7. Describe and give the theory of Carey Foster's method of determining accurately the difference between the resistances of two nearly equal coils.

What important constant is generally determined by this method, and how?

8. A galvanometer, a resistance p, and a battery of resistance B, are joined up in circuit, a shunt S being across the terminals of the galvanometer. A deflection of the galvanometer is produced, and it is found that when the resistance p is increased to p', and the shunt S diminished to S', the same deflection of the galvanometer is produced. Show that the resistance of the galvanometer is

9. Explain what is meant by sympathetic resonance.

Describe Koenig's system of resonators and the mode in which it is employed to determine the harmonics that accompany a fundamental note on a particular instrument.

10. Give a short account of Helmholtz's theory of vowel sounds, and the experimental evidence he adduced in favour of it.

What part in speech do the consonants play, and how can your statement be verified?

11. If r and r' be the distances of radiant point and

image on the axis of any mirror (concave or convex), and fits focal length, prove the formula

rr' = ƒ2.

Explain, with the assistance of diagrams, how this formula is applicable to all cases.

12. Prove the formula

1 − 1) = ( ~ − 1 ) ( − 1 ).

d D

State and explain the convention as to signs which renders this formula applicable to all kinds of lenses.

NATURAL PHILOSOPHY.-PART II.

PRACTICAL EXAMINATION.

The Board of Examiners.

1. Find the volume of the given ball by calculation and by displacement.

2. Find the radius of curvature of the given spherical surface.

3. Find the mean radius of the given capillary tube. 4. Determine g by means of a simple pendulum.

5. Determine the specific gravity of the given solid.

6. Determine Young's modulus for the given wire by stretching.

7. Determine the coefficient of friction for the given solids.

8. Determine the velocity of sound by resonance, and correct your result for temperature.

9. Determine the focal length of the given lens.

10. Determine the magnifying power of the given telescope.

11. Determine the candle power of the given lamp.

12. Determine the coefficient of expansion of the given solid.

13. Determine the specific heat of the given solid.

14. Compare the magnetic moments of the given magnets.

15. Calculate the constant of the given galvanometer.

16. Find the resistance of the given coil.

NATURAL PHILOSOPHY.-PART III.

The Board of Examiners.

1. Prove that the potential energy of a mass m, with respect to the earth at an infinite distance from it, ismgr, where r radius of the earth.

If we receive from the sun 27 calories per second on a square centimetre directly exposed, find what mass of meteors falling in a year from an infinite distance would supply this:

Gravity at sun's surface

28 g.

Radius of sun = 700,000 kilometres.

Distance from earth to sun = 148,000,000 kilometres.

2. Describe Forbes's method of determining the conductivity of a metal.

3. Prove the formula for the efficiency of a perfect engine.

Why is it that the efficiency of a good gasengine is greater than that of a steam-engine?

4. A given mass of a perfect gas is allowed to expand into a perfectly empty vessel; determine by how much its capability of doing work is diminished.

5. Find the distribution of electricity on a conducting sphere connected with the earth and under the influence of an external electrified point.

6. Describe the sliding condenser, and prove the expression for its change of capacity as the inner cylinder is moved through a given distance.

Describe fully how the capacity of such a condenser for any position of the movable cylinder is accurately determined.

7. Give an account of Rowland's investigation of the magnetic properties of iron.

8. Describe the construction and discuss the relative advantage of

(a) Ring and drum armatures.

(b) Open coil and closed coil armatures.

9. Describe a transmission diffraction grating, and how to use it to determine the wave length of sodium light.

Give the elementary theory of the grating.

10. A parallel beam of plane polarized light is passed through a solution of sugar and an ordinary prism, and examined through an analyzer. Describe the phenomena seen, and show how to make the experiment so as to determine the relation between the rotation of the plane of polarization and the wave length of the light.

NATURAL PHILOSOPHY.-PART III. AND B. Sc.

PRACTICAL EXAMINATION.

The Board of Examiners.

1. Determine the moment of inertia of the given system.

2. Determine, making all corrections, the volume of the given solid.

3. Find Young's modulus for the given substance.

4. Determine the refractive index of the given prism.