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." MOUNTAIN. The fable of the mountain which, after alarming the whole neighborhood with its outcries in labor, was ridiculed by all present when it became delivered of a mouse, is at once ancient and universal. The company, however, who thus gave way to ridicule were not a company of philosophers. Those who mocked should in reality have admired. A mountain's being delivered of a mouse was an event as extraordinary, and as worthy of admiration, as a mouse's being delivered of a mountain. A rock's producing a rat is a case absolutely prodigious, and the world never beheld anything approaching to such a miracle. All the worlds in the universe could not originate a fly. Thus, in cases where the vulgar mock, the philosopher admires; and where the vulgar strain their eyes in stupid astonishment, he often smiles. NAIL.