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EXAMINATION FOR GRADUATION IN CLASSICS.

November 1873.

G

R Ε Ε Κ.

I. GREEK GRAMMAR. 1. Tabulate the consonants in Greek, according to the organs by

which they are produced and their power. 2. Give the declension in full of , κρέας, μείζων, όστις, η

ή, τετυφώς, , contracting where proper. 3. Explain the origin of the forms μέλαινα, λυθείσα, πράσσω, τύπτειν,

πίπτω, πέπεισμαι. 4. Give the comparative and superlative of the following :-κούφος,

αισχρός, ταχύς, ράδιος, σαφώς, άγχι, ήδέως. · 5. Give the pres. fut. 2d aor. and perf. act., and the 1st aor. and

perf. pass. of verbs formed from the stems λαβ, φαν, πραγ,

φθαρ, θε, ε, πιθ, λιπ. 6. Inflect the 1st aor. ind. mid. of åyyémw, the plup. pass. of

φαίνω, and the 2d aor. imp. act. of τίθημι. 7. Mention some of those verbs which are treated as transitive in

Greek, though intransitive in Latin. 8. How are the subjunctive and optative generally used in final

sentences ? 9. Explain the following phrases :-οι από σκηνής, προ πολλού ποιεί

σθαι, δι' ουδενός ποιείσθαι, διά μακρού, οι αμφί Πλάτωνα, ως επί το

πολύ, δίκην όφλεϊν, δίκην διδόναι, τα γενόμενα ει θέσθαι. 10. Render into Attic Greek :We ought not to censure those ac- | Ου κατηγορητέος ούτος ο πράγμα ειμί, δι' tions by which one may virtuously | ός άν τις μετ' αρετή πλεονεκτέω, αλλά και better his condition, but those men | άνθρωπος, ο περί ο πράξις, εξαμαρτανων ή ο who transgress in deeds or deceive | λόγος εξαπατών, και μη δικαίως χρώμενος in words, and do not employ them aúrós. justly.

II. HERODOTUS, Book IX. Translate :

93. Του τον πατέρα έφερε ομοίως καρπόν."

III. SOPHOCLES, Philoctetes.
Translate :

1409-1430. Μήπω γε--Οίτης πλάκα.
1140-1157. Ανδρός του το μεν σ αρκώς αιόλας.

IV. HOMER, Iliad, VIII. IX.
VIII. 413-424. Πή μέματος;- έγχος αείραι.

IX. 462-473. Ενθ' εμοί- θαλάμοιο θυράων.
Translate and parse παρεσκευάδατο, φθινόπωρον, έπεστεώς, αραιρημένος,

ακαλυφή, μαλαχθής, τητώμενος, εξαπάφοιτο, κηάμενοι.

V. HISTORY AND ANTIQUITIES OF GREECE.

1. A brief account of the constitutional changes effected by Solon. 2. Life of Xenophon, and some account of his works. 3. The causes and results of the Sacred War. 4. A map of Greece, with divisions, and position of principal towns,

rivers, and mountains. 5. Explain the following terms :- επιστάτης, πρόεδροι, θητες, σεισάχ

θεια, θεσμοθέται, πένταθλον, ηλιαία, εφέται.

University of St Andrews.

EXAMINATION FOR THE M.A. DEGREE.

SATURDAY, April 17, 1875.

NATURAL PHILOSOPHY.

1. Prove that if three forces are in equilibrium each is proportional to the sine of the angle contained by the other two. . What additional condition must be fulfilled in order that the converse of this theorem may be true ?

Three strings, joined at a point, carry 3, 4, and 5 pound-weights hanging over the rim of a smooth circular and horizontal table. Assuming that sin. 36° 52' = 6 nearly, place the strings on the table so that there shall be equilibrium.

2. Find the resultant of two forces which act on a rigid body in parallel directions.

What is a couple, and how may a body on which a couple acts be kept at rest?

3. State the laws of friction.

A body rests on a rough inclined plane, and is supported by a force acting parallel to the base of the plane. Find the limits between which this force may be varied consistently with the maintenance of equilibrium.

4. A weight P supports a weight W hanging from a single movable pulley, with the strings not parallel. Find the condition of equilibrium, neglecting the weights of the pulley and string.

If the weight W be given, what are the limits to the possible values of P?

5. Determine the motion of an elastic ball after oblique impact on a smooth fixed plane.

A ball, projected from one side of a room, returns, after oblique impact at the opposite side. Compare the times of going and returning across the floor. 6. Assuming the formulae

v=u + at, s=ut + } ať, prove that

v2 = u? + 2 as. Show how to find the time of flight of a body projected vertically upwards, and the height to which it will rise.

7. Find the acceleration of a particle which rests on a smooth inclined plane.

Prove that the velocity acquired in falling down an inclined plane is the same as that acquired by falling freely through the height.

8. When a solid is immersed in a liquid it is pressed upwards by a force equal to the weight of the liquid displaced.

A piece of sodium weighs 8 grammes in air, and 1.07 grammes in naphtha, whose specific gravity is known to be •84. Find the specific gravity of the sodium.

9. Explain the construction of the mercury barometer, and describe an experiment to prove that the mercury is sustained in the barometer by the pressure of the atmosphere.

10. Enunciate Boyle's Law, and show how it may be verified experimentally.

11. Describe Rumford's and Davy's experiments on the conversion of mechanical energy into heat.

What is the mechanical equivalent of heat and its numerical value ?

How did Joule determine it ? ****. 12. Define Work, and show how the work done by an expanding gas is measured.

Explain Watts Indicator, and Indicator Diagrams.

13. A ray of light is successively reflected in the same plane by two plane mirrors. Prove that the final deviation of the ray is double the inclination of the mirrors.

Describe an astronomical instrument and its uses, in which this arrangement is employed.

14. Investigate the equations for the path of a ray refracted through a prism in a principal plane.

Find the deviation, when the angle of the prism and angle of incidence are small.

15. The absolute indices of refraction of two media being given, find their relative index.

If for water and glass the indices are and }, what is the index when a ray passes out of water into glass ?

16. Give some account of Wheatstone's researches on the velocity of the transmission of electricity through a wire.

17. Define the terms Electro-motive Force, Current-strength, and Resistance; and enunciate Ohm's Law.

18. Describe the phenomena of Electro-dynamic and Magnetoelectric Induction, giving some account of Faraday's researches.

Explain the construction and action of Wheatstone's or Siemens' Magneto-electric machines.

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