SECOND PAPER.

PROFESSOR CARBERY.

1. Describe the causes, course, and result of the war between France and Savoy during the reign of Henry IV. 2. Give a brief account of-(a) Marshal Biron; (b) CinqueMars; (c) Louvois.

3. Trace the progress of the war between France and Spain from the conclusion of the Thirty Years' War to the Peace of the Pyrenees.

What advantages accrued to France from this peace? 4. Give an account of the risings and final overthrow of the Huguenots during the reign of Louis XIII.

5. Give the names of the principal French generals engaged in the war of the Spanish Succession. Briefly describe the military operations of the French in Italy during this war.

6. Sketch briefly the leading features in the history of Russia from the Mogul conquest to the end of the line of Ruric.

7. Give an account of the origin of the Swiss League. Mention some of the battles gained by the Confederates in defence of their liberty.

When was their independence formally acknowledged ? 8. Describe the foundation of the Kingdom of Sicily. Explain the expression Kingdom of the Two Sicilies.' 9. Write notes on—(a) Gustavus Vasa; (b) Charles XII. of Sweden; (c) Bernadotte.

LOGIC.
SECTION A.

REV. PROF. DArlington.

1. Show how a statement may be expressed formally either as an A, an E, an I, or an O Proposition. Does this change of form involve any material change of meaning, and is its application of any practical value in Logic?

2. What is the special use of the Second Figure of Syllogism? Construct an example of a real argument (not in letters) in one of the moods of this Figure. Reduce Baroko both directly and indirectly.

3. Explain and discuss the following assertion :-' In a disjunctive proposition the positing of one alternative does not warrant the sublating of the other, though the sublating of one posits the other.'

SECTION B.

REV. PROF. WOODBURN.

4. Classify the Fallacies which are incident to Formal Reasoning, and give one example under each of your divisions.

5. Distinguish Induction from Probable Reasoning. Do we reach anything but Probability by the aid of the Inductive process?

6. Explain and give an example of the Method of Residues. Is it rightly called an Inductive' Method?

MATHEMATICS.

FIRST PAPER.

SECTION A.

PLANE GEOMETRY.

PROFESSOR DIXON.

[Logarithmic Tables supplied.]

1. Construct a square equal to a given polygon.

2. If two chords of a circle intersect within it, prove that the rectangle contained by the segments of one of them is equal to that contained by those of the other.

3. Construct one of the common tangents to two given circles, and indicate on figures the positions of all the common tangents in different cases.

4. In a given circle inscribe a rectangle whose length shall be twice its breadth.

5. In a right-angled triangle prove that the hypotenuse is divided by the perpendicular drawn to it from the opposite vertex into parts whose ratio is the duplicate of the ratio of the sides.

6. Four points are taken on a circle, and the six lines joining them are drawn. Prove that the rectangles contained by two pairs of these, rightly chosen, are together equal to the rectangle contained by the other pair.

(b) x2 + 2x + √2x2 + 4x + 9 = 13.

8. The sum of an arithmetical progression of six terms is 12 and the sum of the squares of its terms is 94. Find its first and last term.

9. Find the number of different words that might be formed out of the letters of the word cataract taken all together. Find also the number of different words of seven letters that might be formed.

10. Prove the expansion according to the binomial theorem of (1 + x)" when n is a positive integer.

11. A boy lodges £1 in the bank on his seventh birthday, and a similar amount on each succeeding birthday until his twenty-first when he draws all that stands to his credit. Find, to the nearest sixpence, how much he should get if the bank allows him compound interest at the rate of 2 per cent. per annum.

SECOND PAPER.

PLANE AND SPHERICAL TRIGONOMETRY AND SOLID GEOMETRY.

SECTION A.

PROFESSOR BROMWICH.

[Logarithmic Tables supplied.]

1. Given a, b, A in a plane triangle ABC, find a quadratic for c, proving the formula.

Show that this quadratic may lead to two, one, or no admissible values for c; and explain how to distinguish between the cases. Given a = 35, b + c = 57, A = 32°, solve the triangle completely.

=

2. P, Q, A, B are four points in one plane; the angles PAB, QBA are right angles, PBA = 50°, QAB 40°, the distance AB = 1200 feet: find the distance from A of the point of intersection of PQ and AB.

3. Find the radius of the circumcircle of a triangle ABC in terms of a, b, c.

Prove that the diameter of the circumcircle which passes through A is divided by BC in the ratio tan B tan C: 1.

4. In a spherical triangle C = 90°, prove that

cos A cos a sin B.

Solve the triangle, given a = 30°, b = 50o.

5. Prove that the shortest distance between two given straight lines (not in one plane) is perpendicular to each of the lines; explain how to construct such a line.

A is a fixed point, PBQ is a fixed plane to which AB and a second fixed line CD are perpendicular; a variable line through meets the plane in P, and the shortest distance between AP and CD is RS. If the rectangle BP. RS is constant, prove that P must lie on one of two fixed lines (which are parallel to each other).

SECTION B.

PROFESSOR MCWEENEY.

6. If R and r, are the radii of the circumcircle of a triangle and of the circle escribed to side a, show that

If the circumcircle of a triangle is the same size as one of the escribed circles, prove that the cosine of one of the angles of the triangle is equal to the sum of the cosines of the other two.

7. Prove that, in a trihedral angle, the sum of any two of the plane angles is greater than the third.

Prove that the sum of the angles in a gauche quadrilateral is less than four right angles.

8. If two spheres intersect show that their common section is a circle. Express the radius of this circle in terms of the radii of the spheres and the distance between their centres. 9. Prove that in a spherical triangle

Infer by means of the polar triangle the formula for tan ja in terms of the angles.

10. In a spherical triangle = 78°, B = 84°, C = 100°, find the sides.

MATHEMATICAL PHYSICS.

FIRST PAPER.

PROFESSOR MORTON.

1. Show that three forces acting in the sides of a triangle can never be in equilibrium, and that four forces in the sides of a parallelogram will be in equilibrium only when the forces are proportional to the sides in which they act.