8. Consider the importance attached by Spencer to the subordination of proximate to remote satisfactions in the evolution of morality. 9. “From the dawn of life, then, egoism has been dependent upon altruism as altruism has been dependent upon egoism." Explain and comment. NATURAL PHILOSOPHY.- Part I. The Board of Examiners. No candidate is to attempt more than TEN questions. 1. Explain how the fundamental unit of time (the mean solar second) is arrived at. Explain the difference between solar and sidereal time. 2. State the triangle of forces. Describe fully the apparatus used, and the method of using it, to verify experimentally the triangle of forces. 8. Define work, and investigate by the principle of work the relation between the "power" and the “weight” in the case of a screw. 4. The diameters of the piston and the ram of a hydraulic press are 2 inches and 18 inches respectively, and the lengths of the arms of the lever working the piston are 2 inches and 18 inches. Find the load that can be supported by a force of 20 lbs. weight on the end of a lever. 5. A body which weighs 14 lbs. in air and 12 lbs. in water, floats in mercury whose specific gravity is 13.6. What proportion of its volume will be immersed ? 6. Reduce the temperatures 98o and — 37.8° on the Fahrenheit scale to the Centigrade, and also to the Absolute scale. 7. A bar A B of iron and a bar CD of zinc are placed perpendicularly side by side, the ends A and C resting on a firm horizontal plane. If AB be 6 feet long, what must be the length of CD so that the distance BD may be the same at all temperatures, the coefficients of linear expansion of iron and zinc being .000012 and .000029 respectively? 8. State and explain the inverse square law. (a) For radiant heat. 9. How do you explain the colour of bodies seen (a) by transmitted light, () by reflected light ? Define “ complementary colours,” and describe how you would demonstrate them experi mentally. 10. Describe an experiment to demonstrate that the electricity produced by a voltaic battery is the same as that produced by a frictional machine. 11. State the laws of the magnetic action of a voltaic current. Describe the tangent galvanometer, and how to arrange it to compare the strengths of two currents. 12. Describe fully the single needle system of tele graphy. Give a sketch showing the connections of galvanoscopes, commutators, batteries, &c., at both ends of a single needle telegraphic circuit. NATURAL PHILOSOPHY.-Part II. The Board of Examiners. No candidate is to attempt more than TEN questions. 1. State Kepler's Laws, and explain how they were applied by Newton to assist in establishing the law of gravitation. 2. Explain what is meant by surface tension, and describe any method by which it can be measured. Prove the formula 2T cos a h rpg for the capillary elevation in a small cylindrical tube, the letters having their usual significations. 3. Define the terms dew-point, relative humidity, and explain how you obtain the latter from the former. 4. Describe fully the experiments you would make, and give the calculations necessary for determining the apparent expansion of mercury in glass. 5. Show that the intensity of the illumination due to light received from a spherical luminary whose intrinsic brightness is i, at a point from which the luminary subtends a cone of semi-vertical angle a, on a surface the normal to which makes an angle o with the axis of the cone is equal to un sin? a cos 0. 6. Give a geometrical construction for the path of a ray of light through a prism, and by its means prove that the deviation is a minimum when the ray passes symmetrically through the prism; and a maximum when the ray enters or leaves one face of the prism perpendicularly to that face. 7. Define the coefficient of elasticity for a gas. What is its value for a gas at constant temperature, and what is its value under the circumstances which occur in the propagation of sound ? 8. In what way do variations of temperature affect the pitch of the note given by (1) an organ-pipe, (2) a piano-wire ? Give reasons for your answer. 9. Describe how to compare the moments of two magnets by a statical method, and prove any formulæ required. 10. It is required to reduce the sensitiveness of a galvanometer whose resistance is 100 ohms to one-sixth, and at the same time to supply it with an outside resistance which shall render its total resistance in circuit the same as before. What should be the resistance of the shunt, and of the compensating resistance ? 11. State the law which determines the quantity of heat generated by a given electric current in flowing through a conductor of given resistance. Two cells have internal resistances, each equal to 3 ohms. In one case they are joined up in series with a wire of 3 ohms resistance in the external circuit. In another case they are joined up in parallel with the same wire in circuit. Compare the total heat evolved in the two cases respectively, and show in each case its distribution between cells and wire. 12. Give a sketch showing the connections of batteries, keys, galvanoscopes, relays, sounders, &c., at both ends of a telegraphic line (Morse system), the sounders being worked by local currents. |