parallel to this, and of which the origin is a double point, the branches touching the axes of coordinates. 10. Determine the polar equation of the circle which touches the curve r = f(0) at the point ri, 01, and passes through another point r2, 02 on the curve, and hence derive the expression for the radius of curvature in polar coordinates. a 11. Prove that Sp (x) dx = ƒ¢ (a − x) dx. 0 xdx a2 cos2x+b2 sin2 x (x2 — a2)2 + (y2 — b2)2 = b4 where a > b, and find the volume generated by the revolution of this curve about the axis of y. COMPARATIVE ANATOMY AND ZOOLOGY. Professor McCoy, M.A., Sc.D. 1. Give as fully as you can Milne Edwards' theory of cycles and order of development of the lamellæ of stony corals, and the modifications which are suggested by the observed development of the membranous septa in young Actiniæ. 2. Describe the Hydrospires of the Blastoidea and the structure and classification generally of the Crinoidea. 3. In what respects do the Spatangidæ differ from the other Echinida? Detail as many abnormal peculiarities special to certain genera as you can in the group. 4. In what characters do the classes of the Articulata agree and differ? 5. What are the chief reasons for and against the systematic separation of the Molluscoidea from the Mollusca? Define as many Classes of each division as you can. PHYSICAL GEOLOGY AND MINERALOGY. Professor Mc Coy, M.A., Sc.D. 1. Explain as fully as you can the nature and origin of all the kinds of planes observable in Rock masses. = 2. Taking the horizontal distance 100, work out several cases of the depth and thickness of different strata at different angles of dip, and give examples of the methods of calculating the "throw" of faults. 3. Give as fully as you can the whole of the Earthquake movements named by Mallet, with their approximate characteristics of direction, velocity, and order of succession, and their geological effects, with the methods of determining the position of the central impulse. 4. Write down the mineral constituents of as many as you can of the igneous and metamorphic rocks. 5. Write down the indices of all the faces of as many fundamental or primary forms of crystals as you can, according to the methods of Whewell and Miller, and give the general symbols for the forms according to the systems of Weiss and Naumann. DEDUCTIVE LOGIC. The Board of Examiners. 1. What is the relation of Formal Logic to Truth? 2. How would you distinguish between Intuition and Thought? Characterise fully the products of Thought, and show the bearing of your division on logical science. 3. How does Veitch state the question of the primum cognitum? And what is his reply? 4. On what grounds does Veitch admit the Principle of the Sufficient or Determining Reason among the laws of thought? Add any comments. 5. What is Venn's interpretation, for the purposes of Symbolic Logic, of the existential import of propositions? Can this interpretation be applied to the traditional logic, consistently with the recognised forms of immediate and mediate inference? 6. (a) Show the equivalence of x = xy, x = = oy, and xy 7. Of my property, the portion insured consists of merchandise in Melbourne, and buildings in the country. What can be said generally of my Melbourne property? Work this in such a way as to show the use of Venn's fractional forms, and illustrate diagrammatically. 8. Given ab = y, and bd = z as premisses, find ad in terms of z and y. Also, from the same data determine the expression ad + ad in terms of z and y. Show your symbolic working. INDUCTIVE LOGIC. The Board of Examiners. 1. "One effect may have several causes.' Is this true? And, if so, in what sense? Refer, in your answer, to Venn's remarks on this subject. 2. Venn mentions the tendency, in Mill's Logic, to regard certain original collocations, or certain groups of natural objects (say the species of animals and plants) as lying beyond the bounds of scientific reach, and being in fact "uncaused." What passages in Mill's Logic are here referred to? Subject his doctrine to critical examination. 3. What meaning do you attach to the explanation of laws of Nature? and what are the limits of such explanation? 4. "It is incorrect to say that any phenomenon is the effect of chance." "It is frequently impossible to ascertain the cause of a phenomenon till we have first eliminated the effects of chance." Explain the meaning of Chance in these two passages. How do you know in the cases last referred to that chance has been eliminated? 5. State, and consider, Venn's argument that, even in calculating the probabilities of throws of dice or coins, we proceed from our experience of a series, extending the rule thus obtained by induction and analogy. 6. Should a distinction be drawn between Probability before and Probability after the event? Give your reasons. 7. Compare, generally, the method recommended by Bacon with that which he condemned. 8. Give an account of the various ways, enumerated by Bacon, in which idola tribus lead to error. MENTAL PHILOSOPHY. The Board of Examiners. 1. On what grounds did Descartes affirm the existence of a material world independent of the percipient mind? |