First, when a body is moved with simple motion in a fluid medium which hath no vacuity, it changes the situation of all the parts of the fluid ambient which resist its motion; I say there are no parts so small of the fluid ambient, how far soever it be continued, but do change their situation in such manner, as that they leave their places continually to other small parts that come into the same.
For (in the same [second figure]) let any body, as K L M N, be understood to be moved with simple circular motion; and let the circle, which every point thereof describes, have any determined quantity, suppose that of the same K L M N. Wherefore the centre A and every other point, and consequently the moved body itself, will be carried sometimes towards the side where is K, and sometimes towards the other side where is M. When therefore it is carried to K, the parts of the fluid medium on that side will go back; and, supposing all space to be full, others on the other side will succeed. And so it will be when the body is carried to the side M, and to N, and every way. Now when the nearest parts of the fluid medium go back, it is necessary that the parts next to those nearest parts go back also; and supposing still all space to be full, other parts will come into their places with succession perpetual and infinite. Wherefore all, even the least parts of the fluid medium, change their places, &c. Which was to be proved.
It is evident from hence, that simple motion, whether circular or not circular, of bodies which make perpetual returns to their former places, hath greater or less force to dissipate the parts of resisting bodies, as it is more or less swift, and as the lines described have greater or less magnitude. Now the greatest velocity that can be, may be understood to be in the least circuit, and the least in the greatest; and may be so supposed, when there is need.
If a fluid be moved with simple circular motion, all the points taken in it will describe their circles in times proportional to the distances from the centre.
4. Secondly, supposing the same simple motion in the air, water, or other fluid medium; the parts of the medium, which adhere to the moved body, will be carried about with the same motion and velocity, so that in what time soever any point of the movent finishes its circle, in the same time every part of the medium, which adheres to the movent, shall also describe such a part of its circle, as is equal to the whole circle of the movent; I say, it shall describe a part, and not the whole circle, because all its parts receive their motion from an interior concentric movent, and of concentric circles the exterior are always greater than the interior; nor can the motion imprinted by any movent be of greater velocity than that of the movent itself. From whence it follows, that the more remote parts of the fluid ambient shall finish their circles in times, which have to one another the same proportion with their distances from the movent. For every point of the fluid ambient, as long as it toucheth the body which carries it about, is carried about with it, and would make the same circle, but that it is left behind so much as the exterior circle exceeds the interior. So that if we suppose some thing, which is not fluid, to float in that part of the fluid ambient which is nearest to the movent, it will together with the movent be carried about. Now that part of the fluid ambient, which is not the nearest but almost the nearest, receiving its degree of velocity from the nearest, which degree cannot be greater than it was in the giver, doth therefore in the same time make a circular line, not a whole circle, yet equal to the whole circle of the nearest. Therefore in the same time that the movent describes its circle, that which doth not touch it shall not describe its circle; yet it shall describe such a part of it, as is equal to the whole circle of the movent. And after the same manner, the more remote parts of the ambient will describe in the same time such parts of their circles, as shall be severally equal to the whole circle of the movent; and, by consequent, they shall finish their whole circles in times proportional to their distances from the movent; which was to be proved.
Simple motion dissipates heterogeneous and congregates
homogeneous bodies.
5. Thirdly, the same simple motion of a body placed in a fluid medium, congregates or gathers into one place such things as naturally float in that medium, if they be homogeneous; and if they be heterogeneous, it separates and dissipates them. But if such things as be heterogeneous do not float, but settle, then the same motion stirs and mingles them disorderly together. For seeing bodies, which are unlike to one another, that is, heterogeneous bodies, are not unlike in that they are bodies; for bodies, as bodies, have no difference; but only from some special cause, that is, from some internal motion, or motions of their smallest parts (for I have shown in chap. IX, [art. 9], that all mutation is such motion), it remains that heterogeneous bodies have their unlikeness or difference from one another from their internal or specifical motions. Now bodies which have such difference receive unlike and different motions from the same external common movent; and therefore they will not be moved together, that is to say, they will be dissipated. And being dissipated they will necessarily at some time or other meet with bodies like themselves, and be moved alike and together with them; and afterwards meeting with more bodies like themselves, they will unite and become greater bodies. Wherefore homogeneous bodies are congregated, and heterogeneous dissipated by simple motion in a medium where they naturally float. Again, such as being in a fluid medium do not float, but sink, if the motion of the fluid medium be strong enough, will be stirred up and carried away by that motion, and consequently they will be hindered from returning to that place to which they sink naturally, and in which only they would unite, and out of which they are promiscuously carried; that is, they are disorderly mingled.
Now this motion, by which homogeneous bodies are congregated and heterogeneous are scattered, is that which is commonly called fermentation, from the Latin fervere; as the Greeks have their Ζύμη, which signifies the same, from Ζέω ferveo. For seething makes all the parts of the water change their places; and the parts of any thing, that is thrown into it, will go several ways according to their several natures. And yet all fervour or seething is not caused by fire; for new wine and many other things have also their fermentation and fervour, to which fire contributes little, and sometimes nothing. But when in fermentation we find heat, it is made by the fermentation.
If a circle made by a movent moved with simple motion, be commensurable to another circle made by a point which is carried about by the same movent, all the points of both the circles will at some time return to the same situation.
6. Fourthly, in what time soever the movent, whose centre is A (in [fig. 2]) moved in K L N, shall, by any number of revolutions, that is, when the perimeters B I and K L N be commensurable, have described a line equal to the circle which passes through the points B and I; in the same time all the points of the floating body, whose centre is B, shall return to have the same situation in respect of the movent, from which they departed. For seeing it is as the distance B A, that is, as the radius of the circle which passes through B I is to the perimeter itself B I, so the radius of the circle K L N is to the perimeter K L N; and seeing the velocities of the points B and K are equal, the time also of the revolution in I B to the time of one revolution in K L N, will be as the perimeter B I to the perimeter K L N; and therefore so many revolutions in K L N, as together taken are equal to the perimeter B I, will be finished in the same time in which the whole perimeter B I is finished; and therefore also the points L, N, F and H, or any of the rest, will in the same time return to the same situation from which they departed; and this may be demonstrated, whatsoever be the points considered. Wherefore all the points shall in that time return to the same situation; which was to be proved.