a philosopher, in the neighborhood of mount krapak, argued with me that motion is essential to matter.

“everything moves,” says he; “the sun continually revolves on its own axis; the planets do the same, and every planet has many different motions; everything is a sieve; everything passes through a sieve; the hardest metal is pierced with an infinity of pores, by which escapes a constant torrent of vapors that circulate in space. the universe is nothing but motion; motion, therefore, is essential to matter.”

“but, sir,” said i to him, “might not any one say, in answer to what you have advanced: this block of marble, this cannon, this house, this motion, are not in motion; therefore motion is not essential?”

“they do move,” he replied; “they move in space together with the earth by the common motion, and they move so incontestably — although insensibly — by their own peculiar motion, that, at the expiration of an indefinite number of centuries, there will remain not a single atom of the masses which now constitute them, from which particles are detaching themselves every passing moment.”

“but, my good sir, i can conceive matter to be in a state of rest; motion, therefore, cannot be considered essential to it.”

“why, certainly, it must be of vast consequence whether you conceive it to be, or conceive it not to be, in a state of rest. i still repeat, that it is impossible for it to be so.”

“this is a bold assertion; but what, let me ask you, will you say to chaos?”

“oh, chaos! if we were inclined to talk about chaos, i should tell you that all was necessarily in motion, and that ‘the breath of god moved upon the waters’; that the element of water was recognized in existence, and that the other elements existed also; that, consequently, fire existed; that there cannot be fire without motion, that motion is essential to fire. you will not succeed much with chaos.”

“alas! who can succeed with all these subjects of dispute? but, as you are so very fully acquainted with these things, i must request you to inform me why one body impels another: whether it is because matter is impenetrable, or because two bodies cannot be together in one place; or because, in every case of every description, the weak is driven before the strong?”

“your last reason is rather more facetious than philosophical. no person has hitherto been able to discover the cause of the communication of motion.”

“that, however, does not prevent its being essential to matter. no one has ever been able to discover the cause of sensation in animals; yet this sensation is so essential to them, that, if you exclude the idea of it, you no longer have the idea of an animal.”

“well, i will concede to you, for a moment, that motion is essential to matter — just for a moment, let it be remembered, for i am not much inclined to embroil myself with the theologians — and now, after this admission, tell me how one ball produces motion in another?”

“you are very curious and inquisitive; you wish me to inform you of what no philosopher ever knew.”

“it appears rather curious, and even ludicrous, that we should know the laws of motion, and yet be profoundly ignorant of the principle of the communication of motion!”

“it is the same with everything else; we know the laws of reasoning, but we know not what it is in us that reasons. the ducts through which our blood and other animal fluids pass are very well known to us, but we know not what forms that blood and those fluids. we are in life, but we know not in what the vital principle consists.”

“inform me, however, at least, whether, if motion be essential to matter, there has not always existed the same quantity of motion in the world?”

“that is an old chimera of epicurus revived by descartes. i do not, for my own part, see that this equality of motion in the world is more necessary than an equality of triangles. it is essential that a triangle should have three angles and three sides, but it is not essential that the number of triangles on this globe should be always equal.”

“but is there not always an equality of forces, as other philosophers express it?”

“that is a similar chimera. we must, upon such a principle, suppose that there is always an equal number of men, and animals, and moving beings, which is absurd.”

by the way, what, let me ask, is the force of a body in motion? it is the product of its quantity multiplied by its velocity in a given time. calling the quantity of a body four, and its velocity four, the force of its impulse will be equal to sixteen. another quantity we will assume to be two, and its velocity two; the force with which that impels is as four. this is the grand principle of mechanics. leibnitz decidedly and pompously pronounced the principle defective. he maintained that it was necessary to measure that force, that product, by the quantity multiplied by the square of the velocity. but this was mere captious sophistry and chicanery, an ambiguity unworthy of a philosopher, founded on an abuse of the discovery of the great galileo, that the spaces traversed with a motion uniformly accelerated were, to each other, as the squares of the times and velocities.

leibnitz did not consider the time which he should have considered. no english mathematician adopted his system. it was received for a while by a small number of geometricians in france. it pervaded some books, and even the philosophical institutions of a person of great celebrity. maupertuis is very abusive of mairan, in a little work entitled “a, b, c”; as if he thought it necessary to teach the a, b, c, of science to any man who followed the old and, in fact, the true system of calculation. mairan was, however, in the right. he adhered to the ancient measurement, that of the quantity multiplied by the velocity. he gradually prevailed over his antagonists, and his system recovered its former station; the scandal of mathematics disappeared, and the quackery of the square of the velocity was dismissed at last to the extramundane spaces, to the limbo of vanity, together with the monads which leibnitz supposed to constitute the concentric mirror of nature, and also with his elaborate and fanciful system of “pre-established harmony.”