It was the usual error, however, of Leibnitz and his followers, to push the meta physical principles of science into extreme cases, where they lead to conclusions to which it was hardly possible to assent. The Academy of Sciences at Paris having pro posed as a prize question, the Investigation of the Laws of the Communication of Mo tion,' John Bernoulli presented an Essay on the subject, very ingenious and profound, 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, this conclusion was objected to, and D'Alembert, in his Eloge on the au thor, remarks, that, even in the collision of elastic bodies, it is difficult to conceive how, among the parts which first come into contact, a sudden change, or a change per saltuat, can be avoided. Indeed, it can only be avoided by supposing 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 restrictions, may be very use ful in our researches, and is often so, even to those who profess to reject its assistance. It is admitted that the law of continuity generally leads right, and if it sometimes lead wrong, the true business 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 in dications uncertain.
The discourse of Bernoulli, just referred to, brought another new conclusion into the field, and began a controversy among the mathematicians of Europe, which bated for many years. It was a new thing tp see geometers contending about the truths of their own science, and opposing one demonstration to another. The spectacle must have given pain to the true philosopher, but may have afforded consolation to many who had looked with envy on the certainty and quiet prevailing in a region from which they found themselves excluded.
Descartes lad estimated the force of a moving body, by the quantity of its motion, or by the product of its velocity into its mass. The mathematicians and philosophers who followed-him did the same, and the product of these quantities was the measure of force universally adopted. No one, indeed, had ever thought of questioning the con formity of this measure to the phenomena of nature, when, in 1686, Leibnitz announced in the Leipsic Journal the demonstration of a great error committed by Descartes and others, in estimating the force of moving bodies. In this paper, the author endea
voured to show, that the force of a moving body is not proportional to its velocity simply, but to the square of its velocity, and he supported this new doctrine by very plausible reasoning. A body, he says, projected upward against gravity, with a double velocity, ascends to four times the height ; with the triple velocity, to nine times the height, and so on ; the height ascended to being always as the square of the velocity. But the height ascended to is the effect, and is the natural measure of the force, therefore the force of a moving body is as the square of its velocity. Such was the first reasoning of Leibnitz on this subject,—simple, and apparently conclusive ; nor should it be.forgotten that, during the long period to which the dispute was lengthened out, and notwithstand ing the various shapes which it assumed, the reasonings on his side were nothing more than this original argument, changed in its form, or rendered more complex by the combination of new circumstances, so as to be more bewildering to the imagination, and more difficult either to apprehend or to refute.' John Bernoulli was at first of a different opinion from his friend and master, but came at length to adopt the same, which, however, appears to have gone no farther till the discourse was submitted to the Academy of Sciences, as has been already mentioned. The mathematical world could not look with indifference on a question which seemed to affect the vitals of mechanical science, and soon separated into two parties, in the arrangement of which, however, the effects of national predilection might easily be discovered. Germany, Holland, and Italy, declared for the vis viva; England stood firm for the old doctrine ; and France was divided betVgeen the two opinions. No contro versy, perhaps, was ever carried on by more illustrious disputants ; Maclaurin, Stir ling, Desaguliers, Jurin, Clarke, Mairan, were all engaged on the one side, and on the opposite were Bernoulli, Herman, Poleni, S'Gravesende, Musehenbroek ; and it was not till long after the period to which this part of the Dissertation is confined, that the debate could be said to be brought to a conclusion. That I may not, however, be obliged to break off a subject of which the parts are closely connected together, I shall take the liberty of transgressing the limits which the consideration of time would prescribe, and of now stating, as far as my plan admits of it, all that rhpects this ce lebrated controversy.