pressure corresponding is 1.0136 dynes per sq. cmr. Hence find the value of k for dry air at 0° C.

5. Give a general explanation of the action of oil in stilling waves of water.

or 5. What is Surface Tension? How is it measured? How much will the surface of mercury be depressed in a glass tube of 0.5 mm. diameter, the surface tension of mercury being 418 dynes per cmr. at 20° C., its density 13.54, and the cosine of the angle of contact 0·703?

HEAT.

6. In determining the specific heat of solids by the method of mixture, how are the thermal capacities of the calorimeter and of the thermometer obtained and allowed for? Construct an example in general terms.

or 6. State the circumstances upon which rate of cooling depends. How is cooling practically allowed for in elementary laboratory experiments on heat? Justify the method.

7. Which equation expresses more accurately the law of Charles, VV, (1 + at) or V = V。 (1 + a)? How did Regnault use the former to determine a, and what are his principal conclusions?

or 7. Write down the connexion between the pressure intensity, volume, and absolute temperature of a given mass of gas.

A quantity of dry air contained in a cylindrical vessel 1 ft. long, closed by a moveable piston, is

at atmospheric pressure and at temperature of 80° F. If the piston be pushed down 3 inches and the temperature reduced to 40° F., what will the pressure of the air be? How will the result be affected if the air be moist?

8. Give the theory of freezing mixtures with an example.

or 8. What is meant by the Isothermals of a body? Shew that, with the usual convention as to axes of pressure and volume, they slope downwards from left to right for a stable substance.

9. A platinum sphere 3 inches in diameter and a copper sphere 1 inch in diameter are heated to the same temperature and allowed to cool; which will cool faster? The radiating powers of platinum and copper are as 17 to 7, their densities as 21 to 9, and their specific heats as 1 to 3. or 9. Steam enters the condenser at a temperature of 212° F., and the water pumped out to the boiler has a temperature of 110° F., while the temperature of the injected water is 60° F. What quantity of water must be supplied for each pound of steam which enters the condenser, the latent heat of steam at 212° F. being 966-6?

MAGNETISM AND ELECTRICITY.

10. Define unit pole and magnetic field intensity. Find the dimensions of the latter and the factor for converting it from the ft. gr. sec. system of units to the c.g.s. system. E.g., the value of H in the former system for Melbourne is at present 5·1, find the number representing it in the latter system.

or 10. Describe with calculation the method of surveying a magnetic field by observing the oscillations of a small compass needle.

11. Define the absolute and the practical units of Electric Capacity. Find the capacity of a given sphere in terms of each unit, e.g., that of the earth assumed to be a sphere of radius 4,000 miles.

or 11. Find the energy of electrification of a condenser of capacity C raised to a potential V from zero by a charge Q.

12. The poles of a voltaic cell, E.M.F. 2 and resistance 1, are connected by two wires whose resistances are 2 and 3 respectively. Find the strength of the current in each wire.

or 12. A current is to be sent through a wire whose resistance is 10 Ohms, by a battery of 20 cells, each of which has an E.M.F. of 1 Volt and a resistance of 2 Ohms. How should the cells be connected so as to give the strongest current ?

13. If two points at different electric potential be joined by a conductor, a current will flow from one point to the other. Illustrate this by an experiment with a sheet current, and shew how equipotential lines might be marked out on the sheet.

or 13. Describe and explain the "Loop test" for determining a fault between two stations on a telegraph line connected by two wires.

NATURAL PHILOSOPHY.-PART III.

Professor Andrew.

Candidates must not answer each of two alternative questions.

Candidates must shew some knowledge in each division of the paper, and a satisfactory knowledge in two divisions.

DYNAMICS.

1. State, and for uniplanar forces prove, the principle of the conservation of Static Energy,

and enumerate the classes of forces which may be omitted in applying the principle.

or 1. Find the tension at any point of a common catenary in terms of a length of the uniform chain. If a smooth flexible string be suspended over two smooth cylindrical pegs, prove that the free ends will rest at the same level.

2. Define the Moment of Inertia of a body about a point and about a straight line. Write down that of a circular disc of given mass about a normal through its centre and about a diameter. Find that of a right circular cone of given height and radius of base about a generating line.

or 2. A vertical beam of rectangular cross section, length a, breadth b, depth c, has the lower end fixed, and is strained by a force P applied at the upper end in a direction_parallel to b. The modulus of rupture is s. When on the point of rupture 6Pascb2. Assuming this, prove that a horizontal beam of oak 6 in. wide, 1 ft. deep,

supported on two points 10 ft. apart, will bear on it a brick wall 9 in. thick and less than 114 ft. high without breaking, the modulus of rupture of oak being 10,032 lbs. weight per sq. in., and a cubic foot of brickwork weighing 112 lbs.

3. State d'Alembert's principle, and shew how to apply it to determine the motion of a body about a fixed axis when acted on by any given forces.

A perfectly rough circular horizontal board is capable of revolving freely round a vertical axis through its centre, and rests on a smooth horizontal table. A man whose weight is equal to that of the board walks on and round it at the edge; when he has walked once round the board what will be his position on the table?

or 3. Describe the construction and mode of using Kater's pendulum to determine g. Shew how it may be used when the times of vibration are very nearly equal and the position of its centre of mass is also approximately known.

4. Explain fully why in the University Ballistic Pendulum the frame is prolonged beyond the axis of suspension and carries a lump of lead. or 4. The vertical half ring of a gyroscope is made to rotate about its vertical axis; the inner ring, carrying the revolving disc, then rotates about its horizontal axis. Explain this fully.

HEAT AND LIGHT.

5. Describe and explain fully an experimental method of determining the value of y.

or 5. Define a wave. Describe any form of wave