It will be observed that while the Laplacian hypothesis is concerned in the main with the progressive development of the solar system, and systems of a like order surrounding other stellar centers, whose existence is highly probable, the origin and development of the stellar universe is a vaster problem which can only be undertaken and completed in its broadest bearings when the structure of the stellar universe has been ascertained.
Darwin's important investigations in 1877-1878 on tidal friction may be here related. Before his day acceptance of the ring-theory of development of the moon from the earth had scarcely been questioned; but his recondite mathematical researches on the tidal reaction between a central yielding mass and a body revolving round it brought to light the unsuspected effect of tides raised upon both bodies by their mutual attraction. The type of tides here meant is not the usual rise and fall of the waters of the ocean, but primeval tides in the plastic material of which the earth in its early history was composed. The Newtonian law of gravitation afforded a complete explanation of the rise and fall of the waters of the oceans, but as applied to the motions of planets and satellites by the Lagrangian formulæ, it presupposed that all these bodies are rigid and unyielding. However, mutual tides of phenomenal height in their early plastic substances must have been a necessary consequence of the action of the Newtonian law, and they gradually drew upon the earth's rotational moment of momentum.
In its very early history, before there was any moon to produce tides, the earth rotated much more rapidly, that is, the day was very much shorter than now, probably about five or six hours long. And with the rapid whirling, it was not a Laplacian ring that was detached, but a huge globular mass was separated from the plastic earth's equator. Darwin shows that the gravitative interaction of the two bodies immediately began to raise tides of extraordinary height in both, therefore tending to slow down the rotational periods of both bodies. Action and reaction being equal, the reaction at once began driving the moon away from the earth and thereby lengthening its period of revolution. So small was the mass of the moon and so near was it to the earth, that its relative rotational energy was in time completely used up, and the moon has ever since turned her constant face toward us. Tides of sun and moon in the plastic earth, acting through the ages, slowed down the earth's rotation to its present period, or the length of the day.
Moulton, however, has investigated the tidal theory of the origin of the moon in the light of the planetesimal hypothesis, concluding that the moon never was part of the earth and separated therefrom by too rapid rotation of the earth, but that the distance of the two bodies has always been the same as now. The more massive earth has in its development throughout time robbed the less massive moon in the gradual process of accretion. So the moon has never acquired either an ocean or atmosphere, and this view is acceptable to geologists who have studied the sheer lunar surface, Shaler of Harvard among the first, and laid the foundations for a separate science of selenology.
Tidal friction has also been operant in producing sun-raised tides upon the early plastic substances which composed the planets: more powerfully in the case of planets nearer the sun; less rapidly if the planet's mass is large; also less completely if the planet has solidified earlier on account of its small dimensions. So Darwin would account for the present rotation periods of all the planets: both Mercury and Venus powerfully acted on by the sun on account of their nearness to him, and their rotational energy completely exhausted, so that they now and for all time turn a constant face toward him, as the moon does to the earth; earth and possibly Mars even yet undergoing a very slight lengthening of their day; Jupiter and Saturn, also Uranus and probably Neptune, still exhibiting relatively swift axial rotation, because of their great mass and great original moment of momentum, and also by reason of their vast distances from the central tide-raising body, the sun.
By applying to stellar systems the principles developed by Darwin, See accounted for the fact, to which he was the first to direct attention, that the great eccentricity of the binary orbits is a necessary result of the secular action of tidal friction. The double stars, then, were double nebulæ, originally single, but separated by a process allied to that known as "fission" in protozoans. Indeed, Poincaré proved mathematically that a swiftly revolving nebula, in consequence of contraction, first undergoes distortion into a pear-shaped or hour-glass figure, the two masses ultimately separating entirely; and the observations of the Herschels, Lord Rosse and others, with the recent photographic plates at the Lick and Mount Wilson observatories, afford immediate confirmation in a multitude of double nebulæ, widely scattered throughout the nebular regions of the heavens.
Jeans of Cambridge, England, among the most recent of mathematical investigators of the cosmogony, balances the advantages and disadvantages of the differing cosmogonic systems as follows, in his "Problems of Cosmogony and Stellar Dynamics": "Some hundreds of millions of years ago all the stars within our Galactic universe formed a single mass of excessively tenuous gas in slow rotation. As imagined by Laplace, this mass contracted owing to loss of energy by radiation, and so increased its angular velocity until it assumed a lenticular shape…. After this, further contraction was a sheer mathematical impossibility and the system had to expand. The mechanism of expansion was provided by matter being thrown off from the sharp edge of the lenticular figure, the lenticular center now forming the nucleus, and the thrown-off matter forming the arms, of a spiral nebula of the normal type. The long filaments of matter which constituted the arms, being gravitationally unstable, first formed into chains of condensation about nuclei, and ultimately formed detached masses of gas. With continued shrinkage, the temperature of these masses increased until they attained to incandescence, and shone as luminous stars. At the same time their velocity of rotation increased until a large proportion of them broke up by fission into binary systems. The majority of the stars broke away from their neighbors and so formed a cluster of irregularly moving stars—our present Galactic universe, in which the flattened shape of the original nebula may still be traced in the concentration about the Galactic plane, while the original motion along the nebular arms still persists in the form of 'star-streaming.' In some cases a pair or small group of stars failed to get clear of one another's gravitational attractions and remain describing orbits about one another as wide binaries or multiple stars. The stars which were formed last, the present B-type stars, have been unusually immune from disturbance by their neighbors, partly because they were born when adjacent stars had almost ceased to interfere with one another, partly because their exceptionally large mass minimized the effect of such interference as may have occurred; consequently they remain moving in the plane in which they were formed, many of them still constituting closely associated groups of stars—the moving star clusters.
"At intervals it must have happened that two stars passed relatively near to one another in their motion through the universe. We conjecture that something like 300 million years ago our sun experienced an encounter of this kind, a large star passing within a distance of about the sun's diameter from its surface. The effect of this, as we have seen, would be the ejection of a stream of gas toward the passing star. At this epoch the sun is supposed to have been dark and cold, its density being so low that its radius was perhaps comparable with the present radius of Neptune's orbit. The ejected stream of matter, becoming still colder by radiation, may have condensed into liquid near its ends and perhaps partially also near its middle. Such a jet of matter would be longitudinally unstable and would condense into detached nuclei which would ultimately form planets."