10. A weight W is placed on a plane which is made to descend vertically with an acceleration f; find the pressure on the plane.

II. Find the relation which connects the distances of two conjugate foci from a thin concave lens. Explain the statement that the deviation produced by a thin lens is constant.

12. A conical vessel with its axis vertical is filled with a fluid; compare the pressures on the curved surface when the base is lowest, and when the vertex is lowest.

DR. TARLETON.

13. A weight P, moving down a rough inclined plane, draws a weight Q up another rough inclined plane by means of a cord passing over a smooth pulley whose axis coincides with the line of intersection of the two inclined planes; the two weights and the pulley are in the same vertical plane which is at right angles to the line of intersection of the two inclined planes; the cord and pulley are supposed to be without weight. Find the tension of the cord.

14. Find the condition which must be fulfilled by a system of forces acting on a rigid body in order that it should be equivalent to a single force.

15. Explain the phenomenon of the aberration of light. Assuming that the Earth's motion is uniform, and that the apparent orbit of a fixed star caused by aberration lies in the tangent plane to the celestial sphere drawn through the star's real position, prove that the fixed stars aberrate in ellipses, and determine when the aberration is greatest.

16. Show how to construct a vertical sun-dial facing the south. What correction must be applied to the time as given by the sun-dial, and what is its amount when greatest?

17. What is meant by the circle of chromatic aberration produced by a lens? Show how to determine its diameter.

18. A spherical shell composed of matter whose specific gravity is σ, and filled with gas whose specific gravity is s, just floats in air whose specific gravity is a; find the thickness of the shell.

Ethics.

MR. BARLOW.

1. "Sed si qualis sit animus ipse animus nesciet, dic, quæso, ne esse quidem se sciet? ne moveri quidem se? ex quo illa ratio nata est Platonis, quæ a Socrate est in Phædro explicata." State the argument fully.

2. What were the opinions of Aristoxenus, Xenocrates, and Dicaarchus, concerning the nature of the soul?

3. What, according to Cicero, is the "naturalis sedes animi," and what are the sources of the soul's felicity when it has attained that state of existence ?

4. What was the opinion of the Stoics concerning a future life? How does Cicero comment upon it?

5. Various circumstances, noticed by Butler, should lead us to conclude that the beginnings of a righteous administration may be found in nature ?

6. Against the whole notion of moral discipline by rewards and punishments, an objection has been urged on ethical grounds; what is the objection, and how is it met by Butler ?

7. Discuss the following question:-Whether the opinion of necessity, supposed consistent with possibility, with the constitution of the world, and the natural government which we experience exercised over it, destroys all reasonable ground of belief that we are in a state of Religion?

8. Butler shows that our ignorance affords a satisfactory solution of certain difficulties in the system of the Divine Government; what objections have been urged against this mode of arguing, and how does Butler reply?

9. What practical reflections does he urge upon the consideration of those who imagine that doubtfulness in the evidence of Christianity affords a ground of complaint?

10. Butler holds that the supposed doubtfulness of the evidence for revelation, so far from affording a positive argument that it is not true, implies a positive argument that it is true; for what reasons?

MR. CONNER.

1. How does Butler answer the question, "Why should we not endeavour to suppress and get over regard to others, and restraints of different kinds which hinder us from going the nearest way to our own good"?

2. Give an outline of his proof that there are as real and the same kind of indications in human nature that we were made for society as that we were intended to take care of our own private good.

3. How does he show that there is such a thing as natural superiority of one principle to another quite distinct from degrees of strength?

4. With what qualifications is the assertion to be understood, "Benevolence is the sum of virtue"?

5. What proofs of the justness of this account of virtue were offered by Dr. Hutcheson ?

6. What is his doctrine of a moral sense? What objection does Dr. Smith make to it?

7. State the Stoical paradoxes and illustrations. Why does Dr. Smith suppose that they did not form part of the system of Zeno?

8. What analogies between moral virtues and the arts, and what differences, does Aristotle mention?

9. Περὶ ἡδονὰς καὶ λύπας ἐστὶν ἡ ἡθικὴ ἀρετή. What proofs of this does he give?

10. How does he defne ἀνδρεία, ἀλήθεια, φιλία νέμεσις ? What are he extremes between which each of these is μεσότης ?

History, Political Science, and English Literature.

PROFESSOR BARLOW.

HISTORY.

1. Write notes in explanation of the following assertions which occur in Hallam's constitutional history of England:

(a). "We are much indebted to the memory of Barbara duchess of Cleveland, Louisa duchess of Portsmouth, and Mrs. Eleanor Gwyn."

(b). "Nothing can more demonstrate the incompatibility of the tory system with the existence of a representative assembly, than the history of the long parliament of Charles II."

(c). "The government of James II. will lose little by comparison with that of his father."

2. In illustration of the importance of the treason bill of 1695, Hallam remarks that "one instance at least had occurred since the Revolution, of charges unquestionably false in their specific details, preferred against men of eminence by impostors who panted for the laurels of Oates and Turberville." What was this?

3. Give a short account of the proceedings of the parliament that met in February, 1621.

4. What reasons have been assigned for the quarrel between Edward IV. and the Earl of Warwick?

5. Write an account of the battle of Fontenoy.

6. Give a sketch of the life of the "great Condé."

7. Note the most important events in French history from 1515 to 1547.

8. Who was (a) Carmagnola, (b) Agutus, (c) Guarnieri ?

9. What account does Hallam give of the condition of Italy at the accession of Frederic Barbarossa?

10. Write an explanatory note on the following sentence in Hallam's "Middle Ages:"

"The dissensions which still separate and render hostile the followers of Mohammed may be traced to the first events that ensued upon his death."

POLITICAL ECONOMY.

1. What are the advantages and disadvantages of a double standard of the currency? How are the two metals retained in circulation in England?

2. The question between the large and the small systems of production as applied to agriculture stands, in many respects, on different grounds from the general question between great and small industrial establishments?

3. Mention the principal causes of diversity in the effective strength of the desire of accumulation. What examples does Mill give of its deficiency, and of its excess?

4. Mill asserts that, cæteris paribus, those trades are generally the worst paid in which the wife and children of the artisan aid in the work; how does he account for the fact?

5. What are Mr. Senior's views as to the economic effects of Absenteeism?

6. Ricardo considers that it is the interest of the labouring classes that revenue should be spent rather on services than on commodities; source of his mistake, according to Senior?

7. Explain the different effects of Taxation on the prices of manufactured commodities and agricultural produce.

8. Monopolies may be divided into four kinds?

9. How does Senior expose the error of the popular opinion that the tendency of tithes to increase in amount is greater than that of rent? 10. Give his enumeration of the different modes in which wealth may be employed as Capital.

1. Mention the most remarkable works produced in England between 1350 and 1400, and state the origin of each-English, French, or Italian.

2. What are the means by which it has been attempted to ascertain the order in which the works of Shakspeare were written, and the date of each work? What are the characteristics of the works of the earliest, the middle, and the last periods of Shakspeare's career as an author? 3. Name some of the best short lyrical poems belonging to each of the following periods:

(a). The Elizabethan period: ending 1620.

(b). 1620-1700.

(c). 1700-1800.

(d). 1800-1870.

What are the characteristic excellences of the lyrical poetry of each period?

4. Give a full account of any remarkable prose work of the eighteenth century.

JUNIOR SOPHISTERS.

Mathematical Physics.

MR. TOWNSEND.

I. An observer is situated in one of the two temperate zones; how would he determine which of the two by observations on the diurnal path of the Sun ?

2. Express the angular distance between the centres of the Sun and Moon, at the commencement of a solar eclipse, in terms of the horizontal parallaxes and apparent semi-diameters of the two bodies.

3. Determine the position in its orbit at which a superior planet, viewed from the Earth, will appear to differ most from the circular form.

4. Prove that the centre of gravity of a triangular frame is the centre of the circle inscribed in the triangle formed by joining the middle points of the sides of the frame.

5. Required, in lbs., the force F, which, acting freely for one minute upon the mass of 1 cwt. weight, will get up in it a velocity of 100 ft. per second.

6. Given the two connected weights in an "Atwood machine," determine the tension on the connecting cord.

MR. LESLIE.

7. Describe the apparent annual motion of the Sun in the heavens, and explain its effect upon the seasons.

8. How is the velocity of light computed by means of the aberration of light? What apparent motion does aberration give to a star in the ecliptic ?

9. How are the obliquity of the ecliptic and the positions of the equinoxes determined?

10. A body is projected up a rough inclined plane with a velocity due to the height h; the inclination of the plane is 60°, and the angle of friction is 30°; find the height of the plane.

II. An inelastic body impinges on another of twice its mass at rest; show that the impinging body loses two-thirds of its velocity by the impact.

12. Given the velocities of two bodies estimated in any direction, find the velocity of their centre of gravity estimated in the same direction.