8. A force F, acting at a point 0, is equibrated by three parallel forces P, Q, R acting at three points A, B, C in the same plane with 0; required the values of P, Q, R.

9. Determine, by any method, the position of the centre of gravity of a hemispherical bowl of uniform thickness and density.

10. The two equal weights in an Atwood's Machine are each 1 lb.; required the additional weight which should be appended to one of them so as to bring it down from rest through 1 foot in 1 second.

II. Investigate the differential equation of the motion of a body falling under the action of gravity down an arc of a cycloid; and find by integration the entire time of descent from the initial to the lowest point. 12. Integrate, by reduction to elementary differentials, the expressions

13. Forces act at the centres of gravity of the faces of a triangular py- | ramid, at right angles to these faces, and proportional to their areas; prove that they are in equilibrium.

14. Three rods are connected by free joints or hinges at their extremities, and the system is in equilibrium when acted upon by forces applied perpendicularly at the middle points of the rods; prove that the strain at each angular point is the same, and acts in the direction of the tangent to the circumscribing circle.

15. A two-wheeled carriage, whose weight is W, is just capable of being set in motion on a horizontal plane by a force F; the radii of the wheel and axle being R and r, determine the coefficient of friction between them.

16. What relations connect the different units in the equation F=mf? Find the unit of time when the unit of space is a yard, and the unit of weight is the weight of the unit of mass.

17. A weight P, after falling freely through h feet, begins to pull up a heavier body Q by means of a cord passing over a pulley, as in Atwood's Machine; find the height through which it will lift it.

1. A string is fastened to a fixed point A, and passes over a fixed pulley B in the same horizontal line with A; between A and B a ring 0 runs on the string with a weight M attached to it; this is balanced by a weight M'hanging vertically from Bat the other end of the string; if M'

is increased or diminished, find when the velocity of M is a maximum, and when it vanishes.

2. A smooth circular tube revolves round a vertical diameter; calculate the velocity of a heavy body which rolls within it without friction, setting out from a given point without initial velocity.

3. The ordinate y to the diameter of a circle (the origin at the centre) produced so that y': y :: 2r : r + x; find the area of the curve generated; and find the points of inflexion.

5. Three forces P1, P2, P3 act at the three points 19121, 222, 43 1/353, in the three directions a1 B171, a2 ß2 y2, aзßзyз; required the conditions (a) that they should have a unique resultant, (b) that it should pass through the origin.

6. A triangular lamina, of uniform thickness and density, is suspended from a fixed point by three cords attached to its three vertices; prove geometrically, or otherwise, that the tension on each cord is proportional to its length.

7. Determine, in finite terms, the entire time of two bodies, of given masses, falling into each other from rest, through a given distance; their force of mutual attraction varying inversely as the square of the distance.

8. Investigate the series for the entire time of descent from a given to the lowest point of a given circular arc; proving at the same time the general formula of reduction for the several integrals involved.

MR. LESLIE.

9. A uniform isosceles triangle is placed within a smooth hemispherical bowl; find the position in which it will rest.

10. A body describes an ellipse under the action of a force in a focus; prove that its velocity at any point may be resolved into two constant velocities whose directions are perpendicular to the radius vector and the axis major; and hence find the law of force.

Deduce the same result from the equations of motion.

11. A particle is moving in a parabola about a centre of force in the focus, and, when it arrives at a given point, the absolute force is suddenly doubled; determine the subsequent path of the particle.

12. Determine the formulæ of reduction for the integrals

and find the values of these integrals when n = 2.

Classics.

SOPHOCLES.

MR. MAHAFFY.

Translate the following passages into English:

1. Beginning, πάτερ, θεοὶ φύουσιν ἀνθρώποις φρένας, κ. τ. λ. Ending, λόγοις τοιούτοις, οἷς σὺ μὴ τέρψει κλύων

2. Beginning, ὅστις γὰρ αὐτὸς ἢ φρονεῖν δοκεῖ, κ. τ. λ. Ending, καὶ τῶν λεγόντων εὖ καλὸν τὸ μανθάνειν.

Antigone.

Ibid.

3. Beginning, ΚΡ. ὅδ', ὡς ἔοικε, τῇ γυναικὶ συμμαχεῖ. κ.τ.λ. Ending, ΚΡ. κλαίων φρενώσεις, ὤν φρενῶν αὐτὸς κενός.

Ibid.

4. Beginning, Λογος μέν ἐστ' ἀρχαῖος ἀνθρώπων φανεὶς, κ. τ. λ. Ending, κρουνοὶ διερραίνοντο κρηναίου ποτοῦ.

Trachinia.

5. Beginning, καί μοι δυσθεράπευτος Αἴας, κ. τ. λ. Ending, ὀργαῖς ἔμπεδος, ἀλλ ̓ ἐκτὸς ὁμιλεῖ.

6. Beginning, οὗτοι σοὶ μούνᾳ, τέκνον, κ. τ. λ. Ending, βήματι μολόντα τάνδε γᾶν Ορέσταν.

1. Translate :

Ajax.

Eleetra.

οὔτε γὰρ ὁ τὰν Κρίσα

βουνόμον ἔχων ἀκτὰν

παῖς Αγαμεμνονίδας ἀπερίτροπος

οὔθ ̓ ὁ παρὰ τὸν ̓Αχέροντα θεὸς ἀνάσσων.

Translate and explain the following scholium on this passage :-ἀπο κοινοῦ δὲ ληπτέον τὸ ἀπερίτροπος, πολλάκις γὰρ τὸ κατὰ κοινοῦ λαβόμενον διαφορῶς νοεῖται.

2. Translate :

τοῦ χάριν τίνων

ἔθυσεν αὐτὴν;

Schol.—ἤγουν τίνος χάριν ἀποδιδοὺς ἐθυσίασεν; τοῦτο δηλοῖ τὸ τίνων, ἤγουν ἀποδιδούς. ἔστι δὲ μετοχὴ καὶ οὐ γενικὴ πληθυντική. 3. Explain accurately (quoting authorities), the connexion of the drama with the worship of Dionysus.

4. Give some account of the tragic writers who preceded Eschylus. 5. Explain the following terms :—ὑποκριτὴς, βομβεῖν, πάροδος, ἔξωστρα, ὑπόρχημα, κόμμος.

6. Discuss the defects of Greek tragedy, and illustrate them from the plays of Sophocles.

7. By what peculiarities of style are Sophocles' later tragedies distinguished from his earlier? What were the causes of this change of style?

MR. PALMER.

Translate the following passages :—

1. Beginning, Ge. O vir fortis, atque amicus. Verum hoc sæpe, Phormio,... Ending, Prior bibas, prior decumbas; cœna dubia apponitur.

TERENCE, Phormio, act II. sc. ii. 10-28.

2. Beginning, C. Censen' talentum magnum exorari potesse... Ending, Me vituperas? fur! etiam fur! trifurcifer!

...

PLAUTUS, Aulalaria, act II. sc. iv. 30-47.

3. Beginning, Mes. In scirpo nodum quæris. Quin nos hinc domum.... Ending, Quia nemo ferme huc sine damno devortitur.

Ibid., Menachmei, act II. sc. i. 21-39.

4. Beginning, Pe. Servientis servitutem ego servos introduxi mihi, Ending, Aufer illam offam penitam! probus hic conger frigidus:"

Ibid., Miles Gloriosus, act III. sc. i. 148-145.

5. Beginning, Ag. Ita me di ament, tardo amico nihil est quidquam iniquius,.

Ending, Nec tibi obnoxii sumus istuc, quid tu ames aut oderis.
Ibid., Pomulus, act III. sc. i. 1-15.

1. What is known of the life of Terence? what was his literary position, and in what did its difficulty consist?

2. Contrast the æsthetic culture of the age of Plautus with that of the age of Terence.

3. What depressing influences tended to check the development of comedy at Rome?

4. Write out the epigram ascribed to Caesar, which accurately sums up the judgment of antiquity on Terence.

5. Explain the following: comœdia togata: eomœdia palliata : fabula prætextata: contaminatio.

6. State some of the more common instances of synizesis in ordinary pronunciation, as exhibited in the language of Terence, and scan the following lines:

Habent despicatam, et quæ nos semper omnibus cruciant modis.
Non me fecisse causa sed amoris. Scio.

Dolet dictum imprudenti adolescenti et libero.

7. What practice does Plautus employ in his prologues? best parallel to the prologues of Terence?

с

What is the

8. Plautus, in a well-known passage, alludes to the imprisonment of Nævius?

9. Mention any peculiarities in syntactical construction you have noticed in Plautus.

10. Explain the following words and phrases used by Plautus in an unusual sense: scurra, arbitror, superstitiosus, numero; and the following phrases used by him: pars Herculanea: ad incitas redigere: ad plures descendere.

MR. FERRAR.

Translate the following passage into Greek Verse:

Bacchus, that first from out the purple grape
Crush'd the sweet poison of misused wine,
After the Tuscan mariners transform'd,
Coasting the Tyrrhene shore, as the winds listed,
On Circe's island fell: (Who knows not Circe,
The daughter of the Sun, whose charmed cup
Whoever tasted lost his upright shape,

And downward fell into a grovelling swine?)
This Nymph, that gazed upon his clustering locks
With ivy berries wreathed, and his blithe youth,
Had by him, ere he parted thence, a son
Much like his father, but his mother more,

Whom therefore she brought up, and Comus named:
Who, ripe and frolic of his full-grown age,
Roving the Celtic and Iberian fields,

At last betakes him to this ominous wood;
And in thick shelter of black shades imbower'd
Excels his mother at her mighty art,

Offering to every weary traveller
His orient liquor in a crystal glass,
To quench the drought of Phoebus.

MILTON.

Translate the following passage into Greek Prose :

Res postulare videtur Africa situm paucis exponere, et eas gentis, quibuscum nobis bellum aut amicitia fuit, adtingere. Sed quæ loca et nationes ob calorem, aut asperitatem, item solitudines, minus frequentata sunt, de is haud facile compertum narraverim: cetera quam paucissumis absolvam. In divisione orbis terræ plerique in partem tertiam Africam posuere : pauci tantummodo Asiam et Europam esse; sed Africam in Europa. Ea finis habet, ab occidente, fretum nostri maris et oceani; ab ortu solis, declivem latitudinem, quem locum Catabathmon incolæ adpellant. Mare sævum, importuosum: ager frugum fertilis, bonus pecori, arbori infecundus cœlo, terra, penuria aquarum. Genus hominum salubri corpore, velox, patiens laborum: plerosque senectus dissolvit, nisi qui ferro, aut bestiis, interiere: nam morbus haud sæpe quemquam superat.

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