Imágenes de páginas

rather like that of a small m enlarged into a capital with loops singular. Learn both the contracted and the uncontracted at bottom, as employed often by ourselves when writing Mr., forms I am about to give of d, ý oaons, clear, to rapes, and or Mrs., or Messrs. It consists of an oval loop commencing ý tpimpns, a trireme, or galley with three banks of rowers. with a hair-stroke on the left, becoming thick and curved as it


Plural. turns round from left to right, and becoming again a hair-stroko Nom. d, n oanns, το σαφες ; (σαφε-ες) σαφείς, (σαφεα) σαφή. in the same direction as before, but lower, in order to form the

Gen. (σαφεος) σαφούς; (σαφε-ων) σαφών. complete loop. The second is the body of the letter I, which

Dat. (σαφε-ϊ) σαφεί; σαφεσι. is the same in German as in English handwriting; and the Acc.

(σαφε) σαφή, σαφες ; (σαφε-ας) σαφείς, (σαφε-α)σαφή. thii is like the ordinary pot-hooks of our text-hand, tapered at

Voc. σαφες, σαφες; (σαφε-ες) σαφείς, (σαφε-a) σαφή. the commencement of their formation. The capital letter A is formed of the first elementary leg

Dual, inverted, and the third added to it with a small loop joining the

N.A.V. σαφε-, σαφη.

G.D. two together. It is, in fact, the small a enlarged, with round

σαφε-ιν, σαφούν. instead of angular turns at top and bottom. The capital letter


Plural. B is formed of the second elementary leg, with a loop at top Nom.

η τριηρης,

(τριηρε-ες) τριηρεις. and bottom, the whole being made like our capital writing letter Gen. (τριηρε-ος) τριηρους, τριηρε-ων and τριηρων. L, with a small loop terminating the last hair-stroke exactly Dat. (τριηρε-1) τριηρει, τριηρέ-σι. like our small writing b. The letter C is exactly like our letter Acc. (τριηρε-α) τριηρη, (τριηρε-ας) τριηρεις. L in writing, with a small hook placed at the top loop. The Voo.


(τριηρε-ες) τριηρεις. letter D is more like the form 9 of the Greek letter th, or theta,

Drial. than anything we know. It scarcely deserves the name of a

N. A.V. τριηρε-€ and τριηρη. letter, being a mere flourish of the pen. The letter E is like


τριηρε-οιν and τριηρούν. our manuscript C with its lower half written below the line, and crossed by a curve, indicating the separation of the loop

I subjoin the declension of the proper names Ewkpatos, and the scroll. The letter F is the second elementary leg with Socrates, and Tepikaens,

Pericles; as strictly proper names, they a small hook at the top, and crossed in the middle with a fine

are found only in the singular. hair-stroke. The letter G is formed of the first elementary leg Nom. Σωκρατης. (Περικλεης) Περικλής. inverted, with the second attached to it by a small loop at the


Σωκρατους. (Περικλεε-ος) Περικλεους. top, and lengthened below the line like our own G. It is, in Dat. Σωκρατει. (Περικλεε-ϊ) (Περικλεει) Περικλεί. fact, like the small letter g enlarged, with the angular turn of

Acc. Σωκρατη. (Περικλεε-α) Περικλεά. its elementary leg rounded. The letter H is like our capital Voc. Σωκρατες. (Περικλεες) Περικλεις. Ginverted, with a small loop between the top and bottom parts

Mark the contraction in the dual of τριηρεε into τριηρη, and of it. The letters I anid J are like our own letters of similar not into the usual form in -el. name, sound, and position in the alphabet. The letter K is In adjectives in -ns, -es, when these terminations are preceded like onr R badly shaped, and having a small hook at the top of by a vowel, ea is commonly contracted into å, as in the proper the middle stroke. T'he letter L is exactly like our own. The noun IIepikaea, and not into n, as in capra, caoi; for example, letter M consists of the first elementary leg doubled, and the ακλεης, unrenowned, malkes ακλεεα into ακλεά, in the masculine third attached to the second by a small hook at the top. The and feminine accusative singular, and in the neuter nomina. letter N is of the samı, form, excepting that the first leg is not tive, accusative, and vocative; so vying forms vyră. doubled. The letter O is the first part of the letter A, with Proper names of this termination as well as Åpns, Mars, in a small loop at top.

the accusative singular, follow the first as well as the third The letter P is very like the P used by us in writing the

declension, and are therefore denominated heteroclite, (that is word per, in per cent., per pound, etc., only the top is round,

of different declensions); accordingly we have both Ewrpain and and the final loop is more marked. The letter Q is like the

Ewrpatny. But in those ending in -aans, the accusative in -1x letter G, with the bottom sharpened, and the hair-stroke from

is not Attic, and therefore not allowable. it turned the contrary way. It is sometiines made like the

VOCABULARY. letter 0, with a hook attached to it at the bottom. The letter R is very like our own, only its first part consists of the first Αισχρος, .a, -ον, Δουλεια, ας, ή, sla. Ποταμος, -ου, , a

shameful. elementary leg. The letter S consists of the first elementary

very, servitude.

river. leg, terminating in a small hook or curve at top. The letter T Ακρατης, -ες, immo- Ελεαιρω, I pity. Σοφιστης, -ου, ο, και consists of the letter I terminated squarely at the bottom, and


'Elwins, ec, marshy. sophist. near that point crossed by the elementary leg of the small

Αληθης, -EC, true, Επαμεινωνδας, -ου, ό, Σοφοκλής, -ους, ό, alphabet from left to right. The letter U consists of a double


Epaminodas. Sophocles.

Αναξαγορας, -ου, ο, Ηρακλής, ους, pot-hook, to which is attached the third elementary leg by a

, Σωτηρια, -ας, Anaxagoras.

Hercules. small loop at top. The letters V and W are only the letters

vation. of the small alphabet enlarged, with the angular torns rounded

Ατυχης, •ες, unfor. Ivềuen, , India. Τοπος, -ου, ο, και

tunate. like the first two in the letter M. The letter X is exactly like

Kulapos,-ov,ó, a reed. place.
The letters Y and Z are like the small letters y

Αφανης, -ες, αnknown, Ομιλια, inter. Tpaypdia, -asr,tra. and z enlarged, with their angular turns rounded.

course (with dat.) / gedy.


1. Αί Σοφοκλεους τραγωδιαι καλαι εισιν. 2. Τον Σωκρατη επι

τη σοφια θαυμαζομεν. 3. Σωκρατει πολλοι μαθηται εισιν. 4. Η THE THIRD DECLENSION (continued).

Ινδικη παρα τε τους ποταμους και τους έλωδεις τοπους φερει I must now direct your attention to nouns ending in -95,-ES; -WS καλαμους πολλους. 5. Λεγε αει τα αληθη, ω παι. 6. Αναξαγορος, (gen, -ωος),-ως and .ω (gen. -0ος), and in-ας (gen. -αος), -ος (gen. | ο σοφιστης, διδασκαλος ην Περικλεους. 7. Ω 'Ηρακλεις, τους -Eos). The stem of these words ends in o; the o remains at

ατυχεσι σωτηριαν παρεχε. 8. Επαμεινωνδας πατρος ην αφανούς. the end and before a consonant, but disappears in the middle 9. Ελεαιρε τον ατυχή ανθρωπον. 10. Ορεγεσθε, ω νεανια, αληθων between two vowels. In the dative plural one σ disappears; | λογων. 11. Οι ακρατείς αισχραν δουλειαν δουλευουσιν. for example, ó Doc, a jackal, toic Ow.oi. Of these words, let us consider first those which end in -915,

EXERCISE 36.- English-GREEK. -ES. The terminations -ns (m. and f.), -E5 (n.), belong only to 1. Socrates had (in Greek, to Socrates was) wonderfol wisdom. adjectives, and to proper names terminating in adjective forms 2. Pity unfortunate men. 3. We pity unfortunate men. 4. in -νης, -λης, γενης, -κρατης, -μηδης, «πειθης, -σθενης, and (-κλεης) | Many youths were disciples of Socrates. 5. Socrates had (in -klñs. The neuter presents the pure stem.

Greek, to Socrates was) much wisdom, 6. They admire the The words of this class sofl'er contraction in all the cases, wisdom of Socrates. 7. The immoderate (man) serves a shamefal except the nominative and vocative singular, and the dative servitude. 8. We admire the beautiful tragedies of Sophocles. plural, after dropping the o. The words ending in -klens being 9. True words are believed. 10. I pity the life of immoderate contracted into -adis, again nndergo contraction in the dative 11. Have not intercourse with immoderate men.

i, sal

[ocr errors]

our own.



[ocr errors]

η ηχώ,

Ν.Α.V. ηχω.

G.D. ηχοιν.

I next take up words in -ως (gen. -ωος); and in -ως And -ω the 7 they may be contracted in the same manner; Kepas follows (gen. -oos = -ous). The terminating o belongs to the stem. And kpeas throughout, but with the contracted forms. It has also first -ως (gen. -ωοs); for example, ο, ή θωs, a jackal, and ο ήρως, | regular forms with τ; thus, κερας, κερατος, and κερως και κερατι a hero.

and kepą, etc.; tepes, however, has the two forms only in the Singular. Plural. Singular. Plural. plural, the contracted are the more common- – this, τερά, τερών. Nom. ο, ή θως, θω-ts. ο ήρως,


VOCABULARY. Gen. θω-0s, θω-ων. ήρω-05, ήρω-ων.

•ας, Dat.


ή, Ευεξια (ευ & εχω),-ας, Σαλπιγξ, «ιγγος, ή,
θω-σι. ήρω-ι,


ή, well-being, weal. a trumpet. Acc.


θω-ας. ηρω-α αnd ήρω, ήρω-ας αnd ήρως. Voc.

θω-ES. ήρως,


Διατροφη, -ης, ή, Θεμελιον, -ου, το, ο Σημαινω, I give a nourishment. foundation.

sign (σημα, αείgη), Dual.

Δυσκολος, -ον, dis-| Πεμπω, I send. I signify. Ν.Α.Υ. θω-. G.D, θω-οιν Ν.Α.V. ηρω-. G.D. ηρω-οιν. satisfied, gruir- | Προβατον, -ου, τo, a Υπαρχω, I exist.

bling, hard.


Φαρμακον (whence I also give specimens of nouns in -ws and -w (gen. -005 =

ος =-ους).

Ελαφος, «ου, ή, Προτρεπω, I turn to- pharmacy), -ου, το, These are all feminine. The ending -ws, in ordinary speech, is


wards, exhort, en. medicine, mcans preserved only in the substantive alows, modesty, sense of shame;


of healing. the dual and plural are formed according to the termination -os of the second declension : thus, αιδοι, ηχοι, κ. τ. λ. Hero follow

EXERCISE 39.-GREEK-ENGLISH. the forms of ý aidws, modesty, respect, and i nxw, echo.

1. Οι θεοι τοις ανθρωποις τερα πεμπουσιν.

2. Των εν γήρα Singular. Plural.

Singular. Plural.

κακων φαρμακον ο θανατος εστιν. 3. Τα γερα τους στρατιωτας εις Nom. ή αιδώς, αιδοι.

ανδρειαν προτρεπει. 4. Εξ αιγων και προβατων γαλα και κρεα

ήχοι. Gen, (αιδο-ος) αιδούς, αιδων. (ηχο-ος) ηχούς, ηχων.

προς διατροφην υπαρχει. 5. Κερασι και σαλπιγξιν οι στρατιωται Dat.

7. Καλου γηρας αιδοις. (αιδο-ϊ) αιδοί, (ηγο-ϊ) ηχοι,

6. Ποικιλων κρεων γευομεθα. σημαινουσιν.

ηχοις. Aco. (αιδο-α) αιδώ, αιδους. (::::-α) ηχώ,

θεμελιoν εν παισιν εστιν ή του σωματος ευεξια. 8. Αι ελαφοι

(αιδο-ϊ) αιδοί,

9. Δυσκολος και εν γηρα βιος (sc. εστιν).
(...χο-ϊ) ηχοι, ηχοι.

κερα έχουσιν.

EXERCISE 40.-ENGLISH-GREEK. Ν.Α.V. αιδω. G.D. αιδοιν.

1. Prodigies are sent by (ÚTo with gen.) the gods to men. VOCABULARY.

2. Soldiers are delighted with horns and trumpets. 3. We

taste milk and flesh. 4. Death puts an end to (απολυει) the Βλεπω, I see. Κλειω, ή, the Muse Προσβλεπω,I lookat. evils of old age. 5. The king sends presents to the soldiers. Γοργω, ή,the Gorgon. Clio.

Προσειμι, I am pre- | 6. Presents encourage soldiers. 7. Soldiers are encouraged by Δμως, o, a slave. Λυπηρος, -Q,

sent, I am near,

(dat.) presents. Ερατω, ή, Erato, one Bad.

at, belong to. of the Muses. Λυρικος, , -ον, lyric. Προσωπον, -ου, το, και

KEY TO EXERCISES IN LESSONS IN GREEK.-X. Ευεστω, ή, good con. Λυσιας, -ου, ο, Lysias. face, countenance. dition.

EXERCISE 31,-GREEK-ENGLISH. Πατρως,δ,an uncle on Σεβας, το (only with “Ιστοριογραφος, «ου, the father's side. the nom. and acc.),

1. All men have not the same mind. 2. We masticate our food d, an historian. Πειθω, ή, power of

with our teeth. 3. Dolphins are man-loving (animals). 4. It is the

reverence, Κηπος,-ου,δ, agarden persuasion. Veusw, I lie, deceive. part of a good man to bear all evils with courage. 5. Many districts

of Lybia abound in ivory. 6. All people hate a loquacious man. 7. EXERCISE 37.-GREEK-ENGLISH.

Once the giants had a fight with the gods. 8. We rejoice in the rays

of the sun. 9. It is the office of the nostrils to smell. 1. Όμηρος αδει πολλους ήρωας (Or ήρως). 2. Την των ηρωων αρετην θαυμαζομεν. 3. Οι δμωες βιον λυπηρoν αγoυσιν. 4. Ο

EXERCISE 32.-ENGLISH-GREEK. του πατρωος κηπος καλος εστιν. 5. Ορεγου, ω παι, της αιδους. 1. Ημιν εστιν ελεφας. 2. Εν χωρις της Λιβυης ο ελεφας γιγνεται. 3. Αι 6. Αιδως αγαθοις ανδρασιν έπεται. 7. Λυσιαν επι τη πειθοι και του ήλιου ακτινες τους ποιμενας τερπουσι. 4. Οι αδελφοι τε και αι αδελφοι χαριτι θαυμαζομεν. 8. Τη αιδοι προσεστι το σεβας. 9. Μη | χαιρoυσιν εν ταις ακτισι τον ήλιου. 5. Η αδελφη εστι χαλη. 6. θαυμαζομεν προσβλεπε το Γοργούς προσωπον. 10. Ω Ηχοί, ψευδεις πολλακις τον καλον τον ελεφαντα. 7. Πολλοι ελεφαντες εισιν εν τη Λιβυη. 8. Οδοντων τους ανθρωπους. 11. Παντες ορεγονται ευεστους.

12. Πρεπει

εστιν εργον λεαινειν το βρωμα. 9. Παντος εστι σεβειν το θείον. 10. Τοις παιδι και νεανια αιδώ εχειν. 13. Κλειω και Ερατω Μουσαι εισιν.

θεοις ποτε ην πολεμος προς τους γιγαντας.


1. Kings have a care for their subjects. 2. The flock follows its 1. Homer sings (of) the hero Achilles. 2. The hero Achilles shepherd. 3. Hector is slaughtered by Achilles. 4. The priests is sung by Homer. 3. The bravery of the hero is wonderful. sacrifice oxen to the gods. 5. Cyrus was the son of good parents. 4. We admire the bravery of heroes. 5. Slaves have (say, to 6. The ungrateful dishonour their parents. 7. My son, obey your the slaves is) a sad life. 6. The uncle has (say, to the uncle is) parents.

8. Telemachus was the son of Ulysses. 9. Be willing to a fine garden. 7. All rejoice at their (the) good condition. 8. honour your parents before everything. 10. The idle tales of old women

11. You rule gloriously, o king. 12. Admire, O youth, with (ueta and gen.) modesty the deeds of wear away (weary) the ears.

Old women are very talkative. 13. Shepherds drive the flock of cattle good men. 9. By (dat.) the echo we are often deceived.

to pasture. 14. Homer likens the eyes of Juno to those of an ox,

16. We admire Cyrus, the Nouns in -as and -aos are declined as follows. Only a few 15. Patroclus was the friend of Achilles. neuters belong to this head. The terminating o belongs to the king of the Persians, because of his virtue as well as his wisdom. stem : το σελας, εplendour και το κρεας, lesh.


1. Αί αγελαι επονται τη νομεί. 2. Ο αναξ εχει επιμελειαν του πολιτoυ. Ν.Α.Υ. 1ο σελας.

3. Τα ωτα τειρεται ληρη των γραων. 4. Η γραυς εστι πολυλογοr. 5. Ο το κρεας.

πoιμην αγει την αγελην των βοων προς την πολιν. 6. Βοες θυονται τους θεοις Gen. σελα-0s.


υπο των ιερέων. 7. Οι γονεις στεργονται υπό των τεκνων, 8. Αγαθου εστι Dat. σελα-ϊ and σελα. (κρεα-ι, κρεα.

ποιμενος εχειν επιμελειαν των αγελων. Plural. Ν.Α.V. σελα-α and σελά. (κρεα) κρεα. Gen. σελα-ων. (κρεα-ων) κρεών.

LESSONS IN GEOGRAPHY.--XXIV. Dat. σελα-σι. (κρεα-σι)

EUROPE (continued).

In our present lesson, with a page map of the countries of Ν.Α.Υ. σελα-€.

(κρεα-ε) κρεα.

Southern and Central Europe, we give in a tabular form many G.D. σελα-ον.

(κρεα-οιν) κρεών.

useful facts relating to the most important of the independenti After gelas decline to detas, a goblet; after kpeas decline states of Europe. The first table, as will be seen, exhibits the TO ypas, old age, and to yepas, a present. With these two capitals of these states with the rivers, etc., on which they stand, last may be connected two nouns whose stem ends in t_namely, the area and population of each, and the number of inhabitants TO repas, a prodigy, and to kepas, a horn, since after dropping to every square mile.

[graphic][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][merged small][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][ocr errors][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][ocr errors][subsumed][subsumed][subsumed][ocr errors][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][ocr errors][ocr errors][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][ocr errors][subsumed][subsumed][subsumed][ocr errors][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][ocr errors][ocr errors][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed]


[blocks in formation]

The remaining states of Europe which as yet preserve a sem. | Tables I. and II. are printed in italics to distinguish them from blance of independence, though the rulers of all of them may the small states that are not included in these tables. be considered as being virtually subordinate to the will of THE GERMAN EMPIRE. - The Kingdoms of Prussia, Saxony, Prussia, are included within the limits of the great central Bavaria, and Wurtemberg; the grand-duchies of Oldenburg, territorial division of Europe called Germany. The new German Mecklenburg-Schwerin, Baden, Hesse-Darmstadt, MecklenburgEmpire was constituted by the treaties made at Versailles in Strelitz, and Saxe-Weimar; the duchies of Anhalt, Brunswick, 1871, after the close of the Franco-German War, under the Saxe-Altenburg, Saxe-Meiningen, and Saxe-Coburg-Gotha; the Presidentship of the King of Prussia, who bears the title of principalities of Schwartzburg-Sondershausen, SchwartzburgEmperor of Germany.

Rudolstadt, Waldeck, Reuss-Schleiz, Reuss-Greiz, SchaumburgWe give herewith a list of the states that make up the Ger- Lippe, and Lippe-Detmold; the free cities of Lubeck, Bremen, man Empire, and in every case the names of the states given in and Hamburg, and the provinces of Alsace and Lorraine.


[ocr errors]
[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small]
[ocr errors]



[ocr errors]

To give the reader an accurate idea of the extent of Germany both the other kinds. Then the ratio of the two quantities of and its territorial limits, it should be said that Prussia Proper, this kind will be equal to the ratio (See Lesson XX., Art. 2, comprising the two provinces marked East and West Prussia in Vol. I., page 342) compounded of the ratios of the others. ou map, and Posen, or Prussian Poland, are without the boun. 11. We will work out the previous examples by this rule. daries of Germany. The eastern portions of the duchies of EXAMPLE 1.-Here the acres increase if the men increase, Limburg and Luxemburg, however, are within its limits, and and if the days increase. nine provinces of Austria-namely, Bohemia (1), Silesia (2), Hence, the sixth quantity, &, being days, we haveMoravia (3), Upper Austria (4), Lower Austria (5), Salzburg (6),

12 x 15 Styria (7), Illyria (8), and the Tyrol (9). Tho duchies of Limburg

32 8 x B and Luxemburg, mentioned above, belong to Holland or the

12 x 15 Therefore x = 32 x

= 120 days. Netherlands, as Holland is frequently called. The area of the

8 x 6 whole of Germany, including the whole of Prussia except EXAMPLE 2.--Here the price increases if the weight increases, the parts which have been named, the nine Austrian states, the and if the distance increases. Dutch portions of tho duchies of Limburg and Luxemburg, and Hence, the sixth quantity, x, being weight, we havethe other states named in the lists of the North and South


93 German States, is estimated at 243,375 square miles.

330 63 The Emperor of Germany, as president or head of the several

Or states or kingdoms previously enumerated, represents the empiro in all cases of international law, and in respect of declaring Therefore x = y cwt. = 3 cwt. 1 qr, 14 lbs. war, making peace, treaties, &c. Notwithstanding, before any EXAMPLE 3.-If 27 men can do a piece of work in 14 days declaration of war can be made by him, he must obtain the of 10 hours each, how many hours a day must 24 boys work, in consent of the Bundesrath, a council of delegates of all the order to complete the samo in 45 days, the work of a boy being confederate governments. The Emperor is also the commander- half that of a man?

27 men do the work in in-chief of the whole army and navy in time of war, as he is

140 hours;
1 man

27 x 140 hours; also in time of peace, except in the cases of the kingdoms of

27 x 140 Bavaria and Wurtemburg.

24 boys or 12 men


27 x 140
And therefore

is the number of hours in the days, which


27 x 110 are such that 45 contain



27 x 110 And

hours = 7 hours, the answer. 8. In Simple or Single Rule of Three, the method of performing

12 x 45 which was explained in the last lesson, it will be found that

EXAMPLE 4.-How long will 20 men take to build a wall 10 questions of the following kind often occur :EXAMPLE 1.-If 8 men can reap 32 acres in 6 days, how feet high, if 11 men require 17 days to build one of the same

length, but only 7 feet high? many acres can 12 men reap in 15 days?

This we will work by the rule. Such questions can always be solved in a manner similar to

Here the amount of wall built increases if the number of me the following:

is increased, and if the time they work is increased.
Since 8 men can reap

acres in
6 days,

If æ be the time required, we have therefore
acres in
6 days,



7, 17 11
1 man
acres in

10 x 2 11 x 17 187
8 x 6
Therefore a =

121x days.


15 Therefore, 12 men

12 x

acres in 1 day, 8 x 6


32 And 12 men

12 x 15 x acres in 15 days. 1. If 12 horses can plough 11 acres in 5 days, how many horses can
8 x 6

plough 33 acres in 10 days?
And 12 x 15 x = 120 days, the answer.

2. If 40 gallons of water last 20 persons 5 days, how many gallons 8 x 6

will 9 persons drink in a year ? EXAMPLE 2.-If the carriage of 6 cwt. 3 qrs. for 124 miles 3. If 16 labourers earn £15 12s, in 18 days, how many labourers costs £3 45. 8d., what weight would be carried 93 miles for will earn £35 23. in 24 days? £1 4s. 3d.?

4. If 24 men can saw 90 loads of wood in 6 days of 9 hours each,

how many loads can 8 men saw in 36 days of 12 hours each ? Since 6 cwt. 3 qrs. is carried 124 miles for £3 4s. 8d., or £34, 5. If 6 men can make 120 pairs of boots iu 20 days of 8 hours each, Therefore, 6cwt.

1 mile for

how many days will it take 12 men to make 360 pairs, working 10 12+

hours a day?

36 And 1 cwt.

6. If 12 men can build a wall 30 feet long, 6 feet high, and 4 feet

thick in 18 days, how long will it take 36 men to build a wall 360 feet Therefore, 1 cwt.

93 miles for £93 X


long, 8 feet high, and 6 feet thick ? 124 x 63

7. If £250 gain £30 in 2 years, how much will £750 gain in 5 years? 1.o., for £1.

8. What will £500 gain in 4 years, if £600 gain £42 in 1 year? £1 4s. 3a. Heuco cwts. will be carried 93 miles for £1 4s, 3d.

9. If 8 persons spend £200 in 9 months, how much will 18 persons L!!

spend in 12 months ?
£1 4s. 3d.
2 = 3.

10. If 15 men working 12 hours a day can hoe 60 acres in 20 days,

how long will it take 30 boys working 10 hours a day to hoe 96 acres, The answer therefore is 3; cwt., or 3 cwt. 1 qr. 14 lbs,

3 men being equivalent to 5 boys ? 9. Questions of this kind can always be solved by the method

11. If the sd. loaf weighs 48 oz. when wheat is 54s. a quarter, what

is the price of wheat when the 6d, loaf weighs 32 oz. 8 dwt. ? given above-i.e., by finding what quantity of one kind corresponds to one unit of each of the other kinds. Thus we have would 1464 barrels last for 1 month ?

12. If 35 barrels of water last 950 men 7 mouths, how many men found, in the first example, how many acres can be reaped by

13. If 13908 men consume 732 barrels of flour in 2 months, in bor one man in one day. In the second example we have found long will 425 men consume 175 barrels ? what is the cost of carrying one cwt. one mile. After this has 14. If 3 men with 4 boys earn £5 1f3. in 8 days, and 2 men with been done, the process is easy.

3 boys enrn £4 in the same time, in what time will 6 men and 7 boys The result, can, however, be always arrived at more simply earn 20 guineas ? by means of the following rule, which depends, however, upon

15. If 5 men with 7 women earn £7 133, in 6 days, and 3 men with an algebraical principle which we cannot explain here.

3 women earn £3 3s. in the same time, in what time will 6 men with

12 women earn £60 ? 10. Double Rule of Three. There are five quantities given to find a sixth. Call this should be the weight of the shilling loaf when wheat is 78. 6d. a bushel?

16. If the penny loaf weigh 6 oz. when wheat is 58. a bushel, srbst sixth quantity o. These six quantities will consist of 3 kinds

17. If 20 men can perform a piece of work in 12 days, how many in pairs.

Observe which kind increases with the increase of men will perform a piece of work half as large again in a fifth part of

1 man

[ocr errors]


1 day;



[ocr errors]


1 mile for £124

[ocr errors]
« AnteriorContinuar »