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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, s raons, clear, to capes, and or Mrs., or Messrs. It consists of an oval loop commencing ý tpinpns, 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-stroke Nom. o, n capns, το σαφες ; (σαφε-ες) σαφείς, (σαφεα) σαφή. in the same direction as before, but lower, in order to form the


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

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

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

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

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

N.A.V. σαφε-€, σαφη. two together. It is, in fact, the small a enlarged, with round

G.D. σαφε-οιν, 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. ή τριηρης,

(τριηρε-ες) τριηρεις. and bottom, the whole being made like our capital writing letter Gen. (τριηρε-δς) τριηρους, τριηρε-ων aad τριηρων. L, with a small loop terminating the last hair-stroke exactly Dat. (τριηρε-1) τριηρει,

τριηρε-σι. like our small writing b. The letter C is exactly like our letter Aco. (τριηρε-α) τριηρη,

(τριηρε-ας) τριηρεις. L in writing, with a small hook placed at the top loop. The Voc. τριηρες, ,

(τριηρε-ες) τριηρεις. letter D is more like the form 3 of the Greek letter th, or theta,

Dual. 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

G.D. our manuscript C with its lower half written below the line,

τριηρε-οιν and τριηρούν. and crossed by a curve, indicating the separation of the loop

I subjoin the declension of the proper names Lwxpatnis, and the scroll. The letter F is the second elementary leg with Socrates, and Nepidens, 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 Gen. Σωκρατους. . (Περικλεε-ος) Περικλεους. top, and lengthened below the line like our own G. It is, in Dat. Σωκρατει. . (Περικλε€-7) (Περικλεει) Περικλεί. fact, like the small letter g enlarged, with the angular turn of Aco. Σωκρατη. . (Περικλεε-α) Περικλεά. . its elementary leg rounded. The letter H is like our capital Voc. Σωκρατες. . (Περικλεες) Περικλεις. . G inverted, 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 and 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 -975, -es, when these terminations are preceded like our R badly shaped, and having a small hook at the top of by a vowel, ea is commonly contracted into i, as in the proper the middle stroke. The letter L is exactly like our own. The noun Teplied, and not into 7, as in rapea, raon; for example

, letter M consists of the first elementary leg doubled, and the ardens, unrenowned, makes akneea into akieâ, in the masculine third attached to the second by a small hook at the top. The and feminine accusative singular, and in the neuter nominaletter N is of the same form, excepting that the first leg is not tive, accusative, and vocative; so üyens forms úgia. doubled. The letter O is the first part of the letter A, with

Proper names of this termination, as well as Apns, 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 heteroclito (that is word per, in per cent., per pound, etc., only the top is round, of different declensions); accordingly, we have both Ewkpatn and and the final loop is more marked. The letter Q is like the Swepatny. But in those ending in -kans, the accusative in my 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 sometimes made like the letter O, with a hook attached to it at the bottom. The letter

VOCABULARY. R is very like our own, only its first part consists of the first Aloxpos, -ον, Δουλεια, ας, ή, ala-| Ποταμος, -ου, ο, elementary leg. The letter S consists of the first elementary shameful,

very, servitude.

river. leg, terminating in a small hook or curve at top. The letter T Akpatns, -es, immo-Eneatpw, I pity. Σοφιστης, -ου, ο, ο consists of the letter I terminated squarely at the bottom, and derate.

'EAwồns, -es, marshy. sophist. near that point crossed by the elementary leg of the small Annons, •es, true, Erauelvavoas, -ov, , Loponais, -ovs, d, alphabet from left to right. The letter U consists of a double honest.

Epaminondas. Sophocles. pot-hook, to which is attached the third elementary leg by a Avatayopas, -ov, o, 'Hpakañs, ous, D, Ewropia, -as, 8, salsmall loop at top. The letters V and W are only the letters Anaxagoras.


vation, of the small alphabet enlarged, with the angular turns rounded Atuxns, •es, unfor- Ivôlkn, ñ, India. Τοπος, -ου, like the first two in the letter M. The letter X is exactly like tunate.

Καλαμος,-ου,δ,a reed. place. our own. The letters Y and Z are like the small letters y Aparys,-es,unknown, 'Ouidia, inter-Tpayqoia

, -as, 4, traand z enlarged, with their angular turns rounded.

course (with dat.). gedy.


1. Αι Σοφοκλεους τραγωδιαι καλαι εισιν, 2. Τον Σωκρατη επι THE THIRD DECLENSION (continued).

τη σοφια θαυμαζομεν. 3. Σωκρατει πολλοι μαθηται εισιν. 4. Η

Ινδικη παρα τε τους ποταμους και τους ελωδεις τοπους φερει ! I MUST now direct your attention to nouns ending in -ης, -ες; -ως καλαμους πολλους. 5. Λεγε αει τα αληθη, ω παι. 6. Αναξαγορας, (gen. -wos), -ws and -w (gen. -oos), and in -as (gen. -aos), -os (gen. Joplotns, Oldaskalos no slepikAeous. 7. @ 'Hpakles, TOS -Cos). The stem of these words ends in o; the o remains at atuxeri owTmplar Tapexe. 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, d Ows, a jackal, tous Ow-ri. Of these words, let us consider first those which end in-ns,

EXERCISE 36.-ENGLISH-GREEK. -es. The terminations -ns (m. and f.), -es (n.), belong only to 1. Socrates had (in Greek, to Socrates was) wonderful wisdom. adjectives, and to proper names terminating in adjective forms 2. Pity unfortunate men. 3. We pity unfortunate men. 4. in-vos, -195,-yevns, -kpatns, -unons, -TELOns, odevns, and (-Khens) Many youths were disciples of Socrates. 5. Socrates had (in -KAñs. The neuter presents the pure stem.

Greek, to Socrates was) much wisdom. 6. They admire the The words of this class suffer contraction in all the cases, wisdom of Socrates. 7. The immoderate (man) serves a shameful except the nominative and vocative singular, and the dative servitude. 8. We admire the beantiful tragedies of Sophocles

. plural, after dropping the o. The words ending in -kdens being 9. True words are believed. 10. I pity the life of immoderate contracted into -klas, again undergo contraction in the dative I men. 11. Have not intercourse with immoderate men.

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a hero.




ή ηχω,

Ν.Α.V. ηχω.

G.D. ηχοιν.

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

and κερα, etc.; τερας, however, has the two forms only in the Singular. Plural. Singular. Plural. plural, the contracted are the more common-thug, τερά, τερών. Nom. και, ή θως, θω-ες. δήρως,


Gen. θω-ος, θω-ων. ηρω-ος, ηρω-ων.

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


Ανδρεια, Acc. θω-α,


a trumpet. θω-ας. ηρω-α and ήρω, ηρω-ας αnd ήρως.

ή,well-being, weal. Voc.

«ης, θως, θω-ες. ήρως,

Διατροφη, ήρω-ts.

ή, Θεμελιον, -ου, το, 8 Σημαινω, I give a nourishment. foundation.

sign (σημα, a sign), Dual.

Δυσκολος, -ον, dis-| Πεμπω, I send. I signify. Ν.Α.V. θω-. G.D. θω-οιν, Ν.Α.V. ηρω-. G.D. ηρω-οιν. satisfied,

grum- Προβατον, -ου, τo, a Υπαρχω, I exist. bling, hard.


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

Ελαφος, «ου, ή, These are all feminine. The ending -ws, in ordinary speech, is

& Προτρεπω, I turn to

pharmacy),-ου, το, stag. .

wards, exhort, en; medicine, preserved only in the substantive aidws, 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. Here follow

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

1. Οι θεοι τοις ανθρωποις τερα πεμπουσιν.

2. Των ν γηρα Singular. Plural.

Singular. Plural.

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

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

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

ποος διατροφην υπαρχει. 5. Κερασι και σαλπιγξιν οι στρατιωται Dat. (αιδο-i) αιδοί,

7. Καλου γηρως αιδοις. (ηχο-ϊ) ηχοι,

σημαινουσιν. 6. Ποικιλων κρεών γευομεθα.

ηχοις. Acc. (αιδο-α) αιδώ, αιδους. (ηχο-α) ηχώ, ηχους.

θεμελιoν εν παισιν εστιν ή του σωματος ευεξια. 8. Αι ελαφοι Voc. . (αιδο-ϊ) αιδοί, αιδοι. (ηχο-ϊ) ηχοι,


κερα εχουσιν. 9. Δυσκολος και εν γηρα βιος (sc. εστιν). Dual.

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

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

2. Soldiers are delighted with horns and trumpets. 3. We Βλεπω, I see. Kiew, ý, the Muse pooblemw, I look at. taste milk and flesh. 4. Death puts an end to (anoavei) the

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, «α,

sent, I am near, (dat.) presents. Ερατω, ή, Erato, one sad.

at, belong to. of the Muses. Λυρικος, -η, -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.

Πατρως,δ,an uncle on Σεβας, το (only with


the father's side.

the nom. and acc.),

1. All men have not the same mind. 2. We masticate our food 8, an historian. Πειθω, ή, power of reverence.

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

5. Many districts Κηπος, ου,δ, agarden

Vevou, I lie, deceive. part of a good man to bear all evils with courage.

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.

3. Αί 5. Ορεγου, ω παι, της αιδους. 1. Ημιν εστιν ελεφας. 2. Εν χωραις της Λιβυης ο ελεφας γιγνεται. 6. Αιδως αγαθοις ανδρασιν έπεται. 7. Λυσιαν επι τη πειθοι και του ήλιου ακτινές τους ποιμενας τερπουσι, 4. Οι αδελφοι τε και αι αδελφας χαριτι θαυμαζομεν. 8. Τη αιδοι προσεστι το σεβας. 9. Μη | χαιρoυσιν εν ταις ακτισι του 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 τσικ

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 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. stern : το σελας, splendour και το κρεας, Hesh.


1. Αί αγελαι επονται τα νομεί. 2. Ο αναξ εχει επιμελειαν του πολιτoυ. Ν.Α.Τ. το σελας.

3. Τα ωτα τειρεται ληρό των γραων. 4. Η γραυς εστι πολυλογος.. 5. ο το κρεας. Gen.

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


υπο των ιερεων. 7. Οι γονείς στεργονται υπο των τεκνων. 8. Αγαθου εστι Dat. . σελα-ϊ and σελα. (κρεα-1)


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


EUROPE (continued).

IN our present lesson, with a page map of the countries of σελα-€.


Southern and Central Europe, we give in a tabular form many G.D. σελα-οιν. (κρεα-οιν) κρεών.

useful facts relating to the most important of the independent After senas decline to detas, a goblet; after kpeas decline states of Europe. The first table, as will be seen, exhibits the

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 nonns whose stem ends in r-namely, the area and population of each, the number of inhabitants to 70 tepas, a prodigy, and to kepas, a horn, since after dropping every square mile, and the approximate amount of standing army.

good men.

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The remaining states of Europe which as yet preserve a sem- NORTH GERMAN CONFEDERATION.—The Kingdoms of Prusblance of independence, though the rulers of all of them may sia (1) and Saxony (2); the grand-duchies of Oldenburg (3), be considered as being virtually subordinate to the will of Mecklenburg-Schwerin (4), Mecklenburg-Strelitz (5), and Saxe Prussia, are included within the limits of the great central Weimar (6); the duchies of Anhalt (7), Brunswick (8), Saxeterritorial division of Europe called Germany. The states of Altenburg (9), Saxe-Meiningen (10), and Saxe-Coburg-Gotha (11); North Germany, with the exception of the German states of the principalities of Schwartzburg-Sonderhausen (12), SchwartzAustria, which is at present excluded from all participation in burg-Rudolstadt (13), Waldeck (14), Reuss-Schleiz (15), SchaumGerman affairs, are twenty in number, and form a federal union burg-Lippe (16), and Lippe-Detmold (17); and the free cities of for defensive and commercial purposes under the name of the Lubeck (18), Bremen (19), and Hamburg (20). North German Confederation. Southern Germany contains SOUTHERN GERMAN STATES.—The kingdoms of Bavaria (1) six states. In the following list of each the names of the states and Würtemburg (2); the grand-duchies of Baden (3) and Hessegiven in Tables I. and II. are printed in italics to distinguish Darmstadt (4); and the principalities of Reuss-Greiz (5) and them from the small states that are not included in these tables. Lichenstein (6).


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12 x 45


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. our 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, a, being days, we haveMoravia (3), Upper Austria (4), Lower Austria (5), Salzburg (6),

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

8x6 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 the duchies of Limburg and Luxemburg, and Hence, the sixth quantity, x, being weight, we have the other states named in the lists of the North and South

93 German States, is estimated at 243,375 square miles, while the

335 population may be approximately stated at 44,650,000. The

Or affairs of the North German Confederation are managed by a

9 diet or parliament, composed of representatives elected by the

Therefore x = y cwt. 3 cwt. 1 qr. 14 lbs, different states and the German provinces of Prussia in propor- EXAMPLE 3.-If 27 men can do a piece of work in 14 days tion to their inhabitants. The diet meets at Frankfort-on-the of 10 hours each, how many hours a day must 24 boys work, in Maine, formerly a free city, but which was absorbed by Prussia order to complete the same in 45 days, the work of a boy being at the close of the “Seven Weeks' War" with Austria in 1866, half that of a man ? with the kingdom of Hanover, the electorate of Hesse-Cassel,

27 men do the work in 140 hours; the duchies of Nassau, Schleswig, Holstein, and Lauenburg, Therefore

1 man

27 x 140 hours;

27 x 140 and small portions of Hesse-Darmstadt and Bavaria.

24 boys or 12 men

hours; 27 ~ 140

And therefore is the number of hours in the days, which LESSONS IN ARITHMETIC.-XXXIII.

27 x 140

are such that 45 contain hours, RULE OF THREE-SINGLE AND DOUBLE (continued).

27 x 140

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 length, but only 74 feet high?

feet high, if 11 men require 17 days to build one of the same 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 men the following :

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

acres in 6 days, If x be the time required, we have therefore-
1 man
acres in 6 days,

17 ī
And 1 man
acres in 1 day;

10 x 2 11 x 17 187
Therefore x =

= 12 days. Therefore, 12 men

acres in 1 day,


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

plough 33 acres in 10 days ? = 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 4s. 8d., what weight would be carried 93 miles for will earn £85 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. 88., or £3}, 5. If 6 men can make 120 pairs of boots in 20 days of 8 hours each, Therefore, 6) cwt.

1 mile for

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

hours a day? And 1 cwt.

1 mile for £

6. If 12 men can build a wall 30 feet long, 6 feet high, and 4 feet 124 x 61

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

3,5 Therefore, 1 cwt. 93 miles for £93 X

long, 8 feet high, and 6 feet thick ? 124 x 60

7. If £250 gain £30 in 2 years, how much will £750 gain in 5 years? i.e., for en

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

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

spend in 12 months ?
£1 4s. 3d.

= ?= 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 i0 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 is the price of wheat when the 60. loaf weighs 32 03. 8 dwt.?

11. If the 8d. loaf weighs 48 oz. when wheat is 543. a quarter, what 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 months, 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 hom 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 16s. in 8 days, and 2 men with been done, the process is easy.

3 boys earn £4 in the same time, in what time will 6 men and 7 boss The result, can, however, be always arrived at more simply earn 20 guineas ? by means of the following rule , which depends, however, upon 3 women earn .£3 38. in the same time, in what time will 6 men will

15. If 5 men with 7 women earn £7 13s. in 6 days, and ! men with an algebraical principle which we cannot explain here.

12 women earn £60 ? 10. Double Rule of Three. The five qnantities given to find a sixth. Call this should be the weight of the shilling loaf when wheat is 7s.6d. a bushel?

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

17. If 20 men can perform a piece of work in 12 diys, bow many - which kind increases with the increase of men will perform a piece of work half as large again in a bith part of








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8 x 6

12 x
8 x 6

12 x 15 x

8 x 6


And 12 x 15 x



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