University of Virginia Library

LAPLACE'S HYPOTHESIS

In 1796, 41 years following Kant's principal contributions, Laplace published an extensive untechnical volume on general astronomy. At the end of the volume he appended seven short notes. The final note, to which he gave the curious title "Note VII and last,'' proposed a theory of the origin and evolution of the solar system which soon came to be known as Laplace's Nebular Hypothesis. There are several circumstances which indicate pretty clearly that Laplace was not deeply serious in proposing this hypothesis:

1. Its method of publication as the final short appendix to a large volume on general astronomy.

2. He himself said in his note that the hypothesis must be received "with the distrust with which everything should be regarded that is not the result of observation or calculation.''

3. So far as we know he did not submit the theory to the test of well-known mathematical principles involved, although this was his habit in essentially every other branch of astronomy.

4. Laplace, in common with Kant, laid great stress upon the fact that the satellites all revolve around their planets from west to east, nearly in the common plane of the solar system; yet 6 or 7 years before Laplace's publication, Herschel had shown and published that the two recently discovered satellites of Uranus were revolving about Uranus in a plane making an angle of 98° with the common plane of the

solar system. While Laplace might not have known of Uranus's satellites in 1796, on account of existing political conditions, there is no evidence that he considered or took note of the fact when making minor changes in his published papers up to the time of his death in 1827. It is a further interesting comment on international scientific literature that Laplace died without learning that Kant had worked in the same field.

Laplace and his contemporary, Sir William Herschel, had been the most fruitful contributors to astronomical knowledge since the days of Sir Isaac Newton. Herschel's observations had led him to speculate as to the evolution of the stars from nebulæ, and as a result interest in the subject was widespread. This fact, coupled with Laplace's commanding position, caused the nebular hypothesis to be received with great favor. During an entire century it was the central idea about which astronomical thought revolved.

Laplace conceived that the solar system has been evolved from a gaseous and hot nebula; that the nebulosity extended out farther than the known planets; and that the entire nebulous mass was endowed with a slow rotation that was uniform in angular rate, as in the case of a rotating solid. This gaseous mass was in equilibrium under the expanding forces of heat and rotation and the contracting force of gravitation. Loss of heat by radiation permitted corresponding contraction in size, and increased speed of rotation. A time came, according to Laplace, when the nebula was rotating so rapidly that an outer ring of nebulosity was in equilibrium under centrifugal and gravitational forces and refused to be drawn closer in toward the center. This ring, rotating as a solid, maintained its position, while the inner mass contracted farther. Later another ring was abandoned in the same manner; and so on, ring after ring, until only the central nucleus was left. Inasmuch as the nebulosity in the rings was not uniformly distributed, each ring broke into pieces, and the pieces of each ring, in the progress of time, condensed into a gaseous mass. The several large masses formed from the abandoned rings, respectively, became the planets and satellites of the solar system. These gaseous masses rotated faster and faster as their heat radiated into space, they abandoned rings of gaseous matter just as the original mass had done, and these secondary rings condensed to form the satellites; save that, in one case, the ring of gas nearest to Saturn for some reason formed a solid (!) ring about that planet, instead of condensing into one or more satellites. Thus, in outline, according to Laplace, the solar system was formed.

The first half of the nineteenth century found the nebular hypothesis accepted almost without question, but a tearing-down process began in the second half of the century, and at present not much of the original structure remains standing. This is due in small part to discoveries

since Laplace's time, but chiefly to a more careful consideration of the fundamental principles involved. We have space to present only a few of the more salient objections.

1. If the materials of the solar system existed as a gas, uniformly distributed throughout what we may call the volume of the system, the density of the gas would be exceedingly low: at the most, several hundred million times less dense than the air we breath. Conditions of equilibrium in so rare a medium would require that the abandonment of the outer parts by the contracting and more rapidly rotating inner mass should be a continuous process. Each abandoned element would be abandoned individually; it would not be vitally affected by the elements slightly farther out in the structure, nor by the elements slightly nearer to the center. Successive abandonment of nine gaseous rings of matter, each ring rotating as if it were a solid structure, is unthinkable. The real product of the cooling process in such a nebula would undoubtedly be something in the nature of a spiral nebula, in which the matter would revolve around the nucleus the more rapidly the nearer it was to the nucleus. If the matter were originally distributed uniformly throughout the rotating structure, the spiral lines might not be visible. If it were distributed irregularly, the spiral form here and there could scarcely fail to be in evidence to a distant observer.

2. Laplace held that the condensation of each ring would result in one planet, rotating on its axis from west to east; this apparently by virtue of the fact that in a ring rotating as a solid the outer edge travels more rapidly than the inner edge does, and therefore, the west to east direction of rotation must prevail in the planetary product. If now, as we firmly believe, each constituent of such an attenuated ring must rotate substantially independently of other constituents, those nearer the inner edge of the ring will possess the higher speeds of rotation, and the preponderance of kinetic energy in the inner parts of the ring should give the resulting planetary condensation a retrograde direction of rotation.

3. According to Laplace the satellites should all revolve around their primaries from west to east. Eight of the satellites do not follow this rule.

4. If the materials composing the inner ring of Saturn were abandoned by the parent planet, as this planet contracted in size and rotated ever more and more rapidly, then the ring should revolve about the planet in a period considerably longer than the planet period. The reverse is the fact. The rotation period of the equatorial region of the planet itself is 10 h. 14 m., whereas the inner edge of the ring system revolves about the planet once in about five hours.

5. The inner satellite of Mars revolves once in 7 h. 39 m., whereas Mars requires 24 h. 37 m. for one rotation. According to the Nebular Hypothesis, the period of the satellite should be the longer.

6. Laplace's hypothesis would seem to require that the orbits of the planets be circular or very nearly so. The orbits of all except Venus and Neptune are quite eccentric, and Mercury's orbit, which should have the nearest approach to circularity, is by far the most eccentric.

7. If the planetary rings were abandoned by centrifugal action, we should expect the Sun to be rotating in the principal plane of the planet system. The major planets, from Venus out to Neptune, are revolving in nearly a common plane. The Sun, containing 99 6/7 per cent. of all the material in the system, has its equator inclined 7° to the planet plane. This discrepancy is a very serious and I think fatal objection to Laplace's hypothesis, as Chamberlin has emphasized.

8. Laplace assumed a nebula whose form was a function of its rotational speed, its gravitation, its internal heat, and, although he does not so state, of its internal friction. He did not distribute the matter within the nebula to conform in any way to the distribution as we observe it to-day, but he let the entire structure contract, following the loss of heat, until the maintenance of equilibrium required the successive abandoning of seven or eight rings. He mentions a central condensation, but gives no further particulars. Thirty years ago Fouché established clearly that the condensing of Laplace's assumed nebula into the present solar system would involve the violent breaking of the law known as the conservation of moment of momentum. Fouché proved that a distributio n of matter beyond any conception of the subject by Laplace must be assumed. Fully 96 per cent. must be condensed in the central nucleus at the outset, and not more than 4 per cent. of the total mass must lie outside of the nucleus and be widely distributed thoughout the volume of the solar system. Chamberlin puts the case very strongly in another way. If the planet Mercury was abandoned as a ring of nebulosity, the equatorial velocity of the remaining central mass must at that time have been in the neighborhood of 45 km. per second, as this is the orbital speed of Mercury. If the central mass condensed to the present size of the Sun, the Sun's equatorial velocity of rotation should now be fully 400 km. per second, in accordance with the requirement of the rigid law of constancy of moment of momentum. The Sun's actual equatorial velocity is only 2 km. per second!

In several other respects the hypothesis of Laplace, as he proposed it, fails to account for the facts as they are observed to exist.

Poincaré devoted his unique talents to the evolution problem shortly before his death. He recognized that the Laplace hypothesis is not tenable except upon such an assumed distribution of matter as was defined by Fouché. Accepting this modification, and extending the hypothesis to involve the application of tidal interactions at many points throughout the solar system, Poincaré expresses the opinion that the Laplacian hypothesis, of all those proposed, is still the one which best

accounts for the facts.[3] However, he does not utilize the hypothesis of rings rotating as solids, for he finds it necessary to conclude that the planetary masses in the beginning must have had retrograde rotations. In the large planetary masses of Jupiter and Saturn, for example, the materials which form the outer retrograde satellites were abandoned while the rotations were still retrograde, and when the diameters of the planetary masses were several scores of times their present diameters. In these extended masses the Sun would create tidal waves, and here, as always, such waves would exert a retarding effect upon the rotations. A time would come, Poincaré thought, when these planets would rotate once in a revolution; that is, present the same face to the Sun; and this is in fact a west to east rotation. Further contraction of the planetary masses would give rise to increasing rotational speeds in the west to east direction. The materials which form the inner satellites of Jupiter and Saturn were abandoned successively after the west to east direction of rotation had become established. According to modifications of the same theory, tidal retardation has slowed down Saturn's speed since the abandonment of the materials which later condensed to form the inner ring of that planet; or, possibly, the ring materials encountered resistance after the planet abandoned them, with the consequence that the ring drew in toward the planet and increased its speed; and similarly in the case of Mars and its inner satellite.

To me this modification of the Laplacian hypothesis is unsatisfactory, for several reasons. To mention only one: if Jupiter was a large gaseous mass extending out as far as the 8th and 9th satellites, the gaseous body was very highly attenuated; friction in the outer strata would be essentially a negligible quantity, and tidal retardation would not be very effective; and it would be under just these conditions that loss of heat from the planet should be most rapid and the rate of increase of retrograde rotation resulting therefrom be comparatively high. It would seem that the rotation of the planet in the retrograde direction must have accelerated under the contractional cause, rather than have decreased and reversed in direction under an excessively feeble tidal cause.

The recognized weaknesses of Laplace's hypothesis have caused many

other hypotheses to be proposed in the past half century. The hypotheses of Faye, Lockyer, du Ligondes, See, Arrhenius, and Chamberlin and Moulton include many of the features of Kant's or Laplace's hypotheses, but all of them advance and develop other ideas. It is unfortunate that space limits do not permit us to discuss the new features of each hypothesis. (To be continued.)