The Plurality of Worlds

by William Whewell

18. But perhaps something more may be founded on the ramified and straggling form which belongs to many of the nebulæ. Under the powers of Lord Rosse's telescope, a considerable number of them assume a shape consisting of several spiral films diverging from one centre, and growing broader and fainter as they diverge, so as to resemble a curled feather, or whirlpool of light.[8] This form, though generally deformed by irregularities, more or less, is traceable in so many of the nebulæ, that we cannot easily divest ourselves of the persuasion that there is some general reason for such a form;—that something, in the mechanical causes which have produced the nebulæ, has tended to give them this shape. Now, when this thought has occurred to us, since mathematicians have written a great deal concerning the mechanics of the universe, it is natural to ask, whether any of the problems which they have solved give a result like that thus presented to our eyes. Do such spirals as we here see, occur in any of the diagrams which illustrate the possible motions of celestial bodies? And to this, a person acquainted with mathematical literature might reply, that in the second Book of Newton's Principia, in the part which has especial reference to the Vortices of Descartes, such spirals appear upon the page. They represent the path which a body would describe if, acted upon by a central force, it had to move in a medium of which the resistance was considerable;—considerable, that is, in comparison with the other forces which act; as for example, the forces which deflect the motion from a straight line. Indeed, that in such a case a body would describe a spiral, of which the general form would be more or less oval, is evident on a little consideration. And in this way, for instance, Encke's comet, which, if the resistance to its motion were insensible, would go on describing an ellipse about the sun, always returning upon the same path after every revolution; does really describe a path which, at each revolution, falls a little within the preceding revolution, and thus gradually converges to the centre. And if we suppose the comet to consist of a luminous mass, or a string of masses, which should occupy a considerable arc of such an orbit, the orbit would be marked by a track of light, as an oval spiral. Or if such a comet were to separate into two portions, as we have, with our own eyes, recently seen Biela's comet do; or into a greater number; then these portions would be distributed along such a spiral. And if we suppose a large mass of cometic matter thus to move in a highly resisting medium, and to consist of patches of different densities, then some would move faster and some more slowly; but all, in spirals such as have been spoken of; and the general aspect produced would be, that of the spiral nebulæ which I have endeavored to describe. The luminous matter would be more diffused in the outer and more condensed in the central parts, because to the centre of attraction all the spirals converge.

19. This would be so, we say, if the luminous matter moved in a greatly resisting medium. But what is the measure of great resistance? It is, as we have already said, that the resistance which opposes the motion shall bear a considerable proportion to the force which deflects the motion. But what is that force? Upon the theory of the universal gravitation of matter, on which theory we here proceed, the force which deflects the motions of the parts of each system into curves, is the mutual attraction of the parts of the system; leaving out of the account the action of other systems, as comparatively insignificant and insensible. The condition, then, for the production of such spiral figures as I have spoken of, amounts really to this; that the mutual attraction of the parts of the luminous matter is slight; or, in other words, that the matter itself is very thin and rare. In that case, indeed, we can easily see that such a result would follow. A cloud of dust, or of smoke, which was thin and light, would make but a little way through the air, and would soon fall downwards; while a metal bullet shot horizontally with the same velocity, might fly for miles. Just so, a loose and vaporous mass of cometic matter would be pulled rapidly inwards by the attraction to the centre; and supposing it also drawn into a long train, by the different density of its different parts, it would trace, in lines of light, a circular or elliptical spiral converging to the centre of attraction, and resembling one of the branches of the spiral nebulæ. And if several such cometic masses thus travelled towards the centre, they would exhibit the wheel-like figure with bent spokes, which is seen in the spiral nebulæ. And such a figure would all the more resemble some of these nebulæ, as seen through Lord Rosse's telescope, if the spirals were accompanied by exterior branches of thinner and fainter light, which nebulous matter of smaller density might naturally form. Perhaps too, such matter, when thin, may be supposed to cool down more rapidly from its state of incandescence; and thus to become less luminous. If this were so, a great optical power would of course be required, to make the diverging branches visible at all.

20. There is one additional remark, which we may make, as to the resemblance of cometary[9] and nebular matter. That cometary matter is of very small density, we have many reasons to believe:—its transparency, which allows us to see stars through it undimmed;—the absence of any mechanical effect, weight, inertia, impulse, or attraction, in the nearest appulses of comets to planets and satellites:—and the fact that, in the recent remarkable event in the cometic history, the separation of Biela's comet into two, the two parts did not appear to exert any perceptible attraction on each other, any more than two volumes of dust or of smoke would do on earth. Luminous cometary matter, then, is very light, that is, has very little weight or inertia. And luminous nebulous matter is also very light in this sense: if our account of the cause of spiral nebulæ has in it any truth. But yet, if we suppose the nebulæ to be governed by the law of universal gravitation, the attractive force of the luminous matter upon itself, must be sufficient to bend the spirals into their forms. How are we to reconcile this; that the matter is so loose that it falls to the centre in rapid spirals, and yet that it attracts so strongly that there is a centre, and an energetic central force to curve the spirals thither? To this, the reply which we must make is, that the size of the nebular space is such, that though its rarity is extreme, its whole mass is considerable. One part does not perceptibly attract another, but the whole does perceptibly attract every part. This indeed need the less surprise us, since it is exactly the case with our earth. One stone does not visibly attract another. It is much indeed for man, if he can make perceptible the attraction of a mountain upon a plumb-line; or of a stratum of rock a thousand feet thick upon the going of a pendulum; or of large masses of metal upon a delicate balance. By such experiments men of science have endeavored to measure that minute thing, the attraction of one portion of terrestrial matter upon another; and thus, to weigh the whole mass of the earth. And equally great, at least, may be the disproportion between the mutual attraction of two parts of a nebulous system, and the total central attraction; and thus, though the former be insensible, the latter may be important.

21. It has been shown by Newton, that if any mass of matter be distributed in a uniform sphere, or in uniform concentric spherical shells, the total attraction on a point without the sphere, will be the same as if the whole mass were collected in that single point, the centre. Now, proceeding upon the supposition of such a distribution of the matter in a nebula, (which is a reasonable average supposition,) we may say, that if our sun were expanded into a nebula reaching to the extreme bounds of the known solar system, namely, to the newly-discovered planet Neptune, or even hundreds of times further; the attraction on an external point would remain the same as it is, while the attraction on points within the sphere of diffusion would be less than it is; according to some law, depending upon the degree of condensation of the nebular matter towards the centre; but still, in the outer regions of the nebula, not differing much from the present solar attraction. If we could discover a mass of luminous matter, descending in a spiral course towards the centre of such a nebula, that is, towards the sun, we should have a sort of element of the spiral nebulæ which have now attracted so much of the attention of astronomers. But, by an extraordinary coincidence, recent discoveries have presented to us such an element. Encke's comet, of which we have just spoken, appears to be describing such a spiral curve towards the sun. It is found that its period is, at every revolution, shorter and shorter; the amplitude of its sweep, at every return within the limits of our observation, narrower and narrower; so that in the course of revolutions and ages, however numerous, still, not such as to shake the evidence of the fact, it will fall into the sun.

22. Here then we are irresistibly driven to calculate what degree of resemblance there is, between the comet of Encke, and the luminous elements of the spiral nebulæ, which have recently been found to exist in other regions of the universe. Can we compare its density with theirs? Can we learn whether the luminous matter in such nebulæ is more diffused or less diffused, than that of the comet of Encke? Can we compare the mechanical power of getting through space, as we may call it, that is, the ratio of the inertia to the resistance, in the one case, and in the other? If we can, the comparison cannot fail, it would seem, to be very curious and instructive. In this comparison, as in most others to which cosmical relations conduct us, we must expect that the numbers to which we are led, will be of very considerable amount. It is not equality in the density of the two luminous masses which we are to expect to find; if we can mark their proportions by thousands of times, we shall have made no small progress in such speculations.

23. The comet of Encke describes a spiral, gradually converging to the sun; but at what rate converging? In how many revolutions will it reach the sun? Of how many folds will its spire consist, before it attains the end of its course? The answer is:—Of very many. The retardation of Encke's Comet is very small: so small, that it has tasked the highest powers of modern calculation to detect it. Still, however, it is there: detected, and generally acknowledged, and confirmed by every revolution of the comet, which brings it under our notice; that is, commonly, about every three years. And having this fact, we must make what we can of it, in reasoning on the condition of the universe. No accuracy of calculation is necessary for our purpose: it is enough, if we bring into view the kind of scale of numbers to which calculation would lead us.

24. Encke's comet revolves round the sun in 1,211 days. The period diminishes at present, by about one-ninth of a day every revolution. This amount of diminution will change, as the orbit narrows; but for our purpose, it will be enough to consider it unchangeable. The orbit therefore will cease to exist in a number of periods expressed by 9 times 1,211; that is, in something more that 10,000 revolutions; and of course sooner than this, in consequence of its coming in contact with the body of the sun. In 30,000 years then, it may be, this comet will complete its spiral, and be absorbed by the central mass. This long time, this long series of ten thousand revolutions, are long, because the resistance is so small, compared with the inertia of the moving mass. However thin, and rare, and unsubstantial the comet may be, the medium which resists it is much more so.

25. But this spiral, converging to its pole so slowly that it reaches it only after 10,000 circuits, is very different indeed from the spirals which we see in the nebulæ of which we have spoken. In the most conspicuous of those, there are only at most three or four circular or oval sweeps, in each spiral, or even the spiral reaches the centre before it has completed a single revolution round it. Now, what are we to infer from this? How is it, that the comet has a spiral of so many revolutions, and the nebulæ of so few? What difference of the mechanical conditions is indicated by this striking difference of form? Why, while the Comet thus lingers longer in the outer space, and approaches the sun by almost imperceptible degrees, does the Nebular Element rush, as it were, headlong to its centre, and show itself unable to circulate even for a few revolutions?

26. Regarding the question as a mechanical problem, the answer must be this:—It is so, because the nebula is so much more rare than the matter of the comet, or the resisting medium so much more dense; or combining the two suppositions, because in the case of the comet, the luminous matter has much more inertia, more mechanical reality and substance, than the medium through which it moves; but in the nebula very little more.