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Golden in show, is but a wreath of thorns,
Brings dangers, troubles, cares, and sleepless nights
To him who wears the regal diadem,

When on his shoulders each man's burden lies;
For therein stands the office of a king,
His honour, virtue, merit, and chief praise,
That for the public all this weight he bears:
Yet he, who reigns within himself, and rules
Passions, desires, and fears, is more a king;
Which every wise and virtuous man attains;
And who attains not, ill aspires to rule
Cities of men or headstrong multitudes,
Subject himself to anarchy within,

Or lawless passions in him, which he serves.

MILTON.

EXAMINATION FOR LICENSE IN ENGINEERING.

MR. TOWNSEND.

THEORETICAL MECHANICS.

1. A uniform beam supported on a rough horizontal rests against a smooth vertical plane; given the coefficient of friction, determine its limiting position of equilibrium.

2. In an isosceles wedge, whose equal faces of cleavage are equally rough, given the coefficient of friction, and the angle of cleavage, determine the ratio of the forces requisite to force it into and to extract it again from any given position.

3. A bank of earth, whose upper surface is horizontal, rests against a vertical rectangular wall of given dimensions; given the density and natural slope of the earth, determine the moment of its pressure to overturn the wall.

4. In a suspension bridge uniformly loaded horizontally along its entire length, given the span, elevations of supporting piers, and entire weight of roadway, determine the tension at the lowest point of each chain.

5. Prove that the strength of an elastic rectangular beam to resist fracture by bending at any point varies as the product of the breadth into the square of the depth at the point.

6. A uniform horizontal beam, of any section, density, and elasticity, is first supported and then fixed at both extremities; required the ratio of the central deflections produced by its own weight in the two cases.

7. A body, falling vertically under the action of gravity, draws another by a connecting cord along a rough horizontal plane; given the coefficient of friction, determine the tension on the cord.

8. A sphere rolls down a rough inclined plane, and a cube of equal weight slides down the same plane; determine the coefficient of friction of the latter, in order that the times of descent of the two should be equal.

9. A uniform bar revolving round a fixed axis strikes with one extremity against a fixed obstacle; if the axis experience no shock at the moment of collision, determine its position with respect to the bar.

PRACTICAL MECHANICS.

1. A block of granite, 20 tons weight, rests on a rough plane inclined 27°35' to the horizon; if the least force applied parallel to the plane that will suffice just not to move it downwards be 1 ton 7 cwt., calculate the coefficient of friction.

2. A wall of limestone (sp. gr. = 2.65), 80 ft. long, 30 ft. high, and 1 ft. thick, sustains the pressure of a roof applied along its upper internal edge, and inclined 35° 30′ to the horizon; required the extreme weight of the roof that will just not overturn the wall.

3. A rectangular reservoir of water is 25 ft. deep, 48 and 24 ft. broad at the surface and base, respectively, and 150 ft. long throughout; calculate the entire pressures of the water on its sloping and vertical faces.

4. A uniform horizontal bar, 25 ft. long, 6 in. deep, and 2 in. thick, is fixed at one extremity and free at the other; calculate the deflection produced at the latter by the vertical force which, applied horizontally, would extend or compress it . oo1 inch.

5. A train, weighing 50 tons, is impelled along a horizontal road by a constant pressure of 550 lbs; if the friction be 8 lbs. per ton, calculate its velocity after moving from rest for 10 minutes, and the space it describes in that time.

6. A hollow cylinder of cast iron (sp. gr. =7.25), 20 ft. long, 6 in. thick, and 2 ft. mean radius, revolves round its axis four times per minute; calculate in foot pounds the entire amount of work accumulated in it.

THEORY OF THE STEAM-ENGINE.

MR. GALBRAITH.

1. What is the pressure of steam corresponding to the temperature 320° F. ?

2. Calculate the relative volume. How much does it differ from that given by the empirical formula?

3. Prove the formula

Work done = w(1 + λog. Expansion).

4. Calculate the value of the coefficient if the expansion is oneeighth.

5. Show how the result may be arrived at by Simpson's rule.

6. What are the values of k and e in the fundamental equations of the steam-engine. Calculate their values if the expansion is one-eighth.

7. Find the pressure in the cylinder before the steam is cut off from the following data :-Expansion, ; diameter, 54 in.; stroke, 4 ft. 4 in.; revolutions, 21; evaporation, 3 cub. ft.

8. Find the diameter of the cylinder of an engine to work at 150 H.P., when the steam is cut off at ; stroke, 5 ft. 4 in.; revolutions, 18; evaporation, 1.2 cub. ft.

DR. DOWNING.

1. An unfinished excavation for a new road, in progress, is found to give the following section on the centre line :

[blocks in formation]

At the point A, which is the zero of distance, and where the staff reading is 8.00 ft., the depth of excavation required to bottom the cutting is 3.50 ft. And at G, where the section terminates, the depth, in like manner, is to be 1.80 ft.

Calculate the depths at B, C, D, E, and F, so that the road may have a uniform gradient from end to end, when the cutting is finished to the required depth; and also compute the gradient which the above data give. The distances were taken from point to point, and not from the first point, A.

2. A wrought iron beam, 80 feet in clear span, and having 14 square inches area in the transverse section of the bottom flange, at the centre of the span, is loaded with a uniformly distributed weight, so as to produce 5 tons strain, per square inch at that point. Calculate the transverse area required in the bottom flange, at every 10 ft. of the span from either abutment, so as that the same strain of 5 tons per square inch may not be exceeded.

3. In a wrought iron beam, 100 ft. in clear span, and having 20 square inches area in the transverse section of the bottom flange, at the centre of the span is loaded with a single weight at the centre, so as to produce a strain of 4.5 tons per square inch at that point. Calculate the area required in the bottom flange at every 10 ft., from either abutment, so that the same strain of 4.5 tons per square inch may not be exceeded. State also the modification which the area computed, in this and the former question, must comply with in the parts near the abutment.

4. A beam of wrought iron, 30 ft. in clear span, has an average strain of 3.21 tons per square inch in the top, and 2.73 tons per square inch in the bottom. Calculate the length to which the bottom is lengthened, and the top shortened, by these strains.

5. Draw up a specification for a wrought iron girder, as to the quality of the iron employed, and as to the quality of the workmanship in the plates at top and bottom, and in the riveting.

6. Calculate the number of cubic yards of earthwork in the embankment with the following dimensions:-Slopes, 2 to 1; base, 30 ft. The lengths being, from A to B 460 ft., from B to C 220 ft., from C to D 480 ft., and from D to E 700 ft.; the depths being at A = 0, at B = 17, at C27, at D = 27, and at E = 0. The contents of each separate block must be given in cubic yards, as well as the total amount.

7. Calculate the land required for the above embankment, giving each part separately, in acres and decimals.

8. Calculate the number of square yards in the slopes of the embankment, dimensions same as No. 6.

9. Draw up a specification of an embankment for a reservoir according to the most approved method, and point out the defects in the method of construction of the dam on the Sheffield Waterworks, which has recently failed.

10. Draw up a specification for the excavations and embankments on a line of railway.

II. A railway cutting, 30 ft. base, with slopes of 2 to I, has a transverse inclination of the surface of the ground at the rate of 10 to 1; calculate the half widths on each side, measured on the sloping surface of the ground from the centre pegs, at points where the depths of the cutting are 20 ft., 24 ft., and 30 ft.

12. Calculate the discharge in cubic feet per minute of a new water course with the following data:-side slopes, 2 to 1; bottom width, 14 ft.; depth of water, 2 ft. 6 in.; fall per mile, 3 ft.

13. A rectangular channel, 8 ft. wide, and with the water flowing 3 ft. 6 in. in depth, has a fall of 10 in. per mile; compute the discharge in gallons per 24 hours.

14 Calculate the ultimate strength, in tons, of a cast iron beam; span in the clear between the abutments, 31 ft. 8 in.; depth outside, 27 in.; area of the bottom flange, 12 in. wide by 1 in. deep.

15. Calculate the ultimate strength, in tons, of a wrought iron beam; clear span, 30 ft.; depth, 22 in.; the area of the bottom flange being formed by two angle irons, each 3′′ × 3′′ × 1′′ in., riveted together through the vertical plate.

16. Calculate the central deflection of a wrought iron beam, 30 ft. in clear span, and 3 ft. deep; the load upon the beam being such that the compression on the top and tension below have caused the bottom to become 0.01782 ft. longer than the top; the curve into which the beam is bent being supposed to be an arc of a circle, and the top and bottom flanges concentric arcs of this circle: the length of top flange having become 29.99037 ft., and of the bottom 30.00819 ft.

17. Compute the weight of a wrought iron beam, of uniform section, consisting of a vertical plate 22 inches deep, andths inch thick; the top consisting of two angle irons, each 4′′ × 4′′ × 4′′ inch, and the bottom of two angle irons 3" x 3" x 4" inch, in both cases riveted together through the vertical plate; the total extreme length being 31 ft. 6 in.

18. A railway cutting has a base of 30 feet, side slopes of 2 to 1, and a transverse inclination of the ground at the rate of 10 to 1; calculate the increase of the transverse area, in square feet, of the trapeziums at the points where the depths of excavation are 20 ft. and 30 ft., respectively, above the areas which we should have if the surface of the ground were level transversely with those same depths.

19. In the same circumstances of excavation as in No. 18, let the distance between the two heights of 20 ft. and 30 ft. be 500 ft.; compute the increased amount of excavation in cubic feet above that which we should have if the ground were level transversely.

20. Calculate the horizontal thrust of a brick arch, span 100 ft., rise 20 ft., the depth at the key 2 ft. 3 in., and the weight of the brickwork being taken at 120 lbs. per cubic foot, the outside width of the bridge being 30 ft., and the curve of the arch the segment of a circle.

21. Enumerate the several conditions with respect to the curve of equal horizontal thrust in an arch so that it may be considered safe; and give a geometrical construction by which the curve may be drawn in any given bridge.

22. Calculate the discharge in cubic feet per minute of a pipe running full under pressure; diameter, 0.75 ft.; rate of fall, one in 352.

23. Describe the method by which the discharge of the main reservoir at the Gorbals waterworks was regulated so as to give a quantity equal to that required in the town, under the circumstances of the varying demand, and varying depth in the reservoir.

24. Draw up a specification of brickwork, as to the material, and as to the workmanship, also as to the mortar, without following any one particular specification in the Text-book; the brickwork to be Arch-sheeting; Tunnelling; Footings of large walls; and in a retaining wall with stone facing, and in the case of the wall being constructed altogether in brickwork.

25. Give a specification for a timber viaduct for a double line of railway, consisting of timber piles and horizontal girders, including the planking, painting, pile driving, and whatever preserving process may be adopted.

26. Describe and sketch the fish joint, as applied to some one of the forms of railway bars, and mention the practice by which the same object was previously attempted to be attained. State also the nature of the strains which come upon all the parts of the fish joint when a driving wheel is passed over the joint.

27. Give a specification for permanent way, including the preparation of the formation level, the requisite bench marks, the ballasting and boxing, the timber work as to its quality and method of fixing; mentioning all the advantages and disadvantages which have been claimed for, and urged against, the two systems of timbering.

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