Voc. Abl. (object) 0! Acc. -ās ENGLISH. (subject) to or for. by, with, or from. -ā by, with, or from. Abl. Here you may remark that in the singular two case-endings are the same-namely, those of the nominative and the vocative, both being a; and that in the plural taken with the singular, four case-endings are the same namely, in the plural those of the nominative and the vocative; in the singular, the genitive and the dative. This undoubtedly is a defect in the language. By practice only can you learn in reading to ascertain which, in any particular instance, the writer intended; the difficulty, however, is not so great as you might imagine. sign. Observe that in the example, after the word mensa, a, stand 1 and fem. Here 1 with a noun denotes the first declension, as afterwards 2 with a noun will denote the second declension, 3 with a noun the third declension, and so on; f. or fem. denotes the feminine gender, and intimates that mensa is a noun of the feminine gender. It may appear strange to you that a thing which in English is of the neuter " gender," as being without sex, should in the Latin be of the feminine gender. So, however, it is. In Latin, one way of determining gender is by the termination. Thus, all nouns ending in a (with an exception which will be pointed out by-and-by), are of the feminine gender. And as all nouns ending in a are of the first declension, so all nouns of the first declension, generally speaking, are of the feminine gender. Decline the following nouns like mensa :— EXERCISE 15.-LATIN-ENGLISH. 1. Rana coaxat. 2. Rana sæpe est præda ciconiæ. 3. Ciconia nocet ranæ. 4. Ciconia devorat ranam. 5. O rana, coaxas. 6. Aqua turbatur a ranâ. 7. Plantæ florent. 8. Terra vestitur copià plantarum. 9. Procellæ nocent plantis. 10. Terra gignit plantas. 11. O plantæ, 12. Terra vestitur plantis. quam pulchre ornatis terram! On this exercise I must give a few words of explanation. In the sentence Ciconia nocet ranæ, you have the object in the dative case. Generally the object is in the accusative case, but noceo is one of the verbs which govern their object in the dative instead of in the accusative case, as will be more fully set forth hereafter. After the passive verb turbatur, you have the instrument rană with the preposition a; whereas after the passive verb vestitur, you have copia without the preposition. The reason is that, in Latin, when the instrument is a person or living creature, the preposition a is usual; but it is not used when, as in the second case, the instrument is a thing, that is, something without life. Vestitur is not given in the vocabulary to this declension, because it has been given before. Here, as in other instances, words, the English of which has been previously stated, are repeated without the English, in order to secure attention and to assist the memory by repetition. As the English sign of the dative is to or for, so you must use the one or the other as the sense requires. And as the English sign of the ablative is by, with, or from, so must you use either by, or with, or from, according as the English idiom requires. EXERCISE 16.-ENGLISH-LATIN. 1. The plants flourish. 2. The storm injures the plant. 3. Plants are injured by the storm. 4. Frogs are swallowed by the stork. 5. The earth produces plants. 6. Plants are produced by the earth. 7. O plants, how beautifully are you produced by the earth! 8. I praise abundance of water. 9. The storm moves the waters. 10. The waters are moved by the storm. After having learnt each vocabulary, you will do well to try to ascertain what words in it have representatives in English. These English representatives (denoted by the initials E. R.) are words in English derived more or less directly from the corresponding Latin words. Thus, from aqua we have E. R. aquatic; from copia, we have E. R. copious; from herba we have E. R. herb; from præda we have E. R. prey; from terra we have E. R. terrene, etc. You will soon acquire skill in discovering the E. R. in all cases, and in the discovery you will gain an aid to memory, as well as an insight into the exact original meaning of many English words. Indeed, you should never allow a Latin word to pass you without endeavouring to ascertain whether it has any E. R., and if any, whether one or more, what they are, and what their signification. Adjectives in the feminine gender are declined like mensa. This you see exemplified in the following example : Bonam puellam, a good girl. Alba rosa, a white rose. Ancilla, a maid-servant. Bone puellæ, O good girls! Ab. Bonis puellis, by good girls. manner write out and learn by Pulchra columba, a beautiful pigeon. Quadrata mensa, a square table. OBS.-The Latin word ne is employed in asking a question, and is placed after a word and joined to the word it follows; the Latin word an is employed in asking a question, and is placed before a word or sentence; nonne asks a question with not included, as, nonne vituperas? dost thou not blame? EXERCISE 17.-LATIN-ENGLISH. 1. Est mihi pulchra alauda. 2. Estne tibi pulchra alauda ? 3. Mea alauda est pulchra. 4. Estne mea alauda pulchra ? 5. Nonne est 10. tua alauda pulchra ? 6. Tua columba valde est pulchra. 7. Est mihi girl EXERCISE 18.-ENGLISH-LATIN. 1. I have a pigeon. 2. Thou hast a good girl. 3. Hast thou a good 4. I have not a good girl. 5. Thy lark is beautiful. 6. Is not the island great? 7. The island is not great. 8. Hast thou a Lood maid-servant? 9. I have not a good maid-servant. the girl (the girl's lark) is beautiful. 10. The lark of In dea, a goddess, and filia, a daughter, the dative and the ablative end in ābus, instead of is; thus, deabus, to or by the goddesses; filiabus, to or by the daughters. This change is made in order to distinguish the dative and the ablative cases of these feminine nouns from the same cases of the corresponding masculine nouns, namely, deus, a god; which has deis or diis, in the dative and ablative; and filius, a son, which has filiis. Nouns of the first declension which denote male beings are of the masculine gender (denoted by m). This fact remains a fact, though the termination of those nouns should happen to be feminine. Thus, nauta, a sailor, is masculine, though its termination is the same as that of mensa, a table, and puella, a girl. Masculine nouns of the first declension are declined like feminine nouns of the first declension. Observe, however, that they take their adjectives in the masculine; that is, the adjectives agree not in form but in sense with these masculine nouns of the first declension, as in the following example : Lafeuillade; but the voyage, which took place in 1667, produced no new discovery. The discoveries of the Russians in the north of Asia must be noticed. At the beginning of the seventeenth century they knew nothing of the coasts of Siberia beyond the Yenisei. War and conquests laid open to the emperors the way to thisimmense region. In the space of less than a century, the whole of Northern Asia, from the frontiers of China to the Frozen Ocean, was brought under the dominion of Russia. Geography was benefited by this annexation, which gave to the Russians new facilities for performing useful explorations in these in. hospitable countries. In 1728 Behring made the important discovery of the strait which separates Asia from America, and rendered the peopling of the New World no longer a question of difficulty or doubt. The northern circumpolar. regions had not been the theatre of any important expedition, from that of Baffin, above mentioned, until the middle of the eighteenth century. The era of scientific expeditions was now begun. Geography, so long retarded in her progress to perfection, proceeded with a sure and rapid step. This was the most brilliant period of the history of navigation from the time of the great discoveries of the sixteenth century. It was particularly remarkable for the positive character of its results. Bougainville, who had gained renown in the wars of Canada, anticipated that which he gained as a navigator, by an expedition to the Malouine or Falkland Islands, where he went to found a French colony in 1764. Tho circumnavigation of the world by Commodore Byron, also begun in the same year, produced very important results; and so did the voyages of Wallis and Carteret, in clearing up some practical questions relating to the geography of Oceania. Carteret, in particular, determined the geographical positions (that is, the latitudes and longitudes) of several islands in the direction of New Britain; his vessel having been the first English man-of-war which had touched at the island of Celebes. Three years after his first voyage, in 1767, Bougainville undertook his grand expedition to circumnavigate the globe. short stay in the river La Plata, he was detained in the Strait of Magellan no less than fifty-two days. He then entered the South Pacific Ocean, or South Sea, as it was then called, and discovered the islands of Pomotou, which he called the DanTrépidus auriga, a timid charioteer.gerous Archipelago. He then entered the chief port of Tahiti, VOCABULARY. DECLENSION OF SUBSTANTIVE AND ADJECTIVE. G. Plural. N. Boni nautæ, good sailors. [sailors. D. Ac. Bonos nautas, good sailors. N. Bonus nauta, a good sailor. heart V. Boni nautæ, O good sailors! Bonus agricola, a good husbandman. | Magnus Nerva, great Nerva. EXERCISE 19.-LATIN-ENGLISH. 1. Pérfuga Jugurthæ est mihi. 2. Malus pérfuga est tibi. 3. Poetam bonum laudo. 4. Bonus poeta laudatur. 5. Equa laudatur ab auriga. 6. Nautæ ad insulam navigant. 7. Boni nautæ patriam laudant. 8. Aquila a poetis sæpe laudatur. 9. Agricolæ magnopere delectantur plantis. 10. Erras, O nauta! 11. Nonne erratis, aurige? 12. Tristitia poetarum bonorum est mihi. 13. Umbras silvarum magnopere amo. 14. Agricolæ per silvam equitant. EXERCISE 20.-ENGLISH-LATIN. 1. Hast thou a deserter? 2. Is the deserter bad? 3. Good poets are praised. 4. I praise good poets. 5. Good husbandmen praise (their) native country. 6. The native country of good poets is praised. 7. The pirate rides through the wood. 8. The sailor sails to the island. 9. The mare of the good charioteer is good. LESSONS IN GEOGRAPHY.-VI. DISCOVERIES OF THE EIGHTEENTH CENTURY. IN 1700 Dampier, at this time celebrated for his buccaneer (piratical) expeditions, discovered some new islands contiguous to New Guinea, or Papua. Wood Rogers sailed round the world in three years and three months; and encouraged by his successful expedition, the maritime powers proceeded to attempt similar enterprises, hitherto considered as extremely dangerous. Towards the end of the preceding century, France had also made expeditions into the Southern Ocean. Her first vessel which appeared in the Pacific Ocean was commanded by one After a or Otaheite; and his transactions with the inhabitants of New Cythera were not only pacific but amicable. He next visited the Samoa or Navigator's Islands, touched at Papua or New Guinea, discovered to the east of it an assemblage of islands which he called the Louisiade Archipelago, several of the Admiralty Isles, and another called by his own name near Solomon Isles. In the same direction he discovered several other islands of less importance, which had been seen by other navi gators; and having visited New Ireland, discovered by Carteret he arrived at Batavia; whence he sailed to Europe by the Cape of Good Hope. This expedition was well received in France and in Europe; it had made several important discoveries, and had been marked with interesting episodes which were related with spirit and talent; and created a still greater desire for circumnavigating expeditions. The greatest navigator of modern times is acknowledged to be Captain James Cook. His first voyage to the Pacific had for its grand object the observation of the transit of Venus, that is, the passage of this planet in its orbit over the disc of the sun, a phenomenon alike important in astronomy, navigation, and geography. Having received his promotion from the rank of master in the Royal Navy to that of lieutenant, he was put in command of the Endeavour, a small ship of 370 tons, in which he left England in August, 1768. After touching at Rio de Janeiro, he proceeded to the Strait of Lemaire, in order to double Cape Horn. Tierra del Fuego did not present to him such a dreadful aspect as it did to Wallis; the naturalists of the expedition, Sir Joseph Banks and his friend Dr. Solander, a Swedish gentleman, a pupil of the eminent botanist Linnæus, collected there some plants and animals. One of their excursions, however, nearly proved fatal to them. Having ascended a mountain whose vegetable products they wished to examine, they were overtaken by the shades of evening and the coldness of a severe frost. Dr. Solander was on the point of perishing under its influence, when the wise importunity, or rather pertinacity, of his companions saved his life, by hindering him from giving way to sleep, the forerunner of death. Having spent several hours in great distress, and having witnessed two of their servants sink under its power, the imprudent explorers with much difficulty reached the coast. After this delay in the Strait of Magellan, Cook stood out for Tahiti, where the astronomical observations entrusted to the care of the expedition were to be made. The natives of Tahiti welcomed this expedition in the same way as they had done that under Bougainville, in a hospitable and agreeable manner. During their three months' residence in this island, Cook and his learned companions made an ample collection of specimens of its natural history, and of observations n the manners and customs of its natives. They then visited several other islands of the Tahitian group, and gave to the whole archipelago the name of the Society Islands. They explored New Zealand, and found the natives the very opposite of the Tahitians in their disposition, both hostile and cruel. They discovered that this country, supposed to have been a single island, consisted of two separate islands divided by a expedition proceeded directly southward; but in latitude 67° 13' S. it met with rocks which appeared to be impassable. No attempt was made to get beyond this obstacle, and the expedition returned northward to the nearest cape, under the con viction that if any southern continent existed, it could only be at a very great distance, and quite in the vicinity of the south pole. The two vessels, which were separated from each other among the ice, proceeded to New Zealand, where they again met. After useless explorations to the east of this island, as far as the 46th parallel of latitude, Captain Cook made for the Society Islands, where he remained until the health of the expedition was recruited. A second attempt to discover the southern continent soon brought the expedition to latitude 71° S., but here again the passage to the south was blocked up by ice, and it was obliged to return northwards. In a new exploration of the seas of Oceania, Captain Cook re-discovered Easter Island, which Commodore Byron, Carteret, and Bougainville had searched for in vain; he also discovered some new islands belonging to the strait, which now bears the name of Cook; but they durst not examine the interior of the country, as it would have been too dangerous to have ventured into the midst of a race of cannibals, whose savage habits were very soon observed by the expedition. Cook left the shores of New Zealand on the 31st of March, 1770, and in twenty days afterwards beheld those of New Holland, or Australia, where he discovered Botany Bay, an inlet on which stands Sydney, the metropolis of our Australian colonies, and one of the most important of our colonial settlements. Proceeding northward, he was nearly shipwrecked in latitude 16° S. by the vessel striking on a coral rock. The Endeavour was providentially saved, and enabled to reach a small harbour where she was repaired, and put into a condition to resume her homeward voyage, which she completed without meeting any further disaster. The second voyage of Captain Cook, undertaken in July, 1772, had for its object the discovery of that great southern land which had been for ages supposed by navigators and geographers to exist in the southern part of the Great Pacific Ocean, and which Abel Tasman fancied he had seen when he landed on New Zealand. Two vessels called the Resolution and the Adventure were put under the command of Captain Cook. The Marquesas group, returned to Tahiti, and re-visited Tongataboo and the Friendly Islands, where he discovered Savage Island, and Batoa or Turtle Island, belonging to the group of the Feejee Islands; he then re-established several points of New Guinea, and discovered Tanna, Erromango, and several other islands of the group called the New Hebrides, as well as New Caledonia and Norfolk Island. The point of departure for a third exploration of the Antarctic or Southern Seas was New Zealand. Captain Cook endeavoured to reach the south pole in a more easterly direction than formerly. Having arrived at latitude 55° 48' S., he sailed towards Cape Horn, and continued his route towards the east. In this route he discovered the island of South Georgia, to the east of Tierra del Fuego; and south east of the former a group of islands which he called Sandwich Land. Here he terminated his voyage toward the southern circumpolar regions. He had circumnavigated the globe in high southern latitudes, and had demonstrated that no southern continent existed in the immenso zone which he had explored. The hypothesis of its existence was thrown many degrees nearer the south pole; and the illusion of this problematic continent, so richly endowed by nature, was dissipated for ever! In this remarkable expedition Captain Cook was absent from nately, ended the life of the greatest navigator of modern times. Captain Clerke, who was second in command, took charge of the expedition, and sailed to the north-east in search of the passage to the Atlantic; but the same obstacles compelled him to abandon the enterprise, and he died on the voyage home. To attempt to describe all the benefits which the discoveries of Captain Cook have conferred on the sciences of geography and hydrography, is more than can be done in this historical sketch of these very memorable expeditions. This illustrious navigator determined with accuracy the geographical positions of the places which he discovered or visited, rectified numerous errors in the maps and charts of the century in which he flourished, and accelerated the progress of the science to which these remarks form our introduction, in a degree hitherto unknown. Mathematical geography has, since this time, taken her place among the exact sciences. In concluding this lesson, we may remark that Cook lifted the veil of darkness which hung over the extremities of the Pacific Ocean, and the junction of the continents of Asia and America. His last voyage, by disclosing the vast breadth of America at the latitude of Behring Strait, made the hopes of discovering the north-western passage darker than ever. That continent had, previous to the time of the English navigator, been considered as terminating to the north in a point or cape, after passing which, the navigator would find himself at once in the South Seas, and in full sail to China or Japan. But the discovery of Cook showed that there was found intervening a space of land of nearly three thousand miles in breadth, a very large portion of the circumference of the globe. Hence, geographers viewing the coast running northward from Behring Strait, Hudson Bay, and Baffin Bay, all enclosed by land, received the impression, and constructed their maps accordingly, that an unbroken mass of land reached onwards to the pole, and that all these boundaries were for ever barred against the enterprising navigator. LESSONS IN ARITHMETIC.-XI. 10. To reduce fractions to equivalent fractions having the same denominator. RULE.-Find the least common multiple of all the denominators. Multiply the numerator and denominator of each fraction by the quotient obtained from dividing the least common multiple by that denominator. EXAMPLE. Reduce,,,, to a common denominator. 1260 is the least common multiple of 9, 7, 10, 12 (see page 134), and the quotients of 1260 by these respectively are 140, 180, 126, 105. Multiplying each numerator and each denominator by these numbers respectively, we get 110, 11, which are fractions equivalent to the given ones, and all of which have the same denominator. 900 756 It may be observed that the common denominator found in this case is the least. Any common multiple of the denominator of the original fractions would have given fractions with the same common denominator; but the least common multiple gives, of course, the least common denominator. 11. Fractions may also often conveniently be made to have the same denominator by the following method:-Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator. The reason of this will be clearly seen from an EXAMPLE.-Reduce,,,, to fractions having the same common denominator. Following the rule, we get for the first fraction—. 2 × 6 × 5 × 9 3 x 6 x 5 x 9 where we have multiplied the numerator 2, and denominator 3, by 6 × 5 × 9, the product of the denominators of the other fractions. The fractions will therefore be much as 3 × 6 × 5 × 9, the common multiple of 3, 6, 5, and 9, which we have taken, is not the least common multiple. 12. We are enabled by this means to find which of two fractions is the greater. For instance, if we wished to know which of the four fractions given in Art. 11 is the greatest, having reduced them to a common denominator, 810, we are able to say that the second fraction,, is the greatest, because it contains the greatest number of the 810 parts into which the unit is divided, viz., 675; and in the same way we see that the order of magnitude of the four fractions is IP EXERCISE 24. Place in order of magnitude the following sets of fractions :1. 1, 4, 3, 4. 3. 1. £, & à. 5. A. 11. 1. f. 2. 4, 1, 1, 1. 4. 48, 180, 1. 11. 6. I TO or, as it could be written, 1 (Art. 8). We have here effected the addition, i.e., found a single fraction which is equal to the sum of the two given ones, by reducing the fractions to a common denominator, 15. The same method will apply to any other two or more frac tions. Hence we are able to enunciate the following Rule for the Addition of Fractions. numerators so formed for a numerator, and take the common Reduce the fractions to a common denominator, add the new denominator for a denominator. The single fraction so formed will be the sum of the given fractions. fraction, before commencing the operation, to its lowest terms, Obs. It will generally be most convenient to reduce each if it is not already in them, and then to take the least common denominator. Rule for the Subtraction of Fractions. Roduce the two fractions to a common denominator, subtract the less numerator from the greater for a numerator, and take the common denominator for a denominator. The fraction so formed will be the difference of the given fractions. The same observation with respect to the least common denominator, which was made with reference to the rule for Addition, evidently applies equally to that for Subtraction. N.B. In all cases a whole number must be treated as a fraction having a denominator unity. For instance, to subtrac from 2. 2 = 1 = 1. 7 x 3 x 6 x 5 2. Simplify the following expressious |