(α) ἡμέας στασιάζειν χρεόν ἐστι ἔν τε τῷ ἄλλῳ καίρῳ καὶ δὴ καὶ ἐν τῷδε περὶ τοῦ ὁκότερος ἡμέων πλέω ἀγαθὰ τὴν πατρίδα ἐργάσεται.

(*) τῶν τινὲς Φοινίκων, τῶν αἱ νέες διεφθάρατο, ἐλθόντες παρὰ
βασιλέα διέβαλλον τοὺς Ἴωνας, ὡς δι ̓ ἐκείνους ἀπολοίατο αἱ
νέες, ὡς προδόντων.

(ε) εἰ γὰρ ἀναγκασθείη ἀπολαμφθεὶς ὁ Πέρσης μένειν ἐν τῇ Εὐ-
ρώπῃ, πειρῷτο ἂν ἡσυχίην μὴ ἄγειν, ὡς ἄγοντι μὲν οἱ ἡσυχίην
οὔτε τι προχωρέειν οἷόν τε ἔσται τῶν πρηγμάτων οὔτε τις
κομιδὴ τὸ ὀπίσω φανήσεται, λιμῷ τε οἱ ἡ στρατιὴ διαφθαρέεται,
ἐπιχειρέοντι δὲ αὐτῷ καὶ ἔργου ἐχομένῳ πάντα τὰ κατὰ τὴν
Εὐρώπην οἷα τε ἔσται προσχωρῆσαι κατὰ πόλιάς τε καὶ κατὰ
ἔθνεα, ἤτοι ἁλισκομένων γε ἢ πρὸ τούτου ὁμολογεόντων.
() καλέσας δὲ τοὺς θῆτας προηγόρευέ σφι ἀπαλλάσσεσθαι ἐκ
γῆς τῆς ἑωυτοῦ. οἱ δὲ τὸν μισθὸν ἔφασαν δίκαιοι εἶναι ἀπολα-
βόντες οὕτω ἐξιέναι. ἐνθαῦτα ὁ βασιλεὺς τοῦ μισθοῦ πέρι
ἀκούσας, ἦν γὰρ κατὰ τὴν καπνοδόκην ἐς τὸν οἶκον ἐσέχων ὁ
ἥλιος, εἶπε θεοβλαβὴς γενόμενος· “ Μισθὸν δὲ ὑμῖν ἐγὼ ὑμέων
ἄξιον τόνδε ἀποδίδωμι,” δέξας τὸν ἥλιον.

2. Write down the Attic equivalents of the non-Attic wordforms in passage (e) above.

3. Translate into English, extracts from Euripides, Alcestis.

4. Translate the following passages, and write notes on the grammatical construction or meaning of the words underlined

(α) ἱερὸς γὰρ οὗτος τῶν κατὰ χθονὸς θεῶν

ὅτου τόδ' ἔγχος κρατὸς ἁγνίσῃ τρίχα.

(δ) μὴ πρός σε θεῶν τλῇς με προδοῦναι,
μὴ πρὸς παίδων, οὓς ὀρφανιεῖς,
ἀλλ ̓ ἄνα τολμα

σοῦ γὰρ φθιμένης οὐκέτ ̓ ἂν εἴην
ἐν σοὶ δ' ἐσμὲν καὶ ζῆν καὶ μή

σὴν γὰρ φιλίαν σεβόμεσθα.

(ε) οὐκ ἦλθες ἐν δέοντι δέξασθαι δόμοις·
πένθος γὰρ ἡμῖν ἐστί· καὶ κουρὰν βλέπεις
μελαμπέπλους στολμούς τε.

(α) ΗΡ. εἰ γὰρ τοσαύτην δύναμιν εἶχον ὥστε σὴν
ἐς φῶς πορεῦσαι νερτέρων ἐκ δωμάτων
γυναῖκα, καί σοι τήνδε πορσῦναι χάριν.
ΑΔ. σάφ' οἶδα βούλεσθαί σ ̓ ἄν.

ARITHMETIC AND ALGEBRA.

TWO HOURS AND A HALF.

PASS.

1. The floor space of a room is 224 square feet; the wall space, including doors and windows, is 660 square feet; and the diagonal of the floor is 452 ft. Find the dimensions of

the room.

2. The difference between the simple interest and the true discount on a certain sum for a year at 4 per cent. per annum is 1s. 8d.; find the sum.

3. Solve the equation

√(5x+6)+√(3x-2)=√(15x+10),

and verify the roots found.

4. Solve the equations

ax-by=2

x(ax+by)=2b(ab+1)

5. Find the value of 3-32-7x+6 when is replaced by (5+13).

6. Shew that the sum of the roots of the equation ax2+bx+c=0

Find a value of k in the equation 18x2+45x+k=0 so that one root may be double the other.

8. Find three numbers which are to one another as 3:4:7, and

such that the sum of the greatest and least exceeds the other by 9.

9. Find the last term and the sum to n terms of a given A.P. The sum of 80 consecutive terms of an A.P. is 6480, and the difference between the sum of the odd terms and the sum of the even terms is 80; find the series.

10. The sum of the first three terms of an infinite G.P. is, and the sum to infinity is. Find the tenth term.

TRIGONOMETRY.

TWO HOURS AND A HALF.

PASS.

1. What is a radian?

The arc of a certain sector is 3 inches, and the radius 5 inches in length. Find the angle of the sector in radians and in degrees. [Take T=22/7].

2. Given cos A=12/37, find tan A.

1 4K

3. If sec 0=x+ -, prove that sec0+tan0=2k or 2/κ.

4. By means of a figure, prove the formula for expanding

sin(A+B).

7. In the triangle ABC, prove the following relations

8. The sides of a triangle are 17, 25 and 28 feet respectively, find the cosine of the smallest angle.

Also find the sine of that angle, and the area of the triangle. 9. A rock is observed from a steamer to be right ahead, at an estimated distance of one mile and a-half. If the steamer alters its course by 30°, how near will it pass to the rock?

GEOMETRY AND MENSURATION.

TWO HOURS AND A HALF.

PASS.

1. Describe a parallelogram equal to a given rectilinear figure, and having an angle equal to a given angle.

2. If the middle points of the sides of a quadrilateral be joined in order, a parallelogram will be formed whose area is half that of the given quadrilateral.

3. Divide a given straight line into two parts so that the rectangle contained by the whole and one part may be equal to the square on the other part.

4. In equal circles the arcs which subtend equal angles, whether at the centres or at the circumferences, are equal to one another.

P is a variable point on the circumference of a given segment APB of a circle. Shew that the line bisecting the angle APB always passes through a fixed point.

5. Inscribe a square in a given circle.

6. If two triangles be equiangular to one another, the sides about the equal angles shall be proportional, those sides which are opposite to equal angles being homologous. If ABC is a triangle and BD, CD are drawn perpendicular to AB, AC respectively and CE is drawn perpendicular to AD to meet AB in E, prove that

AE: AC::AC: AB.

7. ABCDE is a pentagonal field. CK, DM, EN are perpendicular to AB and AN=95 chains, EN=1·62 chains, AM=2.54

chains, DM=1.83 chains, AK=3·77 chains, CK=1:45 chains, AB=4.25 chains. Find the area of the field in acres, roods and perches.

8. Find the volume of a mast in the form of a frustum of a cone, the length of the mast being 34 feet, and the diameters of the two ends 18 inches and 15 inches respectively.

JUNIOR FRENCH PROSE COMPOSITION AND UNSEEN

TRANSLATION.
PASS.

1. Translate into French

(a) A tempestuous night closed the memorable day of Albuera.
The rain, which during the action had fallen heavily at
intervals, became more constant and severe as evening
advanced; and the streams which rolled down the heights
and mingled with the waters of the river were not un-
frequently observed to be deeply tinged with blood. The
village of Albuera had been plundered and destroyed by
the enemy: every house was roofless; every inhabitant
had disappeared; and had there been a place of shelter
near, there was neither carriage nor beast of burden by
which the wounded could have been removed. Throughout
the night, and during the following day, the dead and the
disabled lay upon the field as they had fallen; and nothing
could be more painful than the groans and complainings
of the wounded.

(b) The death of Nelson was felt in England as something
more than a public calamity: men started at the intelli-
gence and turned pale, as if they had heard of the loss of
a dear friend. An object of our admiration and affection,
of our pride and of our hopes, was suddenly taken from
us; and it seemed as if we had never till then known how
deeply we loved and reverenced him.
So per-

fectly, indeed, had he performed his part that the maritime
war after the battle of Trafalgar was considered at an
end: the fleets of the enemy were not merely defeated,
but destroyed. It was not, therefore, from any selfish
reflection upon the magnitude of our loss that we mourned
for him; the general sorrow was of a higher character.