1. Discuss the following reading :—

a. Dicit tanquam in Platonis Toλereia non tanquam in Romuli faece

sententiam.

b. Sed, si ita placuit, laudemus.

c. Clodius ergo, ut ais, ad Tigranem? Velim Syrpiae condicione. d. Quarum alteram non libebat mihi scribere, quia abscideram.

e. Habet enim Campana lex exsecrationem in coitione candidatorum. f. Bibliothecam mihi tui pinxerunt constructione et sillybis.

g. Pascor bibliotheca Fausti; fortasse tu putabas his rebus Puteolanis et Lucrinensibus.

h. Tuae tantum habent mysteriorum ut eas ne librariis quidem fere committamus Lepidum quo exedar.

2. Translate and explain the following:

a. Quin etiam quod est subinane in nobis afficitur quadum delectatione. Hac quidem cura certe iam vacuum est. Iacet enim ille sic ut πTσs Curiana stare videatur.

b. De republica nihil habeo ad te scribere.

c. Eo biduo quum esset summa annonae caritas. d. Postridie S. C. factum est id quod ad te misi.

e. Velim mihi mittas de tuis librariis duos aliquos. f. Baburns. Alabarches.

g. Quod me mones ut et πολιτικῶς me geram et τὴν ἔσω γραμμήν teneam, ita faciam.

h. De Entychide gratum; qui vetere praenomine, novo nomine T. erit Caecilius, ut est ex me et ex te junctus Dionysius, M. Pomponius.

i. Sed nihil tam pusillum, nihil tam sine voce, nihil tam verum. Haec tu tecum habeto. In Andromacha tamen major fuit, quam Astyanax. In ceteris parem habuit neminem.

3. What was the nature of the monarchy which Julius Cæsar aimed at founding?

4. Discuss the question whether Julius Cæsar or Augustus should properly be regarded as the first of the Roman emperors.

5. What was the relation of the Roman senate to Julius Cæsar? Give an account of his financial reforms.

6. Write a short essay on the respective place in Roman literature of Hortensius, Lucretius, Varro, Catullus, showing how far these may be regarded as types of general epochs in Roman development.

MR. MAHAFFY.

Translate the following passage into Latin Prose:

I hasten to respond to your questions about Quintus. He is a lad of good talents, but somewhat lazy; I cannot make him rise before day as

I do, to read my Aristotle. He does not seem extravagant, though I know he has some debts. As for that silly affair with the lady, he barely got off without having his fingers burnt. By the bye, if I may be allowed a digression about my own affairs, what about the money I lent Dolabella? Is he in earnest in saying he will pay it, or not? If not, I should really like to prosecute him; yet I fear public opinion. Pray write to me, as you promised, about all your affairs, and about all the state secrets; you can trust my messengers with any letter. If you want money from me, let us borrow it from Coelius, for until Dolabella pays up, I have no cash in hand at all. I was obliged to delay this letter a day, because I was suffering from a slight attack in my eyes. hear you have had an increase to your family since, upon which I congratulate you, but I hear the child is delicate. When I return to Rome, I intend bringing you some valuable copies of philosophical books, which I am getting transcribed over here. I am longing for letters from you. Farewell.

I

Translate the following passage into Greek Prose :

When music imitates the modulations of grief or joy, it either actually inspires us with those passions, or at least puts us in the mood which disposes us to conceive them. But when it imitates the notes of anger, it inspires us with fear. Joy, grief, love, admiration, devotion, are all of them passions which are naturally musical. Their natural tones are all soft, clear, and melodious; and they naturally express themselves in periods which are distinguished by regular pauses, and which upon that account are easily adapted to the regular returns of the correspondent airs of a tune. The voice of anger, on the contrary, and of all the passions which are akin to it, is harsh and discordant. Its periods too are all irregular, sometimes very long, and sometimes very short, and distinguished by no regular pauses. It is with difficulty, therefore, that music can imitate any of those passions; and the music which does imitate them is not the most agreeable. A whole entertainment may consist, without any impropriety, of the imitation of the social and agreeable passions. It would be a strange entertainment which consisted altogether of the imitations of hatred and resentment.

Translate the following passage into Greek Verse :—

A. The joy-importing morn springs, as they say,
From night, her mother. Thou shalt hear a joy
Beyond thy hopes to hear: The town of Priam
Is fall'n beneath the conquering arms of Greece.
B. What said'st thou? Passing credence fled thy word.
A. In Troy Greece triumphs. Speak I clearly now?
B. Joy steals upon me, and calls forth the tear.
A. Thy glist'ning eye bespeaks an honest heart.
B. Does aught of certain proof confirm these tidings?
A. It does: Why not? unless the Gods deceive us.
B. Perchance the visions of persuasive dreams.

A. Sport of the slumb'ring soul; they move not me.
B. Hath then some winged rumour spread these transports?
A. As a raw girl's, thou hold'st my judgment cheap.
B. How long hath ruin crush'd this haughty city?
A. This night, that gave this infant morning birth.

Translate the following passage into Latin Verse :

Nor earth, nor air, nor seas, nor fire,
Nor aught that fate can interpose
Nor open scorn nor secret foes
Shall tear me from my heart's desire.
Like those antique imperial dyes

Which age nor use can e'er efface,
But win from Time a nobler grace,
Stamped on my soul thy image lies.

While Faith still vivifies this frame,

Or Memory prompts one soul-felt sigh
And Hope looks upward to the sky,
This heart shall beat, for thee the same.

No mortal strength nor skill can sever
The link which kindred atoms binds,
Nor less, congenial kindred minds,
United once, are one for ever.

JUNIOR FRESHMEN.

Mathematics.

Α.

SYLVESTER.

MR. WILLIAMSON.

1. Given the sum of two lines, and the difference of their squares; determine the lines by a geometrical construction.

2. Construct a rectangle equal to a given rectilinear figure, proving

the previous proposition on which the construction depends.

3. Given the base and the vertical angle of a triangle; find the locus of its vertex, and give the geometrical construction.

4. Find the value of the expression

7. In a right-angled triangle, let squares be constructed on the sides, and from the extremities of the base erect perpendiculars to the base, to meet the sides of the squares which are parallel to the sides of the triangle; prove that these perpendiculars form the sides of a square standing on the base, which will be equal to the sum of the squares on the sides.

8. Cut a line so that the rectangle under the whole line and one part shall be equal to the square of the other part; and show that the greater segment will be cut in the same manner by taking on it a part equal to the less.

9. Given the base and vertical angle of a triangle, construct the locus of the vertex.

10. A horse being bought for a certain sum, and being sold for £119, there was as much gain per cent. on the transaction as the horse cost; what was the cost of the horse?

11. Solve the equations,

√ x + m2 + √ x − n2 = (n − m),

à ax2 - 1 + à a (ic2 + 4x) + ( 1 + a)2 = (x + 1) Ë.
a.

12. Resolve the following quantities each into the sum of two squares:
(25x2 + 20x + 13),
(16x2 - 24x+58).

MR. BURNSIDE.

13. The difference between the squares of the sides of a triangle is equal to twice the rectangle under the base, and the distance of the foot of the perpendicular on the base from its middle point.

14. If the sum of the squares of the sides of a quadrilateral be equal to the sum of the squares of the diagonals, the quadrilateral will be a parallelogram.

15. Given base, vertical angle, and the length of a perpendicular from the extremity of the base on the opposite side; construct the triangle. 16. Solve the equation

(a + x)3 + (a − x)3 = b.

1. Given the four sides of a quadrilateral, prove that the rectangle under its diagonals is a maximum when it is inscribable in a circle.

2. Prove that the line joining the vertex of a triangle to the highest point in its inscribed circle divides the base into segments whose difference is equal to the difference of the sides.

3. If a system of circles cut two given circles orthogonally, prove that they are coaxal.

4. If a circle touches two fixed circles, prove that the line joining the points of contact passes through a fixed point.

5. On a given line construct a regular pentagon, and show how to describe a regular pentagon of given area.

6. Describe a circle touching two given circles, and having its centre on a given right line.

DR. TRAILL.

7. If a quadrilateral be circumscribed to a circle, prove that the line joining the middle points of its diagonals passes through the centre of

the circle.

8. Describe a circle touching a given straight line and two given circles.

9. Given base, difference of base angles, and locus of vertex a right line intersecting the base; construct the triangle.

10. If squares be constructed on the sides of any triangle, and if the extremities of the base be joined to the remote corners of the squares on the opposite sides, prove that these connecting lines intersect on the perpendicular from the vertex on the base of the triangle.

II. Given base and ratio of sides, prove that the locus of the vertex is a coaxal circle of the system which has the extremities of the base for limiting points.

12. Inscribe the rectangle of maximum area in a given segment of a circle.

MR. BURNSIDE.

13. If perpendiculars be let fall from any point of the circumference of a circle on the sides of an inscribed quadrilateral, the rectangle under