For most of the seventeenth century, the accepted explanation for why the planets go round the Sun was that they are carried, like straws caught in a whirlpool.
This was not a fringe position. It was the view of the most influential philosopher in Europe, it was taught across France for a hundred years, and it had one enormous advantage over the theory that replaced it: it made sense.
What Descartes Proposed
René Descartes published his Principia Philosophiae in 1644, and his physics starts from a refusal. There is no such thing as empty space. Extension is the essence of matter, so wherever there is extension there is matter, and a vacuum is a contradiction in terms. The universe is a plenum, full to the edges.
Given that, motion has to be circulation, because in a full universe a body can only move if something else moves round to take its place. So the cosmos consists of vast circulating eddies of fine matter, which he called tourbillons, one around each star. The Sun sits at the centre of ours and the planets are simply swept along by the flow.
Gravity in this scheme is a consequence of the swirling. The fine celestial matter is more strongly flung outwards than coarse terrestrial matter is, so the coarse matter gets displaced towards the centre. Heavy things do not fall because they are attracted downwards. They fall because they are pushed down, by something being flung up past them.
Every effect is produced by contact between moving pieces of matter. Nothing acts on anything it is not touching. That was the whole point.
Why It Was Attractive, and Why Newton Was the One Being Weird
We are used to hearing that Descartes was wrong and Newton was right, which makes the fifty years of resistance to Newton look like stubbornness. It was not.
Newton’s proposal was that bodies attract each other across empty space, instantaneously, with nothing in between and no mechanism. To a seventeenth century natural philosopher this was not an unfamiliar theory. It was a step backwards into magic. The whole project of the scientific revolution had been to replace occult sympathies and influences with pushes and pulls between things in contact. Attraction at a distance is precisely what that project had been trying to eliminate.
Newton knew it, and never claimed otherwise. In the General Scholium added to the second edition in 1713 he wrote that he had not been able to discover the cause of gravity from the phenomena, and that he framed no hypotheses. In private he speculated about an ether that might transmit it, and got nowhere. He offered a law, not an explanation.
His title says what he thought about the alternative. Philosophiae Naturalis Principia Mathematica, the mathematical principles of natural philosophy, set against Descartes’ Principia Philosophiae. Same word, and the addition of the crucial one.
What Book II Is Actually For
The Principia has three books. Book I develops the mathematics of motion under central forces in a void. Book III applies it to the solar system. Book II sits between them and is the part almost nobody reads.
Book II is about motion in resisting fluids, and its purpose is destruction. It is roughly two hundred pages assembled to show that vortices cannot do what Descartes needed them to do.
The argument that finishes the job concerns periods. Newton analyses how a rotating fluid behaves when carried round by a central body, works out how the period of a particle in such a flow must vary with its distance, and gets that the period goes as the square of the distance.
Kepler’s third law, established from Tycho’s observations, says the square of the period goes as the cube of the distance, so the period goes as distance to the power of three halves.
Two and three halves are not the same number. A vortex, treated properly with the mathematics of fluids, does not reproduce the motions we actually observe in the sky. Descartes’ universe is qualitatively plausible and quantitatively wrong, and Newton ends the book by remarking that the hypothesis of vortices is beset with many difficulties.
He had two further arguments and they are both lethal.
Comets go the wrong way. Comets cross the planetary orbits at every angle, some of them travelling backwards relative to the planets, on paths tilted steeply out of the ecliptic. A single fluid eddy carrying everything round in one direction cannot contain an object moving against the current at sixty degrees to the plane. Newton kept coming back to comets because they are the observation a vortex cannot survive.
The planets would slow down. If space were full of fluid, orbiting bodies would meet resistance and their orbits would decay measurably. There is no sign of it. Book II’s careful treatment of resistance is what makes that objection quantitative rather than rhetorical.
Fifty Years of French Resistance
Britain accepted Newton quickly. France did not, and the reasons were partly national and partly serious.
Bernard le Bovier de Fontenelle, secretary of the Académie des Sciences, was still a Cartesian when he wrote Newton’s official eulogy in 1727. French physics textbooks taught vortices into the 1730s and beyond.
Voltaire, who had spent time in England and come back a convert, put the situation better than anyone in his Lettres philosophiques of 1734: a Frenchman arriving in London finds the world quite changed, because he left it full and finds it empty. In Paris the universe is composed of vortices of subtle matter, in London there is nothing of the kind. What acts as gravitation in London is a pushing in Paris.
Émilie du Châtelet’s French translation of the Principia, with her commentary, is what eventually made the book properly available in France, and it remains the standard French version.
How It Was Settled: By Measuring the Earth
What ended the argument was not philosophy. It was a survey.
The two theories make opposite predictions about the shape of the Earth. Newton’s, based on a rotating self gravitating fluid body, says the Earth must bulge at the equator and flatten at the poles. The Cartesian account, with the vortex squeezing the planet, implies the opposite: elongated at the poles, like a lemon.
This is testable. Measure the length of a degree of latitude at different places: on a flattened Earth a degree is longer near the poles, on an elongated one it is shorter. The Cassini family’s measurements in France appeared to support the lemon, which kept the Cartesians in business for years.
The Académie eventually sent two expeditions to settle it, one to Lapland under Maupertuis and one to Peru. They came back with an answer: the Earth is flattened. Voltaire congratulated Maupertuis as the great flattener of both the Earth and the Cassinis.
After that, vortices were finished, and it is worth noticing how they died. Not by being shown to be philosophically incoherent, which they were not, but by making a prediction about the length of a degree of latitude in Finland and getting it wrong.
Descartes Was Not Simply Wrong
Two things ought to be said in his favour.
The first is that his instinct about action at a distance was vindicated, eventually, by the other side. Nobody today thinks gravity is an instantaneous pull across a void. General relativity replaced it with the geometry of spacetime, which is a local, contact theory in which nothing acts on anything distant and the influence propagates at the speed of light. Descartes’ demand for a mechanism in the intervening medium was the right demand. He simply had no way of producing a correct one, and insisting on it for two centuries would have been worse than accepting Newton’s silence about causes.
The second is that his mathematics outlasted his physics. The coordinate geometry he invented is the language in which the refutation of his own cosmology is now written, and the equations of general relativity are written in his coordinates too.
Reading the Book That Did It
Book II is usually skipped, and it has a reputation for being the weakest part of the Principia, which is fair in one sense: several of its results on fluid resistance are wrong or superseded, and Newton rewrote parts of it repeatedly.
But its position in the work is not an accident, and reading it in place makes the design of the whole book clear. Newton proves what a central force does in a void, then spends two hundred pages showing that the leading alternative cannot account for the sky, and only then turns to the solar system. He is removing the competition before making his claim, and he is doing it in the most rigorous notation available to him for exactly that reason.
Our edition of the Principia includes Book II complete, vortices and all, which is where the argument with Descartes actually takes place rather than in any of the famous passages.
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