"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 ought to have considered. No English mathematician adopted

There is always an equality of active forces, under two limi❤ tations; first, that if a variable force, depending on the time or place of a body, influences its motion, it is no longer the sum of the forces that remains the same, but the sum of active forces with the addition of a certain variable quantity depending on that force. Secondly, that this equality of active forces ceases to exist as often as we are compelled to suppose a change which does not take place insensibly. Thus, the principle may be true as a mathematical principle and meet the definition, but not as a metaphysical principle.

VOL. V.

K

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 neigbourhood with its outcries in labour, 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.

We only ask here, from the censors of books, permission to transcribe from that which the Dominican missionary Labat, proveditor of the holy office, has written concerning the nails of the cross, into which it is more than probable no nail was ever driven.

"The Italian priest who conducted us had sufficient interest to get us, among other things, a sight of the nails with which our Saviour was fastened to the cross. They appeared to me very different from those which the Benedictines show at St. Denis. Possibly those belonging to St. Denis served for the feet, and the others for the hands. It was necessary that those for the hands should be sufficiently large and strong to support all the weight of the body. However, the Jews must either have made use of more than four nails, or some of those which are shown to the faithful are not genuine. History relates, that St. Helena threw one of them into the sea, to appease a furious tempest which assailed the ship in which she had embarked. Constantine made use of another, to make a bit for the bridle of his horse. One is shown entire at St. Denis in France; another also entire at the Holy Cross of Jerusalem at Rome. A very celebrated Roman author of our day asserts, that the iron crown with which they crown the emperors in Italy was made out of one of these nails. We are shown at Rome and at Carpentras two bridle bits also made of these nails, not to mention more at other places. To be sure, several of them are discreet enough to say, that it is the head or point only of these nails which they exhibit."

The missionary speaks in the same tone of all the relics. He observes in the same passage, that when the body of the first deacon St. Stephen was brought from Jerusalem to Rome, in 557, and placed in the tomb of the deacon of St. Lawrence, "St. Lawrence made way of himself to give the right hand to his

predecessor; an action which procured him the name of the civil Spaniard." *

Upon this passage we venture only one reflection, which is, that if some philosopher had said as much, in the Encyclopædia, as the Dominican Labat, a crowd of Pantouillets, Nonottes, Chiniacs, Chaumeix, and other knaves, would have exclaimed-Deist, atheist, and geometrician! According to circumstances things change their names.

Selon ce que l'on peut être

Les choses changent de nom.

NATURE.

Amphytrion-Prologue.

Dialogue between the Philosopher and Nature.

THE PHILOSOPHER.

WHAT are you, Nature? I live in you; but I have been searching for you for fifty years, and have never yet been able to find you.

NATURE.

The ancient Egyptians, whose lives it is said extended to twelve hundred years, attached the same reproach to me. They called me Isis; they placed a thick veil over my head; and they said that no one could ever raise it.

PHILOSOPHER.

It is on that account that I apply immediately to yourself. I have been able to measure some of your globes, to ascertain their courses, and to point out the laws of motion; but I have never been able to ascertain what you are yourself.

Are you always active? Are you always passive? Do your elements arrange themselves, as water places itself over sand, oil over water, and air over oil? Have

This same missionary Labat, who never fails to fall rudely on the relics and miracles of the other monks, speaks with a noble assurance of all the prodigies and pre-eminences of the order of St. Dominic. No writer has carried conventual self-love so far. ás Labat.

you a mind which directs all your operations-as councils are inspired as soon as they meet, although the individual members composing them are often ignorant? Explain to me, I entreat, the enigma in which you are enveloped.

NATURE.

I am the great universal system. I know nothing farther. I am no mathematician, and yet everything in and about me is arranged agreeably to mathematical laws. Conjecture, if you can, how all this is effected.

PHILOSOPHER.

Certainly, since your great universal system knows nothing of mathematics, and yet the laws by which you aré regulated are those of the most profound geometry, there must necessarily be an eternal geometrician, who directs you, and presides over your operations.

NATURE.

You are perfeetly right; I am water, earth, fire, air, metal, mineral, stone, vegetable, and animal. clearly perceive that there is an intelligence in me: you possess an intelligence, although you see it not. Neither do I see mine; I feel this invisible power; I am unable to know it: why should you, who are only a very minute portion of myself, be anxious to know what I myself am ignorant of?

PHILOSOPHER.

We are curious. I should be pleased to learn how it is, that while so rough and coarse in your mountains, and deserts, and seas, you are at the same time so ingenious and finished in your animals and vegetables?

NATURE..

My poor child, shall I tell you the real truth? Is have had bestowed upon me a name that does not at all suit me: I am called nature, while I am all art.

PHILOSOPHER,

That word deranges all my ideas. What! is it possible that nature should be nothing but art?

NATURE.

It is undoubtedly the case. Do you not know that there is infinite art in those seas and mountains which you represent as so rough and so coarse? Do you not know