows that his be either a hoop-shaped ring or a quoit- genetic ring, having less than half the shaped ring. One further fact must be circumference, and less than half the vernoted. In a much flattened or lense- tical thickness, (the spheriod being then shaped spheroid, the form of the ring will certainly as oblate if not more oblate,) vary with its bulk. A very slender ring, must have had considerably greater width taking off just the equatorial surface, will-must have been less hoop-shaped, and be hoop-shaped; while a tolerably massive ring, trenching appreciably upon the diameter of the spheroid, will be quoitshaped. Thus, then, according to the oblateness of the spheroid and the bulkiness of the detached ring, will the greatest thickness of that ring be in the direction of its plane, or in a direction perpendicular to its plane. But this circumstance must greatly affect the rotation of the resulting planet. In a decidedly hoop-shaped nebulous ring, the differences of velocity between the inner and outer surfaces will, in the first place, be very small. In the second place, such a ring aggregating into a mass whose greatest diameter is at right angles to the plane of the orbit, that mass will have a strong tendency to rotate in a direction at right angles to the plane of the orbit; and this tendency will establish itself with but slight modification. Where the ring is but little hoopshaped, and the difference of the inner and outer velocities also greater, as it must be, the opposing tendencies-one to produce rotation in the plane of the orbit, and the other rotation perpendicular to it will both be influential, and an intermediate plane of rotation will be taken up. While, if the nebulous ring is decidedly quoit-shaped, and therefore aggre more approaching to the quoit-shaped; notwithstanding difference of density, it must have been at least two or three times as broad in the line of its plane. Consequently, Saturn has a rotatory movement in the same direction as the movement of translation, and in a plane differing from it by thirty degrees only. In the case of Jupiter, again, whose mass is three and a half times that of Saturn, and whose orbit is little more than half the size, the genetic ring must, for the like reasons, have been still broader decidedly quoit-shaped, we may say; and there hence resulted a planet whose plane of rotation differs from that of his orbit by scarcely more than three degrees. Once more, considering the comparative insignificance of Mars, Earth, Venus, and Mercury, it follows that the diminishing circumferences of the rings not sufficing to account for the smallness of resulting masses, the rings must have been slender ones-must have again approximated to the hoop-shaped; and thus it happens that the planes of rotation again diverge more or less widely from those of the orbits. Taking into account the varying oblateness of the original spheroid in the successive stages of its concentration, and the different proportions of the detached rings, it seems to us that the respective | lites repeats in miniature the relations of rotatory motions may be satisfactorily accounted for. Not only the directions, but also the velocities of rotation are thus explicable. It might naturally be supposed that the large planets would revolve on their axes. more slowly than the small ones; this would be most in conformity with our ordinary experiences. It is a corollary from the nebular hypothesis, however, more especially when interpreted as above, that while large planets should rotate rapidly, small ones should rotate slowly; and we find that in fact they do so. Other things equal, a concentrating nebulous mass that is diffused through a wide space, and whose outer parts have, therefore, to travel from a great distance to the common centre of gravity, will acquire a high axial velocity in the course of its aggregation; and conversely with a small mass. Still more marked will be the difference where the form of the genetic ring conspires to increase the rate of rotation. Other things equal, a genetic ring that is broadest in the direction of its plane will produce a mass rotating faster than one that is broadest at right angles to its plane; and if the ring is absolutely as well as relatively broad, the rotation will be very rapid. These conditions were, as we saw, fulfilled in the case of Jupiter; and Jupiter goes round his axis in less than ten hours. Saturn, in whose case, as above explained, the conditions were manifestly less favorable to rapid rotation, takes ten hours and a half. While Mars, Earth, Venus, and Mercury, whose rings must have been slender, take more than double the time: the smallest taking the longest. Not only thus do the various phenomena of rotation consist with the nebular hypothesis, but this hypothesis gives us a more or less feasible solution of sundry peculiarities that, in its absence, are either anomalous or meaningless. THE SATELLITES. From the planets, let us now pass to the satellites. Here, beyond the conspicuous facts commonly adverted to, that they go. round their primaries in the same directions that these turn on their axes, in planes diverging but little from their equators, and in orbits nearly circular, there are several significant traits that must not be passed over. One of them is, that each set of satel the planets to the sun, not only in the respects just named, but also in the order of their sizes. On progressing from the outside of the solar system to its center, we see that there are four large external planets and four internal ones, which are comparatively small. The same contrast holds between the outer and inner satellites in every case. Among the four satellites of Jupiter, the parallel is maintained as well as the comparative smallness of the number allows the two outer ones are the largest, and the two inner ones the smallest. According to the most recent observations made by Mr. Lassell, the like is true of the four satel lites of Uranus. In the case of Saturn, who has eight secondary planets revolving round him, the likeness is still more close in arrangement as in number: the three outer satellites are large, the inner ones small; and the contrasts of size are here much greater between the largest, which is nearly as big as Mars, and the smallest, which is with difficulty discovered even by the best telescopes. Moreover, the analogy does not end here. Just as with the planets, there is at first a general increase of size on traveling inwards from Neptune and Uranus, which do not differ very widely, to Saturn, which is much larger, and to Jupiter, which is the largest; so of the eight satellites of Saturn, the largest is not the outermost, but the outermost save two; so of Jupiter's four secondaries, the larg est is the most remote but one. Now these analogies are inexplicable upon the theory of final causes. For purposes of lighting, if this be the presumed object of these attendant bodies, it would have been far better had the larger been the nearer: at present their remoteness renders them of less service than the smallest. To the nebular hypothesis, however, these analogies give further support. They show the action of a common physical cause. They imply a law of genesis, holding in the secondary systems as in the primary system. Still more instructive shall we find the distribution of the satellites-their absence in some instances, and their presence in other instances, in smaller or greater numbers. The argument from design fails to account for this distribution. Supposing it be granted that planets nearer the Sun than ourselves, have no need of moons (though, considering | nine times as great when it is three times that their nights are as dark, and, rela- as rapid; and so on. Now the detachtively to their brilliant days, even darker ment of a ring from a planet-forming body than ours, the need seems quite as great) of nebulous matter, implies that at its -supposing this be granted; what is to equatorial zone the centrifugal force has be said of Mars, which, placed half as far become so great as to balance gravity. again from the Sun as we are, has yet no If the rotation is very rapid, further conmoon? Or again, how are we to explain centration, leading to increased rapidity the fact that Uranus has but half as many of rotation, will soon again raise the cenmoons as Saturn, though he is at double trifugal force to an equality with gravity the distance? While, however, the cur--will soon again cause the detachment of rent presumption is untenable, the nebu- a ring. That is to say, the detachment of lar hypothesis furnishes us with a quite rings will be most frequent from those satisfactory explanation. It actually en- masses in which the centrifugal tendency ables us to predict, by a not very complex bears the greatest ratio to the gravitative calculation, where satellites will be abun- tendency. Though it is not possible to dant and where they will be absent. The calculate what were the proportions these reasoning is as follows: two tendencies had to each other in the genetic spheroid which produced each planet, it is possible to calculate where they were the greatest and where the least. While it is true that the ratio which centrifugal force now bears to gravity at the equator of each planet, differs widely from that which it bore during the earlier stages of concentration; and while it is true that this change in the ratio, depending on the degree of contraction each planet has undergone, has in no two cases been the same; yet we may safely conclude that where the ratio is still the greatest, it has been the greatest from the beginning. The satellite-forming tendency which each lane thad, will be approximately indicated by the proportion now existing in it between the aggregating power and the power that has opposed aggregation. On making the requisite calculations, we find that the facts completely harmonize with this inference. The following table shows what fraction the centrifugal is of the centripetal force in every case, and the relation which that fraction has to the number of satellites. In a rotating nebulous spheroid that is concentrating into a planet, there are at work two antagonist mechanical tendencies the centripetal and the centrifugal, While the force of gravitation draws all the atoms of the spheroid together, their tangential momentum is, in part, resolvable into a force impelling them to fly asunder. The ratio which these opposing tendencies bear to each other, differs according to the velocity of rotation. In a mass that has no rotation there is no centrifugal force. Conversely when the velocity at which a mass rotates exceeds a certain point, the centrifugal force becomes so great that, overcoming not only the gravitation, but the cohesive attraction, it causes the mass to fly to pieces. And between these extremes, the ratio which the centrifugal force bears to gravitation varies, other things equal, as the square of the velocity. Hence, the aggregation of a rotating nebulous spheroid will be more or less strongly opposed by this outward impetus. of its particles: the opposition, in equal spheroids, being four times as great when the rotation is twice as rapid; formity with observation is that of Venus. Against the alternative supposition, that In Venus, it appears that the centrifugal the equality occurred by accident, the force is relatively a very little greater than probabilities are, as Laplace says, infinity in the Earth; and according to the hypo-to-one. But to this arrangement, which thesis it ought, therefore, to have a satel- is explicable neither as the result of design lite. Of this seeming anomaly there are nor of chance, the nebular bypothesis furtwo explanations. In the first place, not nishes a clue. In his "Exposition du not a few astronomers have asserted that Systeme du Monde," Laplace shows, by Venus has a satellite. Cassini, Short, reasoning too detailed to be here repeated, Montaigne of Limoges, Roedkier, and that under the circumstances such a relaMontbarron, professed to have seen it; tion of movements would be likely to esand Lambert calculated its elements. tablish itself; and he further shows that Should it, however, ultimately be proved there would, from the same causes, result that they were mistaken, there is still the that lateral oscillation of the moon known fact, that the diameter of Venus is vari- as its libration. ously estimated; and that a very small change in the data would make the fraction less instead of greater than that of the Earth. This seeming discrepancy, then, slight as it is, is very probably not real; and if it is not real, the correspondence between calculation and fact is complete. We can not but think that this correspondence, even as it now stands, is one of the strongest confirmations of the nebular hypothesis. Certain more special peculiarities of the satellites must be mentioned as highly suggestive. One of them is the relation between the period of revolution and that of rotation. No discoverable purpose is served by making the Moon go round its axis in the same time that it goes round the Earth for our convenience a more rapid axial motion would have been equally good; and for any possible inhabitants of the Moon, much better. Among Jupiter's satellites, which severally display these same synchronous movements, there also exists a still more remarkable relation. "If the mean angular velocity of the first satellite be added to twice that of the third, the sum will be equal to three times that of the second;" and "from this it results that the situations of any two of them being given, that of the third can be found." Now here, as before, no conceivable advantage results. Neither in this case can the connection have been accidental: the probabilities are infinity to one to the contrary. But again, according to Laplace, the nebular hypothesis supplies a solution. Are not these significant facts? CONCLUDED IN NEXT NUMBER. SUB-TITLES AND TOPICS.-Saturn's Rings-Den sities of Sun and Planets-The Earth once liquid An exploded Planet-Temperatures of the Sun and Planets-Hurricanes in the Sun, etc. |