4. Describe and give the theory of the optical method of determining the focal length of a spherical mirror of small curvature.

5. Show that two thin lenses in contact achromatise if their focal lengths are of opposite signs and directly proportional to the dispersive powers of

their material.

6. A parallel beam of homogeneous light falls on a screen. If a straight fine wire be interposed in the path of the beam, determine the effect on the

screen.

7. Determine, by Cornu's method, the illumination produced by light diffracted at a grating.

8. Give a short account of Kundt's investigations on anomalous dispersion.

9. Describe fully how to determine the directions and the relative magnitudes of the axes of an elliptically polarized ray.

10. Describe some good form of polarimeter, and show how, by its means, the rotation of the plane of polarization may be accurately determined. Why is it that a pair of Nicol's prisms are unsuitable for this experiment?

NATURAL PHILOSOPHY.

ELECTRICITY AND MAGNETISM.

The Board of Examiners.

1. Discuss the application of the terms conservation and incompressibility to electricity, citing and explaining fully what fundamental experiments seem to you to justify the application.

Criticise the expression inertia of electricity.

2. Determine the distribution of electricity on the surface of a conducting sphere connected with the earth due to the presence of an electrified point external to it.

3. Describe fully and give the theory of Thomson's Absolute Electrometer.

4. Describe fully any accurate method for determining the specific inductive capacity of a dielectric.

5. Prove that the capacity of any number of cordensers joined together in cascade is equal to the reciprocal of the sum of the reciprocals of their respective capacities.

From three one-third microfarad condenser. how many condensers of different capacities ca;1 be obtained by combining them?

6. Show that the equation of motion of a ballistic galvanometer needle making small vibrations can be put in the form

Prove that the vibrations are isochronous, and show how to determine the values of

from observations of the swinging needle.

K and

μ

7. Prove that the line integral of magnetic force round a closed path that embraces a wire carrying a current C is 4 C.

A circular ring of non-magnetic material and rectangular section, the edges of the section being parallel to the plane and axis of the ring and equal to 2x and 2y respectively, is uniformly wound with wire all round the ring as a continuous helix. If there be n turns of wire per linear centimetre of the mean circumference of the ring, and if a be its mean radius, prove that the total number of magnetic lines that traverse the ring, due to a current C in the wire, is equal to

8. Describe how to compare two very low resistances. Give the theory of the method.

9. Give a short account of thermo-electric phenomena. Describe how a thermo-electric diagram is constructed, and show how to obtain Tait's formula

E = X (t2 — t2) ( (Th)

for the thermo-electric power.

2

10. Describe how to compare the coefficients of self induction of two coils, and give the theory of the method.

NATURAL PHILOSOPHY.

SPECIAL COURSE-ELECTRIC LIGHTING.

Professor Lyle.

1. Describe the construction of an open coil and of a closed coil armature.

Explain the action of each, and discuss their relative merits.

2. Describe the construction, and give the theory, of a constant potential compound-dynamo.

3. Obtain the theoretical formula for the efficiency of a transformer;

or

Describe an experimental method of determining the efficiency of a transformer.

4. Describe the three-wire system, and the alternatecurrent transformer system of electric lighting.

5. Describe Cardew's volt meter, and any form of alternate-current meter.

6. Draw up a complete plan for lighting both streets and houses of a small town, say of half-a-mile radius.

7. A large house is lighted on the continuous current plan, the current being supplied from the city mains. Describe fully what devices are necessary, and how they are arranged in order to secure safety to property and person.

8. Describe fully how to determine the insulation resistance of an installation.

N.B.-The first three questions count double.

of

NATURAL PHILOSOPHY.-PRACTICAL.

FIRST DAY.

The Board of Examiners.

1. Examine the accuracy of ruling of a diffraction grating.

2. Determine Poisson's ratio for indiarubber.

3. Determine the specific gravity of pumice, making

all corrections.