By this demonstration it is manifest, that circular motion about an unmoved axis shakes off and puts further from the centre of its motion such things as touch, but do not stick fast to its superficies; and the more, by how much the distance is greater from the poles of the circular motion; and so much the more also, by how much the things, that are shaken off, are less driven towards the centre by the fluid ambient, for other causes.
Such things as are moved with simple circular motion, beget simple circular motion.
10. If in a fluid medium a spherical body be moved with simple circular motion, and in the same medium there float another sphere whose matter is not fluid, this sphere also shall be moved with simple circular motion.
Let B C D (in [fig. 5]) be a circle, whose centre is A, and in whose circumference there is a sphere so moved, that it describes with simple motion the[the] perimeter B C D. Let also E F G be another sphere of consistent matter, whose semidiameter is E H, and centre H; and with the radius A H let the circle H I be described. I say, the sphere E F G will, by the motion of the body in B C D, be moved in the circumference H I with simple motion.
For seeing the motion in B C D (by [art. 4] of this chapter) makes all the points of the fluid medium describe in the same time circular lines equal to one another, the points E, H and G of the strait line E H G will in the same time describe with equal radii equal circles. Let E B be drawn equal and parallel to the strait line A H; and let A B be connected, which will therefore be equal and parallel to E H; and therefore also, if upon the centre B and radius B E the arch E K be drawn equal to the arch H I, and the strait lines A I, B K and I K be drawn, B K and A I will be equal; and they will also be parallel, because the two arches E K and H I, that is, the two angles K B E and I A H are equal; and, consequently, the strait lines A B and K I, which connect them, will also be equal and parallel. Wherefore K I and E H are parallel. Seeing, therefore, E and H are carried in the same time to K and I, the whole strait line I K will be parallel to E H, from whence it departed. And, therefore, seeing the sphere E F G is supposed to be of consistent matter, so as all its points keep always the same situation, it is necessary that every other strait line, taken in the same sphere, be carried always parallel to the places in which it formerly was. Wherefore the sphere E F G is moved with simple circular motion; which was to be demonstrated.
If that which is so moved have one side hard and the other side fluid, its motion will not be perfectly circular.
11. If in a fluid medium, whose parts are stirred by a body moved with simple motion, there float another body, which hath its superficies either wholly hard, or wholly fluid, the parts of this body shall approach the centre equally on all sides; that is to say, the motion of the body shall be circular, and concentric with the motion of the movent. But if it have one side hard, and the other side fluid, then both those motions shall not have the same centre, nor shall the floating body be moved in the circumference of a perfect circle.
Let a body be moved in the circumference of the circle K L M N (in [fig 2.]) whose centre is A. And let there be another body at I, whose superficies is either all hard or all fluid. Also let the medium, in which both these bodies are placed, be fluid. I say, the body at I will be moved in the circle I B about the centre A. For this has been demonstrated in the [last article].
Wherefore let the superficies of the body at I be fluid on one side, and hard on the other. And first, let the fluid side be towards the centre. Seeing, therefore, the motion of the medium is such, as that its parts do continually change their places, (as hath been shown in [art 5]); if this change of place be considered in those parts of the medium which are contiguous to the fluid superficies, it must needs be that the small parts of that superficies enter into the places of the small parts of the medium which are contiguous to them; and the like change of place will be made with the next contiguous parts towards A. And if the fluid parts of the body at I have any degree at all of tenacity (for there are degrees of tenacity, as in the air and water) the whole fluid side will be lifted up a little, but so much the less, as its parts have less tenacity; whereas the hard part of the superficies, which is contiguous to the fluid part, has no cause at all of elevation, that is to say, no endeavour towards A.
Secondly, let the hard superficies of the body at I be towards A. By reason, therefore, of the said change of place of the parts which are contiguous to it, the hard superficies must, of necessity, seeing by supposition there is no empty space, either come nearer to A, or else its smallest parts must supply the contiguous places of the medium, which otherwise would be empty. But this cannot be, by reason of the supposed hardness; and, therefore, the other must needs be, namely, that the body come nearer to A. Wherefore the body at I has greater endeavour towards the centre A, when its hard side is next it, than when it is averted from it. But the body in I, while it is moving in the circumference of the circle I B, has sometimes one side, sometimes another, turned towards the centre; and, therefore, it is sometimes nearer, sometimes further off from the centre A. Wherefore the body at I is not carried in the circumference of a perfect circle; which was to be demonstrated.