GENERALIZATION OF PRINCIPLES. 83 



tary ones. The " hypothesis" assumed by Huyghens 

 was this ; " that if any weights are put in motion 

 by the force of gravity, they can not move so that 

 the center of gravity of them all shall rise higher 

 than the place from which it descended." This 

 being assumed, it is easy to show that the center 

 of gravity will, under all circumstances, rise as 

 high as its original position ; and this consideration 

 leads to a determination of the oscillation of a 

 compound pendulum. We may observe, in the 

 principle thus selected, a conviction that, in all" 

 mechanical action, the center of gravity may be 

 taken as the representative of the whole system. 

 This conviction, as we have seen, may be traced 

 in the axioms of Archimedes and Stevinus; and 

 Huyghens, when he proceeds upon it, undertakes 

 to show 8 , that he assumes only this, that a heavy 

 body cannot, of itself, move upwards. 



Clear as Huyghens's principle appeared to him- 

 self, it was, after some time, attacked by the Abbe 

 Catelan, a zealous Cartesian. Catelan also put 

 forth principles which he conceived were evident, 

 and deduced from them conclusions contradictory 

 to those of Huyghens. His principles, now that 

 we know them to be false, appear to us very gra- 

 tuitous. They are these ; " that in a compound 

 pendulum, the sum of the velocities of the com- 

 ponent weights is equal to the sum of the velocities 

 which they would have acquired if they had been 

 8 Hor. Osc. p. 121. 



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