3. Define the terms dew-point, relative humidity, and explain how you obtain the latter from the former.

4. Describe fully the experiments you would make, and give the calculations necessary for determining the apparent expansion of mercury in glass.

5. Show that the intensity of the illumination due to light received from a spherical luminary whose intrinsic brightness is μ, at a point from which the luminary subtends a cone of semi-vertical angle a, on a surface the normal to which makes an angle 0 with the axis of the cone is equal to sin2

μπ

a cos 0.

6. Give a geometrical construction for the path of a ray of light through a prism, and by its means prove that the deviation is a minimum when the ray passes symmetrically through the prism; and a maximum when the ray enters or leaves one face of the prism perpendicularly to that face.

7. Define the coefficient of elasticity for a gas.

What is its value for a gas at constant temperature, and what is its value under the circumstances which occur in the propagation of sound?

8. In what way do variations of temperature affect the pitch of the note given by

(1) an organ-pipe,

(2) a piano-wire?

Give reasons for your answer.

9. Describe how to compare the moments of two magnets by a statical method, and prove any formulæ required.

10. It is required to reduce the sensitiveness of a galvanometer whose resistance is 100 ohms to one-sixth, and at the same time to supply it with an outside resistance which shall render its total resistance in circuit the same as before. What should be the resistance of the shunt, and of the compensating resistance ?

11. State the law which determines the quantity of heat generated by a given electric current in flowing through a conductor of given resistance.

Two cells have internal resistances, each equal to 3 ohms. In one case they are joined up in series with a wire of 3 ohms resistance in the external circuit. In another case they are joined up in parallel with the same wire in circuit. Compare the total heat evolved in the two cases respectively, and show in each case its distribution between cells and wire.

12. Give a sketch showing the connections of batteries, keys, galvanoscopes, relays, sounders, &c., at both ends of a telegraphic line (Morse system), the sounders being worked by local currents.

NATURAL PHILOSOPHY.-PART II.

PRACTICAL EXAMINATION.

The Board of Examiners.

Candidates may select any SIX of the following experiments, and will be asked to perform not more than THREE of those selected.

1. Determine the ratio of the circumference and diameter of the given circle.

2. Verify Hooke's Law for the given spring.

3. Find the boiling point of the given liquid.

4. Determine the latent heat of steam.

5. Find the focal lengths of the two given lenses.

6. Determine, by the method of reflexions, the radius of curvature of a convex surface.

7. Find the magnifying power of the given telescope when used for the examination of a distant object.

8. Verify the inverse square law for like magnetic poles.

9. Determine the magnetic dip.

10. Determine, by the P.O. Box, the resistance of the given conductor.

AA

11. Determine the resistance of the given coil by the simple substitution method.

12. Arrange the apparatus needed to produce a pure spectrum on the screen.

NATURAL PHILOSOPHY.-PART III.

The Board of Examiners.

1. Describe Regnault's method of determining the specific heat of a gas at constant pressure.

State the results he arrived at by his experi

ments.

2. A given mass of a perfect gas is allowed to expand into a perfectly empty vessel; determine the change in its entropy.

3. Ifλ be the latent heat of change of state expressed in work units, and v the increase in volume of the unit mass of the substance after passing from one state to the other, prove that—

λπυθ

dp
do

where p is the pressure and 0 the temperature.

4. Define the terms "plane of incidence," "plane of polarization," "principal plane of a crystal."

State and explain the relations between the principal plane in Iceland spar, and the planes of polarization of the two refracted rays.

5. Describe Fresnel's rhomb, and the method of using it to obtain circularly polarized light.

6. Light polarized in a plane perpendicular to the plane of incidence, falls on the plane surface of a transparent medium at an angle of incidence p. Making the same assumptions as Fresnel, if the amplitude of the incident ray be unity, that of the reflected ray will be

tan (-)

tan (+)

where is the angle of refraction.

Hence explain Brewster's law for the polarizing angle.

7. Prove, completely, from first principles, that the force just outside a charged conductor is equal to Απρ.

8. Prove, completely, from first principles, that the magnetic force near the centre within a very long helix, carrying a current C, is equal to 4n C, where n is the number of turns of the helix per linear centimetre.

9. Give, as fully as you can, the reasoning by which it is established that the E.M.F. of induction round any circuit is equal to the rate of decrease of the number of magnetic lines of force which pass through the circuit in the positive direction.

10. Describe the construction of an alternate current transformer, and explain its theory in general

terms.

Describe briefly the high-tension system of electric lighting, and explain its advantages and disadvantages.