GENERALIZATION OF PRINCIPLES. 361 



as a subject for their prize dissertation the laws of the impact of bodies. 

 Bernoulli, as a competitor, wrote a treatise, upon Leibnitzian principles, 

 which, though not honored with the prize, was printed by the Academy 

 with commendation.' 4 The opinions which he here defended and 

 illustrated were adopted by several mathematicians ; the controversy 

 extended from the mathematical to the literary world, at that time 

 more attentive than usual to mathematical disputes, in consequence of 

 the great struggle then going on between the Cartesian and the New- 

 tonian system. It was, howevec, obvious that by this time the interest 

 of the question, so far as the progress of Dynamics was concerned, was 

 at an end ; for the combatants all agreed as to the results in each par- 

 ticular case. The Laws of Motion were now established ; and the 

 question was, by means of what definitions and abstractions could they 

 be best expressed ; a metaphysical, not a physical discussion, and 

 therefore one in which "the paper philosophers," as Galileo called 

 them, could bear a part. In the first volume of the Transactions of 

 the Academy of St. Petersburg, published in 1728, there are three 

 Leibuitzian memoirs by Hermann, Bullfinger, and Wolff. In England, 

 Clarke was an angry assailant of the German opinion, which S'Grave- 

 sande maintained. In France, Mairan attacked the vis viva in 172S ; 

 "with strong and victorious reasons," as the Marquise du Chatelet 

 declared, in the first edition of her Treatise on Fire. 1 * But shortly 

 after this praise was published, the Chateau de Cirey, where the 

 Marquise usually lived, became a school of Leibnitzian opinions, and 

 the resort of the principal partisans of the vis viva. " Soon," observes 

 Mairan, "their language was changed ; the vis viva was enthroned by 

 the side of the monads." The Marquise tried to retract or explain 

 away her praises; she urged arguments on the other side. Still the 

 question was not decided; even her friend Voltaire was not converted. 

 In 1741 he read a memoir On the Measure and Nature of Moviny 

 Forces, in which he maintained the old opinion. Finally, D'Alembert 

 in 1743 declared it to be, as it truly was, a mere question of words; 

 and by the turn which Dynamics then took, it ceased to be of any 

 possible interest or importance to mathematicians. 



The representation of the laws of motion and of the reasonings 

 depending on them, in the most general form, by means of analytical 

 language, cannot be said to have been fully achieved till the time of 

 D'Alembert; but as we have already seen, the discovery of these laws 



14 Discours sur Us Loix de la Communication da Mbuvemcnt. > 5 ilout. iii. 



