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.

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:

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:

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.

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

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.

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.

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.

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.

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.

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.

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.

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 revolutionsrevolutions 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.