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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?
QUESTIONS IN PRACTICAL GEOMETRY, BUILDERS' WORK, &c.
Set to Candidates for the Situation of Clerk of the Works in the Engineering Branch of the War Department.
PRACTICAL GEOMETRY AND MENSURATION.
1. How much paper, 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?
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. 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?
PRACTICAL GEOMETRY, BUILDERS' WORK, ETC.
5. Compare the contents of a triangular and hexagonal pyramid, one side of the base in each being 5 feet, and their altitude 3 feet.
6. Construct a plain scale of 174 feet to an inch, and pen in the lines in Indian ink.
7. A semicircular arch of 16 feet span is intersected by an arch 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 which the good adjustment is doubtful, how would you test it?
1. State what you know of the different kinds of limestone in this country, and of their economic value.
What are the objections to "shelly" limestone, and when
it is used for building what precaution should be observed with respect to the portion exposed?
2. State how the quality of granite is affected by an excess of quartz, or mica, or feldspar. Should you consider, generally, a fine or coarse grained granite to be preferable? What effect has sulphuret of iron on the granite in which it occurs?
3. State the materials with which you are acquainted suitable for lining furnaces or limekilns.
4. What points would you consider in selecting material for a road covering? Name, in the order of their fitness for this purpose, the materials with which you are acquainted.
5. Certain limes, if not properly treated, will swell after they have been made into mortar and introduced into work. How does this arise, and what precautions would you observe in the preparation of the mortar, to prevent it? 6. What do you consider to be a fair proportion of sand, gravel, and lime, for a foundation of a building under ordinary circumstances? What are the conditions under which you consider that these proportions should be varied?
7. What are the characteristics of a good brick? What crushing force per square inch should such a brick be capable of supporting?
8. What thickness of mortar would you allow in joints in ashlar work, and in brick work?
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?
C. PLAN DRAWING, DESIGNING, ETC.
Time allowed, 6 hours.
1. Give a design for a footbridge 30 feet span and 6 feet wide,
the scantlings to be figured.
2. Give a design for an iron roof 30 feet span.
3. Also a timber roof boarded and slated of the same span, showing
the calculations for the scantlings.
4. Give a 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 bricknogging 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 be over the gateway and about 25 feet long.
(5.) Parliamentary Paper. Emperor of Morocco's Loan. 1861. (6.) Do. Kertch and Yenikale Prize Money. May, 1862. (7.) Do. Employment of British Officers under Government of China. 1862.
(8.) Do. Assassination of Dr. McCarthy. 1862.
[Any of the above, or other Parliamentary Papers, may be obtained of the Publisher, 34, Parliament Street.]
Set to candidates for the Admiralty who selected Euclid as a subject for Examination.
1. If two triangles have two angles of one equal to two angles of the other, each to each, and one side equal to one side, viz. the side adjacent to the equal angles in each; then shall the other sides be equal, each to each, and also the third angle of the one to the third angle of the other.
2. To a given straight line apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
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 of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
4. The diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote: and the greater is nearer to the centre than the less.
5. A segment of a circle being given, describe the circle of which it is the segment.
6. If the outward angle of a triangle made by producing one of its sides be divided into two equal angles by a straight line which also cuts the base produced, the segments between the dividing