GENERALIZATION OF PRINCIPLES. 87 



principles which belong to this branch of mechanics. 

 But this assumption of Huyghens was an example 

 of a more general proposition, which by some 

 mathematicians at this time had been put forward 

 as an original and elementary law ; and as a prin- 

 ciple which ought to supersede the usual measure 

 of the forces of bodies in motion ; this principle 

 they called " the Conservation of Vis Viva." The 

 attempt to make this change was the commence- 

 ment of one of the most obstinate and curious of 

 the controversies which form part of the history 

 of mechanical science. The celebrated Leibnitz 

 was the author of the new opinion. In 1686, he 

 published, in the Leipsic Acts, "A short Demon- 

 stration of a memorable Errour of Descartes and 

 others, concerning the natural law by which they 

 think that God always preserves the same quantity 

 of motion ; in which they pervert mechanics." The 

 principle that the same quantity of motion, and 

 therefore of moving force, is always preserved in 

 the world, follows from the equality of action and 

 re-action ; though Descartes had, after his fashion, 

 given a theological reason for it ; Leibnitz allowed 

 that the quantity of moving force remains always 

 the same, but denied that this force is measured 

 by the quantity of motion or momentum. He 

 maintained that the same force is requisite to raise 

 a weight of one pound through four feet, and a 

 weight of four pounds through one foot, though 

 the momenta in this case are as one to two. This 



