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University of St Andrews.

EXAMINATION FOR THE M.A. DEGREE.

APRIL 1876.

MORAL PHILOSOPHY.

1. State the great questions in Ethics.

2. Compare the moral systems of Socrates and Plato, shewing that the one system was the legitimate development of the other.

3. Give Aristotle's general definition of virtue, and his particular definitions of ávöpeia, owppooúmn, élevdepiorns, apaórns.

4. State the doctrine of the Stoics regarding God, and deduce from that doctrine their theories regarding Virtue, Pleasure, Free-will, and Death.

5. Give Hobbes's definitions of Good, Evil, Pity, Will; and estimate the value of his speculations.

6. What are the opinions of the following moralists regarding the essence of Virtue :-Cudworth, Clarke, Hutcheson, Mandeville, Hume, and Adam Smith ?

7. Describe the peculiar views of Mackintosh regarding Conscience, Will, and the Standard of Morality.

8. Enumerate the chief Utilitarian Philosophers in the order of Time, mentioning the chief Ethical Work of each.

9. State the principal arguments for and against Utilitarianism. 10. Summarise Smith's account of Licentious Systems.

11. Mention the various classes of outward influences which may modify the growth of Philosophical Theories ; and illustrate your remarks by reference to the life of a philosopher.

12. Classify duties.

13. What duties arise from man's relations to beings inferior to himself ?

14. Give some account of the growth of moral opinion regarding suicide.

15. Is the principle of final causes legitimately applicable in ethical research ? Give reasons and illustrations.

16. State all that you believe to be implied or assumed by the moralists who hold that the rightness or wrongness of actions is intuitively apprehended.

University of St Andrews.

EXAMINATION FOR THE M.A. DEGREE.

WEDNESDAY, APRIL 19, 1876.

NATURAL PHILOSOPHY.

(Answer eighteen questions.) 1. Enunciate the theorem called “the parallelogram of forces;” and, assuming it as regards the direction, prove it as regards the magnitude of the resultant.

Two forces which act at a point are inclined at an angle of 120°. If one force be doubled and the other halved, the direction of the resultant is turned through an angle of 60°. Compare the forces.

2. Define the moment of a force about a point, and show how it niay be represented by a geometrical construction

Prove that the algebraic sum of the moments of two forces which are not parallel, about any point in their plane, is equal to the moment of their resultant.

3. Find the centre of gravity of a triangular lamina (or triangle) of uniform thickness and density.

If the middle points of its sides be joined and the triangle so formed removed, show that the centre of gravity of the remaining mass is the same as that of the original triangle.

4. Determine the condition of equilibrium on a smooth inclined plane, (a) when the power acts parallel to the plane, (b) when it acts horizontally.

What was Stevinus's solution of the first of these problems?

5. Enunciate Newton's third law of motion. Give his own illustrations of the law. State the argument by which he proved it to be true for attractions; and describe the experiment by which he verified it in a case where two bodies attracted each other.

6. Unequal weights are connected by a string which passes over a pulley. Regarding the string as perfectly flexible and inextensible, and neglecting its weight and the inertia and friction of the pulley, determine the motion of the weights, finding their acceleration, tbeir velocity after a given time from rest, and the distance which they have described.

7. The times of descent down all chords drawn through the highest or lowest points of a circle in a vertical plane are equal, and the velocities acquired are proportional to their lengths.

Describe Newton's method of determining the Coefficient of Restitution in impact, and state the resulting law of impact.

8. State the law of transmission of pressure by a fluid.

Explain the construction and action of the Hydraulic Press; and determine its mechanical advantage.

9. The difference of pressures on a given small area at different depths in a fluid is equal to the weight of a column of the fluid whose base is the given area and whose height is the difference of depths.

Show how the principles of hydrostatics, involved in this and the preceding question, are needed to prove that the height of the column of mercury in a barometer is proportional to the pressure of the atmosphere.

10. Describe the construction and action of the common airpump.

If the volume of the barrel be {th of that of the receiver, show that after 4 strokes of the piston the density of the air in the receiver will be about half what it was at first.

11. Explain how the scales of thermometers are constructed so that the indications of the instruments shall be comparable.

Investigate a formula to express Fahrenheit in terms of Centigrade readings.

At what temperature do the Fahrenheit and Centigrade thermometers read alike?

12. Define unit of heat, capacity for heat, and specific heat ; and explain one of the methods by which specific heat is determined.

If 3 pounds of mercury at 100° C. be mixed with 1 pound of water at 0° C., and the temperature of the mixture be 9°C., what is the specific heat of mercury ?

13. Describe Joule's experiment by which he proved that when air expands without doing work its temperature remains sensibly unchanged.

What would happen if the air did work ?

Explain the formation of the clouds which seem to cling to the tops of hills, especially on the west coast of Scotland during westerly winds.

14. How was the velocity of light first determined ? Explain Fizeau's method of determining the velocity of light. 15. State the laws of the reflexion and refraction of light.

Explain what is meant by the Index of Refraction, and the Critical Angle.

16. Describe Oersted's fundamental experiment in Electromagnetism, and give Ampère's mnemonic rule regarding it.

17. Describe the construction and give the theory of the Tangent Galvanometer.

18. Define the Electro-static and Electro-magnetic Units of Electricity.

Deduce their dimensions in relation to the fundamental units of dynamics.

Candidates for the Neil-Arnott Prizes will answer the following

along with 12 of the preceding questions :19. Find the equation to the path of a projectile referred to horizontal and vertical co-ordinate axes.

Apply the equation to determine the direction of projection, with a given velocity, from one point, so that the projectile may pass through another given point.

Or, as an alternative, give a geometrical solution of the problem.

20. What instrument equivalent to the arrangement described in the preceding question No. 6 is employed to verify the laws of motion by experiment?

Assuming that the effect of the inertia of the pulley and friction wheels on the motion has been found by experiment to be equivalent to that of a mass 6 m, show how to adjust the masses of the moving weights so that their acceleration shall be successively a = 1, and a = 2, that of gravity being assumed to be g = 32.

These arrangements being made, describe experiments to verify the second law of motion.

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