Scholium

I have supposed the fluid to consist of matter of uniform density and fluidity.

A globe placed anywhere in the fluid may propagate with the same motion of its own, at distances from itself continually equal, similar and equal motions in the fluid in the same interval of time.

The matter, by its circular motion, endeavours to move away from the axis of the vortex. It thus presses all the matter that lies beyond.

This pressure makes:

• the attrition greater, and
• the separation of the parts more difficult

Consequently, it reduces the matter’s fluidity.

If the parts of the fluid are denser or larger in one place than the others, the fluidity will be less at that place. This is because there are fewer surfaces where the parts can be separated from each other.

In these cases, the fluidity’s defect is from the smoothness or softness of the parts, or some other condition.

Otherwise, the matter where it is less fluid will cohere more, and be more sluggish. It will receive the motion more slowly, and propagate it farther than agrees with the ratio above.

If the vessel be not spherical, the particles will move in lines not circular, but answering to the figure of the vessel.

The periodic times will be nearly as the squares of the mean distances from the centre.

In the parts between the centre and the circumference, the motions will be:

• slower where the spaces are wide
• swifter where they are narrow

But yet, the particles will not go to the circumference because of their greater speed.

This is because:

• they will then draw less curved arcs.
• the conatus of going away from the centre is as much reduced by the reduction of this curvature as it is augmented by the increase of the velocity.

As they go out of narrow into wide spaces, they go away a little farther from the centre.

But in doing so, they are retarded.

When they come out of wide into narrow spaces, they are again accelerated.

And so each particle is retarded and accelerated by turns forever.

These things will come to pass in a rigid vessel. This is because the state of vortices in an infinite fluid is known by Corollary 6.

This proposition investigates the properties of vortices to find whether celestial phenomena can be explained by them.

The periodic times of the planets revolving about Jupiter are in the sesquiplicate ratio of their distances from Jupiter’s centre.

The same rule accurately applies also to the planets that revolve about the sun.

Therefore if those planets are carried round in vortices revolving about Jupiter and the sun, the vortices must revolve according to that law.

But here we found the periodic times of the parts of the vortex to be in the duplicate ratio of the distances from the centre of motion.

This ratio cannot be diminished and reduced to the sesquiplicate, unless either:

• the matter of the vortex is more fluid the farther it is from the centre, or
• the resistance arising from the lack of lubricity in the fluid should be augmented with it in a greater ratio than that in which the velocity increases.
  • This is as the velocity that separates the parts of the fluid goes on increasing.

But neither of these suppositions are reasonable.

The more gross and less fluid parts will go to the circumference, unless they are heavy towards the centre.

For the sake of demonstration, I proposed a Hypothesis that the resistance is proportional to the velocity.

Nevertheless, the resistance is most probably in a less ratio than that of the velocity.

• In this case, the periodic times of the vortex will be in a greater than the duplicate ratio of the distances from its centre.

Some think that the vortices move:

• faster near the centre
• then slower to a certain limit
• then again faster near the circumference

In this case, no certain and determinate ratio can be obtained from the vortex.