[142] Dr. WHEWELL, ON THE TRANSFORMATION OF HYPOTHESES 



persons well acquainted with mechanical principles, satisfy themselves with this distinction ; 

 for they could hardly fail to see that the mechanical effect of any portion of fluid depends 

 upon the total mass moved, not on the size of its particles. 



Attempts made to exemplify the vortices experimentally only shewed more clearly the force 

 of this difficulty. Huyghens had found that certain bodies immersed in a whirling fluid 

 tended to the center of the vortex. But when Saulmon* a little later made similar experi- 

 ments, he had the mortification of finding that the heaviest bodies had the greatest tendency 

 to recede from the axis of the vortex. " The result is," as the Secretary of the Academy 

 (Fontenelle) says, " exactly the opposite of what we could have wished, for the [Cartesian] 

 system of gravity : but we are not to despair ; sometimes in such researches disappointment 

 leads to ultimate success." 



But, passing by this difficulty, and assuming that in some way or other a centripetal force 

 arises from the centrifugal force of the vortex, the Cartesian mathematicians were naturally led 

 to calculate the circumstances of the vortex on mechanical principles ; especially Huyghens, 

 who had successfully studied the subject of centrifugal force. Accordingly, in his little trea- 

 tise on the Cause of Gravitation, (p. 143) he calculates the velocity of the fluid matter of the 

 vortex, and finds that, at a point in the equator, it is 17 times the velocity of the earth's rotation. 



It may naturally be asked, how it comes to pass that a stream of fluid, dense enough to 

 produce the gravity of bodies by its centrifugal force, moving with a velocity 17 times that of 

 the earth (and therefore moving round the earth in 85 minutes), does not sweep all terrestrial 

 objects before it. But to this Huyghens had already replied (p. 137), that there are particles 

 of the fluid moving in all directions, and therefore that they neutralize each other's action, so 

 far as lateral motion is concerned. 



And thus, as early as this treatise of Huyghens, that is, in three years from the publica- 

 tion of Newton's Principia, a vortex is made to mean nothing more than some machinery or 

 other for producing a central force. And this is so much the case, that Huyghens commends 

 (p. 165), as confirming his own calculation of the velocity of his vortex, Newton's proof that 

 at the Moon's orbit the centripetal force is equal to the centrifugal ; and that thus, this force 

 is less than the centripetal force at the earth's surface in the inverse proportion of the squares 

 of the distances. 



John Bernoulli, in the same manner, but with far less clearness and less candour, has 

 treated the hypothesis of vortices as being principally a hypothetical cause of central force. 

 He had repeated occasions given him of propounding his inventions for propping up the 

 Cartesian doctrine, by the subjects proposed for prizes by the Paris Academy of Sciences ; in 

 which competition Cartesian speculations were favourably received. Thus the subject of the 

 Prize Essays for 1730 was, the explanation of the Elliptical Form of the planetary orbits and of 

 the Motion of their Aphelia, and the prize was assigned to John Bernoulli, who gave the 

 explanation on Cartesian principles. He explains the elliptical figure, not as Descartes him- 

 self had done, by supposing the vortex which carries the planet round the sun to be itself 

 squeezed into an elliptical form by the pressure of contiguous vortices ; but he supposes the 

 planet, while it is carried round by the vortex, to have a limited oscillatory motion to and 



• Acad. Par. 1714. Hist. p. 106. 



