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8. Explain why a balloon rises, and why the higher it gets the slower it rises. Why does it ever cease to rise?
9. Describe the construction of the common suction pump and its operation. (Draw a diagram of the pump.)
10. A piece of wood floats in a cup of water under the receiver of an air-pump. Will it sink deeper or rise higher when the air is exhausted \ Why?
1. If two weights, P and Q, acting perpendicularly on a straight Lever on opposite sides of the fulcrum balance each other, determine the position of the fulcrum and the pressure on it.
The scale-pans of a Balance are of unequal weight, and its arms consequently also of unequal length; find the true weight of any substance from its apparent weights, when placed in the two scale-pans respectively.
2. If two forces, acting at any angles on the arms of any Lever, balance each other, they are inversely as the perpendiculars drawn from the fulcrum to the directions in which the forces act.
3. If three forces, represented in direction and magnitude by the sides of a triangle taken in order, act on a point, they will produce equilibrium.
Two forces whose magnitudes are \J3 X P and P, respectively, act at a point in directions at right angles to each other; find the magnitude and direction of the force which will balance them.
4 In that system of Pulleys, in which the same string passes round any number of pulleys, and the parts of it between the pulleys are parallel, there is equilibrium (neglecting the weights of the pulleys) when P: W :: 1 : the number of strings (w) at the lower block.
5. Prove that when a body is suspended from a point, it will rest with its Centre of Gravity in the vertical line passing through the point of suspension. Hence show how the Centre of Gravity of any plane figure of irregular outline may practically be determined
6. Describe an experimental proof, that, if the pressure at any point of a fluid be increased, the pressure at all other points will be equally increased. By what short form of words is this property of fluid pressure sometimes described?
In the common Hydraulic Press, are the fluid pressures and tendency to break uniform throughout the cylinders?
7. Prove that if a body floats in a fluid, it displaces as much of the fluid as is equal in weight to the weight of the body; and it presses downwards, and is pressed upwards, with a force equal to the weight of the fluid displaced.
A uniform cylinder, when floating vertically in water, sinks to a depth of 4 inches; to what depth will it sink in alcohol of specific gravity 0.79?
8. Describe the construction of the Condenser, and the mode of its operation.
A cylinder, filled with atmospheric air, and closed by an air-tight piston, is sunk to the depth of 500 fathoms in the sea; required the compression of the air (assume specific gravity of sea water to be 1.027, specific gravity of mercury 13.57, and height of Barometer 30 inches).
OF JUNE, 1874.
ANCIENT HISTORY AND GEOGRAPHY.
[Take the first three, and one other; four in all.]
1. Name in the order of time the successive conquests made by the Romans, and note distinctly the position of each conquered state or district.
2. By a map or by words represent or describe Sicily. Point out its place in Grecian and in Roman history.
3. Name eight places that were noted in ancient times: four Greek, and four Roman. Give their situation, and show their importance in history.
4. What objects would a Roman be sure to point out to a stranger visiting Rome in the time of Augustus 1 Describe some of them. Show, by a rough plan, their position relatively to each other, and connect them with events in Roman history.
5. The legislation of Solon.
6. The Gracchi and the Agrarian Laws. State precisely the character of these laws.
MODERN AND PHYSICAL GEOGRAPHY.
1. Upon what principle is Mercator's map constructed? How do the parallels and meridians appear upon it 1 What distortion is produced in the forms of the countries 1
2. Draw an outline map of Africa and put upon it, in their proper positions, the equator, and the meridian of Greenwich. Give also the names of the bodies of water surrounding the continent, and the positions of important islands near the coast.
3. What is shown by a profile of a country 1 Draw a profile of South America, from the mouth of the Amazon to the Pacific Ocean.
4. Describe the southern coast of Europe, giving the names of countries, bodies of water, important islands, principal seaports, and largest rivers.
5. What time is it at Madras when it is eight o'clock in the morning at Boston 1 Longitude of Madras, 80° E.; of Boston, 71° W.
6. Where is the Great Bear Lake 1 Why was it so named? What other large lakes are near it 1 Which continent has the smallest number of lakes? Where are the principal salt lakes, and why are they salt 1
7. Where does the Colorado River rise and empty? What are the most striking physical features of the country through which it flows?
Answer the same questions for each of the following rivers: — Columbia; Niagara; Hudson; Seine; Ganges.
8. What cities of Europe are in nearly the same latitude as New York 1
9. Describe two water routes between Marseilles and Hong Kong.