3. Given the map of a property, in which coal is known to exist. Explain how you would determine the strike of the coal-bed; and state where you would recommend the owner to sink a shaft.

4. What is the coal-miner's rule called the "Rule of the V-shaped outcrop ;" and give the explanation of it.

5. Give a general description of the "Pillar and Stall;" and "Long Wall" methods of working collieries.

6. Draw a rough plan of Coed Talon Mine, North Wales, from the following description:

1. There are two shafts close together.

2. Three levels are extended from the shafts, viz.,

a. The principal horse road.

b. A dip level for water and air way.

c. A rise level, the thick pillars of which defend the horse way from the pressure of the workings.

3. Witchets (or boards), are driven out of the rise level c, 6 yards wide, and are holed into each other by intersections of similar width; leaving the pillars 3 yards square.

4. Three drifts are extended to the rise of the shafts, on the same principle as the levels already described.

7. If an engine make 16 strokes in drawing a kibble to the surface from a shaft, the depth of which is 80 fathoms, with round ropes not lying on each other; what must be the diameter of a flat rope cage, so constructed that the engine may make the same number of strokes as before, the thickness of the rope being inch.

8. At what point in a shaft will two kibbles meet, if the radius of the cage be 4 feet, the thickness of the rope 1 inch, and the depth of the shaft 1200 ft.

9. The "Stamps" at Polberro are worked at the following rate:

This machinery stamped in 1854, of tin ore, 30,201 tons. Express in horsepower the work done in pulverizing 100 tons of this ore, assuming the stamps to work 10 hours per day for six days in the week.

10. Define the following mining terms:-Shafts, winzes, stopes, levels, cross-cuts.

II. What are the chief minerals and substances found in lodes in connexion with metallic ores.

12. Classify the ores of copper geologically, and state their mode of occurrence in a mine.

13. What are the ores of Nickel, and where are they found in Great Britain?

14. What are the principal ores of manganese? How is their com mercial value determined?

E. gr. "Manganese guaranteed 60 per cent. f. o. b., Liverpool, at

60s. per ton."

What is the meaning of this statement?

15. It is required to sink a vertical shaft on the end of a level, and the diallings from the bottom of an old downright shaft are as follows:

You are required to enter the results of your calculation in the follow

ing form:

N. B.-Double credit will be allowed for Questions 1, 9, 15.

SCHOOL OF ENGINEERING.

Junior Class.

DR. SALMON.

A.

1. If the tangent of an angle be, find the sine, cosine, and tangent of its double.

2. Find from the equation

sin 0+ cos 02.

3. Solve to three decimal places the equation

0.3x2 -0.013x=4.75.

4. Calculate the logarithm of 2 in Napier's system.

5. Find the base and base angles of a triangle whose sides are 313.456, 412.789; and the contained angle 48° 15′ 15′′.

6. In the same case, find the base directly without first finding the base angles.

7. By what formulæ are the corresponding problems solved for spherical triangles?

8. Eliminate c between the equations

с

a2b2+ c2 2bc cos A, b2 = a2 + c2 2ac cos B;

and reduce your result to the simplest form.

8. Construct the traces of a plane through a given point and a given line.

9. Construct the points of intersection of a given line and a given

cone.

1. If the square of one side of a triangle be equal to the sum of the squares of the other two, prove that the triangle is right-angled.

2. Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of the sides.

3. If two chords in a circle intersect, the rectangles under their segments are equal?

4. Prove that the rectangle under two sides of a triangle is equal to the rectangle under the perpendicular and the diameter of the circumscribing circle.

5. The sides of a triangle are 2, 3, 4; what is the diameter of the circumscribing circle?

7. Prove that the logarithm of a product is equal to the sum of the logarithms of the factors.

8. Divide x − y by x3- ys; and reduce to the simplest form the sum of 5V8 and V1.

12. Prove that, in a plane triangle, c = a cos B + b cos A, and eliminate c between this equation and b = = c cos A+ a cos C.

MR. M. ROBERTS.

1. A weight of 25.3 lbs. just balances a weight of 83.2 lbs. on a wheel and axle; if the radius of the axle is 6.69 inches, find that of the wheel. 2. Find the height to which a body, projected vertically with a velocity of 83 feet per second, will ascend.

3. A cord, 5 feet long, is able to bear a weight of 37 lbs. ; a ball, attached to the end of the cord, revolves horizontally 252 times in a minute, and just breaks the cord. Find the weight of the ball.

4. A weight of 13 lbs. draws another of 7 lbs. over a pulley through 4 feet; they are then suddenly detached. Find their respective velocities at the end of 4 seconds.

5. A weight of 25 lbs. raises another of I cwt. 13 lbs., by means of a wheel and axle whose radii are 2 feet and 4 inches respectively. Find the space through which the lifting weight descends in 8 seconds of time.

6. What is meant by the dynamical measure of a force? If the length of a seconds pendulum at London is 39.14 inches, find the dynamical measure of gravity.

7. A globe 1 feet in diameter is half immersed when floating in water; find its weight.

8. The pressure on the base of a cylindrical vessel filled with water is 0.11687 ton; find the height of the vessel, if it is equal to two-thirds of the diameter of the base.

9. Two bodies which weigh each 61⁄2 lbs. in air, weigh together 43 lbs. in water, and one of them alone weighs 5 lbs. in water; find their specific gravities.

10. If the elastic force of a mass of gas whose volume is 100 cubic inches be 30.275 inches of mercury; calculate its elastic force, if it be allowed to expand to a volume of 387 cubic inches.

EXAMINATION FOR ADMISSION TO THE MILITARY CLASS, OCTOBER, 1859.

ARITHMETIC AND MENSURATION.

1. If the length of a degree on the Earth's surface be assumed to be 365,000 feet, calculate the number of miles in the Earth's diameter ?

2. From the fact that the distance of the pole from the equator is ten million metres, calculate the number of miles in the earth's diameter.

3. From the fact that two cubic inches of water weigh 505 grains, and that mercury is 133 times heavier than water, calculate the number of cubic inches in a ton of mercury.

4. Calculate to four places of decimals the number of inches in the side of a cubical box which will just hold this quantity of mercury.

5. Find, by a Practice sum, how much must be paid on a debt of £759 198. 2d., at a composition of 138. 7d. in the pound.

6. How much will it cost to replace a cistern if £1 118. 6d. per cwt. be allowed for the lead, which weighs 6 cwt. I qr. 10 lbs., the new one weighing 8 cwt. 2 qrs. 14 lbs., and the price of the new lead being 40s. 6d. per cwt. ?

7. State the following question according to the Double Rule of Three, and find the answer:-A beam 28 ft. long, 1 ft. 3 in. broad, and 10 inches thick, costs £4 188. 6d. ; what will be the price of a beam 21 ft. long, 1 ft. 8 in. broad, and 1 ft. thick.

8. A vessel is valued at £5000, its cargo at £8000; what premium must be paid to cover both loss and premium, the rate of insurance for the vessel being 85s. per cent., and that for the cargo 1128. per cwt.?

9. A number in the duodecimal scale is expressed by 53718; find its expression in the senary scale.

10. Calculate by duodecimal arithmetic the weight of gunpowder, 55 lbs. to the cubic foot, which will be required to fill a chamber 4 ft. 3 in. long, 2 ft. 7 in. wide, and 3 ft. 2. in deep. The answer to be given in the decimal scale.