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5. Write notes on the metre of the following lines :

" That croaks the fatal entrance of Duncan.” b. “ Tears in his eyes, distraction in his aspect.”

Bounty, perseverance, mercy, lowliness.” d.

“ That of an hour's age doth hiss the speaker.”

My letters conjuring to that effect.”

Classics.

SOPHOCLES.

MR. GRAY.

Translate the following passages into English :1. Beginning, ΧΟ. είην όθι δαίων, κ. τ.λ. Ending, μολεϊν γά τάδε και πολίταις.

Edip. Col., 1044-1095. 1. Beginning, TΕ. γνώσει, τέχνης σημεία της έμής κλύων, κ. τ.λ. Ending, εμοί γάρ ούτος ηγεμών, άλλοις δ' εγώ.

Antigone, 998-1014. 3. Beginning, ο μέν χρόνος δή διά χρόνου προϋβαινέ μοι, κ. τ.λ. Ending, ουκ ενθάδ' οι πλοί τοϊσι σώφροσιν βροτών.

Philoctetes, 285-304. 4. Beginning, ΔΗ. τοιούτον εκβέβηκεν, οίον, ήν φράσω, κ. τ.λ. Ending, κάδρων τοιαύτα.

Trachinie, 672-688. 5. Beginning, ΗΔ. ώ φάος άγνόν, κ. τ.λ. Ending, αικώς οικτρώς τε θανόντος.

Electra, 86-102.

1. Sophocles effected a thorough change of the whole essence and organization of tragedy? These changes are prominently shown in his Electra, compared with the Orestea of Æschylus ?

2. Point out the particular situations which form the turning points of the different plays, and the ethical ideas which are asserted in them.

3. What is meant by the “irony' of Sophocles ?

4. Sophocles has been obliged for once to avail himself of the “Deus ex machina”?

5. Give an account of the revolt of Samos from the Athenians in B. C. 6. Grote points out some circumstances respecting this revolt, as illustrating the existing condition of the Athenian empire ?

440.

7. Mention the principal operations in which the Athenians were engaged from B. C. 477–463.

LATIN SATIRISTS,

MR. FERRAR.

Translate the following Passages into English Prose :1. Beginning, Hospite venturo, cessabit nemo tuorum. Ending, Quam primum prædam rupto gustaverat ovo.

JUVENAL, Sat. xiv. 59-85. 2. Beginning, Sæpe oculos, memini, tangebam parvus olivo,. Ending, Mænaque quod prima nondum defecerit orca.

PERSIUS, Sat. iii. 44–76. 3. Beginning, Stemmata quid faciunt? quid prodest, Pontice, longo.... Ending, Atria, nobilitas sola est atque unica virtus.

JUVENAL, Sat. viii. 1-20. 4. Beginning, Vix tamen eripiam, posito pavone, velis quin..... Ending, Jejunus raro stomachus vulgaria temnit.

KORACE, Sat. lib. II. sat. ü. 23-38.

1. What is Merivale's account of Caius' journey to the Rhine ? 2. What were the chief measures of Claudius ?

3. Trace the descent of Messalina from Marcus Antonius, the Triumyir.

4. Write a note on the influence of the Jews in the early times of the Empire.

5. What is the order of the words in a Latin Proposition ?

6. What is the construction of the words, fido, invideo, occumbo, opus, liber, and alienus ?

7. Who were the Quæstores Classici, and when were they first appointed ?

8. Two different alphabets reached Italy.

9. What are the roots of the words, socius, sacer, lucus, nidus, cor, prex, censeo, Castor, cæcus, and Cocles ?

MR. ABBOTT.

Translate the following passage into Greek Prose :-
Beginning, I never met with a consideration that is more finely spun,.
Ending, but thou art no longer the person whom he reproaches.

SPECTATOR, No. 355.

Translate the following passage into Greek Verse :Beginning, Vol. Should we be silent, and not speak, our raiment,... Ending, Our comfort in the country.

SHAKSPEARE, Coriolanus, act v. sc. iii.

Translate the following passage into Latin Prose :Beginning, It had been hard for him that spake it Ending, without which the world is but a wilderness.

Bacon, EssaysOf Friendship.

Translate the following passage into Latin Lyric Verse :-
Beginning, Where awful summits rise around, ......
Ending, In the soft dreams of poesy.

HEMANs, The Minstrel Bard.

SENIOR FRESHMEN.

Mathematics.

DR. SALMON.

n

=0; v

1. Find what relation must be satisfied by the coefficients of the general equation of the second degree, if one of the asymptotes passes through the origin.

2. Prove that the condition that the right line 1a + + vy should touch ła + v mß + V ny is

2 λ

He and reciprocally the condition that it should touch

1

B Y is vī+mu + v nv = 0.

3. If tangents to two circles make with each other a constant angle, find the locus of their intersection. 4. In a spherical triangle, prove that

tan ka- tan fb cos C– tan {c cos B cos (B C)
tan fb – tan ja cos C – tan fc cos A cos (A -C)

+

n +

5. Prove that

sin b sin c + cos b cos c cos A = sin B sin C - cos B cos C cos a. 6. It is required to find the locus of the intersection of two variable tangents to a conic, which intercept on a fixed tangent a portion which subtends a constant angle at one of the foci. Solve this problem by reciprocation.

DR. SHAW.

7. Given one focus of an ellipse, a tangent, and its point of contact, and the radius of curvature at the point; construct the axis major.

8. Two constant angles turn round two fixed points ; a side of one constantly intersects a side of the other on a fixed right line. Show that the remaining two sides intersect on a conic passing through the two fixed points. 9. Show that the solution of

204 + px3 + 92% + rx +8=0 can be reduced to that of quadratics

(i.) if p3 – 4P9 + 8r = 0,

or (ii.) if pes 498 + y2 = 0. 10. Prove geometrically that

cot @ + cosec 0 = cot 10; and hence sum the series

cosec 0 + cosec 20+ cosec 40+ &c. to n terms. 11. Show that of all the triangles which stand on 20 as base, and have their vertices on a given right line, that which has the least perimeter has for its area

c cos 0

(P2 - c sin20);

P where P is the perpendicular let fall from the middle point of 2c on the given right line, and 0 is the angle between this line and the base.

12. A draws a ball four times from a bag containing two white and eight black balls, replacing each time the ball he has drawn ; find the chance that he will have drawn (i.) two white and two black; (ü.) not less than two white.

MR. WILLIAMSON.

13. The locus of the centres of equilateral hyperbolæ, circumscribing a given triangle, is the circle which passes through the middle points of its sides?

14. Given three points and a focus of a conic; determine its centre by a geometrical construction.

15. Without assuming the expression for the radius of curvature of an ellipse, prove that the length of the chord of the osculating circle which

202 passes through the centre is

16. Given two sides of a spherical triangle, find when its area is a maximum; and show how to construct the triangle in that case.

17. Given one base angle of a right-angled spherical triangle, prove that the difference of the sides which contain it is a maximum, when their sum is equal to a quadrant. 18. Solve the equations

* + y + z = b,
ax+ By + y2 = ha,
a x + B2y + y2z = hs.

DR. SALMON.

1. Find the radius of curvature at any point of a parabola.

2. Find the equation of the pair of lines joining to the origin the intersection of the line 1x + my + n, with the conic given by the general equation.

3. Given two tangents and two points on a conic, what is the envelope of the chord of contact of the conic with the two tangents ? 4. Eliminate 0 from the equations

a cos 0 + b sin 0 =c, a'cos 0 + b'sin 0 = c. 5. One of the roots of the cubic

28 – px2 + q3 —q=0 is double another; reduce the finding it to a quadratic equation.

6. In a spherical triangle, if three lines through the vertices meet in a point, three lines equally inclined to the sides will also meet in a point ?

DR. SHAW.

7. From any point P let fall a perpendicular PN on its polar with respect to an ellipse, and produce PÑ to meet the axis major in N'. Prove

62
PN'. NN' (a2-x2);

a2

and hence deduce an expression for the normal in terms of the diameter parallel to the tangent.

8. Find the locus of intersections of tangents which cut at right angles, the curve being a parabola. 9. In a plane triangle, if the angles and sides receive small variations,

c&B +b cos A8C=0, a, 6 being constant.
cos C8b + cos Bòcro, a, A being constant.

80 tan A = b8C, A, B being constant. 10. On the sides of a triangle a, b, c as diameters, three circles are described, intersecting in P, Q, R. Show that the perimeter of the triangle PQR = that of abc x 4 sin Asin B sin C.

prove that

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