Epitome Astronomiae Copernicanae: Liber IV, part 5
4. Nor does the office of the Sun in the world seem to persuade otherwise, that as being about to illuminate all things he has obtained light in his body, so being about to warm all things, heat, being about to give life to all things, bodily life himself, being about to move all things, himself the principle of motion, and so should have a soul in himself.
Will you add also a mind or intelligence to the soul of the Sun, to govern this his motion about his axis? For the offices of motion there is absolutely no need of mind. For the quarter toward which the Sun is turned is from the first origin of things; the constancy of the rotation and of the periodic time, as explained above, depends on the constant proportion of the moving power to the stubbornness of the matter. The direction of the axis of the solar body toward the same quarter perpetually is rather a rest than a work of mind, since from the first origin of things no impression of this motion was made on the axis. The direction of the axis, moreover, the middle circle between the extremes of the axis, the poles, necessarily follows, and remains while the axis remains, being subordinate to the same fixed points perpetually. Finally, the very grasping of the planetary bodies, which the rotated Sun carries around, is a bodily virtue, not animal, not mental.
And let these things be said on account of the motion. For the rest, what conjectures the consideration of the celestial harmonies may supply concerning intelligence, see on that book V of the Harmonics, the last chapter.
Does the Sun, then, carry the planets round by the gyration of his body? And how can this be, since the Sun lacks hands with which to grasp a planet absent at so great an interval and carry it round turned with himself? In place of hands he has the virtue of his body, sent out in straight lines into the whole amplitude of the world, which, by the very fact that it is a species of the body, is rotated together with the body of the Sun like a most rapid vortex, sweeping through that whole amplitude of the circuit, however far it reaches, as swiftly as the Sun turns himself in his most narrow space about the centre.
Could you make the matter clear by an example? Here there comes to our aid that sympathy of the magnet and the little iron tongue imbued with the magnet, whose virtue it has drunk in by rubbing. Turn the magnet in the neighbourhood of the tongue, and the tongue will be turned at the same time. Although the grasp is of a different form, you see nevertheless that here too no contact of bodies intervenes.
The example is certain, but obscure: explain what that virtue is and to what kind of things it belongs. As there are two bodies, the mover and the moved, so there are also two powers by which the motion is administered: one is passive and inclines more to matter, namely the likeness of the body of the planet with the body of the Sun in corporeal form, and a part of the planetary body friendly to the Sun, the opposite part hostile; the other power is active and more partakes of form, namely that the body of the Sun has force to attract the planet by its friendly part, to repel it by the hostile, and finally to retain it, if it be so situated that it turns neither the friendly part to the Sun nor the hostile.
How can it be that the whole body of the planet is like or cognate to the body of the Sun, and yet a part of the planet is friendly to the Sun, a part hostile? Evidently, when a magnet draws a magnet, the bodies are cognate, yet the drawing is made by one part only, the repulsion by the opposite. This friendship and enmity, therefore, are named from the effect of coming together or flight, not from a dissimilarity of the bodies.
Whence, however, is that diversity of the opposite parts of the same body? In magnets the diversity is from the situation of the parts in the whole. For if you break a magnetic stone AB at CD, the fragments, however they are transposed, attract each other only by the same parts of each fragment CD as those which before in the entire stone looked to the same quarter of the world: but if the fragments are so applied that the situation of the parts among themselves is the former one, as CAD, BCD: then the fragments repel each other.
In the heavens the matter is a little differently ordered.
For the Sun possesses this active and energetic faculty of attracting or repelling or retaining the planet not in one quarter, as a magnet, but in all the parts of his body. It is therefore credible that the centre of the solar body answers to one extremity or pole of a magnet, but the whole surface to the other pole of the magnet. And so in the bodies of the planets, that part or extremity which at the first origin of things and in the first placing of the planet looked toward the Sun is cognate to the centre of the Sun, and is drawn by the Sun; but that which was extended from the Sun toward the fixed stars has obtained the nature of the solar surface, and if it be turned toward the Sun, the Sun repels the planet from himself.
That I may understand better the force of the Sun’s rotation, say what you think would have been if the Sun were not rotated? As a magnet does not cease to attract a magnet turned toward it with its friendly part until it brings it to contact of the bodies and wholly unites it to itself, but the one turned toward it with the hostile part it either turns and, when turned, likewise attracts, or if it cannot turn it, repels, and leaves it no place within the sphere of its virtue, if indeed nothing hinders: so we must think also of the Sun, that if he were not turned about his axis, none of the primary planets would go round the Sun, but part of them would sail up to the Sun perpetually until they were united to him by contact, the part which turns its hinder side to the Sun would be expelled toward the fixed stars, but those which present their side to the Sun would stick in their place wholly immovable, the attractive virtue of the Sun struggling with the repulsive.
What, then, happens now, the Sun being rotated about his axis? Evidently, the body of the Sun being turned, that virtue also is turned, as, a magnet being turned, the attractive force of one part is transferred to other and other quarters of the world. And since the Sun by that virtue of his body has seized a planet, whether drawing it, or repelling it, or doubtful between the two, he carries it also around with himself, and with it perhaps all the ethereal air poured round. For by drawing and repelling he retains, and by retaining carries around.
If this were so, all the planets would be restored in the same time as the Sun. Indeed, if this alone were so. But it has been said above that besides this carrying force of the Sun there is also a natural inertia in the planets themselves toward motion, by which it comes about that they are inclined, by reason of matter, to remain in their place. The carrying power of the Sun and the impotence of the planet, or material inertia, fight therefore with one another; each has its part of the victory, the former removes the planet from its seat, the latter snatches its own, that is the body of the planet, somewhat out of those bonds by which it had been grasped by the Sun, so that it is laid hold of by another and another part of this circular virtue and as it were of the solar circumference, namely by that which next succeeds the one from which the planet had just extricated itself. In the figure let the species of the rotated solar body be understood under the outer circle, marked with points, and let such a circle be understood to be drawn through whatever situation of the planet, at A, B, C, D, E, F, G or H. Let the Sun be turned and with him his species from right to left: let the planet A be first grasped by that part of the species of the Sun which is marked by the radius A, let the radius A move in a certain space of time to the place of the radius D and draw the planet, but reluctant and extricating itself, so that in the same space of time it is propelled only from A to B, and so the first radius has left the planet behind it by the space BD; but in turn the radius H has now succeeded and laid hold of the planet in B. For as far as A is advanced to D, so far has H advanced to B.
But if all things are effected by natural powers, which labour and fight with the inertia of the matter to be moved, how can the planets preserve their periodic times, so that they are always among themselves as exactly equal as possible? More easily than by the presidency of a mind: for since the proportion of the whole carrying virtue to the matter of the globe to be carried is invariable, it follows that the periodic times also are perpetually equal.
Why, however, does one of the planets extricate itself more than another from this rapture, so that Saturn in one hour is carried on through only 240 miles, Mercury through 1200 according to Copernicus? 1. Because that virtue, flowing out from the body of the Sun, has the same degrees of weakness in different intervals as the intervals themselves have, or the amplitude of the orbs described through these intervals; this is the chief cause. 2. There is also some cause in the inertia or resistance, greater or less, of the planetary globes themselves, by which it comes about that the proportion answers only by half: but of this a little later more.
The body of the planet is always the same, but it is expelled, as you say, by the Sun and allured to him; it passes through, therefore, different degrees of carrying virtue; the proportion of the virtue to the body of the planet does not therefore remain constant. Not indeed, if we consider the parts of one revolution, and therefore also the same planet becomes swifter in one part of the revolution, as above in E, than in another, A, as will be said below. But notwithstanding this, the whole carrying virtue collected through all those degrees into which the planet comes within one revolution is always and at every return of the same quantity.
How can this be, that the virtue emanating from the body of the Sun is weaker at the greater interval at A than near the Sun at E? What afflicts it or renders it weak? Because that virtue is corporeal and partakes of quantity: wherefore it can be scattered and attenuated. Since, therefore, there is as much virtue diffused into the most ample orb of Saturn as is gathered in the most narrow orb of Mercury, it is most thin, part by part, in the orb of Saturn and therefore also weakest, but densest near Mercury and therefore strongest.
If it were a question of the body of the Sun itself, I could concede in it this natural power of moving: but you lead this material power out from the body, and establish it without a subject in the most ample ether: this seems absurd. That it ought not to seem absurd is plain from the example of the magnet, to which this same could be objected. But in neither case is this force without an analogous subject. For as in the very fountain the subject of the natural faculty is the body of the Sun, or the fibres extended from the centre to his circumference, so also in this very outflow I think we must distinguish in thought between the immaterial species of the solar body, flowing out as far as the planets and beyond, and its force or energy, which grasps and moves the planet at close quarters, so that the former is the subject of the latter, though it is not a body but the immaterial species of a body.
Could you give an example of this? A genuine example is in the light and heat of the Sun. There is no doubt that, as the Sun is wholly luminous, so he is also wholly ignited and, on account of the density of matter, to be compared altogether to a glowing mass of gold, or of something denser. Now from that light of the Sun there goes forth and glides down to us a species not corporeal, not material, which we call the light or rays of the Sun, which nevertheless receives quantities and accidents: for it flows out in straight lines, is condensable or attenuable and altogether divisible by mirrors and glasses, by reflection, that is, and refraction, as we are taught in optics. Yet this species of solar light carries also heat itself, and according to the measure of its strength, greater or less, with which it falls upon bodies capable of illumination, it warms also more or less. As, therefore, that species or light, which species we know for certain flows down from that light of the Sun, is the subject of the heating faculty, likewise extended from the Sun by the species: so also the immaterial species of the body of the Sun, glided down as far as the planets, has as its companion the species of that energetic virtue in the body of the Sun, which strives to unite to itself like things and to repel unlike.
A more evident example is in the same light, when, passing through coloured glasses or cloths, or communicated to coloured surfaces, it itself is coloured: where it cannot be denied that light (although it is the immaterial species of that light which had fallen upon the coloured body) becomes the subject of that colour and as it were a vehicle also outward.
What if this light itself, and not another species of the body of the Sun, were also the subject of that apprehensive faculty by which the Sun grasps the bodies of the planets? Not simply: for it seems rather to be followed that the immaterial species of the body itself flows out, to which species both the force of grasping and light cleave, and to the light both heat and colour, each derived from its own fountain.
State the causes of this distinction of the immaterial species of one and the same solar globe. 1. It is necessary that the matter of the solar body be something distinct from the light in it. For the motion of the rays of light in a straight line takes place in a moment, but the rotation of the solar body is made in time. But if we established that the bare species of light is the subject and vehicle of the grasping virtue, the one light of the Sun would claim for itself the whole essence of its body. For what is originally in the thing is the same as is found in the species of the thing. 2. To the light that has glided down quantities belong, without doubt not wholly according to the inmost essence of light, but according to something different from the light itself, namely because it is in a quantified body and because the species of both body and light, joined, glide down. 3. The species of light glides down from the surface of a luminous body, or, at the most, even from the depth of a transparent body, yet as if from the surface. So light is considered as a surface and has the same things as other surfaces in motion and impact; from the body, however, which is illuminated within the surface, it suffers nothing, because it does not descend from the interior corpulence of its fountain: the force of grasping a body must descend from a body, that it may be a moving cause analogous to its movable object. So also it admits the dimensions of the body and moves bodies not only according to the surface but also insinuating itself into their matter. 4. Hence also no matter of the surface presented hinders light from illuminating that surface in a moment; what, however, does hinder light, namely the opaque, hinders perpetually and is never overcome, so long as the opaque remains. But the virtue of grasping does not conquer the whole: for the resistance of the matter in the body of the planet obstructs and detracts from it, by which it comes about that the planet does not exactly follow the grasping force advanced, but is left behind and deserted by it; in which mutual contention there is place for time. 5. Of the same cause is this diversity also, that light is bounded and impeded by the opaque surfaces of bodies, so that it does not penetrate further to other bodies placed in the same straight line. But this force, which carries the planet round by grasping it, is not impeded by its surface, but penetrates into the body which it grasps, and through the body penetrates also into the body of a further planet, if it happen that two planets fall with the Sun into a straight line: so that the motion is nowise disturbed by the interposition of bodies. But if the motion proceeded from the illumination of light, this absurdity would happen, that as often as the upper planet were eclipsed by the lower, so often its motion would cease meanwhile, until the lower by its speed tore itself out of the line. 6. Finally, that the motion of the planets is not necessarily from the bare light of the Sun is plain from examples of other things, where a like motion of celestial things takes place without light, as may be seen in the magnet and will appear below from the example of the Moon, which is moved by the Earth, a body by no means luminous. Although then also the illumination of the Moon and the Earth will find its parts, which although it co-operates in many ways to move the Moon, yet does not do so of itself, but only fortifies the moving species of the Earth, as will be said in its place.
What similarity is there between the species of light and this virtue of grasping? The similarity is most complete in the very genesis and conditions of the species of each: the descent of each from the luminous body is made in a moment, each passes through a medium great and small without loss, not subject to toll; nothing perishes on the way from its fountain, nothing between the fountain and the illuminable or movable is dispersed. The efflux of each is therefore immaterial, not such as that of odours with diminution of substance, not such as that of heat from a seething furnace, and whatever else is similar, by which media are filled: for nowhere is that species except in the opposite and meeting body, light indeed on its opaque surface, the moving virtue in the whole corpulence, but in the space intermediate between the Sun and the surface it is not, but was. But if a concave spherical surface of an opaque body should meet it, each solar species would with its whole stores, with which it had gone out from the body of the Sun, be dispersed over that concavity, so that there would be as much of it in a wide and more remote sphere of this kind as in a narrow and near one. And since the proportion of convex orbs is the duplicate of the proportion of the diameters, that species would be made twice as thin in unequal orbs, the farther; and again, because circles have the same simple proportion as diameters, in length the species is thinner by the same proportion by which it is more remote from the fountain.
Whence are the arguments of this comparison drawn? Of light these properties are demonstrated in optics; of the moving virtue of the Sun the same are proved by analogy, preserving the difference between the works of illumination and of motion and between the objects of each, and they are found consonant with astronomical experiments.
For since one and the same planet, as will be said below, in truly equal parts of the eccentric circle but distant from the Sun by unequal intervals, spends unequal delays, and that in this very proportion of the intervals: it follows, therefore, that the moving virtue also is attenuated in length in the same proportion in which light is attenuated in length, in the proportion, namely, of the amplitude of the circles of which those intervals or semidiameters are. In this figure let the Sun be S, the same planet CA nearer and FD more remote, and let DH, AI be equal parts of the eccentric (understand in opposite places of the eccentric), DH indeed the more remote, AI the nearer. As, therefore, SD stands to SA, so the delay of the planet in DH to its delay in AI. From this follows also this, that as SD is to SA, so conversely is the density of the lower light CA in length to the density of the more remote light FD.
But light is attenuated in the duplicate proportion of the intervals, that is in the proportion of the surfaces: why, then, is not the moving virtue also made weaker in the duplicate rather than in the simple proportion? Because the moving virtue has as its subject the species of the solar body, not as it is bare body, but as it is constituted in the motion of rotation about its own axis and immovable poles. Although, therefore, the species of the solar body is attenuated in length and breadth, no less than light, yet that attenuation avails to weaken the moving virtue only by reason of length, since the local motion which the Sun imparts to the planets is made only in length, in which direction also the parts of the body of the Sun itself are movable, and not in breadth toward the poles of the body, with respect to which the Sun is immovable.
Yet the movable bodies also have breadth no less than length, wherefore they are carried by this virtue as it has its length, so also its breadth; why, then, would not the moving virtue be weakened also in breadth and so in the duplicate proportion of the intervals? Indeed the bodies of the planets have not only these two dimensions, but also a third, of thickness or height, and they occupy this virtue plainly in three ways, and for this reason the grasping, carrying and moving virtue of a single planet is not one circle, lacking breadth, but consists of infinite circles, as it were, parallel in breadth and in height; but it does not follow on that account that the attenuation of this virtue ought to be in the duplicate or triplicate proportion of the intervals or semidiameters. For as elsewhere in geometry the proportion of equimultiples is the same, so also here in physics, as one least physical line, as a part of the planetary body, stands to the thinness of one virtuous circle, constituted in the simple proportion of the intervals, so stand also the infinite least physical lines, as all the parts of the planetary body, disposed in breadth as in height, to as many circles of moving virtue, all and each of which have force of moving only in length, none in breadth, none in height, neither singly nor joined together. As, therefore, single lines or fibres of two planetary bodies, taken alone, would be moved by single circles of moving virtue in the simple proportion of the intervals, so also all the fibres of the planetary globe together are moved by all the circles of virtue together in the same simple proportion: since that breadth and height of the moving virtue is not of its essence, but an accident to it from the movable thing.
Are not these things more difficult to believe, concerning the species of the body and virtue of the Sun carrying round the planets (especially the Earth), than those earlier doctrines of the philosophers concerning intelligences, moving souls and solid orbs? It does no harm that they are difficult to believe, provided they are the easier to comprehend, and that nothing can be objected to them of what was objected to orbs and intelligences, or anything else by which impossibility is proved. For first, however they surpass belief, there is nevertheless a genuine example in the magnet. Next, if anyone doubts whether magnetic, that is terrestrial, faculties are in the heavens, and whether the Earth, a heavy body, can be transposed from place to place by the immaterial species of the Sun, let him look at the Moon, which he sees, cognate to the Earth, going round with no solid orb beneath. That the species of bodies passing mutually to and fro avail to impart motion is plain in the same Moon, which by an emitted species moves the seas for us. We do not therefore lack examples. Nor does the mode weary us, which we perceive by mind what it is: the incredible strength alone of this species keeps us in suspense. But here we can rightly answer with Ptolemy that it is by no means fair to estimate the virtues of divine works by our weakness, their greatness by our smallness. The estimation of mode and of figures belongs to mind, but of magnitude or smallness, that is of indefinite quantities, there ought to be no account in this estimation.
IV. Of the causes of the proportion of the periodic times.
You said at the beginning of this speculation concerning motion that the periodic times of the planets are found most exactly in the sesquialter proportion of their orbs or circles; I ask what is the cause of this? Four causes concur to constitute the length of the periodic time. The first is the length of the journey, the second the weight or abundance of matter to be transported, the third the strength of the moving virtue, the fourth the bulk or space into which the matter to be carried is spread. For as it happens in a mill, whose wheel the impetus of the river turns, that the broader and longer the wings, boards or oars you fix to the wheel, the greater force of the river, poured out through the breadth and depth of the rushing stream, you draw off into the machine: so also it happens in this celestial vortex of the solar species rushing into a gyre, which causes the motion, that the more spacious the body (as figure 63, A, D), the more widely and deeply it occupies the moving virtue, as BCA, understood for breadth: the more swiftly also, other things equal, it is carried forward and the more quickly it completes its periodic journey.
Now the circular journeys of the planets are in the simple proportion of the intervals: for as SA is to SD, so also stands the whole circle BA to the whole circle ED; the weights or abundance of matter in different planets are in the half proportion of the intervals, as was proved above, so that always the higher has more matter and therefore is also moved on more slowly and accumulates more time into its period, since already before, by reason of the journey, it required more time. For a mean proportional SK being taken between SA and SD, the intervals of two planets, as SK stands to the greater SD, so stands the abundance of matter in the planet A to that in the planet D: the third and fourth causes compensate each other in the comparison of different planets, while the simple and the half of the proportion of the intervals constitute the sesquialter of the same: the periodic times, therefore, are in the sesquialter proportion of the intervals: as if SD, SK, SA, SL be continually proportional, then as SL is to SD, so will be the periodic time of the planet A to that of the planet D.
Prove that in the comparison of two planets the weakening of the moving virtue is exactly balanced by the amplitude with which the movable bodies of the planets occupy it. The masses or spaces of the bodies are in the simple and direct proportion of the intervals, as was demonstrated above. That is, as SA stands to SD, so stands the mass of the body of the planet in A to the mass of the other planet in D. Now the moving virtue also is dense and strong in the simple proportion of the same intervals, but inverted; for as the same interval SA stands to SD, so stands the strength of the species CA to the strength of the species FD. Therefore, in the proportion in which that virtue is weakened, in the same, conversely, it is occupied; for example, Saturn is carried by a virtue ten times weaker than the Earth, but conversely by his body occupies ten times more of the virtue of his region than the Earth by her body of the virtue of her region; and the whole virtue which Saturn occupies by his mass being divided into ten parts, which are equal in space to the whole virtue which the Earth occupies, each of these parts or spaces of virtue has only a tenth part of the strength which that one has which the Earth occupies: wherefore those ten, with their ten tenths gathered into one, are in power equal to that single one by which the Earth is carried. So if in that amplitude of the rarer globe of Saturn there were no more matter than in the narrowness of the body of the denser Earth, the globe of Saturn would be carried in one year through as great a space of his orb as is the length of the whole orbit of the Earth, and so would complete his own orbit in ten years. But now he has about three times more matter and weight than the Earth, wherefore he requires a time three times longer, namely thirty years.
What need was there to teach this compensation? Would it not have been equally easy, in order to expedite the demonstration, to establish that there is plainly no cause of such unequal motion, neither in the different degrees of the moving virtue nor in the different amplitude of the planetary globes? For this demonstration of the different periods in the planets and of their proportion, that it is the sesquialter of the proportion of the intervals, it made no difference whether this or that were established: but if we had now advanced to the different delays of one and the same planet at different intervals, we could not have expedited the cause, from the same kind of things, why the delays in precisely equal arcs follow the proportion of the intervals.
What, then, is the cause why, the farther from the Sun any arc of the eccentric of equal parts is distant, the longer delays the planet weaves in it, and that in the very proportion of the intervals? That very weakening evidently of the moving virtue, which, no otherwise than light, is extended at the longer interval from the Sun, SD, in length ED more prolixly than the extension BA of the same part at the shorter interval SA; and so what is then occupied of it by the body of the planet, as FD, is weaker than what is occupied by the same, CA, being brought nearer, of the denser virtue.
For here the three remaining causes are lacking to us. For the arc or journey is supposed on both sides of the same length, as DH, AI; the density of the body remains the same, and likewise the quantity of the figure, because FD and CA is here one and the same planet: there remains the strength of the virtue alone. But of this more in what follows.
Some greater difficulty than above seems to occur here. For the planet, made nearer to the Sun, occupies not only longer arcs of the circles of the moving virtue, but also more crowded ones: wherefore it ought rather to extend its delays in the duplicate than in the simple proportion of the intervals? Nay, the same is said as above and the same answered. For although Saturn did not then descend for us into the orb of the Earth, yet we compared with the space of virtue occupied by Saturn not merely that virtuous space which the Earth would have occupied in the orb of Saturn, but altogether that which the Earth would occupy in her own proper orb. Therefore, as before, that the circles are more crowded is to be ascribed to the species of the body, which is something distinct from the inhering moving virtue, which, tending to length alone, receives no gain from that condensation of its subject in breadth, except that a thin line, lacking breadth, has no natural force even in length; where the breadth of such a line is reckoned not by density but by space, on account, namely, of the breadth of the bodies to be carried, as I also warned above.