FOOTNOTES:

FOOTNOTES:[16]Mémoires de l'Académie de Montpellier, tom. i.[17]The Tides, p. 327.[18]Mémoires de l'Académie de Montpellier, tom. viii.[19]C. Wolf,Bulletin Astronomique, tom. i., p. 596.[20]American Journal of Science, vol. xxxviii., p. 3.[21]G. H. Darwin,Nature, vol. xxxi., p. 506.[22]Proceedings of the American Philosophical Society, vol. xxii., p. 109.[23]De Vries,Die Mutationstheorie, Bd. II., p. 714.[24]Formation Mécanique du Système du Monde.See alsoLe Problème Solaire, by the Abbé Th. Moreux, p. 63et seq.[25]Revue des Questions Scientifiques, January, 1904.[26]The Earth's Beginnings, p. 247.[27]Astrophysical Journal, vol. xi., p. 130.

[16]Mémoires de l'Académie de Montpellier, tom. i.

[17]The Tides, p. 327.

[18]Mémoires de l'Académie de Montpellier, tom. viii.

[19]C. Wolf,Bulletin Astronomique, tom. i., p. 596.

[20]American Journal of Science, vol. xxxviii., p. 3.

[21]G. H. Darwin,Nature, vol. xxxi., p. 506.

[22]Proceedings of the American Philosophical Society, vol. xxii., p. 109.

[23]De Vries,Die Mutationstheorie, Bd. II., p. 714.

[24]Formation Mécanique du Système du Monde.See alsoLe Problème Solaire, by the Abbé Th. Moreux, p. 63et seq.

[25]Revue des Questions Scientifiques, January, 1904.

[26]The Earth's Beginnings, p. 247.

[27]Astrophysical Journal, vol. xi., p. 130.

TIDAL FRICTION AS AN AGENT IN COSMOGONY

Theeffects of tidal friction are of almost infinite complexity. How it will act in each particular case cannot be predicted offhand; it is a matter for detailed inquiry. Mutually countervailing influences have to be taken into account, nor is the balance easy to strike. The manner of its inclination may, indeed, often depend upon qualities and relations of the bodies concerned which lie outside the range of what can be distinctly ascertained. All that may be hoped for, then, is to arrive at estimates neither misleading by their ostensible precision, nor yet so vague as to be wholly uninstructive, of the part played by tidal forces in moulding the history of connected globes.

The assumption that they attract one another as if the mass of each were collectedat its centre, is one of those convenient fictions without which the advancing feet of science would be impeded by tangled thickets of illusory refinements and superfluous elaborations. The fiction would correspond with fact only if the globes were truly spherical, and they could be truly spherical only if they were ideally rigid. Cosmic bodies, however—suns and planets alike—are actually plastic spheroids; they can, to be sure, be treated without sensible error as attractive points when their distances are very great relatively to their diameters; but upon a closer approach inequality of action supervenes. The component parts of the gravitating masses respond, each individually, and in a measure independently, to the graduated pulls exercised upon them, and tidal strains begin variously to take effect.

Their historical significance was in part divined by Kant. His penetration of so recondite a secret is truly astonishing. A struggling young pedagogue in a remote Prussian province, profoundly learned, though no more than half skilled in technical acquirements, saw by intuition what escaped the acumen of all the great geometers of theeighteenth century—namely, that the moon turns one perpetual face towards the earth, because its primitive rotation was stopped by the friction of earth-raised tides. He perceived besides that a reciprocal action of the same kind must affect the earth, and will continue to affect it until the day coincides in length with the month. Nor did he fail to point out that, in a molten state of the globes, the process would advance with comparative rapidity. To one solitary thinker, then, it became apparent, already in 1754,[28]that oceanic tides are, in cosmogony, of negligible importance compared with bodily tides.

There is no substance in nature that will not change its shape through prolonged stress, and the more readily the nearer it approaches to the fluid condition. The heaping-up of the waters on the earth's surface at the bidding of the moon is thus a differential effect. Continents heave and subside as well as oceans, though not nearly to the same extent. The measurable rise of water serves to gauge the relative mobilities of the solid globe and of its liquid envelope. If the former did not yieldat all to the pull so readily obeyed by the latter, the tides would, in fact, be greater than they actually are in the proportion of about three to two, the ratio indicating for the earth an effective rigidity at least equal to that of steel.[29]Were there no discrepancy in rigidity between the various parts of our terraqueous world, tides would fail to be perceptible. The ocean and the bed of the ocean would rise and fall together, and to the same extent. In the far past therewasno discrepancy. The viscous earth took, as a whole, the form momentarily impressed upon it by the unequal attractions of the sun and moon on its variously distant sections, with the upshot of bringing the year, month, and day into relations so familiar as to appear inevitable.

Tidal friction does not merely act as a check upon rotational speed. One element of motion in a system cannot be altered without some counter-change in the others. They are coupled up together like a train of geared wheels. From the principle of the conservation of moment of momentum, we know withcertainty that a loss in one direction must be compensated by a gain in some other. Tidal friction had, then, reactive consequences. They were first adverted to by Julius Robert Mayer in 1848,[30]and were brought prominently into view in the series of investigations begun by Professor Darwin in 1879. The rotational momentum removed from the earth by the drag of a circulating wave of deformation must assuredly have reappeared in some other part of the system. It was restored, all but the percentage wasted as heat, by the widening of the lunar orbit.[31]Concomitantly with the slackening of the earth's axial rate, the moon retreated from its surface, pulled forward by the tidal crest continually in advance of its position. This redressed the balance by augmenting orbital momentum, while at the same time diminishing the moon's linear velocity. The importance of this secondary frictional effect in the history of the earth-moon system was the virtual discovery of Professor Darwin.

That system occupies a critical situation inthe solar cortège. The planets interior to it have no satellites; the planets exterior to it (Neptune making probably only an apparent exception to the rule) have two or more. The earth alone is truly binary; and the moon is not only its solitary companion, but it is by far the largest companion-body, relatively to the mass of its primary, to be found within the precincts of the solar domain. These circumstances are certainly not disconnected one from the other, and they obviously depend upon a single cause. Solar tidal friction was here the determining factor. The apportionment of satellites to the various planets was, beyond doubt, in great measure prescribed by the degrees of retarding power exerted on their axial movement through the agency of sun-raised tides in their still plastic bodies. Hence, the disruptive rate of spinning needed for the separation of satellites was never attained by either Mercury or Venus; they remained moonless for all time, and exposed, through the cutting down of their rotational velocity, to uncompensated extremes of temperature. How the earth was to fare in both respects long hung in the balance. Rightlyto forecast its destiny would, indeed, have demanded no common perspicuity in an intelligent onlooker from some other sphere. Although the solar brake acted upon terrestrial rotation with no more than one-eleventh the power brought to bear upon that of Venus, it nevertheless sufficed during uncounted ages to hinder acceleration from reaching the pitch involving instability.

Our embryonic planet had long ceased to be nebulous, and had, in fact, shrunk by cooling nearly to its present dimensions before the die was cast. Then, at last, the hurrying effects of contraction prevailed over the slowing down due to tidal resistance, axial speed overbore equilibrium, and the spheroid divided. Now globes thus far advanced in condensation are apt to split less unequally than globes in a more primitive stage; and the moon, because late-born, was of large size. Its mass is 1/81 that of the earth; the masses of Titan and Saturn are as 1 to 4,600; while Jupiter's third and greatest satellite contains only 1/11300 part of the matter englobed in the parent-body. Moreover, Professor Darwin has made it clear that the satellites of Jupiter and Saturn revolvenow in orbits not widely remote from those at first pursued by them; while the moon, on the contrary, started on its career almost, if not quite, from grazing contact with its primary. Owing to these two exceptional circumstances—its considerable relative mass and its close initial vicinity—the moon wielded over the earth tidal influence incomparably more powerful than that exerted by any of its compeers in the sun's realm.

The lunar-terrestrial system offers, accordingly, an example unique among those in solar subordination of a pair of globes, the mechanical relations of which have been settled on their present basis by the predominating agency of bodily tides. It holds forth, too, the one case in which origin by fission was possible. Professor Darwin's communication to the Royal Society in 1879 occasioned on this point a remarkable diversion of ideas. Saturn's rings were at last, through the reasonings contained in it, perceived to be illustrative of only one among many feasible modes of cosmic growth. It became clear that a single cut-and-dried method would not answer all the infinitely varied purposes ofcreative design. Annulation might have served its turn, but there were alternatives. A fresh standpoint was virtually attained, and the wide prospect commanded by it begins already to spread out invitingly before the gaze of investigators.

But whether the moon emerged from the earth as a protuberance, or was abandoned by it as an irregular equatorial ring, it was revolving, when our theoretical acquaintance with it begins, in a period of not less than two and not more than four hours, quite close to the earth's surface; while the nearly isochronous rotation of the earth was conducted with all but disruptive rapidity. The situation is so suggestive that it needs only a short and tolerably safe leap in the dark to reach the conclusion that the two masses had very recently been one. With their division, at an epoch estimated to have been about sixty million years ago, the process began by which the moon was pushed back along a widening spiral course to its present position, the vanished rotational momentum of the earth cropping up again in the augmented orbital momentum of the moon. And thetransformation is, at least in theory, still going on.

Tidal friction has further capabilities. The transference of momentum from one part of a system to another is only the most obvious among the crowd of its results. Scarcely an element of movement escapes its influence. It increases, as a rule, orbital eccentricity. The smallest initial deviation from circularity develops, through the inequality of accelerative action thence ensuing, into pronounced ovalness. That of the moon's path can in this way be accounted for. Moreover, its plane was, in all probability, shifted simultaneously and under compulsion of the same power, from its original coincidence with the earth's equatorial plane to the level it now occupies. The obliquity of the ecliptic, too, is partially explicable on the same principle. 'The present motion of the two bodies' (to quote Professor Darwin's words), are 'completely co-ordinated by the theory that tidal friction was the ruling power in their evolution.' Holding this clue, we are enabled to trace them back to the start of their dual existence, and to follow the insensible modifications bywhich their state was moulded to its actual form.

In no other satellite-system is this possible. No moon besides our own possesses a stock of orbital momentum large enough to intimate for it an analogous history. Planetary attendants elsewhere travel nearly in their original tracks; the fluid ripples raised by them on the surfaces of their primaries lacked power to displace them sensibly. Their own rotation, indeed, seems to have been completely destroyed. Destroyed, that is, relatively to the destroying body. There is a certainty that some, there is the strongest likelihood that all, of the Jovian and Saturnian satellites turn unchangingly the same face towards their primaries. They rotate in the period of their several revolutions, just as our moon does, and as a consequence of the same cause. Tidal friction, however, appears to have been otherwise of subordinate importance in shaping their dynamical relations.

The agency will not, then, serve in all cases for adeus ex machinâ. It is not indiscriminately efficacious. The modes of its action have, in each of the systems considered,to be delicately distinguished. The stage of development arrived at by the bodies affected, their degree of viscosity, their comparative mass and bulk, their modes of motion, all avail profoundly, and it may be incalculably, to modify the outcome. The facility of error in estimates of the kind is illustrated by Professor Darwin's remark that the magnitude of the tide-raising force is only one factor of the product.[32]The other is relative movement. Now, in the case of the moon the former continually augmented retrospectively, while the latter fell off. Tidal generative power varies inversely as the cube of the distance; in antique times, then, when the earth and moon revolved contiguously, the bodily distortions they mutually produced were beyond question on an extremely large scale. Yet, because of the near coincidence of the periods of the globes, they must have been almost inoperative for frictional purposes. The travelling of the piled-up matter over their surfaces was too slow to lend it much power as a friction-brake. The insignificant waves raised by the sun were, we are led to believe, because of theirswift relative motion, more influential at that early epoch in checking terrestrial rotation than the colossal, but nearly stationary waves due to the moon.

Numerical calculations, where they are practicable, afford the only safe guide to this intricate field of inquiry. It does not suffice to show that tidal action would have been of the kind required—would have taken the right direction—for bringing about some apparently anomalous result. Proof must, besides, be forthcoming that the action would have been of adequate power. Plausible guesses on the subject may be entirely fallacious. The machine, even if properly constructed for the end in view, may work too feebly for its attainment. We are, for instance, assured that no difficulty connected with the sense of planetary rotation need impede acceptance of the theory of planetary origin from separated rings, since even if the embryo globes gyrated the wrong way at the outset, solar tidal friction would promptly have reduced them to conformity with the general current of movement. This is true in principle, but will it bear quantitative investigation? Many promisinghypotheses have broken down under the weight of figures; whether this particular one is strong enough to survive their application remains to be seen. We are, indeed, sure of its validity as regards Mercury, but the efficacy of tidal friction decreases as the sixth power of increasing distance, and the actual rotation of Venus furnishes an enigma sufficiently perplexing to discourage scrutiny of its dimly discerned antecedent conditions. As regards the earth and the exterior planets, the question could only be answered with the help of information which is not forthcoming.

The unexpected circumstance that the newly-discovered ninth Saturnian moon circulates from east to west can thus be no more than tentatively explained by invoking this agency of change. Admitting (as we seem bound to do) that satellites are the offspring of the planets they attend, there is no evading the conclusion that the small body under discussion was thrown off from a primary endowed with a rotation opposite to that now possessed by it. And the reversal must have been completely brought to pass before the eighth satellite, Japetus, came into existence. Thecrux is most arduous; there is no other resource for meeting it but to consider the effects on planetary rotation of solar tides, and this Professor W. H. Pickering, the discoverer of Phœbe, has done.[33]But a cause may be true without being sufficient; and close calculation will be needed to determine, in this instance, how the matter stands.

Professor Darwin's researches were fruitful just because they were definite. They demonstrated, once for all, the diverse faculties of tidal friction as a cosmogonic agency, and indicated clearly the departments of cosmogonic change in which its competence lay. They availed, moreover, to determine for the earth-moon system the amount of work actually done by tidal friction in these several departments, and to prove its large excess over the corresponding output in any other sub-system falling within the sphere of observation. This memorable result suggests that our terrestrial home may be singular, not only in its evolutionary history, but in the innumerable adjustments fitting it to be the abode of life.

The relations of the earth and moonadumbrate, and scarcely more than adumbrate, the physical influences mutually exerted upon each other by numerous twin-globes in stellar space. Tidal friction is of maximum power in systems formed of equal masses; and those of double stars are seldom widely disparate. Most, if not all of them, were, besides, primitively very near neighbours, so that their symmetry must have been marred by conspicuous tidal deformations. The results upon their development have been expounded in detail by Dr. See. One of the most remarkable is the high average eccentricity of their orbits. Visual binaries, with few exceptions, travel in considerably elongated ellipses, while spectroscopic binaries as a rule pursue approximately circular paths. Dr. See's argument that the eccentricity of the more spacious systems was acquired under the influence of tidal friction, during the long course of progressive separation, is well-nigh irresistible.

True, this line of explanation is not wholly clear of obstacles and incongruities. Yet they may probably be described as of a complicating, rather than of a contradictory kind. The theory of tidal friction is not a universalsolvent of the difficulties encountered in the study of double stars. That the mode of action it deals with had a contributory share towards regulating their mechanical arrangements may, nevertheless, be regarded as certain, while the potency and perhaps even the manner of its operation varied extensively from system to system. What precisely it effected in each lies beyond our range of determination. For the data available regarding the viscosity, density, and axial movements of embryo star-pairs must always be too scanty and insecure to provide a basis for rigorous computations. The mystery of the fore-time can never be entirely dissipated. Enough if we can look at it through a glass which darkens, without distorting, the objects presented in its field of view.

FOOTNOTES:[28]Sämmtliche Werke, Bd. VI., pp. 5-12, 1839.[29]G. H. Darwin,Encyclopædia Britannica, article on 'Tides.'[30]Dynamik des Himmels, p. 49.[31]Darwin,Philosophical Transactions, vol. clxxii., p. 528.[32]Philosophical Transactions, vol. clxxi., p. 876.[33]Harvard Annals, vol. liii., p. 58.

[28]Sämmtliche Werke, Bd. VI., pp. 5-12, 1839.

[29]G. H. Darwin,Encyclopædia Britannica, article on 'Tides.'

[30]Dynamik des Himmels, p. 49.

[31]Darwin,Philosophical Transactions, vol. clxxii., p. 528.

[32]Philosophical Transactions, vol. clxxi., p. 876.

[33]Harvard Annals, vol. liii., p. 58.

THE FISSION OF ROTATING GLOBES

Fewpeople need to be told that a rotating fluid mass is shaped very much like an orange. It assumes the form of a compressed sphere. And the reason for its compression is obvious. It is that the power of gravity, being partially neutralized by the centrifugal tendency due to axial speed, decreases progressively from the poles, where that speed has a zero value, to the equator, where it attains a maximum. Here, then, the materials of the rotating body are virtually lighter than elsewhere, and consequently retreat furthest from the centre. The 'figure of equilibrium' thus constituted is a spheroid, a body with two unequal axes. In other words, its meridional contour—that passing through the poles—is an ellipse, while its equator is circular.

Now we know familiarly, not only that a spinning sphere becomes a spheroid, but that the spheroid grows more oblate the faster it spins. The flattened disc of Jupiter, for instance, compared with the round face of Mars, at once suggests a disparity in the rate of gyration. But there must be a limit to the advance of bulging, or the spheroid, acceleratedad infinitum, would at last cease to exist in three dimensions. Clearly this unthinkable outcome must be anticipated; at some given point the process of deformation must be interrupted. A breach of continuity intervenes; the train is shunted on to a branch line. Nor is it difficult to divine, in a general way, how this comes to pass. Equilibrium, beyond doubt, breaks down when rotation attains a certain critical velocity, varying according to circumstances, and the spheroid either alters fundamentally in shape or goes to pieces.

So much plain common-sense teaches, yet the precise determination of the course of events is one of the most arduous tasks ever grappled with by mathematicians. M. Poincaré essayed it in 1885;[34]it was independentlyundertaken a little later by Professor Darwin;[35]and the subject has now been prosecuted for eighteen years, chiefly by these two eminent men, with a highly interesting alternation of achievement, one picking up the thread dropped by the other, and each in turn penetrating somewhat further into the labyrinth. The results, nevertheless, are still to some extent inconclusive; they indicate, rather than indite, the genetic history of systems. A strong light is, indeed, thrown upon it; but in following its guidance, the limitations of the inquiry have to be borne in mind. The chief of these are, first, that the assumed spheroid is liquid; secondly, that it is homogeneous. Neither of these conditions, however, is really prevalent in nature, so that inferences based upon them can only be accepted under reserve. They were adopted, not by choice, but through the necessities of the case. There was no possibility of dealing mathematically with bodies in any other than the liquid state. The equilibrium of gaseous globes defies treatment,except under arbitrary restrictions.[36]Nor is it possible to cope with the intricacies of calculation introduced by variations of interior density. Cosmical masses, as they actually exist, are nevertheless strongly heterogeneous, so that at the utmost only an approximation to the genuine course of their evolution can be arrived at by the most skilful analysis. Yet even an approximate solution of such a problem is of profound interest. We can here only attempt briefly to specify its nature.

The course of change by which the equilibrium of a rotating liquid spheroid is finally overthrown has, at any rate, been satisfactorily tracked. When its spinning quickens to a disruptive pitch, it acquires three unequal axes instead of two. The equator becomes elliptical like the meridians. A 'Jacobian ellipsoid' is constituted. To this new form, it would seem, a long spell of stability must be attributed; only its major axis becomes more and more protracted as cooling progresses, and with cooling, contraction, and with contraction the increase of axial velocity. Then at last a crisis once more supervenes; there is a collapse of equilibrium, and its re-establishment involves the sacrifice of the last vestige of symmetry. An 'apioid,' or pear-shaped body, replaces the antecedent ellipsoid; and its apparent incipient duality suggested to M. Poincaré that the furrow unequally dividing it might deepen, with still accelerated gyration, into a cleft, splitting the primitively single mass into a planet and satellite. But this eventuality, he was careful to note, had no direct bearing on Laplace's hypothesis, which dealt with a nebula condensed towards the centre, while the fissured apioid was liquid and homogeneous.[37]

Professor Darwin followed out the conditions of this remarkable pear-shaped body to a closer degree of approximation than its original investigator had done, and succeeded in virtually demonstrating its conditional stability. But his analysis tended to smooth away the characteristic peculiarities of its shape, and, so far, to diminish the probability of its ultimate disruption. Mr. Jeans, on the other hand,from an elaborate study of a series of cigar-shaped figures which in theory follow a parallel course of development to that pursued by ellipsoids, derived, by strict mathematical reasoning, the actual separation of a satellite from one end of a parent-cylinder. The representative figures reminded Professor Darwin 'of some such phenomenon as the protrusion of a filament of protoplasm from a mass of living matter.' 'In this almost life-like process' he saw 'a counterpart to at least one form of the birth of double stars, planets, and satellites.'[38]

But the resemblance, when examined dispassionately, seems shadowy and evasive, especially when we confront it with the case of double stars. Here, indeed, an entirely different set of conditions comes into play from that postulated by Poincaré and Darwin, since stars are certainly not liquid bodies.[39]They are most likely gaseous to the core, though the indefinite diffusiveness incident to gaseity is restricted by their condensed photospheric surfaces. This circumstance intimates thepossibility that the results arrived at for liquid globes by mathematical analysis may, with qualifications, be extended to stars; but the necessary qualifications, unfortunately, are vague and large; for too little is known regarding the physical condition of stellar spheres to warrant assumptions that might provide a secure basis for research.

The evolution of binary stars can then only be treated of inferentially, not rigorously; and we must, at the outset, discard the idea that it is illustrated by the phenomena of double nebulæ. Many such objects thought to supply clinching visual arguments for the actual effectiveness of slow cosmic fission proved, on the application to them of the late Professor Keeler's searching photographic methods, to be knots on spiral formations. Their mutual relations are then entirely different from what had been supposed by telescopic observers; they are, in fact, still structurally connected, and the mode of their origin, however inviting to conjecture, scarcely comes within the scope of definitely conducted inquiries. Their future destiny is no more accessible to it than their past history, and only by a daring flight ofimagination can we see in spiral nebulæ the prototypes of double stars.

Questions as to the mode of genesis of these latter systems have, in recent years, acquired extraordinary interest. Conclusive answers cannot, indeed, at present be given to them, because the terms in which they are couched lack distinctness, owing to our lack of knowledge; but probable answers may legitimately supply their place, at leastad interim, above all when their probability is heightened almost to certainty by the accumulation of circumstantial evidence.

Observations and investigations of stellar eclipses have created a new department of astrophysics, and have vastly widened the domain of cosmogony. They have brought to notice a number of systems, not merely in a primitive, but seemingly in an inchoate stage of development. The periods of occulting stars are nearly all of them less than seven days, although one extending to thirty-one has lately been recognised; and the comparative length of the intervals of obscuration shows them to be produced by the circulation in narrow orbits of distended globes. Theseare characteristic symptoms of juvenility, for, as we have seen, orbits widen and periods lengthen with the efflux of time through the frictional power of bodily tides.

Now the class of stars which obviously and certainly undergo eclipses has some outlying members of a still dubious nature. And their marginal position serves greatly to enhance the present, the prospective, and the retrospective interest attaching to them. These remarkable objects vary in light continuously. Their phases are not, like those of Algol, mere interruptions to a regular course of steady shining. They progress without a moment's sensible pause; they are represented graphically by a smoothly-flowing, symmetrical curve. The eclipses by which they are occasioned—if they are so occasioned—must, accordingly, succeed each other in a strictly unbroken series. No sooner has one terminated than the next commences. One star passes first behind, then in front of its companion, and their combined brightness is seen undimmed only during the few moments of actual maximum. This means that they revolve in contact; they are separated by no sensible gap of space.

Goodricke's variable, β Lyræ, is held to be thus constituted. The possibility, at least, of employing the 'satellite-theory' to account for its changes was demonstrated some years ago by Mr. G. W. Myers, of Indiana.[40]He found the system to be composed of two barely separated ellipsoids, circulating in the visual plane, and producing, by their successive transits, two unequal eclipses in the course of each period of 12·91 days. The joint mass of the pair is just thirty times that of our sun, but their mean density has the almost incredibly small value of 1/1200 that of water. Their real existence is conditional upon the possibility that masses much more tenuous than atmospheric air should radiate with the intensity of true suns. Spectroscopic observations are not wholly unfavourable to Mr. Myers's hypothesis, but their interpretation is hampered by discrepancies so numerous and perplexing that no secure inference can be derived from them. Moreover, the star supposed to be alone presented to view at the principal minimum is that giving the bright-line spectrum; yet it is compulsorily assumed, in orderto meet the exigencies of the situation, to be much more massive, while much less intrinsically bright, than its companion. This is disquieting, but nearly everything connected with β Lyræismore or less disquieting.

A variable of the same type, but much fainter, was made the subject of a similar inquiry by Mr. Myers in 1898.[41]U Pegasi never attains ninth magnitude; hence, spectroscopic complications equally with spectroscopic verification remain at present out of sight. The star, nevertheless, excites keen interest, and claims sustained attention. Its light-curve has been laid down with exquisite accuracy at Harvard College, and shows two slightly unequal minima to be comprised within a period of nine hours, signifying, on the adopted theory, the occurrence of alternating eclipses at intervals of four and a half hours. The distance from centre to centre of the occulting stars, the smaller of which is of about eight-tenths the brightness of the larger, 'does not materially differ,' Mr. Myers tells us, 'from the sum of their radii, suggesting the probable existence of the "apioidal" form of Poincaré.' If they do not actuallycoalesce, the component bodies revolve in contact, and rotate synchronously. Thus, it is hard to say whether U Pegasi should be accounted as a single pear-shaped mass spinning in the time of light-change, or as a close couple circulating freely in that identical period. The mean density of the system appears to lie between one-third and one-fourth that of the sun.

Another specimen of the 'dumb-bell' system is possibly met with in R2Centauri. The narrow range of its variation makes it a delicate object to observe; but Mr. A. W. Roberts, who first noticed its peculiarity in 1896, has since accumulated an extensive series of wonderfully accurate visual determinations of its fluctuating brightness, and has besides rendered them the basis of an able and exhaustive theoretical discussion.[42]The double period of R2Centauri is restricted to fourteen hours thirty-two minutes. Within this brief span quadruple phases are included—that is to say, two evenly balanced maxima and two slightly disparate minima. These result, Mr. Roberts concludes, from the mutual eclipses of interpenetrating ellipsoids,one somewhat more luminous than the other, revolving—if they can properly be said to revolve—in an orbit inclined 32° to the visual plane. They are of just one-third the solar density, and the forms satisfying photometric requirements by the varying areas of luminous surface presented to sight in different sections of their path show a surprising agreement with the bi-prolate figure given by Professor Darwin's analysis as the shape of a body on the verge of disruption through accelerated rotatory movement. The inference is, then, almost irresistible that R2Centauri really exemplifies the nascent stage of binary stars. To establish this completely, however, spectroscopic data are needed; and they are difficult to procure for a star below the seventh magnitude.

No such obstacle impedes the investigation of the analogous, but much brighter object, V Puppis. Detected as a spectroscopic binary by Professor Pickering in 1895, this star traverses so wide an orbit in the short period of thirty-five hours as to imply—if the published details are correct—that the pair possess no less than 348 times the gravitational powerof the sun. They are, nevertheless, according to Mr. Roberts, fifty times more tenuous, and each globe should have a diameter of about 16½ million miles; yet nothing of all this is incredible. The light-curve of V Puppis, as traced by Mr. Roberts, is closely modelled upon that of U Pegasi. And he postulates similar conditions of eclipse. It rests with the spectroscope to determine whether those conditions are realized or not.

Probably all short-period variables are binaries, with coincident orbital- and light-cycles. But all are not occulting binaries. There are some—we are still ignorant of their proportionate numbers—which undergo a course of light-change, apparently compatible with an occulting hypothesis, yet certainly escape eclipse. Professor Campbell has made it unmistakably clear that ζ Geminorum is thus constituted.[43]Two stars are present, but their plane of motion is inclined at an unknown angle to the line of sight; it does not approximate to coincidence with it. Now the possibilityis not excluded that V Puppis belongs to the same class. Mr. Roberts's assumptions are, indeed, in themselves plausible, and they may at any moment be proved, by a few well-timed spectrograms, to be undeniably true.

The one conclusive test of their truth is the cessation of radial movement at epochs of minimum. Evidently, if the diminution in lustre be due to an eclipse, the eclipsing and eclipsed bodies must be crossing the line of sight just when the obscuration is deepest. There is no evading this geometrical requirement, and it must be rigorously complied with in the circular orbits traversed by bodies revolving in contact. Before, then, Mr. Roberts's theory of V Puppis can be accepted with implicit confidence, it has to be ascertained whether a zero of radial speed is reached concurrently with the photometric minima. If so, these may be unhesitatingly set down as eclipse-phenomena; if, on the contrary, the decline in brightness prove to be unrelated to a slackening of speed, then the supposition that it accompanies and indicates a transit must be peremptorily discarded. Moreover, the spectroscopic verdict as regards V Puppis can safely be applied to stars with similar light-curves, especially to R2Centauri and U Pegasi, and may serve to clear away some of the intricacies connected with the exceptional system of β Lyræ. The measurement of a single spectrographic plate might thus, by deciding the test-case of the binary in the poop of Argo, be made essentially to supply the lack of desirable, but at present unattainable determinations as regards a considerable number of analogous objects.

The existence of stellar systems of the 'dumb-bell' type would violate no mechanical law. 'Roche's limit' does not apply to globes comparable in size. The range of disparity within which it holds good has not, indeed, been theoretically established; but it may be said, in general terms, to concern the relations of planets and satellites (to use a purposely vague phrase), not those of double stars. What the law asserts is that a subordinate small body cannot revolve intact at a less distance than 2·44 radii of its primary from that primary's centre, if their mean density be the same. For satellites of slighter consistencethe limit should be extended. Our own moon, for instance, could never have circulated, without being rent in pieces by tidal strains, in an orbit less than 22,000 miles in diameter.[44]

Bodies of co-ordinate mass are, however, exempted from the prohibitive rule against mutual approach. No analytical veto is imposed upon the origin by fission of double stars, or upon the subsistence of stellar Siamese twins. The inequalities of their mutual attractions avail to distort, not to disrupt, such embryo globes. Their individuality, therefore, once created, is in a manner indestructible. It tends, in fact, to become more pronounced as the orbital span gradually widens through the reactive effects of tidal friction. The 'dumb-bell' condition may then be regarded as in a manner transitory. Nor can we be assured of its actuality otherwise than by the peculiar nature of the eclipses attending upon it, taken in connection with correlated spectroscopic observations proving eclipses of the kind veritably to take place. The disclosure, by such means, of systems so strangelyconditioned promises to afford a deeper insight than would else have been possible into the cosmical order, and fills a blank page in the marvellous history of sidereal birth and growth.

FOOTNOTES:[34]Acta Mathematica, vol. vii., Stockholm, 1885.[35]Proceedings Royal Society, vols. xlii., lxxi.;Philosophical Transactions, vols. cxcviii., cxcix., Series A.[36]J. H. Jeans,Philosophical Transactions, vol. cxcix., Series A, p. 1.[37]Figures d'Équilibre d'une Masse Fluide, p. 172.[38]Proceedings Royal Society, vol. lxxi., p. 183.[39]J. H. Jeans,Astrophysical Journ., vol. xxii., p. 93.[40]Astrophysical Journal, vol. vii., p. 1.[41]Astrophysical Journal, vol. viii., p. 163.[42]Monthly Notices, vol. lxiii., p. 627.[43]Astrophysical Journal, vol. xiii., p. 90;Science, July 27, 1900.[44]G. H. Darwin,The Tides, p. 327.

[34]Acta Mathematica, vol. vii., Stockholm, 1885.

[35]Proceedings Royal Society, vols. xlii., lxxi.;Philosophical Transactions, vols. cxcviii., cxcix., Series A.

[36]J. H. Jeans,Philosophical Transactions, vol. cxcix., Series A, p. 1.

[37]Figures d'Équilibre d'une Masse Fluide, p. 172.

[38]Proceedings Royal Society, vol. lxxi., p. 183.

[39]J. H. Jeans,Astrophysical Journ., vol. xxii., p. 93.

[40]Astrophysical Journal, vol. vii., p. 1.

[41]Astrophysical Journal, vol. viii., p. 163.

[42]Monthly Notices, vol. lxiii., p. 627.

[43]Astrophysical Journal, vol. xiii., p. 90;Science, July 27, 1900.

[44]G. H. Darwin,The Tides, p. 327.

WORLD BUILDING OUT OF METEORITES

Theidea is seductive that we see in every meteoric fire-streak a remnant of the process by which our world, and other worlds like or unlike it, were formed. It is not a new idea. Chladni entertained it in 1794; and it has since from time to time been revived and rehabilitated with the aid of improved theoretical knowledge and a larger array of facts. Survivals are tempting to thought. It costs less effort to realize differences in degree than differences of kind. The enhanced activity of familiar operations is readily imagined, while perplexity is apt to shroud the results of modes of working strange to experience. Hence the presumption in favour of continuity; nor can it be said, even apart from our own mental inadequacy, that the presumption isother than legitimate. Nature is chary of her plans, lavish of her materials. Her aims are characterized by a majestic unity, but she takes little account (that we can see) of surplusage or wreckage. Now, it seems likely that meteorites represent one or the other of these two forms of waste stuff. They are analogous, apparently, either to the chips from shaped blocks, or to the dust and rubbish of their destruction. Let us consider what it is that we really know about them.

It cannot be said that the sources of our information are scanty. Fully one hundred millions are daily appropriated by the earth as she peacefully spins through the ether. Their absorption leaves her unaffected. It produces no perceptible change in her internal economy, and makes no sensible addition to her mass. The hundred millions of small bodies taken up have, nevertheless, in Professor Langley's opinion, an aggregate weight of more than one hundred tons.[45]And this increment is always going on. Yet its accumulated effect is evanescent by comparison with the enormous mass of our globe. That it was more considerablein past ages than it is at present might be plausibly conjectured, but cannot reasonably be maintained. Geological deposits contain—unless by some rare exception—no recognisable meteoric ingredients. There is nothing to show that the earth was subject to a heavier bombardment from space during the Silurian era than in the twentieth century. Nor could the whole of its constituents have been, in any case, thus provided. Out of kiln-dried fragments, like the Mazapil iron or the 'thunder-stones' of Adare, a terraqueous planet could not have been formed. This objection, urged by Mr. O. Fisher,[46]is seemingly irrefutable.

Meteorites signify their existence to us, in general, only by the bale-fires of their ruin; but in a few cases their tangible relics come to hand. Those substantial enough to escape total disintegration through atmospheric resistance to their swift movements plunge into the sea or bury themselves in the earth, and in a certain proportion of cases find their way to museums and laboratories, where they are subjected to the searching investigationdemanded by their exotic origin. Its results are scarcely what might have been expected. Aerolites—as these samples from space are distinctively called—are not chemically peculiar; they consist exclusively of the same elementary substances composing the crust of the earth; but their mineralogy is strongly characteristic. They are extremely complex structures, formed apparently in the absence of water, and with a short supply of oxygen; the further condition of powerful pressure is indicated with some probability, nay, with virtual certainty for those including small diamonds,[47]while prolonged vicissitudes of fracture and re-agglomeration are possibly recorded by the brecciated texture of many of these rockytrouvailles. Their aspect is thus anything but primitive; each fragment tacitly lays claim to an eventful history; they suggest a cataclysm, of whichwe behold in them the shattered outcome. The nature of such cataclysms is scarcely open to conjecture; only a hint regarding it may be gathered from the circumstance that the most profound terrestrial formations are those which approximate most closely to the mineralogical peculiarities of meteorites.

Nevertheless, the only ascertained relationships of meteorites are with comets. In every system of shooting stars the primary body most probably is, or at any rate was, a comet. Each appears to be the offspring of a cometary parent, and developspari passuwith its decay. The view has hence been adopted, and not without justification, that comets in their primitive integrity are simply 'meteor-swarms.' Assent may be given to it with some qualifications which we need not here stop to discuss. What immediately concerns us is the interesting question as to the constitution of meteor-swarms. What is the real meaning of the term? What does it convey to our minds? A meteor-swarm may be defined as a rudely globular aggregation of small cosmical masses, revolving under the influence of their mutual attraction, round their common centre ofgravity. Each must revolve on its own account, though all have the same period; and their orbits may be inclined at all possible angles to a given plane, and may be traversed indifferently in either direction. From this tumultuous mode of circulation collisions should frequently ensue, but they would be of a mild character. They could not be otherwise in a system of insignificant mass and correspondingly sluggish motion. We are considering, it must be remembered, only cometary swarms, as being the only collections of the sort that come, even remotely, within our ken; and comets include the minimum of matter. This we are entitled to infer from the fact that none of those hitherto observed, whether conspicuous or obscure, newly arrived from space, or obviously effete, have occasioned the slightest gravitational disturbance to any member of our system.

A cometary swarm, if left to itself, might eventually shape itself into a reduced model of the 'Saturn' planetary nebula. Colliding particles should, owing to their loss of velocity, subside towards the centre, and accrete into a globular mass. A predominant current of movementwould, through their elimination, gain more and more completely the upper hand; and it would finally, with the inevitable diminution of energy,[48]be restricted almost wholly to the principal plane of a system, composed essentially of a rotating nucleus encompassed by a wide zone of independently circulating meteorites. But this mode of evolution is not even distantly followed by comets. It would be possible only if they were isolated in space, and, in point of fact, their revolutions round the sun are of overwhelming importance to their destinies. The sun's repulsive energy causes them to waste and diffuse with expansion of splendid plumage. Under the sun's unequal attraction at close quarters they are subject to disruption, and the upshot of the tidal stresses acting upon them is the dispersal of their constituent particles along the wide ambit of their oval tracks.

We are, nevertheless, invited to look further afield. Cometary meteor-swarms may be only miniature specimens of the contents of space. Why should not remote sidereal regions be thronged with similar assemblages, colossalin their proportions, countless in number? And may they not supply the long-sought desideratum of a suitable 'world-stuff' for the construction of suns and planets? From some such initial considerations as these Sir Norman Lockyer developed, in 1887, a universal meteoritic hypothesis, designed on the widest possible lines, based on promising evidence, and professing to supply a key to the baffling enigma of cosmical growth and diversification. The meteoric affinities of comets formed its starting-point; comets were assimilated to nebulæ; and from nebulæ were derived, by gradual processes of change, all the species of suns accessible to observation. The view was of far-reaching import and magnificent generality, but its value avowedly rested on a body of facts of a special kind. In this it differed from the crowd of ambitious speculations regarding the origin of things by which it had been preceded. In this it attained an immeasurable superiority over them, if only the testimony appealed to could be established as valid. Indeed, it is scarcely too much to say that, whether it were valid or not, the mere circumstance of having called the spectroscope as a witness in the high court of cosmogony constituted an innovation both meritorious and significant.

The spectrum of the nebulæ was a standing puzzle. A theory which set out by making its meaning plain secured at once a privileged position. This was seemingly accomplished by Sir Norman Lockyer through the means of some simple laboratory experiments on the spectra of meteorites. Certain 'low temperature' lines of magnesium given out by the vapours of stony aerolitic fragments were shown to fall suspiciously close to the chief nebular lines previously classed as 'unknown.' The coincidences, it is true, were determined with low dispersion, and were published for what they were worth, but they looked hopeful. Their substantiation, had it been feasible, would have marked the beginning of a new stadium of progress. Nature, however, proved recalcitrant. The suggested agreements avowed themselves, on closer inquiry, as approximate only; magnesium light makes no part of the nebular glow, and nebulium, its main source, evades terrestrial recognition. The light of cosmic clouds issui generis—itincludes no metallic emissions; while the fundamental constituents of meteorites are metals variously assorted and combined.

The decipherment of the nebular hieroglyphics was the crucial test; its failure to meet it left the hypothesis seriously discredited; for coincidences between spectral rays, common to nearly all the heavenly bodies, naturally counted for nothing. Yet the investigation had its uses. The energy with which it was prosecuted, the ingenuity and resource with which it was directed, told for progress. There has been a clash of arms and a reorganization of forces. Thought was stirred, observation and experiment received a strong stimulus, fresh affluents to the great stream of science began to be navigated. Efforts to prove what had been asserted were fruitful in some directions, and the work of refutation had inestimable value in defining what was admissible, and establishing unmistakable landmarks in astrophysics.

The discussion, it must be admitted, threw very little light on the part played by meteorites in cosmogony. Their world-building function remains largely speculative. Doubts of manykinds qualify its possibility, and lend it a fantastic air of unreality. But this may in part be due to a defect of imaginative power with which the universe was not concerned. Waiving, then, preliminary objections, we find ourselves confronted with the fundamental question: Given a meteor-swarm of the requisite mass and dimensions, is there any chance of its condensing into a planetary system? Sir Norman Lockyer set aside this branch of his subject. His hypothesis was, in fact, 'pre-nebular.' He assumed that the small solid bodies with which it started would, in course of time, become completely volatilized by the heat of their mutual impacts, and that the resulting gaseous mass would thenceforward comport itself after the fashion imagined by Laplace. Professor Darwin regarded the matter otherwise. It seemed to him possible to combine the postulates of the meteoric and nebular theories in a system planned on an original principle. For this purpose it was necessary to excogitate a means of rendering the kinetic theory of gases available for a meteor-swarm. 'The very essence,' he wrote,[49]'of the nebular hypothesis is the conception of fluid pressure, since without it the idea of a figure of equilibrium becomes inapplicable.'

M. Faye abandoned this idea; he built up his planets out of incoherent materials, thereby avoiding the incongruities, but forfeiting the logical precision of Laplace's stricter procedure. Professor Darwin consented to forfeit nothing; he stood forward as a syncretist, his object being to 'point out that by a certain interpretation of the meteoric theory we may obtain a reconciliation of these two orders of ideas, and may hold that the origin of stellar and planetary systems is meteoric, whilst retaining the conception of fluid pressure.' For the compassing of this end he adopted a bold expedient. Fluid pressure in a gas is 'the average result of the impacts of molecules.' Fluid pressure in a meteor-swarm might, he conceived, be the net product of innumerable collisions between bodies to be regarded as molecules on an enormously magnified scale. The supposition is, indeed, as Kepler said of the distances of the fixed stars, 'a big pill to swallow.' Between molecules and meteorites lies a wide unbridged gap. The machinery ofgaseous impacts is obscure. It can be set in motion only by ascribing to the particles concerned properties of a most enigmatical character. These particles are, however, unthinkably minute; and in sub-sensible regions of research the responsibilities of reason somehow become relaxed. We are far more critical as to the behaviour of gross, palpable matter, because experience can there be consulted, and is not unlikely to interpose its veto.

Meteorites are, doubtless, totally dissimilar from molecules, however many million-fold enlarged; and they would infallibly be shattered by collisions which only serve to elicit from molecules their distinctive vibrations. Moreover, the advance of the shattering process would admittedly end the prevalence of fluid pressure. So that the desired condition, even if initially attained, would be transitory. There is, besides, a radical difference between a group of bodies in orbital circulation and a congeries of particles moving at haphazard, unconstrained by any predominant law of force. A meteoric swarm belongs to the first category; it is a community swayed in some degree by a central power; while the gaseous contents of aretort or a balloon obey purely individual impulses. The analogy looked for by Professor Darwin can then scarcely be said to exist, and his paper stands out as a monument of ingenious mathematical treatment applied to an ideal state of things.

An aggregation of revolving meteorites has no figure of equilibrium, and it is through the consequences necessarily resulting from this property that mathematicians are enabled to trace the progressive changes of a rotating fluid mass. In the absence of any such direct means of attack, their position regarding the problem presented by an assemblage of flying stones is not much better than that occupied by Kant, face to face with an evolving universe. It seems, nevertheless, clear that a meteor-swarm can be impelled to condense no otherwise than through the effects of collisions among its constituents. When the irregularities of movement upon which their occurrence depends are got rid of, the system must remainin statu quo. Order makes for permanence; a tumultuary condition is transient. The eventual state of the system can, however, be no more than partially foreseen.Bodies arrested in their flight should fall inward, hence a central mass would form and grow; but the production of planets would seem to be conditional upon the existence of primitive inequalities of density in the swarm. These might serve as nuclei of attraction for meteoric infalls, not yet completely exhausted, but plying with harmless fire one at least of the globes they helped to shape.

There could, indeed, on this showing, have been no such harmonious succession of events as constituted the predominant charm of Laplace's scheme. The planets should be supposed to have issued pell-mell out of a chaos; or, rather, the chaos should have contained from the beginning the seeds of a predestined cosmos. Its evolution would have been like that of the oak from the acorn, an unfolding of what was already essentially there. And it may be that at this stage of penetration into the past, the unaided human intellect meets itsne plus ultra. There is a vital heart of things which we cannot hope to reach. Thought instinctively pauses before the vision of the symbolical brooding dove.

To resume. Meteoric cosmogony has arational basis. The modes of action it demands are still operative. Enfeebled almost to evanescence compared with the vigour they must have needed to be efficacious in world-building, they continue to make play in our nocturnal skies. They make play, it is true, with a very small quantity of material; but it may even now be distributed elsewhere in relatively enormous profusion, and in the solar system itself it presumably was much more abundant formerly than it now is. The earth has been raking up meteoric granules by hundreds of millions daily during untold ages, and her zone of space is still very far from being swept clean. The persistence of the supply, however, may be occasioned by the continual arrival of reinforcements from interstellar realms.

Comets appertain to, and travel with, the sun's cortège, and this is also inevitably true of comet-born meteors. But a multitude besides circulate independently of comets, and with much higher velocities. Their orbits are, then, hyperbolic; they belong to the category of 'irrevocable travellers,' and by their capture we are privileged to possess genuine shreds of sidereal matter. Universal space containsprobably a vast stock of them, yet there is nothing to prove their collection into swarms. The spectroscope supplies no assurance to that effect; it has given its verdict against the meteoric constitution of nebulæ and temporary stars. And if we admit, through the persuasion of mineralogical testimony, that the aerolites so strangely landed on terrestrial soil are really the débris of ruined worlds, we can see for them no chance of restoration. Solitary they are, even if they occasionally pursue one another along an identical track, and solitary they must remain. Bodies do not of themselves initiate mutual circulation. Planetary or stellar outcasts cannot become re-associated into a gravitational system. Of a cosmic swarm, as of a poet, it may be said,Nascitur, non fit; and their birth-secret is undivulged.

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