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Dů Du Drie.

Brûlable Bru-lab” That is to be Flute Flute Flute. III, NAME AND SOUND OF THE VOWELS.



A cask, 43. 0, 0.—The o has, in French, three different sounds : short, Brûlot Bru-lo Fireship. Mûre Mure


Bru-lay To burn, Sûreté Sur-tay Safety. as in cob; broad and prolonged, as in cord; and full, as in Brûler

Crů Kru


Sur Sure Certain. coat. The short sound, as in cob, is the most common one. The

SECTION XIV.-PLAN OF THE EXERCISES IN COMPOSING o has a broad and prolonged sound, as in cord, when followed

FRENCH. by an r, thus-castor, encore, etc. The full sound, as in coat,

Hitherto the student has been occupied exclusively in acis always given to the o when it has a circumflex accent over it. quiring facts, forms, and principles, and in translating, by the It is also full when final, as in coco, loto, etc., and when aid of these, French into English, and again, English into followed by a mute consonant, as in mot, dos, etc.

French. Following still the plan of the work, let him now EXAMPLES OF THE SHORT SOUND.

undertake the higher business of endeavouring to compose in

French. With this intent, let him take some of the words FRENCH. PRONUN. ENGLISH FRENCH. PRONUN. ENGLISH. Bloc

given for this purpose in the following lists, and seek to incorBlok Block, Gobelet Gob'-lay Cup.

The words taken Bodine

porate them in sentences entirely his own.


Lo-kal Local.
Botte Bot


from the lists are to be used merely as things suggestive of Mod

Fashion. Crosse Kross Crosier. Morale Mo-ral Moral. thought. The form which, in any given case, the sentence may

assume, should be determined by the models found in the EXAMPLES OF THE BROAD, PROLONGED SOUND. sections preceding; for every sentence which the pupil has once FRENCH, Proxun. ENGLISH, FRENCH. PRONUN. ENGLISH. mastered in the regular course of the sections, is, or should be, to Castor Kas-tor Beavor. Essor Es-sor Flight.

him, a model on which he may at pleasure build other construcButor Bu-tor Bittern.


Port. tions of his own. Indeed, this constructing sentences according Encore Aun-kor Again. Bord

Shore. to models—that is, shaping one's thoughts according to the Corde Kord

Cord, Corridor Kor-ree-dor Corridor. forms and idioms peculiar to a foreign tongue—is the true and EXAMPLES OF THE FULL SOUND ACCENTED.

only secret of speaking and writing that language well. The

pupil, therefore, as he passes along in the ordinary course of the Frenci. PRONUN. ENGLISY. FRENCH. PRONUN. ENGLISH.

sections, should frequently be found applying his knowledge in Cite Kote

Prévöt Pray-vo Provost, Depot

the way of actually composing independent sentences; and thas Day-po Storehouse. Rile Role

Part. Dime Domne

he will soon acquire a facility and accuracy in the language, Dome. Roti Ro-tee (trill Roast-meat. Dröle Drole (trill Rogue.

the r)

which is hardly otherwise attainable at all.




Trône Trone Throne.
Pole Pole
Pole. Votre Votr

Yours. The words in the following lists are given as suggestive of


In conducting the exercise a particular word is

selected, as relieur (bookbinder), and the student is required to FRENCH, PRONUX, ENGLISH, | FRENCH. PRONUN. ENGLISH compose a French sentence containing this term. He is duly Mot Μο

Word. Zéro


Zero. notified that he is at liberty to take any thought suggested by Dos Back, Lo

the word, and to produce a sentence of any form found in any Repos R'po Repose. Os o


of the sections; regard being had all along to all the rules, notes, 44. U, u.—Name, U, u; sound, like the letter u in the English exceptions, etc., that may bear upon the case. Thus, adopting word brunette,

as a model the sentence, Votre marchand est bien obligeant The sound of this vowel is peculiar, and very diffionlt for (Sect. XVI., Résumé), or, Le Danois a-t-il quelques pommes? (Sect. Englishmen to obtain. We have no sound in the English lan. XVII. 7), etc. etc., let him endeavour to produce others of the guage which exactly corresponds to it. The nearest approach like kind. to it is the sound of u in the word brunette.

A little practice will render the exercise both easy and in.

teresting. It will soon come to be easy to incorporate not only EXAMPLES.

one, but two, three, or more of the words taken from the lists. FRENCH, Prostx. ENGLISE. FREXCE. PRONUN. ENGLISH. But Bu Tribu Tre-bu Tribe.

1. PROFESSIONS ET MÉTIERS.—PROFESSIONS AND TRADES. Ela Ay-la Elect. Tribune Tre-bune Gallery. Acteur, m., actor.

Fruitière, f., fruit-woman. Justice Zhus-teess Justies, t'ne 'ne Ome. Apothicaire, m., apothecary. Gantier, m., glover. Lune Lune Noon. T'nits t-nee-tay Crity. Artiste, m., artist,

Graveur, m., engraver. Nature Na-turo Nature. Crne t'rne t'rn, Aumonier, m., chaplain.

Horloger, m., clock and watchmaker. Plus Plu More Verta Ver-ta Virtuo Auteur, m., author.

Instituteur, m., institutrice, I., 45. Û, Û CIRCUMFLEX.—Name, ', w; sound, like the letter

Barbier, m.,

schoolmaster, mistress.
Bijoutier, m., jerceller.

Imprimeur, m., printer, u in the English word brunette.

Blanchisseuse, f., sasherwoman. Joaillier, m., jeweller. It must be acknowledged, however, that the English letter u Boucher, m., butcher.

Maçon, m., mason, bricklayer.' does not represent the correot sound of the French th, which is a Brasseur, m., breuer.

Naitre d'école, m., schoolmaster. combination of sounds not recognised in our language. Still, Brodense, 1., embroiderer.

Manouvrier, m., day-labourer. wo must use it as the representative of the sound of the French Charbonnier, m., coalman. Marehand-de-chevaux, maquignon, #l, for the want of a better one.

Charlatan, m., quack.

m., horse-dealer.

Maréchal ferrant, m., farrier, The following rule has also been given, and found useful - Charretier, m., cartman.

Chandronnier, m., coppersmith. shoeing-smith. The sound of the French w is based upon that of English e. Pro

Chirurgien, m., suren.

Maréchal, m., blacksmith. nounce the English letter s as naturally as possible, observing at Cordier, m., ropen aier.

Moissonneur, m., reaper. the same time the position of the internal organs of the mouth. Corroyeur, m., currier.

. Musicien, m., musician. Now keep these organs in the same position as nearly as pos. Coutelier, m., cutler.

Naturaliste, m., naturalist. sible, protrudo the lips as if to whistle, drawing them nearly Couturièr, f., seinster.

Orateur, m., orator. together at the same time, and then try to pronounce the Couvreur, m., slater, tiler. Orfèvre, m., gold and silver smith. English e again, which will give you the correct sound of the Cure, m., ticar,

| Pape, m., pope. French

Dentiste, m., dentist.

Pitre, m., shepherd, herdsman. Practise often aloud, according to the directions of this rule, Drapier, m., draper.

Perruquier, m., hairdresser. and success will crown your efforts. The rule has never ret Epicier, m. gnar.

Eeek'siastique, m., dergyman. Philosophe, m., philosopher. failed at the correct sound of the French' u in this Evêque, m., bester

Poissonnier, m, poissonnière, 1.,

jismonger. uded by the patient, persevering, and deter- Fauchenr, m., muset.

Pridiesteur, m., preacher. wupil.

Friper, m., a declar in old clothes. Prêtre, m., priest








Rafinear de sucre, de sel, refiner | Sellier, m., saddler.

Il n'a pas autant de ceux-ci que de He has not so many of these as ci of sugar, of salt. Serrurier, m., locksmith.

ceux-là ?

those. Ramoneur de cheminées, m., chim- Tapissier, m., upholsterer.

En a-t-il moins que votre frère ? Has he less of them) than your Rey-teeper.

Teinturier, m., dyer.
Relieur, m., bookbinder.
Tisserand, m., uceaver.
Il en a tout autant.

He has quite as many.
Savetier, m., cobbler.
Tonnelier, m., cooper.

Sculpteur, m., sculptor.
Vitrier, m., glasier.

Bleu, -e, blue.
Fer, m., iron.

Manuscrit, m., 2. L'HOMME.—MAN.

Courage, m., courage. Fromage, m., cheese. script. [smith. Ancêtres, m. pl., ancestors. Gendre, m., son-in-law.

Davantage, more. Hollandais, m., Dutch- Maréchal, m., blackArrière-petit-fils, m., great-grandson. Grand-père, m., grandfather. Drap, m., cloth.

Modestie, f., modesty. Bean-fils, in., son-in-law, step-son. Grand' mére, f., grandmother.

Ennemi, m., enemy. Italien, -ne, Italian, Soie, f., silk, Beau-frère, m., brother-in-law. Jeune homme, m., young man.

Espagnol, -e, Spaniard. Jardin, m., garden.

Très, very.
Beau-père, m., father-in-law, step-Jeune fille, f., young woman, girl. Estampe, f., engraving. Manteau, m., cloak. Verre, m., glass.
Jeunesse, f., youth.

Belle-fille, t., daughter-in-law, step- Jumeau, m., jumelle, f., tuin,
Marraine, f., godmother.

1. Êtes-vous aussi content que votre frère ? 2. Je suis aussi Belle-mère, f., mother-in-law, step- Mari, m., husband.

content que votre frère. 3. Votre père a-t-il autant de courage Naissance, f., birth.

que de modestie ? 4. Il a moins de modestie que de courage. Belle-sæar, f., sister-in-law. Nourrice, f., nurse.

5. Le libraire a-t-il autant de manuscrits que d'estampes ? 6. Bizieul, m., great-grandfather. Nouveau marié, bridegroom.

Il a plus de celles-ci que de ceux-là. 7. A-t-il autant d'amis Bru, I., daughter-in-law.

Nouvelle, mariée, bride. Descendants, pl., descendants, Orphelin, m., orpheline, f., orphan. que d'ennemis ? 8. Il a plus de ceux-ci que de ceux-là. 9. A-t-il Enfance, i., childhood. Parrain, m., godfather.

autant de pain que de fromage ? 10. Il a tout autant de celuiEpoor, m., épouse, f., consort. Petit-fils, grandson.

ci que de celui-là.

11. Le maréchal a-t-il plus de chevaux que Pamille, f., family. Petite-fille, granddaughter.

votre frère ? 12. Il en a plus que mon père et plus que mon Femme, f., woman, wifo. Veuf, m., widower.

frère. 13. N'avez-vous pas froid ? 14. Non, Monsieur, je n'ai Hançailles, f. pl., betrothal. Veuve, widow.

pas froid, j'ai très chaud. 15. Avez-vous deux manteaux de Fiancé, m., fiancée, f., betrothed. Vieillesse, f., old age.

drap? 16. J'en ai un de drap et un de velours bleu. 17. N'avez

vous pas plus de verres que d'assiettes ? 18. Nous en avons SECTION XV.-COMPARISON OF ADJECTIVES, ETC.

davantage.* 19. Le maréchal a-t-il plus de fer que d'acier ? 1. Adjectives and adverbs are always compared in French, as 20. Il n'a pas autant de celui-ci que de celui-là. 21. Il a moins they often are in English, by means of adverbs.

de celui-ci que de celui-là. 22. Les Hollandais ont-ils de beaux Plas beau, plus souvent, Handsomer, oftener.

jardins ? 23. Leurs jardins sont très beaux. 24. Les jardins

des Italiens sont plus beaux que ceux des Espagnols. 2. The comparative of equality is expressed by aussi—que, cs, or as much-03, before an adjective, an adverb, or a pronoun.

EXERCISE 26. Anssi aimé que son frère, As much

loved as his brother.

1. Are you more attentive than your sister? 2. I am not so

attentive as your brother. 3. Have you more courage than my Autant de-que de, as much, or as many—as, before a sub- brother ? 4. I have quite as much. *5. Has the blacksmith as stantive.

much money as iron ? 6. He has more of the latter than of the Antant de crayons que de plumes, As many pencils as pons.

former. (Sect. VIII. 5.) 7. Has he moro modesty than the Antaat de science que de modestie, As much science as modesty.

Spaniard ? 8. He has more. 9. He has more than your friend's 3. The comparative of superiority is expressed by plus-que, sister. 10. Are you not cold, Sir? 11. No, Sir, but I am afraid re-than, before an adjective, an adverb, or a pronoun.

and sleepy. 12. Has the Dutchman more cheese than the

Italian? 13. He has more cheese and more money. 14. Have Il est plus docile que son frère, He is more docile than his brother,

you as much English silk as Italian silk ? 15. I have more of Plus de que de, more—than, before a noun.

this than of that. 16. Who has more friends than the Spaniard ? Ilus de bonté que de jugement, More goodness than judgment,

17. Your friend has more. 18. Has the Spaniard as much of 4. The comparative of inferiority is expressed by pas si ; pas 20. Have we more silk cloaks than cloth cloaks ?

your money as of his ? 19. He has less of mine than of his.

21. We sussi; moins--que, not so ; not so ; lessthan, before an adjec. have more of these than of those. 22. Have you good cloaks? tive, an adverb, or a personal pronoun.

23. Yes, Sir, I have good cloaks, good hats, and good leather Vous n'êtes pas si grand que votre You are not so tall as your sister. shoes. 24. Have you more plates than dishes ? 25. I have not Strur,

more plates than dishes, but I have more glasses than plates, Il est moins poli que son cousin, He is less polite than his cousin.

26. Are you not very cold? 27. No, Sir, I am neither cold nor Pas tant de; pas autant de ; moins de que de, not so much, warm. 28. Has your carpenter wood ? 29. Yes, Sir, he has

so many; less ; fewerthan, before a substantive, a demon wood, money, cheese, and meat. 30. Who has more money than strative, or possessive pronoun.

the carpenter ? 31. The Dutchman has more. 32. Who has Il n'a pas tant de courage que de He has not so much courage as

more engravings than books ? 33. The bookseller has more of patience, patience.

these than of those. 34. Are you as attentive as your friend ? D a moins d'argent que de viande, He has less money than moat. 35. I am more attentive than my friend.

5. Tont autant-que is used for quite as many--as; as much,
just us much, or as many.
J'en ai tout autant que vous,
| I have quite as many as you.


PARSING AND COMPOSITION. a rez-vous antant de livres anglais, Have you as many English books as

By parsing is meant the telling of the parts (pars, Latin, a part) que de livres italiens ? Italian books?

of speech of which a composition consists. Parsing, besides J'en ai tout autant. I have just as many.

assigning the parts of speech, states the condition in which J'ai autant de ceux-ci que de I have as many of these as of those. the words are, and the relations in which they stand. In its

ceux-là. Il est aussi heureux que vous.

complete form, parsing cannot be done until the student is He is as happy as you.

acquainted with the entire grammar. But he may parse as he Avez-vous plus d'assiettes que de Have you more plates than dishes ? plata ?

goes, and as far as he goes. Viewed in this light, parsing is a J'ai plus de ceux-ci que de ceux-là. I have more of these than of those.

sort of practical review made by the student of what he has Esti plus complaisant que ses Is he more obliging than his brothers ? done at each step of his progress. Such a practice, if pursued frères ?

to the end, leads to a system of complete parsing. And such a Le Français a-t-il moins de légumes Has the Frenchman feirer regetables practice will greatly conduce to a thorough familiarity with the que de fruits ?

than fruits ? Da moins de livres que de many. He has fewer books than manuscripts. Davantage means more. It can never be placed before a noun. scrits.

It may be used instead of plus at the end of a sentence.

parts of speech, I


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The great difficulty with young writers is to find materials. LESSONS IN FRENT

In consequence, historical subjects are most suited to them. SECTION 1.-FRENCH PRONUN

Arbete for But in historical subjects, mere copying is easy, and hence it is

W&S apt to be substituted for original composition. It is, then, danIII. NAME AND SOUND Or

pranie wrth the gerous to entrust boys with mere historical subjects. As, 43. O, 0.—The o has, in French, thr:

* wandered however, I write for young men and young women, I shalí as in cob; broad and prolonged, em

un iegarsing, supply historical subjects; and, in order that the source of coat.

widus, in the information may be accessible to all my scholars, I shall take The short sound, as in cob, is t!

w already some of these subjects, at least at the first, from the Bibl o has a broad and prolonged sou

y successivo And narrative being the easiest form of composition, I shall by an r, thus-castor, encore, ete.

sunt. I will begin with supplying you with subjects for short narratives. is always given to the o when it h:

Here, then, is your first

HISTORICAL THEME. It is also full when final, as

God made the world. followed by a mute consonant, a

Now this is the method you are to observe. Read carefully, EXAMPLES OF TH

and as often as necessary, the account given in the commenceFRENCH. PRONUN. ENGLISH

ment of the book Genesis of the creation of the universe. Bloc Blok Block.

When you have impressed the record on your mind, close tha Bodine Bo-deen Keel.

wwwde wand give as full an Bible, and, taking slate and pencil, write down as much as Botte Boot.

possible in your own words, and in simple sentences, the subCrosse Kross


och en an, which has the stance of the account. Look over what you have written and EXAMPLES OF THE Bi. sunds beginning with a correct it. Having corrected it according to the best of your

own judgment, compare it with the original. Compare it first FRENCH. PRONUX. ENGLIE

de word mind; it comes in relation to the facts ; if in respect to the facts your report is Castor Kas-tor Beaver. Butor


sunt valour, the conduct not correct, make it correct. Compare it next in regard to the Encore Aun-kor Again.

spelling, and correct your spelling by the spelling of the Bible. Corde Kord


with its adjective virtuous Again compare it as to the words. You have one word, the w perb dislikes.

Bible has another. If your word is positively inaccurate, strike EXAMPLES OF TI!.

Domause it avers or declares it out, and put in its place the scriptural word. But a deviation FRENCK. PRONUN. ENGL lery, it constitutes the predi. in word on your part is desirable rather than not, for it shows Côte

Hill . which is stated of the subject, that you have comprehended the meaning of the passage, and Dépôt Day-po Store

that you possess, instead of a mere slavish imitation, a power of whject to the verb dislikes. The reproduction which may in time enable you to write truly Drôle Drole (trill Ro.

original compositions. If, therefore, your word is only somether) Nôtre Notr Ou .* por PARSING.

what legs appropriate than the word in the sacred page, let it Pole Pole


The language of truth is plain. stand; but at the same time ask yourself, and endeavour to EXAMPLES OF Tory is the food of vanity. The smiles of ascertain, why your word is less suitable. Should you, as you

stanoy in friendship denotes a generous can hardly fail to do, at least as your mind grows and your FRENCH. PRONUN. I from love. Ode vice is more expensive taste improves, meet in the Scriptures with forms of expression Mot Mo

o is never sullen. The proper test of which seem to you specially happy or specially forcible, tranDos Do

number of offenders lessen the disgrace scribe them into a little note-book, kept in the pocket, ever at Repos R'po I name of God with a song. Go to the ant, hand to receive memoranda, or things deserving to be remembered,

44. U, u.- Namo, to the upright. o dosoft answer turned in things requiring explanation, things illustrative of important word brunette.

2x quietly submits to the yoke. The love truth, etc.; and having transcribed them, look at them from The sound of this wil. Idunar, in a little for the time to time until you have made them permanently your own. Englishmen to obta we have no sound in the Engush ial- what may be called domestic history, out of which you guage which exa

responds to it. The nearest approach like kind. nt supply of useful and interesting materials. to it is the sea Sachin brunette.

A little practice I mean the occurrences and events of your teresting. It will sbeir humblest details. Here you may find

one, but two, three, or as a FREN

persons . Tre-bu

hrough the cxorcisos in parking, By domestic history arbonnier, m., coalman.


history during a day.

Gallery. Acteur, m., actor.
One. Apothicaire, m., apothecary. te every minute particular, such as
Artiste, m., artist.

you took, where you took them,
Aumonier, m., chaplain.

house, where you went to, what irtue Auteur, m., author.

whom you conversed, what was Barbier, m., barber.

?s and pleasures are closed and Carnever mind that your the time you rose, the meal juturière, f., seamster.

Bijoutier, m., jeweller.

ot commit the folly of thinking

Blanchisseuse, f., washerwoman.
transcription would be right. you retire to your laps With

Boucher, m.,

ir notice. You are learning to

ell only by beginning with that deuse, f., embroiderer.

you are poetically inclined, you

Write down on your sleutelier, m., cutler.
arretier, m., cartman.

me alone for a while; it is
audronnier, m., coppersmith.
nirurgien, m., surgeon.

ir sounds. It is good sense Xirdier, m., ropemakor.

ct English that I want to lead rroyeur, m., currier.

purpose practice in prose is 1

Cery rigid with yourself ; pass ouvreur, m., slater, tiler.

O as particular as if you were vicar.


according to the best of På

orrect, copy it out into an Drapier, m., draper.

to receive your attempts at Ecclésiastique, m., clergyman.

Epicier, m., grocer.

neatly and as well in Evêque, m., bishop.

fisition to neatness, which I Faucheur, m., mouer.

Prédie attainment of accuracy. Fripier, m., a dealer in old clothes. Prête in looking back on your



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may draw a constaa
well acquainted with the pre- own home, even in ti?
the end of each successive themes enough. Take
a short composition out of
, you may choose as your

My own
given you to parse, and
well as you can. At first,
er mind that your thoughts the times at which you left there

duti Di



tion. Composition is the such a subject unworthy of you
und then put down what inform yourself, and can begin wis
vur own thoughts. with which you are familiar. If it'
ials for composition, it may narrate
ins. Suppose that the

A morning
write is this proposi. But begin with prose ; let rhy

very easy to tag together simila and good feeling expressed in corre yon to, and for so important

indispensable. ad the import of the

But whatever your their
no error; correot all pri
writing for the pro
your ability, pro

Its composit


Do na

Pois as

earlier efforts, and comparing together your power of execution It may be useful to beginners to see the same thought exas it was at different periods.

pressed in simple propositions—that is, propositions or sen. It may be desirable to show you in an example how an tences, not having more than one subject and one object. humble there may be well treated in composition. I take for

BAKING.The same in simple sentences. the purpose one of Pestalozzi's “Paternal Instructions." It is

Baking is a fruit of civilisation. Indeed, all cooking is a fruit of en the domestic business of

civilisation, The savage knows of no preparation for his food. The BAKING.

savage eats everything raw. The brutes eat everything raw. The Baking, like all cooking, is a fruit of civilisation.

The savage

brutes also eat with greediness. With similar greediness does the kod no preparation for his food; he eats everything raw, like the savage take his food.

Art may be employed in preparing food. In a brutes; and accordingly he eats it like them, with brutal greediness. proper diet food is prepared by art. Baking, therefore, is an imporA proper diet is possible only when the food is prepared by art. tant business. Indeed, cooking in general is an important business. Baking, therefore, and every other sort of cooking, is a far more impor. Cooking is thought to be important. Still more important in reality tant business than at first sight it appears to be. By baking we is baking. By baking we procure the most wholesome of all putri. procure the most wholesome of all nutriment-that bread which, as a ment. By baking we obtain bread. Bread is a common necessary of cammoc necessary of life, we daily ask of God in the most comprehen. 'life. We daily ask bread of God. We ask bread of God in the most Eire of all prayers.

comprehensive of all prayers.



mult tan mit



tating the copies we have placed before them, if they tried to

copy capital letters at this stage of their instruction. The reason OUR readers, who have accompanied us thus far in our lessons is this, that the letters which the pupil has hitherto been copying in Penmanship, finding that they are now beginning to form consist, for the most part, of a straight stroke, while there is letters composed of the bottom-turn, the top-turn, and the top not a single capital letter that is not formed of sweeping curves, and bottom tain, with comparative ease, may be wishing to which cannot be made in a sufficiently graceful manner, unless hasten on a little more rapidly, and to be trying their hand at the learner has obtained that pliancy of wrist, freedom of exewriting capitals as well as the small letters. This is a laudable cution, and command over his pen, which can only be acquired wish, without doubt, and one which will be gratified in due by constant practice on the simpler letters. If he were time; but, for the present, our learners must be content to now to try to trace out the curves, that form the letter A advance slowly, remembering that slow progress is the curest he would find that his hand would begin to shake, and his and safest method of attaining proficiency in any art, as the down-stroke be crooked and ragged throughout, owing to the papil is thereby saved from the danger of hurrying on from one change of direction in which he is compelled to turn his pen ; point to another, for the sake of novelty, before he is thoroughly and when he returned to the easier letters, he would further grounded in the rudiments of the art that he is seeking to acquire. find that the check he has received had rendered him less Many who now find themselves able to make a thick down-stroke able to write letters that he had previously formed with ease. of uniform breadth throughout, such as is found in the letter For this reason we continue our copies in large text, as I would lose much of the facility with which they are now imi- exhibited above.


11. To multiply by 5.-Annex 0 to the multiplicand, and


To divide by 5.--Multiply by 2 and cut off the last figure, half (continued).

of which will be the remainder. 6. To divide by 10, or any power of 10.

To multiply by 15.--Annex 0, and to the result add its half. If the dividend have more ciphers for its right-hand figures To divide by 15.-Multiply by 2, cut off the last figure, and than occur in the power of 10 by which it is to be divided, we divide by 3; prefix the remainder so obtained to the figure cut need only take away from it the number of ciphers in the divisor off ; half the number so formed will be the true remainder. to obtain the quotient. Thus, 873000 divided by 100 and 1000 EXAMPLE.—To divide 327 by 15:respectively, gives quotients 8730 and 873. But suppose that

2 x 327 = 654 the dividend has no ciphers for its right-hand figures. Take,

3) 65,4 for instance, the case of 87346 divided by 100. Cut off the two right-hand figures—viz., 46—from the dividend; then 873 will

21 quotient, be the quotient and 46 the remainder. This is evident by

Leaving 2 as remainder from 65. exhibiting the process analytically, thus :

Putting this 2 before the figure cut offviz., the 4—we get 24, 87316 = 87300 + 46

which divided by 2 gives 12, the full remainder. = 873 X 100 + 46

To multiply by 75.—Annex two ciphers to the dividend, and Therefore 873 is the quotient, and 46 the remainder.

subtract from it its fourth part. The same rule applies to dividing by any power of 10.

To divide by 75.-Multiply by 4, cut off two figures, and 7. Next, suppose the divisor to be not a power of 10, but to divide by 3. Place before the two figures cut off the remainder have ciphers for its extreme right-hand figures; for instance, to got by dividing by 3, and divide the number so obtained by 4; divide 2764 by 300. There being two ciphers in 300, cut off this will give the whole remainder. the two right-hand figures-viz., 64—from the dividend, and Thus, to divide 2351 by 75, we have divide the 27 by 3; this gives 9, which will be the quotient,

and the 64 will be the remainder. This is evident by exhibiting
the process analytically, thus :-

2764 = 2700 + 64
= 9 X 300 + 64

31 for quotient,
Therefore 9 is the quotient, and 64 the remainder.

With remainder 1 from the 94. 8. In this last case there is no remainder after dividing 27 Prefixing this 1 to the 04 cut off, we have 104, which divided by 3. But suppose we have 2964 to divide by 300:

by 4 gives 26, the full remainder. Proceeding as before, cutting off the

300) 2964

To multiply by 125.-Annex three ciphers, and divide by 8. 64 and dividing 29 by 3, we get a quotient

To divide by 125.--Multiply by 8, and cut off the three right9 and a remainder 2. But evidently this

9-264 remainder. hand figures. These three figures divided by 8 give the reremainder is in reality 2 hundreds, or

mainder, the other figures being the quotient. 200; and therefore, since 64 is also left over, the whole

The truth of these processes will be better understood after remainder will be 264. Hence, in this case, any remainder the learner has read the chapter on Fractions. which is left must be prefixed to the figures cut off, in order to give the whole remainder. The process is exhibited analytically

EXERCISE 14. as follows :

1. Work the following sums in division by means of the 2964 = 2900 + 64

artifices shown above := 2700 + 200 + 64

1. 6035 – 5.

7. 3875 – 125.

13. 7853 • 55. =9x 300 + 264

2. 32561 – 5.

8. 1125 – 75.

14. 4860 25. Hence 9 is the quotient, and 264 the remainder.

3. 1256 + 15.

9. 3825 + 225.

15. 94880 25. 9. We subjoin one other example:

4. 3507 45.
10. 8450 +5.

16. 25426 - 125. To divide 25329483 by 723000.

5. 2350 + 25.
11. 43270 + 5.

17. 2876 • 175.
6. 42340 + 25.
12. 2673 * 35.

18. 8250 * 275. Cutting off three figures, viz., 483, from the dividend since there are three ciphers in the divisor--we divide 25329 by 723, nines repeated.

12. To multiply by a number represented by any number of by the common process of Long Division. This gives a quotient 35, and a remainder 24. Hence the required quotient is 35, and

Annex as many ciphers to the multiplicand as there are nines the whole remainder will be got by prefixing the 24 to the in the multiplier, and from the number so formed subtract the figures 483 cut off from the dividend. Hence the whole re

original number. Thus, to find 49276 x 99 — mainder is 24483. The process is analytically exhibited as

4927600 follows:

49276 subtract
25329483 = 25329000 + 483
= 35 X 723000 + 24000 + 483

4878324 Answer.
= 35 X 723000 + 24183

Hence the quotient is 35, and the remainder 24483.

1. Work the following examples in multiplication :-

1. 4791 x 99. I 2. 7301 × 999. / 3. 6034 999. | 4. 463 x 9999. 1. In one pound there are ten florins; how many pounds are there in 200 florins? In 340 florins? In 560 florins ?

13. To multiply in one line by a number expressed by turo 2. In one metre there are 100 centimetres; how many

figures. metres are there in 65000 centimetres ? In 765000 centimetres ? by the units' figure of the multiplier, add the product got bf

To the product of any figure in the multiplicand, multiplied In 4320000 centimetres ? 3. Work the following sums in division :

multiplying the figure next on the right of the figure first men

tioned by the figure in the tens' place of the multiplier. Write 1. 26750000 100000. 3. 582367180309 – 100000000.

down the units' figure of the number obtained by this process, 2. 141360791 - 1000000. 4. 3360000 – 17000.

and carry on the other (or others) as in common multiplication. 4. How many vehicles at 70 pounds apiece, can you buy for EXAMPLE.- To multiply 5768 by 73 in one line :7350 pounds ?

5768 5. How many barrels will it take to pack 36800 pounds of

73 pork, allowing 200 pounds to a barrel ?

421064 10. We do not go into a detailed explanation of the following

Thus, we say artifices, which are often useful in performing calculations with

3 x 8= 24; write down 4 and carry 2 out writing, or in mental arithmetic, as it is called. The truth

3* 6+ 2 = 20; 2) + 7 8=76; write down 6 and carry 7 of them will readily be seen by any one who has mastered the

3 * 7+7=28; 28 + 7 + 6 = 70; write down 0 and carry 7 previous processes, and their explanation will be a useful exer- 3* 5+7= 22; 22 + 7 * 7 = 71; write down 1 and carry 7 cise for the student.

7 * 5+7= 42, which write down.

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