NEWTON S PRINCIPIA. 297 



stratum whose density was equal to its own, were thus 

 dragged round the sun. Those planets which had satellites 

 were themselves the centres of smaller whirlpools in which 

 their secondaries revolved according to the same laws by 

 which they themselves were carried round the sun. The 

 ellipticity of the orbits were accounted for by supposing 

 the vortices themselves not circular. Such was the theory 

 as given by Descartes. It was open to so many ob 

 jections that it was greatly changed in character by his 

 successors. Newton proved that the original theory could 

 not be made to agree with Kepler s laws. Bernoulli* 

 imagined the vortices to be circular, and accounted for the 

 elliptic path of the planet by a combination of an os 

 cillatory movement with the circular motion of the whirl 

 pool. Bouguer then showed that the two portions of the 

 curve which the planet would describe in its oscillations 

 from aphelion to perihelion would not be equal or similar. 

 D Alembert showed that an elliptic vortex was, under the 

 circumstances of the case, impossible. The theory was 

 always unsatisfactory : all sorts of suppositions were made 

 in vain by Huygens, Perrault, Villemot, Mollieres, Ga- 

 maches, &c. They never could explain one phenomenon 

 without contradicting another. 



Newton of course considers the Cartesian theory as it 

 was originally given by its author. We shall confine our 

 selves within the same limits. The theory has no longer 

 any adherent, and there can be no advantage in attacking 

 that which no one defends. 



2. If the particles of a fluid did not exert any action on 

 each other, a vortex in which the velocity was any function 

 of the distance would be possible. For suppose the whole 

 fluid in any cylinder to be revolving round the axis ; 



* Montucla, ii. 327. 



