jkct.ii.] DISSERTATION SECOND. 55 



as if the doctrine of the vis viva were a matter of as palpa- 

 ble absurdity as the denial of one of the axioms of geometry. 1 

 Now, the truth is, that the argument in favour of living for- 

 ces is not at all liable to this reproach. One of the effects 

 produced by a moving body is proportional to the square of 

 the velocity, while another is proportional to the velocity 

 simply; and, according to which of these ways the force it- 

 self is to be measured, may involve the propriety or impro- 

 priety of mathematical language, but cannot be charged with 

 absurdity or contradiction. Absurdity, indeed, was a re- 

 proach that neither side had any right to cast on the other. 



A dissertation of Mairan, on the force of moving bodies, in 

 the Memoirs of the Academy of Sciences- for 1728, is one 

 of those in which the common measure of force is most ably 

 supported. Nevertheless, for a long time after this, the opi- 

 nions on that subject in France continued still to be divided. 

 In the list of the disputants we should hardly expect to find 

 a lady included, if we did not know that the name of Madame 

 du Chastellet, along with those of Hypatia and Agnesi, was 

 honourably enrolled in the annals of mathematical learning. 

 Her writings on this subject are full of ingenuity, though, from 



1 In all the arguments for the vis viva, this learned metaphysi- 

 cian saw nothing but a conspiracy formed against the Newtonian 

 philosophy. "An extraordinary instance," says he, " of the 

 maintenance of the most palpable absurdity we have had in late 

 years of very eminent mathematicians, Leibnitz, Bernoulli, Her- 

 man, Gravesende, who, in order to raise a dust of opposition 

 against the Newtonian philosophy, some years back insisted with 

 great eagerness on a principle which subverts all science, and 

 which easily may be made appear, even to an ordinary capacity, 

 to be contrary to the necessary and essential nature of things.' 1 

 This passage may serve as a proof of the spirit which pre- 

 vailed among the philosophers of that time, making them ascribe 

 such illiberal views to one another, and distorting so entirely 

 both their own reasoning and those of their adversaries. T] 

 spirit awakened by i [ -overy of fluxions h r :d rot yt 



sided. 



