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that attended the worship of "the image that fell down from Jupiter," and such was the terror of the Ephesians that their temple would be destroyed a second time, that, in the words of the sacred historian, "when they heard these sayings they were full of wrath, and cried out, saying, Great is Diana of the Ephesians;" and having assaulted Paul, and created a violent uproar, the mob continued to utter the same cry, without intermission, for the "space of two hours," in the chief city of Asia. (Acts xix. 23-28.)

The temple of Diana, at Magnesia, was built under the direction of Hermogenes. He made its general dimensions the same as for a double range of columns; but, in order to afford more space to the porticoes, he omitted the inner range. Thus a clear space was left between the outer range and the body of the building; and thus he established the style called the pseudo-dipterick. Vitruvius speaks with great veneration of this architect. The temple of Minerva Ulea, at Tegea, designed and erected under the direction of Scopas, was of singular construction. The peristyle of the temple was of the Ionic order; the interior was divided into three aisles by two rows of Doric columns, and over these were placed others of the Corinthian order. The sculpture upon the two pediments was executed by the artist himself.

The simplicity and severity of the Doric order having now been abandoned, the artists of Greece Proper, not to be behind the inventors of the Ionic order, by an effort of genius, gave birth to a third order, which surpassed the Ionic in delicacy of proportion and richness of decoration. This order was named the Corinthian. The merit of its invention is generally ascribed to Callimachus, a celebrated sculptor of Athens, who is supposed to have reached the zenith of his fame about 540 B.C. He is said to have taken the idea of this order from observing the leaves of the acanthus growing round a basket which had been placed, with some favourite trinkets, upon the grave of a young Corinthian lady; the stalks which rose among the leaves having been formed into slender volutes by a square tile which covered the basket. In the Corinthian order the column is more elegant, and the capital longer and more ornamented than in the Ionic, spreading in the form of a basket, and commingling the richest and lightest vegetation with the decorations of preceding orders. The top of the capital, instead of being square, assumes the curvilinear form, having angular projections supported by elegant volutes. The mouldings possess more beautiful ornaments than those of the Ionic or the Doric. The frieze is usually ornamented with scrolls of foliage; in the cornice, the corona is supported by modillions, which represent the extremities of the beams of the roof, and are usually carved into a scroll (see Fig. III, a.). These elegant improvements introduced into their orders rendered the Greeks the real masters of architecture; because, previous to their invention, the Egyptians and the Asiatic nations in general followed no precise rule in their constructions; but as soon as the orders were founded on rational proportions, of an exact and invariable nature, they were imitated in the edifices of every other nation.

extent in every part of their empire; hence it is in edifices constructed under their influence that the most perfect speci mens are found. It was only in the construction of temples that the turbulent states of Greece could unite; and in consequence of this union, they constructed edifices of great magnitude and splendour. Many of this description were built and maintained at the expense of confederate states, and even of all Greece such were the temples at Delphi, Delos, Ephesus, Olympia, Eryx, etc.-and these temples had territorial revenues, besides being enriched by private donations. The Greeks appear to have made the greatest progress in the arts, and to have constructed the most admirable of their edifices, during the period from the age of Solon and Pythagoras to the era of Alexander the Great. Their architecture prevailed in the countries where they extended their influence along the coast of Asia. Alexander and his successors introduced it into Egypt, and probably in the cities he built on his route to India. To the westward it extended to Sicily, Italy, and the south of France. After the brilliant period to which we have alluded, the manners of the Greeks became Asiatic; their sublime spirit of independence was subdued; and although they continued for ages to be the instructors of their Roman conquerors, their glory in the arts declined, and with it the purity and elegance of the Greek architecture.

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Some words of both the masculine and feminine gender often drop the of the accusative case, as d Aayws, the hare: To λαγω ; ὁ Αθως, Mount Athos, τον Αθω; ἡ έως, the dawn, always has την έω.

Aynpws,-wv, free from
old age, deathless
(a, not; ynpws,
old age).
Aeros, -ov, d, an
eagle.
Aixuaλwтos, -ov, 8,
a prisoner.
Avôpetos, -a,
manly, brave.
Ardpoɣews, w, 5,
Androgens (a pro-
per name).
Araya, I lead away.
Baive, I walk, go.

-ον,

VOCABULARY.

most, very many. Πτερον, ου, το, Β

feather, wing. 'Padios, -a, -ov, easy. Σαμιος, του, δ, & 50

Evedpeuw, I lie in Miras, -a, ó, Minos
wait, capture.
(a proper name).
Eлaivos,-ov, ô, praise. News, -w, d, a temple.
Ευχομαι, I pray (with | Πλειστος, -η, -ον,
dat.).
Ηρα, -ας, ἡ, Hera
(called by the
Latins, Juno).
Θηρεύω,Ihunt, catch.
Θηρευτης, ου, ό, ε
huntsman.
Kri(w, I found, build.
Λαμβάνω, I take.
Mereλews, -w, d, Me-
nelaus (a proper
name).

While awarding every credit to the ingenuity of the Greeks, however, it must not be forgotten that in the columns of several temples in Upper Egypt, whose shafts represent bundles of reeds or lotuses bound together in several places by fillets, the capitals are formed by several rows of delicate leaves. In the ruins of Ellora, in India, the capitals of the columus are also composed of similar ornaments; and the Persians, at their great festivals, were accustomed to introduce ornaments of flowers at the tops of the pillars in their public apartments. From tradition, report, or personal observation, Callimachus might be made acquainted with these examples, and might be led to the composition of the Corinthian capital, the chief ornament of the Greek school. The Corinthian order, although distinguished for its richness and even luxuriousness of decoration in all its details, is essentially the most simple in its general character, and easiest in execution. The finest examples of this order were to be seen at Athens, in the monument of Lysicrates, the Tower of the Winds, the Stoa or public piazzas, and the Arch of Adrian, at Athens; the Pantheon of Agrippa, and the three columns of the Campo Vaccino, at Rome. The Corinthian order appears to have been but 1. Τοις Θεοις νεῳ κτίζονται. 2. Ου ραδιον εστιν επί καλών y artially employed in Greece before the time of the Roman | βαίνειν. 3. Διωκόμεν τους λαγως. 4. Ανδρόγεως ην ὁ Μινω νίας. onquest; but the Romans themselves employed it to a great 5. Οἱ λαγω θηρεύονται ὑπο των θηρευτων. 6. Ευχον τῷ ίλες Θεῷ.

mian. Σεβομαι, I venerate, worship. Taws, w, i, a pes cock. "Tios, -ov, d, a son 'Doweр, even as.

EXERCISE 15.-GREEK-ENGLISH.

7. Οι αετοί τους λαγως ενεδρεύουσιν. 8. Σέβεσθε τους ίλεως | But when a word ends in r, the r is either discarded or changed θεους. 9. Οἱ ανδρείοι αγορων επαινον λαμβανουσιν. 10. Ευχου | into s; as: τον Θεον ίλεων εχειν. 11. Οἱ θεοι τοις αγαθοις ίλεως εισιν. Αν ήδοναι απαγουσι τον πλειστον λεῶν ὡσπερ αιχμαλωτον. Οι Σαμίοι Ήρα καλους τα ως τρεφουσιν. 14. Τῳ τα καλα πτερα

εστιν,

EXERCISE 16.-ENGLISH-GREEK.

12.

13.

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Nominative.

πέπερι, pepper;

Stem. πέπερι,

Genitive.

πέπερι-ος.

σωματι

σωμα, body;

σωματος.

τερατ,

τέρας, a prodigy;

τερατος.

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ν

Acc. πολιν. βοτρυν.

ναυν,

βουν.

If the stem ends in a consonant, a instead of v is found in the accusative, as φλεβ, φλεψ, φλεβα, a vein ; κορακ, κοραξ, κορακα, a raven; λαμπαδ, λαμπας, λαμπαδα, a torch.

The vocative is the same as the nominative or as the stem.

The genders of the third declension are best learnt by practice.

The third declension may be distinguished from the first and the second by the fact that it adds a syllable to the nominative, while in them all the cases have the same number of syllables. Nouns which have the same number of syllables in all the cases are termed parisyllabic (in Latin par, equal), and nouns which lengthen the genitive and the cases derived from it, are termed imparisyllabic (Latin im [in], not). Hence the first and second declensions are called parisyllabic, and the third is called imparisyllabic.

In order to facilitate the acquisition of a knowledge of the nouns of the third declension, and to afford you thorough prac tice in them, I shall divide those nouns into several classes: *. 1. NOUNS WHOSE STEM ENDS IN A CONSONANT;

and of these I give in the first place

α. Nouns of which the Nominative gives the pure Stem. The case-endings are appended to the nominative.

Nom. Gen.

Dat.

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The forms of the third declension in Greek are various, and can be learnt only by attentive practice. Some aid may, how. ever, be given by means of classification.

παιάνι.

Acc. Voc.

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Acc. Voc. Neuter nouns have the nominative, the accusative, and the vocative alike. The student who is acquainted with Latin will readily see how much this Greek third declension corresponds with the Latin third declension.

The terminations given above are affixed to the stem. The stem is, in some words, the same as tho nominative; thus, λείμων, λειμων-os, a meadow, where the ending os is simply added to λειμων. In masculine and feminine nouns, however, the stem often appears in the nominative in an altered form. When the stem is so altered, you must find it before you affix the case-endings to it. In order to find the stem, remove the | genitive termination from the noun; what remains is the stem; €9., κορακος (of a crow), the os is the sign of the genitive, which being removed, leaves κορακ as the stem ; and κορακ is, for the | sake of euphony, lengthened in the nominative into κορακs, that is, κοραξ; for the laws of sound in Greek endure at the end of a word only these consonants, namely, v, ρ, σ (ξ, ψ); the other consonants are either changed or thrown away. Hence the T in the stem of Xenophon is dropped, as Ξενωφωντος, Ξενωφωντ, Ξενωφων. Neuter nouns present the stem in the nominative.

|

Ν.Α.Υ. παιᾶνε. λειμων-ε. Ξενοφωντ-ε. νεκταρ-ε. G.D. παιάνοιν. λειμων-οιν. Ξενοφωντ-οιν. νεκταρ-οιν. The datives plural in full would be παιανσι, λειμωνσι, Ξενοφωντσι, but the y is dropped before σι for the sake of euphony. Απολλων, Apollo; Ποσειδων, Poseidon (in Latin, Neptunus), are declined thus :-Απόλλων, Απολλων-ος, Απολλων-ι, Απολλων-α, also Απολλω-α and Απολλω, thus making the accusative singular in Απολλω; 60 Ποσειδων

Απολλων, Ποσειδων, and σωτηρ, a deliverer, Saviour, have the short vowel in the vocative, as ω Απολλον, ω Ποσειδων, ω σωτερ. The neuters of this subdivision end in p (ap, op, wp, up); TO πῦρ, fre, has του πυρος.

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Χειρ, -OS, , the
hand; dat. xepoi,
dat. dual, xepov.
Xopos, -ov, ó, a cho-

ral dance.

Yny, -os, ó, a wasp.

EXERCISE 19.-GREEK-ENGLISH.

1. Φευγε τους θήρας. 2. Χειρ χειρα νίζει. 3. Απέχου του ψηνος. 4. Οἱ λειμωνες θαλλουσιν. 5. Oi σтpаTIWTα adovσ παιάνα. 6. Εν πυρι χρυσον και αργυρον γιγνωσκομεν. 7. Hoλλot παρα κρατηρι γιγνονται φίλοι πλείστοι δε εχθροι. 8. Oi aveрwо τέρπονται κιθαρα και θαλια και, χοροις και παιᾶσιν. 9. Of 'EXANves τον Απολλω και τον Ποσειδω σεβονται. 10. Οἱ σπουδαιοι μαθηται τα Ξενοφώντος βιβλια ήδέως αναγιγνώςκουσιν.

EXERCISE 20.-ENGLISH-GREEK.

1. Avoid wild beasts. 2. They avoid a wild beast. 3. Wash the (thy) hands. 4. Keep ye from wasps. 5. A soldier is delighted with the cry of victory. 6. The cry of victory delights soldiers. 7. O earnest scholars, read the books of Xenophon. 8. The books of Xenophon are read by (Tо, gen.) carnest scholars. 9. We delight in beautiful meadows (dat.). 10. The meadows bloom. 11. Poets worship Apollo. 12. The poet worships Poseidon.

KEY TO EXERCISES IN LESSONS IN GREEK.-VI.
EXERCISE 11.-GREEK-ENGLISH.

diagrams, of which Fig. 11 shows the world in eastern and western hemispheres on the meridians of 160° W. long. and 20° E. long.; while Fig. 12 shows the world on the plane of the equator in northern and southern hemispheres; and Fig. 13 the world on the plane of the horizon of London in hemispheres— the one containing the greatest quantity of land, and the other the greatest quantity of water that can be obtained in single hemispheres by any similar bisection of the globe in any plane of a great circle. The land in the northern hemisphere is considered to occupy rather more than two-fifths of the whole hemisphere, and the land in the southern hemisphere about one-eighth of the whole hemisphere. The land preponderates in the north. castern quarter of the globe, and the water in the south-western quarter. Scarcely any land has yet been discovered in the south frigid zone, and the limits of the land in the north frigid zone have not hitherto been correctly ascertained. By far the greater portion of the land lies within the north temperate zone; the greater part of the remainder lies within the torrid zone; still less within the south temperate zone; and the least within the torrid zone; the greater part of the remainder within the south north frigid zone. The greater part of the sea lies within the temperate zone; still less within the north temperate zone; and the least within the north frigid zone.

On looking at a globe or map of the world, the student will perceive that all the great and continuous tracts of land, commonly called continents (from the Latin continens, holding together), become pointed as they stretch towards the south, by which they are made to assume a pyramidal or triangular form at the extremity. The continents of North and South America and of Africa are the most remarkable illustrations of this fact. In consequence of this tendency to taper towards the south, so narrow is the connecting link or neck of land (commonly called an isthmus, from the Greek 100μos, isth'-mos, a neck, or narrow passage) between North America and South America, that little more than forty miles of land separate Panama from Porto Bello, on opposite sides of the Isthmus of Darien. The southern dissi-points of the other two continents are well known; Cape Horn

1. Pursue honourable deeds, O beloved youth. 2. Obey the words of thy teacher. 3. Thou learnest excellent things from the excellent. 4. A faithful friend partakes of (your) good and (your) bad things (fortunes). 5. The gods (eo) care for men. 6. Men worship (θεραπεύουσιν) the gods. 7. Danger attends many works. 8. Good things are mixed with bad. 9. The bad man is hostile to (at enmity with) gods and men. 10. Men rejoice in good (men or things). O God, grant good fortune (happiness) to our friends. 12. O slave, bear the wine to the young man. 13. Wine (ó orvos) does not pate, but begets cares. 14. Glory follows a difficult achievement.

EXERCISE 12.-ENGLISH-GREEK.

11.

1. Οι αγαθοι τῷ Θεῷ πείθονται. 2. Ου πείθονται τῷ Θεῷ οἱ κακοι, 3. Πείθεσθε, ω καλοι νεανίαι, τῳ διδασκαλῳ. 4. Οι κακοι τοις αγαθοίς εχθροι εισιν. 5. Των κακών απέχον. 6. Οἱ εσθλοι των παίδων επιμελονται (φροντίζουσι) 7. Μη τῳ ψευστου λόγῳ πιστευε, ω φιλε παι. 8. Hoλois doyous έπεται κίνδυνος. 9. Οἱ εσθλοι νεανίαι τους διδασκαλους θεραπεύουσιν.

EXERCISE 13.-GREEK-ENGLISH.

1. Virtue, not time, is the measure of life. 2. Death liberates men from labours and evils. 3. Wine rejoices the minds of men. 4. With ten thousand trials honourable things arise (are produced). 5. The divinity conducts the bad to judgment. 6. A faithful friend in a difficult division (strife) is worth silver and gold. 7. There are many diseases among men. 8. Counsel leads to good. 9. Silence brings honour to a youth. 10. The door is shut by bars. 11. Art nourishes men. 12. O beloved disciples (scholars), strive after wisdom and virtue.

EXERCISE 14.-ENGLISH-GREEK.

1. Τῳ θανάτῳ απολύονται των κακῶν οἱ άνθρωποι. 2. Τῷ βίῳ πολλοί πόνοι CTOVTAL, 3. Η του Θεου σοφια προς ευδαιμονίαν τους εσθλους αγει. 4. Τοις του κρίτου λογοις επου. 5. Οι του νέου λογοι εισι κακοι. 6. Η λύρα τας του θυμου μερίμνας λυει. 7. Νεφ προσήκει ἡ ἡσυχία, 8. Τους αγαθούς τρέφει ή τέχνη. 9. Ο μοχλος κλείει την θύραν.

LESSONS IN GEOGRAPHY.-XX. NATURAL DIVISIONS OF THE EARTH'S SURFACE. THE whole surface of the globe contains, as we have seen in the last lesson (page 166), about 197,000,000 square miles. The land is considered to contain about 52,000,000 square miles; and consequently, the water or sea to contain about 145,000,000 of square miles. This makes the proportion of the water to the land nearly as 13 to 36, or, speaking in general terms, approximately as 3 to 1. The proportion of the land to the whole surface of the carth is about 4 to 15, or rather more than that of 1 to 4. There is much more land in the northern hemisphere than in the southern; and considerably more in the eastern hemisphere than in the western; this may be seen at once by looking at a map of eld; but it is more clearly seen by looking at a terrestrial accurate idea of the relative proportions of land and earth's surface may be gained from the annexed

must be considered as that of South America, notwithstanding the Strait of Magellan; and the Cape of Good Hope that of Africa. Here it may be useful to remark that when a tapering point of land projects into the sea, it is called a cape, from the Latin caput, a head, a fgurative but very natural expression for the extremity of the land, which may be considered as the top or vertex of the triangular shape which it assumes when jutting out from the continent to which it belongs. When the land thus projecting into the sea is elevated considerably above the sea-level, it is called a promontory, from the Latin pro, in front of; and mons, a mountain-that is, mountain-land in front of the continent. The English term headland is often used for capes and promontories on a small scale, connected with the land; so is also the term naze or ness, from the Saxon næse, or German nase, a nose, or projection from the face. With regard to the term strait, which is applied to a narrow passage of the sea between two continents, or between a continent and an island, or between two islands, it is evidently derived from streht, the past participle of the Saxon verb streccan, to stretch, and bears the same relation to the water that the term isthmus does to the land.

In reference to the continents of Europe and Asia, there is also the general tendency to taper towards the south; in the former continent, however, this tendency is greatly obstructed by the vicinity of the African continent, so that the Iberian Peninsula (Spain and Portugal) does not so manifestly assume the triangular form. Still this tendency is partially developed in various parts of the south of this continent; as in the conformation of Italy and Greece, which taper, but very irregularly, towards the south, evidently in consequence of the feebler action of the Mediterranean Sea, as compared with the full play of the great Atlantic and Pacific Oceans. In the latter continent, the tendency to taper toward the south has been divided in such a manner as to present the three peninsulas of Arabia, India, and Malacca, of which the two former are pretty regular in form; but the latter, in combination with what is called the Eastern Peninsula, is very irregular in this respect.

The term island is well known to signify a portion of land, whether large or small, which is completely surrounded by water. This word is derived from the Danish öie, an eye, and is literally eye-land, or land so called because it is surrounded by water, as

the eye in the face is encircled with the eyelids and the surrounding skin.

WESTERN HEMISPHERE

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The term peninsula, from the Latin pene, almost, and insula, originally signified land nearly surrounded by water; that is, according to the etymology, almost an island: but it is now more frequently applied to the triangular-shaped portions of land which taper in any direction, and jut out from the great continents, as in the three cases above mentioned in Asia. The great European peninsulas have also been mentioned; namely, Greece, Italy, and Spain and Portugal combined; to these may be added the large peninsula of Sweden and Norway, and the smaller peninsula of Jutland or Denmark, the latter of which is an exception to the general

SOUTH TEMPERATE ZONE South

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NORTH FRIGID ZONE NORTH TEMPERATE

the north-east, and Polynesia in the south-west. Without regarding artificial divisions, the land on the surface of the globe is naturally divided into three great sections, namely, 1st. The Old World, in the eastern hemisphere, comprehending the vast, united, triple continent of Europe, Asia, and Africa, which extends from Cape EASTERN REMISPHERE Severo, or North-east Cape, the most northerly point of Siberia, in the Arctic Ocean, to the Cape of Good Hope in the South Atlantic Ocean, a distance of 8,400 miles; and from Cape Verd, the most westerly headland of Africa, in the North Atlantic Ocean, across the Isthmus of Suez to the east coast of China on the Pacific Ocean, a distance of about 9,000 miles. 2nd. The New World, in the western hemisphere, comprehend

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rule, as it points northward. The continents of South America and Africa are justly entitled to the name of peninsulas; the former being attached to North America by the Isthmus of Panama or Darien, and the latter to Asia by the Isthmus of Suez. From the consideration of the series of islands which lies between the peninsula of Malacca and the small continent of Australia, there is reason to believe that the latter was in former ages connected with Asia, as South America now is with North America; Australia, and the island of Tasmania, to the south of it (and no doubt originally forming a part of it), then most probably constituting the apex of the great triangularshaped peninsula (tapering to the south, according to the general law)

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ing the great, united, double continent of North and South America, with the neighbouring islands, extending from still undefined limits in the Arctic Ocean to Cape Horn, a distance of about 9,000 miles; and from the western shores of the Atlantic Ocean to the eastern shores of the Pacific Ocean, a distance varying in breadth from 40 to 3,500 miles. 3rd. Oceania, comprehending the continent of Australia and the groups of islands in the East Indian Archipelago or Malaysia, Australasia, Micronesia, and Polynesia, the principal of which are the Sunda Isles, the Philippines, Borneo, Papua or New Guinea, Tasmania, New Zealand, and the various clusters of isles scattered far and wide over the Pacific.

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in which this vast southern continent once terminated. It is further worthy of remark, in speaking of the great continents which become pointed as they approach the south, that their projections most generally terminate abruptly in lofty mountain chains, which there dip beneath the waters of the ocean.

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The Old World, so called because its history is known for a period of nearly 6,000 years, is composed of the three great sections denominated continents, namely, Europe in the north-west, Asia in the north-east, and Africa in the south-west, taking Jerusalem as the central point. Europe is separated from Asia by a boun

In regard to the divisions of the land on the surface of the globe, we find that by the older geographical writers it was divided into four great parts, called quarters of the world; namely, Europe, Asia, Africa, and America. This division, however, is very incorrect, inasmuch as it leaves out the continent of Australia, the great island of Borneo, etc., and vast groups of smaller islands scattered through the ocean, and valuable for their population and prodace. A more common and more accurate division is that of Europe, Asia, Africa, North America, South America, and Oceania, six great portions, of which the first five are continental, and the sixth continental and insular. Oceania is further subdivided by geographers into four parts, namely, Malaysia in the north-west, Australasia in the south-west, Micronesia in

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dary composed of a mountain chain called the Oural or Ural Mountains; the river Oural or Ural; the Caspian Sea; Mount Caucasus, a range of mountains stretching from the Caspian Sea to the Black Sea; and a chain of inland seas, the Sea of Azov, the Black Sea, the Sea of Marmora, and the Archipelago, the north-eastern arm of the Mediterranean. These four bodies of water are connected by the Strait of Kertch or Yenikale, the Bosphorus, and the Dardanelles. Asia is separated from Africa by the Arabian Gulf and the Isthmus of Suez. Europe is separated from Africa by the Mediterranean Sea.

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15 East 30 Long 46

The New World, so called because its history is known for a period of rather more than 350 years, is composed great sections denominated continents, namely, Nort

For instance, suppose it to be required to find the value of 375 cwt. 3 qrs. 21 lbs. at £4 14s. 6d. per cwt. First find the value of 375 cwt. at £4 14s. 6d. per cwt. by the previous method. This will be done as follows:£ 8. d. 375 0 0

375 cwt. would cost at £1 per cwt.

and South America, which are connected with each other by the |
Isthmus of Darien or Fanama (pronounced pan-a-mar'). Between
these continents, on the eastern side, north of the equator and
within the torrid zone, are situated the West Indies, a range of
islands stretching in a curved line from the Gulf of Florida to
the mouth of the Orineco. South of Asia, and east of the
Arabian Sea, consisting parily of the continent and partly of the
islands south of it, are situated the East Indies, lying almost
wholly within the torrid zone, and comprehending the penin-
sulas of India and Further India, Hindostan within and India
beyond the Ganges, with the is and of Ceylon and the group of
islands denominated the East Indian Archipelago, the Asiatic
Archipelago, or Malaysia. Sumatra, Borneo, and Celebes, Again, by the previous working-
the principal of these islands, are situated directly under
the equator.

The relative position of the greater part of the places mentioned in this lesson may be ascertained from an inspection of the figures in the preceding page, or the Map of the World in page 144. Our readers will find it useful, when studying our Lessons in Geography, to make a map of the world on a large scale according to the directions given in the last lesson, and to mark in the position and name of each place, as soon as it occurs for the first time.

LESSONS IN ARITHMETIC.-XXIX.

PRACTICE.

8. Definition.-Any fraction of a quantity the numerator of which is unity, is called an aliquot part of that quantity. Thus 4s. and 6s. 8d. are each aliquot parts of a pound, being respectively and of it.

In finding the value of any given compound quantity from the given value of any other given quantity of the same kind, a convenient form of multiplication, called Practice, is often employed. It depends, as will be seen, upon the principles of fractions and the judicious choice of aliquot parts.

9. EXAMPLE 1.-Find the value of 3589 cwts. at £1 11s. 6d. per cwt.

This might be effected in various ways. We might, for instance, reduce the money to farthings, multiply by 35S9, and then reduce the result to pounds, shillings, and pence; or we might reduce the money to the fraction of a pound, and then, multiplying by 3589, reduce the resulting fraction to pounds, shillings, and pence. But we may also evidently obtain a correct result if we divide the whole sum into portions, multiply each of these portions separately by 3589, and then add the results together. This we are able to do, simply by the aid of aliquot parts, as follows:

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3589 cwts. at £1 per cwt. will cest
Since 108. is £, 3589 ewts. at 10s, each will cost
£3589, or .
Since 1s. is 1 of 10s., 3589 cwts. at 1s. each will
cost of the same number at 10s. each, or of
£1794 10s., which is

Since 6d. is of 1s., 3589 cwts at 6d. each will cost of
the same number at 1s. each, or of £179 9s., or
Since d. is of 6d., 3569 cwts, at d. each will cost
of the same number at 6d. each, or
£89 14s. 6d., which is

of

Since d. is of d., 55-9 ewts. at 14. each will cost i of the same number at d. each, or of £7 92. 6 d., which is

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Hence 3589 at £1 + 3559 at 10s. +3589 at 1s. + 3589
at 6d. + 3589 at 3d. + 3569 atd. will cost.
The above is the explanation of the process, which may be
arranged as follows:-

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10s. which is of £1
48.
6d.

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of £1
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1 of 1 cwt., or
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of 1 qr.,
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Therefore 375 cwt. 3 qrs. 21 lbs, would cost . £1776 6 1 } The fraction being of a farthing. If, however, the fractional part of the farthing were put in terms of a fraction of a penny, the result would be written £1776 6s. 11d.

11. Sometimes, by inspection, we can see that one or both of the compound quantities which are expressed in different denominations can be simply expressed as a fraction of one of the denominations. This will much simplify the operation.

EXAMPLE. Find the value of 24 cwt. 1 qr. 9 lbs. 5 oz. at £2 5s. 6d. per cwt.

Here it is readily seen that 1 qr. 9 lbs. 51 oz. is of a cwt.
Honce the question is reduced to finding the value of 24 cwt.

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