III.

       CONVERSATION WITH A GEOMETRICIAN.

       Table of Contents

      It sometimes happens that a man has no answer to make, and yet is not persuaded. He is overthrown without the feeling of being convinced. He feels at the bottom of his heart a scruple, a repugnance, which hinders him from believing what has been proved to him. A geometrician demonstrates to you, that between a circle and a tangent, you may thread a number of curves, and yet cannot get one straight line to pass. Your eyes, your reason, tell you the contrary. The geometrician gravely answers you, that it is an infinitesimal of the second order. You stare in stupid silence, and quit the field all astonished, without having any clear idea, without comprehending anything, and without having any reply to make.

      Consult but a geometrician of more candor, and he explains the mystery to you.

      "We suppose," says he, "what cannot be in nature, lines which have length without breadth. Naturally and philosophically speaking, it is impossible for one real line to penetrate another. No curve, nor no right line can pass between two real lines that touch one another. These theorems that puzzle you are but sports of the imagination, ideal chimeras. Whereas true geometry is the art of measuring things actually existent."

      I was perfectly well satisfied with the confession of the sensible mathematician, and, with all my misfortune, could not help laughing on learning that there was a quackery even in that science, which is called the sublime science. My geometrician was a kind of philosophical patriot, who had deigned to chat with me sometimes in my cottage. I said to him:

      "Sir, you have tried to enlighten the cockneys of Paris, on a point of the greatest concern to mankind, that of the duration of human life. It is to you alone that the ministry owes its knowledge of the due rate of annuities for lives, according to different ages. You have proposed to furnish the houses in town with what water they may want, and to deliver us at length from the shame and ridicule of hearing water cried about the streets, and of seeing women inclosed within an oblong hoop, carrying two pails of water, both together of about thirty pounds weight, up to a fourth story. Be so good, in the name of friendship, to tell me, how many two-handed bipeds there may be in France?"

      THE GEOMETRICIAN.—It is assumed, that there may be about twenty millions, and I am willing to adopt this calculation as the most probable, till it can be verified, which it would be very easy to do, and which, however, has not hitherto been done, because one does not always think of every thing.

      THE MAN OF FORTY CROWNS.—How many acres, think you, the whole territory of France contains?

      THE GEOMETRICIAN.—One hundred and thirty millions, of which almost the half is in roads, in towns, villages, moors, heaths, marshes, sands, barren lands, useless convents, gardens of more pleasure than profit, uncultivated grounds, and bad grounds ill cultivated. We might reduce all the land which yields good returns to seventy-five millions of square acres; but let us state them at fourscore millions. One cannot do too much for one's country.

      THE MAN OF FORTY CROWNS.—How much may you think each acre brings in yearly, one year with another, in corn, seeds of all kinds, wine, fish-ponds, wood, metals, cattle, fruit, wool, silk, oil, milk, clear of all charges, without reckoning the tax?

      THE GEOMETRICIAN.—Why, if they produce each twenty-five livres, (about twenty English shillings), it is a great deal; but not to discourage our countrymen, let us put them at thirty livres. There are acres which produce constantly regenerating value, and which are estimated at three hundred livres: there are others which only produce three livres. The mean proportion between three and three hundred is thirty; for you must allow that three is to thirty as thirty is to three hundred. If, indeed, there were comparatively many acres at thirty livres, and very few at three hundred, our account would not hold good; but, once more, I would not be over punctilious.

      THE MAN OF FORTY CROWNS.—Well, sir; how much will these fourscore millions of acres yield of revenue, estimated in money?

      THE GEOMETRICIAN.—The account is ready made; they will produce two thousand four hundred millions of livres of the present currency.

      THE MAN OF FORTY CROWNS.—I have read that Solomon possessed, of his own property, twenty-five thousand millions of livres, in ready money; and certainly there are not two thousand four hundred millions of specie circulating in France, which, I am told, is much greater and much richer than Solomon's country.

      THE GEOMETRICIAN.—There lies the mystery. There may be about nine hundred millions circulating throughout the kingdom; and this money, passing from hand to hand, is sufficient to pay for all the produce of the land, and of industry. The same crown may pass ten times from the pocket of the cultivator, into that of the ale-housekeeper, and of the tax-gatherer.

      THE MAN OF FORTY CROWNS.—I apprehend you. But you told me that we are, in all, about twenty millions of inhabitants, men, women, old and young. How much, pray, do you allow for each?

      THE GEOMETRICIAN.—One hundred and twenty livres, or forty crowns.

      THE MAN OF FORTY CROWNS.—You have just guessed my revenue. I have four acres, which, reckoning the fallow years with those of produce, bring me in one hundred and twenty livres; which is little enough, God knows.

      But if every individual were to have his contingent, would that be no more than five louis d'ors a year?

      THE GEOMETRICIAN.—Certainly not, according to our calculation, which I have a little amplified. Such is the state of human nature. Our life and our fortune have narrow limits. In Paris, they do not, one with another, live above twenty-two or twenty-three years, and, one with another, have not, at the most, above a hundred and twenty livres a year to spend. So that your food, your raiment, your lodging, your movables, are all represented by the sum of one hundred and twenty livres.

      THE MAN OF FORTY CROWNS.—Alas! What have I done to you, that you thus abridge me of my fortune and life? Can it then be true, that I have but three and twenty years to live, unless I rob my fellow-creatures of their share?

      THE GEOMETRICIAN.—This is incontestable in the good city of Paris. But from these twenty-three years you must deduct ten, at the least, for your childhood, as childhood is not an enjoyment of life; it is a preparation; it is the porch of the edifice; it is the tree that has not yet given fruits; it is the dawn of a day. Then again, from the thirteen years which remain to you, deduct the time of sleep, and that of tiresomeness of life, and that will be at least a moiety. You will then have six years and a half left to pass in vexation, in pain, in some pleasures, and in hopes.

      THE MAN OF FORTY CROWNS.—Merciful heaven! At this rate, your account does not allow us above three years of tolerable existence.

      THE GEOMETRICIAN.—-That is no fault of mine. Nature cares very little for individuals. There are insects which do not live above one day, but of which the species is perpetual. Nature resembles those great princes, who reckon as nothing the loss of four hundred thousand men, so they but accomplish their august designs.

      THE MAN OF FORTY CROWNS.—Forty Crowns and three years of life! What resource can you imagine against two such curses?

      THE GEOMETRICIAN.—As to life, it would be requisite to render the air of Paris more pure—that men should eat less and take more exercise—that mothers should suckle their own children—that people should be no longer so ill-advised as to dread inoculation. This is what