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ENGLAND.

PRELIMINARY GENERAL EXAMINATION.- Christmas, 1867.

THURSDAY, December 19th.-Afternoon, 2 to 4.

MECHANICS.

1. How may we ascertain the direction and amount of the resultant strain produced at a fixed point by two pressures of known amount applied at the fixed point in known directions ?

2. Two equal weights hang at the ends of a string (whose weight is left out of consideration) passed over two fixed pulleys in the same horizontal line, and a smaller weight is hung from the string at the point midway between the pulleys. Show first, that however great the end weights may be compared with the middle weight, the part of the string between the pulleys can never be quite straight;

and secondly, that with any given set of weights, the distance of the middle point of the string from the horizontal line will be less or greater in proportion as the pulleys are nearer to, or further from, each other.

3. Define the term Centre of Gravity. How does the position of the centre of gravity of a resting body affect its stability ?

It is impossible to keep standing upright sidewise with one foot and one shoulder in contact with a vertical wall and at the same time to lift the other foot. Explain the cause of the impossibility.

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4. Explain what is meant by the moment of a force with respect to a point.

A ladder is lying on the ground with its feet against the wall of a house, and a man at a window vertically above (to which the ladder would just reach) proposes to raise the ladder by pulling a rope fastened to its further end. Show that the pulling effort he must make will continually decrease as he goes on raising the ladder.

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5. Define a Lever, and give an example of each of the three kinds of Levers.

A straight lever (which balances horizontally when no weights are attached to it) remains in balance when weights of 5 lbs. and 7 lbs. respectively are hung at the ends of the

The length of the longer arm being 131. inches, determine the length of the shorter arm.

Where is the centre of gravity of this lever ?

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arms.

6. Define Motion. Explain what is meant by the composition of Motions.

A tide flowing northward at the rate of six miles an hour, wafts boat which is being propelled eastward at the rate of eight miles an hour: prove that the boat will move in a straight line at the rate of ten miles an hour.

[In the following questions, the resistance of the air is neglected, and the force causing

the fall is supposed constant.] 7. A body falling from rest falls through 16 feet during the first second; how far will it fall in the first twelve seconds ? What velocity will it have at the end of the twelfth second ?

8. Show that, if bodies are let fall from the same point at different instants, their distances apart will continually increase by equal amounts in equal times.

ENGLAND.

PRELIMINARY GENERAL EXAMINATION.—Christmas, 1867.

WEDNESDAY, December 18th. Afternoon, 41 to 6.

ALGEBRA.

v 1. Add together fax? +ja+x— as, - sax+jas, - a x — 203.?

2. Take — 2203 + 2y— 3xy2 from x2y— 2.cy? + 3ys. r 3. Multiply a3 — a?b+63 by az-ab + 5%.

4. Divide x*—2x2 + 3x-2 by +1.

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5. Find the Greatest Common Measure of

4.3 -11c+3 and 2013 - 72 +9.

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6. Explain the term Multiple, and find the Least Common Multiple of 22 - xy +y?, 22 + xy, 13+y.

7. Extract the Square Root of ** +23-3422–2x+ 4.

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10. Solve the following equations :-

2x - 3 (i.) Ś (2.c—1)

+ 1;

4 8
6
2

1
3x - 5 2x 2 - 2
(ii.) 7x-y= }(2x+y)

+? 2y-1 (7.-y) = 75

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11. A cistern is filled in 30 minutes by a pipe A, and emptied in 40 minutes by a pipe B. After A has been running by itself for 10 minutes, B is opened ; in what time would it then be filled ?

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ENGLAND.

PRELIMINARY GENERAL EXAMINATION.-Christmas, 1867.

THURSDAY, December 19th.-Afternoon, 4 to 6.

NATURAL HISTORY,

I. BOTANY. 1. How may Exogenous plants be readily distinguished from Endogenous ? To which of these classes do each of the following belong :- Wheat, Oak, Lily, Dock ?

2. What parts of their respective plants are Tea, Cork, Coffee, Onion, Potato, Radish, Celery.

3. Draw outlines of leaves of the following forms: lanceolate, cordate, palmate, ovate, pinnate.

4. What is the function of the Sap? Explain the process of its ascent and assimilation in plants.

5. Assign to their proper Class, Order, or Family, either in the Natural or in the Linnæan arrangement, the following plants :the daisy, the rose, the pea, the cabbage, the mint, mignonette, parsley, clover, wheat, endive.

II. ZOOLOGY. 1. Make a table of the principal Orders of the Class Aves, with examples.

2. Point out the distinctive characters of the Mammalian Order Carnivora. Give the names of the principal Families of the Order, with examples.

3. Describe the characters of the dentition in Ruminantia, Rodentia, and Insectivora.

4. Explain the terms Coleoptera, Lepidoptera, Hemiptera; and give examples of these divisions of insects.

5. Arrange under the proper Order, Class, and Sub-kingdom, the following animals; and give, where you can, the proper systematic name of each :—the camel, the goat, the dog, the turkey, the eagle, the duck, the whale, the salmon, the pilchard, the bee, the beetle, the snail, the crab.

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