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SATURDAY, JUNE 9, from 2.30 to 4.30 P.M.
D. Mathematics. (Third Paper.)
1. Explain the terms-mass, equilibrium, tension, moment of a force, velocity, acceleration.
2. Prove that if three forces applied at a point are in equilibrium they can be represented in direction and magnitude by the three sides of a triangle taken in order.
ABCDEF is a regular hexagon; three forces applied at a point, parallel to AB, AD, AE, are in equilibrium: if the value of the greatest is 6 lbs., what is the value of each of the others?
3. Find the magnitude and position of the resultant of two unequal and unlike parallel forces; and shew that the algebraical sum of their moments about any point in their plane is equal to the moment of their resultant about the same point.
Weights of 7 lbs. and 11 lbs. respectively are suspended at the ends of a weightless rod, one foot long; and a weight 15 lbs. at a point 5 inches from the smaller weight: find (1) about what point the rod will balance if suspended by a single string; and (2) if it be suspended by two strings attached to points three inches from the ends, what the tension of each string will be.
4. Define the centre of gravity of a body; and find the height above a plane of the centre of gravity of heavy particles whose masses are m1, m2, &c., and whose heights above the plane are 1, x2, &c.
If two weights balance one another on a wheel and axle, and the system is displaced by pulling down either of the weights; prove that the height of their common centre of gravity remains unchanged.
5. If a cube, of which each edge measures 6 inches, is placed with four of its edges horizontal on an inclined plane, rough enough to prevent sliding, and of which the altitude is to the base as 3:2; how much of the top of the cube must be cut off by a plane parallel to its base in order that the remaining part may not fall over?
6. Explain the action of a screw; and apply the principle of virtual velocities to determine the relation between the power and weight.
7. A heavy particle, projected vertically upwards, strikes against an elastic surface from which it recoils with the same velocity with which it impinged: prove that its velocity on returning to the point from which it was projected is the same as if it had risen to the height due to its velocity of projection, and then fallen.
With what velocity must a heavy particle be projected downwards from an elevation of 100 feet in order that it may meet half-way a particle projected vertically upwards at the same moment with a velocity of 40.25 feet per second? [9 = 32.2.]
8. Prove that the path of a projectile in a vacuum is a parabola; find the height of the directrix of the parabola above the point of projection; and shew that the velocity at any point is equal to that acquired by falling to that point from the directrix.
9. A body weighing 24.15 lbs. is moved by a constant force, and acquires in a second a velocity of 3 feet per second: what weight would the force statically support?
SATURDAY, JUNE 9, from 9.30 A.м. to 12.
E. Physical Science.
1. State the proposition known as the parallelogram of forces. How may its truth be proved by experiment?
2. What is meant by the statement that 'the centres of suspension and oscillation of a compound pendulum are convertible?' How may the value of gravity be ascertained by means of a pendulum?
3. Shew how to determine the specific gravity of a substance heavier than water by means of Nicholson's hydrometer. 4. Describe Bianchi's air-pump.
1. Describe the process by which Dulong and Petit determined the absolute expansion of mercury.
2. Shew how to determine the specific heat of a substance by the method of mixtures.
3. How may the amount of aqueous vapour present in the air be determined?
4. What is meant by the mechanical equivalent of heat? Describe an experiment for determining its value.
Light and Sound.
1. Describe some form of telescope.
2. What is meant by phosphorescence? Describe Becquerel's phosphoroscope.
3. How does polarised light differ from common light? Explain why light becomes polarised after passing through a Nicol's prism.
4. What are the three qualities of a musical sound? Describe the syren.
FRIDAY, JUNE 8, from 2.30 to 5 P.M.
E. Physical Science.
1. Define the term Element.' Write a short account of the materials with which Chemistry has to deal, of the objects at which it aims, and of the general methods which it employs.
2. How is ammonia gas prepared? What are its characteristic properties? How could you show that it is a compound of hydrogen and nitrogen?
3. How would you prepare the two gaseous oxides of carbon? What are their properties? and how has their composition been determined?
4. Describe the chief physical characters of sulphur and phosphorus, and give a short account of the combinations of phosphorus with oxygen.
5. Write equations explaining the chemical reaction between the following:
Nitric acid with copper.
6. Describe experiments to prove that air is a mechanical mixture.
7. Give an account of the constituents and mode of manufacture of coal gas. How is its illuminating power estimated? 8. In what forms is calcium carbonate found in nature?
9. Write an account of the metallurgy of lead.
10. What do you understand by the term 'specific heat' of a substance. What use does the chemist make of such information?
WEDNESDAY, JUNE 6, from 2.30 to 5.30 P.M.
The tubes marked A, B, C, and D contain single substances. You are requested to find out by their reactions what these substances are, and to write a careful account of your experi
The substances were:-, A. Ammonium Phosphate; B. Zinc Carbonate; C. Calomel; D. Lead Sulphate.
SATURDAY, JUNE 9, from 2.30 to 5 P.M.
E. Physical Science.
1. How does the nutrition of an animal differ from that of a plant (1) in respect of substances assimilated, (2) in the mode in which they are assimilated?
2. Point out the chief differences between the Vertebrate and Invertebrate types.
3. What are the osteological points of difference between mammalia and aves?
4. Describe the minute structure of the liver. What forms does this organ assume in the invertebrate animals?
5. Compare inter se the action of the various digestive juices of the alimentary canal.
6. What changes are produced (1) in the air, (2) in the blood by the function of respiration?
7. Draw out a classification of the Mollusca with a short account of the characters of the groups in which you arrange them.
8. What are the principal characters of the organisation of (1) elasmobranch, (2) ganoid fishes?
9. Describe some of the chief agencies in the distribution of animal and vegetable life.
WEDNESDAY, JUNE 6, from 10 A.M. to 1 P.M.
1. Make preparations of and describe with a diagram, the Archegonium of a Fern.
2. Dissect (1) the flower, (2) the germinating seeds, before you, laying out and naming the parts.
3. The Vessel before you contains numerous forms of animal and vegetable life. Make preparations for the Microscope of any objects you find, giving a name and short description of each.
4. Write a short description of the objects marked A and B. The flowers, seeds, and objects were:—2. (1) Symphytum orientale Boraginae; (2) Barley and Mustard. 3. Protococcus, Englana, Scenedesmus, Vorticella, Spirogyra, Infusoria, etc. 4. A. Skull of Hedgehog; B. Shell of Pecten covered with Serpulæ, Barnacles, etc.
FRIDAY, JUNE 8, from 9.30 A.M. to 12.
E. Physical Science.
Botany and Vegetable Physiology.
1. Enumerate the chemical elements required by plants for their life and growth, and the sources from which they are derived. In what forms are they taken up? and in what parts of the plant are they elaborated?