GREY SCHOLARSHIP EXAMINATION. GEOLOGY. Examiner: PROFESSOR A. P. W. THOMAS. All questions to be illustrated with sketches or sections where possible. 1. Give some account of the phenomena of local metamorphism, and the changes produced by it in various sedimentary rocks. 2. What explanations may be given of a break in the geological record? Discuss the question how far breaks in the geological record are general. Quote evidence on this point. 3. Give some account of the conditions under which the Triassic Rocks of North-Western Europe were accumulated. Describe the usual lithological characters of the rocks and mention the included fauna. How far does the fauna represent the life of the period? 4. Write an account of the fauna of the oldest fossiliferous rocks. What evidence does such a fauna give on the question of the evolution of organic forms? 5. Describe the distribution and mode of occurrence of coaldeposits in New Zealand. What variations may be traced in the composition of the coal? What evidence have we as to the age and mode of accumulation of the deposits? 6. Give a succinct account of the most salient features in the geological structure of the country around Auckland. What fossil evidence have we of the age of the rocks? (b) Shew that, when an integral function of x is divided by x-a, the remainder is obtained by substituting a for x in the dividend. (c) Shew how to find the square root of a surd of the form x + √y. (d) Find the number of permutations of a number of things when they are not all unlike. 4. Explain the apparent paradox that the sum of an infinite geometrical progression may be a finite quantity. 5. For what limits of y is x real in the equation— 6. Out of 5 masters and 3 boys, a committee of 6 is to be chosen. In how many ways can this be done, (i.) when there are four masters in the committee, (ii.) when there is a majority of masters? N SINCLAIR SCHOLARSHIP EXAMINATION. 7. (a) Shew that in an obtuse-angled triangle, if a perpendicular is drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice a certain rectangle. (b) Shew that, if from any point outside a circle, a tangent and a secant be drawn, then the rectangle, contained by the whole secant and the part of it outside the circle, is equal to the square on the tangent. (c) Shew that similar triangles are to one another in the duplicate ratio of two corresponding sides. 8. Shew that, if the opposite angles of a quadrilateral are equal, it is a parallelogram. 9. Describe a circle that shall have a given radius and touch a given circle and a given straight line. 10. O is the centre of the circle circumscribing a triangle ABC; D, E, F are the feet of the perpendiculars from A, B, C on the opposite sides; shew that OA, OB, OC are respectively perpendicular to EF, FD, DE. 12. An isosceles triangle of wood is placed on the ground in a vertical position facing the sun. If 2a be the base of the triangle, b its height, and 30° the altitude of the sun, find the tangent of half the angle at the apex of the shadow. 13. Solve = 3, 4 sin (0+). cos (0 14. Prove that, in any triangle |