han C. If each had travelled a mile an hour faster, they would hav t met an hour sooner; and if A had travelled half a mile an hour slower and B half a mile an hour faster, they would have met 2 miles further from D. Find the rate of travelling of each, and the distance between C and D.

THURSDAY, 19TH DEC., 10 A.M. TO 1 P.M.

GEOMETRY.

F. S. EVANS, M.A.; J. MARSH, Esq.

PART I.

N. B.-Capital letters are to be used in all your Geometrical figures, and also throughout the whole of your work in referring to those figures.

I. (a.) Define an obtuse-angled triangle. What objection is there to this definition? Enunciate the proposition of the first book which proves the correctness of the definition.

(b.) Give Euclid's definition of a square. Point out how Euclid assumes more than is necessary in this definition. (c) What is meant by a corollary to a proposition?

(d.) When is one proposition said to be the converse of another? (e) Explain clearly what is meant by the indirect method

of proof.

II. Draw a straight line perpendicular to a given straight line of unlimited length from a given point without it.

(a.) Why is the straight line said to be of unlimited length ?

(b.) In the construction, why is a point taken on the other side of the straight line to that on which the given point is? Could it not be taken on the same side?

III. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, namely, the sides which are opposite to equal angles in each, prove that the other sides shall be equal, each to each, and also the third angle of the one equal to the third angle of the other.

(a.) PQR, STV are two triangles having the angles QPR, PQR equal to TSV, STV respectively, and the side PR equal to the side TV. Are these triangles equal in every respect? Give reasons for your answer,

IV. Describe a right-angled parallelogram that shall be equal to a given triangle.

V. If a straight line be divided into any two parts, prove that the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.

VI. From any point D in the side CA of a right-angled triangle ABC, of which C is the right-angle, two straight lines DE, DF are drawn perpendiculars to CA and the straight line drawn through B at right angles to AB respectively, meeting this latter straight line in the points E and F respectively. Prove that the rectangle AD, DC is equal to the rectangle EB, BF.

PART II.

VII. In every obtuse angled triangle, prove that the square on the side subtending an acute angle is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.

(a.) ABC is a triangle having the angle at C obtuse; the side BA is produced to E, and AE is made equal to AB. Prove that the square on ED (D being the point where the perpendicular from A meets BC produced) together with three times the square on BD is equal to four times the square on AB.

VIII. Prove that the opposite angles of any quadrilateral figure inscribed in a circle are together equal to two right angles.

(a.) ABCD is a quadrilateral figure inscribed in a circle; the opposite sides AB and DC are produced to meet in P, and the opposite sides AD and BC are produced to meet in Q. If from P the straight lines PNK and PML be drawn parallel to AD and BC respectively, and from Q the straight lines QLK and QMN be drawn parallel to AB and DC respectively, shew that the quadrilateral KLMN is equal in all respects to the quadrilateral ABCD.

IX. 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; prove that the rectangle contained by the whole line which cuts the circle and the part of it without the circle is equal to the square on the line which touches it.

THURSDAY, 19TH DEC., 2 TO 5 P.M.
INDIAN HISTORY.

W. STEVENSON, M.A.; C. WATERS, M.A.

PART I.

I. Recount the chief facts in the lives of Sakya Muni and Asoka. What reasons are given to account for the rapid spread of Buddhism?

II. Name the chief Hindu kingdoms in the North of India and their approximate boundaries about the year 1000. How did their rulers generally behave towards each other when the Mahomedans entered, and what was the consequence? Name those who made the stoutest resistance to Mahmud of Ghizni and Mahomed Ghory.

III. Name the Mahomedan emperor, with the dates of his reign, (1) most distinguished for useful public works; (2) for erecting beautiful buildings; (3) for variety of fortune; (4) for cruelty; (5) for religious toleration; (6) for religious intolerance. Give briefly the grounds for each answer.

IV. Name the Hindu kingdoms in the Deccan subdued by the Moguls, the date of the conquest of each, and the king or dynasty reigning at the time. The empire was larger-was it also stronger at the close of Aurangzebe's reign than at its commencement, and if not, why not?

V. What was the position of affairs in the Carnatic, when Clive marched against Arcot? Give an account of his operations in that campaign.

PART II.

VI. Write a brief account of affairs in Oude from 1773 until its annexation.

VII. Describe fully the circumstances which led to the first two Mahratta Wars, and enumerate the battles fought in the second one. What were the chief causes of the downfall of the Mahrattas, and when was their power finally crushed?

VIII. Give the substance of the treaties made by the English with Hyder and Tippu at the conclusion of each of the Mysore Wars.

IX. Of what historical importance are the following persons and

places? Lalla Moolraj, Shah Sujah, Akber Khan, Kareem Khan, Moodkee, Meanee, Kalunga, Shapooree.

X. Give an account from its commencement of the war which was going on when Lord Ellenborough became Governor-General. What grounds had the English for entering upon this war ?

FRIDAY, 20TH DEC., 10 A.M. TO 1 P.M.

ENGLISH HISTORY.

J. T. MARGOSCHIS, F.R.G.S.; D. SINCLAIR, M.A.

PART I.

I. When did the following persons live, and for what were they severally remarkable? Dunstan ; Strongbow; Wolsey; Gaveston; Jack Cade.

II. Give the dates and causes of the following battles, and state what were the most important results of each :

Evesham; Halidon Hill; Poictiers; Bosworth; Shrewsbury.

III. Sketch the rise and progress of the English Parliament up to the time of Edward the Second.

IV. Give a short account of the reign of Edward the Fourth, and show that in respect of genealogical descent his claim to the English crown was more valid than that of his rival.

V. State briefly (1) the nature of the Feudal System, (2) the reason for the summoning the Council of Clarendon and the decision arrived at by that Council, (3) the provisions of the Magna Charta.

PART II.

VI. What were the various subjects of dispute that arose between Charles I. and the Parliaments and that ultimately led to the Civil War. Mention (1) with dates, the first and the last battle fought in this war, and (2) the names by which the followers of the opposing parties were respectively known.

VII. Describe briefly the nature of the Habeas Corpus Act, the Reform Bill, the Stamp Act, and the Act of Settlement, and mention the Statesmen whose names are intimately associated with the passing of the first three.

VIII. In what reigns did the war of the Spanish Succession, the war of the Austrian Succession, and the Seven Years' War take place, and who were the contending parties in each. Name with dates (1) a battle fought in each and (2) the treaties by which they were severally concluded. What were the terms of the treaty by which the first was terminated.

IX. What were the political opinions held by the Trimmers, the Root-and-branch Men, and the Chartists.

X. (a.) In what connection do Lady Jane Grey, Thomas Cromwell, and John Wilkes figure in history.

(b.) What led to the trial of the seven Bishops and to the trial of Sacheverell.

XI. In what year were the English and Scottish Parliaments united and what were the chief terms of the union.

FRIDAY, 20TH DEC., 2 TO 5 P.M.

GENERAL GEOGRAPHY.

REV. E. SELL; GEO. DUNCAN, Esq.

PART I.

I. What and where is each of the following:-Jeddo, Bight of Biafra, Titicaca, Texas, Zambesi, Terra del Fuego, Seistan, Natal, Dardanelles, Sierra Leone, Congo, Everest.

II. St. Helena, Cuba, Formosa, Socotra, Canary Isles, Bourbon, Newfoundland, Madagascar, Hong Kong, Mauritius, Tasmania, Borneo, Java, New Zealand. State in a tabular form (a) where the above-mentioned islands are situated, and (b) to what Governments they respectively belong. How do the last four lie in relation to Australia.

III. Compare and contrast the physical features of North and South America.

IV. Telegraphic communication is established between Sydney and San Francisco, passing through Java, Singapore, Madras, Bombay, Suez, Gibraltar, Falmouth, Valentia, Newfoundland, New York to San Francisco. What seas or countries does the wire cross in passing from one place to the next?