1. In the equations which express the condition of a double-acting engine in uniform motion, what are the values of the quantities e and k ?

2. Calculate their numerical values for an expansion of one-half, the clearance being supposed equal to one-twentieth.

3. Calculate the horse-power of a condensing engine from the following conditions:

Diameter 80 inches.
Revolutions 18 per minute.

6 feet.
Evaporation = 2 cubic feet.

Expansion one-half. 4. In this case, what is the value of the pressure in the cylinder before the steam is cut off ?

5. Deduce an expression for the diameter of cylinder in inches of a condensing engine working with steam of low pressure, in terms of the evaporation, expansion, horse-power, and velocity of piston. 6. Prove the following expression for the horse-power :

P + f + y
H. P. =


42 CS

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7. Prove that the maximum horse-power for a given expansion corresponds to the least possible velocity.

8. What is the expansion which corresponds with the absolute maximum horse-power?

9. Express the velocity of the piston of a locomotive in feet per minute, in terms of the velocity of train in miles per hour; also the pressure of steam in the cylinders due to the weight of train, in terms of the number of tons in the engine, tender, and carriages on a level rail.

10. How must this expression be modified if the train ascend or descend a gradient of 1 in n?


1. A wall of brickwork (weighing 112 lbs. per cubic foot), 2 ft. 3 in. thick, and 23 ft. high, sustains on the inner edge of its summit a certain pressure on every foot of its length; the direction of the pressure is inclined to the horizon at an angle of 65o. Find its amount when it will just not overthrow the wall.

2. In the last question, if the pressure is applied by means of a bracket at a horizontal distance of 2 ft. 6 in. from the inner edge of the wall, determine the amount when it will just not overthrow the wall.

3. Two rafters, AB, AC, are each 24 ft. long, and their feet are tied by a wrought iron rod whose length is 40 ft.; a weight of ths of a ton is suspended from A. Find the strain on the tie. If the rod have a section of ths of a square inch, find the weight suspended from A which will break the tie. [The tenacity of wrought iron is 67,200 lbs. per square inch.)

4. Determine the elongation of a steel bar, 2} in. square and 35 ft. long, when subjected to a strain of 50 tons. [The modulus of elasticity is 29,000,000.]

5. A river wall of Aberdeen granite (specific gravity 2.625), 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 thickness of the base is 12 ft., what is the height of the wall ?

6. A wall of Portland stone, 25 ft. high and i} ft. thick, has to sustain on each foot of its length a thrust equal to a weight of 3 cub. ft. of stone, acting in a direction inclined to the vertical at an angle of 60°. Find the point of a bracket to which this pressure must be applied so that the line of resistance may cut the base 3 in. within the extrados.

7. A mass of earth (specific gravity 1.6), whose surface is horizontal, presses against a revêtement wall of brickwork whose section is rectangular ; the top of the wall is on the level of the ground, and its height is 18 ft. If the natural slope of the earth is 30°, find the requisite thickness of the wall to enable it to sustain the pressure of the earth.

8. A beam fixed at one end only has a uniform load of intensity w, and an additional load W at the extreme end of the projecting portion; find the greatest bending moment.



1. Describe the blowpipe characters of red stilbite.
2. Describe the physical and blowpipe characters of tinstone.

3. How is gadolinite distinguished from the minerals that most nearly resemble it; and what are they?

4. Name the important earthy constituents that the blowpipe fails to detect readily.

5. Give the blowpipe characters of barytocalcite. 6. The underlay of East Pool, South Lode, is 24° 30' N. from grass for 105 fathoms, when it reaches the granite, and changes its underlay to - 40° N., along the junction of the granite and slate, for 88} fathoms; what is the total depth of the lode at this point.

*7. At Pedn-an-drea mine, the underlay of the Engine lode is 37° N., and that of Martin's lode, which lies 25 fathoms to the south of it, is 46' 30'N. At what depth will these two lodes intersect?

* 8. A diagonal shaft was found to underlay and measure as follows:

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Find the depth of the end of shaft, and the point at which a perpendicular shaft should be commenced to reach the end.

* Questions marked thus count double. In addition to the preceding examination, the Candidates were examined orally on the principles of Geology and Mining, and were required to produce Geological sections made by themselves in the field.



1. Calculate the proportions of nitre, oil of vitriol, and water, necessary to yield 16 avoirdupois ounces by weight of nitric acid, having the formula HO, NO3 + 3H0.

2. Give the reactions which occur during the solution of silver and of bismuth in nitric acid.

3. Terchloride of gold may be reduced by oxalic acid, green vitriol, and arsenious acid. Describe the reactions which occur in each of these


4. 100 lbs. of a magnesian limestone, containing nothing but carbonate of lime and carbonate of magnesia, left when burned 54.15 lbs. What is its atomic composition ?

5. Explain the process by which chlorine is developed, and the products formed when the gas is passed into a solution of green vitriol.

6. How would you prepare hydrogen and arsenietted hydrogen ? and, if these gases were mixed, how would you determine the amount of each ?

7. Describe the chemical operations by which the value of a hydraulic lime may be estimated.

8. If a gallon of water includes 7 grains of lime and 4 grains of magnesia, what is its degree of hardness?

9. Describe minutely the manner of making the analysis of bone earth.

10. How would you prepare nitrous oxide ?—and how by the voltaic eudiometer would you effect its analysis ?

11. Gypsum is often found as a six-sided prism, terminated at each end by oblique dihedral summits. Give the formula of the mineral, and the notation of its faces.

12. In what particulars do dioptase and chrysocolla agree, and in what do they differ?

13. A mineral from Glenarm, having the form of a hexangular dodecahedron, the apices and basal edges of which were tangentially truncated, was found by Rammelsberg to have the following composition :








100.46 Describe the mode of effecting its analysis, and give its formula, its name, and the notation of its different faces.

14. Give the formulæ and crystalline systems of the following minerals :

1. Electric calamine.
2. Glance copper.
3. Mispickel.
4. Sparry iron ore.
5. Bournonite.

6. Malachite.
15. How is galena smelted, and what is the theory of the process ?


1. Calculate the horizontal strain in the top and bottom flanges in either of the two wrought iron main girders in a bridge for carrying a single line of railway over a river. Clear span, 126 ft.; depth of beam, 11 ft. ; weight of each main girder, 29.5 tons; total moving load when the bridge is covered, 149.5 tons; total weight of the rails, cross girders, sheeting of timber, and gravel, 39.5 tons. The computation to be made as in Mr. E. Clark's large model.

2. Compute the available area in the top and bottom flanges at the centre, necessary to meet the requirements of the Board of Trade in this bridge.

3. If the above be constructed as a lattice beam, and the first diagonal rising from the abutment make 45° with the horizontal; calculate, with the above data, the compression produced in it, and the requisite transverse section of metal.

4. If the camber of the bottom flange be made 2 inches at the centre of a wrought iron girder, 140 ft. span, calculate its amount at 20 ft. and at 35 ft. from the centre, the curve being an arc of a circle.

5. Prove the following. Rule for determining the quantity of water in gallons per 24 hours, delivered from the catchment basin draining into an impounding reservoir :

40,000 * M * I = gallons in 24 hours ; M being the area in square miles, I the depth in inches of the available rain-fall.

6. Calculate the discharge of a pipe 32 in. in diameter, having a fall of 150 ft. in 12 miles.

7. Calculate the number of cubic yards in an excavation having the following dimensions :— Width at formation level, 18 ft.; slopes, 1 to 1,

[blocks in formation]


<....110 ft. ........350 ft. . . 290 ft. ........89 ft. > 8. Calculate the land required for the above cutting, without including fencing; and if the fencing be 4 yds. on each side, compute the additional quantity of land.

9. A stream being completely dammed up, and the discharge taking place altogether by a sluice, prove that the height to which the water is raised above the sill of the sluice, which height is represented by H, has the following value :

H= x 0.04065,

82 in which S is the area in square feet of the sluice.

10. If the discharge, as in Question No. 9, took place over the crest of weir whose length is 1 feet, prove that the rise of the water above the crest, represented by H, is



H = 0.429

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11. In the case of the piers of a bridge, or other partial obstruction, let L, V, and S be the width, velocity, and transverse area of the river uninfluenced by the obstruction, and I, v, and s the corresponding values at bridge; the depth at s being p, and that at S being p + x, or, in other words, ac being the surface fall at the site of the work. Prove that

29 | m2 72 p2 L(P+X) m being the coefficient of contraction.

12. Describe, in full detail, the method of ranging the centre line of a tunnel on the surface between the two points chosen for the entrances ; and also the method of transferring this line to the headings below.

13. In a tunnel through solid rock, describe and sketch the method of carrying on the excavation, and securing the ventilation; stating the rate of progress that may be expected in the various parts of the work, and the position of the bedding of the rock most favourable in a tunnel.

14. In a tunnel through clay, describe and sketch the method of timbering up the different lengths, describing the technical terms used.

15. Deduce the modulus of elasticity, in lineal feet and in pounds weight, for wrought iron when in extension, and the same when under compression.

16. Two bars of wrought iron, each 3 inches broad and i} thick, were compressed until they began to sink down, one having 10 ft. length with 46,050 lbs., the other 7.5 ft. long with 91,746 lbs.; calculate the power of the length to which the ultimate strength is proportional.

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