MR. W. R. ROBERTS.

11. Prove that the area of the triangle formed by any pair of conjugate semi-diameters of an ellipse is constant.

12. If two ellipses having equal axes be placed vertex to vertex, and one of them roll upon the other, show that either of its foci will describe a circle about a focus of the latter.

13. Find (a-B)2282 for the biquadratic

αox + 4α1x3 + 6a2x2 + 4a3x + a4 = 0.

14. Find the equation of the circle cutting orthogonally the circles

2. Apply the differential calculus to find the co-ordinates of a point on an ellipse the normal at which is at the greatest possible distance from the centre, and express the maximum distance in terms of the axes of the ellipse.

3. Find the length of a chord PN of an ellipse which is normal to the curve at P; and show that it may be expressed in the form

where p is the central perpendicular on the tangent at P.

4. Prove that the locus of the centre of an equilateral hyperbola inscribed in a given triangle is the polar circle of the triangle.

(a) How is it shown, by the aid of this theorem, that the four polar circles of the four triangles obtained by omitting in turn each of four given right lines are coaxal?

in which 80, 81, 82, &c., are the sums of the powers of the roots, in terms of the functions of the coefficients H, I, J of a biquadratic equation.

MR. F. PURSER.

6. From a point P two tangents are drawn to an ellipse; find the locus of P when the rectangle under the perpendiculars on these from one of the foci is constant.

7. Two parabolæ have equal parameters, and a common axis and directrix, their vertices being symmetrically situated with respect to the directrix show that either is the locus of centres of rectangular hyperbola which osculate the other most closely.

8. Prove that the orthocentre of a triangle inscribed in a rectangular hyperbola lies on the curve.

(a) What form does this theorem assume when-(a) two, (b) three of the vertices of the triangle become coincident?

9. The rules of the parcel post prescribe that the length of the parcel shall not exceed 3 ft. 6 in., nor the sum of length and girth 6 ft.

Show that, assuming the parcel to have a uniform section perpendicular to its length, the maximum volume will be attained when the section—(a) has the form of a circle; (b) having a circumference of 4 ft.

11x2+2y2+4x2 + 12xz − 4xy = 0.

12. If a, B, y be the roots of the equation

15. Show that the circles described upon the six common chords of any two equilateral hyperbolas as diameters cut one another orthogonally in opposite pairs.

Classics.

MR. MAHAFFY.

I. Beginning, παύεσκε μὲν γὰρ ἐνθέους γυναῖκας εὔιόν τε πῦρ, κ. τ. λ. Ending, Μοῖραι μακραίωνες ἔσχον, ὦ παῖ.

SOPHOCLES, Antig., 962-987.

2. Beginning, ὁ μὲν ἦν ποταμοῦ σθένος, ὑψίκερω τετραόρου, κ. τ. λ. Ending, ὥστε πόρτις ἐρήμα.

ID., Trach., 507-530.

3. Beginning, ΧΟ. Ορεστέρα παμβῶτι Γα, μᾶτερ αὐτοῦ Διὸς, κ. τ. λ. Ending, Αἴας ὁ μείζων ταῦθ ̓ ὁρῶν ἠνείχετο.

ID., Philoc., 391-411.

4. Beginning, ὑπερτελής τε, πόντον ὥστε νωτίσαι, κ. τ.λ. Ending, ὤτρυνε θεσμὸν μὴ χατίζεσθαι πυρός.

ID., Agam., 286–304.

1. How did Sophocles contrast his own style with that of Eschylus ?

2. Write a note on his female characters.

3. Give the order (so far as it is known) of his extant plays.

4. Write a note on the vocative case.

5. What is the history of the word aryan?

6. Trace the root spac in aryan languages.

7. What is M. Müller's classification of roots?

8. Sketch the early literary contacts of Greece and Rome.

MR. GRAY.

Translate:

1. Beginning, Ge. O vir fortis atque amicus.
Ending, non tu hunc habeas plane praesentem deum?

TERENCE, Phormia, ii. 2. 10-31.

PLAUTUS, Captivi, iii. 5. 57-109.

2. Beginning, Ty. Quor ergo iratus mihi's?.... Ending, Redauspicandum esse in catenas deuuo.

3. Beginning, St. Stasime, fac te propere celerem, recipe te ad, Ending, Recipe te ad erum.

ID., Trinum., iv. 3. I. 1–20.

Translate :

1. Beginning, Extremum Tanain si biberes, Lyce, .. Ending, Coelestis patiens latus.

HORACE, lib. iii. Carm. x.

2. Beginning, Adduxere sitim tempora, Virgili : .... Ending, Dulce est desipere in loco.

Ibid., lib. iv. xii. 13-28.

3. Beginning, Roges, tuum labore quid iuvem meo, Ending, Circaea tangat moenia.

....

Ibid., i. 15-30.

4. Beginning, At graviter cecidi. Quid enim mirabile, si quis, .... Ending, Si non ferre doles, at meruisse dole.

1. Explain the following:

OVID, Epist. ex Ponto., i. vii. 49-70.

Regnata Laconi rura Phalantho.

Laestrygonia Bacchus in Amphora
Languscit.

Telegoni iuga parricidae.

Lycambae spretus infido gener

Aut acer hostis Bupalo.

Achaemenium costum.

2. Mark the quantities of the following words, and quote lines in support:-Proserpina, fortuitum, fidicen, Porsena, caprificos.

3. Write explanatory notes on the following:-Taurica terra, Cynicus Sinopeus, Neoclides, Taprobane, Oricum.

4. Give a summary of the historical events referred to in the fourth book of the Odes.

5. To whom are we indebted for any knowledge we have of the 'Ludi Seculares'? On what other occasions were they celebrated? By what names did they go under the Republic ?

6. What is the proper meaning of the word Epode? What is Horace's own name for these poems? Quote all the passages in which he refers to them.

7. State accurately the powers conferred on Augustus by the proconsular imperium and the Potestas Tribunicia.

8. Write a note on the authenticity of the imperial history.

9. Describe the organization of Gaul by Augustus.

10. Who won Syria for the Roman people? Give its boundaries, and name its principal cities?

MR. L. C. PURSER.

Translate into Greek Prose :

I am far, very far, from wishing to proceed hastily in this most delicate matter. I feel that, for the good of India itself, the admission of natives to high office must be effected by slow degrees. But that, when the fulness of time is come, when the interest of India requires the change, we ought to refuse to make that change lest we should endanger our own power, this is a doctrine of which I cannot think without indignation. Governments, like men, may buy existence too dear. "Propter vitam vivendi perdere causas "is a despicable policy both in individuals and in states. In the present case, such a policy would be not only despicable, but absurd. The mere extent of empire is not necessarily an advantage. To many governments it has been cumbersome; to some it has been fatal. It will be allowed by every statesman of our time that the prosperity of a community is made up of the prosperity of those who compose the community, and that it is the most childish ambition to covet dominion which adds to no man's comfort or security. It is scarcely possible to calculate the benefits which we might derive from the diffusion of European civilization among the vast population of the East.

Translate into Latin Prose :

The city was filled with reports of the fearful prodigies which were now remembered to have occurred before the outbreak of the present troubles; of comets and meteors, supposed to have announced the approaching downfall of the nation; men and chariots had battled in the air; the gates of the Temple had burst open of their own accord; and on the solemn day of Pentecost, a voice "more than human" had been heard exclaiming, "Let Us depart hence !"

While, however, these portents struck terror into the hearts of the multitude, bolder spirits were not wanting among them, who consulted no omen but the voice of patriotism, and maintained that the nearer ruin impended, the nearer was the hour of deliverance. The day was at hand,