7. Analyse the deductive and inductive processes, and discuss the function and value of the Syllogism in connection with both. to the views of Aristotle, Bacon, Whately, Hamilton and Mill.

Refer

8. Explain and exemplify the following technical phrases: Ground of Induction; Empirical Laws; Uniformities of Causation; Colligation of facts; Classification by Type; Joint Method of Agree ment and Difference; Method of Means; Experimentum Crucis; Argument from Analogy; Elimination of Chance.

9. "Why is a single Instance, in some cases, sufficient for a complete Induction, while in others, myriads of concurring instances, without a single exception known or presumed, go such a very little way towards establishing an universal proposition ?"

Give an outline of the answer to this question, and consider how far it solves the question of Induction.

10. Discuss the logical limits of the explicability of the Laws of Nature, and whether the methods of Empirical Science can attain to rational Certainty in their results. Does the present state of reasoned knowledge in the sciences furnish evidence of the ultimate rationality or the ultimate incogitability of the universe? Give reasons for your answers and refer to current speculations.

HISTORY OF PHILOSOPHY.
Examiner-REV. W. HASTIE, b. d.

[Only 6 questions to be taken.]

1. Explain the conceptions of the History of Philosophy advanced by Hegel and Lewes, and test their validity by reference to the movement of Greek Philosophy. Discuss the origin of the Greek Philosophy, point out the general influence which determined its development, and compare the chief systems briefly with the Hindu systems as regards their resemblances and differences.

2. Give a careful account of the philosophy of Heraclitus, its relation to previous systems, its special doctrines, and its influence upon subsequent speculation. State what you know of the life of Heraclitus, and refer to his literary remains, quoting any of them.

Or

Expound the Dialectic of Plato, giving its historical antecedents, the Dialogues in which it is unfolded, its essential relation to his philosophy and Aristotle's Criticisms upon it. Compare it with the method of Hegel's Logic.

Sum

3. Give an account of Aristotle's Metaphysics, referring to the parts and the unity of the work, its authenticity and name. marise his discussion of the principles of Being,' Form,' Matter,' 'Potentiality,' 'Actuality,' Causation,' First Mover;' and give an analysis of the first Book.

Trace the influence of Aristotle's Metaphysics on the Mediæval Schools and mention any differences between the Scholastic interpretations and those of recent Critics.

Or

Give an expository and critical account of the psychological doctrines of 1, Plato, 2, Aristotle, 3, The Stoics, 4, The Neo-platonists, pointing out in each case the theory held regarding the nature of the Soul and the origin and limits of Cognition.

4. Give an account of the Scholastic philosophies of the 11th and 12th Centuries as regards the questions at issue, the methods of Speculation, and the systems of Roscellinus, William of Champeaux, Anselm and Abelard. Shew how the questions at issue were dealt with by William of Occam, and estimate his influence upon the history of philosophy.

Or

Give an account of the Arabian Philosophy, as regards its origin method, leading expounders and systems, and permanent tributions to Philosophy.

con

5. Give a summary of the philosophical system of Spinoza, including its sources, method, psychology, ethics and theology. Give an account of his life and works, quote any of his principal definitions, refer to the criticisms of Leibnitz and others upon his system and trace its influence upon modern German speculation.

Or

Trace the development of Berkeley's philosophy through his various works, summarising the last of them. Discuss the validity of Reid's rendering of Berkeley's relations to Locke and Hume; and compare his idealism with that of Fichte.

6. Write a short paper on "The development and principles of Greek Scepticism and modern Agnosticism."

1.

ETHICS.

Examiner-REV. W. HASTIE, B. D.
[5 questions only to be taken.]

Define or describe Ethics, mention its leading questions and the divisions of a complete system, and distinguish it from Esthetics, Jurisprudence and Politics. Point out any important differences between the ancient and the modern Ethical systems, and account for these. Discuss briefly the Logic of Ethics, and criticise the methods and principles of Egoistic Hedonism, Intuitionism and Utili. tarianism.

2. Write concise historical and critical notes on the following expressions: Selfishness; Self-love; Benevolent affections; Moral Sense; Sympathy; Secondary Desires; Principles of action; Casuistry; Determinism; Liberty of Indifference; Heteronomy of the Will; Volitional Characters of feelings; Deontology; Duties of perfect and of imperfect obligation.

3. Give a brief sketch of the pre-Aristotelian attempts to form a theory of Virtue. State Aristotle's theory of Virtue, with some of his illustrations as given in his Ethics. Compare Aristotle's theory

with those of the Stoics and Epicureans; and reproduce Kant's Criticism upon it and give your own.

4. Write a summary of the politico-ethical system of Hobbes referring to his works; and consider how far it was influenced by the historical conditions of the time. Trace the controversy which it originated, down to Butler; and point out any new principies which it raised or established in Ethical philosophy.

Or

Contrast carefully the moral systems of Bentham and Kant, in regard to the essential principles of Ethics. Consider the causes of their differences, the validity of their methods, and their influence upon subsequent Ethical speculation.

5. Write a short historico-critical dissertation on any of the following subjects:

(1.) The immutability of moral distinctions in the light of empirical

variations.

(2.) Recent applications and the applicability of the theory of Evolution to Ethics.

(3.) Free-Will in relation to physical, logical, and historical Law.

PURE MATHEMATICS, II.

Examiner-MR. A. M. NASH, M. A.

1. The circle circumscribing the triangle formed by three tangents to a parabola passes through the focus.

2.

Determine the equation and lengths of the axes of the conic ax2 + 2hxy + by2 + 2gx + 2fg + c = = 0.

3. The locus of the poles of a given straight line, L, with respect to a series of confocal conics is a straight line, M, perpendicular to L. If a parabola be described having its focus at one of the given foci and touching L and M, its directrix will pass through the other focus.

4. The locus of the centres of all the rectangular hyperboles which can be described about a given triangle is the nine points circle of the triangles.

5. Find the equation of the asymptotes of the conic By = ka2, and obtain the condition for a rectangular hyperbola.

6. The product of the perpendiculars from any point of a conic upon the sides of an inscribed triangle ABC bears a constant ratio to the product of the perpendiculars from the same point upon the tangents to the conic at the vertices ABC.

In the circle this ratio is unity: hence obtain a property of the parabola by reciprocation.

7. What is meant by "inversion ?" The inverse of a circle with respect to a point is either a straight line or a circle.

Obtain a property of the circle by inverting the theorem-if A, B, C be three points in order upon a straight line AC 8. Investigate the loci

-

(1) x2 + 2xy + y2 — 2ax + bay + 5a2
(2) SkL

=

AB+ BC.

0, where s 0 represents a conic, and L =

0,

9. Determine the locus of a point from which three tangent lines, mutually at right angles, can be drawn to an ellipsoid.

10. Show that there are only five regular solids.

11. Define the osculating plane, and the binormal of a tortuous curve, and find their equations.

=

12. If the equation to a surface be z principal radii of curvature are given by the equation,

f(xy), prove that the

p2) t }

(1 + ) r2pqs+ (1 +

P √1 + p2 + q + (1 + p2 + q)2

=

The points of the surface 3a2 z x3 + y3 + 3 axy at which the principal curvatures are equal and opposite lie upon the surface

PURE MATHEMATICS, I.
Examiner-MR. A. M. NASH, M. A.

1. Find the number of homogeneous products of r dimensions that can be formed out of n letters.

Determine whether the following series is convergent or diver

2. gent:

a (a + b)p (a + 26)p

3. Find the number of integers which are less than a given number and prime to it.

If n be a prime number 7 3, n + n2 - n3 n is divisible by

5040.

4 Prove the following rule for determining the remainder when a very large number is divided by 37 :

Divide the given number into sets of three figures beginning from the right, as in cube root: add together all these sets, and divide the sum by 37: the remainder is the number required.

Sum to n terms the series

5.

6. ABCD is a quadrilateral inscribed in a circle; AB, BC meet

9. Sum to n terms the series whose nth term is

10. Explain Newton's method of determining the limits to the

roots of an equation.

Apply it to the equation 11. The equation 4

4x4 +7x3-15x + 20x 300 0. 4x3 + 8x2. ·9x + 3: = 0 has one root

between 1 and 2, find it to two places of decimals.

12. Show that the product of two determinants can always be expressed as a determinant. Write down (in the form of a determi nant) the product of

13. Any symmetric function of the differences of the roots of the equation

2. Prove that the problem of finding the nth convergent to a continued fraction in which the quotients recur can always be reduced to the summation of recurring series.