7. Assuming that the specific heat of saturated steam is negative, prove that dry saturated steam becomes superheated by adiabatic compression.

8. If the characteristic equation of a certain substance

be

are small fractions of the same order, shew that the difference of its two specific heats is approximately

1. A large concave and a small convex mirror have a common axis with their reflecting surfaces opposed, as in Cassegrain's telescope.

Determine, in terms of their curvatures and distance apart, the position of the principal focus of the combination.

2. Give Cornu's construction for the spiral curve expressing the effect produced at an external point by a plane wave; and shew from it that this effect is (very approximately) half of that due to the first half-period element.

3. Describe the experiments of Fizeau and Foucault on the interference of rays whose relative retardation is large; and shew how the difference of path in their experiments is calculated.

4. Prove that when ordinary light is incident on a transparent surface the intensities of the rays reflected and refracted at the polarizing angle are in the ratio

(μ2 — 1)2: (μ2 + 1)2 — — (μ2 — 1)2

where μ denotes the refractive index.

Hence find the value of μ for which both rays will be polarized.

5. Give a full account of Jamin's mode of comparing the intensity of the light reflected by metal with that of the light reflected by glass.

6. Explain fully the function of the sounding board in musical instruments.

7. Shew how to compare the degrees of consonance for different musical intervals, the harmonic series for all the notes being supposed complete.

ELECTRICITY AND MAGNETISM.

The Board of Examiners.

1. If a small charged body be placed in front of an infinite slab of uniform dielectric (Sp. Ind. Cap. =K) bounded by a plane face, determine (a)

F

the nature of the electric field both within and without the dielectric, (b) the force between the dielectric slab and the charged body.

2. Describe, with full experimental detail, the mode of measurement of a very small electric resistance.

3. Describe the construction of some good form of Clark's cell, and give an accurate method of determining the relation between its E. M.F. and its temperature.

4. Describe Maxwell's method of comparing two inductances; indicate the practical difficulties inherent in the method, and shew how these are obviated by Niven's modification.

5. If a harmonic E.M.F. operate on a circuit consisting of a coil possessing inductance and a condenser in series with it, determine the pulsating current and the amplitude of the potential difference at the condenser terminals.

6. Prove that the magnetic potential, due to a uniformly magnetised sphere, at any external point is

M cos 0
p2

where M denotes the magnetic moment of the sphere, and are the polar coordinates of the point, referred to the centre and the radius parallel to the direction of magnetisation.

Hence shew that Biot's hypothesis is equivalent to the assertion that the earth is a uniformly magnetised sphere.

7. A uniform magnetic flux N passes through a drum-wound armature which has n conductors closed in series; prove

(a) If the armature be rotated with uniform angular velocity w, the E.M.F. generated is

wn N

Σπ

(b) If the armature be supplied with current Y, the torque generated is

yn N

π

SPECIAL COURSE-HEAT.

The Board of Examiners.

1. Describe fully the construction and mode of employment of Boys's Radiomicrometer, and give some estimate of its order of sensitiveness.

2. Describe some good method of determining the calorific power of gaseous fuel.

3. Discuss the two principal methods of determining J, and shew how the difference between their results may be explained.

4. Determine the form of reversible cycle to which the behaviour of a condensing steam-engine most nearly approximates, and obtain an expression for its efficiency.

5. Obtain a formula expressing the Joule-Thomson thermal effect as a function of the temperature for a substance whose characteristic equation is

6. Express the difference between the latent heat of fusion of a salt and its latent heat of saturated solution (at the same temperature) as a function of the vapour pressures of solution and solvent.

7. Define "Free Energy."

Deduce from the properties of the free energy an expression for the E.M.F. of a simple liquid cell in terms of the concentrations of the solutions and their vapour pressures.

8. Discuss the theoretical basis of Stefan's Law of Cooling.

PRACTICAL EXAMINATION.-FIRST DAY.

The Board of Examiners.

1. Determine by Kundt's method the value of Young's modulus for the given substance.

2. Find the value of Poisson's ratio for indiarubber.