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PROFESSOR STACK.

The Candidates are required to discuss the following Questions :

1. Compare Greek and Roman literature as to their bearing on modern sympathies.

2. Compare Greek and Roman poetry as to the degree and manner in which they were affected by political events, and by religion.

3. Write a note on the Italian influences visible in Roman literature.

4. Compare the influence exercised by the early Tragic and Comic Drama among the Romans, and account for the greater permanence of one of these forms of composition.

5. Write a note on the influence of the mercantile party among the statesmen of the later Roman Republic; and point out some of the important political proceedings and events which appear to be due to their influence.

6. Comment on the statement that, during the last century of the Republic, the Romans had the evils of party life without its countervailing benefits.

7. Write a general comparison of the characteristics, pol and literary, of the Roman State in the sixth and the seventh centuries of the Republic.

MR. ABBOTT.

1. Mention the principal branches of the Aryan family of languages, classifying them according to the antiquity of their forms.

2. Describe the nature of the evidence by which the affinity of these languages is proved.

3. Is there any reason to suppose the existence of a primitive ItaloHellenic tongue after the separation of the Northern European branch ?

4. Make out a scheme of the original personal terminations of the Aryan verb, primary and secondary.

5. How was the imperfect formed in Latin and in Greek respectively? How did it happen that a new form originated in Latin ?

6. How is the formation of tenses by composition proved ?

7. On what Greek form does Bopp base his theory of the origin of the middle suffixes ?

8. This theory does not account for the plural forms ?

9. What is meant by the weight of the personal endings ? Give instances of its effect.

10. Enumerate all the comparative and superlative suffixes of which traces exist in Greek, Latin, or English, and account for the usual forms in these languages.

11. What are the Latin affinities of og relative and ós possessive, respectively? Show by examples that the changes supposed in the Greek words were required by the phonetic laws of that language.

u

12. State the ordinary rule as given by Kühner (Jelf), &c., for the use of the indicative with či in the protasis followed by the optative with åv in the apodosis.

13. State also the rule given for the use of the historic tenses of the indicative with ei, the consequent being also in the indicative with äv.

14. Among the examples of these two rules cited by Kühner are the following :

Of the first-α. ουδ' αν εγώ πεφιδοίμην ούτε σε ούθ' έτάρων, ει μη θυμός με κελεύει.-0d. ι. 6. ή γάρ κεν δειλός τε και ούτιδανός καλεοιμην, ει δέ σοι πάν έργον υπείξομαι όττι κεν είπης.-ΙΙ. α. C. πολλή γάρ άν τις ευδαιμονία είη περί τους νεόυς, εί είς μέν μόνος αυτούς διαφθείρει, οι δ' άλλοι ωφελούσιν.-Plat. Apol.

Of the second-α. και νυ κεν 'Ακτοριώνε Μολιόνε παϊδ' αλάπαξα, ει μη σφωι πατήρ εκ πολέμου εσάωσε.-Ι. λ. ο. ουκ άν ούν νήσων εκράτει ει μη τι και ναυτικόν είχεν.--Thucyd.

If possible, apply the principles stated to these instances ; if not, give a more correct explanation of the constructions.

15. It is an error to found principles of this kind in whole or in part on Homeric usage ?

16. What tenses in Latin have an aoristic sense in the indicative and subjunctive respectively?

17. State fully the laws followed by the tenses and moods in questions and commands put in the Oratio Obliqua in Latin. Change the following examples accordingly into the oblique construction :-“Si ignoscere volo num oblivisci possum ? Si perseveras, hujus reminiscitor, nec commiseris, ut-.”

The Candidates were further examined vivâ voce in the Political and Literary Histories of Greece and Rome.

Moderatorships in Experimental and Natural Science.

Examiners. THOMAS LUBY, D. D. JAMES APJOHN, M. D., Professor of Chemistry. JOSEPH A. GALBRAITH, M. A., Professor of Experimental Philosophy. SAMUEL HAUGHTON, M. D., Professor of Geology. WILLIAM H. HARVEY, M. D., Professor of Botany. EDWARD P. WRIGHT, M. D., Lecturer in Zoology.

DR. LUBY.

1. In the case of the rainbow determine the direction of the emergent pencil after reflections. The problem to which this is reduced may be solved by a simple construction ?

2. In Young's experiment in the case of interference of light, if a be the length of a wave, the place of the nth band is expressed by the formula

nox

;

2c

prove this, stating on what condition it depends, and how to distinguish a dark band from a bright one.

3. Explain Fresnel's experiment for the same purpose, and show what advantages it has over that of Young. 4. In this experiment the place of a band is expressed by the formula

+ β) ηλ
(+b)

;

2a.sin a prove this, explaining the terms.

5. In the case of double refraction by crystals, explain what is meant by the extraordinary index.

6. Give accurately Huyghens' construction for the direction of the refracted rays in the case of double refraction.

7. Show how Huyghens was led to the discovery of polarized light, and to what extent.

8. State the two characters that peculiarly distinguish a polarized ray.

9. The physical nature of common or unpolarized light may be inferred from that of polarized light by a law discovered by Malus; state this law, and show how. Dove's experiment would suggest a different origin for common light.

10. State the principles of Fresnel as modified by Neumann and M‘Cullagh for applying the theory of transversal vibrations to the problem of reflection and refraction at the surfaces of chrystallized media.

11. Prove that when light is polarized in the plane of incidence the amplitudes of the reflected and refracted vibrations are expressed by the formulæ sin (0-0)

sin 20 and v' =

sin (@+ 0') sin (0 +0')' where 8 and O' are the angles of incidence and refraction.

12. State the two principles on which the problem can be solved when the ray is polarized perpendicularly to the plane of incidence.

13. In the case of elliptic polarization determine the equation of the ellipse from the two fundamental equations

2 =a.sin (vt - a) y=b. sin (vt B). 14. Determine the position and ratio of the axes of this ellipse.

PROFESSOR GALBRAITH,

HEAT.

1. Deduce from Regnault's experiments the following expression for

the weight of a gas or vapour in terms of its volume, pressure, density, and temperature,

V (litres) < p (millimetres) x density
W (grammes) =0.4646

273 + t° (C.)
Weight of a litre of dry air at o° C. and 760 mm. = 1.293187
Coefficient of expansion for 1°C.

= 0.00366 2. From this deduce by comparison of English and metrical measures a corresponding formula for the weight in grains in terms of the volume in cubic inches, the pressure in inches, and the temperature in Fahrenheit degrees.

3. If 50 litres of carbonic acid gas at 100° C. and 780 mm. be mixed with 10 litres of hydrogen at 10° C. and 750 mm., what will be the density of the mixture

Density of carbonic acid = 1.529

Density of hydrogen =0.0693 4. If this mixture be contained in a vessel of 50 litres, capacity, and maintained at a temperature of 60° C., what will be its elastic force ?

5. By what experiments and reasoning did Dulong and Petit establish the equation

v = mao (at – 1), in which v is the velocity of cooling in vacuo, o the temperature of the envelope, t the excess of that of the hot body, a = 1.0077, and m a constant depending on the nature of the surface. 6. Proceeding from the equation in the last question, prove that

at
log
mal log a

at - 1 in which equation x is the time of cooling, s the original excess of temperature, and t the excess corresponding to the time a.

7. Helmholtz has computed from Bischof's experiments on basalt that it would take 350 millions of years to cool our earth from an excess of 2000° C. to an excess of 200° C. over the temperature of equilibrium with surrounding space; assuming this, and also that the equilibrium temperature is 10° C., compute by means of the equation in the last question the time it would take the earth to cool down from 50° C. to 25° C., a range of temperature which corresponds to the interval between the earliest possible limit of organic life and the deposition of the London tertiary clays.

8. Let W be the weight of a liquid whose latent heat is 1, and specific heat is c; let W' be the weight of the vessel which contains it, and cits specific heat, let also To be the melting point of the liquid when it changes state ; calculate in terms of these quantities the temperature to which the liquid should be lowered below To in order that when agitated the whole should suddenly congeal into a solid mass at To.

9. Adapt to English measures the theoretical formula for the velocity of sound in a gaseous medium, viz.:

elasticity
density

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as - 1

Х

as

Ikx

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in which v is the velocity in feet per second, t the temperature of the gas, s its specific gravity, and k the ratio of its specific heats under constant pressure and constant volume.

10. Calculate the velocity of sound in an atmosphere of carbonic acid, at a temperature of 50°, k = 1.338 8= 1.529.

ELECTRICITY AND MAGNETISM.

72

1. What is the law of the action of an element of an electric current on a magnetic pole? Deduce from this law the expression for the whole force with which a finite portion of a straight current, considered as a base, acts on the pole considered as a vertex; and show that it is proportional to the sum of the cosines of the base angles directly, and to the altitude inversely.

2. Describe the action of a magnetic bar on a floating circular current, the bar being placed in the axis of the current. How does the force with which one of the poles acts on the current vary? What will be the nature of the motion of the current both outside and between the poles ? What will be the position of stable and of unstable equilibrium ?

3. State the principles on which Ampère's formula for the force with which two current-elements act on each other, namely,

ii'dsds'

F=- -(sin @ sin e' cos & + k cos cos '), is founded; and if the value of k be assumed to be equal – , prove that

iü'dsds' F=

(cos w - cos O cos '), w being the angle between ds and ds'.

4. By means of this formula, investigate the action of one side of a right-angled triangle along which a current runs upon an element of a current running in a parallel direction, and having its middle point situated at the opposite angle.

5. On what does the sensibility of a galvanometer depend when used to measure the intensities of hydro-electric currents and thermo-electric currents ?

6. When will the intensity of a system consisting of b rows of a cells be the same as a rows of b cells ?

7. Let there be 72 cells of equal dimensions, and let the interpolar resistance be equal to half a cell-resistance; ascertain the best and worst arrangements, and compare the intensities in each case.

8. State and prove the expressions for the intensities of the principal, partial, and derived currents corresponding to a given primitive current.

9. Let R be the total resistance between two telegraph stations; let

72

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