5. Find the differential equations of the lines of curvature on any surface.

6. Shew how to integrate the general linear ordinary differential equation of the first order.

7. Shew how to solve the general linear ordinary differential equation with constant coefficients.

8. Shew how to integrate a linear partial differential equation of the first order.

9. A point is in motion in a plane curve; find expressions for the components of acceleration along and perpendicular to the radius vector.

10. Shew that at every 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 conditions of equilibrium of a rigid body resting on a smooth plane.

2. Investigate formula for the coordinates of the centre of gravity of a solid referred to polar coordinates.

3. Establish the differential equation satisfied at any point by the potential of a gravitating system.

4. A particle moves under an attraction in its line of motion varying inversely as the square of the distance of the particle from a fixed point in that line; determine the motion.

5. A particle being acted on by a central attraction determine the polar equation of the orbit, and shew how to determine the position of the particle in its orbit at any instant.

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

7. Obtain the equation of motion of a rigid body about a fixed axis, and shew how to find the pressures on the axis.

Obtain the general equations of motion in two dimensions of a rigid body.

9. Define the centre of pressure of a plane area, and obtain formulæ to determine its position.

10. Investigate the Lagrangian form of the equation of continuity.

SYSTEMATIC ZOOLOGY.

The Board of Examiners.

1. What are the general characteristics of the Protozoa, and into what classes are these animals divided?

2. The order Foraminifera contains naked and shelled sections. Into what families are the shelled forms divided in d'Orbigny's classification, and how are the families defined?

3. Define the order Heliozoa and its subordinate families Actinophryide, Acanthocystidae, and the Clathrulinæ.

4. Describe briefly the chief families of the Radiolaria.

5. Describe the characters of the class Infusoria and its four chief orders.

6. Give the general characters of the Schizomycetidæ, and the chief sections into which they are divided by systematic writers.

7. Describe the families of the order Zoophytaria.

8. Define the subkingdom Vertebrata. Into what classes is it divided?

9. In what characters do the Batrachia agree with, and differ from, Fishes and the higher Reptiles?

10. Define the Teleostea. In what characters do the subordinate groups Cycloida, Ctenoida, Siluroida, Plectognatha, and Lophobranchiata agree and differ?

PHYSICAL GEOLOGY AND MINERALOGY.

The Board of Examiners.

1. In what way may bedding, or planes of deposition in rock masses, be recognised in ordinary and in difficult cases? What causes render these planes obscure in some rocks, and how do you proceed to ascertain the facts in such cases?

2. If the outcrop of a stratum shews a given angle of dip, at what depth would you expect to find it at (1) a given distance measured on a horizontal surface in the direction of the dip; and (2) at the same distance in a direction half-way between the dip and strike?

3. What relations are generally found between the scarp and the talus sides of convolutions of

rocks, and the forces producing the disturbances?

4. What is Metamorphism in rock masses, how is it recognised, to what is it due, and how do aqueous rocks become subject to it?

5. Describe clearly the general distinctive characteristics of Faults and Veins.

6. How are igneous rocks classified? Give examples of the chief groups, founded on chemical and physical considerations.

7. Mention the chief groups of Minerals formed by giving chief value in the classification to the

electro-negative and to the electro-positive constituents respectively.

8. By what geometric and optical characters are each of the various systems of crystallization distinguished?

9. Give the formulæ, percentage composition, and oxygen ratios of the commoner species of Felspars.

10. Give a list of the chief mineral species forming Igneous Rocks, and state how they may be recognised.

STRATIGRAPHICAL GEOLOGY AND

PALEONTOLOGY.

The Board of Examiners.

1. What are the general characters of the Archæan or Azoic Rocks, and what are the opposing views as to the nature of Eozoon, with the arguments for and against each view?

2. Write down the generally-adopted systems, or larger groups, of the fossiliferous stratified Rocks in chronological order.

3. How are the Devonian systems of rocks of (a) The Continent of Europe, (b) South of England, (c) Scotland subdivided into separatelynamed divisions, and what parts of each are supposed to be synchronous ?

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