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rather like that of a small m enlarged into a capital with loops singular. Learn both the contracted and the ancontracted at bottom, as employed often by ourselves when writing Mr., forms I am about to give of d, oaons, 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, i sapns, to capes; (cape-es) gapeis, (rapea) raon. in the same direction as before, but lower, in order to form the

(oapeos) capolls; (cape-wv) rapav. complete loop. The second is the body of the letter I, which

Dat. (cape-i) cadei; Capeol, is the same in German as in English handwriting; and the

(rape-a) cap, capes ; (cape-as) rapeis, (cape-aloaan. third is like the ordinary pot-hooks of our text-hand, tapered at

capes, apes; (cape-es) papeis, (cape-a) raon. 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. rape-e, raon. two together. It is, in fact, the small a enlarged, with round

G.D. Cape-otv, capoiv. 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. m Tonyms,

(tpimpe-es) Tpimpels. and bottom, the whole being made like our capital writing letter

(Tpinpe-os) Tpinpous, opinpe-ev and Tpinpwr. L, with a small loop terminating the last hair-stroke exactly Dat. (Tpinpe-t) Tpimpel, Tpinpe-ci. like our small writing b. The letter C is exactly like our letter

(Tpimpe-a) tpinpr, (Tpenpe-as) tpimpels. L in writing, with a small hook placed at the top loop. The


(Tpınpe-es) Tpinpers. letter D is more like the form 3 of the Greek letter th, or theta,

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

N.A.V. Tpimpe-t and spinpn. letter, being a mere flourish of the pen. The letter E is like

G.D. Tpinpe-olv and tpinpoiv. 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 Xwxpatns, and the scroll. The letter F is the second elementary leg with

Socrates, and Nepikens, 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. Xwkpatns. (Iepuriems) Iepukans. inverted, with the second attached to it by a small loop at the Gen. wkpatous. (Ilepikhee-os) NepikAeous. top, and lengthened below the line like our own G. It is, in Dat. Lwapater. (Ilepik ee-7) (IIepikeet) llepukaci. fact, like the small letter g enlarged, with the angular turn of Aco. Xwkpatn. (IIepikice-a) Tiepikaea. its elementary leg rounded. The letter H is like our capital Voc. Ewkpates. (Ilepik ees) Depikaels. 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 -9s, -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 å, as in the proper the middle stroke. The letter L is exactly like our own. The

noun Tepukaed, and not into 1, as in oopea, raon; for example, letter M consists of the first elementary leg doubled, and the

akmens, 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 runs formy úyia. 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 heteroclite (that is, word per, in per cent., per pound, etc., only the top is round,

of different declensions); accordingly, we have both <wkpatn and and the final loop is more marked. The letter Q 18 like the wapatny. But in those ending in Ans, the accusative in-1 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, -a, -ov, Aouleia, -as, n, sla- | norauos, -ov, d, a 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, -€5, immo-Eneatpw, I pity. ZooloTTS, -00, 6, % consists of the letter I terminated squarely at the bottom, and derate.

| 'EAw&ns, -es, marshy. I sophist. near that point crossed by the elementary leg of the small | Aanons, es, true, Emauelvavoas, -ov, 8, Xoponais, -OUS, 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 Ayatayopas, ou, d, 'Hpakañs, ous, , XwTnpia, -as, , sale small 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. Ivoikn), , India. TOTOS, -ov, d, 4 like the first two in the letter M. The letter X is exactly like

Kanapos,-ov,0,a reed. | place. our own. The letters Y and Z are like the small letters y Apavns,-es,unknown, / 'Ouidia, ý, inter- Tpayqdia, -as, 71, trland z enlarged, with their angular turns rounded.


I course (with dat.). I gedy.


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

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

Ινδικη παρα τε τους ποταμους και τους ελωδεις τοπους φέρει I must now direct your attention to nouns ending in -75,-es; -Wskalauous hollovs. 5. Aeye ael ta annon, w tai. 6. Aratayopes, (gen. -wos), .ws and -w (gen, -00s), and in -as (gen. -aos), -os (gen. 8 GOOISTNS, 018ao kalos ny slepikheous. 7. D'Hpakiers, Toes -EOS). The stem of these words ends in o; the remains at atUxEOT ownpay rapexe. 8. Emauewavdas matpos nv apara the end and before a consonant, but disappears in the middle 9. Elealpe TOV Atvy av pwnov. 10. Opeyere, w reavia, al no between two vowels. In the dative plural one o disappears; Loywy. 11. Oi akpateis aloxpay dovelay DovevovoWY. for example, d Ows, a jackal, tous Ow-ot. Of these words, let us consider first those which end in -os,

EXERCISE 36.-ENGLISH-GREEK. -es. The terminationg -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.. in -vns, Ans, -yevns, - patys, -undns, - teins, - odevns, and (-Kens) Many yonths were disciples of Socrates. 5. Socrates hsd (13 -KAîs. 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 beautiful tragedies of Sophocles plural, after dropping the o. The words ending in - dens being / 9. True words are believed. 10. I pity the life of immoderato -antracted into -Kins, again undergo contraction in the dative I men. 11. Have not intercourse with immoderate men.

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BRITISH ISLES . . . . | London . . . . . | Thames . . .
SWEDEN AND NORWAY . Stockholm. ...Lake Mälar.
RUSSIA IN EUROPE. . St. Petersburg .. Neva . . .
DENMARK . . . . . . Copenhagen . . . The Sound ..
PRUSSIA. . . . . . . Berlin . . . . . Spree . . .
MECKLENBURG-SCHWERIN | Schwerin ... Stor . . .


Hunte. . , HOLLAND




Senne. . . FRANCE. . . .

Paris. .

Seine . .

Aar .



Darm . . BADEN . . . . . .


Rhine. . WÜRTEMBERG . . .

Stuttgart .

Nesenbach. BAVARIA . Munich. ..

Iser . . .

. SAXONY . . . .

Dresden. .

Elbe AUSTRIA . . . .Vienna. .



The Bosphorus. GREECE. . . . .

Gulf of Egina . . .

Athens . . . . . ITALY . . . . . .

Florence . . . .

Arno . . . . . PAPAL STATES ....Rome . . . . .

Tiber . . . . . SPAIN . . . . . . . Madrid. . . . . Manzanares . . . PORTUGAL ... .. Lisbon, ... Tagus . . . . . .


291,900 2,043,400

14,500 137,070

4,835 2,417 10,900 11,315 211,850 15,235 3,240 5,900 7,675 29,620

6,780 227,235 203,630

19,950 107,500

4,890 182,760 36,510


5,351,100 65,845,500

1,601,000 22,770,000

548,500 295,250 3,372,650 4,893,000 37,472,750 2,534,250

852,250 1,369,300 1,721,000 4,690,000 2,225,250 34,671,000 15,500,000

1,332,500 24,150,000

692,000 16,302,000 3,585,000

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The remaining states of Europe which as yet preserve a sem-1 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), Sase-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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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), Styria (7), Illyria (8), and the Tyrol (9). The duchies of Limburg

8x6 and Luxemburg, mentioned above, belong to Holland or the

Therefore x = 32 *.= 120 days. Netherlands, as Holland is frequently called. The area of the 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, æ, 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

315 69 * 124; population may be approximately stated at 44,650,000. The affairs of the North German Confederation are managed by a

Or = diet or parliament, composed of representatives elected by the

Therefore r = 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 x 140,

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

are such that 45 contain *- *1 hours, RULE OF THREE-SINGLE AND DOUBLE (continued).

12 8. In Simple or Single Rule of Three, the method of performing

And 27 * 140 hours = 7 hours, the answer.

4 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 :

feet high, if 11 men require 17 days to build one of the same EXAMPLE 1.-If 8 men can reap 32 acres in 6 days, how 1

length, but only 74 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 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 therefore1 man

acres in 6 days,

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And 1 man ,

acres in 1 day; 8 x 6

Therefore x = 1952 12.= 15 = 124 days.


20 Therefore, 12 men , 12*5 acres in 1 day, 8 x 6

EXERCISE 52.-EXAMPLES IN DOUBLE ROLE OF THREE. And 12 men „ 12 x 15 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 ? And 12 x 15 x = 120 days, the answer.

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

will 9 persons drink in & 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 £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 £3%, 5. If 6 men can make 120 pairs of boots in 20 days of 8 hours each, Therefore, 6) cwt.

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 fi 61

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 69

7. If £250 gain £30 in 2 years, how much will £750 gain in 5 years? i.e., for £47.

8. What will £500 gain in 4 years, if £600 gain £42 in 1 year?

9. If 8 persons spend £200 in 9 months, how much will 18 persons Hence 21 ds. 3d. cwts, will be carried 93 miles for £1 4s. 30. Hence. Lily

spend in 12 months ? 1

10. If 15 men working 12 hours a day can hoe 60 acres in 20 days, 207 = == 3.

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 8d. loaf weighs 48 oz, when wheat is 54s. a quarter, wha: given above-i.e., by finding what quantity of one kind corre

is the price of wheat when the 6d, loaf weighs 32 oz. 8 dwt.?

12. If 35 barrels of water last 950 men 7 months, how many men sponds to one unit of each of the other kinds. Thus we have

would 1464 barrels last for 1 month ? 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 bon 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 sito been done, the process is easy.

3 boys earn £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 13s. in 6 days, and 2 men wild an algebraical principle which we cannot explain here.

3 women earn £3 38. in the same time, in what time will 6 men wila 10. Double Rule of Three.

12 women earn £60 ?

16. If the penny loaf weigh 6 oz. when wheat is 5s. a bushel, The five quantities given to find a sixth. Call this

should be the weight of the shilling loaf wben wheat is 7s.6d. a bus These six quantities will consist of 3 kinds

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

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