GENIUS. OF genius or demon, we have already spoken in the article ANGEL. It is not easy to know precisely whether the peris of the Persians were invented before the demons of the Greeks, but it is very probable. It may be, that the souls of the dead, called shades, manes, &c., passed for demons. Hercules, in Hesiod, says that a demon dictated his labours. "It is impossible for us to say, that demons are neither mortal or eternal, for all that has life either lives eternally, or loses the breath of life by death; and Apuleius has said, that as to time, the demons are eternal. What then remains, but that demons hold a medium situation, and have one quality higher and another lower than mankind; and as, of these two things, eternity is the only higher thing which they exclusively possess, to complete the allotted medium, what must be the lower, if not misery ?" This is powerful reasoning! As I have never seen any genii, demons, peris, or hobgoblins, whether beneficent or mischievous, I cannot speak of them from knowledge. I only relate what has been said by people who have seen them. The demon of Socrates had so great a reputation, that Apuleius, the author of the "Golden Ass," who was himself a magician of good repute, says in his Treatise on the Genius of Socrates, that a man must be without religion who denies it. You see that Apuleius reasons precisely like brothers Garasse and Among the Romans, the word genius Bertier, Thou dost not believe that was not used to express a rare talent, as which I believe; thou art therefore with- with us: the term for that quality was out religion. And the Jansenists have ingenium. We use the word genius insaid as much of brother Bertier, as well differently in speaking of the tutelar deas of all the world except themselves. {mon of a town of antiquity, or an artist, These demons, says the very religious or musician. The term genius seems to and filthy Apuleius, are intermediate have been intended to designate not great powers between ether and our lower talents generally, but those into which region. They live in our atmosphere, invention enters. Invention, above every and bear our prayers and merits to the thing, appeared a gift from the gods-this gods. They treat of succours and bene-ingenium, quasi ingenitum, a kind of fits, as interpreters and ambassadors. { divine inspiration. Now an artist, howPlato says, that it is by their ministry ever perfect he may be in his profession, that revelations, presages, and the mira- if he have no invention, if he be not oricles of magicians, are effected. "Cæterum ginal, is not considered a genius. He is sunt quædam divinæ media potestates, only inspired by the artists his predecesinter summum æthera, et infimas terras,sors, even when he surpasses them. in isto intersitæ æris spatio, per quas et It is very probable that many people desideria nostra et merita ad deos com- now play at chess better than the inventor meant. Hos Græco nomina demonias of the game, and that they might gain nuncupant. Inter terricolas cœli co- the prize of corn promised him by the lasque victores, hinc pecum, inde dono-Indian king. But this inventor was a rum: qui ultrò citroque portant, hinc petitiones, inde suppetias: ceu quidam utriusque interpretes, et salutigeri. Per hos eosdem, ut Plato in symposio autumat, cuncta denunctiata, et majorum varia miracula, omnesque præsagium species reguntur." St. Augustin has condescended to refate Apuleius in these words : genius, and those who might now gain the prize would be no such thing. Le Poussin, who was a great painter before he had seen any good pictures, had a genius for painting. Lulli, who never saw any good musician in France, had a genius for music. Which is the most desirable to possess, a genius without a master, or the attainment of perfection by imitating and surpassing the masters which precede us? If you put this question to artists, they will perhaps be divided; if you put it to the public, it will not hesitate. Do you like a beautiful Gobelin tapestry better than one made in Flanders at the commencement of the arts? Do you prefer modern masterpieces of engraving to the first wood-cuts? the music of the present day to the first airs, which resembled the Gregorian chaunt? the makers of the artillery of our time to the genius which invented the first cannon? every body will answer yes. All purchasers will say, I own that the inventor of the shuttle had more genius than the manufacturer who made my cloth, but my cloth is worth more than that of the inventor. In short, every one in conscience will confess, that we respect the geniuses who invented the arts, but that minds which perfect them are of more present benefit. French, English, and Spanish people, to feel this difference. We have said, that the particular genius of a man for an art is a different thing from his general talent; but this name is only given to a very superior ability. How many people have talent for poetry, music, and painting; yet it would be ridiculous to call them geniuses. Genius, conducted by taste, will never commit a gross fault. Racine, since his Andromache, Le Poussin, and Rameau, have never committed one. Genius, without taste, will often commit enormous errors; and, what is worse, it will not be sensible of them. But, properly speaking, is genius any-les. There is not a single well-detailed thing but capability? What is capability but a disposition to succeed in an art? Why do we say the genius of a language? It is, that every language, by its terminations, articles, participles, and shorter or longer words, will necessarily have exclusive properties of its own. By the genius of a nation is meant the character, manners, talents, and even vices, which distinguish one people from another. It is sufficient to see the map of all the Grand Turk's possessions in Asia; all is placed at random, excepting some few large towns, the crumbling remains of which are still existing. In the States of the Great Mogul something is known of the relative positions of Agra and Delhi; but from thence to the kingdom of Golconda everything is laid down at a venture. It is known that Japan extends from about the thirtieth to the fortieth degree of north latitude; there cannot be an error of more than two degrees, which are about fifty leagues; so that, relying on one of our best maps, a pilot would be in danger of losing his track or his life. Happily, that which has often been traced by geographers, according to their own fancy, in their closets, is rectified on the spot. In geography, as in morals. it is very difficult to know the world without going from home. But in As for the longitude, the first maps of the Jesuits determined it between the hundred and fifty-seventh and the hun- It is not with this department c: dred and seventy-fifth degree; whereas, knowledge as with the arts of poetry, it is now determined between the hun-music, and painting. The last works of dred and forty-sixth and the hundred and these kinds are often the worst. sixtieth. the sciences, which require exactness raChina is the only Asiatic country ofther than genius, the last are always the which we have an exact measurement; best, provided they are done with some because the Emperor Kam-hi employed degree of care. some astronomical Jesuits to draw exact maps, which is the best thing the Jesuitsography, in my opinion, is this :-your have done. Had they been content with measuring the earth, they would never have been proscribed. In our western world, Italy, France, Russia, England, and the principal towns of the other states, have been measured by the same method which was employed in China; but it was not until a very few years ago, that in France it was undertaken to form an entire topography. A company taken from the Academy of Sciences dispatched engineers or surveyors into every corner of the kingdom, to lay down even the meanest hamlet, the smallest rivalet, the hills, the woods, in their true places. Before that time, so confused was the topography, that on the eve of the battle of Fontenoi, the maps of the country being all examined, every one of them was found entirely defective. One of the greatest advantages of ge fool of a neighbour, and his wife almost as stupid, are incessantly reproaching you with not thinking as they think in the rue St. Jacques." See," say they, "what a multitude of great men have been of our opinion, from Peter the Lombard down to the Abbé Petit-pied. The whole universe has received our truths; they reign in the Faubourg St. Honoré, at Chaillot and at Etampes, at Rome and among the Uscoques." Take a map of the world; shew them all Africa, the empires of Japan, China, India, Turkey, Persia, and that of Russia, more extensive than was the Roman empire; make them pass their finger over all Scandinavia, all the north of Germany, the three kingdoms of Great Britain, the greater part of the Low Countries, and of Helvetia; in short make them observe, in the four great diIf a positive order had been sent from visions of the earth; and in the fifth, Versailles to an inexperienced general to which is as little known as it is great in give battle, and post himself as appeared extent, the prodigious number of races, most advisable from the maps, as some- who either never heard of those opinions, times happened in the time of the minis- or have combatted them, or have held ter Chamillars, the battle would infalli-them in abhorrence, and you will thus bly have been lost. oppose the whole universe to the Rue St. Jacques. A general who should carry on a war in the country of the Morlachians, or the Montenegrians, with no knowledge of places but from the maps, would be at as great a loss as if he were in the heart of Africa. You will tell them that Julius Cæsar, who extended his power much further than that street, did not know a word of all which they think so universal; and that our ancestors, on whom Julius They will then, perhaps, feel somewhat ashamed at having believed that the organ of St. Severin's church gave the tone to the rest of the world. GEOMETRY. Cæsar bestowed the lash, knew no more flower-bed half a foot from one another." of them than he did. The child wishes to know how many tulips there will be. He runs to the flower-bed with his tutor. The parterre is inundated, and only one side of the flower-bed appears. This side is thirty feet long; but the breadth is not known. The master in the first place easily makes him understand that these tulips must border the parterre at the distance of six inches from one another. Here are already sixty tulips for the first row on that side. There are to be six lines. The child sees that there will be six times sixty, or three hundred and sixty tulips. But what will be the breadth of this bed, which I cannot measure? It will evidently be six times six inches, which are three feet. THE late M. Clairaut conceived the idea of making young people learn the elements of geometry with facility. He wished to go back to the source, and to trace the progress of our discoveries and the occasions which produced them. This method appears agreeable and useful; but it has not been followed. It requires in the master a flexibility of mind which knows how to adapt itself, and an accommodating spirit which is rare among those who follow the routine of their profession. He knows the length and the breadth. He also wishes to know the superficies. Is it not true, his teacher asks him, that if you were to run a rule three feet long and one foot broad over this bed, from one end to the other, it would succes It must be acknowledged that Euclid is somewhat unattractive; a beginner cannot divine whither he is to be led. Euclid says, in his first book, that "if a straight line is divided into two equalsively have covered the whole? Here, and into two unequal parts, the squares of the unequal segments are double of the squares of half the line, and of the portion of it included between the points of intersection." then, we have the superficies; it is three times thirty. This piece of ground is ninety square feet. A few days after, the gardener stretches a cord lengthwise from one angle to the other; which cord divides the rectangle into two equal parts. This, says the pupil, is the same length as one of the two sides. TUTOR. No. It is longer. PUPIL. How? If I pass a line over this cross-line, which you call a diagonal, it will be no longer than the two others.When I form the letter N, is not this line, which joins the two straight strokes together, of the same height as they are? TUTOR. It is of the same height, but not of the same length; that is demonstrated. -Bring down this diagonal to one of the sides, and you will find that it exceeds it. PUPIL. that the two triangles which divide the And by how much precisely does it square are equal, and then, by tracing a exceed it? TUTOR. There are cases in which this can never be known; as it will never be known precisely what is the square root of five. PUPIL. But the square root of five is two and a fraction. TUTGR. very simple figure, leads him to a comprehension of the famous theorem which Pythagoras found established among the Indians, and which was known to the Chinese-that any figure constructed on the larger side of a right-angled triangle is equal to the two similar figures constructed on the other sides. If the young man wishes to measure But this fraction cannot be expressed the height of a tower, or the breadth of a in figures, since the square of a number river which he cannot approach, each composed of a whole number and a frac-theorem immediately has its application; tion cannot be a whole number. So, in and he learns geometry practically. geometry, there are lines, the relations of which cannot be expressed. PUPIL. Here, then, is a difficulty in my way. -What! shall I never know my accompts? Is there, then, nothing certain ? TUTOR. It is certain that this sloping line divides the quadrangle into two equal parts; { but it is no more surprising that this small remainder of the diagonal line has not a common measure with the sides, than that in arithmetic you cannot find the square root of five. You will not therefore the less know your accompts; for if an arithmetician { tells you that he owes you the square root of five crowns, you have only to reduce these five crowns into smaller pieces; as, for instance, into liards, and you will have twelve hundred of them; the square root of which is between thirty-four and thirty-five; so that you will make your reckoning within a liard. Nothing must be made a mystery in arithmetic or in geometry. If he had merely been told that the product of the extremes is equal to the product of the means, he would have found this nothing more than a sterile problem: but he knows that the shadow of this stick is to the height of the stick as the shadow of the neighbouring tower is to the height of the tower. If, then, the stick be five feet, and its shadow one, and the shadow of the tower is twelve feet, he says, as one is to five, so is twelve to the height of the tower; then it is sixty feet. He wants to know the properties of a circle. He knows that the exact measure of its circumference cannot be had. But this extreme exactness is unnecessary in practice. The unrolling of a circle is its measurement. He will know that, this circle being a sort of polygon, its area is equal to a triangle, the short side of which is the radius of the circle, and its base the mea{sure of the circumference. The circumferences of circles are to one another as their radii. These first openings sharpen the young Circles having the general properties man's wit. His master having told him of all similar rectilinear figures, and these that the diagonal of a square is incom-figures being to one another as the squares mensurable-not measurable by the of their corresponding sides, the areas of sides and the base, informs him that with the circles will also be proportional to this line, the value of which can never the squares of their radii. be known, he will nevertheless produce a square which shall be demonstrated to be double of any given square. Thus, as the square of the hypothenuse is equal to the squares of the two sides, a circle, of which this hypothenuse For this purpose, he first shows him is the radius, will be equal to two circles |