PHILOSOPHICAL SOCIETY OF WASHINGTON. 87 



littles the labors of Newton, who should have made his discovery 

 (de novo from his own breast) by a geometrical process and not 

 from the observed facts ! 



But my principal object in referring to this curious fallacy was 

 to give an attempt of my own to show its fallacy by a " reductio ad 

 absurdum." 



I can prove by an entirely similar process, with equal plausibility, 

 that the force of gravity must vary inversely as the cubes of the dis- 

 tances. Instead of a pyramid take a cone. Let the centre of the 

 earth be the vertex of a cone. Place two spheres or molecules of 

 different sizes,* tangent to the cone, at different distances from the 

 vertex. Whatever the nature of gravity, its influence at the distance 

 of each sphere must be equally diffused throughout the solid contents or 

 volume of each sphere. Therefore its intensity or force will be as much 

 less at the greater sphere, as contrasted with its influence at the nearer 

 and smaller sphere, as the volume of the latter is to the volume of the 

 former. But these volumes or solid contents vary as the cubes of 

 their radii, or as the cubes of their distances from the vertex. 

 Therefore the force of gravity varies inversely as the cubes of the 

 distances. 



The oracular " Q. E. D." could have been placed to this fallacy 

 with full as much propriety as in the former case, for I have used 

 nearly identical words. Of course they are both pure assumptions. 

 Neither are mathematically true, and the one destroys the other, as 

 they are contradictory. But the first is true as arrived at by severe 

 induction from the observed facts. 



If I was a professor of logic, I should give these as specious ex- 

 amples of the danger of false premises, and of the ease with which 

 they could be manufactured. 



Indeed, the authors first named would imply that there could in 

 the science of mechanics be no central forces, no empirical laws. 

 Indeed, they would reduce the whole planetary system, the whole 

 cosmos, to a geometrical necessity; and they would lose that inter- 

 esting exposition in physical astronomy as to the wisdom and benefi- 

 cence exhibited in the planetary system as it exists. 



In the well-known discussion of central forces by Poisson, the 

 equation of the curve when referred to co-ordinate axes is ascer- 



* The word molecules, being now a favorite word with the physicists, might 

 suit the casuist a little better. 



