I. W. ROBERTSON, Skeld.-Dr. Smith's Smaller Histories of Greece and Rome (Murray); Workman's 'Matriculation Questions, with Advice to Students' (Hughes); and Autenrieth's Homeric Dictionary (Macmillan) will probably be of service to you. 2. JUVENIS, Huddersfield.-You will find the Syllabus you ask for in the February issue of this journal. You might use Fitch's 'Lectures on Teaching' in addition to your other textbook. 3. J. S., Earls Heaton.-Dr. Johnson once said to Boswell, Sir, hell is paved with good intentions.' This is evidently the phrase to which you refer. 4. B. E. L.-Mr. Furness's admirable Variorum edition of 'Macbeth,' published by A. R. Smith, and price 155., is the best you could get. You will find a cheaper one in the Clarendon Press series and in the Rugby editions. 5. EBOR.-Lyell's' Geology' would suit your purpose. 6. DOMINICA, Cotmanhay.-See Query 14, January, '82, issue of our journal. 7. D. A., Nottingham, and GLACIER, Darwen, have forgotten to give their real names and addresses. Their queries will be answered on their doing so. 8. W. SEYMOUR, South Shields.—In a square garden a tree is so placed that its distances from three corners are 8, 10, and 13 perches, respectively; find the area of the garden. = 23+x +3 X- 3 23 20 52 2 2 2 2 I = (23+ ) (23 − x) (x+3) (x − 3) 202 I = 201 (529 — x2) (x2 — 9) ; But sin DAO = cos (90° — DAO) = cos BAO: 538x2-x-4761 .. cos? BAO = 328x2. 400x2 But sin? BAO +cos? BAO = I. 400x2 = 400x2 = 6057 54289 6057 2 54289 12114 42175 4 205*3655... 2 x2 205 3655233 = 2 438.3655... 27'434. 202 = 2 or 2 2 219-1827... or 13.717... = I It is evident that the value 13 717 is inapplicable. .. area of garden 219.1827 perches. = I ac. I ro. 19:1827 poles. = 9. PUZZLED.-If you want us to answer your question, please be at the trouble to send it, and not refer us to a book where it may be seen. 10. LEIGH.-Hughes's Graduated Exercises in Arithmetic, or the same author's Government Inspection Cards. 11. JUNIUS.-You will find all the information you need in the Syllabus issued by the Science and Art Department. 12. INQUIRER.-The term 'Practical Geometry' shows that the problems have to be worked practically. 13. E. H. S.-We regret to state that your query must be held 17. P. P.--Three consecutive angular points of a parallelogram are (a, 0), (h, k), (o, b), respectively; find the co-ordinates of the other angular point, and the equations to the diagonals. The first angular point (a, o) is on the axis of x, and the third angular point (o, b) is on the axis of y .. It is evident that the co-ordinates of the fourth angular point are (ah), (b −k). The general equation to the straight line which passes through two given points is : (X2− x1) (V − Y1) = (Y2 −Y1) (x − x1). The two given points for one diagonal are (a, 0), (0, b), and for the other (h, k), {(a− h), (b−k)}. 20. E. JENKINS, Pontardawe.-Consult the 'Science Directory,' which may be had through any bookseller. 21. EUREKA.—No, but if you have difficulty with any particular question, we shall be happy to help you in the Query Column. No answers are published. 22. ALPHA.-Write to Mr. J. Strugnell, National Society's Depository, Westminster. 23. PUZZLED.-We only answer one question at a time. Get (a) Gardner's 'How to Draw a Map,' (b) Johnston's 'Atlas.' 29. JEMMY JOHNSON.-By all means sit for scholarship. Write to Messrs. Longmans for their 'Civil Service Guide.' 30. SEVERN. (a) No syllabus issued. See questions in previous Nos. of PRACTICAL TEACHER. (b) Application should be made at once. (c) Writing and composition good. 31. J. E. ROWLEY.-No paper issued. Avail yourself of our Query Column. 32. W. H. G.-(a) Right style-high percentage. (b) Most probably. 33. PUPIL TEACHER.-The trade does not know the book, which is probably out of print. 34. CURIOUS. The word you mention occurs in Mr. Tennyson's Dream of Fair Women': 'Moreover, it is written that my race Hew'd Ammon, hip and thigh, from Aroer Aroer was a town by the bank of the river Arnon. See the 2nd and 3rd chapters of the Deuteronomy of Moses. We should advise you to give a spare moment to your spelling. people do not make oblidge spell oblige. Most required to support it. Prove that, cos (a + x) tan A being the co-efficient of friction. 36. Aλpa.-A heavy wire is bent at its middle point, so as to contain an angle of 60°; it is suspended from one of its ends; find its position in equilibrium. (Magnus' 'Mechanics.') If C and B be the middle points of the two parts, and CB be bisected in D, D must be vertically under A the point of suspension. The position of the wire may be found by drawing a horizontal line through A, and marking off a distance AE equal to√ of a, where a is the length of half the wire, and then dropping a vertical EF equal to of a. If AF be joined and √7 an equilateral triangle described on it, the two sides will be the position of the wire. A 2 a a sin 120° :: : .. sin ADC = FAD = 4 ADC (I. 29), .. cos EAF sin ADC 37. NORMAN H.-No. I query in Geometry is to bisect any triangle by a line drawn parallel to one side. Your query is a particular case, and can be solved in the same way, or thus:Bisect AC, one of the sides of the equilateral triangle in D, and erect the perpendicular DE=AD. Join AE, and with centre A and radius AE describe an arc cutting AC in F. Through F draw FG parallel to BC. Then AGF shall be half the triangle ABC. It can be proved by the same method as the general case. In the deduction you refer to it would have been preferable to prove that AE falls nearer to AC, the greater side, than AD. The proof is very simple. 38. SPHINX, Cornwall.-0ávw from Ovýσкw, active voice, subjunctive mood, 2nd aorist, first person singular; you for you, Homeric for als (see smaller Liddell and Scott, page 487), dative feminine plural; ávéσxeTo from ávexw (Liddell and Scott, page 60), 2nd aorist, middle voice, indicative mood, 3rd singular; Tel0OVTO, augment dropped-usual with Homer,-from Teilw (Liddell and Scott, 523), passive voice, indicative mood, imperfect tense, 3rd plural; TovTO (see Liddell and Scott, 256) from πw, middle roual, imperfect, sine augment; móμny, middle voice, indicative mood, imperfect tense, 3rd plural. SECOND YEAR.-(continued.) MALE CANDIDATES. Geography. Two hours and a half allowed for this Paper. Every candidate must draw one of the maps in Question 1. Not more than seven of the other questions may be answered. 1. Draw a map of (a) Ireland. Or (b) British North America. Or (c) The Colonies of Queensland, New South Wales, and Victoria, N.B. Each map should be drawn on a scale sufficient to occupy all the blank space available. If the candidate put in, and correctly number the lines of latitude and longitude, it will add to the value of the exercise. Places must not be indicated by letters or figures, referring to a list of names at the side, but the names thems.lves must be insertea in the map. 2. Show that the coast of England is generally bold and deeply indented, and name the districts whica present especial exceptions to this statement. 3. Describe the positions of, and the historical associations connected with, St. Albans, Ely, Tewkesbury, Torbay, Stirling, Glencoe, and Carnarvon. 4. Name the counties in which the towns of Preston, Wakefield, Dundee, Coventry, Bolton, Belfast, Pais ey, Halifax, Dudley, and Stroud are situated, and state the principal industries of each district. 5. The rivers of Scotland are navigable only for short distances, but possess wide estuaries.' Explain the physical character of the country in its bearing upon this statement. 6. No part of Ireland is more than sixty miles distant from some inlet of salt water.' Explain this statement and name some of the principal inlets. 7. Describe fully the great central plain of Ireland. 8. Describe the position of Aden, Lagos, Singapore, and Barbadoes, and gives the dates and circumstances of their being annexed to the British Empire 9. Name the chief plains and plateaux of Hindustan, and give a brief description of the most southerly plateau. 10. Give some of the historical associations connected with Benares, Lahore, Seringapatam, Plassy, Arcot, and Lucknow. 11. Enumerate the chief exports of Natal, Queensland, and Jamaica. 12. Name the principal rivers of the Canadian Dominion, the towns on their banks, and the seas into which they flow. 13. Describe briefly a voyage by sea from London to Cape Town, Galle, and Calcutta. 14. Give some account of the climate, the native race, and the chief productions of New Zealand. 15. Describe fully the boundaries and physical features of Western Australia. In the equilateral triangle ABC, BD, and CE, which bisect the angles at B, C, intersect each other in O and the opposite sides in 1, E; show that OD=OE. 2. To divide a given straight line into two parts so that the difference of the squares on the whole line and on one of the parts may be equal to a given rectangle, which is not greater than the square on the whole line. 3. If a straight line touch a circle the straight line drawn from the centre to the point of contact shall be perpendicular to the line touching the circle. Find the locus of the points, from which tangents can be drawn to a given circle equal to its radius. 4. To draw a chord through a given point within a given circle that shall be equal to a given line. Show that this is only possible within certain limits, and draw the longest and shortest chords that can be drawn through the point. 5. In a circle the angle in a semicircle is a right angle. The circle ABC passes through the centre of the circle DBC; find the point of intersection of the tangents to DBC at the points BC. 6. In equal circles, the angles which stand upon equal arcs are equal to one another, whether they be at the centres or circumferences. Show that the arcs subtended by one of the angles of an equilateral triangle, and by one of the smaller angles of a right angled isosceles triangle, which are inscribed in a circle, are in the ration of 4: 3. 7. If from any point without a circle two straight lines be drawn, one of which cuts the circle but does not pass through the centre, and the other touches it, the rectangle contained by the whole line, which cuts the circle and the part of it without the circle, shall be equal to the square on the line which touches it. If perpendiculars BD, CE be drawn from the angular points, B, C of the triangle ABC upon the opposite sides, show that the rectangle contained by AB and AE is equal to the rectangle contained by AC and AD. 8. In a given circle inscribe a triangle equiangular to a given triangle. If the given triangle be equilateral and its base equal to the radius of the circle, compare the areas of the two triangles. 9. To inscribe an equilateral and equiangular pentagon in a given circle. Show that the line drawn from the apex of the isosceles triangle, required in the figure, to the intersection of the lines bisecting the angles at the base, is greater than the radius of the circle. 10. The sides about the equal angles of triangles which are equiangular to one another are proportional. II. In a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to one another. If the segments of the base are in the ratio of 4 : 1, find the ratio of the squares on the sides. 12. Two circles ABC and ABD, intersect in A, B, show that the tangent to ABD at A cannot be parallel to the tangent to ABC at B, unless the circles are equal. 13. Two equal circles touch another circle externally at the extremeties of a diameter: if the radius of the latter circle be double of the radius of the others, compare the areas of the squares constructed on the diagonals of the rhombus formed by the common tangents to the circles. 14. To find a point without two given circles from which four equal tangents of given length can be drawn to the two circles. 15. Show that the circle which passes through the middle points of the side of a triangle passes through the feet of the perpendiculars from the angles upon the opposite sides. Algebra and Mensuration. Three hours allowed for this Paper. Candidates are not permitted to answer more than twelve of these questions. The solution must be given at such length as to be intelligible to the Examiner, otherwise the answer will be considered of no value. [NOTE.-In all problems, where required, the circumference of a circle may be assumed to be=(2)ths of the diameter. Not more than 2 decimal places are required in the answers.] b 9. If a, b be employed as bases of logarithms, show that log M=log. axlog. M. Given log. 15 1.1760913, log. 2 = .3010300, find log. 3, log. 225, and log. √75. 10. Find a for nula to express the present value of an annuity, to commence at the end of m years and then to continue n years. 11. The sum of four numbers in arithmetical progression is 194, and the sum of the products taken two and two together is 1381; find the numbers. 12. Given n straight lines, of which no three pass through the same point and only two are parallel, find the number of intersections of the lines. 13. Find in chains the area of the largest rectangle that can be enclosed by 240 hurdles each 18 feet long. 14. Find the radius of a hollow sphere which is an inch thick, and contains the same amount of gold as a solid sphere whose radius is 7 inches. 15. The sides of a right-angled triangle are in arithmetical progression and its area is 150 feet; find its sides. 16. The densities of two similar cones vary directly as the squares of their heights, find the height of the larger cone weighing 216 times as much as the smaller, which has a height of six feet. 2. Distinguish 'productive' and 'unproductive labour.' Under which of the two heads would you place the construction and maintenance of a park for the people, the labour of railway servants employed in pleasure traffic on Sundays, and the duties of over-lookers of labour? Give your reasons. 3. Give approximately the amount of the English public debt; explain the term Consols, and give some reasons for the price of Consols in 1881. 4. Explain the terms Fair Trade,' Free Trade,'' Reciprocity,' and 'Most favoured nations clauses 'in treaties of com merce. 5. Explain generally how a large increase in our carrying trade and foreign investments may have effected the relative amounts of exports and imports in the sum total of English commerce. 6. Show the effects of a bad harvest at home on the home trade and manufactures. 7. State some of the chief advantages and disadvantages of a bi-metallic system of coinage. 8. Show generally what effect the growth of a large manufacturing town has upon the value of land in the immediate neighbcu hood. 9. Point out the chief advantages which enable a farmer in the West of America to compete with the English farmer in the home market. 10. What data would be required for determining whether an agricultural labourer earning 15s, a week is in a better or worse pos tion than a labourer in a la ge town earning 25s. a week? 11. Give reasons showing that each trade tends to have a certain rate of profit, and account for the difference of the rates of profit in a large co-operative store and in a shop in a country village. 12. Distinguish between saving and parsimonious habits: name some of the safest modes of investing small savings, and account for the variation in the amounts of interest to be fairly expected in each that you have named. 13. Show the advantages of co-operation between the capitalist and his workmen in obviating disputes about wages and recourse to arbitration. 14. Discuss the question whether a high rate of interest is compatible with security of investment. 15. Enumerate the principal articles that have been totally or partially relieved from taxation in the present reign, and explain the principles on which a high rate of duty is still leived on certain articles. FIRST YEAR. MALE CANDIDATES. Mental Arithmetic. N.B. Do not turn this paper till you are told to do so. You are to enter the answer in the space ( > left for it after each question. Nothing is to be written on this paper, except the particulars required in the above table, and the answers (which must be written in ink) to the questions on the other side. No erasures or alterations are permitted. They will be marked as errors. 1. (6017+1008) − (4018+ 1007)= 2. 1007 × 1009= 3. Tr of 3'5×4}= 4. Goods bought for Is. 7d. sold for 2s. 2d., the gain per cent. = 5. 133-132 - 123 = 6. If 12 score cost £11 5s., the price of one article= 7. The number of francs, at rod. each, in 50 guineas= 8. The real value of £1,000 in the 3 per cent. stocks when an investment produces 24 per cent. = 9. Compound interest on £250 for 3 years at 20 per cent. = 10. The number of cubic feet in a box 5 feet long, 4 feet broad, 16 inches deep. 11. The prime numbers in 289289 are= 12. The average of 2023, 2045, 2075, 3017= 13. The accommodation of a school 56 feet long, 20 feet broad, 12 feet high, at 80 cubic feet per child= 14. The remainder of (7365 × 5087)÷9= Write the passage dictated to you by the Examiner. (For the Examiner.) One passage is given for Candidates of both Years. The passage should be read once distinctly, and then dictated once, in portions as marked. If the room is large, and there is danger of your not being heard at its extremity, you may permit one of the officers of the College to stand half-way down the room, and repeat the words after you, exactly as you give them out. It is essential that there be no complaint on the part of the Candidates that they could not hear or understand: you can prevent this only by clearness, accuracy, and audibility. The characteristic result of this Monarch's policy was the consolidation of Western society. His imperial schemes give place to a growing feudalism, in which independent chieftains sub-divide the imperial domains, forming political organisations with some degree of central activity, and replacing the shapeless chaos of previous centuries. In a life recklessly active | he reformed the coinage, | collected libraries, interfered in religious controversies, attempted the magnificent enterprise | of uniting the Rhine and the Danube, and meditated the task of moulding the discordant Codes | of Roman and barbarian laws | into an uniform system. FIRST YEAR. MALE AND FEMALE CANDIDATES. Languages. Four hours allowed for this paper. Male candidates may answer questions in two languages, Female candidates in one only. Latin. SECTION I. I. Translate into English (a) Prima luce, confirmata re ab exploratoribus, omnem equitatum qui novissimum agmen moraretur præmisit. (b) Titus Labienus castris hostium potitus et ex loco superiore quæ res in nostris castris gereretur conspicatus decimam legionem subsidio nostris misit. Qui cum ex equitum et calonum fuga quo in loco res esset quantoque in periculo et castra et legiones et imperator versaretur cognovissent nihil ad celeritatem sibi reliqui fecerunt. 2, Parse moraretur, castris, gereretur, subsidio, cognovissent, reliqui, sibi. 3. Translate into English Instructo exercitu, magis ut loci natura dejectusque collis et necessitas temporis, quam ut rei militaris ratio atque ordo postulabat, quum diversis legionibus abæ alia in parte hostibus resisterent, sepibusque densissimis, ut ante demonstravimus, interjectis prospectus impediretur, neque certa subsidia collocari, neque quid in quaque parta opus esset provideri, neque ab uno omnia imperia administrari poterant. Itaque in tanta rerum iniquitate fortunæ quoque eventus varii sequebantur. Explain the subjunctive moods in this passage. Account for the case of "diversis legionibus." Might the structure of this sentence have been different? |