is not a demand for labour"? Criticise the theory therein contained. 5. Explain the nature of Increasing Return. 6. Does the Ricardian theory of Rent hold good in the case of leases of building-sites in towns ? 7. Point out the resemblances and differences between a QuasiRent and a Producer's Surplus. 8. Discuss the reasons that have been advanced for the treatment of Land, from the point of view of taxation, as a special form of property. 9. Do the arguments in favour of State-control of Production apply equally to the State-control of Distribution? POLITICAL ECONOMY (SECOND PAPER). WEDNESDAY, 29TH SEPTEMBER 1909-12 NOON TO 2 P.M. (Not more than six questions to be answered.) 1. To what extent and in what sense can a 66 said to exist in any country? wages-fund" be 2. Distinguish between Value and Price; and show the various ways in which values are fixed. 3. Explain the relation of "Utility" to Value on the one hand, and on the other to Demand and Supply. 4. Would Bimetallism be a satisfactory solution of such difficulties as have arisen from time to time in the money-market? 5. Does International Trade benefit equally all the nations which take part in it? 6. Describe briefly the historical development of the relation of the State to the Poor. 7. Explain the economic system of the medieval manor. 8. What were the various influences that produced the rise of sheep-farming in England? 9. Which period of English history do you consider to have produced the greatest development of the mercantile marine? Give the reasons for your view. POLITICAL ECONOMY (FIRST PAPER). FRIDAY, 18TH MARCH 1910-12 NOON TO 2 P.M. (Not more than six questions to be answered.) 1. What is the effect of the exportation of capital upon the condition of industry inside the country? 2. Can the theory of the Wages Fund be said to throw any light upon the question of Unemployment? 3. Explain the relation between Rent and Prices. 4. In what ways does the law of Supply and Demand affect the value of goods whose production is subject to the law of Increasing Return? 5. Of how many different elements do you consider the profits of a joint-stock company to be made up? 6. What will be the probable effect of the action of Wages boards operating in certain selected trades? 7. Are there any cases in which the foreigner can be said to pay the duties that are levied on imported goods? 8. Explain the results of the formation of trusts and cartels upon Production and upon Consumption. 9. Is it economically possible for a nation to spend too little upon luxuries? POLITICAL ECONOMY (SECOND PAPER). SATURDAY, 19TH MARCH 1910-12 NOON TO 2 P.M. (Not more than six questions to be answered.) 1. Should the Economic Interpretation be applied to history without qualification? 2. Explain carefully the functions performed by Bills of Exchange in the organisation of Industry. 3. What causes do you assign for the commanding position held by England in the banking world? 4. Do you consider it possible to secure proportionate equality in the incidence of taxation? 5. State and explain the importance of the conception of a margin in economic theory. 6. Explain what is meant by the "Old Colonial System," and discuss its effect on the history of the Empire. 7. What improvements took place in the methods of English agriculture in the course of the Eighteenth Century? 8. Describe the conditions of the English poor, as revealed by the Report of the Commission of 1834. What measure of success attended the remedies that were devised? 9. How much data have we for calculating the chances of agricultural co-operation to be applied in particular portions of the British Isles? GEOLOGY, INCLUDING MINERALOGY (FIRST PAPER). THURSDAY, 30TH SEPTEMBER 1909–9 TO 11 a.m. 1. Describe the characteristics and mode of origin of the following rock types: pitchstone, mica-schist, basalt, breccia, greensand. 2. What are the conditions which give rise to landslips? Give examples of landslips which have occurred in Britain. 3. Write a short account of the Chalk, and discuss its mode of origin. 4. Give an account of foraminifera, corals, and crinoids as rock-formers. 5. Explain and illustrate by sections the following structures: inlier, reversed fault, unconformity, false-bedding. GEOLOGY, INCLUDING MINERALOGY (SECOnd Paper). THURSDAY, 30TH SEPTEMBER 1909-3 TO 5 P.M. 1. Give a brief account of the volcanic necks in the neighbourhood of St Andrews. 2. Distinguish between lamination, foliation, and cleavage in rocks. 3. Describe the fauna of either (a) the Old Red Sandstone, or (b) the Trias of Britain. 66 4. Explain the origin of sea-lochs, river-terraces, caves, and crag-and-tail." 5. State the composition and describe the mode of occurrence of one important ore of each of the following: lead, copper, tin, iron. QUESTIONS FOR ORDINARY DEGREE OF M.A., FOR FIRST SCIENCE, AND FOR FIRST M.B., Ch.B. EXAMINATIONS. MATHEMATICS (FIRST PAPER). TUESDAY, 28TH SEPTEMBER 1909–9 to 11 a.m. 1. When are two plane polygons said to be similar and similarly situated? ABC......, A'B'C'...... are two similar and similarly situated plane polygons; show that AA', BB', CC', ...... are concurrent. Show that two similarly situated squares have in general two centres of similitude. What are the exceptional cases? 2. A, B, C, D being four collinear points, prove that and if the ratio AB.CD+BC.AD+CA.BD=0; AC.BD BC.AD be written (ABCD), prove that (ABCD)=(CDAB)=λ (say), and deduce the value of (BCDA). 3. If a straight line cuts the sides BC, CA, AB of a triangle in X, Y, Z respectively, prove that BX.CY.AZ=CX.AY.BZ. Show that the tangents drawn through the vertices of a triangle to its circumscribing circle meet the opposite sides in three collinear points. 4. If X, Y, Z are the mid-points of the sides of the triangle ABC, show that the feet of the perpendiculars drawn from the vertices on the opposite sides lie on the circle XYZ. Show that the point in which the three perpendiculars meet is a centre of similitude of the circles XYZ, ABC, and find their other centre of similitude. 5. When is a straight line said to be cut in harmonic section? If ABCD is a harmonic range, and any point O be joined to A, B, C, D, prove that any line cutting OA, OB, OC, OD is also divided harmonically. 6. When are two points said to be the inverse of each other? If A', B' are the inverses of A, B, show that A'B'=AB. R2 where O is the centre of the circle of inversion, and R the length of its radius. Establish by inversion, or otherwise, the theorem: "The sum of the rectangles contained by the opposite sides of a quadri lateral is greater than the rectangle contained by its diagonals"; and mention the exceptional case. 7. Given a tetrahedron ABCD, prove that only one sphere can be (1) inscribed within it, (2) circumscribed about it; and show how to find the centre in each case. 8. If sin is given equal to sin a, show that every possible value of is included in the two formulæ 2n+a and 0 Hence show that cos has four values, and find them. 9. Plot the graphs of cos 20 and 2 cos 0; and obtain from your diagram the general solution (approximate) of the equation cos 20=2 cos 0. Solve directly for cos the equation cos 20=2 cos 0, and reconcile your answer with the solution furnished by your diagram. 10. Establish for any triangle ABC the formula The lengths of the sides containing the right angle of a rightangled triangle are 201 and 199. Assuming that when ĕ is small tan approximates to e, determine the acute angles of this triangle. 11. Find an expression for r, the radius of the inscribed circle of a triangle. B Prove that r (cot+cot +cot 2) = {(a+b+c). 2 2 12. Prove that & the distance between the centres of the inscribed and circumscribed circles of a triangle is given by the equation 2= R2 – 2Rr. Show that if R=2r for the triangle ABC, then (cos A): 3 = 2 13. On the bank of a river there stands a tower 144 feet high, on the top of which stands a flagstaff 24 feet high. From the spot on the opposite bank, directly facing the column, it is observed that the flagstaff subtends the same angle as a man 6 feet high standing at the base of the tower. Calculate the breadth of the river. 14. √1 being represented by i, prove that where n is a negative integer. Assuming the theorem to hold generally, apply it to find expressions for the three cube roots of 1+−3. |