GEOGRAPHY.

Happily, that which has often been traced by geographers, according to their the spot. own fancy, in their closets, is rectified on

difficult to know the world without going In geography, as in morals, it is very from home.

One of the greatest advantages of ge

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. As for the longitude, the first maps of the Jesuits determined it between the hundred and fifty-seventh and the hundred and seventy-fifth degree; whereas, knowledge as with the arts of poetry, It is not with this department of 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. But in sixtieth. China is the only Asiatic country ofther than genius, the last are always the the sciences, which require exactness rawhich 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 fool of a neighbour, and his wife almost measuring the earth, they would never have been proscribed. as stupid, are incessantly reproaching the rue St. Jacques.-"See," say they, you with not thinking as they think in been of our opinion, from Peter the "what a multitude of great men have Lombard down to the Abbé Petit-pied. The whole universe has received our truths; they reign in the Faubourg St. Rome and among the Uscoques." Take Honoré, at Chaillot and at Etampes, at Africa, the empires of Japan, China, a map of the world; shew them all India, Turkey, Persia, and that of Russia, more extensive than was the Roman emįpire; 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 visions of the earth; and in the fifth, make them observe, in the four great diextent, the prodigious number of races, which is as little known as it is great in who either never heard of those opinions, them in abhorrence, and you will thus or have combatted them, or have held St. Jacques. oppose the whole universe to the Rue

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 rivulet, 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.

If a positive order had been sent from Versailles to an inexperienced general to give battle, and post himself as appeared most advisable from the maps, as sometimes happened in the time of the minister Chamillars, the battle would infallibly have been lost.

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.

who extended his power much further
You will tell them that Julius Cæsar,
all which they think so universal; and
than that street, did not know a word of
that our ancestors, on whom Julius

Cesar bestowed the lash, knew no more flower-bed half a foot from one another." {fowerhild wish as o konw how many

of them than he did.

They will then, perhaps, feel some-tulips there will be. He runs to the what ashamed at having believed that the organ of St. Severin's church gave the tone to the rest of the world.

GEOMETRY.

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.

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.

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.

And by how much precisely does it square are equal, and then, by tracing a exceed it?

These first openings sharpen the young man's wit. His master having told him that the diagonal of a square is incommensurable not measurable by the sides and the base, informs him that with this line, the value of which can never 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

having for their radii the two other sides. The knowledge of this enables you to construct a basin of water as large as two other basins together.

The circle can be doubled exactly, though it cannot be exactly squared.

understands it no more than his pupil. Here Malezieux, in his Elements of Geometry, bursts into an extacy. He says positively, that there are incompatible truths. Would it not have been more simple to have said, that these lines have but one common point, on each side of which they separate.

I can always divide a number in thought; but does it thence follow that the number is infinite? Newton, in his integral, and in his differential calculation, does not use this great word; and Clairaut takes good care not to teach in his Elements of Geometry, that a hoop may be passed between a ball and the table on which it lies. A careful distinction should be made between useful and curi. ous geometry.

When accustomed thus to feel the advantages of geometrical truths, the pupil reads in some elements of this science, that if a straight line, called a tangent, be drawn touching a circle in one point, another straight line can never be made to pass between this circle and this line. This is evident enough, and was scarcely worth the trouble of saying. But it is added, that an infinite number of curve lines may be made to pass through this point of contact. This surprises him; and it would surprise older persons: he is tempted to believe that matter is pe- To the useful we owe the proportional netrable. The books tell him that this compasses, invented by Galileo, the meais not matter, that these are lines withoutsurement of triangles, that of solids, and breadth. But if they are without breadth, the circulation of moving forces. Most these metaphysical straight lines will pass other problems may enlighten and one upon another for ever without touch-strengthen the intellect; very few of them ing anything. If they have breadth no curve can pass. The child no longer knows where he is; he finds himself transported into a new world, which has nothing in common with our own.

will be of sensible utility to mankind. Square curves as long as you like—and while displaying extreme sagacity only resemble an arithmetician who examines the properties of his numbers, instead of calculating the amount of his own pro

How shall he believe, that what is manifestly impossible in nature, is true?perty. I well conceive, he will say to a master of the transcendental geometry, that all your circles will meet in C. But this is all you can demonstrate to me. You can never demonstrate that these circular lines pass at this point between the first circle and the tangent.

A secant A G may be shorter than another secant AG H:-granted; but it does not thence follow that your curve lines can pass between two lines which touch. They can pass, the master will reply, because the secant G H as distinguished from the secants A G, and A G H may be an "infiniment-petit" of the second order.

When Archimedes found the specific weight of bodies, he rendered a service to mankind: what service will you render by finding three numbers, so as that the difference of the squares of two of them, added to the cube of the three, will still be a square, and that the sum of the three differences added to the same cube, shall make another square? "Nugæ

difficiles."

GLORY-GLORIOUS.

SECTION I.

GLORY is reputation joined with esteer, and is complete when admiration superadded. It always supposes that which is brilliant in action, in virtue, or in talent, and the surmounting of great

I do not understand what "an infini-is ment-petit" is, says the child; and the master is obliged to acknowledge that he

difficulties. Cæsar, Alexander, had glory. in glory; but this is the case in no reli The same can hardly be said of Socrates.gion but ours. It is not allowable to say that Bacchus, or Hercules, was received into glory, when speaking of their apotheosis.

The saints and angels have sometimes been called the glorious, as dwelling in the abode of glory.

He claims esteem, reverence, pity, indignation against his enemies; but the term glory applied to him would be improper; his memory is venerable rather than glorious. Attila had much brilliancy, but he has no glory; for history, which may be mistaken, attributes to him no virtues : Gloriously is always taken in the good Charles XII. still has glory; for his sense; he reigned gloriously; he extrivalour, his disinterestedness, his liberal-cated himself gloriously from great danger ity, were extreme. Success is sufficient or embarrassment. for reputation, but not for glory. The glory of Henry IV. is every day increas-good, sometimes in the bad sense, acing; for time has brought to light all his cording to the nature of the object in virtues, which were incomparably greater question. He glories in a disgrace which than his defects. is the fruit of his talents and the effect of Glory is also the portion of inventors envy. We say of the martyrs, that they in the fine arts; imitators have only ap-glorified God-that is, that their conplause. It is granted too to great talents, stancy made the God whom they attested but in sublime arts only. We may well revered by men. say, the glory of Virgil, or of Cicero, but not of Martial, nor of Aulus Gellius.

Men have dared to say, the glory of God: God created the world for his glory; not that the Supreme Being can have glory; but that men, having no expressions suitable to him, use for him those by which they are themselves most flattered.

To glory in, is sometimes taken in the

SECTION II.

That Cicero should love glory, after having stifled Catiline's conspiracy, may be pardoned him.

That the King of Prussia, Frederic the Great, should have the same feelings after Rosbach and Lissa, and after being the legislator, the historian, the poet, and the philosopher of his country- that he should be passionately fond of glory, and at the same time, have self-command enough to be modestly so he will, on that account, be the more glorified.

That the Empress Catherine II. should

Vain glory is that petty ambition which is contented with appearances, which is exhibited in pompous display, and never elevates itself to greater things. Sovereigns, having real glory, have been known to be nevertheless fond of vain glory-seeking too eagerly after praise, and being too much attached to the trap-have beeu forced by the brutal insolence pings of ostentation. of a Turkish sultan to display all her False glory often verges towards va-genius; that from the far north she nity; but it often leads to excesses, while vain glory is more confined to splendid littlenesses. A prince who should look for honour in revenge, would seek a false glory rather than a vain one.

should have sent four squadrons which spread terror in the Dardanelles and in Asia Minor; and that, in 1770, she took four provinces from those Turks who made Europe tremble;-she will not be reproached with enjoying her glory, but will be admired for speaking of her successes with that air of indifference and wit-superiority, which shows that they were merited.

To give glory, signifies to acknowledge, to bear witness. Give glory to truth, means acknowledging truth-Give glory to the God whom you serve Bear ness to the God whom you serve.

Glory is taken for heaven-He dwells

In short, glory befits geniuses of this