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6. A directs his carriage (which travels 8 miles an hour) to meet him at the station at 5.30. But he arrives at 4.25 and proceeds to walk (at 4 miles an hour to meet his carriage. At what distance from the station is he when he meets it?

7. Of two rooms of the same width one is a square. The sum of the areas of the two rooms is 64 square yards; and the sum of their lengths is 24 times their common width. Find the dimensions of the rooms.

8. Define duplicate ratio, mean proportional, continued proportion.

There are four numbers a, b, c, d, such that

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shew that is a mean proportional between a and c.

9. Find the square root of 94-12x3-2x2+4x+1, and of 2(x*+y1)+(x− y)2 {(x—y)2 — 2 (x2+y2)}.

THURSDAY, JUNE 12, from 9 to 11 A.M.

D. Mathematics. (Second Paper.)

1. Define-straight line, circle, straight line touching a circle, straight line placed in a circle; and write down Euclid's postulates.

2. If two triangles have two sides of the one equal to two sides of the other, each to each, and have also the angles contained by those sides equal to one another, they shall also have their bases or third sides equal; and the two triangles shall be equal, and their other angles shall be equal, each to each, namely those to which the equal sides are opposite.

3. If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.

4. If two circles touch one another externally, the straight line which joins their centres shall pass through the point of

contact.

5. Describe a circle about a given triangle.

6. In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle.

7. Divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.

8. In a circle the angle in a semicircle is a right angle; but the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

9. Describe an isosceles triangle, having each of the angles at the base double of the third angle.

10. Write down Euclid's definition of and axiom on parallel straight lines, and the enunciations of the first propositions in which each is used.

THURSDAY, JUNE 12, from 2.30 to 4.30 P.M.

D. Mathematics. (Third Paper.)

1. Prove the parallelogram of forces for direction.

E and F being respectively the middle points of the diagonals AC and BD of a quadrilateral ABCD, show that the resultant of forces represented by EB and ED is represented by twice EF.

2. Define centre of parallel forces; and, in the case of forces in one plane, find its distance from a straight line О in the plane, when the distances from OA of the points of application of the parallel forces are all given.

3. Find the centre of gravity of a triangle.

On opposite sides of the same given base are described an isosceles and an equilateral triangle; find the height of the

isosceles triangle when the centre of gravity of the whole figure is at the vertex of the other equilateral triangle which can be described on the same base.

4. The algebraical sum of the moments of two forces which meet at an angle, round any point within the angle, is equal to the moment of their resultant.

A uniform ladder AB, of given weight, rests on a smooth horizontal plane OB and against a smooth vertical wall 04, and is kept inclined at an angle of 45° to the horizon by a horizontal string OB. Determine the tension of the string.

5. Show that the principal of virtual velocities holds for the lever.

What are the requisites of a good balance?

The arms of a false balance, whose weight is 2 lbs., are 6 ins. and 6 ins. Find the real weight of a body which, placed in the pan at the end of the shorter arm, appears to weigh 4 ounces.

6. Define-velocity, acceleration, uniform force, gravity, momentum.

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If g 32 with the ordinary units, then, when the units. are I mile, 1 ounce, and 1 minute, find (1) the value of g; (2) the momentum of a mass of 1 lb. which has been falling for 15 seconds.

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7. Give the three laws of motion and an example of each. 8. Prove the formula s = ut + gt2, for a falling body.

If a body P is let fall from the height of 100 feet, find (932) the velocity, in feet and seconds, with which it reaches the ground.

If with this velocity another body Q is projected vertically downwards from a height of 100 yards at the same time as P is dropped, show that P and Q will reach the ground at the same time; and find Q's final velocity.

9. Show that a body projected in vacuum in any upward direction not vertical will describe a parabola; and find the range on the horizontal plane through the point of projection.

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SATURDAY, JUNE 14, from 9.30 A.M. to 12.

E. Physical Science.

Mechanics.

1. Define Work, and explain how it is measured.

Prove that when a constant force acts on a mass so as to change its velocity, the work done by the force is equal to half the product of the mass into the change of the square of the velocity.

2. What is gravitation?

Describe Attwood's machine for verifying the laws of falling bodies.

3. Explain the hydrostatic paradox, and describe the Hydraulic Press.

4. Describe Fortin's Barometer; and point out the advantages it possesses over the common Cistern Barometer.

Heat.

5. Shew that the coefficient of cubical expansion of solids is three times that of linear.

Describe the Gridiron Pendulum; and give two other instances in the arts of the influence of the expansion of solids.

6. Explain radiation, conduction, convection; and give illustrations of each.

7. Define thermal unit, calorie, specific heat.

What weight of ice at zero must be mixed with 12 lbs. at 18° in order to cool it to 4°?

8. Describe briefly the principle of the ordinary Horizontal Steam Engine.

Distinguish between the Total Work and the Useful Work of an engine; and describe Prony's Friction Brake.

FRIDAY, JUNE 13, from 2.30 to 5 P.M.

E. Physical Science.
Chemistry.

1. Describe some experiments to prove that the substances formed in a chemical change weigh as much as the substances which went to form them.

2. State which of the following substances are chemical elements, which chemical compounds, and which mixtures:lime, lead, blacklead, air, red phosphorus, gunpowder, vermilion.

3. What are the general characters of an acid? How may phosphoric acid be obtained from phosphorus? Why is common phosphoric acid said to be tribasic? Give examples of monobasic and bibasic acids.

4. Mention the principal forms in which silica occurs in nature. Explain how soluble silica can be obtained, how it can be recognised, and how rendered insoluble.

5. What important commercial products are manufactured from common salt, and by what processes?

6. Enunciate the atomic theory, and give the arguments upon which it is founded, clearly distinguishing between fact and hypothesis.

7. How would you prove the composition of carbonic acid (CO2)? Suppose a square centimetre of a leaf to decompose in sunlight 0.11 c. c. of carbonic acid in an hour, what volume of oxygen will be liberated in 5 hours by leaves with a total surface of 2500 sq. cm.? Find also the quantity of carbon assimilated.

8. Write equations expressing the chemical changes which take place in the following operations :

(1) The decomposition by heat of ammonium nitrate, mercuric cyanide, sulphuric acid, lead nitrate.

(2) Chlorine gas is passed through a (a) warm concentrated solution of caustic potash, (b) a solution of potassium ferrocyanide.

9. Describe carefully the preparation and properties of nitric acid. What action takes place when nitric acid is poured upon copper, tin, iron, phosphorus? Explain the ordinary iron protosulphate test for nitric acid.

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