GENERALIZATION OF PRINCIPLES. 357 



of the third law of motion, when the action is direct. This error was 

 retained even in the later editions of the Principia. h 



The question of the centre of oscillation had been proposed by Mer- 

 senne somewhat earlier, 6 in 1646. And though the problem was out 

 of the reach of any principles at that time known and understood, some 

 of the mathematicians of the day had rightly solved some cases of it, 

 by proceeding as if the question had been to find the Centre of Per- 

 cussion. The Centre of Percussion is the point about which the mo- 

 menta of all the parts of a body balance each other, when it is in motion 

 about any axis, and is stopped by striking against an obstacle placed 

 at that centre. Roberval found this point in some easy cases ; Des- 

 cartes also attempted the problem ; their rival labors led to an angry 

 controversy: and Descartes was, as in his physical speculations he 

 often was, very presumptuous, though not more than half right. 



Huyghens was hardly advanced beyond boyhood when Mersenne 

 first proposed this problem ; and, as he says, 7 could see no principle 

 which even offered an opening to the solution, and had thus been re- 

 pelled at the threshold. When, however, he published his Horologium 

 Oscillator ium in 1673, the fourth part of that work was on the Centre 

 of Oscillation or Agitation ; and the principle which he then assumed, 

 though not so simple and self-evident as those to which such problems 

 were afterwards referred, was perfectly correct and general, and led to 

 exact solutions in all cases. The reader has already seen repeatedly in 

 the course of this history, complex and derivative principles presenting 

 themselves to men's minds, before simple and elementary ones. The 

 "hypothesis" assumed by Huyghens was this; "that if any weights 

 are put in motion by the force of gravity, they cannot move so that 

 the centre 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 

 centre of gravity will, under all circumstances, rise as high as its ori- 

 ginal position ; and this consideration leads to a determination of the 

 oscillation of a compound pendulum. We may observe, in the prin- 

 ciple thus selected, a conviction that, in all mechanical action, the cen- 

 tre 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. 



5 B. iii. Lemma iii. to Prop, xxxix. « Mont. ii. 423. 



7 Ilor. Osc. Pref. e Hor. Osc. p. 121. 



