It was objected to the opinion of Leibnitz, that though the doubtA velocity would give four times the ascent, it ought not to be forgotten that it required twice the time : so that in a given time double the velocity would produce only, double the ascent, one part of the ascent with another. This argument was never satisfactorily answered ; and while we cannot help thinking that it ought to have been decisive of the question, we draw from it a conclusion different from that of D'Alembert; we cannot think the dispute a mere question of words. It must be granted that, for all purposes in which time is not an ele ment, the measure of the effect of a force may be the square of the velocity, as exemplified in the instance cited. But when is it that a mechanical effect can be properly estimated without reference to the time in which it is produced i The definition of the words measure and effect may thus without doubt be accommodated either to the idea of Leibnitz or of his opponents; and those who disputed on the ques tion without requiring exact definitions might degenerate into a mere question of words. But it ought to have been a question as to what was the proper meaning of the word effect, in the fundamental phrase " effect of a force," the proper explanation of which must precede all good reasoning in mechanics. If pressure be defined as that which
produces a certain effect [PRESSURE) on our senses, undoubtedly it is a known fact that uncounteracted pressure produces motion; but it is only elm] allowed to act for a finite time : consequently, the element of time is as essential to the conception of the phenomenon as that of pressure or motion. Height in a rectangle gives area ; but it would not therefore be allowable to measure that area by the height ; for there must be a base, or there is no rectaugle at all. But if pressure be merely considered as the cause of motion, and called force iu that sense, it is very difficult to see why the cause, which is only known by the effect, is to be measured by anything but the simple effect. Pro. bably this discussion gave rise to the chapter of the 5I4canique COeste; in which Laplace speculates upon what the laws of motion would have been if force had been as a function of the velocity, instead of as the simple velocity. 'We have never met with any one who could give us an intelligible account of the meaning of this investi gation.