fessors, but openly tendered my talents to the principal himself. I went, had admittance, and offered him my service as a Master of the Greek language, which I had been told was a desideratum in his University. The Principal seemed at first to doubt of my abilities, but of these I offered to convince him, by turning a part of any Greek author he should fix upon into Latin. Finding me perfectly earnest in my proposal, he addressed me thus: "You see me young man, I never learned Greek, and I don't find that I have ever missed it."

III. Subject for Composition:-

way.

Describe any journey you have made by Cart, Canal, or Rail

THURSDAY, 23RD DEC., 10 A.M. TO 1 P.M.

INDIAN HISTORY.

G. OPPERT, PH. D.

I. Give the reasons for the rise and decay of Buddhism in India, and explain the essential differences between Brahmanism and Buddhism.

II. Give a short sketch of the influence of the kings of Ghazni and Ghor on the history of India.

III. Describe the character of Baber, Akbar and Aurangzeb from a political and religious point of view and their position towards the inhabitants of India.

IV. Compare the proceedings of the Portuguese, Dutch, French, and English when settling in India.

V. State the changes which the Government of India underwent when being transferred from the East India Company to the British Crown.

GREEK HISTORY.

I. What was the political state of Greece at the time when the first complications with Persia arose ?

II. What was the position of the Persian Empire when the war with Greece broke out?

III. What were the resources for war on both sides, and how did the actual results coincide with the prospects at the opening of the war?

IV. What were the most important events and who were the leading generals and statesmen during the Grecian war between the years 490 and 479 B. C.?

V. What was the immediate influence of those events on the future relations between Greece and Persia ?

THURSDAY, 23RD DEC., 2 TO 5 P.M.

GEOGRAPHY,

D. SINCLAIR, M.A.

I. (a) By what is Yesso separated from Niphon, Sumatra from Java, Hayti from Puerto Rico, Holstein from Schleswig? (b) Mention (a) the highest summit of the Andes and the highest mountain in Scotland with their respective heights, (b) the chief town in Queensland, (c) the chief seat of the iron manufactures of Russia, (d) the smallest county in England, (e) the most commercial city in Chili, (f) the largest of the Society Islands.

II. With regard to the following countries state (1) the prevailing religion and language and the chief occupation of the people of each, (2) the nature of the Government that obtains in each, and (3) the chief Vegetable and mineral productions that abound in each. Japan, Morocco, Bolivia.

III. What natural advantages from position etc. has enabled Glasgow to rise to be the second city in the United Kingdom?

IV. For what are the following noted either commercially, historically, politically or physically? Gibraltar, Wallachia, Honclulu, The Plateau of Mexico, Strasburg, Ballarat, Galashiels, Peshawur.

V. Sketch the coast line of America from Cape Charles to the mouth of the Amazon, and insert six capes, six river months, and six towns. Also show with reference to it the relative positions of four islands at the mouth of the St. Lawrence, the four largest of the West, India Islands, and Trinidad, Bermuda, Barbuda, Barbadoes.

K

VI. Taking the middle of the island of Sardinia as a centre, and the distance therefrom to Brindisi as a radius, describe a circle, and mark off on the circumference the countries, seas, and gulfs it passes through.

VII. Account for the fact that though New York, London, and Sebastopol are in very different latitudes, the average annual temperature of the three is the same.

VIII. Of what political importance is it to England that the independence of the Kingdom of Belgium should be maintained?

IX. Why is it that vessels plying between London and Sydney, make their outward voyage via the Cape of Good Hope and return via Cape Horn?

X. (a) From what places does London import Cinnamon, Cloves, Cinchona, Arrowroot, and Tapioca? What is the nature of the last three.

(b) Of what countries are the Ourang-outang, Bison, Ornithorynchus, and Jaguar the characteristic animals?

XI. Suppose the Railway from San Francisco to New York to be constructed in a straight line through what States will it pass and what rivers will it cross.?

FRIDAY, 24TH DEC., 10 A M. TO 1 P.M.
ALGEBRA AND GEOMETRY.

E. P. METCALFE, M.A.; J. MARSH, ESQ.

PART I.

I.

If x + y2 + 22 = 1 = a2 + b2 + c2

Show that

(1 ax - by

+(cy - bz) 2.

Solve the Equation

cz) (1 + ax + by + cz) = (az — cx) 2 + (bx — ay) s

II. Determine the condition that the roots of a quadratic equation may be (1) rational (2) irrational (3) equal and of the same sign. If ux2 + bx + c = o have its roots equal and of the same sign,

III. Show how to extract the square root of a binomical surd of the form a +√b.

n

V. If Cr denote the number of combinations of n things taken r together, show without the aid of formulæ that

VI. Find the middie term of (1 + x) 2n. Show that when x is any positive integer except unity

I. If, in a circle, two straight lines, one of which passes through the centre, cut one another, but not at right angles, the rectangle contained by the segments of one of them shall be equal to the rectangle contained by the segments of the other

II. (a) Describe a circle about a given triangle.

(b) Describe a circle which shall pass through a given point and touch two given straight lines.

III. Explain the terms "homologous sides," "duplicate ratio," and "ex equali."

IV. (a) If a straight line be drawn parallel to one of the sides of a triangle, it shall but the other sides proportionally,

(b) ABCD is a parallelogram, a point E is taken in BD the diagonal, and CE is joined; a point F is taken in CE and BF is joined; FG is drawn parallel to DC meeting the diagonal in G, and GH is drawn from G parallel to BF and meeting AB in H: show that AH AB:: DG: DE.

V. ABC is an arc of a circle, OB is the radius drawn from the centre O, and ADC is a chord drawn at right angles to the radius OB and cutting it at the point D; express DB as a ratio between the chord BC and the radius.

VI. If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

FRIDAY, 24TH DEC., 2 TO 5 P.M.
ARITHMETIC.

E. P. METCALFE, M.A.

I. If the value of the rupee varies from 1s. 9d. to 1s. 94d., and the franc from 9 d. to 10d.; find the maximum number of francs which it is always safe to give for Rs. 500.

II. State and prove the rule for reducing a recurring decimal to a vulgar fraction.

If one cubic foot of water weighs 62:37 lbs. Avoir.: reduce the weight of

3.445 × 3:445

1.554 X 1.554

41 X 405

cubic feet to the decimal of a ton.