speak, the other struck him on the head with his hatchet, and then both of them fled. But the king's wife pretended that her husband was not dead, but only stunned by the blow; and she said that he had appointed Servius to rule in his name, till he should be well again. So Servius went forth in royal state, and acted in all things as if he were king, till after a while it was known that the king was dead, and Servius was suffered to reign in his place. Then his rivals saw that there was no hope for them, and they fled from Rome, and lived the rest of their days in a foreign land. Euclid.-1. Euc. I. 34. 2. Euc. I. 41. 3. If from any point in the diagonal of a parallelogram lines to be drawn to the angles, the parallelogram will be divided into two pairs of equal triangles. Grammar. I. "This above all-to thine ownself be true; And it must follow, as the night the day, Thou canst not then be false to any man."-SHAKESPEARE. (a) Analyse the last two lines of the above. (b) Point out and parse those verbs in the above which are in the imperative and infinitive moods. (c) If the word "thine" (thine ownself) is in the possessive case, how do you explain its government? Account also for the case of "our," "them," in the expressions we, our-selves, they, themselves. 29.66 2. Show what is the force of the Latin preposition, or affix, in the following words:-Arrogant, discovery, distil, irrigate, prevent, reflect. Geography.-1. In what countries of Asia or Africa is each of these industries carried on, viz., the cultivation of sugar, coffee, tea, rice, opium, vines, ostrich-farming, and obtaining gold, diamonds, and pearls? Describe fully one of these occupations. 2. Give notes of a lesson to a Second Standard on 66 The Tropics and a Tropical Climate." Illustrate your lesson by reference to Central Africa; and draw a map of the West Coast from Cape Blanco to Cape Negro. Algebra.-i. Multiply a + ab + a2b2 + ab3 + b1 by a − b, and divide ax3-(a2 + b)x2 + b2 by ax-b. 2. Prove the rule for the addition of algebraical fractions. Divide –5+6 3. Solve the equations :- (1). 4(5x — 3) — 64(3 − x) — 3(12x — 4) = 96. (2). 3x + I 9x+8 4 = 12 x + I FOURTH (OR FIFTH) YEAR. Arithmetic.-MALES.- -1. The working expenses of a certain company average £62 10s. per day, and their weekly expenses amount to per cent. of their gross profits for an ordinary year. At the same rate of expenditure and income, how much more net profit will they realise this year than they did in the year 1879? 2. If you buy £500 stock in 3 per cent. Consols at 961, and sell out again at 82, what sum do you lose? 3. A and B each lend £256 for 3 years at 4 per cent. per annum : A at simple, B at compound interest. State in decimals of £1 what is the difference in the total amount of interest which they are each entitled to at the end of the time. 4. A box with square ends 13 ft. wide takes 8432 ft. of board 12 inches wide to make it. What is the length of the lid? 5. Reduce decimals). 520 to the decimal of 1, (to four places of 2401 Answers.-(1) £97 6s. 43d. (2) £66 13s. 719d. (3) £1,578,528. (4) 14 ft. (5) 4068 +. FEMALES.-I. Find the simple interest and amount of £417 7s. 9d. for 1 year 10 months at 43 per cent. 2. A man after paying an income tax of 7d. in the pound, has £248 10s. 8d. left; what was his gross annual income? 3. If a tradesman with a capital of £2,000 gain £50 in 3 months, how long will it take him with a capital of £3,000 to gain £175? Answers.—(1) £33 9s. 6337d.; £450 175. 3323d. (2) £256. (3) 7 months. Grammar. I. "For in that sleep of death what dreams may come, Must give us pause; there's the respect That makes calamity of so long life."-HAMLET. (a) Point out and analyse the substantive and adjective sentences in the above, and show why each is so-called. (b) Parse fully all the pronouns in the above. (c) Give in your own words the meaning of this passage. 2. Mention any four words in our language that are evidently of Latin origin, and four that are evidently of Anglo-Saxon. 3. Give, when you can, the ancient positive forms from which the following comparatives are derived-elder, nether, former, more, further. Geography.-What are the "Tropics?" And what is the meaning of the name? How many degrees are they from the Equator? Draw a map of the coast-line of America, from the Tropic of Cancer to the Tropic of Capricorn, that is (nearly), from Cape Sable to Rio di Janeiro. Mark the lines of longitude and latitude, if you can. 2. Give notes of a lesson on "The Formation of Coral Islands"; or, on "The Wild Animals of North America." History.-i. What do you understand by arbitrary Government? Mention periods of our History when that kind of Government has been attempted in England? 2. Upon what grounds did the right of the British Parliament to tax the American colonists rest? And upon what grounds was it resisted? 3. When, and under what circumstances, has the Government of England been conducted by a Regency? Śketch the character and career of any personage who ever held the rank of Regent. Penmanship.-(Same as for Candidates). Composition.-Write an essay on Wages, and the reasons why some persons are paid better than others. Euclid.-1. Show that if the length of the base of a triangle be a units, and the altitude be b units, the area of the triangle will be algebraically represented by a b. 3. The length and breadth of a rectangular room are measured with a defective foot-rule; the area appears to be 4204 square feet, but is really 400 square feet. Find the error in the rule. C2x3 + etc. (2) x= = ас a+b; x = 5 or 4. (3) ft. Mensuration. -1. One diagonal of a quadrilateral, which lies outside the figure, is 70 feet; and the difference of the perpendiculars upon it from the extremities of the other diagonal is 16 feet. Find the area. 2. The radius of a circle is 174 feet; find the area of a sector which contains 24° 25'. Answers.-(1) 560 sq. ft. (2) 63°403 + sq. ft. preferred; but in reading the plays we feel that the poet not only relates events, but fills the imagination and elevates the soul. Poetry has been employed by great writers in many kinds of composition. Poems narrating great historical events in a complete manner and in a lofty style are called epic poems. The Iliad of Homer, and the Æneid of Virgil, are famous examples of this kind of poem. Dramatic poems are those which are written in the form of dialogues between characters who appear on the stage and carry on the action of the dramas. The Greeks brought this kind of composition to great perfection. Their great dramatists, Eschylus and Sophocles, have, however, been surpassed by our great poet, Shakespeare. A didactic poem is one which is of an instructive nature, as the Georgics of Virgil, which treat of agriculture. An elegy is a poem expressive of lamentation on the death of some person, as Gray's "Elegy," and Tennyson's "In Memoriam." Lyric poetry is written in the form of odes, supposed properly to be set to music. Dryden's "Alexander's Feast,” and Collins' “Ode to the Passions," are examples. Our greatest poet, Milton's "Paradise English literature is especially rich in poetry. Shakespeare, has already been mentioned. Lost" is a religious epic poem of great beauty. Spenser's "Faery Queen," a splendid poem, illustrating the age of chivalry. Chaucer's tales are among the finest in existence. The poems of Dryden and Pope are famous for their admirable versification. Cowper is a great religious poet. Wordsworth's poems are among the finest written in the present century. Alfred Tennyson and Robert Browning are our greatest living writers of poetry. (3) Answer to Mensuration, 2, page 92. Let the parallelogram be ABCD. If we have AB, BC, and the diagonal BD given, then, since BC is equal to AD (Euc. i. 34), we have in the triangle ABD the three sides given, and the area can be found from the formula, Area √ S (s—a) (s—b) (s—c), where s is half the sum of the sides. = If the other diagonal, AC, be given, then we have the three sides AB, BC, CA of the triangle ABC, from which we can find the area. The area of the parallelogram will be found by doubling the area of either the triangles ABD, ABC (Euc. i. 34). (4) Large marbles are a penny a score dearer than small ones. A boy who has bought equal numbers of each kind, finds that on the whole he has got eight for a penny. How much are the small marbles per score? (5th year, January, 1877.) Let x = price of small marbles per score in pence. large .'. x + 1 = .. average price of four marbles |