2. What is meant by the angle of friction? A ladder with a man standing on it, rests, at a given slope, between the ground and a vertical wall. Being given the coefficients of friction at the ends of the ladder, give a geometrical construction to find the range of possible positions for the common centre of gravity of the ladder and the man.

3. A hemispherical shell, made of sheet metal, is closed by a plane base of the same material. Find the centre of gravity of the whole.

4. State the law connecting the tension and the length of an elastic string, pointing out within what limitations it holds true.

A number of equal heavy particles are fastened at equal intervals along an unstretched elastic string-one particle being at an end of the string. If the string now hangs vertically, with this end down, show that the distances between the particles will form an arithmetical progression. The weight of the string itself is supposed to be neglegible.

5. A horizontal plane, carrying a weight, is moving with acceleration ƒ in a direction inclined to the horizon at an angle a. If the weight does not slip on the plane, find in direction and magnitude the reaction between them. What condition must be satisfied in order that the weight may remain in contact with the plane?

6. A weight is attached by a string to a fixed point, and whirls in a vertical circle round this point. Show that the difference of the tensions of the string, when in any two given positions, is independent of the rate at which the weight revolves.

7. Define the coefficient of restitution.' Explain how you could findits value from observations of (1) the angles of incidence and reflection from a smooth vertical wall of a particle moving on a horizontal plane; (2) the heights of successive hops of a ball let fall on a floor.

8. Find an expression for the angle at which the corner of a bicycle track should be banked up to make it safe for a rider going round at given speed.

9. Two particles are vibrating with simple harmonic motion, the one having twice the frequency of the other. If they pass through the centres of their swings with the same velocity, find the ratio of their amplitudes.

10. A projectile is discharged at elevation a with velocity u. Find the time at which the distance described horizontally from the starting-point is equal to that risen vertically above it. Interpret your result for cases where a < 45°.

SECOND PAPER.

PROFESSOR BERGIN.

1. A rectangle is immersed in a fluid, with a side in the surface; divide it by a horizontal line into two parts, on which the pressures shall be equal.

2. A triangular plate is immersed vertically with its base in the surface of a fluid: determine the moment of the fluid pressure on either face round the base.

3. Define the metacentre.

the stability of a ship?

How does its position affect

4. Deduce the relation connecting the distances of conjugate points from a double convex lens.

5. What is the condition that a combination of two thin prisms of different kinds of glass should be achromatic?

6. Describe an astronomical refracting telescope, and deduce a formula for its magnifying power.

7. Find the distance of the Sun in miles, being given that its parallax is 8.8".

8. What is meant by precession of the equinoxes?

9. Define sidereal, apparent solar, and mean solar time.

10. Explain any method of finding the difference in longitude of two stations on the Earth.

EXPERIMENTAL PHYSICS.

FIRST PAPER.

MR. HENRY.

1. Describe some experimental method of measuring the coefficients of friction of solids, and explain how the laws of friction may be demonstrated.

2. State the law of universal gravitation and explain the evidence on which it rests.

3. Describe some method of illustrating the existence of surface tension in liquids.

4. How do you account for the fact that faint taps on one end of a long beam of wood may be heard without much loss of intensity at the other? What circumstances would tend to interfere with this audibility?

5. Give an expression for the velocity of sound in any medium. Explain the form the expression takes for the case of air, and state how the velocity calculated from it agrees with that found from observation.

6. Explain resonance. Point out how it is exemplified in the case of an organ-pipe and of a piano, and note any points of difference in the two cases.

7. Describe an astronomical telescope giving details of the construction of the optical parts.

8. How would you measure, experimentally, the proportion of a beam of light transmitted by a plate of glass?

9. Explain the terms dispersion,' 'anomalous dispersion,' and irrationality of dispersion.'

10. Show, with the aid of a diagram, how a real image of an object may be formed by means of a combination of a concave and a convex lens, the concave lens having the shorter focal length, and trace the rays fixing the position of the image.

SECOND PAPER.

PROFESSOR MCCLELLAND.

1. Describe how to construct and use an air-thermometer for measuring temperatures.

2. State and explain in what respects the phenomenon of boiling differs from that of evaporation.

3. Describe how you would determine the pressure of saturated water vapour at a temperature of 50° C.

4. Describe a method of determining the mean coefficient of expansion of mercury between 0°C. and 100° C.

5. Explain the action of the electrophorus. How is it consistent with the conservation of energy that an unlimited charge can be obtained from the electrophorus after once electrifying the insulating part?

6. Enumerate the differences in magnetic properties of soft iron and steel. What bearing have these differences on their practical applications?

7. Explain clearly why the current in a circuit does not rise instantaneously to its maximum value when the circuit is closed.

8. With two cells each of E.M.F. 1.5 volts and internal resistance 0.5 ohm, what is the greatest current that could be produced through a resistance (a) of 10 ohms, (b) of 0·1 ohm ?

9. How is light obtained from electrical energy in (a) the arc lamp, (b) the incandescent lamp?

10. Describe the construction and action of some form of electric motor.

PRACTICAL PHYSICS.

1. By means of the apparatus provided, verify the principle of Archimedes.

2. Find the dew-point.

3. Find the focal length of the given concave lens.

CHEMISTRY.

[All Chemical changes must be expressed both in words and by equations. Candidates who neglect this instruction will not receive full credit for their answers.]

SECTION A.

PROFESSOR LETTS.

1. Calculate the atomic weight of a metal from the following data:

(a) Composition of one of its oxides-Metal, 21 parts by weight: Oxygen, 8 parts by weight.

(b) Specific heat, 0.114.

(e) Isomorphism of the oxide whose composition is given above, with spinelle ruby.

2. Describe two methods for obtaining washing soda from common salt.

3. Give two methods for preparing pure phosphoretted hydrogen, and two for preparing the impure gas. What renders the latter spontaneously inflammable, and how may it be removed?

SECTION B.

PROFESSOR RYAN.

4. How would you show that the formula for sulphurous acid anhydride is SO2?

5. Write equations representing the action of

(a) Sodium hydroxide on sodium acetate.
(b) Copper on sulphuric acid.

(c) Tin on nitric acid.

(d) Zinc on nitric acid.

(e) Chlorine on slaked lime.

6. Contrast the elements chlorine and manganese.

h