FIRST PAPER.

N.B.-Only 14 questions to be answered.

1. Define the following terms: wave, equal times, radian, weight, dyntach, hydrometer.

2. Prove that the distances described in successive equal intervals of time by a body, which starts from rest and is uniformly accelerated, are as the odd numbers.

3. Give illustrations of mass and weight, (5 of each), which contrast with one another, to shew the difference between these two properties of matter.

4. A body of 6 lbs. pulls by its weight another body of 4 lbs. along a smooth horizontal table by means of a connecting cord; find the time taken to move through 965 feet, the distance described in the last second, and the tension of the cord.

5. A piece of platinum of 15 lbs. mass is attached to 10 lbs. of iron, and the whole is found to balance 1 lb. in mercury (s.g. 13.6); the platinum by itself balances 6 lbs. in mercury; find (1) the specific gravity of the platinum, (2) the s.g. of the iron, (3) the weight in water of the iron.

6. Find in dyntachs the rate at which a fire-engine works, which discharges 10 kilograms of water per second with a velocity of 1500 tachs.

7. Enunciate Newton's third law of motion: give 4 illustrations of it: how can it be said that Newton in this law laid the foundation of the science of energy?

8. Determine the loss of visible kinetic energy when two spheres without rotation impinge directly. What becomes of it?

9. Define a dimensional equation. Write down the dimensional equations of angular velocity, energy, angle, pressure-intensity, and density.

10. Three bodies P, Q, R, of masses 30, 15, and 10 kilograms respectively, are connected by strings AB, and BC, whose lengths are 5 m., and 70 cm. Q, R, BC, and half of A Blie on the edge of a table vertically under a peg, over which the other half of AB is placed holding P. If P be now allowed to fall freely, find the motions of P, Q, and R, the tensions of the strings after both become stretched, and the measures of the impul sive tensions which set and Rin motion.

Friction and the masses of the strings may be neglected, and g = 980.

11. The dimensions of a room are 10 metres, 5 m., and 8 m.; find the difference between the mass of air in the room when the temperature is 10° and pressure 78 cm., and when 20° and pressure 73 cm.

12. Steam at 100° and 76 cm. pressure is forced into a mass of snow at 0°; how many grams of snow are melted by a gram of steam?

13. What is meant by a space being saturated with aqueous vapour? Define the dew-point and explain how it is practically determined.

14. Define temperature and thermal equilibrium. Enunciate the principle assumed in the measurement of temperature.

15. Enunciate the laws of reflection and refraction of radiant energy.

16. What is the aberration of light? How can the velocity of light be determined by it?

17. Define totul reflection. Find the relation between the critical angle and index of refraction.

18. Trace the path of a ray of white light through a prism. What is dispersion of light?