bent into a circular arc, and prove fully the several steps of the investigation.

The top and bottom flanges are supposed to be parallel, and the material so proportioned as to sustain the above stress at every point of the span.

14. Describe a cast-iron girder of 30 feet span, which has to sustain a uniform load of 18 tons, and prove in detail that the dimensions you give are sufficient.

15. Give a full account of the mode of manufacture of Portland cement, its applications, &c., and a specification for it.

MIDDLE AND JUNIOR CLASSES.

MECHANICS AND HYDROSTATICS.

MR. GALBRAITH.

1. If the point whose mass is m be part of a system of points m, m', m", m", &c., and if this point be transported to another position, what is the effect thereby produced on the position of the centre of gravity of the system?

2. Prove that the centre of gravity of a tetrahedron is the middle point of the line joining the middle points of any pair of opposite sides.

3. Prove that the moment of inertia of a plane triangle is the same as that of three material points situated at the middle points of the sides, and whose masses are each one third of the triangle.

4. State the laws of friction, and give the construction for determining the force required to maintain a heavy body in equilibrium on an inclined plane, friction being taken into account.

5. Deduce from first principles an expression for the quantity of work stored up in a body revolving round a fixed axis with a given angular velocity.

6. If a heavy body, retained by a fixed axis, fall from one position to another, prove that the velocity acquired by the centre of gyration is that due to the descent of the centre of gravity.

7. What is the depth below the surface of the centre of pressure of a circular plate, the plate being vertical, and its centre 20 feet below the surface of the water.

8. There is a pump lifting water 29 feet: the diameter of the piston is I ft.; the play of the piston 3 ft.; and the pump makes 10 strokes per minute. Find how many gallons will be discharged per minute? and also the pressure on the piston.

9. Deduce the general equation for a diving bell sunk in salt water. 10. Find the expression for the moments of inertia of a rectangular parallelopipedon round its three edges a, b, and c.

MIDDLE CLASS.

MECHANICS, HYDROSTATICS, AND OPTICS.

1. State and prove D. Bernouilli's theorem as to the steady flow of fluids in tubes running full.

2. A double cube of cast iron stands on its base one foot square. How many foot pounds must be expended in order to overturn it round an edge of the base? One cube foot = 450 lbs.

3. Find with what momentum must this double cube be struck at its centre of gravity, in a horizontal direction, so as to overturn it.

4. Deduce from first principles the expression for the deviation of a ray of light in passing nearly perpendicularly through a thin lens.

5. Give Professor Townsend's construction for determining the direction of the emergent ray.

6. Explain the principle on which a pocket lens assists the eye in examining small objects, and give the expression for its magnifying

power.

7. If a girder supported at both ends be uniformly loaded, prove that if S be the coefficient of rupture the length of the girder, d is depth, and W the breaking weight.

8 Sad W =

8. If a beam be curved by a load, prove the following equation:

from it deduce the deflection at the end of a semi-girder loaded by Wat that point.

JUNIOR CLASS.

CHEMISTRY AND MINERALOGY.

DR. APJOHN.

1. Write the formulæ of oxalic acid and oxalate of ammonium, and explain how the former may be converted into the latter.

2. Give the formula of ferrocyanide of potassium, and explain its action on sulphate of copper.

3. Explain the modes of preparing N2O, and NO, and mention the properties by which they are distinguished.

200

4. Describe and explain Marsh's method of testing for arsenious anhydride.

5. By what ready method would you distinguish common limestone from dolomitic limestone?

6. How is sulphide of hydrogen prepared, and what action does it exert when passed into solutions of the following metals acidulated by hydrochloric acid, viz. :—

Ferric sulphate.

Cupric acetate.
Zinc sulphate.
Cadmium chloride ?

7. What is Bartholet's rule relating to double decompositions?

8. Write a table showing in groups the atomicities of the different elements.

9. How is barium sulphate converted into barium chloride, and what is the action of sulphuric acid on the latter salt?

10. Mention the principal gases which compose the atmosphere, the proportions by volume in which they are present, and the method of analysis to be employed with the view of determining these proportions. 11. Give Rose's notation of the face of an octahedron occurring in each crystalline system.

12. To each student the same ten minerals were submitted, whose names, formulæ, and crystalline systems were required of him.

1. If tan A =

and tan B =

√3

find the value of sin (2A + B). 2 21

2. Show how the sines and cosines of small angles are found, and determine the values of sin 30' and cos 30', to 6 places of decimals.

3. The sides of a triangle are 347°51, 458.72, and 539°23; calculate its angles and its area.

4. Find, to 6 decimal places, by aid of logarithmic tables, the value of

5. The base of a triangle is 1471, and the base angles are 47° 41' 10", 39° 32′ 24′′, respectively; calculate the sides.

du

; find

I

dx

7. Prove Maclaurin's theorem, and find the expansions of sin x, and sin - 1x, in ascending powers of x.

8. Being given one angle and the area of a triangle, determine it so that the sum of its sides shall be a minimum.

9. Find the greatest value of the fraction

12. Give a formula for approximating to an area by the method of equidistant ordinates; and apply it to find the area, being given the following ordinates in feet: 0, 35, 7°25, 9, 12*15, 13°35, 15, 17, 16, 14'75, 12'2, 10, 85, 6, 425: with an interval of 2-2 feet.

13. Show how to determine the superficial area of the portion of a sphere included between two parallel planes. A sphere of 20 feet radius is cut by two parallel planes, at distances of 4 and 10 feet from its centre: determine, approximately, the included portion of the surface.

14. Find, by descriptive geometry, the traces of a plane which passes through three given points.

15. Find, by descriptive geometry, the length of the perpendicular drawn from a given point to a given plane.

DR. DOWNING.

1. In a square 1.25 inches in the side, inscribe an equilateral triangle, and measure its side on the diagonal scale.

2. Give a general construction for describing any regular polygon on a given line. Describe a heptagon on a line 1 inch long.

3. Draw a scale 3 miles

=

2.63 inches, showing furlongs, and attach a diagonal scale to read chains; also give the Representative Fraction. 4. Draw a scale of 32, showing feet and inches.

5. Draw Plan and Elevation of a cylinder, radius of base I inch, height 2 inches, its axis making an angle of 57° with the horizontal plane.

6. Draw in isometrical projection a truncated cone, 2'-3′′ high, base 1'-3" radius, top 9" radius, scale inch

one foot.

7. How do you show that the ratio 49: 60 represents the ratio of the isometrical projection of a line to the original line?

8. Construct the plane containing three given points not lying in the same straight line.

9. How do you find the real form of the triangle made by the lines joining three points in space.

EXAMINATION FOR DEGREE OF LL.B.

REGIUS PROFESSOR OF LAWS.

1. Explain the following expressions :

The Science of Jurisprudence.

The Science of Positive Morality.

The Science of Ethics.

The Science of Legislation.

The Science of Morals.

2. State the distinguishing marks of sovereignty and independent political society.

3. Give Austin's analysis of the forms of supreme government.

4. Is the power of the sovereign capable of legal limitation? Whence have arisen the doubts upon the subject?

5. Give Bentham's criticism on

The contract of Hobbes.

The social contract of Rousseau.

The contract of Locke.

6. All the functions of law may be referred to four heads? Why is Liberty not ranked among the principal objects of Law?

7. What is the true idea of property? What does Bentham mean when he says, "Property and Law are born together, and die together" ?