3. Investigate completely the motion of a particle under gravity sliding on the smooth curve y = = c sin2 s/a in a vertical plane, y being the vertical ordinate and s the arc, and the velocity zero when y = c.

4. Investigate the moment of inertia of the tetrahedron ABCD, the planes through A being at

right angles, about a line through A and the centre of volume.

5. Find the time of a small oscillation under gravity of a thin rod of length placed inside a fixed

smooth vertical hoop of radius r.

6. Two discs, with given centres of gravity, masses, and moments of inertia, are moving in a plane in a given manner. Suddenly they become rigidly attached to each other. Find the general formulæ for the motion immediately afterwards.

7. Find the centre of mass of one of the two similar portions of a solid sphere cut off by two planes through the centre.

8. Investigate the tension of a heavy string about to slip on a rough vertical curve.

9. A smooth uniform elliptical disc slides in a vertical plane between two rods, each inclined at 45° to the horizon in that plane.

Shew that there are four positions of equilibrium, and determine their stability.

PHYSICAL GEOLOGY AND MINERALOGY.

The Board of Examiners.

1. How are igneous and aqueous rocks generally distinguished? Discuss carefully the more important exceptions to the general rules.

2. In ordinary stratified rocks, how are the planes of deposition determined in the more difficult cases? How are the strata differentiated, and what differences may circumstances produce in the period of time represented by each?

3. What is "false bedding," and its significance?

4. Explain Babbage's theory of the rising of isothermal planes in the crust of the earth.

5. Describe the usual characteristics of metamorphism in rocks.

6. Enumerate as many as you can of the more common rock-forming minerals.

7. How are the different systems of crystallisation defined and recognised?

8. What are pseudomorphs? How do they originate, and how are they recognised?

9. What are the chemical and physical characters of the more common kinds of felspars found as constituents of igneous rocks?

10. How are the different oxides of silicon characterised? How do the different kinds of quartz originate; and how are the "acidic" and "basic" igneous rocks characterised and supposed to arise?

STRATIGRAPHICAL GEOLOGY AND

PALEONTOLOGY.

The Board of Examiners.

1. Illustrate by sketches the mode of formation of geological sections from geological maps, mentioning the methods of using the instruments employed.

2. What is understood by the term "Geological Formations"? What are the chief differences between the views of the older and of the more modern geologists as to the grounds of accepting certain groups of strata as Formations"?

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3. What Oolitic genera of Coal Plants are present in, and which are absent from, carboniferous coalLearing rocks?

4. Give the generic characters of the more common Polyzoa of the Coralline Crag, and state the range in time of each.

5. Write down all the subdivisions usually adopted by geologists of the Tertiary and of the Lower Palæozoic Formations in the chronological order of their successive depositions.

6. Give in detail the modern subdivisions of the Laurentian, Cambrian, and Silurian geological systems, with the more characteristic fossils of each.

7. Enumerate as many as you can of the species of fossils peculiar to the London Clay, the Bagshot Sands, the Red Crag, the Aymestry Limestone, and of the cornstone and marl of the Old Red Sandstone.

8. Give the generic characters of Harpes, Catenipora, Ampyx, Asaphus, and Diplograpsus, with the geological range of each.

9. What are the peculiar characteristics and the ranges in time of Favosites, Cystiphyllum, Pleurodyctium, Petraia, and Calceola?

10. Give the generic characters of Coccosteus, Chiracanthus, Diplacanthus, Diplopterus, and Holoptychius, with the geological range of each.

DEDUCTIVE LOGIC.

The Board of Examiners.

1. Determine, concerning each of the following names, whether it is univocal or equivocal; singular, general, or collective; abstract or concrete; connotative or non-connotative:

Volume, brotherhood, dictionary, noble, parliament, astronomy, nation, emotion, England, the Legislative Assembly of Victoria, home, truth, the Chief Justice of Victoria, pity, recollection.

2. How would you treat, logically, (a) Exceptive, (b) Exclusive, (c) Indefinite, propositions? Give an example of your treatment of each.

3. Given a minor premiss in E or O, what must be the character of the major premiss in order that a valid conclusion may be drawn in a categorical syllogism? Justify your answer by referring to the principal rules of syllogism.

4. Give an example, in significant terms, of an enthymeme of the second order, expanding it into a

syllogism, then into an epicheirema, and lastly into a Sorites.

5. How would you define a Dilemma? Give examples of the different kinds of Dilemma.

6. On what principle did Hamilton found his doctrine of the quantification of the predicate? Give his list of propositional forms. On what grounds has it been held that no more than five thoroughly quantified propositional forms should be recognised?

7. What is the original meaning of ignoratio elenchi? Mention and describe the principal forms of this fallacy.

8. Examine the following, stating them in logical form, and pointing out fallacies if any :—

(a) Every good government tends to promote the prosperity of the country; the administration of Lord X is not a good government, and therefore has not that tendency.