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GREEK-JUNIOR CLASS.

(FIRST YEAR HONOURS AND SECOND YEAR PASS.)*

AUTHORS.

1. Translate into English, extracts from Thucydides, Book III.; Sophocles, Electra and Ajax.

2. Translate with notes, historical or grammatical

(α) ἑλὼν οὖν [ἀπὸ τῆς Νισαίας] πρῶτον δύο πύργω προέχοντε μηχαναῖς ἐκ θαλάσσης καὶ τὸν ἔσπλουν ἐς τὸ μεταξὺ τῆς νήσου ἐλευθερώσας ἀπετείχιζε καὶ τὸ ἐκ τῆς ἠπείρου, ἢ κατὰ γέφυραν διὰ τενάγους ἐπιβοήθεια ἦν τῇ νήσῳ οὐ πολὺ διεχούσῃ τῆς ἠπείρου.

(1) ὕστερον δὲ τοὺς μὲν χοροὺς οἱ νησιῶται καὶ οἱ 'Αθηναῖοι μεθ' ἱερῶν ἔπεμπον, τὰ δὲ περὶ τοὺς ἀγῶνας καὶ τὰ πλεῖστα κατελύθη ὑπὸ ξυμφορῶν, ὡς εἰκός, πρὶν δὴ οἱ ̓Αθηναῖοι τότε τὸν ἀγῶνα ἐποίησαν καὶ ἱπποδρομίας, ο πρότερον οὐκ ἦν.

(ε)

ἐκ γὰρ συνέδρου καὶ τυραννικοῦ κύκλου
Κάλχας μεταστὰς οἷος ̓Ατρειδῶν δίχα,
ἐς χεῖρα Τεύκρου δεξιὰν φιλοφρόνως
θεὶς εἶπε κἀπέσκηψε παντοία τέχνη
εἶρξαι κατ' ἦμαρ τοὐμφανὲς τὸ νῦν τόδε
Αἴανθ ̓ ὑπὸ σκηναῖσι μηδ' ἀφέντ' ἐαν,
εἰ ζῶντ' ἐκεῖνον εἰσιδεῖν θέλοι ποτε,

GREEK HISTORY.

(FIRST YEAR HONOURS AND SECOND YEAR PASS.)*

ONE HOUR AND A HALF.

Not more than FOUR questions to be attempted.

1. How was the Confederacy of Delos originally organised? Trace briefly the steps by which the Confederacy was transformed into an Athenian Empire.

2. Describe the influences which promoted and hindered the unity of Greece.

3. Describe briefly the work of Pericles in connection with the completion of Athenian Democracy.

• For Second Year Honours see "Greek-Senior Class," under Third Year.

4. Sketch briefly the career of Themistocles so as to exhibit clearly his importance in Greek History.

5. What were the main operations and events of the first seven years of the Peloponnesian War? Trace, if possible, the strategic ideas involved, i.e., the object aimed at in the various operations.

6. Briefly sketch the history of the Lydian kingdom, and explain its importance in connection with the History of Greece.

LOGARITHMS AND TRIGONOMETRY.

TWO HOURS AND A HALF.

PASS.

(A) LOGARITHMS.

1. State and prove the rules which determine the characteristics of common logarithms.

[blocks in formation]

(iii.) 2sin A (sin+sin+2sin B(sin+sin4)

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2

=sin A+ sin B+ sin C.

4. Solve the triangle in which the sides measure 3.4721, 4.1392

and 5.8421 inches.

(B) TRIGONOMETRY.

5. Find the area, the in-radius and the circum-radius of the triangle in question 4.

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(ii.) a cos A+bcos B+ccos C=4 R sin A sin B sin C.

7. The horizontal straight line AB runs east and west, and the distance AB is 200 yards. The station C bears N. 13oE. and N. 54°W. at A and B respectively, and the elevation of C at A is 14°. Find the height of C above A or B.

8. If a perpetual annuity of £70 per annum is worth £2000, find the present value of an annuity of £100, for 20 years, the first payment being due at the end of 7 years.

STATICS.

TWO HOURS AND A HALF.

1. Enunciate the theorem known as the Triangle of Forces. If PA, PB are two straight lines, and if C is a point on AB such that m×CA=nX CB, prove that forces represented by mx PA and nx PB are together equivalent to a single force represented by (m+n) x PC.

2. Find the resultant of two unequal forces, acting in opposite directions, but not in the same straight line.

3. In the case of parallel forces, prove that the sum of the moments of the components about any point is equal to the moment of the resultant about that point.

A, B.... F are six points arranged at successive intervals of one inch along a straight line. If forces 1, 3, 5 act at A, C and E downwards, and forces 2, 4, 6 at B, D and F upwards, find the magnitude and position of the resultant.

4. Find the centre of gravity of a triangular lamina.

5. A straight rod ABC consists of two portions, viz., AB=a, of uniform density r, and BC=b, of uniform density 8. Prove that the centre of gravity divides the rod in the ratio ra2+s(2ab+b2): r(a2+2ab)+8b2

and that its distance from the middle point of the rod is (r~8)ab÷(ra+8b).

6. Find the relation between Power and Weight in the system of n movable weightless pulleys, each of which rests in the loop of a string, supported at one end and attached at the other to the block of the next pulley.

7. Write a short article (of 15 or 20 lines) on Friction. 8. Two equal, weightless rods AB, AC are hinged at A, and a weightless string DE, of half the length, connects their middle points. The whole being set up (like a capital letter A) on a smooth table, a weight W is suspended from the hinge A. Find the tension of the string.

ANALYTICAL GEOMETRY.

TWO HOURS AND A HALF.

PASS.

1. Find an expression for the distance between two given points (x'y'), (x" y′′).

Determine the centre of the circumscribed circle of the triangle formed by the straight lines x+y=5, x−y+1=0, 3x-y+1=0.

2. Find the equation to the straight line joining two given points.

In what ratio does the straight line joining (1, 4) and (5, 0) divide the straight line joining (4, 2) and (-2, 5)?

3. Obtain a formula for the angle between two given straight lines, and deduce the condition that they may be at right angles.

Any straight line is drawn through the point (2, −3), and a perpendicular is drawn to it from the point (5, 2). Find the equation of the locus of the foot of this perpendicular. 4. Shew that the equation x2+y2+2gx+2fy+c=0 represents a circle, and find its centre, and radius.

Prove that the straight line 3x+5y+9=0 touches the circle x2+ y2—7x+y+4=0, and determine the point of contact. 5. Find the equation to a circle which touches the three straight. lines 4x+3y-2=0, 12x-5y+6=0 and y=0.

6. Obtain the equation to the circle in polar coordinates, and thence prove that the rectangle contained by the segments of a chord of a circle passing through a fixed point is

constant.

7. Find the equation to a tangent at any point of the parabola y=4ax.

The tangent at P to y2-4ax meets the axis in T. Shew that the locus of a point Q on PT such that TQ:QP::1:2 is the parabola 3y2+4ax=0.

8. The focus of an ellipse is (2, 0), its directrix is x=-1, and its eccentricity; find its equation, the coordinates of its centre, and the lengths of its major and minor axes.

SENIOR FRENCH I.

PROSE COMPOSITION, TRANSLATION AT SIGHT, Erc.

1. Translate into French

sea.

PASS.

From time immemorial the poets have taxed their energies to render in words the beauty of the earth; and so infinite in variety is that beauty, so ever growing, and so ever changing, that the latest picture by the latest poet seems, if he have the true eye for nature, as fresh and unworn as the description of Homer. But this is not so with the After a few epithets the poet can say nothing to recall the beauty of her whose deepest and most abiding charm is oneness-monotony of voice, and even monotony of colour, save for such reflected hues as she can steal from the riches of heaven. The truth, of course, is that while the sea seems to be alive, but is really a mere waste of dead matter tossed about unconsciously by the winds, the earth, though without motion, contains within her warm bosom, not only a nursery of life, but very life itself. This is why it is so easy for the literary artist to paint the With very few exceptions the poets do not attempt to do it, but instead depict the sensations and emotions to which the sea gives birth in its impact on the body and the soul of man.

sea.

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