STEWART, LOCKE, AND COUSIN.

1. Give Stewart's account of the views of Aristotle, Locke, Malebranche, Berkeley, Condillac, and Voltaire on the vision of distant objects. Discuss his criticism of Aristotle's remark, and of Locke's theory.

2. What were the controversies carried on concerning the origin of language? Consider the views of Locke, Leibniz, Smith, and Rousseau, and the difficulties raised by them.

3. Stewart totally misunderstands Kant when he endeavours to show that he was anticipated by Cudworth? He was naturally misled by the explanation of Willich ?

4. Cousin criticizes four points in the third book of Locke's Essay; discuss the soundness of his arguments.

5. Give an abstract of Cousin's argument against representative ideas. 6. Locke's views on Law and on Moral Ideas? In his reply to Lowde's objections, he makes a remarkable statement concerning innate ideas?

MAC CULLAGH PRIZE EXAMINATION.

THEORETICAL DYNAMICS.

PROFESSOR JELLETT.

1. Show that the proof of Poisson's theorem

(a, b) = const.

extends to all cases, whatever be the number of independent variables. 2. Determine the form of the integral which, combined with any one of the equations of areas, will give the illusory result

0=0

3. If two integrals, when combined, give an illusory result, any two combinations of them, when similarly combined, will also give an illusory result.

4. Calculate the value of the function

(y, a)

in the case of the problem of rotation, where y, a are the angles which determine the position of the invariable plane.

5. If a, b, c,... ...k, be the arbitrary constants which enter into the integration of a system of differential equations, prove Lagrange's formula for the variation of any one of them, k, sc.

a, ß, &c., λ, μ, &c., being the initial values of the independent variables, and of their differential coefficients with regard to the time.

6. Determine the value of the disturbing function to the second approximation, and show that if the first approximation contain no nonperiodic terms, no such terms will appear in the second approximation.

7. If a trajectory can be described freely under the action of a force A, and also under the action of a force B, it can also be described freely under the combined action of A and B, where A and B severally satisfy the condition

Xdx + Ydy + Zdz = a perfect differential.

MR. TOWNSEND.

1. Investigate the law of the motion of a system of bodies termed by Sir W. Hamilton the principle of varying action; and state exactly what other principles of motion necessarily hold or fail with it.

2. Give Sir W. Hamilton's statement of the ordinary principle of stationary action, as he has termed it; and show, as he has done, that, though theoretically contained in, it is practically useless as compared with, that of varying action.

3. The seven ordinary first integrals of the equations of motion of a free system of bodies, subject only to their mutual actions, are necessarily involved in, and result immediately from, the principle of Sir W. Hamilton's theory; verify this.

4. For such a system of bodies determine, as he has done, the characteristic function V1 of their relative motion round their centre of gravity; and investigate the law of its variation in the form given by him.

5. Explain fully the mathematical grounds on which Jacobi considered the second partial differential equation, to be satisfied by the characteristic function, as encumbering Sir W. Hamilton's theory.

6. For the particular example of the elliptic undisturbed motion of a planet round the Sun, give Jacobi's investigation of the values of and t in the forms given by Sir W. Hamilton.

SUPPLEMENTAL DIVINITY EXAMINATION.

JUNIOR CLASS.

PROFESSSOR'S LECTURES.

1. State, in the words of Scripture, the principles which Natural Religion must involve.

2. The à posteriori argument for the existence of God may be stated in a form more satisfactory than that given by Reid?

3. What is the essence of all forms of Pantheism ?

4. On what does the consciousness of our existence as persons depend? 5. Two errors are usually committed by religious writers on the subject of the origin of evil?

6. Give any one of the popular objections to the efficacy of prayer. 7. How should you reply to this objection?

8. How is the name of Antiochus Epiphanes connected with the preservation of the Hebrew Scriptures?

9. The Christian Scriptures were exposed to a similar danger?

10. That Greek was spoken vernacularly in Palestine in the days of our Lord appears from more than one historical consideration?

11. Show distinctly how the fixing the date of the composition of the Gospels may be used as a conclusive reply to the mythical hypothesis of Strauss.

12. What account does M. E. Rénan givę of the origin of the belief in our Lord's Resurrection?

13. This suggestion is in contradiction to the entire narrative of the facts as recorded in the New Testament?

14. What aspect of the predictive element of prophecy may be illustrated by the history of David at Keilah?

15. What is the criterion of Vincentius of Lerins of what is Catholic doctrine ?

16. In what sense must the relations which subsist between the Persons of the Trinity always be understood?

17. What modern form of heresy may be refuted by bearing this consideration in mind?

18. What modern religious error has sprung from the usual reaction which followed the rejection of the Adoptionist Heresy by the Council of Frankford ?

19. What aspect of the doctrine of the Atonement has been supposed to be cleared up by the notion of "Imputation"?

20. How far is S. Anselm's view of the Atonement open to criticism?

ECCLESIASTICAL HISTORY.

1. Give a brief sketch of the leading facts in the life of S. Gregory Nazianzen.

2. What are the dates of the Four Ecumenical Councils?

3. Define accurately the heresies which were condemned by each Council.

4. State the true doctrine as to the Person of Christ in opposition to both Nestorianism and Eutychianism.

5. Give some account of the acts of Constantine which were most favourable to the establishment of Christianity.

6. State the names and dates of the Emperors who, before Constantine, had been friendly to the Church.

7. Define accurately Pelagianism and Semipelagianism. What do you mean by "Preventing Grace" ?

8. What was the Synod known as the "Latrocinium"?

9. What was the case of S. Hilary of Arles?

10. What illustrations of "Puritanism", strictly so called, do we meet in the history of the early Church?

COMPOSITION.

Develope the doctrine which may be inferred from the strict meaning of the following words :

"The Son of Man came not to be ministered unto, but to minister, and to give His life a ransom for many."-S. Matt., xx. 28.

EXAMINATION IN CIVIL LAW.

PROFESSOR ANSTER.

1. Give the definition of Usufruct which you find in the Institutes, and explain the meaning of that definition.

2. Use and Usufruct are distinguished in the Roman System; say how. 3. The proposition in the English Law that a "Use cannot be limited on a Use," is but one case of a more extensive proposition of the Roman Law; state that proposition.

4. A certain class of Servitutes were called Servitutes prædiorum; why are they so called?

5. You are told of pupillaris substitutio in a Roman father's will; explain this fully.

6. "Non solum autem Proprietas per eos quos in potestate habetis acquiritur vobis sed etiam Possessio." Explain this sentence. How is it that there should be more difficulty, as the statement seems to imply, in the supposition of a slave acquiring possession for his master than property?

7. State a case in which a slave acquires possession for his master.

8. The general principle, on which the distinction between acquiring property or possession for his master or owner depends, is not violated in the seemingly exceptional case in which possession is acquired for such master or owner; explain this.

9. A slave made heres in a will is the property of another master at the time adeunda hereditatis; to whom does the hereditas belong? To the person who was his master at the time of the will being made, and whom we may suppose the testator to have known to be his owner?-or to his owner at the time adeunde hereditatis?

10. In whom is the property in navigable rivers stated to be in the Institutes?

11. What is Justinian's statement of the property in the banks of navigable rivers?

12. The sea and its shore are said to be communia omnium; rivers are said to be publica. Explain the words communia omnium and publica so as to exhibit the distinction, if any.

13. The sea shore-litus maris-is said to be commune omnium. This is stated in the Institutes with a real or seeming exception; give the statement as you find it in the Institutes.

.

14. Explain the words res nullius. There are two distinct applications of the phrase, having important effects on property and its acquisition; define and describe each.

15. To what principle does Justinian refer the original right of property?

16. How many heirs may there be in a Roman testament? State the language of the Institutes on the subject.

17. Give Justinian's definition of Derelict.

18. The second book of the Institutes commences with the words, "Superiore libro de jure Personarum exposuimus; modo videamus de Rebus, quæ vel in nostro patrimonio vel extra nostrum patrimonium habentur." What is meant by the words, "in nostro patrimonio vel extra nostrum patrimonium habentur" ?

19. What is meant by the words, "res universitatis"?

20. Property acquired without the regular Roman form of sale, was said to be not "in dominio" but "in bonis" of the purchaser. When a fixed time had elapsed, it was the purchaser's "in dominio"-his (to use their language) by "usucapio." To have "usucapio" commence, there should be "bona fides" and "justa causa." Explain "bona fides."

21. Explain "justa causa" in detail, exemplifying the meaning which the words are intended to express.

22. "Error falsæ causæ non parit usucapionem." Explain this.