MIXED MATHEMATICS.

Examiner-MR. W. BOOTH, B. A.

1. When a particle is in motion in any curve, find its accelerations along, and perpendicular to the tangent, (a) a particle projected with a velocity u is acted on by a force which produces an acceleration f in the plane of motion inclined at an angle a to the direction of motion, find the intrinsic equation of the curve described and shew that the particle will be moving in the opposite direction to that of projection at the time

3. If v vv" be the velocities at three points P, Q, R, of the path of a projectile where the inclinations to the horizon are a a― B, - 28, and if tt' be the times of describing PQ, QR respectively, 2 cos 8

a1

then v't vt' and +

4. A particle being acted on by a central force, determine the polar differential equation of the orbit. If the nth pedal of a rectangular hyperbola be taken with reference to the centre of the Shew that this pedal will be the orbit of a particle moving

curve.

5. A particle descends a rough circular tube from the extremity of a horizontal diameter if it stops at the lowest point then

6. A vertical cylindrical vessel contains four fluids A, B, C, D, which do not mix, when will the pressure on the curved surface (D) be equal to the sum of the pressures on the curved surfaces A, B, C. 7. Prove completely the equation p Ap (1+ at). If V be the volume in litres, p the pressure in millimetres of mercury, t tempera

=

mine the numerical value of this constant to four places of decimals. 8. Write an explanatory note on the expressions, "steady motion", parallel sections", "equation of continuity" obtain the equation in the form

CHEMISTRY.

Examiner-MR. JOHN ELIOT, M. A.

1. Give an outline of the methods used in the condensation 10 of the so-called permanent gases and explain why the older attempts were not successful.

2. Phosphorus is by some chemists classed as a triad and by 10 others as a pentad element. What are the arguments used to support each assertion, and what is the value of the arguments used?

3. Potassium Chloride, Bromide, and Iodide are present in a 8 single solution. How would you recognize the presence of each constituent ?

4. A solid substance contains the following ingredients. 12 NA CL, NA, HPO4, CA (NO3)2, SIO, AG NO3, and BA SO1. Explain how you would analyse it qualitatively.

5. Give an outline of the metallurgy of iron and steel and explain the chemical actions involved.

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6. What is meant by the theory of phlogiston and who was its author. How far was the theory consistent with facts?

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7. Give a short history of the development of the theory of 10 'compound radicals."

8. Starting with the elements Carbon and Hydrogen, de- 12 scribe a series of synthetical processes by which you can produce alcohol and acetic acid without the use of any compound of organic nature.

9. Give the constitutional formulæ both symbolic and graphic 10 of the following compounds: Ethyl Lactic Acid, Glycol, Allylic Alcohol, Tartaric Acid, and Benzole.

=

10. The quantitative analysis of a gas suspected to contain, 12 ethyl hydride, carbon monoxide and hydrogen gave the following data Vol. of combustible gas 32. Contraction on explosion with excess of O 46 Vol. of CO2 produced 17. What is the percentage composition of the gas by volume?

HEAT.

Examiner-MR. JOHN ELIOT, m. a.

1. State the two laws of Thermodynamics. Also examine briefly the evidence on which they are based.

2. Define a reversible cycle. Sketch briefly the series of operations which occur in a closed reversible cycle in the order adopted by Clerk Maxwell. Deduce Sir William Thomson's general expression for the work done by a reversible engine of finite range

where T and t are the extreme temperatures, H the heat taken in, and Carnot's function of the temperature.

μ

4.

is zero for any closed reversible cycle.

is a perfect differential for any portion of

Give thermodynamic reasons for the adoption of Thomson's scale of absolute temperature. Also prove that assuming the laws of Boyle and Charles, and that no change of temperature occurs when air expands without doing external work the scale will agree with that of the air thermometer.

5. Prove the following properties of perfect gases:

1st. The intrinsic energy is a function of the temperature only. 2nd. The ratio .of the elasticity of constant entropy to that of constant temperature is a constant.

3rd. The specific heats of constant temperature, and pressure are functions of the temperature only (and independent of pressure and density).

6. Prove Avogadro's law that the number of molecules in unit of volume of gases depends only on the pressure and density and not on the nature of the gas. Prove also the law of the equal dilatation of gases by means of the molecular theory of gases

7. State clearly what is meant by surface or superficial tension and superficial energy of a surface film of liquid.

Explain the rise of liquid in a fine capillary tube, and prove that the height to which the fluid rises is inversely proportional to the radius of the tube.

8. State the chief results of Dulong's and Petit's experiments to determine the law of cooling by radiation of bodies, and thence deduce the mathematical expression for the rate of cooling, viz.,

R = k x 1·0077o (1·0077′ — 1) where is the temperature of the

enclosure, and the excess of temperature of the hot radiating surface, and k a constant depending on the nature of the body.

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MAGNETISM, &c.

Examiner-MR. JOHN ELIOT, M. A.

Define thermal conductivity.

Find the law of permanent distribution of heat in a rectangular prismatic bar (whose length is infinite) immersed in a medium of zero temperature, and the extremity of which is kept at a fixed temperature (T).

2. Investigate the potential and strength of field at any point along the axis of a circular voltaic circuit.

3. Find the potential at any external point of a thin magnetic, shell in which the magnetization is everywhere perpendicular to the surface.

4. Sketch the methods usually adopted for determining the dip azimuth and intensity of the action due to terrestrial magnetism at any point on the earth's surface.

5. Find the strength of field at any external point due to a uniformly magnetized sphere.

6. Describe the general effects of charge and discharge in submarine cables.

7. State briefly what you know of the phenomena of Diamagnetism. Adduce some proof that the force of diamagnetism is a polar force.

8. Write a short essay on one of the following subjects :1st. The Degradation of Energy.

4th. The value and uses of hypotheses in Physical Sciences.

ELECTRICITY.

Examiner-MR. JOHN ELIOT, M. A.

1. Find the capacity, density at any point, and energy of a very long and thin cylinder (radius a) at potential A, enclosed in a coaxial cylinder (radius b) at potential B, and of equal length (7.) What change would be made in the formulæ if the space enclosed between the cylinders was occupied by a solid dielectric instead of air.

2. Explain what is meant by an electric image. Employ the method of Electric Images to determine the density of the electrical distribution on an infinite conducting plate at zero potential under the influence of an electrified point.

Find the position of the electric image in the case of a sphere at zero potential under the action of an electrified point (internal or external).

3. Prove in any way Poisson's differential relation connecting potential and density, viz. :

Also obtain the general surface relation at any point on the surface of a conductor R1 cos e + R2 cos 2 + 4 πσ = O where R, and R, are the resultant forces, and the argles which their directions make with the normals drawn on either side of the surface.

4. Prove that the potential energy of a conductor charged to potential V is QV, where Q is the quantity of the electrical charge.

5. Prove that there is one and only distribution of electricity over any equipotential surface due to an electrified system which will produce on all external electrified particles the same action as the given electrified system.

6. Prove that the surface density at any point of a freely electrified spheroid or ellipsoid varies as the distance of the tangent plane from the centre.

7. State Ohm's Law.

Employ it to obtain Kirchoff's equations for determining the currents in any branch of a net work of linear conductors.

8. Describe briefly Wheatstone's bridge. Find the condition which must be satisfied in order that the diagonals may be conjugate to each other.

9.

Obtain the following expression for the indnced current produced by the movement of any conductor in a magnetic field

Current strength

=

Number of lines of force added

Resistance of circuit

State clearly and illustrate the positive direction of lines of force, and of currents which you adopt in the formula.