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2. The object of the memorandum or precis, which should be in the form of a narrative, is that any one who had not time to read the original letters might, by reading the precis, be put in possession of all the leading features of what passed. The merits of such a precis arc —(1) to contain all that is important in the correspondence, and nothing that is unimportant; (2) to present this in a consecutive and readable shape, expressed as distinctly as possible ; (3) to be as brief as is compatible with completeness and distinctness. You are recommended to read the whole correspondence through before beginning to write, as the goodness both of the abstract and of the precis will depend very much on a correct appreciation of the relative importance of the different parts. Brevity should be particularly studied. ARITHMETIC. 1. Explain concrete, abstract, and prime numbers, a measure, a multiple, G.C.M., and L.C.M. 2. How do you prove multiplication by casting out the nines? In what cases will this proof not point out an error in the product ? 3. Of the fractions -gs, j'o'r, and 194, express the difference of the first two as a fraction of the difference of the last two. 4. Which is the better investment, 3 per cents, at 82, or 31 per cents at 95|- ? 5. The Board examined 933 candidates from 1869 to 1879 inclusive; of these, 424 failed. State average number examined and percentage passed each year. 6. The rate of a clock being '0375 per cent, too fast, how much will the clock gain in a week ? 7. A friend of mine and I have the same yearly income from the rent of houses on which we pay the rates. He lives in a town where the rates collected are 2s. in the pound, and I where they are Is. 4d, He pays £9 3s. 4d. more a year in rates. What is our income ? 8. Extract square root of 3-| + 4_+sl + 6J- to four places of decimals. 9. The true length of the year is 365*242264 days, but it is generally taken at 3C5j days; how long will it be before the error amounts to a day ? 10. In the estimates for the year the following salaries were voted for one of the Government departments : 1 at £700, 2 at £450, 1 at £315, 3 at £275, 5 at £250, 1 at £240, 6 at £215, 2 at £200, 1 at £190, 2 at £180, 1 at £105, 1 at £160, 3 at £130, 2 at £115, 1 at £100, 3 at £90, 1 at £80, 2 at £60. A reduction of 10 per cent, was made in all salaries. What was the average salai'y actually paid ? 11. What will a debt of £4,250 amount to if left standing for 2-_ years at 5 per cent, compound interest ? GEOGRAPHY. 1. Describe the southern coast-line of the Continent of Europe, giving the chief capes, bays, rivers, and seaport towns. 2. If you started on a tour through Scotland, what places would you visit, and why ? 8. Name as many rivers as you can that form deltas. 4. Name the principal forest trees of New Zealand, and say in what parts of the colony each is chiefly found. 5. Write what you know of monsoons, trade winds, and rotary storms. LATIN. 1. Translate— Talibus Aeneas ardentem torva tuentis Lenibat dictis animum, lacrimasque ciebat: Ilia solo fixos oculos aversa tcnebat; Nee magis incepto vultum sermone movetur, Quam si dura silex, aut stet Marpesia cautes. Tandem corripuit sese, atque inimica refugit In nemus umbriferum ; conjux übi pristinus illi Respondet curis, aequatque Sychaeus amorem. 2. Scan the first line of the above passage, and the sixth line of the passage in question 4. 3. Give a history of Dido. 4. Translate — Dixerat; at clypeum, tot ferri terga, tot aeris, Cum pellis totiens obeat circumdata tauri, Vibranti medium cuspis transverberat ictu, Loricajque moras, et pectus perforat ingens. Ille rapit calidum frustra de vulncre telum: Una, eademque via sanguis animusquc sequuntur. Corruit in vulnus: sonitum super anna dedere : Et terrain hostilem moriens petit ore cruento. 5. In what cases are the following words in the above passages, and why: Solo, illi, and curis (in question 1); ferri, vibranti, ingens, via, and ore (in question 4) ? 6. Translate — Illi, intermisso spatio, imprudentibus nostris atque occupatis in munitione castrorum, subito se ex silvis ejecerunt, impetuque in eos facto, gui erant in statione pro castris collocati, acriter pugnaverunt: duabusque submissis cohortibus a Caesare, atque his primis legionum duarum, cum hae, perexiquo intermisso loci spatio inter se, constitissent, novo genero puguao perterritis nostris, per medios audacissime perruperunt, sequo iude incolumes receperunt. 7. Why should Caesar have thought it necessary in describing this event to say, "Atque his primus legionum duarum " ?