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The general will free the city from the enemy (plural); good men plant for their offspring also; good men will plant for their children (raig); the messengers report many things; the enemy plot against the king; the enemy will plot against me; I announce many things to the citizens; Achilles is angry with Agamemnon; Achilles will be angry with Agamemnon; thou art angry with thy brother; I was angry (first Aorist) with the enemy; I will entreat my judges; Socrates will not entreat his judges; the good citizens will not entreat their judges; the enemy are destroying Platea; the soldiers will destroy Plates; the soldiers destroyed the city; hear (Aorist) me, O my offspring (plural). One friend believes another (raipos traipy); one friend will believe another; one friend did believe another; they believed; they did believe; they believe; they will believe; thou wilt believe; they two believed; we shall believe; we believe; thou wilt believe; the soldier prevails much by his strength; I prevailed much by my strength.

For some time the struggle was most amusing the fish
pulling, and the bird screaming with all its might - the one
attempting to fly, and the other to swim from its invisible
the gander at one moment losing and the next
enemy
regaining his centre of gravity.

54. The dash is sometimes to be read as a period, with the
falling inflection of the voice.

The favoured child of nature, who combines in herself these
united perfections, may justly be considered as the masterpiece
of creation - as the most perfect image of the Divinity here
below.
Now launch the boat upon the wave - the wind is blowing
off the shore I will not live a cowering slave, in these
polluted islands more.
The wind is blowing off the shore, and out to sea the
streamers fly - my music is the dashing roar, my canopy the
stainless sky- it bends above, so fair a blue, that heaven
seems opening to my view.
He had stopped soon after beginning the tale he had laid
the fragment away among his papers, and had never looked at
it again.
The exaltation of his soul left him - he sunk down- and
his misery went over him like a flood.

---

Mr. Playfair was too indulgent, in truth, and favourable to his friends and made a kind of liberal allowance for the faults of all mankind-except only faults of baseness or of cruelty; against which he never failed to manifest the most open scorn

LESSONS IN READING AND ELOCUTION.-No. V. and detestation. (Continued from page 371, Vol. IV.)

THE DASH.

48. The Dash is a short straight line which occurs in reading, and which is placed between the sentences in such a manner as to be parallel to the top or the bottom of the page. 49. The dash is sometimes used to express a sudden stop, or change in the subject.

50. The dash requires a pause sometimes as short as that of a comma, and sometimes one as long as, if not longer than, that of a period.

51. The dash is frequently used instead of crotchets or brackets, and a parenthesis is thus placed between two dashes. 52. The dash is sometimes used to precede something unexpected; as when a sentence beginning seriously ends humorously.

53. In the following examples, the dash is used to express a sudden stop, or change of the subject.

Examples.

If you will give me your attention, I will show you--but ton, I do not know that you wish to see. Alas! that folly and falsehood should be so hard to grapple with-but he that hopes to make mankind the wiser for his labours, must not be soon tired.

Please your honours, quoth Trim, the inquisition is the vilest. Prithee, spare thy description, Trim; I hate the very name of it, said my father.

The fierce wolf prowls around thee-there he stands listening not fearful, for he nothing fears.

The wild stag hears the falling waters' sound, and tremblingly flies for ward- o'er his back he bends his stately horns- the noiseless ground his hurried feet impress not and his track is lost amidst the tumult of the breeze, and the leaves falling from the rustling trees.

-

-

The wild horse thee approaches in his turn. His mane stands up erect - his nostrils burn he snorts he pricks his ears and starts aside. their meal was

There was silence - not a word was said

-

Towards women he had the most chivalrous feelings of
regard and attention, and was, beyond almost all men, accep-
table and agreeable in their society though without the
least levity or pretension unbecoming his age or condition.
55. The dash is sometimes to be read like a comma, with the
voice suspended.

I have always felt that I could meet death with composure;
but I did not know, she said, with a tremulous voice, her lips
quivering I did not know how hard a thing it would be to
leave my children, till now that the hour is come.
And Babylon shall become she that was the beauty of
kingdoms, the glory of the pride of the Chaldeans
as the
overthrow of Sodom and Gomorrah by the hand of God.
Our land the first garden of liberty's tree-it has been,
and shall yet be, the land of the free.

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Into its deep abyss
kings alike must fall.
She made an effort to put on something like mourning for
her son; and nothing could be more touching than this struggle
between pious affection and utter poverty: a black ribbon or
humble attempts to express by outward signs that grief that
80 - a faded black handkerchief, and one or two more such
passeth show.

56. The dash sometimes precedes something unexpected; as
when a sentence beginning seriously ends humorously.

Good people all, with one accord, lament for Madam Blaize : who never wanted a good word from those who spoke her praise.

The needy seldom passed her door, and always found her before them-God had been thanked, and they began to kind; she freely lent to all the poor- who left a pledge

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world, and demi-gods of fame? Is this your triumph- this your proud applause, children of truth, and champions of her

cause?

At church, in silks and satin new, with hoop of monstrous size, she never slumbered in her pew but when she shut her eyes. Her love was sought, I do aver, by twenty beaux, and more; the king himself has followed her when she has walked before. But now her wealth and finery fled, her hangers-on cut no friend take note of thy departure? short all; her doctors found, when she was dead her last disorder mortal.

Was there ever a bolder captain of a more valiant band? Was there ever but I scorn to boast.

Let us lament, in sorrow sore; for Kent Street well may say, that had she lived a twelvemonth more she had not died to-day.

57. The dash is sometimes used with other pauses to lengthen

them.

God, whom you see me daily worship, whom I daily call upon to bless both you and me and all mankind; whose wondrous acts are recorded in those Scriptures which you constantly read, God, who created the heavens and the earth; who appointed his Son Jesus Christ to redeem mankind: :- God, who has done all these great things, who has created so many millions of men, with whom the spirits of the good will live and be happy for ever; this great God, the Creator of worlds, of angels, and of men, is your Father and Friend.

It is not, therefore, the use of the innocent amusements of life which is dangerous, but the abuse of them; — it is not when they are occasionally, but when they are constantly pursued; when the love of amusement degenerates into a passion; and when, from being an occasional indulgence, it becomes an habitual desire.

In every pursuit, whatever gives strength and energy to the mind of man, experience teaches to be favourable to the interests of piety, of knowledge, and of virtue; in every pursuit, on the contrary, whatever enfeebles or limits the powers of the mind, the same experience ever shows to be hostile to the best interests of human nature.

From the first hour of existence to the last, from the cradle of the infant, beside which the mother watches with unslumbering eye, to the grave of the aged, where the son pours his bitterest tears upon the bier of his father, in all that intermediate time, every day calls for exertion and activity, and moral honours can only be won by the steadfast magnanimity of pious duty.

They say they have bought it. Bought it! Yes; - of whom?-Of the poor trembling natives, who knew that refusal would be vain; and who strove to make a merit of necessity, by seeming to yield with grace, what they knew they had not the power to retain.

It is not the lifeless mass of matter, he will then feel, that he is examining, it is the mighty machine of Eternal Wisdom: the workmanship of Him, in whom every thing lives, and moves, and has its being.

When suffering the inconveniences of the ruder parts of the year, we may be tempted to wonder why this rotation is necessary; why we could not be constantly gratified with vernal bloom and fragrance, or summer beauty and profusion. Then a spirit passed before my face; the hair of my flesh stood up: it stood still, but I could not discern the form thereof: an image was before mine eyes: - There was silence, and I heard a voice - Shall mortal man be more just

than God?

58. The dash is sometimes to be read as a note of interrogation. Is it not enough to see our friends die, and part with them for the remainder of our days — to reflect that we shall hear their voices no more, and that they will never look on us again -to see that turning to corruption, which was but just now alive, and eloquent, and beautiful with all the sensations of the soul?

He hears the ravens cry; and shall he not hear, and will he not avenge, the wrongs that his nobler animals suffer wrongs that cry out against man from youth to age, in the city and in the field, by the way and by the fireside?

Can we view their bloody edicts against us their hanging, heading, hounding, and hunting down an ancient and honourable name as deserving better treatment than that which enemies give to enemies?

Are these the pompous tidings ye proclaim, lights of the

And what if thou shalt fall unnoticed by the living — and

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Seest thou yon lonely cottage in the grove- with little garden neatly planned before its roof deep-shaded by the elms above, moss-grown, and decked with velvet verdure o'er? What shall we call them? - piles of crystal light a glorious company of golden streams- lamps of celestial ether burning bright- suns lighting systems with their joyous

beams.

59. The dash is sometimes to be read like a note of exclama

tion.

What dreadful pleasure! there to stand sublime, like shiprecked mariner on desert coast, and see the enormous waste of vapour, tossed in billows lengthening to the horizon round, now scooped in gulfs, with mountains now embossed hear the voice of mirth and song rebound, flocks, herds, and waterfalls, along the hoar profound!

- and

The chain of being is complete in me; in me is matter's last gradation lost, and the next step is spirit-Deity! I can command the lightning, and am dust!

Above me are the Alps, the palaces of Nature, whose vast walls have pinnacled in clouds their snowy scalps, and throned Eternity in icy halls of cold sublimity, where forms and falls the avalanche-the thunderbolt of snow!

How has expectation darkened into anxiety-anxiety into dread-and dread into despair! Alas! not one memento shall ever return for love to cherish. All that shall ever be known is, that she sailed from her port, and was never heard of more.

A measure of corn would hardly suffice me fine flour enough for a month's provisions, and this arises to above six score bushels and many hogsheads of wine and other liquors have passed through this body of mine-this wretched strainer of meat and drink! And what have I done all this time for God and man? What a vast profusion of good things upon a useless life and a worthless liver!

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Extraneous, sea-water, semi-circle, demi-gods, Seething-hall, Moss-side, plane-trees, bed-side, Birk-knowe, over-canopied, toil-hardened, gray-haired, to-morrow, Sabbath-day, Sardanapalus, ill-requited, thunder-cloud, European, Epicurean, pine-covered, clay-cold, snow-clad, parish-clerk, night-steed, moon-eyed, azure, all-wise, edict, fellow-creatures, icy, wellfounded, omega, fellow-feeling, uniform, prophesy, earth-born, far-wandering, storm-clouds, hymenéal, chamber, either, fairy, lever, apiary, culinary.

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68. Sometimes the ellipsis is indicated by hyphens, | powers of 2 will be the natural numbers, and the indices of those thus,

69. The ellipsis sometimes so closely resembles a dash in its effects, that it is scarcely distinguishable from it.

70. The voice is generally suspended at an ellipsis; but the falling inflection is frequently used when the ellipsis follows a question or exclamation. In some of the following examples the dash and ellipsis are both used.

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Forth we went, and down the valley, on the streamlet's bank, pursued our way, a broken company, mute or conversing, single or in pairs.

Who is here so vile, that will not love his country?
If any, speak; for him have I offended,-I pause for a
reply
None! then none have I offended.
It is in vain to explain :-the time it would take to reveal to
Satisfy my curiosity in writing them.

you

Indeed he is very ill, sir, are very distressed, poor children, too,

Now, if he had married

why, then

would have fainted.

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- Can't help it. Can't help it.

Can't help that, neither.

We
Our

a woman with money, you know,
The suppliant turned pale, and

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on an excursion

I have been, my dear S through the counties which lie along the eastern side of the Blue Ridge. You have my answer: let my actions speak. No, no, Dionysius; remember that it was I alone who displeased thee: Damon could not If he were all Remember haughty Henry, the nephew of his wife, whose word could speed a veteran army to his kinsman's aid.

I would not wound thee, Douglas, well thou knowest; on a desperate cast thy golden

but thus to hazard fortunes

Oh, deeper

Still must I wonder; for so dark a cloud than thou think'st I've read thy heart. Your grace will pardon me for obeying Say no more, my child; you are yet too raw to make proper distinctions. Let them

powers will be the logarithms of the natural numbers. If these definitions be applied to the numbers and their indices in the table of powers, Art. 8, the expression in Art. 14 being also taken into consideration, the construction of the following table will be rendered manifest:

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By means of this table, logarithmic calculations may be exemplified on a small scale, in the following manner.

18. First. To multiply two or more numbers together. It the logarithm of the product (see Art. 10). Thus, to multiply the logarithms of the factors be added together, the sum is 128 by 8, add 7 and together, the logarithms of the factors; the sum 10 is the logarithm of the product 1024. Again, to multiply 4, 8 and 16 continuously together, add 2, 3 and 4, together, the logarithms of the factors; the sum 9 is the logarithm of the product 512,

logarithm of the divisor be subtracted from the logarithm of 19. Secondly. To divide one number by another. If the the dividend, the remainder is the logarithm of the quotient rithm of the divisor from 8, the logarithm of the dividend; the (see Art. 11). Thus, to divide 256 by 64, subtract 6, the loga. remainder 2 is the logarithm of the quotient 4.

20. Thirdly. To find a fourth proportional to three given terms. If the logarithms of the second and third terms be added together, and from the sum, the logarithm of the first term be subtracted, the remainder is the logarithm of the fourth term. Thus, to find a fourth proportional to 8, 32 and 64; if 8: 32:: 64: the fourth term, then add 5 and 6 together, the loga rithms of the second and third terms, and from the sum 11 ... or suppose I address myself to some par-subtract 3, the logarithm of the first term, the remainder 8 is ticular sufferer — there is something more confidential in that the logarithm of the fourth term 256. manner of communicating one's ideas -as Moore says, Heart speaks to heart I say, then, take especial care to write by candle-light.

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logarithm of the number be multiplied by the index of the 21. Fourthly. To find any power of a number. If the (see Art. 12). Thus, to find the square of 16, multiply 4, the required power, the product is the logarithm of that power logarithm of the number, by 2, the index of the square; the product 8 is the logarithm of the square 256.

22. Fifthly. To find any root of a number. If the logarithm of the number be multiplied by the index of the required root, or be divided by its denominator, the quotient is the logarithm of that root (see Art. 13). Thus, to find the cube root of 64, divide 6, the logarithm of the number, by 3, the denominator of the index of the cube root; the quotient 2 is the logarithm of the cube root 4.

23. The nature and use of logarithms having been thus illustrated and exemplified in the system of which the base is 2, we shall now give a full explanation of the system in

common use.

COMMON SYSTEM OF LOGARITHMS.

24. The number 10 has been assumed as the base of the common system of logarithms, because it is the root of the decimal scale of notation, and on this account possesses certain advantages which have led to its universal adoption by mathematicians.

25. The powers of the number 10 being respectively unity with as many ciphers annexed as are denoted by the indices of the different powers, the construction of the following table is sufficiently evident to the student:

100 =1
101 =10

Table of Pourers.

100

= 1000

THE POPULAR EDUCATOR.

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10%

103

101

= 10000

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Sixth Power.

= 10000000

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100000000000 Eleventh Power. 10121000000000000 Twelfth Power.

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to nothing, its logarithm must be infinitely great; in other words, the logarithm of 0 is negative infinity.

29. If the square root of the number 10 be extracted, and then the square root of this root, and of each successive root, the indices of these roots will be the successive powers of, the index of the square root (see Art. 12). Thus, by the common rule for extracting the square root, we have,

Square root of 10.00000 3.16228, index
Square root of 3.162281-77828, index
Square root of 1778281-33352, index
Square root of 133352 = 115478, index
Square root of 115478 107461, index
Square root of 1.07461 1.03663, index 64

etc.

etc.

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1

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107461 Thirty-second root. 101.03663 Sixty-fourth root.

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etc.

Cube root of 1.089021.02883, index

Cube root of 1·028831.00952, index ta
Cube root of 1.00952=100316, index S

etc.

27. If unity, the first natural number, be divided by the successive natural numbers in the preceding table, the quotients will be a series of decimal fractions, viz., 1, 01, 001, etc. The logarithms of these quotients will be found by subtracting On this principle the following table is constructed: the logarithms of the natural numbers from 0, the logarithm of unity (see Art. 11). Now, though it be impossible, arithmetically, to subtract the logarithms 1, 2, 3, etc., from the logarithm 0, yet the operation that should be performed is indicated by placing the sign of subtraction before each of these logarithms, thus: 1,2,3, etc. Hence, the construction of the following table of decimal fractions, with their logarithms, is evident to the student:

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Fanny arracha l'èpine, non sans peine, lava le sang qui coulait de la blessure; puis, prenant son mouchoir, elle en fit un bandage avec lequel elle enveloppa la patte du patient, qui, se sentant soulagé, léchait le cou et les mains de sa petite bienfaitrice, en faisant entendre un grogne28. These logarithms, being of an opposite character to the ment de plaisir; puis il se coucha à ses pieds jusqu'au former, are called negative, while the former are denominated moment où les enfants se disposèrent à regagner l'habitapositive. From the remarks in the preceding article, it is tion. Quand ils se remirent en route, il alla se placer evident that the logarithm of every proper fraction is essentially negative, and that the logarithms of such fractions à côté de Fanny, en fixant sur elle des yeux expressifs et numerically increase in proportion as the fractions themselves qui semblaient l'interroger. Elle lui fit signe de la suivre. decrease in value, compared with unity. Hence, when the Alors, oubliant sa blessure, faisant un bond de plaisir, value of a fraction is indefinitely small, its logarithm nume- l'animal forma cortège à la petite troupe, qui ne tarda pas rically considered must be indefinitely great; and when the à rentrer dans la cour de l'habitation.

value of a fraction is infinitely small, so as to be reckoned equal. A peine avaient-ils franchi la barrière, que le chien prit

-Enfin te voilà retrouvé, mon brave Moustache, s'écria-t-il en flattanti le chien.

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sa course et se précipita vers un groupes rassemblé autour | châtaignier, on fut très surpris de ne le point voir avec d'une sorte de marchand ambulants qui, ayant ouvert plu- Auguste et Fanny.10 On l'appela, on le chercha de tous sieurs ballots, étalait ses marchandises devant les personnes côtés; bientôt tout le monde fut sur pied. Alfred ne parut qui se trouvaient là, en les invitant à faire quelques acqui- pas. Le père et la mère, tous les domestiques parcoururent sitions. Le marchand poussa un cri de joie: en vain les alentours; 12 ils n'en découvrirent aucune trace ;13 désespérés de cet événement, ils se partagèrent en plusieurs bandes; ils allèrent avec leurs voisins, qu'ils avertirent du malheur qui leur était arrivé, à la découverte, et ils s'enfoncèrent dans la forêt qu'ils battirent en tout sens avec la plus scrupuleuse attention.15 Mille fois ils appelèrent l'enfant par son nom, ils n'en reçurent aucune réponse.16 Cependant, les dernières lueurs du jour n'éclairaient plus que faiblement les recherches,17 et rien encore n'était venu calmer les inquiétudes de M. et de Mme Dérambert: les approches de la nuit redoublèrent leurs alarmes.18 Dans leur désespoir, ils ne voulurent jamais consentir à retourner dans leur domicile.19 Ils allumèrent des torches de résine et firent retentir les bois, les vallées, du nom chéri d'Alfred. 20

Alors il se mit à raconter, qu'en traversant la forêt, son chien s'était élancé à la poursuite d'un animal sauvage, qu'il ne s'était aperçu que long-temps après sa disparition, qu'alors il l'avait vainement appelé; Moustache n'était pas revenu. Il avait alors supposé, qu'entraîné par son ardeur son chien s'était égaré, ou bien encore, qu'ayant attaqué quelque bête féroce, il avait succombé dans la lutte.

-Je ne m'étais pas tout à fait trompés ajouta-t-il, car je vois que Moustache a été blessé. Mais quis donc a eu la bonté de le secourir, de panser sa blessure? 14 s'écria-t-il en apercevant le mouchoir qui enveloppait la patte de Moustache.

A ces mots, le chien, comme s'il eut compris ce que venait de dire son maître, se mit à courir au devant des trois enfants 15 qui se dirigeaient de ce côté, et se plaçant près de Fanny, il ne la quitta pas d'un instant, qu'elle ne fût arrivée à l'endroit où se trouvait le marchand.17

16

COLLOQUIAL EXERCISE.

1. Que fit Fanny après avoir ar-
raché l'épine?

2. Que fit-elle de son mouchoir?
3. Comment le chien marqua-t-
il sa reconnaissance ?
4. Où se coucha-t-il ensuite?
5. Que fit le chien de Terre-
Neuve, quand ils se remirent
en route?

5. Quel signe lui fit alors Fanny?
7. Que fit le chien sur le chemin
de l'habitation?

9. Que faisait le marchand am-
bulant ?

10. Que dit son maître en
voyant le chien?

11. Que raconta le marchand?
12. Qu'avait-il supposé?
13. Qu'ajouta-il ensuite?
14. Que demanda-t-il en aperce-
vant le mouchoir ?
15. Comment le chien sembla-t-
il répondre à la question de
son maître?

8. Où courut-il après avoir fran- 16. Où se plaça-t-il?
ehi la barrière ?
17. Quand quitta-t-il Fanny?

NOTES AND REFERENCES.-a. from faire; L. part ii., p. 92.
b. L. S. 36, R. 5.-c. from remettre; L. part ii., p. 102.-d.
from faire.e. forma cortège, escorted.-f. from prendre; L. part
ii., p. 100.g. marchand ambulant, itinerant merchant, pedlar.-h.
te voilà, here you are.-. flattant, caressing.-j. il se mit, he
commenced; L. S. 68, R. 3.--k. trompé, mistaken; L. S. 37, R.
2.-. from comprendre ; L. part ii., p. 82.-m. L. S. 25, R. 2.-
n. see note j. above.-o. quelle ne fût, until she was.

SECTION III.

Alors, remuant la queue et regardant tour à tour Fanny et son maître, Moustache sembla la désigner comme celle qui lui avait donné ses soins. Le marchand apprit alors des enfants ce qui s'était passé ; le pauvre homme no savait comment leur témoigner sa reconnaissance,3 car dans ses longues courses, Moustache était non seulement pour lui un compagnon de route, c'était un véritable ami, un brave défenseur qui l'avait préservé de mille dangers. Il voulait mettre à la disposition des enfants toute sa petite cargaison; mais M. Dérambert s'opposa à ce qu'il fit aucun sacrifice onéreux; seulement, comme il tit que ce refus l'affligeait, il perinit à ses enfants d'accepter quelques jouets de peu de valeur. Le lendemain, le marchand partit en demandant à M. Dérambert la permission de revenir dans quelque temps visiter son habitation, ce qui lui fut accordé de grand cœur.

Trois mois à peine s'étaient écoulés depuis cette époque, lorsqu'un jour, Alfred, s'étant mis à la poursuite d'un papillon, s'écarta sans qu'on fit attention à sa disparition. Sur les dix heures du matin, heure à laquelle les trois enfants avaient l'habitude d'aller à la vallée déjeuner à l'ombre du

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7. Que permit-il à ses enfants
d'accepter?

8. Que demanda à M. Déram-
bert le marchand, à son
départ ?

9. Qu'arriva t il trois mois
après ?

mère et tous les domestiques ?

13. Trouvèrent-ils le petit garçon ?

14. Comment firent-ils ensuite ? 15. Examinèrent-ils

forêt ?

16. Leur

recherche

quelque succès ?

bien la

eut-elle

17. Quelle heure était-il alors? 18. Quel fut l'effet des approches

de la nuit, sur les parents de l'enfant ?

19. Voulurent-ils rentrer chez
eux ?

20. Que firent-ils ensuite?
21. Auguste et Fanny parta-
geaient-ils le chagrin de leurs
parents.

10. A quelle heure s'aperçut-on
de l'absence du petit Alfred?
NOTES AND REFERENCES.-a. L. S. 83, R. 4.-b. from
apprendre; L. part ii, p. 78.--e. from savoir; L. part ii., p. 104.
d. L. S. 81, R. 1.-e. from voir; L. part ii., p. 110.--f. L. part
2h. from mettre; L. part ii., p. 96.-i. L. S. 34, R. 1, 2.—j.
ii., § 49, R. (1).g. s'étaient écoulés, had elapsed; L. S. 44, R.
from paraitre; L. part ii., p. 98.-k, from battre ; L. part ii., p.
80.-1. firent, caused; from faire; L. part ii., 92; also L. S.
31, R. 3, 4.-m, from essayer; L. part ii., § 49, R. (2).

SOLUTIONS.

ANSWER TO THE "FOUR BALL" QUERY,
(p. 224, Vol. IV.)

If the four balls be placed in contact with each other, and

planes be supposed to pass through every three of their centres, they will constitute a tetrahedron, or solid whose four faces are four equal equilateral triangles, and whose cages (the sides of these triangles) are, in this case, each equal to 10 inches. The centre of the fifth ball is a point within this tetrahedron equally distant from its four angular points, which are the centres of the four balls; and the first question is to find the distance of this point from each of the said angular points.

In the figure, iet A B C D be the tetrahedron, each of the triangles A B C, A 3D, ACD, and BCD, being equilateral. Let

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