13. Shew how to determine the partial fraction corresponding to a pair of imaginary roots which are not repeated when a rational fraction is decomposed into partial fractions.

14. Find the volume generated by the revolution about the axis of x of the curve

1. Find the condition of intersection of two straight lines whose equations are given in the symmetrical form, and supposing the condition satisfied form the equation of the plane through the straight lines.

2. Define the polar plane of a point with respect to a conicoid, and find the equation of the polar plane of a given point with respect to the conicoid represented by the general equation of the second degree.

3. Assuming that the terms containing the products yz, zx, xy have been removed from the general equation of the second degree, find the different forms to one of which the general equation is reducible.

4. Find the general functional and differential equations of conoidal surfaces.

5. Find the principal radii of curvature and the lines of curvature on a surface of revolution.

6. Shew how to integrate a homogeneous equation of the first order.

7. Find the condition that a linear equation may be exact, and supposing the condition satisfied find the first integral.

8. Shew how to integrate a linear partial differential equation of the first order with two independent variables.

9. A point is in motion in any curve, find its accelerations along and perpendicular to the tangent at any instant.

10. Define principal axes, and shew that at any point of a material system there are always three principal axes at right angles to each other.

MIXED MATHEMATICS.-II.

Professor Nanson.

1. Find the resultant of two couples whose axes are inclined at any angle.

2. Define the central axis of a system of forces, and prove that at every point of it the value of the

D

principal moment is the same and is less than it is for any point not in the central axis.

3. Establish the differential equation satisfied at every point by the potential of a system attracting according to the law of nature.

4. A particle moves about a centre of attraction varying directly as the distance; determine the orbit and the position of the particle at any time.

5. A particle is projected from a given point in a given direction and with a given velocity, and moves under the action of a central attraction varying inversely as the square of the distance; determine the orbit.

6. A particle moves under given forces on a given smooth surface; determine the motion and the pressure on the surface.

7. Prove that the motion of a body acted on by any forces about its centre of gravity is the same as if the centre of gravity were fixed, and the same forces acted on the body.

8. State and prove the principle of vis viva.

9. If a fluid be at rest under the influence of forces which have a potential, shew that the surfaces of equal potential are also surfaces of equal pressure and of equal density.

10. Investigate the Lagrangian or integral equation of continuity.

PHYSICAL GEOLOGY AND MINERALOGY.

Professor McCoy, M.A., Sc.D.

1. Give examples of (a) chemically, (b) mechanically, (c) organically-formed Rocks, and state the characters and modes of origin referred to in their classification into Igneous, Aqueous, Aerial, and Metamorphic Rocks.

2. What are the "Basic" and the "Acidic" Igneous Rocks? Enumerate the commoner sorts of each, and discuss the main reasons for dividing igneous rocks into Plutonic and Volcanic.

3. What is the general mineral constitution of the Trachytes and the Dolerites? Describe some

of the chief varieties of each group.

4. What are the relations between Faults, Dykes, and Mineral Veins? Describe the more common appearances observable in the chief varieties of each.

5. Describe the modes of origin of the different kinds of Valleys, Hills, Plains and Table-lands, Outliers, and Escarpments.

6. Describe the chief characteristics of "bedding" in rocks, including Dip, Strike, Anticlinal and Synclinal lines, and the way in which inversion. may occur.

7. Calculate the proper angle at which a given angle of dip should be represented on a geological

section at a given oblique angle to the direction of the dip.

8. Describe the chief physical characters made use of in determining Minerals, and how to observe

them.

9. Describe the physical and chemical characters of the following Rock-forming Minerals :(a) Quartz, (b) Calc-spar, (c) Orthoclase, (d) Anorthite, (e) Talc, (f) Hornblende, (g) Augite.

10. Describe Wollaston's reflecting goniometer, and the method of using it for the determination of mineral species.

SYSTEMATIC ZOOLOGY.

Professor McCoy, M.A., Sc.D.

1. On what grounds would you classify disputed members of the Animal as separated from the Vegetable Kingdom?

2. What are the arguments for classifying the Sponges with the Colenterata?

3. Define the families of the Tribes Madrephyllacea and Madreporacea.

4. What are the general characteristics of the Podopthalmata, and how are the Families discriminated, into which the group is divided in ordinary classification?