10. (a). "Heureux si je pouvais, dans l'ardeur qui me presse, Au lieu d'Astyanax, lui ravir ma princesse !"

(b).

"Va donc disposer la cruelle

A revoir un amant qui ne vient que pour elle."

Translate, paying attention to the following criticisms :—

(a). Ma princesse appartient encore au vocabulaire des précieuses. (b). La cruelle, encore Mademoiselle de Scudery.

11. Quote any passages you remember illustrating the Latinisms of Racine.

12. Write out a detailed analysis of any single scene in Athalie.

13. Illustrate by quotations Racine's method of turning into poetry Biblical passages.

Translate into French :

The southern part of Italy is intersected with chains of mountains and full of deep valleys. These valleys abound in vegetation of all kinds— forest trees, fruit trees, vines, and the most lovely flowers, such as never could be found in any but a warm climate. The villages and residences are almost always built on the side or top of some hill, or in the hollow cleft of a steep rock. The Italians do this to be out of the way of robbers, of whom there are many in the centre and south of Italy, who live by plundering travellers, or carrying off the property of the country people who fall in their way.

COMPARATIVE GRAMMAR,

DR. ATKINSON.

Write an Essay on the development of the Romance system of Conjugation from the Latin, with reference especially to the so-called irregular forms in French and Latin.

3. The man of heroic character of the present century compared with the hero of some past age.

4. The romance of chivalry compared with the modern novel.

5. Shakspeare's "Romeo and Juliet."

[One subject to be chosen.]

History.

PROFESSOR BARLOW.

1. What account does Joinville give of the battle of Massoura ? Give his description of the "Greek fire."

2. Give his account of the embassy sent to St. Louis by the "Senex de Montanis." What mistake does Joinville fall into about that prince? He gives a strangely erroneous account of the great Mohammedan schism?

3. Give Asser's history of the year 878.

4. Point out in Magna Charta recognitions of the constitutional principles that the king is the fountain of honour, and the fountain of justice; that the royal person is inviolable, and that the royal power is limited.

5. Discuss the following question:-Did the framers of Magna Charta mean trial by jury, when they spoke of the lawful judgment of a man's peers?

6. Consider the justice of the charge brought against Earl Godwin relating to his share in the death of Alfred the Etheling.

7. Write a short history of the wars between England and Scotland in the reign of Edward III.

8. A memorable attempt was made in the reign of John of France to impose some constitutional check on the irresponsible power of the sovereign? What were the causes of its failure?

9. Give a summary of the most important events in the reign of Louis le Débonnaire.

10. Write a full account of the contest between Philip IV. and Boniface VIII.

DR. INGRAM.

1. How were Toulouse, Provence, and Britany, respectively, united to the Crown of France?

2. How did the question as to the exclusion of females from the throne of France arise in A. D. 1316? Examine the claim put forward by Edward III.

3. Into what three great periods does Hallam divide the history of Italy, from A. D. 1040, to A. D. 1494, and what does he mention as the characteristic features of each period?

4. Relate the history of the change of dynasty at Naples consequent on the fall of the House of Suabia.

5. Give an account of the changes in the government of Florence during the latter half of the thirteenth century.

6. What was the origin of the long-continued conflict between Guelfs and Ghibelins?

7. What was the origin of the connexion between Hungary and Austria? And between Bohemia and Austria ?

8. Discuss the question whether feudal tenures existed in England before the Conquest.

9. Hallam remarks on the different character of the feudal policy in France and in England? Show how the conditions under which it existed in the latter country operated for the advancement of public liberty.

10. Give an account of the gradual establishment of the right of the House of Commons to investigate and chastise abuses of administration.

3. If the tangents of the angles of a triangle be in geometrical progression, whose common ratio is e, show that

sin 2 Ce sin 24.

4. Find the equations of the sides, and the area of the triangle, the co-ordinates of whose vertices are (1, 2), (3, − 2), (5, 1).

--

5. In the same case, find the equation of the circumscribing circle, and the co-ordinates of its centre.

6. Find the equations of the perpendiculars at the middle points of the sides of a triangle, the co-ordinates of whose vertices are given.

DR. TRAILL.

7. What is the chance of throwing with a pair of dice the following: Sixes, Deuce Ace, the numbers 5, 7, 9?

8. If A1 A2 A3 be the lines joining the vertices of a plane triangle to the centre of the inscribed circle, prove the following equation connecting them with the sides and angles of the triangle:

9. Find the locus of the foot of the perpendicular from the origin on a chord of the circle

x2 + y2+ 2gx + 2fy + c = 0,

when this chord subtends a right angle at the origin.

10. Given a point and two fixed lines; draw any two lines through the fixed point, and join transversely the points where they meet the fixed lines. Find analytically the locus of the intersection of the transverse lines.

11. Write down the equation of the locus of a point whose distance from the point (1, 1,) is equal to 3.

12. Find the equation of the line joining the centres of the circles x2+ y2 = 2y and x2 + y2 = 2x.

MR. BURNSIDE.

13. Determine the equation of the tangents drawn from a given point to the circle x2 + y2 — r2 = 0.

14. Given the angles of a triangle; one vertex is fixed, another moves along a right line: determine the locus of the third.

15. Determine the conditions which must be satisfied if the general equation of the second degree

ax2 + 2hxy + by2+ 2gx + 2fy + c=o

represents parallel right lines.

16. In a right-angled triangle, given the radii of the inscribed and circumscribed circles, determine the sides.

17. If

a' = aa2 + 2baß + cẞ2,

c' = aa'2 + 2ba'B' + c,3'2,

b' = aaa' + b (aß' + a′ß) + cßß′,

prove that a'c' - b′a = (ac — b2) (aß′ – a′ß)2.

18. If r, r1, 72, 73 denote the radii of the inscribed and the three escribed circles of a triangle, prove that

1. Find the condition that the four lines,

ax+by+c=0, a'x+b'y+c'=0, a"x+b"y+c"=0, a""x+l""y+c""= o, should touch the same circle.

2. Prove the following determinant equation:

3. A system of equilateral hyperbolas have contact of the second order with a given conic at a given point, prove that the locus of their centres is a circle.

4. Find the condition that two conics, given by their general equations, should be similar to each other. Determine the additional condition that the conics should be equal in every respect.

5. Reduce to its equivalent simple fractions the expression

6. If any equation be transformed so as to have its second term removed, prove that the coefficients of the transformed equation are functions of the differences of the roots of the original equation.

7. There are three parcels of books in another room, and a particular book is in one of them. The odds that it is in one particular parcel are three to two; but if not in that parcel, it is equally likely to be in either of the others. If I send for this parcel, giving a description of it, and the odds that I get the one I describe are two to one, show that the odds are eight to seven against my getting the book.

8. Prove from the general equations of two conics that, if they be similar, the angles between their asymptotes are equal.

9. Find the equation of a parabola, having contact of the third order with an ellipse at the point (x'y').

10. Find the locus of the intersection of lines drawn from the extremities of the axis major of an ellipse to the extremities of any pair of conjugate diameters.

MR. BURNSIDE.

11. Determine the equation of a conic making given intercepts on the axes, when one of its asymptotes passes through the origin.

12. If tangents drawn to a parabola at the points T and T' intersect at the point P, and if the focus be at F, prove that

13. If two chords of a conic be parallel to conjugate diameters, and touch a confocal conic, prove that their sum is constant.

14. Prove that the equations

cy2+2f. yz + bz2 = 0,

az2+2g.zx + cx2 = 0,

bx2+2h. xy + ay2 = 0,

are satisfied simultaneously if abc - 2fgh — af2 — bg2 — ch3 = 0.

15. Prove the formula

tan

= √✓tans. tan § (s − a) tan † (s − 6) tan † (s – c) for the spherical excess of a triangle whose sides are a, b, c.