17. Given the rectangle under two lines, and the difference of their squares, construct them.

18. Draw a line from a point across an angle so as to cut off a triangle of given area.

C.

MR. WILLIAMSON.

1. If each side of a triangle of given species passes through a fixed point, find the locus of the centre of its inscribed circle.

2. Show how to describe the eight circles which touch three given circles.

3. If a system of circles cut three fixed circles at equal angles, prove that they form a coaxal system.

4. The sides of a triangle are 25, 39, and 40; determine the distance between the centres of its inscribed and circumscribed circles.

5. A sum of money lying at interest amounted at the end of a year to £11,130; if the rate of interest had been I per cent. less, and the principal £100 more, the amount would have been the same. Calculate the principal, and the rate of interest.

MR. BURNSIDE.

6. Two lines are drawn so as to be cut harmonically by two given circles; if the lines intersect at right angles, prove that the distance of their intersection from the middle point of the line joining the centres of the circles is of constant length, and determine its value.

7. Given the centres of three circles, and the differences of their radii, prove that their radical centre moves along a right line.

8. Through a given point O show how to draw a right line intersecting two given lines in P, Q, so that the area of the triangle formed by the three lines be proportional to the rectangle OP. OQ.

9. Find values for x, y, z satisfying the equations

y2 + yz + z2 = a2,

x2 + zx + x2 = b2,

x2 + xy + y2 = c2.

10. Removing the radicals from the following equation

√ x2 - a2 + √x2 - b2 + √ x2 - c2 = x,

the result is of the form Px2 = symmetrical functions of a, b,

c.

Q; find P and Q, and show that they are

MR. M'CAY.

11. Given the sides of a quadrilateral, construct it so as to be inscribed in a circle.

12. If λ, μ, v be the perpendiculars from the vertices of a triangle on any tangent to the inscribed circle, and p, q, r the perpendiculars of the triangle, prove

λ μ y
+ +
p Չ r

= 1.

13. Find a point on a line so that the sum or difference of its distances from two fixed points may be given.

14. The vertices of a triangle move on a circle, and two sides touch a fixed circle; prove that the third side touches a fixed circle.

15. If the transverse common tangents to two circles be perpendicular to the direct ones, the eight points of contact of these tangents will lie on two right lines.

Classics.

DEMOSTHENES.

MR. GRAY.

Translate the following passages into English:

1. Beginning, ύστέρα τοίνυν δεκάτη, ἐνάτη, ὀγδόη· κ.τ.λ. Ending, εἰς ταύτην εἶναι πέμπτην.

De Falsa Leg., 59, 60.

2. Beginning, Καὶ τίς μου καταμαρτυρεῖ, φήσει, κ.τ.λ. Ending, δῆλον ὅτι πάνδεινος εἴ τις.

Ibid., 120.

3. Beginning, χωρὶς δὲ τούτων δυοῖν χρησίμοιν κ. τ. λ. Ending, Φωκέων καὶ Πυλῶν, οὐ προήσεσθαι.

Ibid., 151, 152.

4. Beginning, "Ον τοίνυν χρόνον ἦμεν ἐκεῖ καὶ καθήμεθ', κ. τ. λ. Ending, ὧν ἡμῖν ἐδίδου ξενίων, τούτους λύσασθαι.

Ibid., 166.

5. Beginning, "Εστι τοίνυν τις πρόχειρος λόγος πᾶσι, κ. τ. λ. Ending, παρελήλυθ ̓ ἐκεῖνος φενακίζων ὑμᾶς.

6. Beginning, ἔτι τοίνυν ὅταν μὲν ἴδητε δεινότητα, κ. τ. λ. Ending, τῶν ἀκουόντων ἀντιστῇ διακόπτεται.

Ibid., 187.

Ibid., 339, 340.

1. Write such notes on the above passages as you would expect to find in a well edited edition of this speech, omitting no difficulty and explaining all peculiarities of grammar and idiom.

2. Give a short account of the Social war, stating the causes of it, and the injurious effect of it on Athens.

f

3. Enumerate those causes which combined to place Greece at a disadvantage when thrown upon its defence against Macedonia.

4. Give Grote's view respecting the Theoric Fund.

5. What causes disposed the Athenians to conclude the peace of B. C. 346 with Philip? Give at some length the various steps of the negotiation, showing where and how the Athenians were overreached by Philip. Upon one point only, in Grote's opinion, Demosthenes appears open to

censure?

6. There is a disposition to magnify the practical effect of the speeches of Demosthenes: what was his true position, and during what time was his positive influence in determining the proceedings of his countrymen considerable ?

7. How was the burthen of the Trierarchy regulated by the law of Periander, and what were the reforms introduced by Demosthenes ? 8. Explain

διὰ ταῦτ' ἐσπαθᾶτο ταῦτα.
ὅσοιπερ ἦσαν ἐξηγγυημένοι.
ἀγαπητῶς παρατρεφόμενον.
δοῦλος ἦν τῶν ῥήματων τούτων.
νῦν δ ̓ ἀναπεπτωκότες ἦτε.

τὸν ἴδιον κίνδυνον ὑποθείς.

ἠτίμωσεν ὑπακούσαντα τιν αὐτοῦ κατήγορον.
ὑμᾶς κατεπολιτεύσατο Φίλιππος.

MR. TYRRELL.

[No credit will be given for any translation which does not fully explain the jokes and allusions in each passage].

1. Beginning, Ambigua sunt in primis acuta atque in verbo .... Ending, fuit, ut mihi quidem videtur, salsissimus.

CICERO, De Or., ii. caps. 62, 63.

2. Beginning, Atque haec omnia verbo continentur. Ending, Sentin' senem esse tactum triginta minis ?

3. Beginning, Etiam illa, quae minuendi aut augendi.... Ending, quod Asellum ignominia levarit.

4. Beginning, Quem concursum in oppido factum putatis ? Ending, leviter presso vestigio persequebantur.

Ibid., cap. 64.

Ibid., cap. 66.

....

Ibid., in Verr., II. lib. iv. caps. 23, 24.

5. Beginning, Quoniam respondi postremae tuae paginae prima mea, .... Ending, Sed hoc continuo correximus.

Ibid., ad Att., vi. 2, 3.

1. What mistake does Quintilian make about the meaning of the italicised words in the third passage above?

2. What Roman first attempted to Romanize the provincials, and what means did he adopt?

3. Write a note on the part played by "the Cilicians" in Roman history.

4. On what occasion did Cicero first appear as a political orator, and what made his appearance on that occasion significant?

5. What view does Mommsen take of the scope and character of the Catiline and Jugurtha of Sallust?

PREVIOUS MEDICAL EXAMINATION.

CHEMISTRY.

DR. APJOHN.

1. Write the formula of hydrogen potassium tartrate, and explain how it may be converted into soluble tartar. Describe also the mode of

dealing with soluble tartar so as to extract from it tartaric acid.

2. How is hyposulphite of sodium made, and what products does it yield when acted upon with iodine?

3. Aqua-lauro-cerasi when exposed to air gradually becomes turbid. How is this accounted for?

4. There are two carbonates of magnesium in the British Pharmacopoeia. How is each made, and in what respect do they differ from each other?

5. How is liquor zinci chloridi made? and when it includes iron, how is this removed?

6. Write the formula of ferrocyanide, ferrideyanide, and sulphocyanide of potassium, and explain the application of each of them as a test for iron ?

7. If sulphide of hydrogen be passed into separate acidulated solutions of sulphate of copper, sulphate of zinc, chloride of antimony, and liquor arsenicalis, what is its action upon each of these salts ?

8. Every monatonic alcohol has allied to it a series of compounds, viz., an olefine, a paraffin, a simple ether, numerous compound ethers, and an acid. Write the formula of each of these in the case of the ethylic alcohol, and describe how each may be produced.

9. If urine be distilled its urea disappears and the distillate contains carbonate of ammonium. How is this explained?

10. A urinary calculus is found to include uric acid, oxalate of calcium, phosphate of calcium, and triple phosphate. How would you determine the precise amount of each of these constituents?

PHYSICS.

MR. GALBRAITH.

1. Define a unit of heat with reference to British and metric standards. 2. What is the ratio between the two ?

3. How much heat will be required to melt a pound of ice at 32°; how much to raise the melted ice to the boiling point; and finally, how much to boil it away?

4. What is meant by the displacement of zero ? the accuracy of a thermometer?

How would you test