VI.-HISTORY OF MODERN PHILOSOPHY.

Professor Laurie.

1. How was Descartes led, by his consideration of the characteristics of mind and body, to the doctrine of animal automatism?

2. What, according to Spinoza, is the constitution of

person

the human mind? How is the belief in ality affected by his doctrine on this subject?

3. What was Locke's project in his Essay concerning Human Understanding? Show the historical significance of his statement that all knowledge springs from experience.

4. By what arguments did Berkeley seek to show that distance, and real magnitude and situation, are not immediately discerned by sight? Show the connexion between this discussion and his theory of Idealism.

5. Explain the nature and importance of Hume's criticism of the relation of Cause and Effect.

6. Show the historical significance of Reid's contention that judgment and belief precede the apprehension of simple ideas.

7. State Leibniz's doctrine of a hierarchy of monads, and trace the process by which he arrived at

this doctrine.

8. Write a short Essay on the office of criticism in philosophy as conceived by Kant, referring to his attitude towards his predecessors.

SCHOOL OF MATHEMATICS.

MATHEMATICS.-PAPER I.

The Board of Examiners.

Write Essays on not more than three of the following subjects:

(1) Conditions of convergence in the differentiation and integration of series.

(2) The sine-, cosine-, and exponential- integrals. (3) Approximate calculation of definite integrals. (4) The expansion-theorem in spherical harmonics. (5) Discrimination of stationary integrals.

MATHEMATICS.-PAPER II.

The Board of Examiners.

Write Essays on not more than three of the following subjects:

(1) Determination of the chief points and lines of the general conic in trilinears.

(2) The generators of the hyperboloid of one sheet.

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(3) Umbilics and the lines of curvature in their neighbourhood.

(4) A solid of curves.

(5) Curvatures of twisted curves and surfaces expressed in general curvilinear coordinates.

MATHEMATICS.-PAPER III.

The Board of Examiners.

Write Essays on not more than three of the following subjects:

(1) Ordinary differential equations of the first

order.

(2) Solution of linear differential equations by means of definite integrals.

(3) Bessel's equation.

(4) Simultaneous linear partial differential equations with constant coefficients.

(5) Jacobi's last multiplier.

MATHEMATICS.-PAPER IV.

The Board of Examiners.

Write Essays on not more than three of the following subjects :

(1) Astatics.

(2) The steady motion of chains.

(3) Cyclic systems in dynamics.

(4) The energy of gravitating matter.

(5) Potential solutions for circular cylindrical boundaries.

MATHEMATICS.-PAPER V

The Board of Examiners.

Write Essays on not more than three of the following subjects:

(1) The pressure in a moving fluid.

(2) Two-dimensional flow of liquid frem an orifice in a vessel with plane walls, when the pressure is given

(a) At the boundaries of the jet;

(b) Over the plane of the orifice.

(3) The general solution for the velocity of a liquid in which there is a given system of

vortices.

(4) Capillary waves.

(5) The waves of liquid in an oscillating rectangular trough.

MATHEMATICS.-PAPER VI.

The Board of Examiners

Write Essays on not more than three of the following subjects:

(1) The differential identities satisfied by the elements of strain whether infinitesimal or not.

(2) The general solutions for the uniform torsion and flexure of a cylinder—

(a) For an isotropic solid;

(b) For any æolotropic solid.

(3) The equilibrium of naturally curved and twisted wires under terminal forces.

(4) The propagation of waves in an elastic solid. (5) Equipollent loads.