'We now proceed to the nebular theory, which is a conjecture pro posed with much doubt by Laplace, as a possible explanation of the manner in which the motions of the several planets obtained those remarkable resemblances which are found to subsist, without making the inquiry extend to anything except their motions. All the planets move in one direction round the sun, and their satellites move in the same direction round themselves; those that are known to revolve round their axes (and the contrary has been proved of no one of them) also revolve in the same direction, and their equators are not much inclined to their orbits. The excentricities of the planets and satellites are in no case very large, and generally very small ; and the inclinations of their orbits to ono another are generally small. Many nebulas in the heavens appear, when examined, to consist of a bright nucleus sur rounded by nebulous matter ; in others it is found that the apparently nebulous matter consists of stars. This gave Laplace the idea that our System might originally—that is, previously to the establishment of its present order—have been a large nebula, of which the sun was at the centre. Imagine a large nebulous mass in a state of revolution, with a solid, or at least less nebulous, centre, round which it revolves : call this central nucleus the sun. Assume the ordinary laws of matter to be true of this nebulous mass; and also that it extends as far as such an atmosphere can do—namely, until the attraction of the whole upon particles at the equator is equal to the centrifugal force of those particles. If condensation should begin to take place, arising from loss of heat, the mass would revolve more and more rapidly as it was condensed into less and less space ; but it does not follow that the equatorial particles would fall in towards the centre: they are balanced by the equality of the centripetal and centrifugal forces, and might form a ring round the rest of the mass. If the process were conducted with great regularity, this ring and the mass of vapour might undergo continual condensation together, until the increasing velocity of rotation prevented the formation of the ring from continuing. The departures from complete regularity which might exist in the mass might cause disturbances in the formation of the rings, which might end in there being one or more (not many) permanently revolving round the rest of the mass condensed into a solid body, in the manner of Saturn and its rings. Such regular formation, however, might be rarely continued long enough ; and if the rings got broken, each ring would become several masses, which would revolve nearly at the same distance, and nearly with the same velocity : such a result is seen in the four small planets. But as, generally speaking, these masses would, by irregu larities in their velocities, be combined into one • at last, each broken ring would form a new nebulous mass, revolving round the diminished central nucleus ; and if a number of such masses were formed, those nearer to the central mass would move with the greater velocity, and would be both smaller and denser than the external ones : the first circumstance certainly, the second and third most probably. Again, each mass would have a motion of revolution in the same direction [MOTION, DIRECTION or] as the motion round the primary ; for when the ring becomes broken, its internal parts have a somewhat more rapid motion than the external ones, which would give the motion of rotation noticed. And the rotations thus created in the internal masses would probably be greater than those in the external masses. The orbits of the masses would necessarily be nearly circular, and not much inclined to each other; but for irregularities, quite circular, and in the same plane. In each of the nebulous masses thus detached and revolving, condensation might again give rings or satellites, or both; but in all probability the external masses would get more satellites than the internal ones : the orbits of the satellites must be also nearly circular, and not much inclined. All the preceding circumstances, both those which are certain end those which are probable (Laplace confined himself to the former), are actually existing in the Solar System ; consequently this hypothesis, though subject to serious diffi culties, deserves attentive consideration, as often as any new knowledge of the constituent parts of our system shall render a reference to it likely to produce evidence on one side or the other. As a substitute for intelligent creative power, if such a thing were intended, it would do no better than any other ; for, as 31r. Whewell observes, a man with will, power, and conscience, cannot be admitted to be n necessary consequence of the cooling of a nebulous atmosphere. Nevertheless, as exhibiting a possible mode in which the Creator of mind and matter made the laws of formation resemble those of continuation, as far as the motions of the system are concerned, this hypothesis is strikingly explicative of what we really see. But even if we were to take it to be a true explanation, it would only be one step of the ascent, and the next question would be, what' higher process distributed the parts of this nebulous mass in such a manner as to place those outermost which were fit to form a planet so distant from the source of light and heat as Neptune, and to support the appropriate forms of militia] and vegetable life which analogy would induce us to suppose must exist there.
The history of astronomy teaches us that the system in which we live has not undergone any apparent change for more than 2000 years ; and, on inquiring into the connection which exists between one planet and another, or the laws of gravitation, it is found that so far as their mutual actions are concerned, there is no reason why any change ever ifficuld take place. If the central body were the only one which attracted the rest, and as long as the laws of matter remained unal tered, it is certain that nothing could alter the revolutions of a system of planets, unless two orbits intersected, and the planets of those orbits happened to come to the intersecting part at the same time, and to strike each other. But the planets are subject to the action of each other AA well as to that of the sun, and no instant elapses without every orbit undergoing a slight change from every one of the planeta of the other orbits. Jupiter alone produces on the earth's orbit in one year more change than we have any right to say all the comets put together would do in a hundred. And yet the system not only con tinues without any sensible change, but, one circumstance alone ex cepted, to which we shall presently allude, is demonstrably forme I to continue for a most enormous length of time, unless some new action should arise, or some external cause begin to operate. As it is some times stated that a complete mathematical demonstration has been given of the eternal stability of the Solar System, so far as the mutual actions of its parts are concerned—an assertion which is altogether incorrect—it may be worth while to enter a little ou the details of this subject.
The disturbing forces of the planets on each other cannot have their effects calculated all at once; but each force must be divided into an infinite series of terms, the first of which contains all the terms of the first dimension, the second all those of the second, and so on. Of all these terms each is much less in its effect than the preceding; so that in fact the first two dimensions are all that produce any sensible effect in any time which it is worth while to consider. Occasionally it happens that terms of the third and fourth dimensions have been required to be used, but almost all the sensible perturbations of the system depend on terms of the first two orders. Aa far as any effects arising from such terms are concerned, Lagrange and Poisson are ad mitted on all hands to have demonstrated the stability of the Solar System : and considering the nature of the process employed, and there being no appearance of any circumstance which looks likely to lead to a different result in any of the remaining terms of the dis turbing farces, it may be highly probable that a further investigation would show the same thing, if all the dimensions of the disturbing forces were employed. Sir J. Lubbock (` Phil. Mag.,' February, 1331) has pointed out the forms which further investigation would appa rently produce, and which would (unless a detailed investigation should lead to something not discoverable d priori) bear out as certain what we have just stated to be probable. But though all the presumptions lie on the side of those who would assert the proposition absolutely of all dimensions of the disturbing force, it is not yet time to say that it is a certain mathematical consequence of the theory of gravitation.
When the effects of perturbation arc examined, as far as the second dimeusiou of the disturbing force, it appears that the immense masa of the suu compared with that of any planet, the great distance of the planets from each other as compared with their amounts of departure from spherical form, the small excentricities and inclinations of their orbits, and their motions being all in one direction, give the following mathematical consequences of the law of attraction :—First, the longest or major axes of the planets' orbits are not subject to any slow variations of very long period; all their variations being excessively small, and soon destroyed by the production of contrary variations. It is very often stated that the major axes are subject to no variation ; this is to be understood only of secular variation (or of a very long periial). One year is not precisely the same as another to any fraction of a second; but the average year of one long period is precisely the same as that of another ; or at least the mean years of the two periods become more nearly equal the longer the periods are made. But' the executricities and inclinations are subject to long periodic altera tions, the timers of their recurrences not being exactly settled, from the difficulty of their determination. How then is it known that they are periodic I For instance, the executrieity of the Earth's orbit is subject to a yearly diminution of .00004, its value in 1801 being aln. Had this diminution been an increase, as it is in Mercury and Jupiter, it might a priori appear possible that this increase ' should continue until the orbit (preserving the same major axis) should be so elongated that the ultimate approach to and from the sun should give our planet the alternate climates of Mercury and 3lars, and thus no doubt destroy it as the abode of beings constituted like ourselves. It is found, however, that the following relation must exist :—If at any one moment the square of the excentrieity of each planet be multiplied by its mass and the square root of its mean distance from the sun (represented in numbers), the sum of all these products must be the same as it was at any moment past, or will be at any moment future. And if in each product the tangent of the incli nation to a fixed plane be substituted for the excentricity, the result ing equation is true. From such relations as these, and others con nected with them, it is shown that so far as the mutual actions of the planets are concerned, no one excentricity nor inclination can increase indefinitely, but all their changes must be periodic, and confined within rather small limits. The approach of the ecliptic to the equator, for instance, which amounts to about half a second in a year (and which leads speculators sometimes to talk about a past time when the ecliptic passed through the pole, and a future time when it will coincide with the equator), must stop long before the ecliptic reaches the equator, and attain a minimum inclination, after which the two will begin to separate ; the whole oscillation being less than three degrees. The whole result is summed up thus : As far as terms of the second order (inclusive) in the disturbing forces, and as long as only the mutual attractions of the planets act, there is a mathematical certainty that the Solar System will remain in its present state, the elements of the different orbits oscillating about certain mean values. from which they are never very distant : except only the longitudes of the nodes and perihelia, which change with velocities which are always very near to certain mean velocities. The probability is very small that the higher dimensions of the disturbing forces would affect this result, and certainly only in a length of time to which the longest periods known are trifling in comparison.
This last point, however, is of the less importance, since it has become highly probable, within the Last few years, that an external cause does exist, which must, unless there be a counteracting force of which we know nothing, in time cause the destruction of the System. If the planets move in any medium which resists their motions, how ever little, the consequence must be a gradual diminution of their mean distances from the sun, and a gradual increase of their velocities, ending in their absolutely falling into the sun. For the presumption in favour of the actual existence of such a resisting medium, see COMET. This retarding agent seems to show a rapid effect upon so attenuated a mass as Encke's comet, though thousands of years have elapsed without its producing any sensible effect upon the planets. Little as it may concern us directly, these speculations have an interest, both as to the glimpse they give of the possible destiny of our System, and from their association with the history of past and the hope of future discovery. It is to be remembered that no science has drawn out so much of mathematical talent, or indirectly excited such an influence upon other branches of physical research, as the application of the theory of gravitation to the development of the planetary motions.