IN THE HISTORY OF SCIENCE. [143] 



from the center, produced by its being originally, not at the distance at which it would float in 

 equilibrium in the vortex, but above or below that point. On this supposition, the planet 

 would oscillate to and from the center, Bernoulli says, like the mercury when deranged in a 

 barometer : and it is evident that such an oscillation, combined with a motion round the center, 

 might produce an oval curve, either with a fixed or with a moveable aphelion. All this how- 

 ever merely amounts to a possibility that the oval may be an ellipse, not to a proof that it will 

 be so ; nor does Bernoulli advance further. 



It was necessary that the vortices should be adjusted in such a manner as to account for 

 Kepler's laws ; and this was to be done by making the velocity of each stratum of the vortex 

 depend in a suitable manner on its radius. The Abbe de Molieres attempted this on the 

 supposition of elliptical vortices, but could not reconcile Kepler's first two laws, of equal 

 elliptical areas in equal times, with his third law, that the squares of the periodic times are 

 as the cubes of the mean distances*. Bernoulli, with his circular vortices, could accommodate 

 the velocities at different distances so that they should explain Kepler's laws. He pretended 

 to prove that Newton's investigations respecting vortices (in the ninth Section of the Second Book 

 of the Principia) were mechanically erroneous ; and in truth, it must be allowed that, besides 

 several arbitrary assumptions, there are some errors of reasoning in them. But for the most 

 part, the more enlightened Cartesians were content to accept Newton's account of the motions 

 and forces of the solar system as part of their scheme ; and to say only that the hypothesis of 

 vortices explained the origin of the Newtonian forces ; and that thus theirs was a philosophy of a 

 higher kind. Thus it is asserted (Mem. Acad. 1734), that M. de Molieres retains the beautiful 

 theory of the Newton entire, only he renders it in a sort less Newtonian, by disentangling it 

 from attraction, and transferring it from a vacuum into a plenum. This plenum, though 

 not its native region, frees it from the need of attraction, which is all the better for it. These 

 points were the main charms of the Cartesian doctrine in the eyes of its followers ; — the getting 

 rid of attractions, which were represented as a revival of the Aristotelian " occult qualities," 

 "substantial forms," or whatever else was the most disparaging way of describing the bad philo- 

 sophy of the dark ages-f- ; — and the providing some material intermedium, by means of which 

 a body may affect another at a distance ; and thus avoid the reproach urged against the New- 

 tonians, that they made a body act where it was not. And we are the less called upon to deny 

 that this last feature in the Newtonian theory was a difficulty, inasmuch as Newton himself 

 was never unwilling to allow that gravity might be merely an effect produced by some ulterior 

 cause. 



With such admissions on the two sides, it is plain that the Newtonian and Cartesian 

 systems would coincide, if the hypothesis of vortices could be modified in such a way as to 

 produce the force of gravitation. All attempts to do this, however, failed : and even John 

 Bernoulli, the most obstinate of the mathematical champions of the vortices, was obliged to 



* Acad. Par. 1733. not account for the remarkable facts, that all the motions of the 



■f Acad. Sc. 1709. If we abandon the clear principles primary planets, all the motions of the satellites, and all the 



of mechanics, the writer says, " toute la lumiere que nous pou- I motions of rotation, including that of the sun, are in the same 



vons avoir est eteinte, et nous voila replonge"s de nouveau dans , direction, and nearly in the same plane ; facts which have been 



les anciennes ten cbres du Peripatetisme, dont le Ciel nous veuille 

 preserver!" 



It was also objected to the Newtonian system^ that it did 



urged by Laplace as so strongly recommending the Nebular 

 Hypothesis; and that hypothesis is, in truth , a hypothesis of 

 vortices respecting the origin of the system of the world. 



