From hence it follows, that if the perimeters B I and L K N be not commensurable, then all the points will never return to have the same situation or configuration in respect of one another.
If a sphere have simple motion, its motion will more dissipate heterogeneous bodies by how much it is more remote from the poles.
7. In simple motion, if the body moved be of a spherical figure, it hath less force towards its poles than towards its middle to dissipate heterogeneous, or to congregate homogeneous bodies.
Let there be a sphere (as in the [third figure]) whose centre is A and diameter B C; and let it be conceived to be moved with simple circular motion; of which motion let the axis be the strait line D E, cutting the diameter B C at right angles in A. Let now the circle, which is described by any point B of the sphere, have B F for its diameter; and taking F G equal to B C, and dividing it in the middle in H, the centre of the sphere A will, when half a revolution is finished, lie in H. And seeing H F and A B are equal, a circle described upon the centre H with the radius H F or H G, will be equal to the circle whose centre is A and radius A B. And if the same motion be continued, the point B will at the end of another half revolution return to the place from whence it began to be moved; and therefore at the end of half a revolution, the point B will be carried to F, and the whole hemisphere D B E into that hemisphere in which are the points L, K and F. Wherefore that part of the fluid medium, which is contiguous to the point F, will in the same time go back the length of the strait line B F; and in the return of the point F to B, that is, of G to C, the fluid medium will go back as much in a strait line from the point C. And this is the effect of simple motion in the middle of the sphere, where the distance from the poles is greatest. Let now the point I be taken in the same sphere nearer to the pole E, and through it let the strait line I K be drawn parallel to the strait line B F, cutting the arch F L in K, and the axis H L in M; then connecting H K, upon H F let the perpendicular K N be drawn. In the same time therefore that B comes to F the point I will come to K, B F and I K being equal and described with the same velocity. Now the motion in I K to the fluid medium upon which it works, namely, to that part of the medium which is contiguous to the point K, is oblique, whereas if it proceeded in the strait line H K it would be perpendicular; and therefore the motion which proceeds in I K has less power than that which proceeds in H K with the same velocity. But the motions in H K and H F do equally thrust back the medium; and therefore the part of the sphere at K moves the medium less than the part at F, namely, so much less as K N is less than H F. Wherefore also the same motion hath less power to disperse heterogeneous, and to congregate homogeneous bodies, when it is nearer, than when it is more remote from the poles; which was to be proved.
Coroll. It is also necessary, that in planes which are perpendicular to the axis, and more remote than the pole itself from the middle of the sphere, this simple motion have no effect. For the axis D E with simple motion describes the superficies of a cylinder; and towards the bases of the cylinder there is in this motion no endeavour at all.
If a simple circular motion of a fluid body be hindered by a body which is not fluid, the fluid body will spread itself upon the superficies of that body.
8. If in a fluid medium moved about, as hath been said, with simple motion, there be conceived to float some other spherical body which is not fluid, the parts of the medium, which are stopped by that body, will endeavour to spread themselves every way upon the superficies of it. And this is manifest enough by experience, namely, by the spreading of water poured out upon a pavement. But the reason of it may be this. Seeing the sphere A (in [fig. 3]) is moved towards B, the medium also in which it is moved will have the same motion. But because in this motion it falls upon a body not liquid, as G, so that it cannot go on; and seeing the small parts of the medium cannot go forwards, nor can they go directly backwards against the force of the movent; it remains, therefore, that they diffuse themselves upon the superficies of that body, as towards O and P; which was to be proved.
Circular motion about a fixed centre casteth off by the tangent such things as lie upon the circumference & stick not to it.
9. Compounded circular motion, in which all the parts of the moved body do at once describe circumferences, some greater, others less, according to the proportion of their several distances from the common centre, carries about with it such bodies, as being not fluid, adhere to the body so moved; and such as do not adhere, it casteth forwards in a strait line which is a tangent to the point from which they are cast off.
For let there be a circle whose radius is A B (in [fig. 4]); and let a body be placed in the circumference in B, which if it be fixed there, will necessarily be carried about with it, as is manifest of itself. But whilst the motion proceeds, let us suppose that body to be unfixed in B. I say, the body will continue its motion in the tangent B C. For let both the radius A B and the sphere B be conceived to consist of hard matter; and let us suppose the radius A B to be stricken in the point B by some other body which falls upon it in the tangent D B. Now, therefore, there will be a motion made by the concourse of two things, the one, endeavour towards C in the strait line D B produced, in which the body B would proceed, if it were not retained by the radius A B; the other, the retention itself. But the retention alone causeth no endeavour towards the centre; and, therefore, the retention being taken away, which is done by the unfixing of B, there will remain but one endeavour in B, namely, that in the tangent B C. Wherefore the motion of the body B unfixed will proceed in the tangent B C; which was to be proved.