short time. I should like to possess it. Cæsar is reported to have said that if he could gain me over all would be well, but I fear the stress of public opinion, like Hector in the Iliad.

Translate the following passage into Latin Verse:—

When Hector saw his brother Polydore
Writhing in death, a mist o'erspread his eyes;
Nor longer could he bear to stand aloof,
But sprang to meet Achilles, flashing fire,
His keen spear brandishing; at sight of him
Up leaped Achilles, and exulting cried:

Lo! here the man who most hath wrung my soul,
Who slew my loved companion; now methinks
Not long upon the pass of war shall we
Stand separate, nor each the other shun.

Then with stern glance to godlike Hector thus:
Draw near and quickly meet thy doom of death.

LORD DERBY's Iliad.

Translate the following passage into Greek Prose :

You must remember, men of Athens, that not only justice, but interest, urges you to come to our assistance. For if you look on passively, while others are gaining for themselves a great empire, you will yet bitterly repent your sloth and folly. It is idle and absurd to say that our enemies are not at war with you, and therefore should not be attacked without just cause. For while they are professedly our antagonists, they are really yours, since they are opposed to you in interests, and are moreover your rivals in the contest for the presidency over Greece. You may then accomplish two most desirable objects by now assisting us, for you will both put us under a lasting obligation to you, and augment your own power.

Candidates will select one of the following passages for translation into Greek Verse. Preference will be given to Hexameters :—

Awakening up, he took her hollow lute,-
Tumultuous, and, in chords that tenderest be,
He played an ancient ditty, long since mute,
In Provence called "La belle dame sans mercy:"
Close to her ear touching the melody;
Wherewith disturbed, she uttered a soft moan:
He ceased-she panted quick-and suddenly

Her blue affrighted eyes wide open shone :

Upon his knees he sank, pale as smooth sculptured stone.

Leading the way, young damsels danced along,

Bearing the burden of a shepherd's song;

Each having a white wicker overbrimmed

With April's tender younglings: next, well trimmed,

A crowd of shepherds with as sunburnt looks

As

may
be read of in Arcadian books;
Some idly trained their sheep-hooks on the ground,
And some kept up a shrilly mellow sound
With ebon-tipped flutes; close after these,
Now coming from beneath the forest trees,
A venerable priest, full soberly,

Begirt with ministering looks; always his eye
Steadfast upon the matted turf he kept,
And after him his sacred vestments swept.

Logics.

KEATS.

MR. TARTLETON.

1. What is Whately's theory with respect to the nature of mathematical truths?

Show that it is erroneous.

Sir John Herschel, as quoted by Whately, is much more correct in reference to this subject?

2. How does Whately endeavour to reconcile Man's free will with God's foreknowledge? In this discussion he misapplies the word selfcontradiction? He makes use of an expression as strong as would be adopted by a Necessitarian?

3. Give an example of a proposition containing no ambiguous word which may have several distinct meanings. How are these meanings related?

4. Does Whately mean by Reasoning any inference of one assertion from another? How does he try to show that one premiss is not sufficient to warrant a conclusion?

5. What account does Whately give of the Doctrine of Realism, and of the circumstances which tended to foster it? What passage does he quote from Aristotle to show that he was not a Realist ?

6. Give Whately's classification of Fallacies. How does he treat them? 7. Is it ever possible to draw a conclusion from two premises, neither of which has the middle term universal ?

8. What is the meaning of Murray's definition of Philosophy?

9. Show that in Reductio ad impossibile subcontrariety cannot be legitimately employed.

DR. WEBB.

1. State Reid's Rationale of Perception. Stewart mentions a circumstance which it is necessary to state in order to render Reid's doctrine on that subject satisfactory?

2. State Stewart's Theory of Conception. His Theory of Memory would seem to be inconsistent with his Theory of Conception; how is this objection to be removed?

3. Enumerate the Principles of Association. Show in what manner the Association of Ideas has a tendency to warp our speculative opinions. Point out the operation of the same principles on our principles of Action and our Moral Judgments.

4. Point out the difference between Hypothetical and Inductive Theories. Show that Hypothetical Theories have been unjustly censured. What is the Proviso which regulates their use?

5. Give Addison's Theory of Imagination; Burke's Theory of Poetic Pleasure; and Stewart's criticism on the Theory of Burke.

6. What are the different causes which produce facility of Recollection as we advance in the Sciences?

7. D'Alembert mentions what he calls "one of the most curious phenomena of the mind" in connexion with the Sensation of Colour; how does Condillac explain this phenomenon?

8. The Hypothesis of Impressions is not so absurd as the Hypothesis of Images; it is, nevertheless, the more puerile and nugatory of the two? 9. Locke has been charged with inconsistency on the subject of Efficient Causes?

MR. ABBOTT.

1, 2. Discuss the character and origin of our ideas of—

(a). Duration;
(b). Infinity.

3. State Locke's views of our notions of moral good and evil.

4. Show that the idea of spirit has no more difficulty than that of body.

5. Discuss the chief abuses of words, and their remedies.

JUNIOR FRESHMEN.

Mathematics.

A.

DR. STUBBS.

1. A variable circle passing through a given point, and cutting a given segment of a fixed line harmonically, passes also through a second fixed point on the line connecting the given point with the centre of the given segment.

2. When a number of circles have a common radical axis, every line intersects with them at as many pairs of points in involution.

3. Every two circles invert into two whose radii have a constant ratio from any point on a third circle coaxal with themselves.

4. If a quadrilateral be inscribed in a circle, a circle described on the third diagonal cuts the given circle orthogonally.

5. If the opposite sides of a quadrilateral intersect at fixed points, and three of its angles move on fixed lines passing through a point, the fourth angle will describe a given straight line.

6. A quadrilateral is inscribed in a circle, a right line cuts the curve and the opposite sides of the quadrilateral in six points in involution.

MR. TOWNSEND.

7. Prove that every circle cutting two of the three diagonals of a quadrilateral harmonically cuts the third also harmonically.

8. Show that any one of the six anharmonic ratios of four collinear points, or concurrent lines, determines the remaining five.

9. Given three pairs of corresponding points of two homographic systems on a common axis, determine the two double points of the systems. 10. Prove that, for two homographic systems of points on a common axis, the interchangeability of a single pair of correspondents involves that of every pair.

11. Apply the method of homographic division to inscribe in a given circle a triangle whose sides shall pass through given points.

12. Apply the method of inversion to describe a circle passing through a given point, and cutting two given circles at given angles.

MR. LESLIE.

13. Prove that the polars of a point with respect to the angles of a triangle intersect the opposite sides in three points which are on the same right line.

14. Determine the formula by which to calculate the length and position of a segment which cuts two segments of a right line harmonically. 15. If three lines passing through a point intersect a circle, prove that the lines joining the six points so found to any other point of the circle form a pencil in involution.

16. Prove that the pencils formed by connecting two of the vertices of two triangles which are self-reciprocal with respect to a circle with the remaining four have equal anharmonic ratios.

17. Determine the centre and radius of the circle which is inverse to a given line or circle.

18. A variable circle passes through the vertex A of a given angle, and through a fixed point 0; prove that the intercepts AL and AM on the sides of the angle are connected by a relation of the form

p. AL+q. AM = r. AO.

B.

DR. STUBBS.

1. Find the values of x and y from the equations

3. Reduce to the form of a continued fraction, and find the series

351 965

of convergents.

4. Prove that log z=2M {

5. Prove the geometrical proposition from which the sine of 36° is determined, and find it to three places of decimals.

6. Prove that the sum of the radii of the escribed circles of a triangle exceeds the radius of the inscribed circle by four times the radius of the circumscribed circle.

7.

MR. TOWNSEND.

Prove the formula for sin a in terms of sin 2a; and explain the reason of the four different values of the former corresponding to the same value of the latter.

8. Prove De Moivre's theorem for positive integers; and deduce from it the formula for the tangent of the sum of any number of angles in terms of the tangents of the several angles.