1. A wall of brickwork (weighing 112 lbs. per cubic foot) sustains a pressure of 1115 lbs., which is applied by means of a bracket at a horizontal distance of 2 ft. 6 in. from the inner edge of the wall; the pressure is inclined to the horizon at an angle of 65°, and is such as just not to overthrow the wall. Find the height of the wall.

2. The elongation of a steel bar 35 ft. long, when subjected to a strain of 50 tons, is o.o2 ft.; determine in square inches the transverse section of the bar. [The modulus of elasticity is 29,000,000.]

3. A mass of earth weighing 100 lbs. per cubic foot, whose surface is horizontal, presses against a wall of brickwork whose section is rectangular, and the top of the wall is on a level with the ground. If the natural slope of the earth is 30°, and if the thickness of the wall to enable it to sustain the pressure of the earth is 9.82 ft. ; find the height of the wall.

4. A river wall of granite weighing 164 lbs. per cubic foot, whose section is a right-angled triangle, and whose hypothenuse is turned towards the water, just supports the pressure of the water when its surface is on a level with the wall. If the height of the wall is 29 ft. 6 in., find the thickness of its base.

5. A stone wall 30 ft. high and 2 ft. thick has to sustain on each foot of its length a thrust equal to the weight of 3 cubic feet of stone, acting in a direction inclined to the vertical at an angle of 45°. If the pressure is applied at the point of a bracket whose distance from the wall is 7.04 ft., find the distance from the extrados of the point in which the line of resistance cuts the base.

6. Two rafters AB, AC, are each 24 ft. long, and their feet are tied by a wrought iron rod which has a section of gths of a square inch. If a weight of 56,000lbs. suspended from A just breaks the tie, find its length. [The tenacity of wrought iron is 67,000 lbs. per square inch.]

7. If the least pressure that will draw a cubic foot of cast iron down an inclined plane of oak is 146.7 lbs., find the inclination of the plane. [The limiting angle of resistance of cast iron or oak is 33°.]

8. If a line AB is subjected to a continuous pressure throughout its length such that the pressure at any point P is at the rate of kx AP per unit of length, find the amount of the resultant pressure, and its moment round A.



1. Adopting the formulæ used by the French Commissioners, as

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adapted to pounds' pressure on the square inch and the Fahrenheit scale, viz.,

t + 40 P=

147 and

= 147 find the relative volumes of steam corresponding to the pressures, 20 lbs. and 80 lbs. on the square inch, by means of the formula

+ t .

P 2. Compare these results with those which follow from the empirical formula which gives the relative volume in terms of the pressure only, viz.,

с Rel. vol.

P+y 3. Prove that the work done, due to the evaporation of one cubic inch of water, at a temperature t, is expressed as follows:

Work done= 311 (460+ t). 4. Let the temperature of the condenser be 96°, and of the cold water jet 56°, how much water will be required to condense 1 lb. of steam of the standard pressure ?

5. If the law of Boyle and Mariotte be assumed, prove that the work done, after the steam is cut off, is measured by the Napierian logarithm of the expansion.

6. If P' be the pressure in the cylinder before the steam is cut off, prove the following formula for the horse-power :

H. P.

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42 av.



I 1000

7. Apply this formula to the case of a condensing engine, in which the diameter of the cylinder is 48 inches, the stroke 8 feet, the number of revolutions 16, the expansion aths, and the pressure of steam before the cut off 24 lbs.

8. Let the diameter of the cylinder be 54 in., length of stroke 4 ft. 4 in., number of revolutions 21, evaporation 3 cub. ft. per minute, and steam cut off at Aths; required the pressure of the steam before expansion takes place.



1. The percolating power of lower green sandstone beds was found by experiment to be 18 cub. in. per hour, through 15 in. of sand, in a bent pipe of 11 in. diameter, under a pressure of 6 in. of water. Required the area of filter beds that, under 6 in. of water, would discharge as much water as a 11 in. pipe running free.

2. Find the height of a column of water that would force as much water through the sand as would run through the pipe under a 6 in. head.

3. The drainage area of the Mississippi is 1,244,000 sq. m., and its mean annual rain-fall is 30.4 in.; its annual discharge into the Gulf of Mexico is 21,300000,000000 cub. ft. What is the proportion of the rainfall expended in evaporation and vegetation ?

4. The length of the Missouri River, from Madison Fork to the Gulf of Mexico is 4194 miles; and the height of Madison Fork above the sea level is 6800 ft. Supposing the water that leaves Madison Fork to reach the Gulf with a velocity of 11 mile per hour, what is the proportion of its work expended on the road ?

5. Describe the physical and blowpipe characters of the oxides of iron usually employed as ores ?

6. What are the blowpipe characters of copper glance and copper pyrites

7. How do you distinguish between wolfram and tinstone by means of the blowpipe ?

8. A shaft is sunk on a lode to a certain distance, when the lode is found to be separated, and thrown down by a slide; the lode is afterwards recovered by rising on the slide, and again worked. Find the total depth of the working, and the horizontal distance at which a downright shaft should be sunk to reach the end.

Draft. Underlay. ist part of lode, + 114 ft. + 54° 30' Slide,

- 43 o 2nd part of lode, + 73

+ 51 0 9. An oblique shaft was found to measure 89 ft. 6 in, on an angle of 55°15'; and it was also observed that the shaft had declined 3° 45' west from the intended right angle of the east and west lode. Find the amount of error in the bottom of the shaft, and the perpendicular depth of the mine.

10. Two lodes intersect, having the following bearings and underlays:

E. 5° N. 64°N.


No. I.
No. 2.

N. W.


Find the bearing and underlay of their intersection.


1. The centre lines of a railway meet at an angle of 140°, and it is intended to connect them by a curve of 18 chains radius. Calculate in feet and decimals of a foot

a. The tangent lengths from the springing point.
b. The secant point.
c. The length of the arc of the curve.

2. Proceeding to set out the curve by the method of offsets from the springing point, compute the first and the succeeding offsets in No. 1.

3. The centre lines of a railway being found to meet in the middle of a deep river, a line, 530 links long, is measured along the bank from a point A on one line to a point B on the other, the angle at A between B and a ranging rod set up some distance back on line A being 144°, and that at B between A and a ranging rod back on line B being 142°. Calculate

a. The angle of intersection of the two straight lines.

6. The tangent lengths measured from the points A and B, and the secant point; the radius of the curve being 26 chains.

4. In question No. 3 compute the lengths of both rails of the up line, and same of the down line, for that curved portion of the line; the middle space being 6 ft., and the gauge used being the Irish.

5. An engine weighing 29 tons, travels on a curve of 40 chains radius at a rate of 30 miles per hour. Calculate the centrifugal force in tons and in feet per second.

6. The main tubes of the Britannia Bridge have a clear span of 460 ft., and a weight of 1553 tons (which may be taken as uniformly diffused); the depth at middle of span, from centre to centre of cells, 27 ft. 6 in., and the area of metal in the bottom cells 585 sq. in. Compute the strain per square inch in tons on the bottom. And assuming 18.6 tons per square inch as the ultimate resistance to tension of the iron used, calculate the central load the tube would sustain before breaking. The principle of the bent lever, as in the Text Book, is to be employed in the computation.

8. Draw up a statement of all that is given in the “Specifications,” in the several different works, as to the payments to contractors.

9. Write out fully and clearly the specification of any two of the retaining walls in the Text Book.

10. Give the specification for main and thorough drainage, with the detail of the depth, distance apart, and length of the drains; and a detailed estimate per acre. 11. Calculate the number of cubic feet delivered over a weir

Length on crest, 55 feet.

Depth of water on do., 5 inches. 12. To what height must a sluice, 4 ft. wide in the clear, be opened to reduce the depth of water flowing over the weir in No. 11, by 2 in.; the depth from the cill of the sluice to the surface of the water being 7 ft., and its coefficient of contraction taken equal to 0.84.

13. Compute the diameter of two equal pipes to convey the same volume of water as would be brought down by one main 33 in. diameter ; the fall in each case being 8 ft. per mile.

14. Calculate the discharge of a channel having a bottom width of 12 ft., the width at the water surface being 20 ft., and depth of water 3 ft.; and point out the peculiarity of a channel having such side slopes. Fall, 4 ft. per mile.

15. Give a succinct statement of the Ganges Canal from that contained in the “Practical Hydraulics.”

I 2

16. Calculate the number of cube yards in the excavation, with the dimensions following :-Lengths from A to B, 180 ft.; from B to C, 290 ft. ; and from C to D, 310 ft. ; the heights being-at A = o ft.. at B 24 ft., at C = 33 ft., at D = o ft.; the slopes being 2 to 1, and base 30 ft. The contents of each separate block must be brought out in cubic yards.

17. In a wrought iron flanged girder, having equal flanges at top and bottom, let a be the sectional area of either the top or bottom, and a' that of the vertical rib, the depth from centre to centre of flanges being d. Prove that

I (6a + a'); and show the application of this to the computation of the moment of the elastic forces of the transverse section of the beam.

18. Compute the difference of the deflection of a beam under a uniform load, and the same load applied at the centre.

19. The breaking weight of a hollow cast iron column being given in tons by the formula,

d3.5 013.5 42.35

Breaking weight in tons,

11.6 in which d the external and di the internal diameters are in inches, and I the length in feet; calculate the ultimate strength of a column 26 ft. high, and having 13 in. external and 10 in. internal diameter.

20. Calculate the diameter of a solid pillar having the same quantity of metal and same height as in last question, and its ultimate strength.

21. Describe and sketch the method of making the hydraulic press work water-tight, and calculate the diameter of the ram so that at 3 tons to the square inch of pressure it may lift 1000 tons.

22. Give the investigation for the general expression for the strain on a diagonal bar at any given position in the span of a lattice girder, when the weight is applied at the centre of the span.

23. Give the investigation for the strain as in last question, when the load is uniformly applied.

24. It is required to cross a river by a wrought iron girder bridge ; the clear span between the abutments being 86 ft., and having to carry a single line of railway on the narrow gauge. Draw out a figured sketch of the transverse section and elevation, consistent with the usual dimensions, and such as will pass the inspecting officer; the sides or vertical webs being boiler plate, not lattice work.

25. Design a cast iron girder for a span of 22 ft., consistent with the usual proportions, and of such strength as will sustain with perfect safety a load equivalent to a weight of 14 tons applied at the centre. Write out clearly the formula by which you work, and deduce it from the experiments on which it is based.

26. Give a statement of the design and construction of the Bow Bridge, with its chief dimensions, centreing, and coffer dam.

27. State the peculiarities of the tidal action in the Ballyteigue lough prior to its reclamation, and the consequences of the construction of the

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