negro); simia, ae, f. an ape; Syracusae, arum, f. Syracuse; murus, i, m. a wall (E.R. mural); Homérus, i, m. Homer; labor, óris, m. labour adulatio, ónis, 1. flattery (E. R. adulation); similitudo, inis, likeness (E. R. similitude); crus, cruris, n. the leg (from the knee to the ankle); beatus, a, um, happy; beneficus, well doing, beneficent; celeber, bris, bre, sought after, visited (E. R. celebrity); brevis, e, short (E. R. brevity); valen 2, I am strong, I am worth (E. R valid); contemno 3, despise, contemn; affinitas, átis, f. relationship (E. R. affinity); liberalitas, atis, f. liberality; lux, lucis, f. light; ratio, ónis, f. reason (E. R. ratio); simulatio, ónis, f. simulation, pretence, hypocrisy; sol. selis, m. the sum (E. R. solar); sonitus, ûs, m. a sound; accommodatus, a,

In Latin as well as in English, some adjectives depart from the usual modes of comparison. As we say, positive, good; comparative, better; superlative, best; so the Romans said, bonus, good; melior, better; optimus, best. Carefully learn by, stated (E. R. accommodate, commodious); garrulus, a, um, talkative heart the following:

Many Latin adjectives do not take any of these forms of comparison. Such are adjectives which have e before the termination us; as idone-us, fit. These are formed by prefixing magis, more; and maxime, most; as, magis idoneus, more fit; maxime idoneus, most fit; so, pius, pious; magis pius, more pious; maxime pius, most pious. in the same way, form nearly all adjectives and participles ending in ĭcus, imus, inus, ivus, ōrus, undus, andus, and bundus.

(E. K. garrulity); munificus, a, um, free in giving, liberal (E. R. mu nificent); secundus, a, um, favourable (E. R. to second); res secundae, favourable things, that is, good fortune; amabilis, e, worthy to be loved (E. R. amiable); nihil (not declined), nothing; quam, conj. than· non nunquam, adv. sometimes.

EXERCISES.-LATIN-ENGLISH.

Nihil est naturae hominis accommodatius quam beneficentia; nihil est amabilius quam virtus; lux est velocior quam sonitus; nihil est melius quam sapientia; multi homines magis garruli sunt quam hirundines; pauperes saepe sunt munificentiores quam divites; in adversis rebus saepe sunt homines prudentiores quam in secundis; divitissimorum vita saepe est miserrima; simulatio amoris pejor est quam odium; nihil est melius quam ratio; sol major est quam terra: luna minor est quam terra; omnium beatisveterrimus; adulatio est pessimum malum (evil); urbs Syracusae simus est sapiens; Homérus omnium Graecarum poetarum est maxima et pulcherrima est omnium Graecarum urbium; pessimi homines sunt maledici; omnium hominum maledicentissimi sunt fratres tui; in amicitia plus valet similitudo morum quam affinitas ; soror tua amabilior est quam mea.

ENGLISH-LATIN.

In the English meanings added to facilis above, I have given the forms easy, easier, easiest. Here you see changes made at the end of the positive, similar to those you have just been Nothing is worse than the pretence of love; the sun is very instructed to make in the Latin. First, the positive easy is great; the sun is greater than the moon; the life of men is very changed into easi, and then to this, as the stem, we add er times the happiest; the labour is very easy; my labour is easier short; the richest are often the unhappiest; the poorest are somefor the comparative, like the Latin ior, and est for the super-than yours; the customs (character) of men are very unlike; the lative, like the Latin issimus. This similarity of forms indi- king is very free in giving; the worst men are not often happy; cates in the two languages a sameness of origin. As too, in good men are happy; very good men are happiest; God is the English, we use more and most, so do the Latins use, magis, happiest of all; the best men are sometimes despised by the worst; and maxime, to denote the comparative and the superlative. the health of my friend is very weak; thy father's garden is very Magis and maxime must be used for this purpose, in the case beautiful; thy son's garden is more beautiful; the labour is very of adjectives which do not admit the termination forms. difficult; the walls of the city are very low (humilis); most (plurimi) men love their native country; nothing is better than virtue; the port is very much visited; God is the greatest, best, and wisest of all; the customs (or character) of the Lacedemonians were very simple; the horse is very swift; ravens are very black; thy father is very benevolent and very liberal; thy brother builds a very beautiful house; a very beautiful house is built by thy brother; virgins must (debeo) be very modest; thy sister is more modest than thy brother; the ape is like men; is the ape very much like men? of all animals the ape is most like men; nothing is sweeter than friendship; the Lacedemonians were very brave; light is very quick; light is quicker than sound.

Besides expressing the formal degree of comparison, the Latin superlative signifies a very high degree of the quality involved in the positive, as doctissimus, very learned; pater tuus est doctissimus, thy father is very learned. So in English, Milton uses wisest

"the wisest heart Of Solomon he led by fraud, to build

His temple right against the temple of God." Latin comparatives are declined like adjectives of two terminations, and according to the third declension. Thus, positive altus, high, makes comparative altior, higher; altior is masculine and feminine, the neuter is altius.

EXAMPLE OF A COMPARATIVE.-DECLENSION III.

VOCABULARY.

LESSONS IN BOTANY.-No. V.

"I SHOULD like to botanise," is the expression of a wish which we are concerned to gratify. We shall glance, therefore, at systematic botany, by which alone the discrimination or recognition of a plant can be secured. Without such ability, even a knowledge of the properties of the vegetable tribes would be of little or no use. For want of this acquaintance with them, persons have lost their lives by mistaking noxious and poisonous plants for wholesome herbs; and others have administered what they deemed to be salutary and restoring medicines, but which have proved to be deadly poison. It will consequently be evident that the study of systematic botany is one of great utility, associated with ob

Beneficentia, ae, f. well doing, kind action (E. R. beneficence); luna, ae, f. the moon (E. R. lunar); pauper, pauperis, a poor man (E. R. pauper); natura, ae, f. nature; sapientia, ae, f. wisdom (E. R. sa-jects of peculiar interest. pient); odium i, n. hatred (E. R. odious); amor, óris, m. love (E. R. umorous); hirundo, hirundinis, f. a swallow; Lacedemonius, i, m. a Lacedemonian; simplex. simplicis, simple; mos, moris, m. custom; in the plural, character (E. R. morals); velox, velócis, swift (E. R. velocity); corvus, i, m. a raven; niger, nigra, nigrum, black (E. R.

These comparatives and superlatives are evidently formed in the regular way, from such nouns as maledicens, magnificens, and benevolens, two of which, at least, are in use in the language, and have the same meaning as the other positives above given.

Some persons may anticipate difficulty from observing the hard and outlandish names employed in botany; but it should be remembered that this science is not the study of names, but of an admirable and most important branch of the economy of nature; and even the use of a hard name does not necessarily imply that the thing itself is difficult to be understood. Aloysia citriodora is a hard name, yet multitudes who would consider it to be so are well acquainted with the shrub to which it is applied-the sweet-scented verbena; and

the Jasminum officinale is nothing more than that sweetly stance for a stamen, or stamens; and that the other letters fragrant flower the common white jessamine, under another connected with it are nothing more than indicative of succesappellation. sive numbers; as monandria, one stamen, triandria, three stamens, &c. A knowledge of this will carry us through eleven classes of the Linnæan system.

The classes, it must also be remarked, are subdivided into orders, in denoting which the termination gynia is of frequent occurrence. Literally, it means female, but it stands, in this instance, for a pistil; while the preceding part of the word, as monogynia, digynia, or trigynia is formed exactly in the way just noticed, by adding, in each case, e name of a number. There are some persons,

"Who allium call their onions and their leeks;"

but we are not of that number. We prefer the simple English names of plants, and shall generally use them, Many of these are connected with old times and customis; and often do they convey some idea of the uses of the plants to which they are given.

CLASS I--MONANDRIA.

Plants bearing flowers with One Stamen only.

ORDER I. MONOGYNIA. One Pistil.

Of this kind our ditches and muddy ponds produce one example that may be easily procured. It is called mare's-tail, and has neither calyx nor blossom. Its single stamen is terminated by an anther slightly cloven, behind which is the pistil, with its awl-shaped stigma, tapering to a point. The stem is straight and jointed, and the leaves grow in whorls, or circles round the joints; at the base of each leaf is a flower, so that the number of flowers and leaves is equal. Its season of flowering is the month of May.

ORDER II. DIGYNIA. Treo Pistils.

Three British annual plan's, known by the name of the water starwort. They have two petals, curved inwards, but no calyx. They are scientifically called callitriche, from two Greek words meaning beautiful hair.

and generally flowers in June. A single petal forms its corolla or blossom, which is funnel-shaped. The leaves grow in

pairs, and are sometimes variegated with stripes of yellow or
white. The berries have been used by dyers to give a durable
green colour to silk or wool by the addition of alum.
Foremost of the flowers which grace the hedge-bank in
April is the germander speedwell, sometimes called cat's-eye,
and eye-bright. Thus Ebenezer Elliott says,-

"Blue eyebright! loveliest flower of all that grow

In flower-loved England! Flower whose hedge-side gaze Is like an infant's! What heart does not know Thee, clustered smiler of the bank, where plays The sunbeam on the emerald snake, and strays The dazzling rill, companion of the road." The notched leaves of this plant, in shape not unlike the leaves of a rose, but growing opposite to each other on the stem, sufficiently mark this species. We have in our fields, woods, and hedges, thirteen species of the speedwell, but only the germander with three other kinds bloom in April. The rest bloom from spring to autumn. The ash, the duck-weeds, and the sages belong to the same order.

ORDER II. DIGYNIA. Two Pistils.

The sweet-scented spring-grass. It has a spiked panicle, and flowers on short stalks. It flowers in May; grows in pastures and meadows, and is about a foot high. This plant is a true grass, but is separated on account of its naving only two stamens. The pleasant smell of new-made hay is chiefly owing to this plant.

CLASS III.-TRIANDRIA.

Plants bearing flowers with Three Stamens.

ORDER I. MONOGYNIA. One Pistil.

The crocus, having six equal segments, resembling petals, which blossoms in spring. Another plant is known as the autumnal crocus.

The valerian, a numerous species of shrubs or undershrubs, with very variable leaves, and mostly reddish-white flowers. Twelve species are European, and four are British. The officinal, or great wild valerian, grows abundantly by the sides of rivers, and in ditches, and moist woods, in Great Britain. The root has a very strong smell, which arises from a volatile oil. It is used by rat-catchers to destroy rats. It is also employed in medicine, in the form of infusion, decoction,

and tincture.

The yellow iris is a beautiful flower in June. It is often called flag-sedge, and corn-flag, and in Scotland is named water-skeggs. Many people in rural districts value its long acrid root as a cure for the toothache. It is also used for dyeing a black colour, and for making ink. This flower is sometimes found in moist woods. The common purple iris is the fleur de luce, and it derives its name from Louis VII., king of France, who, when setting forth on his crusade to the Holy

Land, chose it as his heraldic emblem.

ORDER II. DIGYNIA. Two Pistils.

confused notions of the Adriatic Sea, of Sicily, and of the south of Italy; and with the greater part of the Italian peninsula, they were wholly unacquainted.

Previous to the Homeric epoch, the Greeks believed in the existence of nations who inhabited the countries situated behind the regions where the sun appeared to them to rise and to set. They imagined that these nations lived in perpetual darkness, and they called them Cimmerians, a word evidently derived from the Hebrew Cimeririm (pronounced Kimeririm,) and signifying darkness. In proportion as they became acquainted with more regions that were enlightened by the sun, (that is, as the limits of the known world were extended by voyage and discovery,) they transported the Cimmerians and their dark abodes to a greater distance. In those early times, the Cimmerians were supposed to inhabit the borders of the Black Sea, near the Thracian Bosphorus, in Italy, and on the east and west, where the world was supposed to terminate. The people who were supposed to live the farthest north, were called Hyperboreans, because they were placed beyond Boreas, or in the extreme north; and those who lived the farthest south, were called Ethiopians,-literally, sunburnt,-because they were situated more directly under the sun's rays; their country lay south of Egypt, and was afterwards called Ethiopia sub Ægypto, or Ethiopia under Egypt; under, evidently signifying farther to the south than the latter country. The ancients generally be lieved that Africa and Asia, or rather Ethiopia and India, were united by land still farther to the south; and they consequently considered the Ethiopians and Indians as near neighbours. This is the ground on which both Virgil and Lucan have supposed the Nile to take its rise in the frontiers of India.

At the Homeric epoch the Greeks generally considered that the earth existed in the form of a disk. This disk was supposed to be centrally divided by the Euxine, or Black Sea, the Egean, and the Mediterranean into two parts, the one north and the other south; these parts were at a later period designated by Anaximander under the names of Europe and Asia, names which had been previously understood in a more restricted sense. The river Phasis in Colchis, or Pontus, on the east, and the straits of Hercules, or Gibraltar, on the west, were supposed to mark the limits of the world. The country of the Cimmerians, who were afterwards confounded with the Cimbri; and of the Macrobians, so called because they were supposed to be longer-lived than other mortals; Elysium, a happy country which had no existence but in the fantasies of the mind; the Fortunate Isles, which at a later period, under the names of Atlantis and Meropis, were the object of the philophic fictions of Plato and Theopompus; the country of the Arimaspi, who saw so clearly because they had only one eye; and of the Gryphons, who guarded the precious metals of the Riphean mountains; Colchis, the country of magic, peopled with monsters and prodigies; all these and inany other ingenious fables, the offspring of the imaginations of the poets Homer and Hesiod, or rather of the people among whom they lived, were mixed up with notions purely geographical,

The grasses and the corn-plants, which were described in and constituted the world at that period a scene of marvels,

Lesson IV.

ORDER III. TRIGYNIA. Three Pistils.

a receptacle of agreeable delusions and formidable mysteries. During the historic ages of Greece, cosmological systems were multiplied to an endless extent. Thales said that the earth

The water chickweed; the jagged chickweed; the allseed. was a sphere; his disciple Anaximander taught that it was

LESSONS IN GEOGRAPHY.-No. II.

NOTIONS OF THE POETS.

HOMER who wrote his poems in the tenth century before the Christian era, appears to have been acquainted with Greece, the Archipelago, the island of Crete, and the coast of Asia on the shores of the Mediterranean. Within these limits, he appears to have travelled; and he was, no doubt, personally acquainted with some of the scenes which he describes. His works, however, show that the geographical knowledge of the Greeks was at that time more limited than that of the Egyptians in the time of Moses, who lived seven centuries before him. On the south, the Greeks only knew the valley of the Nile, and that part of Africa which extends from Egypt to the west as far as Cape Bon, and the commencement of the Atlas chain of mountains; and, on the east, the Syrian desert, Asia Minor, Mesopotamia, and Persia. They possessed only very

a cylinder. Leucippus said that it was a drum, and Heraclides that it was a boat. Many and curious were the notions the ancient philosophers held concerning the globe until voyages of discovery were begun. Herodotus made a great step in the descriptive geography of certain regions, especially in the east of Europe. Yet, notwithstanding his voyages into the three parts of the old world, he fills his narrative with childish tales and dreamy details. He only knew the names of Arabia, Iberia (or Spain), Celtica (or Gaul), the islands of Albion (Great Britain), and the Cassiterides (or Scilly Isles). He had correct notions on Africa, and particularly on Egypt, but the western part of this continent was unknown to him beyond Tripoli. His details on India, besides their uncertainty, are intermingled with fables taken from the legends or popular creeds of the extreme East. Among the tales more or less ingenious, we must not forget the ants that were as large as foxes, and that collected heaps of gold mixed with sand!

Herodotus appears to have been unacquainted with western Europe. He does not speak of Massilia (Marseilles), a city

and found it 5,000 stadia. Accordingly, he multiplied this number by 50. and found the measure of the earth's circumference to be 250,000 stadia. Making allowance for the errors which he committed, for want of the delicate instruments of observation, which we possess in modern times, this was a tolerable approximation to the truth. Syene, indeed, was not on the same meridian as Alexandria, but on one nearly 3o east of the meridian of that city; and instead of being exactly on the tropic, it was about half a degree north of that line. Eratosthenes affirmed the spherical figure of the earth, and asserted that the immensity of the ocean would not prevent vessels from going to India by continually shaping their course westward.

founded by the Phocians a century before he was born. | the distance between the two places, Alexandria and Syenc, Rome, which had been increasing in grandeur for about three hundred years before his time, is not even mentioned by name. Of Italy he only knew the south of that part anciently called Magna Græcia. The extreme west of Africa was equally unknown to the Greeks. Yet the Phenicians had made discoveries in the Atlantic Ocean, and the periplus (sailing round) or coasting voyage of Hanno was executed considerably before Herodotus. The African voyage of the Carthaginian admiral, with the thirty-thousand persons which he had on board his vessels, is acknowledged to be authentic; opinions only differ as to the point where his maritime course terminated. Some will have it that, after having cleared the pillars of Hercules (the Straits of Gibraltar), he went as far as the Gulf of Guinea; while others limit his exploratory voyage to the mouth of the Senegal river. Gossellin fixes the limit at Cape Nun.

Hipparchus, who flourished about sixty years later than Eratosthenes, laid the foundation of astronomical geography, by endeavouring to determine the latitudes and longitudes of Pytheas, a citizen of Marseilles, performed a voyage to the places by observations on the heavenly bodies. He conNorth, before the time of Alexander the Great. He dis-structed a catalogue of the fixed stars, and taught the projeccovered Albion, or Great Britain, and always sailing in a tion of the sphere on a plane surface. Agatharchides, president northern direction, he reached the mysterious place called of the Alexandrian library, who flourished rather before Ultima Thule, which he saw covered with ice, enveloped in Hipparchus, wrote a treatise on the navigation and commerce mist, and as it were immersed in a horrible chaos. But what of the Red Sea, and an account of Egypt and Ethiopia. He was Thule? This is a question which has puzzled all his- was the first who gave a correct description of the Abyssinians; torians and geographers. Some have considered with good he mentions the gold-mines wrought by the ancient kings of reason that this country was Jutland or the coasts of Norway Egypt on the coast of the Red Sea, the process of working called Thulemark; or perhaps Iceland, as Pytheas sailed them, and the sufferings of the miners. He speaks, also, of through the Scandinavian seas, and his remarks relating to the tools of copper found in these mines, supposed to have the coasts of the Baltic have been acknowledged exact. been used by the native Egyptians before the conquest of Others have claimed this appellation for the Shetland Isles on that country by the Persians. The voyages of Eudoxus of the north of Scotland. Cyzicus added new information to what was already gained Aristotle, the great Greek philosopher and naturalist, main-respecting the East. He visited Egypt in the reign of Ptolemy tained that the earth was of a spherical form, and he even Evergetes, about 130 B.C. He made two voyages to India, stated the measure of its circumference at four hundred and afterwards accomplished the circumnavigation of the thousand stadia (a Greek itinerary measure, equal to about African continent. Strabo, who gives an account of his 600 feet). Indications of the existence of Madagascar have voyages and discoveries, attempts repeatedly to throw disbeen noticed in his writings. As to Ceylon, he mentions it credit on the truth of his statements; but they have been under the name of Taprobane, and that a long time before the confirmed by those of later times. age of Ptolemy. The limits of the world according to Aristotle were, on the east, the Indus; on the west, the Tartessus, or the Guadalquivir; on the north, the Riphæan mountains, Albion and Ierne (Ireland); on the south, Libya, in which he places the river Chremetes, which rises out of the same mountains as the Nile, in order to disembogue itself in the Atlantic ocean; an idea which leads to the supposition that he confounded the Nile with the Niger. He admitted that the Caspian sea was a great inland lake, having no communication with any other sea.

The conquests of Alexander the Great, led to the most distinct and extended motions of the ancient world. The most remarkable geographical fact of his reign, was the exploration of the Indus. A fleet of 800 vessels, under the command of Nearchus, descended this river, and went along the coast of Asia to the bottom of the Persian Gulf. The expedition of Alexander opened the eyes of the Greeks, but produced at that. time, no results of any consequence to the science of geography. What was gained by his exploratory voyage, was lost by the dismemberment of his empire; and the historians of the period relapsed into their former ignorance.

By degrees, however, geography assumed the dignity of a science. Eratosthenes, who flourished in the second century before the Christian era, composed a treatise on the subject. He was a native of Cyrene in Africa, and the keeper of the Alexandrian library. By means of instruments erected in the museum of the city of Alexandria, he found the obliquity of the ecliptic, to within half a degree of the truth. He was the first who attempted to determine the circumference of the earth by the actual measurement of an arc of one of its great circles. By means of sun-dials, he found that Syene, near a cataract of the Nile, which was situated, as he thought, on the same meridian as Alexandria, was immediately under the tropic of Cancer, so that at the time of the summer solstice, the sun was vertical to the inhabitants of Syene, and the gnomon had no shadow at noon. Thus, having measured the angle of the shadow of the gnomon at Alexandria, also at the time of the summer solstice, he found the distance of the sun from the zenith at noon, to be 7° 12', or one-fiftieth part of the drcumference of a great circle, viz. 360o. He then computed

QUESTIONS ON THE PRECEDING AND FORMER LESSON. ing the earth does it include? What is the form of the earth? What is Geography? How many kinds of information respectWhat proportion does the highest mountain on its surface bear to its diameter? Had the ancients any proper knowledge of its form? What appearance does the surface of the earth present to the human view taken on the most extended scale? What appearance do the heavens present? State some of the natural notions which mankind form respecting the heavens and the earth. What were the early notions of the Hebrews regarding the structure of the earth and the heavens? Where are we to look for the origin of geographical knowledge? To what source are we indebted for the earliest account of the known divisions of the world? What were the geographical boundaries alluded to by Ezekiel, as referring to the farthest limits of that knowledge in his

day?

What country is considered to be referred to in Scripture under the name of Tarshish? What country did the Romans understand under the name Africa Propria? What were the two different voyages to Tarshish, and how are they comprehended under the same name? What country is understood by the name Ophir ? How was gold transported from Ophir to Jerusalem?

What countries are understood by the names, the Isles, the Isles of the Gentiles, the Isles of the Sea, &c.? What country was known by the name of Sheba? What by Dedan? To what river were the names of the river and the great river applied? What famous cities and empires flourished on the banks of this river? With what countries did they trade? What is meant by the north in Scripture? What were its products mentioned by Ezekiel?

With what parts of the world were the Greeks acquainted in the time of Homer, as appears by his writings? What notions had they of the world previous to his epoch? Who were the Cimmerians? the Hyperboreans? the Ethiopians? and the Marobians? What country was Elysium? the Fortunate Isles? and Colchis? Who were the Arimaspi? and the Gryphons ? Greeks? With what countries was Herodotus acquainted? What What notions regarding the form of the earth had the later cities were in existence unknown to him? Who first made discoveries in the Atlantic Ocean? What is meant by the Periplus of Hanno? What were the discoveries of Pytheas of Marseilles? In what did the geographical knowledge of Aristotle consist? What addition did the conquests of Alexander make to the science of

IMAGINARY QUANTITIES.

A VERY ingenious and useful work on Algebra has just been put into our hands, written by J. R. Young, Esq., late Professor of Mathematics in the Royal Academical Institution, Belfast. In order to enable our more advanced readers to form some opinion of its merit, as an Elementary work, we give the following extract:

απ

"In the instance just adduced, namely a, an operation is apparently performed on pure symbols irrespective of all interpre tation; yet if we really look at what has actually been done, we shall see that it amounts to nothing: when b is written by the side of e a certain operation, called multiplication by b, is directed to be performed on a; except & be a number, we cannot obey this direction; but by writing b underneath, the direction is re-called, so that a, which would be the result of the operations of multipliIcation and division in arithmetic, is here written down free of these operations, because they neutralise one another: their combined effect being to leave a untouched. It is not necessary that we should be able to assign the effect of the combination ab and then the effect upon this of the combination; it is enough that we know, from the general laws of these combinations, that the

second destroys the first and sets a free.

ab

"It is more especially this recognition of the neutralising influence of certain algebraic combinations on one another, apart from all mere arithmetical considerations, that renders what are here called impossible or imaginary quantities so available in algebra, as instruments of investigation, though not admissible into arithmetic: a, whether b be real or imaginary."

ab

GLOSSARY.

"Imaginary or impossible quantities, are those expressions which indicate an even root of a negative quantity; the arithmetical extraction of such a root being almost an impossibility, because no even power of any number, whether positive or negative, can ever be negative. Imaginary quantities thus differ essentially from other surd expressions; the root indicated in each of these latter cannot be accurately exhibited, solely because the quantity under the radical sign differs from a complete power; yet a complete power may always be assigned which shall differ from the incomplete one by a quantity less than any that can be proposed, so that the defect mentioned is never of any practical consequence. But an imaginary quantity admits of no arithmetical representation Most of our writers have aimed at plainness and clearness of either accurately or approximately: the bare idea of arithmetical expression. A few words may need explanation. Let it be revalue is altogether excluded from it; the symbol -4 implies au membered, however, that we do not wish to save our readers the operation upon the -4 of impossible performance; so that if such trouble of thinking; and also that many technical terms can be a symbol were to occur in the answer to any question, we should better explained by their connexion with the subject than by any at once conclude that the solution to that question, in real num-brief definition. Several words which occur in this part are exbers, is an impossibility; and, consequently, that the conditions to plained in the Glossary in No. 5, page 78. be satisfied are incompatible or contradictory. Imaginary quantities thus subserve a very important purpose: whenever they present themselves as here supposed, they effectually apprise us of concealed absurdities among the conditions upon which our reasoning has been based, or which we are aiming to satisfy, and which might otherwise involve us in bewilderment or error. They are thus necessary to give completeness and certainty to our algebraic results, and on these grounds alone are valuable items in our system of symbols. But independently of this office of imaginary quantities, by which they inform us of the fact when the solution of a question is impossible, algebraists turn them to important account as direct instruments of investigation; frequently introducing them with great advantage into inquiries having reference only to real quantities, and terminating only in real results.

s., substantive; s.pl., substantive plural; v.a., verb active;
v.n., verb neuter; a., adjective.

ARSORPTION, s. the act of swallowing up, or imbibing.
APPELLATION, 8. a name, title, term.
APPRECIATE, v.a. to estimate, to value.

ARBITRATION, 8. the settlement of any dispute by persons mutually chosen by the parties.

APPALLING, a. frightful, terrifying.

AUTOMATON, S. a machine which has apparently the power of moving itself.

BRACK'ISH, a. saltish, like sea-water.

CARDINAL, 7. principal, chief, eminent.

CATASTROPHE, s. a final event, generally of an unhappy character.

CONCUSSION, s. the act of shaking; a shock.

COROLLARY, s. an inference, a deduction, surplus.

DISCRIMINATION, 8. a distinction; act of distinguishing one thing from another; a mark.

DOCILITY, 8. aptness to be taught; teachableness.
ELUCIDATION, s. an explanation, or exposition.
EMERGE, vn. to rise out of, to issue from.

EQUATOR, s. a great circle, equally distant from the poles of
the world, dividing the globe into equal parts, north and south.
EXPIRATION, s. the act of breathing out; an end; death.
FEROCIOUS, e. sarsue, fierce, cruel, rapacious.

FRIVOʻLITY, S. unimportance. FRIVOLOUS, &, slight, trifling, of no woment.

GERMINATION, &, the act of sprouting; growth.
IMPREG'SATE, e a. to make prolific, or fruitful.
INDICATE, c.a. to point out, to show.

In his first steps in the study of algebra, the learner naturally looks upon the new symbols of quantity to which he is introduced as nothing more than the familiar figures of arithmetic in disguise. It is not easy, nor would it be prudent to correct this too limited notion at the outset; the more comprehensive scope of the symbolic language of algebra gradually unfolds itself to him as he proceeds, till he at length comes to combine his characters and contract his expressions without any thought towards the numerical processes bearing the same names as those which enter into his symbolical combination. In fact, the important truth discovers itself by degrees, that the thing called algebra is a science in which symbols of any interpretation whatever are subjected 10 certain prescribed lows of combination, in obedience to which various operations may be performed and various results obtained without any reference to the particular characters of arithmetic. This tatter science is no doubt suggestive of the symbolical science of algebra; and the learner sufficiently sees that its laws of combination actually become those of arithmetic, when the particular symbols of the latter re-supernatural ideas. place the more general symbols of the former. In fact, he further sees that, till these general symbols are so repliced by those of arithmetic, many of the so-called operations of ag bra are but operations indicated, not operations executed. If we have to multiply a by b, we write ab or axh, and say that the thing is done; although, in truth, nothing is done, although something, by the sign of operation, is inarcated; we have no idea of the actual formance except each symbol, or the multiplier at least, be interpreted by a number; yet if the so-called product ab is to be divided by b, there is no doubt that the result is a, whatever the multiplier b may have been whether a number or something having no arithmetical meaning. It is true that in the latter case the term 'multiplier' might be objected to as not sufficiently significant, but a similar objection might be made to nearly every term introduced from arithmetic into algebra: the terms have a more comprehensive meaning as well as the symbols

per

INSPIRATION, s. a drawing in of the breath; an infusing of

INCNDATION, & an overflow of water; a deluge.

JUN'OLE, 3. land overgrown with trees, brushwood, and rank vegetation.

MAGNAN'IMOUS, e, great minded, brave.

MAMʼALUKE, OF MAS'ULUC, s. an Egyptian horse-soldier.
MERCENARY, s. a hireling :--a. selfish, base,

PHENOMENON, s. a naturii appearance; also any extraordinary appearance in the works of nature.

Put is sounded as Fin such words as Phenicia, Phrygian,
Sphinx, &c.; thus, Fenicia, Frygian, sfinx, &c.
PRECARIOUS, a. uncertain, dep-naut.
PRECISION, a exact limitation, great nicety.
PRECURSOR, s. a forerunner, a harbinger.

PROBLEM, S. a question proposed for solution or explanation.
PROTU BERANCE, s. a swelling above the rest.

PROTRUSION, s. the act of thrusting forward.