3. State the leading facts known with respect to the cleavage of minerals. Give the directions of cleavage in the order of perfection for each of the following:-gypsum, augite, hornblende, enstatite, orthoclase, muscovite.

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4. Assign to their respective crystalline systems the following: biotite, axinite, millerite, leucite, spodumene, analcime, nephelene, anatase, franklinite, autonite.

5. Give a list of the metals which have been found in the native state. Describe, in the case of any three of them, the conditions under which they occur.

6. Describe the physical characters of the following:-calcite, strontianite, witherite, aragonite, cerussite, siderite, smithsonite.

7. Explain what is meant by paragenesis, illustrating your remarks by reference to 'tinstone'.

8. Give an account of the family characteristics of the zeolites. Name, and give the chemical composition of, any six species.

9. Describe fully the characters of orthoclase felspar. Name its chief varieties.

10. State the chemical composition of-(a) olivine, and (b) iolite. Trace the series of alterations to which each is liable subsequent to its formation.

II. Describe the physical characters, and give the chemical composition, of the chief ores of copper.

12. Name the minerals which are used as 'gems', and describe any four of them.

MR. JOLY.

1. On a vertical right cylinder of 2" diam., determine the projection of a helix of 1" pitch.

2. Find by construction a triangle equivalent in area to a regular hexagon, the sides of which are 11" in length.

3. A column, elliptical in section, stands with its axis vertical to H. P. It is cut by a plane inclined at 30° to H. P., and making 90° with V. P. ; the plane passes completely through the column. Determine by projection the surface of section. Dimensions of column, 2" high; axes of elliptic section, 2′′ and 11′′.

4. What is the R. F. of the Ordnance Map known as 'the 25"'?

5. Construct a scale reading to I ft., and showing 528 ft. on a scale of 10' to one statute mile.

6. Describe a parabola, given its directrix and focus (r′′ distant from directrix). Draw a tangent to the curve at any point on it.

7. A conical depression, 3" deep and 21" wide at top, is exposed to light falling in parallel rays in a direction coincident with the diagonal of a cube; trace on the plan the shadow cast in the cone by its circular edge.

8. Reduce to metric measurement the area of a field of 27 acres.

9. The traces of a plane make 30° and 45° with x, y; find the inclination of the plane to both planes of projection.

IO. Read and explain the vernier scales submitted to you.

MIDDLE AND JUNIOR CLASSES.

DR. TRAILL.

I. Two spheres touch one another; find the distance of their centre of gravity from the point of contact, the radii being 5 and 10 feet, respectively.

2. A heavy particle is placed on a smooth horizontal plane, and it is acted on by a force tending to a fixed point, and proportional to the distance from that point. Show that the motion is oscillatory, and determine the velocity at any point, and the time of a complete oscillation.

3. If a heavy particle be dropped down a well directed towards the centre of the Earth, which side of the well will the particle strike in consequence of the Earth's rotation.

4. A shot weighing 80 lbs. is fired from a gun weighing 5 tons, and leaves the gun with a velocity of 1400 feet per second; find the velocity of the gun's recoil.

5. A ball weighing 10lbs. is projected on a horizontal plane with a velocity of 40 feet per second, and the friction is equal to 4th of the weight; find the distance to which the ball will go before it comes to

rest.

6. Find the time occupied by a stone (sp. gr. = 3.2) in falling from rest through 55 feet of water.

7. A cubic inch of one liquid weighs 300 grains, and of another 400 grains. A body immersed in the first weighs 300 grains, and in the second 100 grains; what is the real weight and the volume of the body?

8. A cylinder floats vertically in a liquid. Compare the forces necessary to raise it and to depress it to an equal extent.

9. Prove that in the steady flow of liquids from an orifice, the velocity generated from rest is that due to the "fall of free level."

10. Find what quantity of cork must be attached to a man whose weight is 168 lbs., and sp. gr. = 1.12, so as to enable him just to float, immersed in water.

MIDDLE CLASS.

MR. CRAWFORD.

1. Describe the various methods of ascertaining a distance (which cannot be directly measured) to a flagstaff on the opposite side of a river

(a) when using the chain alone; and

(b) with a chain and an instrument for measuring angles.

2. If you wanted to measure an offset (at right angles to a base line) towards an object 4 or 5 chains distant, how would you determine the exact point upon the base line from which to start your offset, when working with a chain alone?

3. Explain the process of plotting a survey by the method of “latitude and departure," and show how the necessary distances are obtained.

4. When observations in levelling are made by means of longer sights in one direction than in another, certain corrections should be applied to them. What is the nature of these corrections?

5. To what scale are the general Ordnance Maps of Ireland plotted? and to what datum do the levels marked upon them refer?

6. Describe the various operations necessary in the office and on the ground for a line of railway before beginning to execute the earthworks.

7. What slopes are usually adopted for railway cuttings and embankments in the various kinds of soil?

8. What cubic quantity of excavation in ordinary earth is a fair average day's work for a man where the "lead" does not exceed one "barrow run," the "getters," "fillers," and "wheelers" all being included in the number?

9. What is the usual length of a "barrow-run" in ordinary excavation and explain how it should be regulated according to circum

stances.

10. What, as a general rule, is the average cost of short railway tunnels for double line through ordinary soils? Give a sketch crosssection, with dimensions and calculations of the cubic quantities of excavation and lining per lineal yard of tunnel.

II. What is meant by the expression "hydraulic mean depth," and how is it obtained?

12. Give the formula that expresses the theoretic velocity of water issuing from an orifice, and explain how you obtain the quantity dis

charged in a given time under the various conditions which most frequently occur in practice.

13. Give the formula for the flow of water through an open channel, and show how it is arrived at.

14. Explain the nature and use of the rain-gauge, and give as far as you can the average rainfall at different parts of the British isles.

15. What are the different kinds of drains in most common use for land drainage?

16. Describe the process of laying out a field for drainage purposes. State also what depths would you sink the drains in the case of different soils, and give the approximate cost of drainage per acre in a moderately retentive soil, stating the depth of the drains and their distance apart.

DR. TRAILL.

1. The diameter of the piston of an engine is 80 inches; the mean pressure of the steam is 12 lbs. per square inch, the length of the stroke is 10 feet, the number of strokes made per minute is II. How many cubic feet of water will it raise per minute from a depth of 250 fathoms, its modulus being 0.6?

2. Find the moment of inertia of a rectangular plate whose thickness is K, and its sides a and b, with regard to an axis through its centre of gravity at right angies to its plane.

3. Show that the moment of inertia of a sphere about any diameter is 1 πpr3.

4. Three cog-wheels work on parallel axes; A makes p revolutions per minute, it carries a wheel of my teeth, which works with a wheel of ni teeth on B; B also carries another wheel of m2 teeth, which works with a wheel of n2 teeth on C; find the number of revolutions per minute made by C.

5. If P and Q be two parallel forces acting in contrary directions and keeping a body in equilibrium, which is movable about an axle which rests on a bearing, and if the equilibrium is about to be broken either by Por Q, show that

6. Distinguish carefully the terms "sheer stress," "sheer strain," and "bending moment," and show that a "pure shear strain" consists of a compressive strain in one direction, accompanied by a tensile strain in the perpendicular direction, these strains being each equal to half the shear strain.

7. A horizontal bank of earth [sp. gr. = 1.7] presses against a vertical wall 20 feet high whose top is level with the earth; the "natural slope" of the earth is 45° show that the pressure of the earth on each foot of the length of the wall lies between 1 and 13 tons.

8. If the given exterior forces acting on a jointed frame are in equilibrium, prove that the assumption of the magnitude and position of any two sides determines all the other sides; and if they be not in equilibrium on a given polygonal frame, show how to determine their resultant.

9. Show that the curve of bending moments for a uniformly distributed load is a parabola.

10. Draw the stress diagram of the "Bowstring Roof" having 7 sides on the outer and 6 sides on the inner curve.

MIDDLE CLASS.-SUPPLEMENTAL.

THEORY OF STEAM ENGINE, ETC.

MR. FITZGERALD.

1. Describe how to measure the relation connecting the temperature and pressure of saturated steam.

2. The relative volume of steam at 220° F. is 1200: find the minimum quantity of coal per hour which would supply steam to an engine using 8 cubic feet of steam per stroke, and running at the rate of 30 strokes per min., assuming that 1 lb. of coal can evaporate 8 lbs. of water in the boiler used.

3. Explain the advantages of superheating steam in steam engines.

4. Calculate the difference of temperature of the water at the top and bottom of Niagara, when it falls 165 feet, supposing the work done in falling to be all used in heating the water :

(a) If 100,000,000 tons of water go over per hour, calculate the quantity of heat produced per hour.

B) What is the corresponding power developed?

5. What is meant by a reversible heat engine, and what are the conditions that an engine be reversible? Explain why it is reversible if these conditions be fulfilled.

6. Calculate the horse power indicated by the accompanying diagram, and remark on its peculiarities.

7. Describe the construction of any instrument used for measuring powerful electric currents in amperes.

8. Describe the construction of any electric arc-light regulator.

9. Calculate the electrical energy required to light 24 incandescent lamps in parallel circuit, each lamp requiring an el. m. f. of 44 volts, and a current of 8 amperes, and the resistance of the connections, &c., being .75 ohms.

10. What is meant by saying that an ohm is 109 c. g. s. units of resistance? What is a c. g. s. unit of resistance?