sicT.n.J DISSERTATION SECOND. 51 



hardly possible to assent. The Academy of Sciences at Pa- 

 ris having proposed as a prize question, the Investigation oi 

 the Laws of the Communication of Motion,' John Bernoulli 

 presented an Essay on the subject, very ingenious and pro- 

 found, in which, however, he denied the existence of hard 

 bodies, because, in the collision of such bodies, a finite 

 change of motion must take place in an instant, an event 

 which, on the principle just explained, he maintained to be 

 impossible. Though the essay was admired, tliis conclusion 

 was objected to, and D'Alembert, in his Eloge on the author, 

 remarks, that, even in the collision of elastic bodies, itisdifli- 

 cult to conceive how, among the parts which first come into 

 contact, a sudden change, or a change per saltum, can be 

 avoided. Indeed, it can only be avoided by supposiug 

 that there is no real contact, and that bodies begin to act 

 upon one another when their surfaces, or what seems to 

 be their surfaces, are yet at a distance. 



Maclaurin and some others are disposed, on account of 

 the argument of Bernoulli, to reject the law of continuity 

 altogether. This, however, I cannot help thinking, is to 

 deprive ourselves of an auxiliary that, under certain re- 

 strictions, may be very useful in our researches, and is 

 often so, even to those who profess to reject its assist- 

 ance. It is admitted that the law of continuity generally 

 leads right, and if it sometimes lead wrong, the true bu- 

 siness of philosophy is to define when it may be trusted 

 to as a safe guide, and what, on the other hand, are the 

 circumstances which render its indications uncertain. 



The discourse of Bernoulli, just referred to, brought 

 another new conclusion into the field, and began a con- 

 troversy among the mathematicians of Europe, which last- 

 ed for many years. It was a new thing to see geome- 



' In 17-24. 



