14. A vertical cylinder contains water which is made to rotate uni

I

formly about the axis; if th of the axis be above the surface when there

n

is no rotation, find the greatest angular velocity which can be communicated to the liquid without causing any of it to leave the cylinder.

15. Give Newton's proof of the law of force, for a body moving in an ellipse under the action of a force to the focus.

16. Find when Venus appears brightest, assuming that the Earth and Venus describe circular orbits round the Sun.

17. Two uniform beams, connected at a common extremity by a smooth joint, are placed in a vertical plane, their other extremities, which rest on a smooth horizontal plane, being connected by a string; find the tension of the string and the reaction at the joint.

18. A ray of light passes through a medium, the value of u at any point of which varies inversely as the distance from a fixed point of the medium; find the path of the ray.

Classics.

MR. GRAY.

1.

Translate:

Beginning, ΠΡΟΜ. ὀχλεῖς μάτην με κῦμ ̓ ὅπως παρηγορῶν. κ. τ. λ. Ending, τὸ σόν, πετραία δ ̓ ἀγκάλη σε βαστάσει.

AESCHYLUS, Prom. Vinct., 1000-1018.

2. Beginning, ΕΤΕ. ἀνὴρ δ ̓ ἐπ ̓ αὐτῷ, κεἰ στόμαργός ἐστ ̓ ἄγαν, κ. τ. λ. Ending, ὡς οὐδ ̓ ἂν ̓́Αρης σφ ̓ ἐκβάλοι πυργωμάτων.

ID., Sept. c. Theb., 447-469.

3. Beginning, κύριός εἰμι θροεῖν ὅδιον κράτος αἴσιον ἀνδρῶν, κ. τ. λ. Ending, αἰλινον εἰπέ, τὸ δ' εὖ νικάτω.

ID., Agam., 104-139.

4. Beginning, ΟΡΕΣΤ. ἁπλοῦς ὁ μῦθος· τήνδε μὲν στείχειν ἔσω, κ. τ. λ. Ending, θήσω, ποδώκει περιβαλὼν χαλκεύματι.

ID., Choeph., 554-576.

1. State what you know about the Satyric Drama.

2. Give some account of what is known about Phrynichus and his plays.

3. Explain the terms τὸ κοῖλον, διαζώματα, κατατομαί, κερκίδες, the didascaliæ.

4. What is known about the life of Æschylus? Two personal recollections of him survive?

5. What is peculiar in the action of the Chorus at the end of the Seven against Thebes? A passage in the Agamemnon, too, has excited much criticism concerning the Chorus ? Mr. Mahaffy has suggested a

natural explanation?

6. What modern parallel have we to the Choephori? Give particulars.

7. What authorities have we for the text of Eschylus?

8. What historical information do we get in the Persæ?

9. What interpretations have been put upon the Myth of Prometheus? 10. The Eumenides is a play remarkable for many curious features?

....

1. Beginning, Postremo duo de concursu corpora lata, Ending, Ipse in se trahere et partis conducere in unum.

LUCRETIUS, i. 384-397.

2. Beginning, Denique uti possint sentire animalia quaeque, Ending, Seminibus permixta carentibus undique sensu ?

....

Ibid., ii. 973-990.

3. Beginning, Fit quoque de speculo in speculum ut tradatur imago, Ending, Ac resilire ab rebus ad aequos reddita flexus.

...

Ibid., iv. 302-323.

4. Beginning, Tum ioca, tum sermo, tum dulces esse cachinni, Ending, Disperiisse neque in fructum convertere quisse.

Ibid., v. 1397-1442.

1. Write critical notes on

(a) Namque aliut terris aliut regionibus ipsis
Eventum dici poterit.

(b) At non esse tamen perplexis indupedita

Pungere uti possint corpus penetrareque saxa.
(c) Dum facile in venas cibus omnis inditur et dum
Non ita sunt late dispersa ut multa remittant.
Sunt quaedam corpora quorum
Concursus motus ordo positura figurae
Efficiunt ignis.

2. (a)

(6) Linquitur hic quaedam latitandi copia tenvis
Id quod Anaxagoras sibi sumit.

(c) Unde est haec, inquam, fatis avolsa voluntas.
(d) Haud ut opinor enim mortalia saecla superne
Aurea de caelo demisit funis in arva.

(a) What are the Greek words translated by ordo positura figurae? What is the evasion alluded to in (b)? How does Lucretius answer (c)? Explain (d).

3. Mention any unusual metrical quantities you have observed in Lucretius.

4. How does Lucretius refer to Heraclitus and Empedocles?

5. In what respects does Lucretius differ from Democritus ?

6. What is the Augustan History?

7. Write a note on the nature of historical writing under Trajan, and of philosophical thought.

8. Give the substance of Merivale's remarks on the frequent practice of suicide under the Empire.

9. Give an account of the state of Britain in the time of Hadrian.

10. What is Merivale's estimate of the character of Hadrian?

11. State some particulars showing the progress of the Empire towards uniformity in the age of the Antonines.

12. Write a short criticism on the Meditations of Marcus Aurelius.

13. Who were Rabbi Akiba, Herodes Atticus, Dion Chrysostom, Fronto, Avidius Cassius ?

Let others creep by timid steps, and slow,
On plain experience lay foundations low,
By common sense to common knowledge bred,
And last, to Nature's cause through Nature led:
All-seeing in thy mists, we want no guide,
Mother of arrogance, and source of pride!
We nobly take the high priori road,

And reason downward, till we doubt of God:
Make Nature still encroach upon His plan;
And shove Him off as far as e'er we can:
Thrust some mechanic cause into His place;
Or bind in matter, or diffuse in space.
Or, at one bound, o'erleaping all His laws,
Make God man's image, man the Final Cause,
Find virtue local, all relat on scorn,
See all in self, and but for self be born:
Of nought so certain as our reason still,
Of nought so doubtful as of soul and will.

Translate into Greek Verse:

Here lodged Rob Roy; proud kings have palaces,
And foxes holes, and sheep the sheltering fold;
Fish own the pools, and birds the plumy trees;
And stout Rob Roy possessed this granite hold.
Call him not thief and robber: he was born

A hero more than most that war a star,
And brooked his brawny str n.th with manly scorn
On fraud and force and falsehood to make war.
In these well-trimmed and well-oiled times a man
Moves part of a machine: but then strong will
Shaped each hard-sinewed life to kingly plan,

And ruled by right of might and law of skill.
When kings were weak, lords false, and lawyers knaves,
Rob Roy saved honest men from being slaves.

Translate into Latin Prose :

Orestês, grown to manhood, returned and avenged his father, by killing Ægisthus, according to Homer; subsequent poets add, his mother also. He recovered the kingdom of Mykênæ, and succeeded Menelaus in that of Sparta. Hermione, the only daughter of Menelaus and Helen, was sent into the realm of the Myrmidons in Thessaly, as the bride of Neoptolemus, son of Achilles, according to the promise made hy her father during the siege of Troy.

Here ends the Homeric legend of the Pelopids, the final act of Orestês being cited as one of unexampled glory. Later poets made many additions: they dwelt upon his remorse and hardly-earned pardon for the murder of his mother, and upon his devoted friendship for Pylades; they wove many interesting tales, too, respecting his sisters Iphigeneia and Elektra and his cousin Hermionê,-names which have become naturalized in every climate and incorporated with every form of poetry.

Translate into Greek Prose:

Neither Aristobulus nor Ptolemy (he observes), nor any other competent witness, has recounted this (visit of the Amazons and their queen to Alexander) nor does it seem to me that the race of the Amazons was preserved down to that time, nor have they been noticed either by anyone before Alexander, or by Xenophon, though he mentions both the Phasians and the Kolchians, and the other barbarous nations which the Greeks saw both before and after their arrival at Trapezus, in which marches they must have met with the Amazons, if the latter had been still in existence. Yet "it is incredible to me" that this race of women, celebrated as they have been by authors so many and so commanding, "should never have existed at all." The story tells of Hêraklês, that he set out from Greece, and brought back with him the girdle of

their queen Hippolytê: also of Thêseus and the Athenians, that they were the first who defeated in battle and repelled these women in their invasion of Europe; and the combat of the Athenians with the Amazons has been painted by Mikôn, not less than that between the Athenians and the Persians.

Logics.

MR. ABBOTT.

I. What is the only "externality" that Mill acknowledges as real? Compare his notion of externality with that of Kant and that of the unlearned.

2. Taking this conception of externality, interpret these statements: "I do not believe that the real externality to us of anything except other minds is capable of proof." By what evidence do I know. that the walking and speaking figures which I see and hear possess Minds? I conclude that other human beings have feelings like me, because, first, they have bodies like me

3. Mill holds that as to particular facts of which our assurance is all but perfect it is possible to be not quite certain that we are uncertain. Show that it follows by direct logical inference that we may be certain without knowing that we are certain. Can you give a better analysis of the state of mind referred to by Mill, or a better account of the nature of "doubt" than his ?

4. "To determine what can be cognized by sight alone, we must suppose an eye incapable of these changes which cannot therefore travel along the boundary line that separates two colours, but must remain fixed with a steady gaze on a definite spot." Mention some familiar experiments which prove that the eye at rest can have distinct vision of even a complex figure of several degrees in angular breadth. (One such experiment is founded on the phenomenon of persistent images.)

5. Amongst the grounds on which it has been held that the object immediately known in perception is a modification of mind, Hamilton mentions these two:-(a) that the mind cannot act out of itself; (b) that what knows must be of like nature to what is known. Examine these.

6. What inaccuracy is there in the statement, that in perception an organic action must precede and determine the intellectual action?

7. What is Brown's error as to the notion of Resemblance, and what are Hamilton's arguments against it?

8. State briefly Hamilton's Law of the Conditioned, and give his application of it to the principle of Causality.