when the Lines produced as abovesaid are longer.

All the Planets, we know any thing of, obferve this Law; not only the primary Planets that revolve around the Sun, but the fecondary Planets alfo that revolve about fome primary, as do the Moon, and the Sattelites of Jupiter and Saturn; but here the Area's which are in proportion to the times, are Area's described about a primary Planet, which to its Satellites is as the Sun to the primary Planets. And hence the Orbit of a Planet, and the time of its Revolution being known, you may at every Inftant find the Place of the Planet.

Another Law gives you the Analogy between the periodical Time of each Planet, and its diftance from the Sun; a Law as fcrupulously obeyed as the former, which is that the Time a Planet takes in going round the Sun, is as the fquare Root of the Cube of its mean distance from the Sun.

This Law alfo extends to the secondary Planets; but in this Cafe the periodical Times and Distances, are to be taken from the primary Planets refpectively. By this Law, the distance of two Planets from the Sun, and the periodical Time of the one being given, you may investigate the periodical time of the other; or the periodical Times of two Planets, and the diftance of one of them being given, you may have the distance of the

other.

These

Thefe two Laws being laid down, it is not only fufficient that we fay in general why the Planets move round the Sun; we muft also fhew why they obferve thefe Laws; or at least what we advance, on their Motion, muft not be contradictory to these Laws.

Seeing that both the distances of the Planets from the Sun, and their periodical times are different; the Vortex cannot every where be of the fame Denfity, and the times of its Revolution not the fame every where.

As each Planet defcribes equal Area's in equal Times, it follows that the Beds of the Vortex Matter have their Velocities in a reciprocal Proportion to their distances from the Center.

But, because the periodical Times of the feveral Planets, are in proportion to the fquare Roots of the Cubes of their distances from the Sun, it follows that the Velocities of the fame Beds are in a reciprocal Proportion to the fquare Roots of their distances.

If one of thefe Laws be afcertained, the other becomes neceffarily incompatible. If we would have it that the Beds of the Vortex have the Velocities neceffary for each Planet to defcribe equal Area's about the Sun in equal times; it must follow, for Example, that Saturn would perform his Revolution in 90 Years, which is quite contrary to Experience.

вь.

If

If on the other hand we would indue the feveral Beds of the Vortex, with the Velocities required to make the Periodical Times proportional to the fquare Roots of the Cubes of the distances; we fhall find that the Area's defcribed by the Planets around the Sun will ceafe to be equal in equal Times.

I do not here fpeak of the Objections, raised against the Vortices, which do not feem invincible: nor do I fay any thing of that made by Sir Ifaac Newton, by fuppofing with Descartes, that the Vortex receives its Motion from the Sun, who revolving about his Axis, would communicate this Motion from Bed to Bed, to the utmost verge of the Vortex. Sir Ifaac had, by the Laws of Mechanics fought after the Velocities of the feveral Beds, and found them to be very different from thofe which quadrate with the Rule of Kepler, concerning the proportion between the Periodical times of the Planets, and their distances from the Sun. Bernoulli, in his fine Differtation which won the Academy's Prize, in the Year 1730, has fhewn that Sir Ifaac did not fufficiently confider feveral Things which alter the Calculation. It is true indeed that the faid Thing duly confidered, the Velocities of the feveral Beds are found to differ from what they ought to be for the com

pletion

pletion of this Law, but they come fomewhat nearer than before.

But let the Motion of the Vortex proceed from what Cause foever, the Velocities of the Beds might be brought to agree with one of the Laws we have mentioned; but never with both at the fame time; and yet thefe two Laws are the one as inviolable as the other.

* Vide

A&t. Eru

dit. 1689.

The more Learned have endeavoured to folve this Matter; but Leibnitz in particular could only fay that, throughout the Orbit defcribed by each Planet, there must be a p. 82. & Circulation he calls Harmonic; that is a 1706. p. certain Law of Velocity to make Planets 446. obferve the Law of defcribing equal Area's in equal Times; and that at the fame Time there must throughout the whole extent of the Vortex be a different Property of making the Planets obferve the Proportion between their Periodical Times, and their distances from the Sun: This is all one of the greatest Men of the Age could fay in Defence of the Vortician System.

Bulffinger, in the Differtation which won the Prize in 1728, acknowledges and better demonftrates the neceffity of this different Law in the Fluid which fweeps away the Planets. But it is hard to admit of thefe different circular Beds moving with independant and broken Velocities.

There is another Objection to this Syftem which is not of lefs weight: The feveral Beds of the Vortex, are nearly of the fame Denfities with their respective Planets, for each of the Planets fwims in its particular Bed; and thefe Beds move with prodigious Rapidity; yet we see that the Comets traverse them, without any fenfible alteration of their Course. The Comets themselves may as likely be hurried along by Fluids, which may circulate athwart the Fluids which convey the Planets, without confounding, or disturbing their Course.

Let us now proceed to the Doctrine of Gravity according to this Syftem.

CHA P. IV.

Of the Gravitation of Bodies towards the Earth, by Vortices.

A

LL Bodies fall, when not fuftained, and tend to the Center of the Earth. To explain this Phenomenon, Defcartes supposes a vortex of Fluid Matter to circulate with great velocity round the Earth, in a direction parallel with the Equator. It is well known that when a Body describes a

Circle,