SEQUEL TO THE EPOCH OF NEWTON. 207 



may add, that it was modified by its mathematical 

 adherents in such a way as to remove most of the 

 objections to it. A vortex revolving about a center 

 could be constructed, or, at least it was supposed that 

 it could be constructed, so as to produce a tendency 

 of bodies to the center. In all cases, therefore, 

 where a central force acted, a vortex was supposed; 

 but in reasoning to the results of this hypothesis, 

 it was easy to leave out of sight all other effects of 

 the vortex, and to consider only the central force : 

 and when this was done, the Cartesian mathema- 

 tician could apply to his problems a mechanical 

 principle of some degree of consistency. This re- 

 flection 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 laboured. 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, 



