But the only particles which could maintain their locations at that distance in a constant free circular momentum were the ones which could attain their own velocity from the axial rotation at a level which the centripetal force required for equilibrium at those distances. The remaining particles, to the extent that the interaction with the others could not bring them this precise velocity, must either through their excess motion leave the planetary sphere or through their lack of motion necessarily sink back onto the planet. The particles scattered throughout the total extent of the vapour sphere, thanks to the same central law in the motion of their curved momentum, would intersect the extended equatorial plane of the planet from both sides. And in coming together on this plane from both hemispheres, they would stop each other and acc.u.mulate there. Since I a.s.sume that the above-mentioned vapours are the very ones which the planet in its cooling sent back up, all the scattered vapour material will collect close to this plane in a s.p.a.ce not very wide and leave the s.p.a.ce on both sides empty.

In this new and changed orientation, however, the materials will continue exactly the same movement which they maintained while suspended in free concentric circular orbits. In such a manner, the circle of vapours alters its shape, which was completely spheroidal, into the form of an extended plane matching precisely Saturn's equator. But this plane must also, for exactly the same mechanistic reasons, finally a.s.sume the form of a ring, whose outer edge will be determined by the effect of the sun's rays, which with their force scatter and disperse those particles which have distanced themselves a certain way from the mid-point of the planet, as they do with comets. In this way the sun's effect designates the outer limit of their circle of vapours. The inner edge of this emerging ring will be determined by the relationship to the velocity of the planet at its equator. For that distance away from the mid-point where this velocity attains an equilibrium with the power of attraction for that location is the closest approach to the planet where the particles which have arisen from its body are able to describe circular orbits from their own movement acquired from the planet's axial rotation. Because the particles closer than that require a higher velocity for such an orbit, which they cannot have because the movement even on the equator is not faster, they will maintain eccentric orbits which intersect each other, weaken each other's motions, and finally will fall back down onto the planet from which they arose. Now, there we see a wonderfully strange phenomenon, the sight of which since its discovery has always astonished astronomers and whose cause we could not ever entertain even a probable hope of discovering. Now we see that phenomenon arise in an easy mechanistic way, free of all hypotheses. What happened to Saturn, as can be easily seen from this, would happen just as regularly to a comet with a sufficient axial rotation, if it were set at a constant height in which its body gradually could cool down. Nature, left to its own forces, is fertile in excellent results, even in chaos. The development following from this produces such wonderful relationships and harmonies for a creature's common needs that it enables us to recognize with unanimous certainty in the eternal and unchanging laws of their essential characteristics the Great Being in whom they are all united, thanks to their common dependency in a collective harmony. Saturn derives important advantages from its ring. It lengthens its day and under so many moons illuminates its night to such an extent, that the absence of the sun is easily forgotten. But must we then, on that account, deny that the common development of material through mechanical laws, without the need for anything other than their universal efficacy, could have produced the relationships which created advantages for reasoning creatures? All beings have a common dependency on a single cause: the Divine Understanding. They can therefore produce no other consequences after them except those which bring with them an image of the perfection of exactly the same Divine Idea.

Now we will calculate the time of the axial rotation of this celestial body from the relationships of its ring, according to the hypothesis of its development mentioned above. Because all the movement of the ring's particles is a motion derived from axial rotation of Saturn, on whose outer surface they were located, the fastest movement which these particles possess among themselves will be the same as the fastest rotation which occurs on Saturn's outer surface. In other words, the velocity at which the particles of the ring orbit on its inner edge is equal to the velocity of the planet at its equator. But we can easily find that when we look for it in the velocity of one of Saturn's satellites. For we a.s.sume that it is proportional to the square root of the distances from the mid-point of the planet. From the velocity we have discovered, the time of Saturn's axial rotation is immediately given: it is six hours, twenty-three minutes, and fifty-three seconds. This mathematical calculation of an unknown movement for a celestial body, which is perhaps the only prediction of its kind in the real theory of nature, awaits confirmation from the observations of future ages. The telescopes known up to this time do not enlarge Saturn sufficiently, so that we can discover the spots (which we can presume are on its outer surface) in order to perceive its axial rotation through their forward displacement. But the telescopes have perhaps not yet reached that perfection which we can expect of them and which the hard work and skill of the craftsmen seem to promise us. If we once succeed in providing visible confirmation of our conjectures, how certain the theory of Saturn would be and what an overwhelming credibility the entire system which is built upon the same principles would derive from that. The time of Saturn's daily rotation establishes the relationship of the centrifugal force away from the mid-point to the force of gravity at the outer layer. The former is to the latter as 20 is to 32. Thus, the force of gravity is only around 3/5 greater than the centrifugal force. Such a large proportion as this brings about necessarily a very observable difference in the diameters of this planet. And we might apprehend that it would have to develop to such an extent that the observation of this planet, although it is only enlarged a little by the telescopes, would have to be all too clearly visible. But in truth this does not happen, and the theory could thus suffer a disadvantageous blow. A proof based on first principles completely removes this difficulty. According to Huygens' hypothesis, which a.s.sumes that the gravitational force inside a planet is the same throughout, the difference in the diameters is proportional to the diameter at the equator in a ratio twice as big as the proportion of the centrifugal force to the gravitational force at the poles. For example, in the case of the Earth, the force moving away from the mid-point at the equator is 1/289 of the gravitational force at the poles. Thus, in Huygens' hypothesis, the diameter of the equatorial plane is 1/578th greater than the earth's axis. The cause is as follows: the gravitational force, according to what has been a.s.sumed, inside the Earth's cl.u.s.ter in all regions close to the mid-point is as great as it is on the outer surface, but the centrifugal force diminishes as one moves close to the mid-point. Thus, the centrifugal force is not always 1/289th of the gravitational force. For these reasons, the loss in weight of a liquid column on the plane of the equator amounts, not to 1/289th but half of that, i.e., to 1/578th. On the other hand, according to Newton's hypothesis, the centrifugal force, which initiated the axial rotation, on the entire equatorial plane right to the mid point has the same relationship to the gravitational force at a specific location. For the gravitational force inside the planet, a.s.suming the planet has the same density throughout, decreases with the distance from the mid-point in the same proportion as the centrifugal force decreases, so that the latter is always 1/289th of the former. This creates a lightening of the liquid columns at the equatorial plane and a rise in them of 1/289. This difference of the diameters in this theory is increased even more by the fact that the shortening of the axis involves bringing the parts closer to the mid-point, and with that an increase in the gravitational force; the increase in length of the equatorial diameter involves moving parts further from the very same mid-point and thus lessening the gravitational force. For this reason, the flattening of the Newtonian spheroid increases to the point where the difference in the diameters increases from 1/289th to 1/250th.

According to these principles, the diameters of Saturn would have to be in an even larger ratio to each other than 20 to 32. They would have to reach a proportion almost equal to 1 to 2, a difference which is so large that the slightest attentiveness would not miss it, no matter how small Saturn may appear through the telescopes. But from this one should notice that the a.s.sumption of the uniform density, which seems to be quite correctly applied to the case of the earth's sphere, in the case of Saturn deviates far too widely from the reality. This is inherently probable in the case of a planet whose cl.u.s.ter consists, for the greatest part of its content, of the lightest materials and which leaves the heavier sorts of material much freer to settle down toward the mid-point, according to the effects of the gravitational pull, than do those celestial bodies whose much denser material delays the settling down of the material and allows it to harden before the settling can occur. When we also a.s.sume in the case of Saturn that the density of its material in the interior increases as one moves closer to the centre, then the gravitational force no longer declines in this ratio, but the growing density compensates for the deficiency in those parts which are set at heights above the point located in the planet and which contribute nothing by their power of attraction to the planet's gravitational power there (15). When this preponderant density of the deepest material is very large, thanks to the laws of attraction, the density changes the gravitational force which in the interior declines toward the centre into something almost uniform and establishes the ratio of the diameters according to Huygens' proportion, which is always half the ratio between the centrifugal force and the gravitational force. Consequently, since with respect to each other, these were as 2 to 3, then the difference in the diameters of Saturn will not, not 1/3, but 1/6 of the equatorial diameter. Finally, this difference will still be concealed because Saturn, whose axis makes a constant angle of 31 degrees with the axis of its...o...b..tal plane, never orients the position of its axis perpendicular to its equator, as happens with Jupiter.

According to the planet's appearance, this lessens the previous difference by almost one third. Under such circ.u.mstances, and especially considering Saturn's great distance away, we can believe that the flattened shape of its body will not be so easily visible as we have really come to think. However, astronomy, whose progress depends particularly on the perfecting of the instruments, with their help will perhaps be in a position to discover such a remarkable characteristic, if I do not flatter myself excessively.

What I say about the shape of Saturn can, to some extent, serve as a general remark about the theory of heaven. According to an exact calculation, Jupiter has a ratio of the gravitational force to the centrifugal force at its equator of at least 9.25 to 1. If its cl.u.s.ter were of uniform density throughout, in accordance with Newton's theories, this planet should show a difference between its axis and the equatorial diameter even greater than 1/9. But Ca.s.sini found it to be only 1/6, Pound 1/12 and sometimes 1/14. At least all these different observations, which in their difference confirm the difficulty of this measurement, agree in that they establish the difference as much smaller than it would be in Newton's system, or rather, according to his hypothesis of the uniform density. And if we therefore change the a.s.sumption about the uniform density, which permits such a wide discrepancy between theory and observation, into the much more probably a.s.sumption that the density of the planetary cl.u.s.ter is arranged so that it increases towards the centre of the planet, then we will validate the observations not only of Jupiter but also of Saturn, a planet much harder to measure, so as to be able to understand clearly the cause of the smaller flattening of its spherical body.

From the development of Saturn's ring, we have taken the opportunity to venture on the bold step of determining through calculation the time of its axial rotation, something which the telescopes are not capable of discovering. Let us add to this attempt at a physical prediction yet another concerning the very same planet, something whose witnessed validity is to be antic.i.p.ated from the more perfect instruments of future ages.

According to our a.s.sumption, Saturn's ring is an acc.u.mulation of particles which, after they arose as vapours from the outer layer of this celestial body, thanks to the momentum which they receive and continue from the planet's axial rotation, maintain themselves at the alt.i.tude of their distance away in free circular movement. These particles do not have the same periodic orbital times at all their distances, but rather hold to these times according to the square root of the cube of their distance from the planet, if they are to keep themselves suspended according to the laws of the central forces. Now, the time in which, according to this hypothesis, the particles of the inner edge complete their orbit is about ten hours, and the orbital time for the particles on the outer edge is, according to the appropriate calculations, about fifteen hours.

Thus, when the lowest parts of the ring have completed three orbits, the furthest parts have completed only two. Even if we estimate that the interference which the particles create for each other in the plane of the ring through their great dispersal is as insignificant as we like, it is nevertheless probable that the slower movement of the particles further away in each of their orbits gradually delays and r.e.t.a.r.ds the more quickly moving lower parts. On the other hand, the lower parts would have to impart to the upper parts some of their motion, so as to create a more rapid rotation. If this reciprocal interaction were not finally interrupted, this process would last until such a time as all the particles in the ring, both the low ones and those further away, were brought to rotate in the same time, in which state they would be at rest relative to each other and would have no effect in displacing each other. But such a condition, if the movement of the ring ended up like this, would destroy it completely. For if we take the middle of the plane of the ring and establish that the movement remain what it was before and what it must be to be capable of sustaining free orbital movement, the lower particles would not hold themselves suspended at their alt.i.tude, because they would be held back considerably, and they would intersect each other in oblique and eccentric motions. The more distant particles, however, through the impulse of a motion greater than it should be for the central force at their distance from the planet, would move away from Saturn further than the outer boundary set by the effect of the sun and would, of necessity, be scattered behind the planet by the sun's effect and carried away.

But we need not fear all this disorder. The mechanism of the developing ring involves an arrangement which, thanks to the very causes which should destroy the ring, establish it in a secure state by means of which it is divided up into several concentric circular bands which, because of the intervening gaps which separate them, have no more common interaction with each other. For while the particles...o...b..ting on the inner edge of the ring with their faster motion push forward the particles above somewhat and accelerate their orbit, the higher level in velocity provides these particles with an excess of centrifugal force and moves them further away from the place where they were suspended. But if we a.s.sume that while these particles strive to separate themselves from the lower ones, they have to overcome a certain interconnection which, although indeed they are scattered vapours, nevertheless appears to be not entirely insignificant for them, then this increased level of momentum seeks to overcome the interrelationship mentioned above, but does not do so by itself, so long as the excess in the centrifugal force causing them to move around in the same orbital time as the lowest particles does not exceed the central force of their position and their interdependency. And for this reason, the upper particles must undergo a certain tendency to pull themselves away from the lower ones in a band of a certain width in this ring. However, the interconnection remains, but not in a large width, because the velocity of these particles...o...b..ting in equal times increases with the distances more than it should according to the central laws. Thus, when it has gone beyond the level which can sustain the interconnection of the vapour particles, they must tear themselves away and take up a distance away from the planet appropriate to the excess momentum of the orbital forces over the centripetal force at that location. In this way, the intervening s.p.a.ce will be set up, keeping the first band of the ring away from the rest. And in much the same way, the accelerated motion of the particles above, through the rapid rotation of those below and their interconnection with them, which seeks to hinder the separation, will make a second concentric ring, from which the third arises around a moderate intervening gap. We could calculate the number of these circular bands and the width of the intervals between them, if we knew the extent of the interconnection linking the particles to each other. But we can be satisfied that we have generally found out with a good degree of probability the composition of Saturn's ring, which prevents its destruction and keeps it suspended through free movements.

The conjecture gives me no little satisfaction thanks to the hope of seeing it confirmed in future through effective observations. A few years ago there was a report from London that when people observed Saturn with a new Newtonian telescope, an improved model by Bradley, its ring happened to be essentially a combination of many concentric rings, separated by intervening s.p.a.ces. This report has not been taken further since that time (16). The observational instruments have opened up for our understanding the knowledge of the most distant boundaries of the cosmic structure. If now it is particularly up to them to undertake new steps in this business, from the attentiveness of our time to all those things which can expand human ideas we really have probable grounds for hoping that they will turn particularly in a direction which presents them with the greatest expectation of important discoveries.

If Saturn, however, has been so fortunate as to make a ring for itself, why then has no other planet shared this advantage? The reason is clear. The ring must arise from the ascending vapours of a planet, which it gives off in its raw condition. The planet's axial rotation must give these vapours their momentum which they only have to continue when they have reached the alt.i.tude where they can attain an exact equilibrium between the planet's gravitational power and the motion they have been given. Thus, we can easily determine by calculation the alt.i.tude to which the vapours from a planet must rise, if they are to maintain themselves in a free circular motion by means of the motions which they had at the planet's equator, provided we know the diameter of the planet, the period of its axial rotation, and the gravitational force on its outer surface. According to the law of central movement, the distance of a body which can go freely in circles around a planet at a velocity equal to the planet's axial rotation is in exactly that ratio to the semi-diameter of the planet as the centrifugal force away from the centre at the equator is to the gravitational force. On the basis of these principles, the distance of the inner edge of Saturn's ring is equal to 8, when we a.s.sume that the half-diameter of the planet is 5. These two numbers are in the same ratio as 32 to 20, which, as we have previously noted, expresses the ratio of the gravitational force to the centrifugal force at the equator. On the same basis, if we establish that Jupiter is to have a ring developed in this way, the smallest half-diameter would have to exceed the half-diameter of Jupiter by a factor of 10. That would exactly match the distance where its most remote satellite orbits around it. For these reasons and also because the vapours rising up from a planet cannot expand so far out from it, it is impossible for Jupiter to develop a ring. If we want to know why the Earth has acquired no ring, we will find the answer in the size of the half diameter, which the inner edge of the ring would have to have had. This would have to have been 289 Earth diameters. With the slowly moving planets the possibility for the development of a ring gets even more remote. Thus, there is no example left where a planet could have acquired a ring in the manner which we have explained, other than the example of the planet which really has one. This is not an insignificant confirmation of the credibility of our manner of explanation.

What makes me almost certain that the ring going around Saturn has not come about in the common way and was not built up through the universal laws of development governing throughout the entire system of planets, which also produced Saturn's satellites, and certain, I say, that no external material provided the material for this ring but that it is a creation of the planet itself, which moved its most volatile parts upward up by its heat and gave them a rotational momentum from its own axial rotation, is this fact: unlike the other satellites of this planet and, in general, all orbiting bodies which accompany a main planet, the ring is not oriented on the common interrelated plane of planetary motions, but deviates from it considerably. This is a certain proof that it did not develop from the common basic material and acquire its motion from the sinking down of this material, but arose from the planet long after its complete development and through the orbital force implanted in the planet, as a part separated from it. It acquired from the planet's axial rotation a related motion and direction.

The pleasure of having grasped one of the strangest peculiarities of Heaven in the full extent of its nature and development has involved us in an extensive discussion. With the permission of our indulgent readers, let us keep going to excess, if that is agreeable, so that after we have permitted ourselves pleasantly arbitrary opinions with a sort of freedom from restraint, we will turn back with that much more caution and return to the truth.

Could we not imagine that the Earth, like Saturn, once had a ring. It might have arisen from its outer layer exactly as Saturn's did and have maintained itself a long time, until the Earth had gone from a much faster rotation than the present one to the existing rate for who knows what reasons. Or we could attribute the building of it to the common basic material sinking down according to the rules which we explained above, which we must not take so strictly if we will indulge in our liking for the unusual. But what a store of beautiful explanations and consequences such an idea offers us. A ring around the Earth! How beautiful the sight for those who were made to live on Earth as a paradise. How much comfort for those whom Nature greeted with a smile on all sides. But this is still nothing in comparison with the confirmation which such a hypothesis can derive from the ancient lore of the creation story, no small recommendation for approval among those people who believe they are not dishonouring revelation but endorsing it when they use it to enn.o.ble the excess displays of their wit. The waters of the firmament, which the Mosaic account talks of, have already caused interpreters no small problem. Would it not be possible for us to use this ring to a.s.sist ourselves out of this difficulty? This ring consisted undoubtedly of vapours rich in water. And in addition to the advantage which it could provide for the first inhabitants on the earth, we have the fact that it was, when necessary, capable of breaking apart in order to punish the world, which had made itself unworthy of such beauty, with deluges. Either a comet, whose power of attraction brought the ring's parts into total confusion, or the cooling in the region where it was positioned united its scattered vapour particles and hurled them down upon the earth in the most horrifying of all inundations. We understand readily what the consequences of this were. The whole world went under water and absorbed, in addition to the foreign and volatile vapours of this unnatural rain, that slow poison which brought all creatures closer to death and destruction. The shape of the pale light bow vanished from the horizon at that time, and the new world, which no longer could remember what it looked like without experiencing terror before this fearful instrument of the divine revenge, saw perhaps with no less dismay in the first rainfall that coloured bow which seems to develop its shape like the first one, but which through the covenant of a forgiving heaven was to be a sign of grace and a memorial to the lasting establishment of the newly changed Earth. The similarity in the form of this memorial sign to the narrated event could make such a hypothesis appealing for those people who follow the prevailing inclination to bring the wonders of revelation into one system with the ordinary laws of nature. I find it more advisable completely to sacrifice the transitory approval which such agreement can arouse for the true pleasure which comes from the perception of regular interconnections when physical a.n.a.logies reinforce each other in the designation of physical truths.

Part Two

Section Six

Concerning the Lights of the Zodiac The sun is surrounded by a subtle and vaporous essence, going around it on its equatorial plane up to a great alt.i.tude with only a small extension on both sides. So far as this is concerned, we cannot be certain whether, as de Martiana states, it touches the outer layer of the sun in the shape of polished gla.s.s (figura lenticulari) or, like Saturn's ring, is always located at a distance away. It may be either of these. But sufficient similarity remains to establish a comparison of this phenomenon with Saturn's ring and to infer a similar origin. If this spread out material is something flowing out from the sun (and it is most probable to consider it in that manner), then we cannot miss the cause which has brought it to the common plane of the sun's equator. The highest and most volatile material, which the sun's fire raises and has for a long time already lifted up from its outer surface will through the same process expand far over it and remain suspended at a distance, according to how light it is, where the forward driving effect of its rays comes into an equilibrium with the gravitational power of these vapour particles, or they will be reinforced by the stream of new particles which continuously come up to them from below. Now, because the sun rotates on its axis, it imparts to these particles torn away from its outer surface a motion equal to the axial rotation. Thus, they maintain a certain orbital momentum by which, in accordance with the central laws, they are driven from both sides in their circular motion to intersect the sun's extrapolated equatorial plane. And thus, because they are driven down to this in equal quant.i.ties from both hemispheres, they pile up there with equal forces and form an extended flat surface on the designated solar equatorial plane.

But regardless of this similarity with Saturn's ring, there remains an essential difference, which causes the phenomenon of the zodiacal light to be quite different from Saturn's ring. The particles of Saturn's ring maintain themselves in freely suspended circular orbits through the implanted rotating motion; but the particles of the zodiacal light are kept at their alt.i.tude by the power of the sun's rays, without which their inherent motion from the axial rotation of the sun would be very insufficient to hold them in free orbits and to prevent their falling down. For since the centrifugal force of the sun's axial rotation is not even 1/40000 of the power of attraction, these vapours which have moved upward would have to be 4000 semi-solar diameters away from it in order to find at such a distance a power of gravitation in equilibrium with their allotted motion. Thus, we are certain that this solar phenomenon is not be a.n.a.lyzed in the same way as Saturn's ring.

Nevertheless, there remains a significant probability that this solar necklace perhaps acknowledges the same cause which Nature collectively acknowledges, namely, the development out of the universal basic material, whose parts, since they were suspended all around the highest regions of the solar world only after the full and complete development of the entire system, moved down to the sun in a late descent, with weaker curved motion from west to east and, thanks to this type of orbital path, intersected the extrapolated solar equatorial plane. By their acc.u.mulation there on both sides, once this motion stopped, they took up a position on this extended plane, in which they maintain themselves always at the same alt.i.tude in part through the power of repulsion of the sun's rays, in part through the real orbital motion they have kept. The present explanation has no value other than what one gives to an a.s.sumption and makes no demand other than for an arbitrary acceptance. The judgment of the reader may direct itself to that option which seems to him most worthy of adopting.

Part Two

Section Seven

Concerning Creation in the Total Extent of its Infinity Both in s.p.a.ce and Time With its immeasurable size and its infinite multiplicity and beauty radiating out from all around it, the cosmic structure presents a silent wonder. If the picture of all this perfection now stirs the imaginative power, from a different perspective the understanding derives another type of delight, when it observes how so much splendour, such an enormous greatness, flows out from one single universal rule in an eternal and justified order. The planetary structure in which the sun at the centre makes all the active spheres of its system orbit in eternal circles by means of it powerful force of attraction is entirely developed, as we have seen, from the originally distributed basic stuff of all planetary material. All the fixed stars which the eye discovers in the high recesses of Heaven and which appear to display a certain excess are suns and central points of similar systems. The a.n.a.logy permits us here no doubt that these were built and developed in the same manner as the one in which we find ourselves, from the smallest particles of elementary materials filling empty s.p.a.ce, the infinite extension of the Divine Presence.

Now, if all planets and planetary systems acknowledge the same sort of origin, if the power of attraction is unlimited and universal, if the power of repulsion is similarly continuously at work, and if in comparison with the Infinite, the large and the small are both small, should not the cosmic structures have acquired in like manner an interconnecting relationship and a systematic coordination among themselves, as the celestial bodies of our solar system have on a small scale, like Saturn, Jupiter, and the Earth, which are special systems on their own and yet are linked together amongst themselves as rungs in a much greater system? If we take one point in the infinite s.p.a.ce in which all the suns of the Milky Way were developed, a point around which, for some unknown reason, the first development of nature out of chaos began, then at that location the largest ma.s.s and a body of uncommon power of attraction will have arisen, which thus would have become capable of forcing all the development in the comprehensive systems within a huge sphere around it to move down towards it as their central point and to build around it on a large scale a system like the one which the same basic material which developed the planets created around the sun on a small scale. Observation makes this supposition almost certain. The army of stars through its orientation in relation to a common plane makes up a system just as much as the planets of our solar system do around the sun. The Milky Way is the zodiac of this higher world order, deviating from its zone as little as possible. Its band is always illuminated by its lights, just as the zodiac of planets is illuminated here and there by the shining of these spheres, although only in a very few points. Each one of these suns, along with its...o...b..ting planets, makes up a particular system of its own, but this does not prevent them from being parts of an even greater system, just as Jupiter or Saturn, in spite of their own satellites, are confined in the systematic arrangement of an ever greater cosmic structure. Can we not acknowledge with such a precise harmony in the arrangement the same cause and manner of production?

Now, if the fixed stars make up a system whose extent is determined by the sphere of the force of attraction of the body located at the centre, will not more solar systems and, so to speak, more Milky Ways arise, which will be produced in the limitless field of s.p.a.ce? With astonishment we have seen figures in Heaven which are nothing other than such systems of fixed stars restricted to a common plane, such Milky Ways, if I may express myself in this way, which present themselves to our eyes in different positions with a weakly glimmering elliptical shape appropriate to their infinite distance away. They are systems, so to speak, of infinitely greater diameter than the diameter of our solar system, but without doubt they arose in the same way, are organized and arranged by the same causes, and maintain themselves by the same dynamics as our system in its arrangement.

If we see these systems of stars once more as links on collective nature's great chain, we have just as many reasons as before to think of them in a mutual relationship and in combinations which, thanks to the laws governing throughout all nature, make up the first development of a new and even greater system, controlled by the force of attraction of a body of incomparably more power than were all former systems, from the centre of their rule-bound positions. The force of attraction, the cause of the systematic arrangement among the fixed stars of the Milky Way, works at a distance even in this cosmic structure to bring them out of their positions and to bury the world in an unavoidable impending chaos, unless the allotted rule-bound forces of motion achieve an equilibrium with the force of attraction and produce from the combination of the two of them that relationship which is the basis of the systematic arrangement.

The force of attraction is without doubt a characteristic of matter as widely extensive as the coexistence which creates s.p.a.ce, because it unites substances through a mutual dependency, or to speak more precisely, the power of attraction is just this common relationship which unites the parts of nature in s.p.a.ce. It extends itself thus through the total extent of s.p.a.ce right into all its infinite distances. If the light from these remote systems, which is only an impressed movement, reaches us, must not the power of attraction, this primordial origin of motion, which antedates all motion, which requires no foreign cause and cannot be halted by any barrier, because it works in the inner core of matter in the universal calm of nature without any external impulse, must not the force of attraction, I say, have set in motion these systems of fixed stars with their material in an undeveloped scattering at the first movements of nature, regardless of their immeasurable distances away? This is, as we have seen precisely on a small scale, the origin of the systematic union and the enduring permanence of its links, the factor which keeps them secure from collapse.

But then what will finally be the end of the systematic arrangements? Where will creation itself cease? We well note that to think of creation in relation to the power of the Infinite Being means it must have no boundaries. We come no nearer to the infinity of the creative power of G.o.d if we enclose its revelation in a sphere described with the radius of the Milky Way than if we enclose it in a ball with a diameter an inch long. Everything finite which has its limits and a determined relationship to unity is a long way distant from equaling infinity.

Now, it would be absurd to set the Divine into effective action with an infinitely small part of its creative capacity and to imagine its infinite power, the treasure house of a true infinity of natures and worlds, incapacitated and locked into an eternal deficiency in practice. Is it not much more appropriate or, to express the matter better, is it not necessary to present the embodiment of creation as something which cannot be measured by any standard, which is how it must be, in order to bear witness to that power. For this reason the field of the revelation of divine properties is just as infinite as these properties (17). Eternity is not sufficient to bear witness to the Highest Essence where it is not united with spatial infinity. It is true that attraction, shape, beauty, and perfection are relationships of the basic elements and of substance making up the material of the cosmic structure. And we notice it in the arrangement which the wisdom of G.o.d still effects at all times.

It is also most appropriate to the wisdom of G.o.d that these develop themselves in an unforced succession out of the universal laws implanted in them. And therefore we can with good reason establish that the order and arrangement of the cosmic structure take place gradually from the supply of created natural matter in a temporal succession. But the basic material itself, whose properties and forces form the basis for all changes, is an immediate result of the Diving Being and itself must be simultaneously so rich and so perfect that the development of its compositions could in the flow of eternity extend over a plane enclosing in itself everything which can be, a plane which has no dimensions, which is, in short, infinite.

Now, if creation is spatially infinite or at least was really already that from the beginning as far as its material is concerned and according to its form or development is prepared to become so, will s.p.a.ce become active with worlds without number and without end? Will then that systematic union, which we have previously mentioned in particular among all the particles extend to the totality and the universe collectively, the All of nature, tied together in a single system through the unifying power of attraction and the centrifugal force? I say yes. If nothing but separate cosmic structures without any unifying relationship to a totality were the only things present, then, if we were to a.s.sume this chain of links as truly endless, we could imagine that a precise equality in the power of attraction in its parts on all sides could keep this system secure from destruction which the inner reciprocal force of attraction threatens them with. But this condition needs to be determined with such precise measurements of the distances proportional to the power of attraction that the slightest displacement would bring destruction to the universe and would deliver it over to collapse. The time would be long, but finally it would have to come to an end. A cosmic arrangement which did not keep itself going in the absence of a miracle does not have the mark of permanence which is the sign of G.o.d's choice. Thus, we find it much more appropriate if we make of creation collectively a single system creating all worlds and world structures and filling all infinite s.p.a.ce and related to a single central point. In a scattered confusion, the cosmic structures might be separated from each other by distances less great and could have an unhindered tendency to rush to dissolution and destruction, unless a certain arrangement in relation to a common central point, the centre of the power of attraction in the universe and the foundation point of all of nature and its systematic movements, were in place.

At this universal central point of all downward movement in all nature, both developed and raw, is undoubtedly located the cl.u.s.ter with the most extensive power of attraction, encompa.s.sing in its sphere of attraction all worlds and ordered systems which time has produced and eternity will produce. We can probably a.s.sume that nature initiated its development and that around its location the systems have acc.u.mulated in the greatest density. Further away from that mid-point, the systems are lost in ever increasing stages of disorder. We could a.s.sume this principle from the a.n.a.logy to our own solar system, and this arrangement could, in any case, serve to show that at great distances not only the common central body but also all the systems moving in close proximity to it collectively combine their power of attraction and, as if they were one cl.u.s.ter, exercise their effect on systems every further away. This will then help to include all nature in its extended infinite totality into one single system.

Now, in order to trace the foundation of this universal system of nature from the mechanical laws of matter striving to develop, in the endless s.p.a.ce of the dispersed elementary basic material some point or other of this matter must have acc.u.mulated with the greatest density, so as to have a.s.sembled through the development going on there more than anywhere else a ma.s.s which serves as the foundation point of the whole universe. It is indeed the case that in an infinite s.p.a.ce no point can really justifiably be called the centre. But thanks to a certain relationship based upon the inherent levels of density, according to which at the time of creation this material had acc.u.mulated more densely particularly at one certain location and its density decreased with the distance away from this point, such a place can correctly be called the centre. And it becomes the mid-point with the development of the central ma.s.s through its stronger power of attraction. It becomes the point to which all the remaining basic material incorporated in particular developments moves down and thus, no matter how far unfolding nature may extend, creates only a single system in creation's infinite sphere.

However, what is important and what, if it wins approval, is worthy of the greatest attention is the fact that, as a consequence of the ordering of nature in this system of ours, creation or, rather, the development nature first begins with this central point and with constantly progressive steps extends itself gradually out into the far distances, in order to fill limitless s.p.a.ce with worlds and order in the progress of eternity. Let us for a moment contemplate this picture with quiet pleasure. I find nothing which can elevate the human spirit to a more n.o.ble wonder than this part of the theory concerning the successive completion of creation, as it opens up for humanity a glimpse into the unending field of the Almighty. If people grant me that the matter which is the building stuff of all worlds is not h.o.m.ogeneous in the entire infinite s.p.a.ce of the divine present but was distributed in accordance with a certain law which perhaps concerned itself with the density of the particles and according to which with the increasing distance from a certain point, like the location of the densest acc.u.mulation, the disorder in this basic material increases, then in the original movement of nature the development will have started in the region near this centre and then, in a progressive temporal sequence, the more remote s.p.a.ce will have gradually developed worlds and planetary structures in a systematic arrangement linked to this centre. Any one finite period, whose duration is connected to the magnitude of the completed work, will, in its development, always produce a sphere only a finite distance from this central point. The remaining infinite part will meanwhile be combating confusion and chaos and will be that much further from a condition of complete development, the further away it is located from already developed nature. As a consequence of this, although from our location we have a view into, as it seems, a fully completed world and, so to speak, into an infinite host of planetary structures systematically united, nevertheless we find ourselves in reality only in proximity to the mid-point of all nature, where it has already developed out of chaos and attained its appropriate completion. If we could step over to a certain sphere, we would there witness chaos and the scattering of the elements, which, in proportion to their proximity to the central point partly leave their raw condition and are closer to their complete development. But with the degrees of distance away they gradually are lost in a total scattering. We would see how the limitless s.p.a.ce of the divine present, in which we find the store of all possible natural developments, buried in a quiet night, full of matter to serve as the stuff of worlds to be produced in the future and full of the initiating energies to bring it into motion. With a weak stimulus these begin those movements with which immeasurable nature in this barren s.p.a.ce is yet still to be activated. Perhaps a succession of millions of years and centuries is to flow by before the sphere of developed nature in which we find ourselves grows to the perfection inherent in it. And perhaps an even longer period will elapse before nature will take such a wide step into chaos. But the sphere of developed nature is ceaselessly occupied with expanding itself. Creation is not the work of a moment. After creation made a beginning by producing an infinity of substances and materials, it is efficacious with constantly increasing degrees of fecundity throughout the total succession of eternity. Millions and numberless millions of centuries will pa.s.s, during which new worlds and new world systems will constantly develop and reach completion, one after the other, in the expanses far from the central point of nature. Regardless of the systematic arrangement among their parts individually, they will have a common relationship to the central point, which became the first point of development and the centre of creation through the capacity of the power of attraction of its preponderant ma.s.s. The infinity of the future temporal succession, through which eternity is inexhaustible, will thoroughly activate all the s.p.a.ce of G.o.d's present and gradually set it into rule-bound regularity, appropriate to the excellence of its design. And if, in a daring picture, we could, so to speak, sum up eternity in a single idea, then we would be able thus to see the entire spatial infinity filled with world systems and a complete creation. However, because, in fact, in the temporal sequence of eternity the part to come is always infinite and the part gone by is finite, the sphere of developed nature is always only a small finite part of that comprehensive totality which has in it the seeds of future worlds and works, in order to develop itself out of the raw state of chaos in longer or shorter periods. Creation is never complete. True, it once began, but it will never cease. It is always busy bringing forth new natural phenomena, new things, and new worlds. The work which it brings into being has a relationship to the time nature expends on it. It needs no less than an eternity to bring the entire limitless extent of infinite s.p.a.ces alive with numberless worlds without end. We can say about nature what the n.o.blest of the German poets writes about eternity.

Eternity! Who knows you?

For you worlds are days and humans moments.

Perhaps the thousandth sun is now turning And thousands still remain behind.

Like a clock animated by a weight, A sun rushes by, moved by the power of G.o.d.

Its impulse comes to an end, and another throbs.

But you remain and do not count them.

(von Haller) There is no small pleasure in letting one's imagination roam over the limits of completed creation into the s.p.a.ce of chaos and to see half raw nature in the vicinity of the sphere of the developed world losing itself gradually through all the stages and shades of incompletion in the entire undeveloped s.p.a.ce. But is that not a culpable daring, people will say, to set down a hypothesis and to praise it as a delightful subject for the understanding when it is perhaps only arbitrary, claiming that nature is only developed to an infinitely small extent and limitless s.p.a.ces still are at strife with chaos, so that they will display in the succession of future times entire hosts of worlds and world systems in all appropriate order and beauty?. I am not so devoted to the consequences which my theory offers that I should not acknowledge how the conjecture about the successive expansion of creation through endless s.p.a.ces containing material in themselves cannot fully counter the charge that it is beyond proof. However, I expect from those who are in a position to appreciate levels of probability, that such a map of infinity, although containing a subject that certainly seems to be concealed forever from human understanding, will not for that reason immediately be seen as a chimera, especially when we take the a.n.a.logy as an aid which must always guide us in such cases where the understanding lacks the guiding threads of indubitable proofs.

However, we can still reinforce the a.n.a.logy with principles worthy of consideration. The insight of the reader who, I may flatter myself, will approve will be able perhaps to multiply these principles with more important ones.

Creation does not bring with it a characteristic constancy. It does not establish for the common striving of the power of attraction, which works through all its parts, such an exact general determination which can sufficiently withstand the tendency of this power to bring destruction and disorder, unless creation allotted the orbital forces which in combination with the central tendency fixes in place a systematic arrangement. When we consider this, we will be required to a.s.sume a common central point for the entire totality of worlds, a point which holds all the parts of this totality together in a united relationship and makes only one system out of the entire comprehensive essence of nature. If we pursue the idea of the development of world systems out of scattered elementary matter, as we have outlined the subject previously, but do not limit the idea here to one particular system, extending it rather to all nature, then we will have to imagine such a distribution of the basic matter in the s.p.a.ce of primordial chaos. This naturally involves a central point of all creation, so that the effective ma.s.s which encompa.s.ses all nature collectively in its sphere of attraction could bring the material together and make the general relationship work, so that all worlds make up only one single structure. However, in limitless s.p.a.ce a sort of distribution of the primordial basic material can hardly be imagined of the sort which is to establish a true central point towards which collective nature sinks down other than one in which the distribution is arranged according to a law of increasing disorder from this point out into the far distances. This law, however, at the same time establishes a difference in the time which a system requires in the different regions of limitless s.p.a.ce to come to its mature development. This period is shorter, the closer the location of the development of a world system is to the centre of creation, because in the closer region the elements of matter acc.u.mulate more thickly; by contrast, the further the distance away from this centre, the longer the time required, because the particles there are more scattered and come together later to develop.

If people think about the entire hypothesis to the full extent that I have stated, as well as about what I will still present, people will at least not consider that there is no excuse for the daring of its claims. We can calculate that the inevitable tendency which each world system brought to completion has to move towards its destruction is among the reasons which can establish that the universe, in contrast to that destruction, is fertile with worlds in other regions, to make up for the deficiency which it has suffered in one location.

Although the entire part of nature that we know about is only equivalent to an atom in comparison with what remains hidden over or under the circles visible to us, it nevertheless confirms this fertility of nature, which is without limit because it is nothing other than the working out of the Divine Omnipotence itself. Numberless animals and plants are destroyed every day and are a sacrifice to mortality. But nature, with its inexhaustible productive capacity, creates just as many over again in other places and fills up the emptiness.

Considerable parts of the earth's surface which we inhabit are being buried once again in the sea out of which they were brought at a favorable time. But in other places, nature makes up for the loss and produces other areas which were hidden deep under water, in order to extend over these areas new riches from her fertile store. In the same way, worlds and world systems go under and are swallowed up in the abyss of eternity. But, on the other hand, creation is always busy organizing new development in other regions of heaven and making up for the loss with advantage.

We should be amazed to admit mortality even in the greatness of G.o.d's work.

Everything finite, with a original starting point, has within itself the mark of its limited nature. It must die and have an end. On account of the excellence of its arrangements, the duration of a world system has a permanence which, according to our ideas, comes close to a limitless time span. Perhaps a thousand, perhaps millions of centuries do not destroy it. But because vanity, which adheres to finite natures, works continuously for their destruction, so eternity will hold in itself all possible periods, in order finally to bring about through a gradual decay the moment of its collapse. Newton, that great admirer of the properties of G.o.d in the perfection of His works, the one who with the deepest insight into the excellence of nature combined the greatest devotion for Divine Omnipotence, saw himself compelled to predict the decay of nature through the natural tendency which the mechanics of movement had to bring it about. If a systematic arrangement comes close to a state of confusion as the essential result of its fallibility over a long period of time, even in the very smallest part that we can imagine, then in the endless current of eternity there must be a moment in time when this gradual diminution exhausts all movement.

However, we need not lament the destruction of a cosmic structure as a real loss for nature. It demonstrates its richness with a kind of dissipation which, when a few parts pay the tribute to mortality, maintains it in the full extent of nature's perfection with numberless new productions. What a countless number of flowers and insects a single cold day destroys. But how little we miss them, regardless of the fact that they are beautiful works of art and proofs of the Divine Omnipotence. In another place, this death will be made up once again with excess. Humanity, apparently the masterpiece of creation, is itself no exception to this principle. Nature shows that it is just as rich and just as inexhaustible in the production of the most excellent of creatures as it is of the most insignificant and that their destruction is a necessary shadow amid the multiplicity of its suns, because producing humanity cost nature nothing. The harmful effects of infected air, earthquakes, and inundations wipe out entire peoples from the surface of the earth, but it does not appear that, on this account, nature has suffered any damage. In the same way, entire worlds and systems leave the stage when they have played out their roles. The infinite nature of creation is large enough that it looks upon a world or a Milky Way of worlds in comparison with it as we look upon a flower or an insect in comparison with the Earth. In the meantime, while nature beautifies eternity with changing scenes, G.o.d remains busy with a ceaseless creation, forming material for the development of even greater worlds.

Who sees with equal eye, as G.o.d of all, A hero perish, or a sparrow fall, Atoms or systems into ruin hurl'd, And now a bubble burst, and now a world.

(Pope) Let us get used to the picture of these terrifying collapses as the customary methods of providence and look at them with even a kind of delight. In fact, nothing is more appropriate to the richness of nature than this. For when a world system in the long sequence of its duration exhausts all the multiplicity which its organization can contain, when it has now become an expendable link in the chain of being, then nothing is more fitting than that it play the last role in the drama of the pa.s.sing changes of the universe, which is part of every finite thing, namely, it gives up what it owes to mortality. Nature demonstrates, as mentioned, even in the small parts of its being this rule of its processes, which eternal fate has prescribed for it on a large scale. And I repeat that the magnitude of what is to pa.s.s away is in this matter not the slightest obstacle, for everything large becomes small. Yes, it becomes just like a point, if we compare it with the infinity which creation will present throughout the succession of eternity in limitless s.p.a.ce.

It appears that for worlds, as for all natural things, this fatal ending is subject to a certain law whose consideration gives the theory something new and appropriate. According to this principle, the fatal ending originates among those celestial bodies located closest to the central point of the universe, just as the production and development first began close to this mid-point. From there the decay and destruction gradually work their way outward into the further distances, in order to bury all the world which has gone through its time, by means of a gradual decline in its motions, finally in a single chaos.

On the other hand, nature is ceaselessly busy on the borders opposite to the developed world producing worlds from the raw material of the scattered elements. While nature on one side close to the mid-point is aging, on the other side it is young and fertile in new generations. The developed world, according to this, finds itself in a limited s.p.a.ce in the middle, between the ruins of what has been destroyed and the chaos of undeveloped nature. If we imagine, as is probable, that a world already growing to completion could last a longer time than it required to become developed, then the extent of the universe will in general increase, regardless of all the destruction which mortality ceaselessly brings about.

However, if we now allow an idea which is just as probable as the arrangement of the divine works is appropriate, then the satisfaction aroused by such a description of nature's changes will be lifted to the highest level of delight.

Can we not believe that nature, which was capable of setting itself up out of chaos into a rule-bound order and a finely tuned system, is equally in a position just as easily to organize itself once more out of the new chaos into which the diminution of motions has lowered it and to renew the first unity?

Might the energies which brought the scattered material stuff into motion and order not be able once more to be made effective by forces from a distance after the motionlessness of the machine rendered them inert and, through the same universal principles, be harmoniously regulated in the way in which the original development was produced? We will not examine the matter very long before conceding, if we consider that, after the final exhaustion of the orbital motions in the cosmic structure has thrown the planets and comets together down onto the sun, the sun's fire must increase immeasurably through the addition of so many large bodies, especially since the furthest spheres of the solar system, as a consequence of the theory we have previously established, contain the lightest and most effective fuel in all nature. This fire, given the highest intensity by the new fuel and the volatile materials, will without doubt not only break down everything into the smallest elements but will also in this way spread them out with an expansive force appropriate to the heat and at a velocity which is not weakened by any resistance in the middle regions. It will scatter them once again in the same wide s.p.a.ce which they occupied before the first development of nature, so that, after the intensity of the central fire is damped down by the almost total destruction of the sun's ma.s.s, through the combination of the forces of attraction and repulsion the old generations, together with their systematically interrelated movements, will be repeated with no less regularity and will present a new cosmic structure. Thus, when a particular planetary system suffers destruction in this way and has been re-established by the essential forces, when indeed this entire play repeats itself again, then finally the period approaches when, in the same manner, the large system of which the fixed stars are links will collectively experience chaos through the lessening of it motion. We will have even fewer doubts here that the uniting of such an endless number of rich fiery store houses as these burning suns, together with their attendant planets, dissolved by the indescribable inferno, will scatter the material making up their ma.s.ses, and there the material will provide for new developments through the same mechanical laws. As a result of this, the barren s.p.a.ce can become active with worlds and systems once again. When we follow this phoenix of nature, which is only burned up in order to live again, renewed once more from its ashes, through all infinity of times and s.p.a.ces, when we see how it progresses, even in the region where it decays and grows old, inexhaustible in new phenomena and, on another border of creation, in the s.p.a.ce of undeveloped raw matter takes constant strides to unfold the plans of the divine revelation to fill eternity as well as s.p.a.ce with its wonders, then the spirit contemplating all this is lost in deep wonder. But still dissatisfied with such great events as these, whose mortality cannot adequately satisfy the soul, he wishes to learn at close hand about that Being whose understanding and whose greatness are the fountain of that light which extends itself over all nature as if out of a central point. With what kind of awe must the soul not contemplate its own essence, when it observes that it is to survive all these changes. It can say to itself what the philosophical poet says concerning eternity: When then a second night will bury this world, When from everything nothing remains but the place, When still many others bright with other stars Will have completed their course, You will be as young as now, just as far from death As eternally alive as now.

(von Haller) Oh, how lucky the soul, when among the tumult of the elements and the ruins of nature, it is set on a height from which it can see rushing past, as it were, below its feet the devastation which the frailty of worldly things brings about.

A blessedness which the understanding might never dare to expect teaches us to hope with conviction for the revelation. For when the bindings which keep us tied to the vanity of living creatures