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13. In an ellipse prove that the line drawn through the focus at right

angles to the focal distance intersects the tangent and the directrix in the same point.

Mixed Mathematics. 1. Assuming the truth of the parallelogram of forces as to direction, prove

its truth as to magnitude. 2. Given the sum of two forces and their resultant, and also the angle

which one of them makes with the resultant. Determine the forces,

and the angle at which they act. 3. State the result of any experiments made with reference to friction. A body weighing 12,000 tons, placed on a plane whore inclination is

1 in 12, and acted on by two chains (each capable of sustaining a strain of 200 tons) in the direction of the plane, is just on the point of moving when the chains break. Find the coefficient of friction

between the body and the plane. 4. An area is cut from one angle of a triangle equal to half the area of

the triangle by a line parallel to the base. Find the centre of

gravity of the remainder. 5. Enunciate the first and second laws of motion, and mention any

experiments which seem to suggest their truth. How is their truth

finally established ? 6. A body moving uniformly in a straight line is suddenly acted on by

a constant force always acting in a given direction. Determine the

subsequent motion. 7. A body of given elasticity is projected vertically upwards with a given

velocity, and strikes against a horizontal plane. Determine the

velocity with which it reaches the ground. 8. Find the line of quickest descent from the focus of a parabola, whose

axis is vertical and vertex upwards, to the curve. 9. Define “ specific gravity,” and show that when a solid is immersed in

a fluid, the weight lost is to the whole weight of the body as the

specific gravity of the fluid is to that of the solid. 10. Explain the principle of the hydraulic press, and find the mechanical

power in a machine of given dimensions. 11. A particle moves in a circle under the action of a central force resident

in an external point. Find the law of force. Is the force attractive or repulsive ?

PRACTICAL GEOMETRY, BUILDERS' WORK, &c.

Practical Geometry and Mensuration. 1. How much paper, 3 yard wide, will be required for a room that is 22

feet long, 14 feet wide, and 9 feet high, if there be 3 windows and 2 doors, each 6 feet by 3 feet ?

PRACTICAL GEOMETRY, BUILDER'S WORK.

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2. How many square feet are contained in a plank whose length is 10

feet 10 inches, and breadth at the two ends 34 feet and 2 feet ?
3. What would be the cost of paving a semicircular alcove with marble at

2s. 6d. a foot, if the length of its semicircular arc was 22:42 feet ?
4. A stone 18 inches long, 17 broad, and 7 deep weighs 278 lbs., how

many cubic feet of this kind of stone will freight a vessel of 230

tons burthen ?
5. Compare the contents of a triangular and hexagonal pyramid, one side

of the base in each being 5 feet, and their altitude 31 feet.
6. Construct a plain scale of 171 feet to an inch, and pen in the lines in

Indian ink.
7. A semicircular arch of 16 feet span is intersected by an arcb springing

from the same level, and of the same rise, but of 10 feet span,
forming groins. Draw the plan of their intersections, and a section

of the smaller arch.
8. Before commencing work with a Theodolite, of wbich the good adjust-

ment is doubtful, how would you test it ?

9. What are the various ways of laying hold of stones that are too heavy

to be moved by hand ? 10. What are the appearances by which you would judge of timber

generally ? What kind of timber is best suited for straight beams,

straight ties, and straight pieces of framework generally ? 11. If you are to use timber naturally seasoned, what arrangements should

you have made in order to carry out the process effectually, and what should be the duration of such seasoning process generally to fit timber for the carpenter or the joiner ?

What timber will best bear being kept constantly wet ?

Plan Drawing, Designing, Etc.

(Time, 6 hours.) 1. Give a design for a footbridge 30 feet span and 6 feet wide, the scant

lings to be figured. 2. Give a design for an iron roof 30 feet span. Dimensions to be figured. 3. Also a timber roof boarded and slated of the same span, showing the

calculations for the scantlings. 4. Give comparison of the expense of building walls 10 feet high, for the

locality best known to you,

1. In brick stone work.
2. In rubble stone work.

3. In brigknogging plastered on both sides. 5. Give a plan and elevation of a gateway and shed for the entrance to

a cemetery, with a specification and estimate of the same. The shed to

over the gateway and about 25 feet long.

GEOMETICAL DRAWING.

Specimen Paper. 1. Show how to erect a perpendicular at the end of a line which does not

admit of prolongation ? 2. Draw any irregular right-lined figure of 6 sides, and reduce it by

construction, to a triangle of equal area. 3. Construct a triangle having two of its sides equal to 3 inches and 4

inches respectively, and the angle opposite the longer side 70°; ascertain and figure the value of the third side and of the remaining

angles without calculation. 4. Draw two lines AB, BC, equal to 27 inches, and 3 inches respectively,

making at B an angle of 140° re-entering towards a point X. From X, A and B, were observed to subtend an angle of 30°, and B and C an angle of 40° : find the position of the point X with reference to A, B and C.

5. Construct a plain scale of 3 chains to 1 inches, and give its repre

sentative fraction ? 6. The observed angle from a point A to two points B and C, of which

the measured altitudes above the horizon from the same point are 30°, and 35° respectively, is 45°. Construct the horizontal angle

between the lines AB and AC. 7. Draw a rough diagram of a beam compass, and explain the method of

setting the instrument for use.

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MORAL PHILOSOPHY.

Specimen Paper.

[Time 3 hours.] 1. Give the derivations of the words Moral and Ethical. Explain how

they indicate the objects of Moral Philosophy. 2. By whom is the name “ Philosopher” said to have been first used ?

How was it related to the name “Sophist”? When and how did that become a term of reproach ? What was the quarrel of Socrates with the Sophists of Athens generally ? Mention any particular Sophists who are introduced into the Dialogues of Plato, and any

thing you may recollcct of their lives and opinions. 3. Pope calls Happiness “ Our being's end and aim.” What Greek Philo

sopher adopted that maxim as the central one of his moral system ? Give his definition of Happiness, and examine the different parts of

it. What is Paley's notion of Happiness ? 4. Give the etymologies of these words :- “ Conscience,” “ Duty," “ Virtue,

Right,"

,” “ Obligation," “ Law.”. Is the meaning of this word the same in Physical and Moral Science ? If not, what

is the difference? 5. “ All this," says a great writer, “is nothing more than the distinction

between mere Power and Authority." What is this distinction ?

What is the application of it to moral questions ? 6. Give a short account of the following philosophers, noting (1) the times

in which they lived, (2) the countries to which they respectively belonged, (3) any remarkable circumstances in their biographies, (4) what was most characteristic in their views of moral subjects : (a) Epicurus, (b) Epictetus, (c) Helvetius, (d) Butler, (e) Bentham,

(f) Kant. 7. Explain and illustrate the difference between the adjectives “ arbitrary”

and" voluntary.". 8. Explain the origin of the words " Appetite," " Affection," " Passion,"

, “Sympathy,” “ Habit,” “ Energy,” and illustrate the use of any of them by eminent writers on Morals.

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MENTAL PHILOSOPHY AND LOGIC.

Specimen Paper.

[Time 3 hours.] 1. Sir W. Hamilton quotes these words from Cicero and Macrobius as ex

plaining the subject of Mental Philosophy : (1) Mens cujusque is est quisque, non ea figura quce digito demonstrari potest. (2) Ergo qui videtur non ipse verus homo est, sed verus ille est a quo regitur quod videtur. Translate these passages. To what theory

about our nature are they opposed ? 2, Give the derivations of these words : observation, attention, reflectior,

apprehersion, comprehension, preception, conception, subject, object, substance. Illustrate from these etymologies what you may re

collect of the use of any of these words in philosophical writings. 3. Explain (by reference to their derivations) the words physiology,

pyschology, pneumatology, ontology. What is Locke's objection to

the study which is indicated by the last of these names ? 4. In what sense and on what grounds has Logic been called the Science

of Names? What class of thinkers have protested against that

description of it, and why? 5. In what sense is Logic an Art of Reasoning ? Why is that account of

it insufficient ? 6. Explain the worú Category. What are Aristotle's Categories ? What

objections bave been made to them? 7. Explain the dictum de omni et nullo. How has the syllogism been

deduced from it? 8. Give some examples of the “undistributed middle," and of popular

fallacies which can be traced to it. 9 Explain and illustrate the words “ Deduction and Induction.” Why is

Experimental Philosophy commonly called also Inductive Philosophy.

HISTORY AND GEOGRAPHY OF INDIA.

Specimen Paper.

[Time, 3 hours.] 1. Write a short account of Buddhism. Where are Buddbists still found

in our Eastern Empire ? 2. Write a short sketch of Sivaji's early history down to his reception at

Delhi. 3. Give an account of the events which led to the battle of Panipat in

1761. What other important events happened about the same time

in other parts of India ? 4. Write an account of Chanda Sahib from his first connection with the

French. 5. Who were the Rohillas ? Write a sketch of their history down to their

conquest by the Nabob Vizier. What became of Fyzoollah Khan ?

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