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LESSONS IN FRENCH.-IV. SECTION L-FRENCH PRONUNCIATION (continued). III. NAME AND SOUND OF THE VOWELS (continued.) 36. BEFORE proceeding to the illustration of the sound and use of e mute or unaccented, let us commend the following extract to the careful perusal of the pupil. Speaking of the unaccented e, it is said "Several of our best orthoepists express themselves thus on that subject:— The proper utterance of the unaccented e characterises, in part, the pronunciation of the gentleman, as the vicious one marks the low-bred and ignorant. The unaccented e is sometimes pronounced and sometimes not; and in that consists a great difficulty for foreigners, who, always pronouncing it full, are long before they are able to follow a French conversation, and thence are inclined to believe that the French speak much faster than any other people. The truth is that the French, taking them in general, do not speak faster than other people; but in conversation, and in familiar reading, they drop the unaccented e as often as they can do it, and thus go quicker through a sentence than does a foreigner, who gives the full sound of u in tub to every unaccented e he meets with. Thus the word contenance, and the phrase je n'ai pas reçu tout le vêtement, will be pronounced by a foreigner and a Frenchman native of Gascony, con-te-nan-ce--je né pa re-çu tou le vê-te-men; whereas a well-bred Frenchman will pronounce, cont-nans-jné pa rsu toul vêt-men, sounding in the first word two syllables only, where the others would sound four; and in the sentence sounding six syllables, where the others would sound ten.'" The French custom of clipping or shortening words as much as possible, in ordinary reading and common conversation, is well illustrated in the following sentence, namely:

:

"Quand vous serez le même, vous me trouverez le méme." This sentence contains thirteen syllables in prose, namely Quand-vous-se-rez-le-même-vous-me-trou-ve-rez-le-même. In poetry, même would have two syllables. However, in familiar reading and conversation, it is pronounced in eight syllables only, viz.:— Quand-vou-srel-mêm-voum-trouv-rel-mêm. The suppression of this e is precisely the reason why foreigners imagine that the French speak so very quickly.

37. E, e, MUTE OR UNACCENTED.--Name, uh; sound, like the sound of the letter u in the English word nut; or, like the sound of the last syllable er in the words over and water, when spoken quickly.

The e mute or unaccented "is a mere emission of the voice without any distinct sound. It either succeeds a consonant, by the articulation of which it becomes sensible, or comes after a vowel, of which it may be considered the prolongation."

It is confessedly difficult to illustrate the sound of this vowel by the aid of English letters, yet it is worthy an honest attempt. True, it may be acquired from a teacher, by sheer imitation; but alas, all learners are not good imitators! If it can be illus. trated by analogous English sounds, it seems quite reasonable to suppose that through this process many more students would understand and acquire it, than if they were left merely to the

doubtful policy of imitation. Let us try.

Before the pupil attempts to pronounce the French words used for examples, let him observe most carefully the sound of the last syllable of the following words, when uttered as they usually are in common conversation, namely:

Moth-er, Broth-er, Nev-er, Sis-ter, Wa-ter. Take any one of the above English words, viz:-the first, moth-er. Pronounce it naturally and aloud with a full voice several times, until the common sound of the last syllable in particular is familiar to the ear. Take each of those words, and thus practise, by pronouncing aloud carefully, but naturally, observing at the same time the sound of the last syllable.

Now, by what combination of letters would you represent that sound? By ur, as in the first syllable of the English word mur-mur? or by uh? Manifestly the latter. Below are a few French words, which you will now proceed to pronounce aloud, giving to the vowel e in each example the last syllable of the word nev-er. Pronounce each of the following French words quickly and abruptly, as if an exclamation mark were placed over each one of them, namely:

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Co like suh.

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That is, like the sound of the last syllable of the English word baker, pronounced rather carelessly.

Take, if you please, another illustration, viz.: the sound of u sound of the French word ne. in the English word nut, as explained above, in illustrating the of e mute or unaccented. This will give the correct sound

The sound of e mute or unaccented resembles the sound of the these two words, viz.-the man. Apply the sound of this e, thus letter e of the word the, which is heard in pronouncing quickly pronounced, to the e in the following words, viz. :-ce, de, je, me, ne, se, te, que, etc.

sound of the English a pronounced naturally. Let the organs Or lastly, the sound of e mute or unaccented is based upon the within the mouth maintain as nearly as possible the same posi tion, whilst the lips are protruded as if to pout or whistle. Then, whilst the mouth is in this position, endeavour to pronounce the English a again; this, in a majority of cases, will give the correct sound of e mute or unaccented. Practise frequently on this last-mentioned plan aloud, and the ear will soon detect the viciousness or correctness of the sound. Most pupils find it will, in due time, overcome every obstacle. more or less difficult to acquire this sound; but perseverance

In illustrating the sound of e mute or unaccented, the followand the apostrophe, thus:

ing signs will be used, sometimes one, again the other, viz.:—uh,

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1. Votre frère a-t-il son encrier d'argent? 2. Il ne l'a plus, il a un encrier de plomb. 3. Avons-nous la lettre de l'étranger ? 4. Oui, Monsieur, nous avons celle de l'étranger. (R. 4.) 5. Votre sœur n'a pas son ardoise, mais elle a son chapeau de satin. 6. Le menuisier a-t-il votre bois ou le sien? 7. Il n'a ni le mien ni le sien, il a celui du jardinier. 8. Avez-vous mon bon parapluie de soie? 9. J'ai votre parapluie de soie et votre parasol de satin. 10. Avez-vous ma bouteille? 11. Je n'ai pas votre bouteille, j'ai la malle de votre sœur. 12. Le domestique a-t-il cette salière ? 13. Il n'a pas cette salière-ci, il a celle-là. 14. Avez-vous le bon ou le mauvais poulet? 15. Je n'ai ni celui-ci ni celui-là. 16. Quel poulet avez-vous ? 17. J'ai celui da cuisinier. 18. Le boulanger a-t-il de la volaille? (Sect. IV. 1.) 19. Le boulanger n'a pas de volaille, il a du lait. (Sect. V. 5.) 20. Avez-vous votre fromage ou le mien? 21. Je n'ai ni le vôtre ni le mien, j'ai celui du matelot. 22. Quelqu'un a-t-il faim? 23. Personne n'a faim. 24. Avez-vous quelque chose? 25. Non, Monsieur, je n'ai rien. 26. Avez-vous le sofa d'acajou de mon menuisier ? 27. Non, Monsieur, je ne l'ai pas. 28. J'ai son joli miroir et son bon crayon.

EXERCISE 14.

28. The stranger has no poultry, but he has money. 29. Your
brother is hungry and thirsty, afraid and sleepy. 30. Is any one
ashamed? 31. No, Sir, nobody is ashamed.
32. Is your
brother right or wrong? 33. My brother is right, and yours is
wrong. 34. Your sister has neither her satin hat nor her
velvet hat. 35. Has the baker the mahogany chest of drawers?
36. He has it not, he has the mahogany sofa. 37. Has the
tinman my plate? 38. He has not your plate, he has mine.
SECTION IX.-THE PLURAL OF NOUNS (§ 8).

1. The plural in French is generally formed, as in English, by the addition of s to the singular.

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4. 3rd EXCEPTION.-The following nouns ending in ou take for the plural:-bijou, jewel; caillou, pebble; chou, cabbage; genou, knee; hibou, owl; joujou, plaything.

Les bijoux, les cailloux, les choux, The jewels, the pebbles, the cabbages.
Les hiboux, les genoux, les joujoux. The owls, the knees, the playthings.

5. 4th EXCEPTION.-The following nouns ending in ail change that termination into aux for the plural:-bail, lease; corail, coral; émail, enamel; soupirail, air-hole; sous-bail, under-lease; travail, labour.

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Les généraux n'ont pas les bijoux.
Les enfants ont-ils les cailloux ?
Les yeux de l'enfant.
Les tableaux de cette église.
Avez-vous les oiseaux de ce bois?
Avez-vous les encriers d'argent de
ma sœur ?

J'ai les bijoux d'argent et d'or de
l'étranger.

Les rois n'ont-ils pas les palais de

marbre?

Baril, m., barrel.
Bas, m., stocking.
Bijou, m., jewel.
Chocolat, m., chocolate.
Chou, m., cabbage.
Dans, in.
Enfant, m., child,

the English the general's horses?

The generals have not the jewels.
Have the children the pebbles?
The child's eyes.

The pictures of that church.

Have you the birds of that wood?
Have you my sister's silver inkstands?

I have the gold and silver jewels of
the foreigner.
Have not the kings the marble
palaces?

VOCABULARY.
Général, m., general.
Gilet, m., waistcoat.
Grand, adj., large, great.
Jardin, m., garden.
Joujou, m., plaything.
Légume, m., vegetable.
Marchand, m., merchant.
Maréchal, m., blacksmith.
Mauvais, e, bad.
EXERCISE 15.

Meunier, m., miller.
Morceau, m., pieco.
Oiseau, m., bird.
Paire, f., pair.
Petit, adj., small.
Poivre, m., pepper.
Qu', que, what.
Rien, nothing.

1. Has your brother that lady's umbrella? 2. My brother has that lady's umbrella? 3. Have you this parasol or that one? 4. I have neither this (one) nor that (one). 5. Have you the stranger's gold watch? 6. No, Sir, I have the baker's. 7. Who has my slate? 8. I have your slate and your brother's. 9. Has the cook a silver salt stand? 10. The cook has a silver salt stand, and a silver dish. 11. Has the cook this poultry or that? 12. He has neither this nor that. 13. Has he this bread or that? 14. He has neither this nor that, he has the baker's good bread. 15. Have you my cotton parasol? 16. I have not your cotton parasol, I have your silk parasol. 17. Has the gardener a leather trunk? 18. The gardener has a leather trunk. 19. Who has my good cheese? 20. Nobody has your cheese, but some one has your brother's. 21. Have you mine or his? 22. I have neither yours nor his, I have 1. Avez-vous les marteaux du charpentier? 2. Nous avons the stranger's. 23. Has the cook this bottle or that broom? les marteaux du maréchal. 3. Les maréchaux ont-ils deux 24. He has this bottle. 25. Have you a lead inkstand? 26. marteaux de bois? 4. Ils ont deux marteaux de fer. 5. Les No, Sir, I have a china inkstand. 27. Has the stranger poultry? généraux ont-ils les chapeaux de soie de l'enfant ? 6. Ils ont

Fer, m., iron.
Fils, m., son.

les bijoux et les joujoux de l'enfant. 7. Les enfants ont-ils les oiseaux de votre bois? 8. Ils n'ont pas les oiseaux de mon bois, mais ils ont les chevaux de mon général. 9. Le maréchal a-t-il une paire de bas de laine? 10. Le maréchal a deux paires de bas de laine. 11. Monsieur, n'avez-vous pas froid ? 12. Non, Monsieur, j'ai chaud. 13. Avez-vous du café ou du chocolat ? 14. Je n'ai ni café ni chocolat. 15. N'avez-vous pas les choux de mon grand jardin ? 16. J'ai les légumes de votre petit jardin. 17. Votre fils, qu'a-t-il ? 18. Mon fils n'a rien. 19. Avez-vous deux morceaux de pain? 20. Le meunier a un morceau de pain et deux barils de farine. 21. L'épicier a-t-il du café, du thé, du chocolat, et du poivre ? 22. Il a du thé et du café, et le chocolat et le poivre de votre marchand. 23. Qui a de l'argent? 24. Je n'ai pas d'argent, mais j'ai du papier. 25. Avez-vous de bon papier ? 26. J'ai de mauvais papier.

EXERCISE 16. 1. Have you my brother's horses?

brother's horses, I have your cousin's hats. 3. Have the blacksmiths good iron? 4. The blacksmith has two pieces of iron. 5. Have you two pairs of stockings? 6. I have one pair of stockings and two pairs of gloves. 7. Has your sister the gold jewels? 8. My sister has the gold jewels and the paper playthings. 9. Have you the cabbages in your garden? 10. We have two cabbages in our garden. 11. Have you the silk hats? 12. The generals have the silk hats. 13. Have you coffee or sugar? 14. We have neither coffee nor sugar. 15. Are your brothers ashamed? 16. My brothers are neither ashamed nor afraid. 17. Who has two barrels of flour? 18. The miller has two barrels of flour. 19. Have the birds bread ? 20. The birds have no bread. 21. Has the merchant tea, chocolate, sugar, and pepper? 22. He has sugar and pepper, but he has neither tea nor chocolate. 23. What has your sister? 24. She has nothing. 25. What is the matter with your brother? 26. Nothing is the matter with him. 27. Is he not cold? 28. He 2. I have not your is not cold, he is warm.

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LESSONS IN PENMANSHIP.-IV.

As it is impossible for any one who is attempting to teach himself the art of Penmanship to write well without practice, we now give three more combinations of pairs of the four letters that the reader has already learned to make, before passing on to other letters of the alphabet in writing, for whose formation strokes are required that differ in shape and character from the first elementary stroke that forms the basis of the letters i, u, t, 1. At this stage of our Lessons in Penmanship, it may not be out of place to say something about the kind of handwriting that the students of this part of the POPULAR EDUCATOR are practising, and to give those who may feel disposed to rule paper for themselves, in imitation of our copy-slips, a few brief instructions that will enable them to do so.

First, with regard to the kind or description of handwriting that is set before our readers in our present series of elementary copy-slips, it should be said that it is called Large Text, and that it is the largest, plainest, and boldest of the four kinds of handwriting usually practised by learners. The three hands that yet remain to be named are termed Text Hand, Round Hand or Half Text, and Small or Running Hand. Of these, Large Text is usually written between lines half an inch apart; Text Hand, between lines one-third of an inch apart; Round Hand, between lines five-twenty-fourths of an inch apart, or

rather less than one-fourth of an inch; and Small Hand, on
single lines, and sometimes between double lines three-
thirty-seconds of an inch apart, or rather less than one-eighth
of an inch. For those who may not have a graduated scale of
inches, we append a printed scale, show-
ing the respective widths of the four
kinds of writing that have been named.

Large Text inch.

Text Hand inch.

Round Hand inch.
Small Hand inch.

Now, to show our readers how to rule a page wherein to copy any of the examples that have been or will be given, let us suppose that the learner wishes to prepare paper for copying t1, as in Copyslip No. 10. First rule two lines, one on either side of the page, close to the margin, from top to bottom, taking care that they are parallel to each other that is to say, at equal distances from each other all the way down. Then rule a line across the top of the page, also close to the margin and at right angles to the parallel lines at the sides of the paper, or square with them," as a joiner would say, and, commencing from this line, set off with compasses along the side lines distances equal to e d, da, ac, cb, in order, as in Copy-slip No. 10, and repeat this as often as the length of the paper will allow, taking care to leave a space of one-fourth of an inch between the last of each set of five lines and the first of the next which

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follows. The distances e d, a c, cb, are each equal to one-fourth of an inch, and da to three-sixteenths of an inch.

By following the above instructions, the learner will be enabled to rule his paper in sets of five horizontal and parallel lines, five lines being required in each set, in this case, to determine the height of the letters and their relative proportions one to another, To rule the diagonal lines (No. 5), set off e xalong the topmost line ee, equal to thirteen-sixteenths of an inch, and draw a straight line through the points bæ. This will serve as your guide line for regulating the remainder of the sloping lines, and all that remains to complete them is to set off spaces along the lines ee, bb, equal to x y or b z, and rule straight lines passing through every succeeding pair of points, commencing from the first pair xb, through which the guide line for regulating the inclined lines was drawn.

LESSONS IN GERMAN.-III.
SECTION V.-THE NOUN. OLD DECLENSION.

THERE are in German four cases, namely: the Nominativ, | answering to the English nominative; the Genitiv, answering to the English possessive; the Dativ, which has no corresponding case in English; and the Accusativ, which answers to the English objective.

Of the four cases, the dative, without a preposition, generally

corresponds to our objective governed by to or for, as :34 gebe dem Manne das Glas. I give (to) the man the glass. Er macht tem Manne einen Hut. He makes (for) the man a hat. Often, however, the dative in German is construed with a preposition, where, as above, the objective is of course employed

in English, as :—

Das Kind ist in dem Hause,

Der Hund ist unter tem Baume. Der Jäger geht nach tem Walte. Der Mann ist auf dem Schiffe. Ta keh ist an tem Tische.

The child is in the house.
The dog is under the tree.
The hunter goes to the forest.
The man is on the ship.
The cook is at the table.

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Nouns ending in 8, B, 3, or two consonants, generally add cs in the genitive, thus, like our words which end with the sound of s, z. 1, soft c or s, forming an additional syllable.

Nem. Das Ros, the horse. Gen. Des Rosses, the horse's. EULES FOR FORMING THE CASES OF NOUNS ACCORDING TO THE OLD DECLENSION.

RULE I. The genitive adds 8 or es to the nominative.
RULE II. The dative drops the 8 of the genitive (§ 13. Note).
RULE III. The accusative is like the nominative.

DECLENSION OF NOUNS ADDING IN THE GENITIVE.

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Auf, on.
Ball, m. ball.
Bruter, m. brother.
Durstig, thirsty.
Freund, m. friend.
Hunt, m. dog.
Gut, m. hat.

The father of the child gives (to) the brother the bird. The ruler of the state sends (to)

the warrior the sword.

VOCABULARY.

In, in.
Korb, m. basket.
Leben, to praise.
Pfert, n. horse.
Sad, m. bag.

Schläfrig, sleepy.
Schüler, m. scholar.
Sein, to be.

RÉSUMÉ OF EXAMPLES.

Der Wolf lebt in dem Walte.
Das Kind liebt den Bruter.
Der Lehrer lobt des Schülers Fleiß.

Der Schnee liegt auf dem Verge. Das Märchen hat des Vaters Hut. Der Sohn des Bäckers hat Brob in rem Korbe; er giebt es tem Bettler.

Sohn, m. son.
Stall, m. stable.
Stuhl, m. chair.
Tischler, m. joiner.
Unter, under.
Wo? where ?
Zimmer, n. room.
Zimmermann, m. car-
penter.

The wolf lives in the forest. The child loves the brother. The teacher praises the scholar's industry.

The snow lies on the mountain. The girl has the father's hat. The son of the baker has bread in the basket; he gives it to the beggar.

EXERCISE 6.

1. Sind Sie der Freund des Bäckers? 2. Nein, ich bin der Freund des Tischlers. 3. Was hat der Freund des Fleischers? 4. Er hat den Hund und das Pferd des Bauers. 5. Wo ist das Mehl? 6. Es ist in dem Sade des Müllers. 7. Wo ist das Korn? 8. Es ist in dem Korbe des Bauers. 9. Wer liebt den Lehrer? 10. Der Schüler liebt den Lehrer. 11. Sind Sie schläfrig? 12. Nein, ich bin durftig. 13. Wo ist der Ball des Bruders? 14. Das Kind hat den Ball des Bruders in dem Hute des Vaters. 15. Wo ist das Pferd des Lehrers? 16. Es ist in dem Stalle. 17. Lobt der Tischler den Zimmermann? 18. Nein, der Sohn des Zimmermanns lobt den Sohn des Lehrers. 19. Wo ist der Stuhl des Tischlers? 20. Gr (Sect. XVIII. 3) ist in dem Zimmer des Lehrers. 21. Liebt der Zimmermann den Lehrer? 22. Ja, er liebt und lobt den Lehrer. 23. Der Mann ist an dem Tische, das Buch ist auf dem Lische, und der Hund ist unter dem Tische.

SECTION VI.-DEMONSTRATIVE PRONOUNS. Dieser" is declined, in the masculine, precisely like the definite article; while in the neuter, as will be seen in the following declension, all its endings, except the dative, are alike [§ 62. (2)].

* By the references in Roman numerals, thus (Sect. XVIII. 3), as above, the learner is directed to Sections in Part I. of these Lessons. References thus [§ 62 (2)] refer to the Sections in Part II.

DECLENSION OF Dieser: MASCULINE AND NEUTER SINGULAR

COMPARED WITH THE DEFINITE ARTICLE.

Masculine.

N. (d-er) dies-er, this;

G. (d-es) dies-cs, of this;

D. (d-em) dies-em, to, for this;

A. (d-en) dies-en, this;

Neuter.

(-as) dies-cs, this;

(d-es) dies-es, of this; (d-em) dies-em, to, for this; (-as) bies-es, this.

DECLENSION OF THE INTERROGATIVE Ber AND THE PERSONAL PRONOUN er AND C8 IN THE SINGULAR.

N. Wer? who?

Masculine. er, he;

G. wessen? whose?

seiner, of him;

D. wem? to, for whom?

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Neuter. es, it; feiner, of it;

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1. Wo ist der Bruder des Steuermanns? 2. Er ist bei dem Caritain in dem Schiffe. 3. Ist der Sohn des Erelmanns auch bei ihm? 4. Nein, er ist in Deutschland. 5. Wo ist der Vater? 6. Er ist bei dem Capitain in tem Zollhause, 7. Lobt ter Capitain ten Sohn des Etelmanns? 8. Ja, und er lobt auch den Vater. 9. Liebt der Etelmann ten Capitain? 10. Ja, er liebt und lobt ihn sehr. 11. Ist dieser Mann der Sohn des Capitains? 12. Nein, er ist der Sohn des Steuermanns. 13. Ist dieser

ihm, to, or for him? ibm, to, or for it; Matrose reich? 14. Nein, er ist arm und fröhlich. 15. Wie alt ist dieser

ihn, him;

VOCABULARY.

Gold, n. gold.

Bürgermeister, m., bur-Haus, n. house.

gomaster, mayor.

Dieser, dieses, this.

Für, for (§ 113).
Garten, m. garden.

Geld, n. money.

Hut'macher, m. hatter. Kupfer, n. copper. Leter, n. leather.

Papier', n. paper. Rod, m. coat.

RÉSUMÉ OF EXAMPLES.

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cs, it.

Sattler, m. saddler. Schneiter, m. tailor. Schuhmacher, m. shoe

maker.

Silber, n. silver. Bon, from, of.

This child

Dieses This youth is poor. is sleepy. This youth's hat is new. This girl's ribbon is beautiful. Do you give this beggar and this child money?

Geben Sie diesem Bettler und tiefem

Kinde Geld?

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1. Wer hat das Papier dieses Mädchens? 2. Dieses Kind hat es. 3. Wessen Buch hat dieser Schüler? 4. Er hat das Buch des Lehrers. 5. Von wem haben Sie dieses Leder? 6. Ich habe es von dem Schuh macher. 7. Für wen ist dieser Apfel? 8. Er (Sect. XVIII. 3) ist für das Kind des Sattlers. 9. Wessen Rock hat der Sohn des Schneiders? 10. Er hat den Rock dieses Freuntes. 11. Von wem hat der Sohn diefes Hutmachers Geld? 12. Er hat Geld von dem Vater. 13. Wo ist der Wagen des Bauers? 14. Der Freund des Lehrers hat ihn. 15. Wessen Haus und Garten hat der Lehrer? 16. Er hat das Haus und den Garten tes Bürgermeisters. 17. Von wem haben Sie diesen Hut? 18. 3d habe ihn (Sect. XVIII. 3) von dem Hutmacher. 19. Für wen ift er? 20. Er ist für den Sohn des Schneiders. 21. Haben Sie Gold, Silber, oter Kupfer für den Lehrer? 22. Ich habe Silber für ihn. 23. Wen liebt das Kind? 24. Es liebt den Bruter des Lehrers.

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Mann? 16. Er ist nicht sehr alt. 17. Ist er frank? 18. Nein, er ist hungrig. 19. Was gibt dieses Märchen tem Kinte? 20. Es (§ 134. 2) gibt ihm nur Zucker. 21. Was geben Sie dem Knechte? 22. Ich gebe ibm Geld. 23. Was gibt der Knecht dem Pferte? 24. Er gibt ihm Heu. 25. Liebt dieses Kind den Lehrer? 26. Ja, und der Lehrer lobt das Kind. 27. 3ft der Jäger noch in dem Walte? 28. Ja, und der Sohn des Etelmauns ist bei ihm. 29. Der Jäger geht nach dem Walde zu dem Vater, und ich gehe zu dem Bruder.

MECHANICS.-II.

THE UNIT OF FORCE.-FORCES APPLIED TO A POINT. HAVING in our first lesson explained the meaning of the word "force," and shown how a force is applied and measured, we shall next consider the simplest kind of mechanical problem, that of several applied to a single point. Before I proceed, however, it is advisable to fix clearly your notions of the "unit of force." I have already laid down the rule, that a force may be measured by the number of fect it would cause the unit ivory ball, equal in weight to a cubic inch of pure water, to move over in one second, when applied to it suddenly by a blow. If the ball move over seven feet, the number 7 should be written for the force; if over a furlong, the number is 660, the feet in a furlong. But suppose it moves over exactly one foot, then it is clear that the numeral 1 should be written; and that particular force is the " one of forces. And the conclusion to which we thus are led is that

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THE UNIT OF FORCE is the force which would,. if applied instantaneously to the unit of mass, make it move over one foot in one second.

But you can clearly see that the force which could produce no greater velocity than this in the ball-which, instead of being ivory, we may take to be a ball of frozen water, a cubic inch in volume-cannot be a very strong force. In fact, it is equal to a little less than eight grains of weight, that is, this unit of force could be balanced by that with which an eight-grain weight pulls downwards. How this is ascertained I cannot here explain to you, as you would require some little knowledge of dynamics to understand the proof. For the present, therefore, you must take my statement on credit.

But this unit is evidently too small for practical purposes. The strains in the mechanical powers, the lever, the wheel and axle, the pulley, etc., and in roofs and bridges, cannot be calculated in grains, on account of the large numbers we should have to operate on. A larger unit is therefore necessary, and the pound weight exactly answers the purpose. We can calculate and measure forces in pounds; or, if the figures in that case be too large, we can calculate them in hundredweights, or even in tons. All that is necessary is to keep clearly in mind what your unit is in your calculation, and to know how to pass from one unit to another. If, in the same calculation, you were to use different units in different places-a pound for instance, in one, and a hundred-weight in another-without reducing the one to the other, the result could be nothing but confusion and error.

But how are you to pass from one unit to another? This is a nice point in practice, as we shall see in due time; but this much is clear, that, if your unit be a hundred-weight, you should multiply all the numbers which represent your forces by 112 (the number of pounds in a hundred-weight), and then these forces will be expressed in pounds. If they are already ex pressed in pounds, then divide by 112, and you will have them

Was sagt dieser Mann tem Lehrer? What says this man to the in hundreds and fractions of a hundred-weight. And so, from

teacher?

hundred-weights you can pass to tons by dividing by 20, and

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