rather like that of a small m enlarged into a capital with loops at bottom, as employed often by ourselves when writing Mr., or Mrs., or Messrs. It consists of an oval loop commencing with a hair-stroke on the left, becoming thick and curved as it singular. Learn both the contracted and the uncontracted turns round from left to right, and becoming again a hair-stroke Nom. 8, oans, το σαφές; (σαφε-ες) σαφείς, (σαφεα) σαφή. in the same direction as before, but lower, in order to form the complete loop. The second is the body of the letter I, which is the same in German as in English handwriting; and the third is like the ordinary pot-hooks of our text-hand, tapered at the commencement of their formation. The capital letter A is formed of the first elementary leg inverted, and the third added to it with a small loop joining the two together. It is, in fact, the small a enlarged, with round instead of angular turns at top and bottom. The capital letter B is formed of the second elementary leg, with a loop at top and bottom, the whole being made like our capital writing letter L, with a small loop terminating the last hair-stroke exactly like our small writing b. The letter C is exactly like our letter L in writing, with a small hook placed at the top loop. The letter D is more like the form 9 of the Greek letter th, or theta, than anything we know. It scarcely deserves the name of a letter, being a mere flourish of the pen. The letter E is like our manuscript C with its lower half written below the line, and crossed by a curve, indicating the separation of the loop and the scroll. The letter F is the second elementary leg with a small hook at the top, and crossed in the middle with a fine hair-stroke. The letter G is formed of the first elementary leg inverted, with the second attached to it by a small loop at the top, and lengthened below the line like our own G. It is, in fact, like the small letter g enlarged, with the angular turn of its elementary leg rounded. The letter H is like our capital G inverted, with a small loop between the top and bottom parts of it. The letters I and J are like our own letters of similar name, sound, and position in the alphabet. The letter K is like our R badly shaped, and having a small hook at the top of the middle stroke. The letter L is exactly like our own. The letter M consists of the first elementary leg doubled, and the third attached to the second by a small hook at the top. The letter N is of the same form, excepting that the first leg is not doubled. The letter O is the first part of the letter A, with a small loop at top. The letter P is very like the P used by us in writing the word per, in per cent., per pound, etc., only the top is round, and the final loop is more marked. The letter Q is like the letter G, with the bottom sharpened, and the hair-stroke from it turned the contrary way. It is sometimes made like the letter O, 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 elementary leg. The letter S consists of the first elementary leg, terminating in a small hook or curve at top. The letter T consists of the letter I terminated squarely at the bottom, and near that point crossed by the elementary leg of the small alphabet from left to right. The letter U consists of a double pot-hook, to which is attached the third elementary leg by a small loop at top. The letters V and W are only the letters of the small alphabet enlarged, with the angular turns rounded like the first two in the letter M. The letter X is exactly like our own. The letters Y and Z are like the small letters y and z enlarged, with their angular turns rounded. LESSONS IN GREEK.-XI. THE THIRD DECLENSION (continued). I MUST now direct your attention to nouns ending in -ns, -es; -ws (gen. -wos), -ws and -w (gen. -oos), and in -as (gen. -aos), -os (gen. -EOS). The stem of these words ends in σ; the o remains at the end and before a consonant, but disappears in the middle between two vowels. In the dative plural one σ disappears; for example, & Ows, a jackal, Tois Ow-01. -ES. Of these words, let us consider first those which end in -ns, The terminations -ns (m. and f.), -es (n.), belong only to adjectives, and to proper names terminating in adjective forms in -νης, -λης, -γενης, -κρατης, -μηδης, -πειθης, -σθενης, and (-κλεης) | -KAS. The neuter presents the pure stem. The words of this class suffer contraction in all the cases, except the nominative and vocative singular, and the dative lural, after dropping the σ. The words ending in -Kλens being tracted into -λîs, again undergo contraction in the dative | Gen. Dat. Acc. Nom. Gen. Dat. Voc. (σαφεος) σαφούς ; (σαφε-ΐ) σαφεῖ; (σαφε-ων) σαφῶν. (σαφε-α) σαφή, σαφές; (σαφε-ας) σαφείς, (σαφε-α)σαφή. σαφές, σαφες; (σαφε-ες) σαφείς, (σαφε-α) σαφή. σαφεοιν, σαφοῖν. Dual. N.A.V. σαφε-ε, σαφη. Singular. Plural. Σωκράτη. (Περικλέης) Περικλῆς. (Περικλεε-.) (Περικλεε-α) (Περικλέει) Περικλεί. Acc. In adjectives in -ns, -es, when these terminations are preceded by a vowel, ea is commonly contracted into a, as in the proper noun Περικλεᾶ, and not into n, as in σαφέα, σαφή; for example, ακλέης, unrenowned, makes ακλεεα into ακλεᾶ, in the masculine and feminine accusative singular, and in the neuter nominative, accusative, and vocative; so yins forms vyiâ. Proper names of this termination, as well as Apns, Mars, in the accusative singular, follow the first as well as the third declension, and are therefore denominated heteroclite (that is, of different declensions); accordingly, we have both Zwxpaтn and Zwkpaтny. But in those ending in Ans, the accusative in is not Attic, and therefore not allowable. Δουλεια, ας, ή, sla-. Ποταμος, -ου, δ, 2 very, servitude. river. Exeaipo, I pity. Σοφιστής, του, δ, ο 'Eλwons, -es, marshy. sophist. Enaμeivavdas, -ov, &, ZopokλÑS, -OUS, &, Epaminondas. Sophocles. 'Hрakλns, -ous, Σωτηρία, -ας, ἡ, salHercules. vation. Ivdiкn, n, India. Τόπος, του, d, a Καλαμος,-ου,δ,a reed. place. 'Ouλia,, inter- Tpayola, -as, ǹ, tracourse (with dat.). gedy. EXERCISE 35.-GREEK-ENGLISH. Avatayopas, -ov, d, tunate. Aparns,-es,unknown, unseen. 1. Αἱ Σοφοκλεους τραγῳδίαι καλαί εισιν. 2. Τον Σωκράτη επί 4. 'H τῇ σοφια θαυμαζομεν. 3. Σωκράτει πολλοι μαθηται εισιν. Ινδική παρα τε τους ποταμους και τους ελώδεις τόπους φέρει καλαμους πολλους. 5. Λέγε αει τα αληθη, ω παι. 6. Αναξαγόρας, & σopioтns, didaσkalos ny Перiкλεоvs. 7. Ω Ηρακλεις, τους ατυχέσι σωτηρίαν παρεχε. 8. Επαμεινώνδας πατρος ην αφανοῦς. 9. Ελεαιρε τον ατυχή ανθρωπον. 10. Ορεγεσθε, ω νεανία, αληθών Aoywv. 11. Οἱ ακρατείς αισχραν δουλειαν δουλευουσιν. EXERCISE 36.-ENGLISH-GREEK. 1. Socrates had (in Greek, to Socrates was) wonderful wisdom. 2. Pity unfortunate men. 3. We pity unfortunate men. 4. Many youths were disciples of Socrates. 5. Socrates had (in Greek, to Socrates was) much wisdom. 6. They admire the wisdom of Socrates. 7. The immoderate (man) serves a shameful servitude. 8. We admire the beautiful tragedies of Sophocles. 9. True words are believed. 10. I pity the life of immoderate men. 11. Have not intercourse with immoderate men. Δύσκολος, -ον, dis Πεμπω, I send. N.A.V. Ow-e. G.D. θω-οιν, Ν.Α.V. ἡρω-ε. G.D. ἡρω-οιν. I also give specimens of nouns in -ws and -w (gen. -oos =-ους). These are all feminine. The ending -ws, in ordinary speech, is preserved only in the substantive αιδως, modesty, sense of shame; the dual and plural are formed according to the termination -os of the second declension : thus, αιδοι, ηχοι, κ. τ. λ. Here follow the forms of ἡ αιδως, modesty, respect, and ἡ ηχω, echo. EXERCISE 37.-GREEK-ENGLISH. 1. Όμηρος αδει πολλους ήρωας (or ήρως). 2. Την των ηρωων αρετην θαυμαζομεν. 3. Οἱ δμωες βιον λυπηρον αγουσιν. 4. 'O του πατρώος κήπος καλός εστιν. 5. Ορεγου, ω παι, της αίδους. 6. Αίδως αγαθοις ανδρασιν έπεται. 7. Λυσιαν επι τῇ πειθοί και χαριτι θαυμαζομεν. 8. Τη αιδοι προσεστι το σεβας. 9. Μη | προσβλεπε το Γοργούς προσωπον. 10. Ω Ηχοι, ψευδεις πολλακις τους ανθρώπους. 11. Παντες ορέγονται ενεστους. 12. Πρεπει παιδι και νεανια αιδῶ εχειν. 13. Κλειω και Ερατω Μουσαι εισικ EXERCISE 38.-ENGLISH-GREEK. 1. Homer sings (of) the hero Achilles. 2. The hero Achilles is sung by Homer. 3. The bravery of the hero is wonderful. 4. We admire the bravery of heroes. 5. Slaves have (say, to the slaves is) a sad life. 6. The uncle has (say, to the uncle is) | a fine garden. 7. All rejoice at their (the) good condition. 8. Admire, Ο youth, with (μετα and gen.) modesty the deeds of good men. 9. By (dat.) the echo we are often deceived. Nouns in -as and -aos are declined as follows. Only a few neuters belong to this head. The terminating a belongs to the εξέτα: το σελας, splendour ; το κρέας, flesh. satisfied, grumbling, hard. Έλαφος, -ου, ἡ, stag. foundation. Σαλπιγξ, ιγγος, ή, a trumpet. Σημαίνω, I give a sign (σημα, a sign), I signify. Προβατον, -ου, το, a Υπαρχω, I exist. sheep. 2. Προτρέπω, I turn to wards, exhort, en, courage. Φαρμακον (whence EXERCISE 39.-GREEK-ENGLISH. 2. Των ν γηρα 1. Οἱ θεοι τοις ανθρώποις τερα πεμπουσιν. κακων φαρμακον ὁ θάνατος εστιν. 3. Τα γερα τους στρατιώτας εις ανδρειαν προτρέπει. 4. Εξ αιγών και προβατων γαλα και κρεα προς διατροφην ὑπαρχει. 5. Κερασι και σαλπιγξιν οἱ στρατιωται 6. Ποικίλων κρεών γενομεθα. 7. Καλου γηρως θεμελιον εν παισιν εστιν ἡ του σώματος ευεξία. 8. Αἱ ελαφοι κερα εχουσιν. 9. Δυσκολος ὁ εν γηρα βιος (sc. εστιν). σημαίνουσιν. EXERCISE 40.-ENGLISH-GREEK. 1. Prodigies are sent by (ύπο with gen.) the gods to men. 2. Soldiers are delighted with horns and trumpets. 3. We taste milk and flesh. evils of old age. 4. Death puts an end to (απολύει) the 5. The king sends presents to the soldiers. 6. Presents encourage soldiers. 7. Soldiers are encouraged by (dat.) presents. KEY TO EXERCISES IN LESSONS IN GREEK.-X. 1. All men have not the same mind. 2. We masticate our food with our teeth. 3. Dolphins are man-loving (animals). 4. It is the 5. Many districts part of a good man to bear all evils with courage. of Lybia abound in ivory. 6. All people hate a loquacious man. 7. 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. EXERCISE 32.-ENGLISH-GREEK. 3. Αν 1. Ημιν εστιν ελέφας. 2. Εν χώραις της Λιβύης ο ελέφας γιγνεται. του ήλιου ακτινές τους ποιμένας τερπουσι. 4. Οἱ αδελφοι τε και αἱ αδελφαί χαιρουσιν εν ταις ακτισι του ήλιου. 5. Η αδελφη εστι χαλη. 6. Θαυμαζόμεν τον καλον τον ελέφαντα. 7. Πολλοι ελέφαντες εισιν εν τη Λιβύη. 8. Οδοντων εστιν έργον λεαίνειν το βρωμα. 9. Παντος εστι σέβειν το θείον. 10. Τοις θεοις ποτε ην πολεμος προς τους γίγαντας. EXERCISE 33.-GREEK-ENGLISH. 1. Kings have a care for their subjects. 2. The flock follows its shepherd. 3. Hector is slaughtered by Achilles. 4. The priests sacrifice oxen to the gods. 5. Cyrus was the son of good parents. 6. The ungrateful dishonour their parents. 7. My son, obey your parents. 8. Telemachus was the son of Ulysses. 9. Be willing to honour your parents before everything. 10. The idle tales of old women wear away (weary) the ears. 11. You rule gloriously, Ο king. Old women are very talkative. 13. Shepherds drive the flock of cattle to pasture. 14. Homer likens the eyes of Juno to those of an ox. 16. We admire Cyrus, the 15. Patroclus was the friend of Achilles. EXERCISE 34.-ENGLISH-GREEK. 12. 1. Αἱ αγέλαι επονται τῷ νομεῖ. 2. Ο αναξ έχει επιμέλειαν του πολίτου. 3. Τα ωτα τειρεται ληρῷ των γραων. 4. Η γραυς εστι πολυλογος. 5. Ο ποιμήν άγει την αγέλην των βοων προς την πολιν. 6. Boες θύονται τοις θεοις ύπο των ἱερέων. 7. Οἱ γονεῖς στέργονται ὑπο των τέκνων. 8. Αγαθου εστε ποιμένος έχειν επιμέλειαν των αγελών. LESSONS IN GEOGRAPHY.-XXIV. EUROPE (continued). IN our present lesson, with a page map of the countries of Southern and Central Europe, we give in a tabular form many useful facts relating to the most important of the independent states of Europe. The first table, as will be seen, exhibits the capitals of these states with the rivers, etc., on which they stand, the area and population of each, the number of inhabitants to every square mile, and the approximate amount of standing army. I. THE CHIEF STATES OF EUROPE THEIR CAPITALS, AREA, POPULATION, ETC. The remaining states of Europe which as yet preserve a semblance of independence, though the rulers of all of them may be considered as being virtually subordinate to the will of Prussia, are included within the limits of the great central territorial division of Europe called Germany. The states of North Germany, with the exception of the German states of Austria, which is at present excluded from all participation in German affairs, are twenty in number, and form a federal union for defensive and commercial purposes under the name of the North German Confederation. Southern Germany contains six states. In the following list of each the names of the states given in Tables I. and II. are printed in italics to distinguish them from the small states that are not included in these tables. NORTH GERMAN CONFEDERATION.-The Kingdoms of Prussia (1) and Saxony (2); the grand-duchies of Oldenburg (3), Mecklenburg-Schwerin (4), Mecklenburg-Strelitz (5), and Saxe Weimar (6); the duchies of Anhalt (7), Brunswick (8), SaxeAltenburg (9), Saxe-Meiningen (10), and Saxe-Coburg-Gotha (11); the principalities of Schwartzburg-Sonderhausen (12), Schwartzburg-Rudolstadt (13), Waldeck (14), Reuss-Schleiz (15), Schaumburg-Lippe (16), and Lippe-Detmold (17); and the free cities of Lubeck (18), Bremen (19), and Hamburg (20). SOUTHERN GERMAN STATES.-The kingdoms of Bavaria (1) and Würtemburg (2); the grand-duchies of Baden (3) and HesseDarmstadt (4); and the principalities of Reuss-Greiz (5) and Lichenstein (6). II. THE CHIEF STATES OF EUROPE THEIR RULERS, REVENUE, NATIONAL DEBT, ETC. To give the reader an accurate idea of the extent of Germany and its territorial limits, it should be said that Prussia Proper, comprising the two provinces marked East and West Prussia in our map, and Posen, or Prussian Poland, are without the boundaries of Germany. The eastern portions of the duchies of Limburg and Luxemburg, however, are within its limits, and nine provinces of Austria-namely, Bohemia (1), Silesia (2), Moravia (3), Upper Austria (4), Lower Austria (5), Salzburg (6), Styria (7), Illyria (8), and the Tyrol (9). The duchies of Limburg and Luxemburg, mentioned above, belong to Holland or the Netherlands, as Holland is frequently called. The area of the whole of Germany, including the whole of Prussia except the parts which have been named, the nine Austrian states, the Dutch portions of the duchies of Limburg and Luxemburg, and the other states named in the lists of the North and South German States, is estimated at 243,375 square miles, while the population may be approximately stated at 44,650,000. The affairs of the North German Confederation are managed by a diet or parliament, composed of representatives elected by the different states and the German provinces of Prussia in proportion to their inhabitants. The diet meets at Frankfort-on-the Maine, formerly a free city, but which was absorbed by Prussia at the close of the "Seven Weeks' War" with Austria in 1866, with the kingdom of Hanover, the electorate of Hesse-Cassel, the duchies of Nassau, Schleswig, Holstein, and Lauenburg, and small portions of Hesse-Darmstadt and Bavaria. LESSONS IN ARITHMETIC.-XXXIII. RULE OF THREE-SINGLE AND DOUBLE (continued). 8. IN Simple or Single Rule of Three, the method of performing which was explained in the last lesson, it will be found that questions of the following kind often occur: EXAMPLE 4.-How long will 20 men take to build a wall 10 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 many acres can 12 men reap in 15 days? Such questions can always be solved in a manner similar to the following: length, but only 74 feet high? This we will work by the rule. Here the amount of wall built increases if the number of men is increased, and if the time they work is increased. If a be the time required, we have therefore The answer therefore is 33 cwt., or 3 cwt. 1 qr. 14 lbs. 9. Questions of this kind can always be solved by the method given above-i.e., by finding what quantity of one kind corresponds to one unit of each of the other kinds. Thus we have found, in the first example, how many acres can be reaped by one man in one day. In the second example we have found what is the cost of carrying one cwt. one mile. After this has been done, the process is easy. The result, can, however, be always arrived at more simply by means of the following rule, which depends, however, upon an algebraical principle which we cannot explain here. 10. Double Rule of Three. Thom 40 quantities given to find a sixth. Call this Those six quantities will consist of 3 kinds which kind increases with the increase of EXERCISE 52.-EXAMPLES IN DOUBLE RULE OF THREE. 1. If 12 horses can plough 11 acres in 5 days, how many horses can plough 33 acres in 10 days? 2. If 40 gallons of water last 20 persons 5 days, how many gallons will 9 persons drink in a year? 3. If 16 labourers earn £15 12s. in 18 days, how many labourers will earn £35 2s. in 24 days? 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? 5. If 6 men can make 120 pairs of boots in 20 days of 8 hours each, how many days will it take 12 men to make 360 pairs, working 10 hours a day? 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 long, 8 feet high, and 6 feet thick ? 7. If £250 gain £30 in 2 years, how much will £750 gain in 5 years? 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 spend in 12 months? 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, 3 men being equivalent to 5 boys? is the price of wheat when the 6d. loaf weighs 32 oz. 8 dwt. ? 11. If the 8d. loaf weighs 48 oz, when wheat is 548. a quarter, what 12. If 35 barrels of water last 950 men 7 months, how many men would 1464 barrels last for 1 month ? 13. If 13908 men consume 732 barrels of flour in 2 months, in how long will 425 men consume 175 barrels ? 14. If 3 men with 4 boys earn £5 16s. in 8 days, and 2 men with 3 boys earn £4 in the same time, in what time will 6 men and 7 boys earn 20 guineas? 15. If 5 men with 7 women earn £7 13s. in 6 days, and 2 men with 3 women earn £3 38. in the same time, in what time will 6 men with 12 women earn £60? 16. If the penny loaf weigh 6 oz. when wheat is 5s. a bushel, what should be the weight of the shilling loaf when wheat is 7s. 6d. a bushel? 17. If 20 men can perform a piece of work in 12 days, how many men will perform a piece of work half as large again in a fifth part of |