III. What are the Laws of Thought, and Canons on which the special rules of syllogism are founded? IV. What do Logicians understand by a Dilemma? How may its validity be tested by Aristotle's "Dictum ?" Give an example. V. Consider shortly Sir W. Hamilton's doctrine of the quantification of the Predicate, and say whether or not you consider it an improvement in formal logic, giving your reasons. VI. State exactly the meaning of the term Induction. Professor Bain remarks that "the semblance of Induction is put on by certain operations purely Deductive." What instances of such are given by him? VII. Enunciate the canon of the Joint Method of Agreement and Difference, and illustrate its application. VIII. How does a plurality of causes affect the experimental methods, and how may a case of plurality best be dealt with? What "further circumstance" is noticed by Professor Bain as working to invalidate the operation of the methods? IX. What is a chance coincidence? How may we determine what coincidences are due to chance and what not? Give examples of the practical utility of the doctrine of averages. X. The full scope of the Deductive method comprises three operations. What are these ? XI. What is meant by an empirical law, and what are the chief criteria of such ? FRIDAY, 18TH FEB., 2 TO 5 P.M. MORAL PHILOSOPHY. W. E. ORMSBY, M.A. LL.D. I. In what sense does Professor Bain use the phrase "Moral duties"? By what two kinds of motives are they enforced? II. What is Professor Bain's answer to the objection that the principle of Utility contains no motives to seek the happiness of others? III. The immediateness of the judgments of the Moral Sentiment has been adduced as a proof of its intuitive character. Give Professor Bain's view, and his illustrations of it. IV. How does Butler show that self love and the particular passions, appetites, and affections are totally different? V. "To do mischief is not the end of envy, but merely the means it makes use of to attain its end." Whence the necessity of this remark to the argument in the first sermon on human nature? Write down as nearly as you can Butler's own summary of that sermon. VI. "Language itself," says Butler, "should teach people another sense of the words following nature, than barely acting as we please" ? VII. What does Butler say regarding the connection between our ideas of wickedness and of punishment? Whence comes it that one class of actions regarded as of good desert is less noticed than another? VIII. What is Mackintosh's Theory of Conscience? If you have not read Mackintosh, state briefly your own views on the subject. IX. Write a short outline of the contribution of Scotland to the Theory of Ethics during the 18th century. X. Select for a more detailed and critical examination the Ethical writings of any one philosopher mentioned in your answer to the preceding question. FRIDAY, 18TH FEB., 10 A.M. TO 1 P.M. E. P. METCALFE, M.A. I. Enunciate the Theorem called the Parallelogram of forces, Assuming that it is true for the direction of the resultant when the forces are commensurable, prove that it is also true when they are incommensurable. II. Show how to find the centre of gravity of a system of heavy particles lying in one plane. If weights of 1, 2, 3, 4, 5, 6, lbs. be placed in order at the angular points of a regular hexagon determine the position of their centre of gravity and its distance from the centre of the figure. III. Prove that any system of forces acting in one plane can be reduced to a single force, and a single couple, A straight line is drawn parallel to one side of an equilateral triangle through the intersection of the straight lines which bisect the angles. If the sides of the quadrilateral thus formed taken in order represent a system of four forces in direction and magnitude, find the moment of the couple necessary to maintain the system in equilibrium. IV. In a system of pullies where there are two blocks and the same string passes round all the pullies, determine the relation between the power and the weight. What force must a man exert in order to sustain himself by means of the rope and pullies-if his weight be W and n the number of strings at the lower block. V. Distinguish between stable and unstable equilibrium. If a heavy cone rests upon a horizontal cylinder-determine the relation between the height of the cone and the radius of the cylinder that the equilibrium may be stable. VI. Investigate the conditions of equilibrium when a body rests upon a rough plane. A uniform beam whose length is 27 lies horizontally upon a rough cylinder at right angles to the axis. Show that the greatest weight that can be attached to one end without causing the beam to slide is 1 Wrtan μ 1 l-r tan μ where W is the weight of the beam, r the radius of the cylinder, and μ the coefficient of friction. VII. If s be the space described from rest by a particle under the action of a uniformly accelerating force ƒ in time t establish the equation If 32 be the measure of the accelerating force of gravity, when a foot and a second are respectively the units of space and time, find the unit of time when the measure of gravity is 24 and the unit of space is one yard. VIII. Show that a body projected in any direction which is not vertical and acted upon by the force of gravity will describe a parabola. An elastic ball is projected from the ground, and at its greatest height strikes a vertical wall. After one rebound upon the ground it reaches a point just half way between the wall and the point of projection, determine the coefficient of elasticity. IX. Show how the height of a mountain may be determined by means of a pendulum. If a seconds pendulum taken to the top of a mountain loses 10 oscillations in 24 hours, find the height of the mountain. FRIDAY, 18TH FEB., 2 TO 5 P.M. N.B.-The answers in Astronomy should be illustrated by figures. I. Define the measure of the density of a body. Obtain the equation IV Jp V. If 20 lbs. be the unit of weight, 4 ft. the unit of length, and second the unit of time, what is the density of the standard substance compared with that of water in the equation W = JPV? II. If two liquids that do not mix together meet in a bent tube, the heights of their upper surfaces above their common surface will be inversely proportional to their densities. A fine tube, bent so as to have two straight arms, rests with each arm inclined at an angle 30° to the vertical, and contains equal . volumes of two liquids of densities p and 2 p, find the vertical height of their common surface. What will be the height of the common surface when it is turned through an angle of 30° in the plane passing through the tube ? III. The pressure of a given quantity of air at a given temperature varies as the space it occupies. (Prove for compression only.) Find the depth to which a diving bell in the shape of a right hollow cone must be immersed in order that the water may rise within to of the height of the bell. IV. Describe Smeaton's air pump, and find the density of the air in the receiver after n strokes. If the top of an open jar receiver be tightly covered with a piece of skin capable of bearing a pressure of 3 lbs. to the square inch, how many strokes can be made before the skin breaks, supposing the pressure of the atmosphere to be 15 lbs. per square inch, and the ratio between the volumes of the cylinder and the receiver to be 1:9 ? =33 47712. Given log. 2 = 30103, and log. 3 V. Explain how the difference of altitude of two stations above the level of the sea can be found by means of the barometer, and find an expression for this difference. Apply the expression when the heights of the barometer are 20 and 25 inches respectively, and the constant of variation 01. 37 66 VI. Define the terms, "Declination circles," Right ascension," "First Point of Aries," and "Hour angle." VII. State Kepler's laws, and apply them in accounting for:(a.) The difference between mean and solar time. (b.) The variation in the apparent diameter of the sun. (c.) The greater the radius of a planet's orbit, the less is its velocity. VIII. (a.) What must be the declination of the sun, so that, at a place situated 58° N. lat., twilight may continue all night? (b.) What is meant by nutation? How is it produced, and how are astronomical observations affected by it? IX. Show that there cannot be more than three lunar eclipses in the year. X. Find the geometrical focus of a pencil of rays after direct refraction at a spherical surface. Ex. refractive index = 3 ; rays incident on a concave mirror whose radius is 5 ft.; distance of the geometrical focus from the centre of the mirror = 10 ft. What is the nature of the incident rays ? XI. When a pencil is refracted through a prism in a principal plane, find the deviation of its axis, |