A singular circumstance may be remarked in the whole of the dispute. The two parties who adopted such different measures of force when any mechanical problem was proposed concerning the action of bodies, whether at rest or in motion, resolved it in the same manner, and arrived exactly at the same conclusions. It was there fore evident, that, however much their language and words were opposed, their ideas or opinions exactly agreed. In reality, the two parties were not at issue on the question ; their positions, though seemingly opposite, were not contrary to one another ; and after debating for nearly thirty years, they found out this to be the truth. That the first men in the scientific world should have disputed so long with one another, without discovering that their opposition was only in words, and that this should have happened, not in any of the obscure and tortuous tracts through which the human mind must grope its way in anxiety and doubt, but in one of the clearest and straightest roads, where it used to be guided by the light of demonstration, is one of the most singular facts in the history of human knowledge.
The degree of acrimony and illiberality which were sometimes mixed in this con troversy was not very creditable to the disputants, and proved how much more men take an interest in opinions as being their own, than as being simply in themselves either true or false. The dispute, as conducted by S'Gravesende and Clarke, took this turn, especially on the part of the latter, who, in the schools of theology having sharp ened both his temper and his wit, accompanied his reasonings with an insolence and irritability peculiarly ill suited to a discussion about matter and motion. His pa per on this subject, in the Philosophical Transactions,' contains many just and acute remarks, accompanied with the most unfair representation of the argument of his antagonists, as if the doctrine of the vis viva were a matter of as palpable absurdity as the denial of one of the axioms of geometry.' Now, the truth is, that the argument in favour of living forces is not at all liable to this reproach. One of the effects produced by a moving body is the square of the velocity, while another is proportional to the velocity simply ; and, according to which of these ways the force itself is to be measured, may involve the propriety or impropriety of mathe matical language, but cannot be charged with absurdity or contradiction. Absurdity, indeed, was a reproach that neither side had any right to cast on the other.
A dissertation of Mairan, on the force of moving bodies, in the Memoires 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 opinions 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 A gnesi, was honourably enrolled in the annals of mathematical learning. Her writings on this subject are full of ingenui ty, though, from the fluctuations of her opinions, it seems as if she had not yet en tirely exchanged the caprice of fashion for the austerity of science. About the same time Voltaire engaged in the argument, and in a Diemoire,' presented to the Academy of Sciences in 1741, contended that the dispute was entirely about words. His reasoning is on the whole sound, and the suffrage of one who united the cha racter of a wit, a poet, and a philosopher, must be of great importance in a country where the despotism of fashion extends even to philosophical opinion.
The controversy was now drawing to a and in effect may be said to have been terminated by the publication of D'Alembert's Dynamique in 1743. I am not cer tain, however, that all the disputants acquiesced in this decision, at least till some years later. Dr. Reid, in an essay On Quantity, in the Philosophical Transactions for 1748, has treated of this controversy, and remarked, that it had been dropt rather than concluded. In this I confess I differ from the learned author. The controversy seemed fairly ended, the arguments exhausted, and the conclusion established, that the propositions maintained by both sides were true, and were not opposed to one another. Though the mathematical sciences cannot boast of never having had any debates, they can say that those that have arisen have always been brought to a satisfactory termi nation.
The observations with which I am to conclude the present sketch, are not precisely the same with those of the French philosopher, though they rest nearly on. the same foundation.
As the effects of moving bodies, or the changes they produce, may vary consider ably with accidental circumstances, we must, in order to measure their force, have re course to effects which are uniform, and not under the influence of variable causes. First, we may measure the force of one moving body by its effect upon another moving body; and here there is no room for dispute, nor any doubt that the forces of such bodies are as the quantities of matter multiplied into the simple power of the velocities, because the forces of bodies in which these products are equal, are well known, if opposed, to destroy one another. Thus one effect of moving bodies affords a measure of their force, which does not vary as the square; but as the simple power of the velocity.