430 HISTORY OF PHYSICAL ASTRONOMY. 



easy to leave out of sight all other effects of the vortex, and to con- 

 sider only the central force ; and when this was done, the Cartesian 

 mathematician could apply to his problems a mechanical principle of 

 some degree of consistency. This reflection will, in some degree, 

 account for what at first seems so strange ; the fact that the language 

 of the French mathematicians is Cartesian, for almost half a century 

 after the publication of the Principia of Newton. 



There was, however, a controversy between the two opinions going 

 on all this time, and every day showed the insurmountable difficulties 

 under which the Cartesians labored. Newton, in the Principia, had 

 inserted a series of propositions, the object of which was to prove, that 

 the machinery of vortices could not be accommodated to one part of 

 the celestial phenomena, without contradicting another part. A more 

 obvious difficulty was the case of gravity of the earth ; if this force 

 arose, as Descartes asserted, from the rotation of the earth's vortex 

 about its axis, it ought to tend directly to the axis, and not to the 

 centre. The asserters of vortices often tried their skill in remedying 

 this vice in the hypothesis, but never with much success. Huyghens 

 supposed the ethereal matter of the vortices to revolve about the 

 centre in all directions ; Perrault made the strata of the vortex in- 

 crease in velocity of rotation as they recede from the centre ; Saurin 

 maintained that the circumambient resistance which comprises the 

 vortex will produce a pressure passing through the centre. The elliptic 

 form of the orbits of the planets was another difficulty. Descartes had 

 supposed the vortices themselves to be oval ; but others, as John Ber- 

 noulli, contrived ways of having elliptical motion in a circular vortex. 



The mathematical prize-questions proposed by the French Academy, 

 naturally brought the two sets of opinions into conflict. The Carte- 

 sian memoir of John Bernoulli, to which we have just referred, was 

 the one which gained the prize in 1730. It not unfrequently hap- 

 pened that the Academy, as if desirous to show its impartiality, di- 

 vided the prize between the Cartesians and Newtonians. Thus in 

 1734, the question being, the cause of the inclination of the orbits of 

 the planets, the prize was shared between John Bernoulli, whose Me- 

 moir was founded on the system of vortices, and his son Daniel, who 

 was a Newtonian. The last act of homage of this kind to the Carte- 

 sian system was performed in 1740, when the prize on the question of 

 the Tides was distributed between Daniel Bernoulli, Euler, Maclaurin, 

 and Cavallieri ; the last of whom had tried to patch up and amend 

 the Cartesian hypothesis on this subject. 



