9. On what terms were stockholders in the old East India Company admitted into the United Company? 10. Investigate the arrangements made by the Guinea and Binney Company, the Royal Adventurers trading to Africa, and the Royal African Company respectively with their creditors. 11. The lowest price of stock of the Royal African Company in each of the undermentioned years was as follows: 1697, 16 (in bank money); 1698, 15; 1700, 15; 1715 and 1716, 15; 1717 and 1718, 16. How are these quotations to be interpreted? 12. What were the financial results of the African trade from 1672 to 1691? N.B.-In the foregoing questions the expressions "East India Company" or "the old Company" are used to describe "The Governor and Company of Merchants of London trading to the East Indies." Similarly, the "new Company" is used for "the English Company trading to the East Indies." POLITICAL ECONOMY (SECOND PAPER). ECONOMIC HISTORY. (Eight questions only to be answered.) 1. Compare Roman and Saxon gilds. Can the 2. Discuss the exclusiveness of early social gilds. monopoly exercised by the gild merchant and Regulated Company be traced back to this characteristic of the gild? 3. Distinguish the respective functions of the gild merchant, the craft gild, the staple, and the Regulated Company. 4. Give some account of the Merchant Adventurers in Bristol, Chester, Hull, Newcastle, and York. 5. Trace the economic results of the Crusade movements. 6. "The most important event in British economic history was the Black Death." Explain the (a) legislative, (b) agricultural effects of this calamity. 7. Trace the growth of the Vagrant Laws, carefully distinguishing them from the Poor Laws. 8. Describe the state of English trade at the end of the fourteenth century. 9. How were towns governed in the fifteenth century? 10. Explain the Poor Law policy of Elizabeth, and show how later Poor Law administration departed from its principles. 11. Describe the connection between economic thought and constitutional progress in British History; or, State how far economic forces were potent in the politics of the latter half of the seventeenth century. 12. What reforms should be introduced to our modern workhouse system? State the points at issue between the supporters of out- and in-door relief. POLITICAL ECONOMY-(THIRD PAPER). 9 A.M. TO 12 NOON. THEORETICAL. (Eight questions only to be answered.) 1. "There are no laws in Political Economy, only assumptions." Criticise this statement so as to indicate your view of economic laws. 2. State how you would propose to measure efficiency in reference to production, and point out the conditions on which efficiency of production depends in any country. 3. Define the conditions of a perfect market, and carefully explain how the marginal and equilibrium price is found in any particular market. 4. State and criticise either Ricardo's or Adam Smith's theory of rent. 5. "Of all the writers on economic questions, Malthus is the one most abused and least understood by his traducers." Examine this statement, and estimate the importance of Malthus' work. 6. Describe the effect of "specialisation" in industry on the mobility of labour. 7. Notice and estimate the force of the main objections that have been made to the system of "profit-sharing." 8. What is meant by (a) "intensity of demand" in international trade, (b) "par of exchange"? 9. Estimate the influence of international trade on rent and wages. 10. Explain the statement that "all credit ultimately rests on a metallic basis." 11. Discuss the relative stability of "gold prices" and of "silver prices." 12. Is "machinery the Frankenstein of our civilisation"? [The Candidate for Honours in Economic Science took Moral Philosophy as a Supplementary Honours subject. For the papers in this subject, vide p. 528, Honours in Mental Philosophy.] EXAMINATION QUESTIONS FOR HONOURS HONOURS IN MATHEMATICS AND NATURAL PHILOSOPHY. MATHEMATICS (FIRST PAPER). 3RD OCTOBER 1901-9 A.M. TO 12 NOON. 1. The bases of two or more triangles having a common vertex are given both in magnitude and position, and the sum of the areas is given. Prove that the locus of the vertex is a straight line. Hence show that in every quadrilateral circumscribed about a circle the mid points of its diagonals and the centre of the circle are collinear. 2. If a cyclic quadrilateral be such that three of its sides pass through three fixed collinear points, the fourth side passes through a fourth fixed point collinear with the other three. 3. If a pencil of four rays be cut by two transversals ABCD, A'B'C'D', then any of the anharmonic ratios of the points A, B, C, D, is equal to the corresponding ratio for the points A,' B', C', D'. Hence show that if a hexagon be inscribed in a circle the intersections of opposite sides-viz., 1st and 4th, 2nd and 5th, 3rd and 6th are collinear. 4. Prove that 2 21 {(x − y)3 + (y − 2)3 + (≈ − x) }2 = 25 { (x − y)3 + (y − z)3 + (% − x)3 } × - Show that the equations x2-a2=zx+xy-yz, y2 — b2=xy+yz - zx, z2 - c2=yz+zx-xy are either (1) inconsistent or (2) insufficient for the determination of the values of x, y, and z. 5. Determine whether the following series are convergent or divergent for various values of x : 6. Find the nth term of the series 2+x+4x2+19x3 +70x1 + 229.x3 +.... it being given that a linear relation exists between every four consecutive terms. Sum to n terms the series 1+5+17+53 +161+485+.... 7. Establish the law of formation of the successive convergents to the continued fraction a+"1 Աջ az and prove that any convergent is nearer to the continued fraction than any preceding convergent. 8. If f(x) be any rational integral algebraic function of X, and f(x) its first derived function, then will where a1, a2, A3⋅ equation f(x)=0. .... are then roots real or imaginary of the Derive from this a method of discovering whether a given equation has or has not equal roots. Solve 26-x-15x1+5x3 +70x2+12x-72=0. 9. A man stands at a distance d from a tower whose height is h, surmounted by a spire whose height is s, and observes that the tower and the spire subtend the same angle. Express s in terms of h and d. If ' be the error in the height of the spire corresponding to a small error h' in the height of the tower, show that 10. Expand sin" in a series of sines or cosines of multiples of according as n is an odd or an even integer. Show that - 210 sin cos 0=sin 110+5 sin 90+7 sin 70 – 5 sin 50 – 22 sin 30-14 sin 0. 11. Resolve into quadratic factors the expression x2n-2ax cos n✪ +a2", and illustrate your result geometrically. r=n-1 Υπ Prove that sin n0=2n-1 II sin (9+). T=0 02 02 ... 12. Prove that sin 0-0 (1-2) (1–297.) (1–3972)... ... .... 1 1 1 222 Sum the infinite series 1+ 2+ 3+ 4+ and deduce the 13. Define the hyperbolic sine and cosine of y, and from your definition show that cosh (a + Bi)=cosh a cos ẞ+i sinh a sin ß. 14. Define generally the logarithm of a+ẞi. Find all the logarithms of the complex a+Bi, a and ß being real. Prove that ii=e where n is any integer. 15. Determine the condition that three straight lines may concur. Prove that, if the perpendiculars from the angular points of one triangle upon the sides of a second concur, the perpendiculars from the angular points of the second upon the sides of the first will also concur. 16. A circle is described on the line joining the centres of similitude of two given circles as diameter: show that the tangents drawn from any point on it to the two circles are in the ratio of the corresponding radii. 17. Find the polar equation of the straight line joining two given points on a conic, and deduce the equation of the tangent at any point. Show that the equation of the locus of the point of intersection of two tangents to =1+e cos 0, which are at right angles to one r 18. The chord joining two points whose eccentric angles are and cuts the major axis of an ellipse at a distance d from the centre; show that tan $_d-a 02 tan = 2 d+a' 2a being the length of the major axis. |