CHAPTER XXVI.

OF THE WORLD AND OF THE STARS.

1. The magnitude and duration of the world, inscrutable.—2. No place in the world empty.—3. The arguments of Lucretius for vacuum, invalid.—4. Other arguments for the establishing of vacuum, invalid.—5. Six suppositions for the salving of the phenomena of nature.—6. Possible causes of the motions annual and diurnal; and of the apparent direction, station, and retrogradation of the planets.—7. The supposition of simple motion, why likely.—8. The cause of the eccentricity of the annual motion of the earth.—9. The cause why the moon hath always one and the same face turned towards the earth.—10. The cause of the tides of the ocean.—11. The cause of the precession of the equinoxes.

[Sidenote: The magnitude and duration of the world, inscrutable.]

1. Consequent to the contemplation of sense is the contemplation of bodies, which are the efficient causes or objects of sense. Now every object is either a part of the whole world, or an aggregate of parts. The greatest of all bodies, or sensible objects, is the world itself; which we behold when we look round about us from this point of the same which we call the earth. Concerning the world, as it is one aggregate of many parts, the things that fall under inquiry are but few; and those we can determine, none. Of the whole world we may inquire what is its magnitude, what its duration, and how many there be, but nothing else. For as for place and time, that is to say, magnitude and duration, they are only our own fancy of a body simply so called, that is to say, of a body indefinitely taken, as I have shown before in chapter VII. All other phantasms are of bodies or objects, as they are distinguished from one another; as colour, the phantasm of coloured bodies; sound, of bodies that move the sense of hearing, &c. The questions concerning the magnitude of the world are whether it be finite or infinite, full or not full; concerning its duration, whether it had a beginning, or be eternal; and concerning the number, whether there be one or many; though as concerning the number, if it were of infinite magnitude, there could be no controversy at all. Also if it had a beginning, then by what cause and of what matter it was made; and again, from whence that cause and that matter had their being, will be new questions; till at last we come to one or many eternal cause or causes. And the determination of all these things belongeth to him that professeth the universal doctrine of philosophy, in case as much could be known as can be sought. But the knowledge of what is infinite can never be attained by a finite inquirer. Whatsoever we know that are men, we learn it from our phantasms; and of infinite, whether magnitude or time, there is no phantasm at all; so that it is impossible either for a man or any other creature to have any conception of infinite. And though a man may from some effect proceed to the immediate cause thereof, and from that to a more remote cause, and so ascend continually by right ratiocination from cause to cause; yet he will not be able to proceed eternally, but wearied will at last give over, without knowing whether it were possible for him to proceed to an end or not. But whether we suppose the world to be finite or infinite, no absurdity will follow. For the same things which now appear, might appear, whether the Creator had pleased it should be finite or infinite. Besides, though from this, that nothing can move itself, it may rightly be inferred that there was some first eternal movent; yet it can never be inferred, though some used to make such inference, that that movent was eternally immoveable, but rather eternally moved. For as it is true, that nothing is moved by itself; so it is true also that nothing is moved but by that which is already moved. The questions therefore about the magnitude and beginning of the world, are not to be determined by philosophers, but by those that are lawfully authorized to order the worship of God. For as Almighty God, when he had brought his people into Judæa, allowed the priests the first fruits reserved to himself; so when he had delivered up the world to the disputations of men, it was his pleasure that all opinions concerning the nature of infinite and eternal, known only to himself, should, as the first fruits of wisdom, be judged by those whose ministry he meant to use in the ordering of religion. I cannot therefore commend those that boast they have demonstrated, by reasons drawn from natural things, that the world had a beginning. They are contemned by idiots, because they understand them not; and by the learned, because they understand them; by both deservedly. For who can commend him that demonstrates thus? "If the world be eternal, then an infinite number of days, or other measures of time, preceded the birth of Abraham. But the birth of Abraham preceded the birth of Isaac; and therefore one infinite is greater than another infinite, or one eternal than another eternal; which," he says, "is absurd." This demonstration is like his, who from this, that the number of even numbers is infinite, would conclude that there are as many even numbers as there are numbers simply, that is to say, the even numbers are as many as all the even and odd together. They, which in this manner take away eternity from the world, do they not by the same means take away eternity from the Creator of the world? From this absurdity therefore they run into another, being forced to call eternity _nunc stans_, a standing still of the present time, or an abiding now; and, which is much more absurd, to give to the infinite number of numbers the name of unity. But why should eternity be called an abiding now, rather than an abiding then? Wherefore there must either be many eternities, or _now_ and _then_ must signify the same. With such demonstrators as these, that speak in another language, it is impossible to enter into disputation. And the men, that reason thus absurdly, are not idiots, but, which makes the absurdity unpardonable, geometricians, and such as take upon them to be judges, impertinent, but severe judges of other men's demonstrations. The reason is this, that as soon as they are entangled in the words _infinite_ and _eternal_, of which we have in our mind no idea, but that of our own insufficiency to comprehend them, they are forced either to speak something absurd, or, which they love worse, to hold their peace. For geometry hath in it somewhat like wine, which, when new, is windy; but afterwards though less pleasant, yet more wholesome. Whatsoever therefore is true, young geometricians think demonstrable; but elder not. Wherefore I purposely pass over the questions of infinite and eternal; contenting myself with that doctrine concerning the beginning and magnitude of the world, which I have been persuaded to by the holy Scriptures and fame of the miracles which confirm them; and by the custom of my country, and reverence due to the laws. And so I pass on to such things as it is not unlawful to dispute of.

[Sidenote: No place in the world empty.]

2. Concerning the world it is further questioned, whether the parts thereof be contiguous to one another, in such manner as not to admit of the least empty space between; and the disputation both for and against it is carried on with probability enough. For the taking away of vacuum, I will instance in only one experiment, a common one, but I think unanswerable.

Let A B (in fig. 1) represent a vessel, such as gardeners use to water their gardens withal; whose bottom B is full of little holes; and whose mouth A may be stopped with one's finger, when there shall be need. If now this vessel be filled with water, the hole at the top A being stopped, the water will not flow out at any of the holes in the bottom B. But if the finger be removed to let in the air above, it will run out at them all; and as; soon as the finger is applied to it again, the water will suddenly and totally be stayed again from running out. The cause whereof seems to be no other but this, that the water cannot by its natural endeavour to descend drive down the air below it, because there is no place for it to go into, unless either by thrusting away the next contiguous air, it proceed by continual endeavour to the hole A, where it may enter and succeed into the place of the water that floweth out, or else, by resisting the endeavour of the water downwards, penetrate the same and pass up through it. By the first of these ways, while the hole at A remains stopped, there is no possible passage; nor by the second, unless the holes be so great that the water, flowing out at them, can by its own weight force the air at the same time to ascend into the vessel by the same holes: as we see it does in a vessel whose mouth is wide enough, when we turn suddenly the bottom upwards to pour out the water; for then the air being forced by the weight of the water, enters, as is evident by the sobbing and resistance of the water, at the sides or circumference of the orifice. And this I take for a sign that all space is full; for without this, the natural motion of the water, which is a heavy body, downwards, would not be hindered.

[Sidenote: The arguments of Lucretius for vacuum invalid.]

3. On the contrary, for the establishing of vacuum, many and specious arguments and experiments have been brought. Nevertheless there seems to be something wanting in all of them to conclude it firmly. These arguments for vacuum are partly made by the followers of the doctrine of Epicurus; who taught that the world consists of very small spaces not filled by any body, and of very small bodies that have within them no empty space, which by reason of their hardness he calls _atoms_; and that these small bodies and spaces are every where intermingled. Their arguments are thus delivered by Lucretius.

And first he says, that unless it were so, there could be no motion. For the office and property of bodies is to withstand and hinder motion. If, therefore, the universe were filled with body, motion would everywhere be hindered, so as to have no beginning anywhere; and consequently there would be no motion at all. It is true that in whatsoever is full and at rest in all its parts, it is not possible motion should have beginning. But nothing is drawn from hence for the proving of vacuum. For though it should be granted that there is vacuum, yet if the bodies which are intermingled with it, should all at once and together be at rest, they would never be moved again. For it has been demonstrated above, in chap. IX, art. 7, that nothing can be moved but by that which is contiguous and already moved. But supposing that all things are at rest together, there can be nothing contiguous and moved, and therefore no beginning of motion. Now the denying of the beginning of motion, doth not take away present motion, unless beginning be taken away from body also. For motion may be either co-eternal, or concreated with body. Nor doth it seem more necessary that bodies were first at rest, and afterwards moved, than that they were first moved, and rested, if ever they rested at all, afterwards. Neither doth there appear any cause, why the matter of the world should, for the admission of motion, be intermingled with empty spaces rather than full; I say full, but withal fluid. Nor, lastly, is there any reason why those hard atoms may not also, by the motion of intermingled fluid matter, be congregated and brought together into compounded bodies of such bigness as we see. Wherefore nothing can by this argument be concluded, but that motion was either coeternal, or of the same duration with that which is moved; neither of which conclusions consisteth with the doctrine of Epicurus, who allows neither to the world nor to motion any beginning at all. The necessity, therefore, of vacuum is not hitherto demonstrated. And the cause, as far as I understand from them that have discoursed with me of vacuum, is this, that whilst they contemplate the nature of fluid, they conceive it to consist, as it were, of small grains of hard matter, in such manner as meal is fluid, made so by grinding of the corn; when nevertheless it is possible to conceive fluid to be of its own nature as homogeneous as either an atom, or as vacuum itself.

The second of their arguments is taken from weight, and is contained in these verses of Lucretius:

Corporis officium est quoniam premere omnia deorsum; Contra autem natura manet sine pondere inanis; Ergo, quod magnum est æque, leviusque videtur, Nimirum plus esse sibi declarat inanis.--I. 363-66.

That is to say, _seeing the office and property of body is to press all things downwards; and on the contrary, seeing the nature of vacuum is to have no weight at all; therefore when of two bodies of equal magnitude, one is lighter than the other, it is manifest that the lighter body hath in it more vacuum than the other_.

To say nothing of the assumption concerning the endeavour of bodies downwards, which is not rightly assumed, because the world hath nothing to do with downwards, which is a mere fiction of ours; nor of this, that if all things tended to the same lowest part of the world, either there would be no coalescence at all of bodies, or they would all be gathered together into the same place: this only is sufficient to take away the force of the argument, that air, intermingled with those his atoms, had served as well for his purpose as his intermingled vacuum.

The third argument is drawn from this, that lightning, sound, heat and cold, do penetrate all bodies, except atoms, how solid soever they be. But this reason, except it be first demonstrated that the same things cannot happen without vacuum by perpetual generation of motion, is altogether invalid. But that all the same things may so happen, shall in due place be demonstrated.

Lastly, the fourth argument is set down by the same Lucretius in these verses:

Duo de concursu corpora lata Si cita dissiliant, nempe aer omne necesse est, Inter corpora quod fuerat, possidat inane. Is porro quamvis circum celerantibus auris Confluat, haud poterit tamen uno tempore totum Compleri spatium; nam primum quemque necesse est Occupet ille locum, deinde omnia possideantur.--I. 385-91.

That is, _if two flat bodies be suddenly pulled asunder, of necessity the air must come between them to fill up the space they left empty. But with what celerity soever the air flow in, yet it cannot in one instant of time fill the whole space, but first one part of it, then successively all_. Which nevertheless is more repugnant to the opinion of Epicurus, than of those that deny vacuum. For though it be true, that if two bodies were of infinite hardness, and were joined together by their superficies which were most exactly plane, it would be impossible to pull them asunder, in regard it could not be done but by motion in an instant; yet, if as the greatest of all magnitudes cannot be given, nor the swiftest of all motions, so neither the hardest of all bodies; it might be, that by the application of very great force, there might be place made for a successive flowing in of the air, namely, by separating the parts of the joined bodies by succession, beginning at the outermost and ending at the innermost part. He ought, therefore, first to have proved, that there are some bodies extremely hard, not relatively as compared with softer bodies, but absolutely, that is to say, infinitely hard; which is not true. But if we suppose, as Epicurus doth, that atoms are indivisible, and yet have small superficies of their own; then if two bodies should be joined together by many, or but one only small superficies of either of them, then I say this argument of Lucretius would be a firm demonstration, that no two bodies made up of atoms, as he supposes, could ever possibly be pulled asunder by any force whatsoever. But this is repugnant to daily experience.

[Sidenote: Other arguments for the establishing of vacuum, invalid.]

4. And thus much of the arguments of Lucretius. Let us now consider the arguments which are drawn from the experiments of later writers.

I. The first experiment is this: that if a hollow vessel be thrust into water with the bottom upwards, the water will ascend into it; which they say it could not do, unless the air within were thrust together into a narrower place; and that this were also impossible, except there were little empty places in the air. Also, that when the air is compressed to a certain degree, it can receive no further compression, its small particles not suffering themselves to be pent into less room. This reason, if the air could not pass through the water as it ascends within the vessel, might seem valid. But it is sufficiently known, that air will penetrate water by the application of a force equal to the gravity of the water. If therefore the force, by which the vessel is thrust down, be greater or equal to the endeavour by which the water naturally tendeth downwards, the air will go out that way where the resistance is made, namely, towards the edges of the vessel. For, by how much the deeper is the water which is to be penetrated, so much greater must be the depressing force. But after the vessel is quite under water, the force by which it is depressed, that is to say, the force by which the water riseth up, is no longer increased. There is therefore such an equilibration between them, as that the natural endeavour of the water downwards is equal to the endeavour by which the same water is to be penetrated to the increased depth.

II. The second experiment is, that if a concave cylinder of sufficient length, made of glass, that the experiment may be the better seen, having one end open and the other close shut, be filled with quicksilver, and the open end being stopped with one's finger, be together with the finger dipped into a dish or other vessel, in which also there is quicksilver, and the cylinder be set upright, we shall, the finger being taken away to make way for the descent of the quicksilver, see it descend into the vessel under it, till there be only so much remaining within the cylinder as may fill about twenty-six inches of the same; and thus it will always happen whatsoever be the cylinder, provided that the length be not less than twenty-six inches. From whence they conclude that the cavity of the cylinder above the quicksilver remains empty of all body. But in this experiment I find no necessity at all of vacuum. For when the quicksilver which is in the cylinder descends, the vessel under it must needs be filled to a greater height, and consequently so much of the contiguous air must be thrust away as may make place for the quicksilver which is descended. Now if it be asked whither that air goes, what can be answered but this, that it thrusteth away the next air, and that the next, and so successively, till there be a return to the place where the propulsion first began. And there, the last air thus thrust on will press the quicksilver in the vessel with the same force with which the first air was thrust away; and if the force with which the quicksilver descends be great enough, which is greater or less as it descends from a place of greater or less height, it will make the air penetrate the quicksilver in the vessel, and go up into the cylinder to fill the place which they thought was left empty. But because the quicksilver hath not in every degree of height force enough to cause such penetration, therefore in descending it must of necessity stay somewhere, namely, there, where its endeavour downwards, and the resistance of the same to the penetration of the air, come to an equilibrium. And by this experiment it is manifest, that this equilibrium will be at the height of twenty-six inches, or thereabouts.

III. The third experiment is, that when a vessel hath as much air in it as it can naturally contain, there may nevertheless be forced into it as much water as will fill three quarters of the same vessel. And the experiment is made in this manner. Into the glass bottle, represented (in figure 2) by the sphere F G, whose centre is A, let the pipe B A C be so fitted, that it may precisely fill the mouth of the bottle; and let the end B be so near the bottom, that there may be only space enough left for the free passage of the water which is thrust in above. Let the upper end of this pipe have a cover at D, with a spout at E, by which the water, when it ascends in the pipe, may run out. Also let H C be a cock, for the opening or shutting of the passage of the water between B and D, as there shall be occasion. Let the cover D E be taken off, and the cock H C being opened, let a syringe full of water be forced in; and before the syringe be taken away, let the cock be turned to hinder the going out of the air. And in this manner let the injection of water be repeated as often as it shall be requisite, till the water rise within the bottle; for example, to G F. Lastly, the cover being fastened on again, and the cock H C opened, the water will run swiftly out at E, and sink by little and little from G F to the bottom of the pipe B.

From this phenomenon, they argue for the necessity of vacuum in this manner. The bottle, from the beginning, was full of air; which air could neither go out by penetrating so great a length of water as was injected by the pipe, nor by any other way. Of necessity, therefore, all the water as high as F G, as also all the air that was in the bottle before the water was forced in, must now be in the same place, which at first was filled by the air alone; which were impossible, if all the space within the bottle were formerly filled with air precisely, that is, without any vacuum. Besides, though some man perhaps may think the air, being a thin body, may pass through the body of the water contained in the pipe, yet from that other phenomenon, namely, that all the water which is in the space B F G is cast out again by the spout at E, for which it seems impossible that any other reason can be given besides the force by which the air frees itself from compression, it follows, that either there was in the bottle some space empty, or that many bodies may be together in the same place. But this last is absurd; and therefore the former is true, namely, that there was vacuum.

This argument is infirm in two places. For first, that is assumed which is not to be granted; and in the second place, an experiment is brought, which I think is repugnant to vacuum. That which is assumed is, that the air can have no passage out through the pipe. Nevertheless, we see daily that air easily ascends from the bottom to the superficies of a river, as is manifest by the bubbles that rise; nor doth it need any other cause to give it this motion, than the natural endeavour downwards of the water. Why, therefore, may not the endeavour upwards of the same water, acquired by the injection, which endeavour upwards is greater than the natural endeavour of the water downwards, cause the air in the bottle to penetrate in like manner the water that presseth it downwards; especially, seeing the water, as it riseth in the bottle, doth so press the air that is above it, as that it generateth in every part thereof an endeavour towards the external superficies of the pipe, and consequently maketh all the parts of the enclosed air to tend directly towards the passage at B? I say, this is no less manifest, than that the air which riseth up from the bottom of a river should penetrate the water, how deep soever it be. Wherefore I do not yet see any cause why the force, by which the water is injected, should not at the same time eject the air.

And as for their arguing the necessity of vacuum from the rejection of the water; in the first place, supposing there is vacuum, I demand by what principle of motion that ejection is made. Certainly, seeing this motion is from within outwards, it must needs be caused by some agent within the bottle; that is to say, by the air itself. Now the motion of that air, being caused by the rising of the water, begins at the bottom, and tends upwards; whereas the motion by which it ejecteth the water ought to begin above, and tend downwards. From whence therefore hath the enclosed air this endeavour towards the bottom? To this question I know not what answer can be given, unless it be said, that the air descends of its own accord to expel the water. Which, because it is absurd, and that the air, after the water is forced in, hath as much room as its magnitude requires, there will remain no cause at all why the water should be forced out. Wherefore the assertion of vacuum is repugnant to the very experiment which is here brought to establish it.

Many other phenomena are usually brought for vacuum, as those of _weather-glasses_, _æolipyles_, _wind-guns_, &c. which would all be very hard to be salved, unless water be penetrable by air, without the intermixture of empty space. But now, seeing air may with no great endeavour pass through not only water, but any other fluid body though never so stubborn, as quicksilver, these phenomena prove nothing. Nevertheless, it might in reason be expected, that he that would take away vacuum, should without vacuum show us such causes of these phenomena, as should be at least of equal, if not greater probability. This therefore shall be done in the following discourse, when I come to speak of these phenomena in their proper places. But first, the most general hypotheses of natural philosophy are to be premised.

And seeing that suppositions are put for the true causes of apparent effects, every supposition, except such as be absurd, must of necessity consist of some supposed possible motion; for rest can never be the efficient cause of anything; and motion supposeth bodies moveable; of which there are three kinds, _fluid_, _consistent_, and _mixed of both_. _Fluid_ are those, whose parts may by very weak endeavour be separated from one another; and _consistent_ those for the separation of whose parts greater force is to be applied. There are therefore degrees of consistency; which degrees, by comparison with more or less consistent, have the names of _hardness_ or _softness_. Wherefore a fluid body is always divisible into bodies equally fluid, as quantity into quantities; and soft bodies, of whatsoever degree of softness, into soft bodies of the same degree. And though many men seem to conceive no other difference of _fluidity_, but such as ariseth from the different magnitudes of the parts, in which sense dust, though of diamonds, may be called fluid; yet I understand by _fluidity_, that which is made such by nature equally in every part of the fluid body; not as dust is fluid, for so a house which is falling in pieces may be called fluid; but in such manner as water seems fluid, and to divide itself into parts perpetually fluid. And this being well understood, I come to my suppositions.

[Sidenote: Six suppositions for the salving of the phenomena of nature.]

5. First, therefore, I suppose that the immense space, which we call the world, is the aggregate of all bodies which are either consistent and visible, as the earth and the stars; or invisible, as the small atoms which are disseminated through the whole space between the earth and the stars; and lastly, that most fluid ether, which so fills all the rest of the universe, as that it leaves in it no empty place at all.

Secondly, I suppose with Copernicus, that the greater bodies of the world, which are both consistent and permanent, have such order amongst themselves, as that the sun hath the first place, Mercury the second, Venus the third, the Earth with the moon going about it the fourth, Mars the fifth, Jupiter with his attendants the sixth, Saturn the seventh; and after these, the fixed stars have their several distances from the sun.

Thirdly, I suppose that in the sun and the rest of the planets there is and always has been a simple circular motion.

Fourthly, I suppose that in the body of the air there are certain other bodies intermingled, which are not fluid; but withal that they are so small, that they are not perceptible by sense; and that these also have their proper simple motion, and are some of them more, some less hard or consistent.

Fifthly, I suppose with Kepler that as the distance between the sun and the earth is to the distance between the moon and the earth, so the distance between the moon and the earth is to the semidiameter of the earth.

As for the magnitude of the circles, and the times in which they are described by the bodies which are in them, I will suppose them to be such as shall seem most agreeable to the phenomena in question.

[Sidenote: Possible causes of the motions annual and diurnal; and of the apparent direction, station, and retrogradation of the planets.]

6. The causes of the different seasons of the year, and of the several variations of days and nights in all the parts of the superficies of the earth, have been demonstrated, first by Copernicus, and since by Kepler, Galileus, and others, from the supposition of the earth's diurnal revolution about its own axis, together with its annual motion about the sun in the ecliptic according to the order of the signs; and thirdly, by the annual revolution of the same earth about its own centre, contrary to the order of the signs. I suppose with Copernicus, that the diurnal revolution is from the motion of the earth, by which the equinoctial circle is described about it. And as for the other two annual motions, they are the efficient cause of the earth's being carried about in the ecliptic in such manner, as that its axis is always kept parallel to itself. Which parallelism was for this reason introduced, lest by the earth's annual revolution its poles should seem to be necessarily carried about the sun, contrary to experience. I have, in art. 10, chap. XXI, demonstrated, from the supposition of simple circular motion in the sun, that the earth is so carried about the sun, as that its axis is thereby kept always parallel to itself. Wherefore, from these two supposed motions in the sun, the one simple circular motion, the other circular motion about its own centre, it may be demonstrated that the year hath both the same variations of days and nights, as have been demonstrated by Copernicus.

For if the circle _a b c d_ (in fig. 3) be the ecliptic, whose centre is _e_, and diameter _a e c_; and the earth be placed in _a_, and the sun be moved in the little circle _f g h i_, namely, according to the order _f_, _g_, _h_, and _i_, it hath been demonstrated, that a body placed in _a_ will be moved in the same order through the points of the ecliptic _a_, _b_, _c_, and _d_, and will always keep its axis parallel to itself.

But if, as I have supposed, the earth also be moved with simple circular motion in a plane that passeth through _a_, cutting the plane of the ecliptic so as that the common section of both the planes be in _a c_, thus also the axis of the earth will be kept always parallel to itself. For let the centre of the earth be moved about in the circumference of the epicycle, whose diameter is _l a k_, which is a part of the strait line _l a c_; therefore _l a k_, the diameter of the epicycle, passing through the centre of the earth, will be in the plane of the ecliptic. Wherefore seeing that by reason of the earth's simple motion both in the ecliptic and in its epicycle, the strait line _l a k_ is kept always parallel to itself, every other strait line also taken in the body of the earth, and consequently its axis, will in like manner be kept always parallel to itself; so that in what part soever of the ecliptic the centre of the epicycle be found, and in what part soever of the epicycle the centre of the earth be found at the same time, the axis of the earth will be parallel to the place where the same axis would have been, if the centre of the earth had never gone out of the ecliptic.

Now as I have demonstrated the simple annual motion of the earth from the supposition of simple motion in the sun; so from the supposition of simple motion in the earth may be demonstrated the monthly simple motion of the moon. For if the names be but changed, the demonstration will be the same, and therefore need not be repeated.

[Sidenote: The supposition of simple motion, why likely.]

7. That which makes this supposition of the sun's simple motion in the epicycle _f g h i_ probable, is first, that the periods of all the planets are not only described about the sun, but so described, as that they are all contained within the zodiac, that is to say, within the latitude of about sixteen degrees; for the cause of this seems to depend upon some power in the sun, especially in that part of the sun which respects the zodiac. Secondly, that in the whole compass of the heavens there appears no other body from which the cause of this phenomenon can in probability be derived. Besides, I could not imagine that so many and such various motions of the planets should have no dependance at all upon one another. But, by supposing motive power in the sun, we suppose motion also; for power to move without motion is no power at all. I have therefore supposed that there is in the sun for the governing of the primary planets, and in the earth for the governing of the moon, such motion, as being received by the primary planets and by the moon, makes them necessarily appear to us in such manner as we see them. Whereas, that circular motion, which is commonly attributed to them, about a fixed axis, which is called conversion, being a motion of their parts only, and not of their whole bodies, is insufficient to salve their appearances. For seeing whatsoever is so moved, hath no endeavour at all towards those parts which are without the circle, they have no power to propagate any endeavour to such bodies as are placed without it. And as for them that suppose this may be done by magnetical virtue, or by incorporeal and immaterial species, they suppose no natural cause; nay, no cause at all. For there is no such thing as an incorporeal movent, and magnetical virtue is a thing altogether unknown; and whensoever it shall be known, it will be found to be a motion of body. It remains, therefore, that if the primary planets be carried about by the sun, and the moon by the earth, they have the simple circular motions of the sun and the earth for the causes of their circulations. Otherwise, if they be not carried about by the sun and the earth, but that every planet hath been moved, as it is now moved, ever since it was made, there will be of their motions no cause natural. For either these motions were concreated with their bodies, and their cause is supernatural; or they are coeternal with them, and so they have no cause at all. For whatsoever is eternal was never generated.

I may add besides, to confirm the probability of this simple motion, that as almost all learned men are now of the same opinion with Copernicus concerning the parallelism of the axis of the earth, it seemed to me to be more agreeable to truth, or at least more handsome, that it should be caused by simple circular motion alone, than by two motions, one in the ecliptic, and the other about the earth's own axis the contrary way, neither of them simple, nor either of them such as might be produced by any motion of the sun. I thought best therefore to retain this hypothesis of simple motion, and from it to derive the causes of as many of the phenomena as I could, and to let such alone as I could not deduce from thence.

It will perhaps be objected, that although by this supposition the reason may be given of the parallelism of the axis of the earth, and of many other appearances, nevertheless, seeing it is done by placing the body of the sun in the centre of that orb which the earth describes with its annual motion, the supposition itself is false; because this annual orb is eccentric to the sun. In the first place, therefore, let us examine what that eccentricity is, and whence it proceeds.

[Sidenote: The cause of the eccentricity of the annual motion of the earth.]

8. Let the annual circle of the earth _a b c d_ (in fig. 3) be divided into four equal parts by the strait lines _a c_ and _b d_, cutting one another in the centre _e_; and let _a_ be the beginning of Libra, _b_ of Capricorn, _c_ of Aries and _d_ of Cancer; and let the whole orb _a b c d_ be understood, according to Copernicus, to have every way so great distance from the zodiac of the fixed stars, that it be in comparison with it but as a point. Let the earth be now supposed to be in the beginning of Libra at _a_. The sun, therefore, will appear in the beginning of Aries at _c_. Wherefore, if the earth be moved from _a_ to _b_, the apparent motion of the sun will be from _c_ to the beginning of Cancer in _d_; and the earth being moved forwards from _b_ to _c_, the sun also will appear to be moved forwards to the beginning of Libra in _a_; wherefore _c d a_ will be the summer arch, and the winter arch will be _a b c_. Now, in the time, of the sun's apparent motion in the summer arch, there are numbered 186¾ days; and, consequently, the earth makes in the same time the same number of diurnal conversions in the arch _a b c_; and, therefore, the earth in its motion through the arch _c d a_ will make only 178½ diurnal conversions. Wherefore the arch _a b c_ ought to be greater than the arch _c d a_ by 8¼ days, that is to say, by almost so many degrees. Let the arch _a r_, as also _c s_, be each of them an arch of two degrees and 1⁄16. Wherefore the arch _r b s_ will be greater than the semicircle _a b c_ by 4⅛ degrees, and greater than the arch _s d r_ by 8¼ degrees. The equinoxes, therefore, will be in the points _r_ and _s_; and therefore also, when the earth is in _r_, the sun will appear in _s_. Wherefore the true place of the sun will be in _t_, that is to say, without the centre of the earth's annual motion by the quantity of the sine of the arch _a r_, or the sine of two degrees and 16 minutes. Now this sine, putting 100,000 for the radius, will be near 3580 parts thereof. And so much is the eccentricity of the earth's annual motion, provided that that motion be in a perfect circle; and _s_ and _r_ are the equinoctial parts. And the strait lines _s r_ and _c a_, produced both ways till they reach the zodiac of the fixed stars, will fall still upon the same fixed stars; because the whole orb _a b c d_ is supposed to have no magnitude at all in respect of the great distance of the fixed stars.

Supposing now the sun to be in _c_, it remains that I show the cause why the earth is nearer to the sun, when in its annual motion it is found to be in _d_, than when it is in _b_. And I take the cause to be this. When the earth is in the beginning of Capricorn at _b_, the sun appears in the beginning of Cancer at _d_; and then is the midst of summer. But in the midst of summer, the northern parts of the earth are towards the sun, which is almost all dry land, containing all Europe and much the greatest part of Asia and America. But when the earth is in the beginning of Cancer at _d_, it is the midst of winter, and that part of the earth is towards the sun, which contains those great seas called the South Sea and the Indian Sea, which are of far greater extent than all the dry land in that hemisphere. Wherefore by the last article of chapter XXI, when the earth is in _d_, it will come nearer to its first movent, that is, to the sun which is in _t_; that is to say, the earth is nearer to the sun in the midst of winter when it is in _d_, than in the midst of summer when it is in _b_; and, therefore, during the winter the sun is in its _Perigæum_, and in its _Apogæum_ during the summer. And thus I have shown a possible cause of the eccentricity of the earth; which was to be done.

I am, therefore, of Kepler's opinion in this, that he attributes the eccentricity of the earth to the difference of the parts thereof, and supposes one part to be affected, and another disaffected to the sun. And I dissent from him in this, that he thinks it to be by magnetic virtue, and that this magnetic virtue or attraction and thrusting back of the earth is wrought by immateriate species; which cannot be, because nothing can give motion but a body moved and contiguous. For if those bodies be not moved which are contiguous to a body unmoved, how this body should begin to be moved is not imaginable; as has been demonstrated in art. 7, chap. IX, and often inculcated in other places, to the end that philosophers might at last abstain from the use of such unconceivable connexions of words. I dissent also from him in this, that he says the similitude of bodies is the cause of their mutual attraction. For if it were so, I see no reason why one egg should not be attracted by another. If, therefore, one part of the earth be more affected by the sun than another part, it proceeds from this, that one part hath more water, the other more dry land. And from hence it is, as I showed above, that the earth comes nearer to the sun when it shines upon that part where there is more water, than when it shines upon that where there is more dry land.

[Sidenote: The cause why the moon hath always one and the same face turned towards the earth.]

9. This eccentricity of the earth is the cause why the way of its annual motion is not a perfect circle, but either an elliptical, or almost an elliptical line; as also why the axis of the earth is not kept exactly parallel to itself in all places, but only in the equinoctial points.

Now seeing I have said that the moon is carried about by the earth, in the same manner that the earth is by the sun; and that the earth goeth about the sun in such manner as that it shows sometimes one hemisphere, sometimes the other to the sun; it remains to be enquired, why the moon has always one and the same face turned towards the earth.

Suppose, therefore, the sun to be moved with simple motion in the little circle _f g h i_, (in fig. 4) whose centre is _t_; and let ♈ ♋ ♎ ♑ be the annual circle of the earth; and _a_ the beginning of Libra. About the point _a_ let the little circle _l k_ be described; and in it let the centre of the earth be understood to be moved with simple motion; and both the sun and the earth to be moved according to the order of the signs. Upon the centre _a_ let the way of the moon _m n o p_ be described; and let _q r_ be the diameter of a circle cutting the globe of the moon into two hemispheres, whereof one is seen by us when the moon is at the full, and the other is turned from us.

The diameter therefore of the moon _q o r_ will be perpendicular to the strait line _t a_. Wherefore the moon is carried, by reason of the motion of the earth, from _o_ towards _p_. But by reason of the motion of the sun, if it were in _p_ it would at the same time be carried from _p_ towards _o_; and by these two contrary movents the strait line _q r_ will be turned about; and, in a quadrant of the circle _m n o p_, it will be turned so much as makes the fourth part of its whole conversion. Wherefore when the moon is in _p_, _q r_ will be parallel to the strait line _m o_. Secondly, when the moon is in _m_, the strait line _q r_ will, by reason of the motion of the earth, be in _m o_. But by the working of the sun's motion upon it in the quadrant _p m_, the same _q r_ will be turned so much as makes another quarter of its whole conversion. When, therefore, the moon is in _m_, _q r_ will be perpendicular to the strait line _o m_. By the same reason, when the moon is in _n_, _q r_ will be parallel to the strait line _m o_; and, the moon returning to _o_, the same _q r_ will return to its first place; and the body of the moon will in one entire period make also one entire conversion upon her own axis. In the making of which, it is manifest, that one and the same face of the moon is always turned towards the earth. And if any diameter were taken in that little circle, in which the moon were supposed to be carried about with simple motion, the same effect would follow; for if there were no action from the sun, every diameter of the moon would be carried about always parallel to itself. Wherefore I have given a possible cause why one and the same face of the moon is always turned towards the earth.

But it is to be noted, that when the moon is without the ecliptic, we do not always see the same face precisely. For we see only that part which is illuminated. But when the moon is without the ecliptic, that part which is towards us is not exactly the same with that which is illuminated.

[Sidenote: The cause of the tides of the ocean.]

10. To these three simple motions, one of the sun, another of the moon, and the third of the earth, in their own little circles _f g h i_, _l k_, and _q r_, together with the diurnal conversion of the earth, by which conversion all things that adhere to its superficies are necessarily carried about with it, may be referred the three phenomena concerning the tides of the ocean. Whereof the first is the alternate elevation and depression of the water at the shores, twice in the space of twenty-four hours and near upon fifty-two minutes; for so it has constantly continued in all ages. The second, that at the new and full moons, the elevations of the water are greater than at other times between. And the third, that when the sun is in the equinoctial, they are yet greater than at any other time. For the salving of which phenomena, we have already the four above-mentioned motions; to which I assume also this, that the part of the earth which is called America, being higher than the water, and extended almost the space of a whole semicircle from north to south, gives a stop to the motion of the water.

This being granted, in the same 4th figure, where _l b k c_ is supposed to be in the plane of the moon's monthly motion, let the little circle _l d k e_ be described about the same centre _a_ in the plane of the equinoctial. This circle therefore will decline from the circle _l b k c_ in an angle of almost 28½ degrees; for the greatest declination of the ecliptic is 23½, to which adding 5 for the greatest declination of the moon from the ecliptic, the sum will be 28½ degrees. Seeing now the waters, which are under the circle of the moon's course, are by reason of the earth's simple motion in the plane of the same circle moved together with the earth, that is to say, together with their own bottoms, neither outgoing nor outgone; if we add the diurnal motion, by which the other waters which are under the equinoctial are moved in the same order, and consider withal that the circles of the moon and of the equinoctial intersect one another; it will be manifest, that both those waters, which are under the circle of the moon, and under the equinoctial, will run together under the equinoctial; and consequently, that their motion will not only be swifter than the ground that carries them; but also that the waters themselves will have greater elevation whensoever the earth is in the equinoctial. Wherefore, whatsoever the cause of the tides may be, this may be the cause of their augmentation at that time.

Again, seeing I have supposed the moon to be carried about by the simple motion of the earth in the little circle _l b k c_; and demonstrated, at the 4th article of chapter XXI, that whatsoever is moved by a movent that hath simple motion, will be moved always with the same velocity; it follows, that the centre of the earth will be carried in the circumference _l b k c_ with the same velocity with which the moon is carried in the circumference _m n o p_. Wherefore the time, in which the moon is carried about in _m n o p_, is to the time, in which the earth is carried about in _l b k c_, as one circumference to the other, that is, as _a o_ to _a k_. But _a o_ is observed to be to the semidiameter of the earth as 59 to 1; and therefore the earth, if _a k_ be put for its semidiameter, will make fifty-nine revolutions in _l b k c_ in the time that the moon makes one monthly circuit in _m n o p_. But the moon makes her monthly circuit in little more than twenty-nine days. Wherefore the earth shall make its circuit in the circumference _l b k c_ in twelve hours and a little more, namely, about twenty-six minutes more; that is to say, it shall make two circuits in twenty-four hours and almost fifty-two minutes; which is observed to be the time between the high-water of one day and the high-water of the day following. Now the course of the waters being hindered by the southern part of America, their motion will be interrupted there; and consequently, they will be elevated in those places, and sink down again by their own weight, twice in the space of twenty-four hours and fifty-two minutes. And thus I have given a possible cause of the diurnal reciprocation of the ocean.

Now from this swelling of the ocean in those parts of the earth, proceed the flowings and ebbings in the Atlantic, Spanish, British, and German seas; which though they have their set times, yet upon several shores they happen at several hours of the day. And they receive some augmentation from the north, by reason that the shores of China and Tartary, hindering the general course of the waters, make them swell there, and discharge themselves in part through the strait of Anian into the Northern Ocean, and so into the German Sea.

As for the spring tides which happen at the time of the new and full moons, they are caused by that simple motion, which at the beginning I supposed to be always in the moon. For as, when I showed the cause of the eccentricity of the earth, I derived the elevation of the waters from the simple motion of the sun; so the same may here be derived from the simple motion of the moon. For though from the generation of clouds, there appear in the sun a more manifest power of elevating the waters than in the moon; yet the power of increasing moisture in vegetables and living creatures appears more manifestly in the moon than in the sun; which may perhaps proceed from this, that the sun raiseth up greater, and the moon lesser drops of water. Nevertheless, it is more likely, and more agreeable to common observation, that rain is raised not only by the sun, but also by the moon; for almost all men expect change of weather at the time of the conjunctions of the sun and moon with one another and with the earth, more than in the time of their quarters.

In the last place, the cause why the spring tides are greater at the time of the equinoxes hath been already sufficiently declared in this article, where I have demonstrated, that the two motions of the earth, namely, its simple motion in the little circle _l b k c_, and its diurnal motion in _l d k e_, cause necessarily a greater elevation of waters when the sun is about the equinoxes, than when he is in other places. I have therefore given possible causes of the phenomenon of the flowing and ebbing of the ocean.

[Sidenote: Cause of the precession of the equinoxes.]

11. As for the explication of the yearly _precession of the equinoctial points_, we must remember that, as I have already shown, the annual motion of the earth is not in the circumference of a circle, but of an ellipsis, or a line not considerably different from that of an ellipsis. In the first place, therefore, this elliptical line is to be described.

Let the ecliptic ♎ ♑ ♈ ♋ (in fig. 5) be divided into four equal parts by the two strait lines _a b_ and ♑ ♋, cutting one another at right angles in the centre _c_. And taking the arch _b d_ of two degrees and sixteen minutes, let the strait line _d e_ be drawn parallel to _a b_, and cutting ♑ ♋ in _f_; which being done, the eccentricity of the earth will be _c f_. Seeing therefore the annual motion of the earth is in the circumference of an ellipsis, of which ♑ ♋ is the greater axis, _a b_ cannot be the lesser axis; for _a b_ and ♑ ♋ are equal. Wherefore the earth passing through _a_ and _b_, will either pass above ♑, as through _g_, or passing through ♑, will fall between _c_ and _a_; it is no matter which. Let it pass therefore through _g_; and let _g l_ be taken equal to the strait line ♑ ♋; and dividing _g l_ equally in _i_, _g i_ will be equal to ♑ _f_, and _i l_ equal to _f_ ♋; and consequently the point _i_ will cut the eccentricity _c f_ into two equal parts; and taking _i h_ equal to _i f_, _h i_ will be the whole eccentricity. If now a strait line, namely, the line ♎ _i_ ♈, be drawn through _i_ parallel to the strait lines _a b_ and _e d_, the way of the sun in summer, namely, the arch ♎ _g_ ♈, will be greater than his way in winter, by 8¼ degrees. Wherefore the true equinoxes will be in the strait line ♎ _i_ ♈; and therefore the ellipsis of the earth's annual motion will not pass through _a_, _g_, _b_, and _l_; but through ♎, _g_, ♈ and _l_. Wherefore the annual motion of the earth is in the ellipsis ♎ _g_ ♈ _l_; and cannot be, the eccentricity being salved, in any other line. And this perhaps is the reason, why Kepler, against the opinion of all the astronomers of former time, thought fit to bisect the eccentricity of the earth, or, according to the ancients, of the sun, not by diminishing the quantity of the same eccentricity, (because the true measure of that quantity is the difference by which the summer arch exceeds the winter arch), but by taking for the centre of the ecliptic of the great orb the point _c_ nearer to _f_, and so placing the whole great orb as much nearer to the ecliptic of the fixed stars towards ♋, as is the distance between _c_ and _i_. For seeing the whole great orb is but as a point in respect of the immense distance of the fixed stars, the two strait lines ♎ ♈ and _a b_, being produced both ways to the beginnings of Aries and Libra, will fall upon the same points of the sphere of the fixed stars. Let therefore the diameter of the earth _m n_ be in the plane of the earth's annual motion. If now the earth be moved by the sun's simple motion in the circumference of the ecliptic about the centre _i_, this diameter will be kept always parallel to itself and to the strait line _g l_. But seeing the earth is moved in the circumference of an ellipsis without the ecliptic, the point _n_, whilst it passeth through ♎ ♑ ♈, will go in a lesser circumference than the point _m_; and consequently, as soon as ever it begins to be moved, it will lose its parallelism with the strait line ♑ ♋; so that _m n_ produced will at last cut the strait line _g l_ produced. And contrarily, as soon as _m n_ is past ♈, the earth making its way in the internal elliptical line ♈ _l_ ♎, the same _m n_ produced towards _m_, will cut _l g_ produced. And when the earth hath almost finished its whole circumference, the same _m n_ shall again make a right angle with a line drawn from the centre _i_, a little short of the point from which the earth began its motion. And there the next year shall be one of the equinoctial points, namely, near the end of ♍; the other shall be opposite to it near the end of ♓. And thus the points in which the days and nights are made equal do every year fall back; but with so slow a motion, that, in a whole year, it makes but 51 first minutes. And this relapse being contrary to the order of the signs, is commonly called the _precession of the equinoxes_. Of which I have from my former suppositions deduced a possible cause; which was to be done.

According to what I have said concerning the cause of the eccentricity of the earth; and according to Kepler, who for the cause thereof supposeth one part of the earth to be affected to the sun, the other part to be disaffected; the apogæum and perigæum of the sun should be moved every year in the same order, and with the same velocity, with which the equinoctial points are moved; and their distance from them should always be the quadrant of a circle; which seems to be otherwise. For astronomers say, that the equinoxes are now, the one about 28 degrees gone back from the first star of Aries, the other as much from the beginning of Libra; so that the apogæum of the sun or the aphelium of the earth ought to be about the 28th degree of Cancer. But it is reckoned to be in the 7th degree. Seeing, therefore, we have not sufficient evidence of the ὁτί (that so it is,) it is in vain to seek for the διότι (why it is so.) Wherefore, as long as the motion of the apogæum is not observable by reason of the slowness thereof, and as long as it remains doubtful whether their distance from the equinoctial points be more or less than a quadrant precisely; so long it may be lawful for me to think they proceed both of them with equal velocity.

Also, I do not at all meddle with the causes of the eccentricities of Saturn, Jupiter, Mars, and Mercury. Nevertheless, seeing the eccentricity of the earth may, as I have shewn, be caused by the unlike constitution of the several parts of the earth which are alternately turned towards the sun, it is credible also, that like effects may be produced in these other planets from their having their superficies of unlike parts.

And this is all I shall say concerning Sidereal Philosophy. And, though the causes I have here supposed be not the true causes of these phenomena, yet I have demonstrated that they are sufficient to produce them, according to what I at first propounded.

[Illustration:

_Vol. 1. Lat. & Eng._ C. XXVI. _Fig. 1-5_ ]

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