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feu ?

southern margin of the volcano. These changes in the form | Vous vous endormez facilement.
and position of cones of eruption give to Vesuvius, at different Je m'éveille de très bonne heure.
epocns, a different appearance. In this eruption of October, Pourquoi vous approchez vous du
1822, in twenty-four hours after the falling in of the great cone Je m'en approche parceque j'ai
of cinders just mentioned, and when the small but numerous
streams of lava had flowed off, then a fiery eruption of ashes
commenced, which continued without intermission for twelve
days, and covered the sides of the mountain.

These different measurements of Vesuvius suggest grounds for a very bold theory in geology. How is it that the north margin of the volcano, that called Rocca del Palo, maintains such a uniformity of height while the other is lowered? The probable cause is that the north margin is in the process of being now raised up gradually by the upward tendencies of subterranean forces. Between the years 1816 and 1822 we are sure that that margin was from 3,970 feet to 4,022. When it was measured, thirty or forty years before, the height was from 3,875 feet to 3,894. How is this? Future investigations will, perhaps, decide how much of this difference is due to errors in measurement, and how much to the actual rise of the mountain

by the expansion of heat from below. "If the lava beds of Rocca del Palo," says A. Von Humboldt, "really become higher we must assume them to be upheaved from below by volcanic forces."

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froid.

Nous nous éloignons du feu.
Nous nous en éloignons.

Nous nous approchons de notre
père.

Nous nous approchons de lui.

Aussi, also.
Aussitôt que, as soon

as.

Canif, m. penknife.
Demoiselle, young lady.
Domestique, m. ser-

vant.

You go to sleep easily.
I awake very early.
Why do you come near the fire!
I come near it because I am cold.
We go from the fire.
We go from it.
We go near our father.
We go near him.

EXERCISE 75.
Encre, f. ink.

Fenêtre, f. window.
Feu, m. fire.
Fourchette, f. fork.
Heure, f. hour, o'clock.
Moins, less, before.
Obligé, e, obliged.

Ordinairement, gene-
rally.
Plume, f. pen.
Pourquoi, why.
Prêt-er, 1. to lend.
Quart, m. quarter.
Taill-er, 1. to mend.

1. Pouvez vous vous passer d'encre? 2. Nous pouvons nous en passer, nous n'avons rien à écrire. 3. Vous servez vous de votre plume? 4. Je ne m'en sers pas; en avez vous besoin? 5. Ne voulez vous pas vous approcher du feu? 6. Je vous suis bien obligé, je n'ai pas froid. 7. Pourquoi ces demoiselles s'eloignent elles de la fenêtre? 8. Elles s'en éloignent parcequ'il y fait trop froid. 9. Ces enfants ne s'adressent ils pas à vous? 10. Ils s'adressent à moi et à mon frère. 11. A quelle heure vous éveillez vous le matin? 12. Je m'éveille ordinairement à six heures moins un quart. 13. Vous levez vous aussitôt que vous vous éveillez? 14. Je me lève aussitôt que je m'éveille. 15. De quels livres vous servez vous? 16. Je me sers des miens et des vôtres. 17. Ne vous servez vous pas de ceux de votre frère? 18. Je m'en sers aussi. 19. Les plumes dont [Sect. 31, R. 8] vous vous servez sont elles bonnes ? 20. Pourquoi votre ami s'éloigne-t-il du feu? 21. Il s'en éloigne parcequ'il a trop chaud. 22. Pourquoi votre domestique s'en approche-t-il? 23. Il s'en approche pour se chauffer. 24. Vous ennuyez vous ici? 25. Je ne m'ennuie pas.

EXERCISE 76.

1. Will you lend me your penknife? 2. I cannot do without it, I want it to mend my pen. 3. Do you want to use my book? 4. I want to use it, will you lend it to me? 5. What knife does your brother use? 6. He uses my father's knife and my brother's fork. 7. Will you not draw near the fire? 8. We are much obliged to you, we are warm. 9. Is that young lady warm enough? [Sect. 34, 3.] 10. She is very cold. 11. Tell her (dites lui) to come near the fire? 12. Why do you go from the fire? 13. We are too warm. 14. Does your

brother leave the window? 15. He leaves the window because he is cold. 16. To whom does that gentleman apply 17. He applies to me and to my brother. 18. Why does he not apply to me? 19. Because he is ashamed to speak to you. 20. Do you awake early every morning? 21. I awake early, when I go to bed early. 22. Why do you go to sleep? 23. I go to sleep because I am tired. 24. Are you afraid to go near your father? 25. I am not afraid to approach him. 26. Can you do without us? 27. We cannot do without you, but we can do without your brother. 28. Do you want my brother's horse? 29. No, Sir, we can do without it. 30. Do you intend to do without money? 31. You know very well that we cannot do without it. 32. Is your brother weary of being here? 33. He is not weary of being here. 34. Come near the fire, my child.

SECTION XXXIX.

1. The verb aller (1 ir. § 62), conjugated reflectively, and preceded by the word en, í. e. s'en aller, corresponds to the English expressions to go away, to leave :

2. INDICATIVE PRESENT OF THE VERB S'EN ALLER, TO GO

Je m'en vais,
Tut t'en vas,

The rule does not apply to the reflective pronoun, which is sometimes Il s'en va, an indirect object.

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3. THE SAME TENSE CONJUGATED INTERROGATIVELY.

Est-ce que je m'en vais ? T'en vas tu?

S'en va-t-il ?

Nous en allons Do we go away?

Do I go away?

nous ? Vous en allez vous ?

Art thou going away? Is he going away? S'en vont ils?

Do you go away?

5. Will you make haste to finish your letter? 6. I make haste to finish it. 7. Does the gardener get angry with his brother? 8. He gets angry against him when he does not make haste. 9. Make haste, my friend, it is ten o'clock. 10. Why do you not make haste? 11. I like to play, but I do not like to study. 12. Do you like to stay at my house? 13. I like to stay there. 14. Are you rejoiced at the arrival of your mother? 15. I rejoice at it. 16. Is not your brother wrong to go away so soon? 17. He is right to go away, he has much to do at home. 18. Do you rejoice at other people's misforDoes he become angry against your tunes? 19. I do not rejoice at them. 20. I rejoice at your

Are they going away?

4. Se facher, to be or became angry, requires the preposition contre or de before the noun or pronoun following it:Se fache-t-il contre votre frère ?

Il se fâche contre lui.

Vous vous fâchez d'un rien.

brother?

He is angry with him.

You get angry at nothing.

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5. Se réjouir, to rejoice, is followed by the preposition de :

Je me réjouis de votre bonheur. I rejoice at your happiness.

success. 21. Does not your brother draw near the fire? 22.
He goes from the fire, he is too warm. 23. Does that young
lady get angry with you? 24. She gets angry at trifles (de
rien). 25. Do you like to be in Paris? 26. I like to be there.
27. Can you do without me to-day? 28. We cannot do with-
out you—make haste to finish your work (ouvrage). 29. Do

6. Se plaire [4 ir. see § 62,] to take pleasure, to delight in any you want your penknife? 30. I want to use it. 31. Make

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Le marchand s'en va-t-il aujourd'hui ?

Nous nous en allons demain.
Je m'en vais quand je suis fatigué.
Pourquoi vous fâchez vous contre
lui ?

Make haste to finish your lessons. Why do you not make haste?

EXAMPLES.
Does the merchant go away to-day?
We are going away to-morrow.
I go away when I am tired.
Why do you get angry with him?

haste to rise, it is six o'clock. 32. Is it fine weather? 33. No, Sir, it rains. 34. Is your father well this morning? 35. Yes, Sir, he is very well.

LESSONS IN ARCHITECTURE.-No. II. AFTER the rough sketch of the origin of architecture in our last, we must notice in proper order that system of construction, the monuments of which cover a great part of the old world. This system had its origin among the Shemitic tribes, which at the commencement of civilisation peopled the fairest part of the globe. This early system, noted for the rudeness of its form, its stability without mortar, and the great size and irregularity of its materials, is attributed to the Pelasgians, a people

Il se plait à jouer, il n'étudie ja- He takes pleasure in playing, he originally from Upper Asia, who, according to Herodotus,

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1. Vous en allez vous bientôt? 2. Je m'en vais la semaine prochaine. 3. Pourquoi vous en allez vous? 4. Parceque je ne me plais pas ici. 5. Vous plaisez vous mieux chez votre tante qu'ici? 6. Je m'y plais mieux. 7. N'avez vous pas tort de vous en aller si tôt? 8. J'ai raison de m'en aller. 9. Ne vous rejouissez vous pas des malheurs d'autrui? 10. Nous ne nous en réjouissons point. 11. Cet homme se fâche-til contre le jardinier? 12. Il se fâche contre lui parce qu'il ne veut pas se dépêcher. 13. Se fâche-t-il bien souvent? 14. Il se fache à tout moment, il se fâche d'un rien. 15. Ne vous dépêchez vous jamais? 16. Je me dépêche toujours quand j'ai quelque chose à faire. 17. Ne vous plaisez vous pas à courir et à jouer? 18. Je me plais à jouer et mon frère se plait à lire. 19. Vous réjouissez vous de l'arrivée de l'ambassadeur Ture? 20. Je m'en réjouis. 21. Ne vous plaisez vous pas en Amérique? 22. Je m'y plais beaucoup mieux qu'en France. 23. Votre écolier ne se plait il pas chez vous. 24. Il se plait chez moi, mais il désire retourner chez son père. 25. Dépêchez vous, il est déjà midi.

EXERCISE 78.

1. At what hour does your friend go away? 2. He goes away every morning at nine o'clock. 3. Do you go away with (@sec) him? 4. I go away with him when I have time.

spread themselves over Phoenicia and Asia Minor, and colonised Greece and Italy. Examples of this style of architecture, called Pelasgic, are found extending from the borders of Persia and Armenia to the western limits of Asia. Crossing the Mediterranean, it spread over Greece, where the most remarkable monuments described by ancient authors, from the age of Hesiod and Homer, are traced, according to tradition, as far back as eighteen centuries before our era. This was the style of construction used in the heroic times of ancient Greece; and at a later period it was employed on certain important occasions.

The migrations of the Pelasgi carried this system into Italy, and we meet it at every step, particularly in the central countries. Examples are also to be seen in nearly all the western islands of the Mediterranean, in the Balearic Isles, and some even on the coasts of France and Spain. In fine, by a remarkable coincidence, travellers who have drawn and described the monuments of Palenque and Papantla, cities of Mexico destroyed long ago, and grown over by forests, exhibit constructions similar to those of the Pelasgi. The gigantic remains of the Pelasgic monuments, to this day subjected to examination by travellers, bear traces of different modes of building. Those which seem to be the most ancient are composed of blocks of stone, or rather of rocks, so rude and so immense that Pausanias, in speaking of the walls of Tyrins, built thirtysix centuries ago, describes them thus:-"These walls are constructed of unhewn stones, and are all of such dimensions that a yoke of oxen could not shake the smallest of them. The interstices are filled up with smaller stones, which serve to unite the larger ones.' These walls present the same appearance now which they did in the days of Homer and of Pausanias. They are about 25 feet thick, and about 43 feet in height. Two temples, close to each other, in the island of Gozo, near Malta, are analogous in their construction to the walls of Tyrins. They are built of immense blocks of stone, forming a sort of artificial hill, in which are placed the naves and arches of the temples; but some of the rocks bear traces of masonry.

It has been proved, by careful examination, that these edifices were dedicated to the gods of Asia. To conclude; the walls of Tarragona, on the east coast of Spain, are constructed, like the preceding, of immense rocks in their natural state. The application of instruments to building, at a later period, caused the edifices of the Pelasgians to assume another form.

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The stones taken from quarries, were cut into irregular polygons, and placed one upon another in such a manner as to make the different faces of the geometrical figures which they employed, coincide, the salient angles filling up the re-entrant angles formed by two adjoining stones. (Fig. 5.) This was the Fig. 5. ordinary manner of building under this system of construction. It is met with from the lake Van, on the frontiers of Armenia, to the west of Italy, Sardinia, and the Balearic Isles; and it is found in temples and in tombs, in pubPelasgic wall. lic and private buildings, and in innumerable military constructions. At last, a third method presents itself in the walls of these early buildings; namely, that in which the stones are fashioned in the square form; and the buildings themselves, assuming the same form, exhibit a greater degree of civilisation; and the invention and application of more exact instruments. The walls of the ancient Mycenae were built in this manner. (Fig. 6.) Fig. 6.

the union of these materials architectural forms, without going through that initiatory process which characterises the origin of all human inventions. Yet the plains of Chaldea soon exhibited constructions which had a great influence over primitive art in the east, and formed the basis of a system which extended its branches even to the west. The want of stones in Mesopotamia soon taught the inhabitants to mould bricks, and their most ancient temple mentioned in the Bible, called the tower of Babel, was an immense pyramid built of bricks piled on one another, and forming, according to report, eight stories or rows, gradually receding from each other. At the top of this building they sacrificed to Baal; at a later period the Chaldean kings placed his statue there, when their artists had made some progress in the art of sculpture. It is probable that this pyramidal-formed temple owed its origin to their remembrance of the practices of those Caucasian countries whence the Shemitic tribes derived their origin. Herodotus gave a glimpse of the truth, when he said that the Scythians made their temples or altars with a great quantity of wood heaped in the form of a pyramid. However the case may be, this very simple form, which appears to have come naturally to the mind of those men who were the first to raise large constructions, spread itself over all Asia; the ancient pagodas of India are built in this form; the most ancient monuments of Lower Egypt and Ethiopia, where the Shemitic tribes settled in Africa, are all of them pyramids. (Fig. 7.) In Asia, Fig. 7.

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The continued and progressive order of these Pelasgic constructions, is one of the most interesting facts in the history of the art of building-particularly when we refer them to an antiquity which goes back to the heroic time of Greece. Doubtless the gradual improvement which is to be seen in the walls constructed by this original people, does not reveal all the revolutions of this art in early antiquity; but it enables us to perceive the progress of the greater part of the civilised world, a progress which it must necessarily follow, because it is the nature of all human inventions to pass from early and rude attempts, to successive periods of improvement and perfection, The Pelasgic monuments, sketched and studied at the present day, extend over a zone, which, comprising the breadth of Western Asia, stretches over Greece and Central Italy; and this is not the whole of the ancient world, as we have already said, in which early monuments composed of rocks in their natural state, have been seen by ancients and moderns; but they have been discovered in all the northern countries, and in Africa, from Egypt to the neighbourhood of Carthage; and we have reason to believe that in these countries, to the primitive constructions, a second period succeeded, more refined in its productions, and forming a step from the first attempts, to the more perfect examples, of which we behold the numerous ruins in India, in Central Asia, in the valley of the Nile, and in the oases of the desert. These monuments of transition, so to speak, have disappeared under early and actual civilisation, and have even escaped the investigation of travellers.

FIRST REGULAR CONSTRUCTIONS, PYRAMIDS, &c. The Pelasgi, proceeding from the Asiatic plateaus (tablelands), directed their steps towards the west; other Shemitic tribes marched towards the south and east, and peopled India, Persia, Assyria, and Arabia, as well as Ethiopia and Egypt. The art of these tribes, like that of the western branch, passed through a rude and primitive state, as we have shownthrough the BETH-EL style, or constructions in unhewn stones. It cannot be supposed that these tribes were more privileged than others, and were able, without previous attempts, to hew stones regularly, to mould and cement bricks, and to give to

Pyramids of Memphis.

whole cities, Ecbatana for example, presented numerous concentric enclosures rising one above another in such a way as to exhibit the pyramidal form. The celebrated gardens of Babylon, formed of numerous terraces, one above another, had also the same configuration. In short, this must be considered as the progress of architecture, when we see that the most ancient religious edifices of the Mexicans are immense pyramids, simple at first like those of Chaldea, and of Lower and Upper Egypt; but at a later period, ornamented with sculpture like the pagodas of India. Ancient public buildings were also found in Mexico of a pyramidal form. It is evident that these first regular constructions were thus generally established; and the greater part of the primitive world adopted them, with the exception of those countries where great political events interrupted the first movements of civilisation and suspended the march of the arts; with the exception also of those whose inhabitants, less endowed by nature, necessarily remained in the rear of civilisation, and only received a movement of this kind from their neighbours, or from an invasion of some

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to follow the road in which they were placed. The want of experience, the absence of instruments and machines prevented them from raising, at first, great edifices with vertical fagades or fronts, such as they were enabled to construct at a later period. To form large foundations, and to raise above them materials with gradual and numerous recesses such as would prevent the fall of the upper parts of the building, was the first law of construction and of statics to which they were obliged to submit. This is so true that after having made their great steps in the art of building, the Indians, the Chaldeans, the Ethiopians, and the Egyptians, and become able builders, they still continued in the path of which the pyramid was starting-point, by raising their edifices in such a manner as to give to their façades a great inclination in order to obtain greater stability; a wise system, which was adopted by the Etruscans when they left Asia, where these principles were long established. They were also spread over a part of Italy, and traces of them are found at Norchia. The same ideas exerted their influence over the early edifices of the Greeks, and they are found in a modified form among the finest specimens of their later architecture. They are recognised, for instance, in the Parthenon, where the inclination of the jambs of the doors and windows still exists. Mexico also bears witness to this, as may be seen in our remarks on the first regular constructions of that country.

QUESTIONS ON THE PRECEDING LESSONS.

Among what early tribes had the Pelasgi style of architecture its origin?

Who were the Pelasgi; and how far back are their monuments

traced?

In what countries are the Pelasgic monuments found; and in what parts of America were similar constructions discovered? How many centuries ago were the walls of Tyrins built, and what was the size of the stones? Where are examples of temples built like these walls to be found?

Where did the square form of stones first appear, and where did brick-building first commence ?

utility, and cannot be depended upon as a satisfactory check upon
the operations. One thing, however, we will admit that where
the application of this method indicates an error, there must be an
error; but the evil is, that it does not indicate the existence of
many errors when they really have been made. The misplacement
of a number, or even a figure, in a sum in addition, or in a product
in multiplication, is a very serious error, and might lead to very
injurious consequences in business, and yet the proof by casting out
the nines would not detect such an error! And it is on this ground
that we object to its practical utility.
EXAMPLE.-Multiply 75432 by 476, and prove the operation by
casting out the nines.

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By casting the nines out of the multiplicand, as shown at page 266, we obtain the remainder 3; by casting the nines out of the multiplier, we obtain the remainder 8; and by multiplying these remainders together, we obtain the product 24. By casting the nines out of this product, we obtain the remainder 6. Now, by casting the nines out of the product of the factors in the above operation, we obtain also the remainder 6. Hence, it is presumed that the operation is right.

If the remainder, arising from casting the nines out of either of the factors, or of both, should be 0, the remainder arising from casting the nines out of the product should also be 0; because the product of 0 by any figure or number is 0.

The proof of division by casting out the nines, proceeds on the tient is one of the factors, the divisor is the other factor, and the same principle as that referred to in multiplication; for the quodividend is their product. To this principle must be added the very simple one, that if the same thing be added to equals, the wholes are equal. Accordingly, when there happens to be a remainder over in the division of one number by another, the remainder arising from the casting out of the nines from this remainder must be added to the product of the remainders of both the factors, in order to get the true remainders of the nines; because the remainder of the division is included in the dividend, or else there would have been no remainder at all. The rule for proving division by casting out the nines, then, is the following:-Cast the nines out of the divisor and the quotient, and multiply these remainders together; cast the nines out of this product, and note the remainder; cast the nines, also, out of the remainder of the noted, and cast the nines out of their sum; the remainder of this casting out should be the same as that arising from casting the nines out of the dividend, if the work be right; this rectitude or accuracy being subject to the same limitations and restrictions, as those above explained under the rule for proving multiplication. EXAMPLE. Divide 7543210 by 476, and prove the operation by casting out the nines.

Divisor. Dividend. Quotient.
476) 7543210 (15847

LESSONS IN ARITHMETIC.-No. XIV. THE proof of multiplication, by casting out the nines, proceeds on the following principle: that if two factors and their product by divided by any number, the product of the remainders of the factors, when divided by that number, will give the same remainder as the product of the factors. Thus, if 24 and 20 be the factors, 480 is their product; and if each of these factors be divided by a number, say 7 for instance, the remainders are 3 and 6, and their product 18, divided by 7, gives the remainder 4; but the product 480 divided by 7, gives the same remainder 4, as we have said. Com-division, and note this remainder: add it to the former remainder bining this principle with what was explained in our last lesson on the subject of finding the remainder of a number divided by 9, the rule for proving multiplication, "by casting out the nines," is as follows:-Cast the nines out of the factors, i.e., the multiplicand and the multiplier, and multiply the two remainders together, cast the nines out of this product, and also out of the product of the factors; if the remainders be the same in both cases, it may be presumed that the work is right. The accuracy of the operation, as we said in our last number, cannot be depended on, for the reasons there stated, and others that might be added: thus, the arrangement of the partial products might be all wrong by the displacement of the products, of the units, or of the tens, or of the hundreds, &c., i.e., of any one by itself or of all of them together; and yet the casting out of the nines would not indicate the fact, but would give the same result as if they were all arranged in a manner perfectly correct. Hence the propriety of giving other methods of proof, as we have done in past numbers,-methods which are sure to detect the slightest inaccuracy, and put the calculator fully on his guard. For doing this, we have been found fault with by a number of individuals, who fancy that if they know any thing at all they must know arithmetic, and that they can teach us, forsooth, better than we can teach them! But true knowledge is always humble, and ready to acknowledge its own deficiencies or mistakes ; it is also anxious to gain useful information from every quarter, and more willing to learn than to find fault. We hope that such persons will take these hints in good part. We assert, without fear of their displeasure, that the method of proving multiplication, or, indeed, any rule in arithmetic, by "casting out the nines," is of no practical

Divisor 476.
Quotient 15847

476

2783

2380

4032

3808

2241

1904

3370

3332

38 remainder

8

7

Product
Remainder 38

56

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Dividend 7543210

METHOD OF PROOF.

The principle of most of these operations was very well explained by some of our correspondents, among whom we must mention the following:-Robert Boland, Great Shelford, Cambridgeshire; J. L. N., Dublin (who applied it most ingeniously to other scales of notation); Charles Currie, Glasgow (who added some curious and ingenious rules for dividing by a number consisting of nines, extracted from old authors); P. G. Anderson, Birmingham; Joseph Webster, Bramley (who applied the proof of casting out the nines to involution and evolution, and gave rules for the same); J. Carey, Clapham; and others. From the review of all the correspondence we have received, we are convinced that many of the observations made on the properties of the number 9, especially in their application to the methods of proving arithmetical operations, are more curious than useful; and that their place may be fairly taken by something of much greater value.

numbers

34765

put down

by the pupils.

27184
36958
47366

numbers

65234

72815

put down

63041
52633

by the teacher.

The following is a method of interesting young pupils in Casting the nines out of the divisor gives remainder 8, and out of the irksome rule of addition. Tell the members of a the quotient gives remainder 7. The product of these remainders class to put down on their slates a sum in addition, a certain 34765 is 56, and casting the nines out of it gives remainder 2; also, cast- number of lines deep, and a certain number of figures broad, 27184 ing the nines out of the remainder of the division gives remainder as in the margin; and to leave room enough below for you 36958 2, and the sum of these remainders is 4. Lastly, casting the nines to add as many lines. This being done, you proceed to 47366 out of the dividend gives the same remainder 4; hence it is pre-add as many lines to each in the following manner:-Looksumed that the work is right; but, as we have said before, this is ing at the first line, write down rapidly the difference between each figure in it and 9; do the same only a presumption. with the second line, then with the third, and so on. You then tell them to add up all the lines, and find the amount of the whole. But before they do this, you may just as well tell them the answer or sum which it will make. You do this by giving them the product of a number consisting of as many nines as there are figures in the breadth, by the figure which indicates the number of lines in the original depth of the sum before you added This operation your own lines to it. will be seen at once in the example placed in the margin. however different the numbers may be which In this operation it is to be observed, that, are put down to be added, it is plain that, by the addition of your figures to them, they must all come to the same sum. Here you multiply 99999, the number composed of as many nines as there are figures in the breadth, by 4, the number of lines in the original breadth, that is, the depth of the numbers put down by the pupils. The reason of this process is so obvious, that we shall leave it for the consideration of those who may be interested in the subject, satisfied that they are sure to make the discovery for themselves.

We were reminded of a curious property of 9 and its multiples by a correspondent, Joseph Bowman, Preston,—namely, that the number 12345679 being made the multiplicand, and the multiples of 9 as far as 81 the multipliers, the products will consist of numbers all composed of the same figure, and that figure will be the number of times 9 which constitutes the multiple employed;

thus:

:

12345679

111111111

9

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399996 Sum.

99999

4

399996 Answer.

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Although we have seen these curious results many years ago, we give our correspondent full credit for his individual rediscovery. Another correspondent, J. L. N. (Dublin), suggests the following curious operation in subtraction as an amusement for the junior classes in a school. Tell the members of a class to put down upon their slates individually any number they please, as in the margin; then, to put down under this number, the same figures written in any other order whatever, taking care that its first figure, or the figure of highest value, shall be less than the one above it; next, to subtract this number, or row of figures, from the one above, and mark out one of the figures of the remainder. Lastly, tell them to add together all the rest of the figures, and be prepared to tell you the result. Then, beginning at one end of the class, ask the number required, subtract it in your mind from the next multiple of 9 above it, and tell the remainder aloud; this remainder will be the number which each individual marked out. Thus; if in the above example 6 were marked out, the sum of the rest of the figures would be 12; now the next multiple of 9 above 12, is 18; and subtracting 12 from 18, you have 6, the number marked out. The principle of this apparent trick is fully explained in our last lesson on Arithmetic. By telling them to cast the nines out of the rest of the figures, and tell you the remainder, the process would be easier, for you would only have to subtract it from 9, and this remainder would be the figure marked out. But this process would more readily reveal your secret. It is to be noted, that when the sum of the rest of the figures is itself 9, or a multiple of 9, the figure marked out may be either 9 or 0. This renders two cases dubious, and diminishes the completeness of the artifice. Pupils rejoice to find their master in a dilemma.

FRENCH EXTRACTS.

HAVING been frequently requested by our correspondents to recommend to the students of French, some book for reading, in order to extend their knowledge of that language, and to give them an interest in some useful study besides, we have selected for their special use, a collection of the most valuable MAXIMS and MORAL SENTIMENTS which the French language affords. This collection is arranged alphabetically, and will be continued in several numbers of the POPULAR EDUCATOR, until complete. When this is done, our readers will be in possession of as fine a body of social morality and experience of the world, as the language of any country

can afford. The names of the authors are added to the sentiments or maxims, to give them zest and authority; those of La Rochefoucauld, La Bruyère, Bacon (our own Francis), Pascal, Montaigne, of the wisdom of their sayings, and the excellence of their STYLE, Fenelon, Montesquieu, and many others, will be a sufficient guarantee

PENSEES MORALES ET MAXIMES.

ACCIDENT.

tirent quelque avantage, ni de si heureux que les imprudents ne Il n'y a point d'accidents si malheureux dont les habiles gens ne puissent tourner à leur préjudice.-La Rochefoucauld.

ACTION.

C'est, en quelque sorte, participer à une bonne action que de la louer de bon cœur.-La Rochefoucauld.

Il faut faire comme les autres: Maxime suspecte, qui signifie presque toujours: il faut mal faire, dès qu'on l'étend au-delà de ces choses purement extérieures, qui n'ont point de suite, qui dépendent de l'usage, de la mode et des bienséances.-La Bruyère,

AGE.

Puisque l'âge diminue nos agréments en nous laissant nos vieillesse, tâchons de devenir plus respectables à mesure que nous défauts, et que la considération est la seule indemnité de la devenons moins aimables.-Levis.

Nous arrivons tout nouveaux aux divers âges de la vie, et nous y manquons souvent d'expérience malgré le nombre des annéesLa Rochefoucauld.

AMBITION.

L'esclave n'a qu'un maître, l'ambitieux en a autant qu'il y a de gens utiles à sa fortune.-La Bruyère.

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