Part 2 (1/2)

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 relations.h.i.+p 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 relations.h.i.+ps 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 relations.h.i.+ps 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 relations.h.i.+ps 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 relations.h.i.+p 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 relations.h.i.+p 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 interrelations.h.i.+p 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 relations.h.i.+p 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 s.h.i.+ning 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 relations.h.i.+p 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 relations.h.i.+p 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 relations.h.i.+p 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 relations.h.i.+p 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 relations.h.i.+ps 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.