kings; and trace the steps by which the plebeians established their claim to share in the government. 6. Describe fully the course of events by which Greece became a Roman province. Give the name of the province. 7. Give an account of the downfall of the Roman Republic, specifying its leading causes. 8. Indicate the extent of the Roman empire under Augustus, and describe briefly the social and political condition of Rome under the Cæsars. 9. Write short accounts of the life and times of Alcibiades, Demosthenes, Fabius Maximus, Marcus Aurelius, and Constantine the Great. 5 6 6 5 EUCLID, ARITHMETIC, AND ALGEBRA MORNING. Examiner-MR. JOHN ELIOT, M. A. N. B.-The figures in the margin indicate full marks. 1. In equal circles, angles, whether at the centres or circum. ferences, have the same ratio that the circumferences on which they stand have to one another. 2. What is meant by a solid angle? Prove that every solid angle is contained by plane angles which together are less than four right angles. 3. Given the base, altitude, and radius of the circumscribing circle of a triangle. Describe it. 4. Inscribe in a given rectangle a rectangle which shall be similar to another given rectangle. 5. Reduce to its lowest terms: 3 3 4 4 and find the value correct to three places of decimals of— 6. If 7 per cent. be gained by selling goods for 695 rupees, what percentage would be lost by selling them for 615 rupees ? 3 5 9. Prove that the sum of the roots of the equation x2 + px 10. Find the number of permutations of n things, taken r together. In how many of these will three given things occur? 11. Find the sums of the following series: (1) (x + y)2 + (x2 + y2) + (x − y) + &c. to n terms. 6 3 5 Find the first two terms in negative powers of x of the expansion of − h)2 + h2)} {(∞ + h)2 + k2 } where x is large compared with either h or k. TRIGONOMETRY AND STATICS-AFTERNOON. N. B.-The figures in the margin indicate full marks. 1. Assuming the ratio of the circumference of the circle to the diameter to be 333: 106, find the length of an arc which subtends an angle of 66° 15′ at the centre of a circle whose radius is 48 feet. What is the circular measure of 176g 66′ 66′′ ·6? 2. Prove that (i) sin (180° — A) = sin A, (ii) sin (A + B) sin A cos B + cos A sin B, and find the values of sin 840°, cos 855°, tan 930°, sin 15°. (ii) 1. A+ B B A 2 sin 2 3 5 8 cos2 A + 8 cos1 A = cos 4A. (iii) cos2 A+ cos2 B - 2 sin A sin B cos (A + B) — } = cos 2 (A + B). = 2mn m2 — n2, Define a logarithm. log (0125), L sin 45°. 6. α = logo x loga y. that a2 = b2 + c2. 2bc cos A. √ x2 + 22, c = x2+ y2, show that '(y2 + z2) (z2 + x2) (x2 + y2) x2y2 + y2x2 + x2z2 In any triangle ABC prove that tan If CD bisects the angle C and meets AB in D, show that 7. Prove that a particle will be at rest under the action of three forces represented in magnitude and way of action by the sides of a triangle taken in order. ABCD is a quadrilateral, and forces acting at a point are represented in magnitude and way of action by AB, DC, BD, and AC; what is their resultant ? 8. If three forces acting in one plane maintain a rigid body in equilibrium, prove that their lines of action either all meet at a point or are all parallel. A uniform heavy rod of length 2a is supported, with its upper end resting at a point A against a smooth vertical wall, by means of a fine string of length 13a attached to the lower end of the 5 rod and to a given point in the wall vertically above A. Find the inclination of the rod to the wall, and show that the tension of the string √39 = × weight of the rod. 6 9. Find the magnitude and direction of the resultant of two like parallel forces acting on a rigid body. A uniform lever of weight W is acted on at the ends A and B by weights P and Q, of which Q is the greater, show that if C be the fulcrum and O the middle point of the lever, OC: AB:: Q P: 2 (P + Q + W). 10. Define centre of gravity. Given the centre of gravity of a part of a body, and also the centre of gravity of the whole body, find the centre of gravity of the remainder. A portion ADE of a uniform triangular lamina ABC is cut off by any straight line DE. If O, Oʻ be the middle points of BC and DE, G the centre of gravity of the whole lamina and w, w, the weight of the whole, and of the portion cut off respectively show that the centre of gravity of the remainder BCED is (1) on the straight line through G parallel to OO', and (2) is at a distance from G = 2 3 w' w 11 Find the ratio between the power and weight for equilibrium in the system of pullies in which each pully hangs by a separate string. If there be three pullies and their weight, beginning with the lowest, be w1, wa, w3 respectively, show that if the weight 201 2w2 4w3 supported be + 3 3 + the mechanical advantage is 2. 3 12. A heavy particle W is supported on a smooth inclined plane, whose inclination to the horizon is a, by two forces each equal to P, one acting along the plane and the other horizontally; Examiner-DR. GEO. KING. 1. Describe the structure of a grain of rice or wheat. Describe stigmata, and state their uses. 2. 3. What is meant by the albumen of the seed? What is its use? 4. Describe generally the circulation of the sap in flowering plants. 5. Write a botanical description of the plant given to you. 6. Describe in botanical terms the objects A and B. 7. What are the chief economic products derived in India from Leguminous plants? 8. What do you mean by the terms rhizome, carpel, calyx node, axil, panicle. 4 5 PSYCHOLOGY-MORNING. Examiner-MR. J. SIME, M. A. N. B.-The figures in the margin indicate full marks. [N. B.-Candidates may answer either of the following series of questions.] Reid's Inquiry. 1. Explain briefly, but distinctly, the general aim of Reid's Inquiry, noticing the function he assigns to common sense. 2. Descartes found something certain in thought. Explain this, and refer to any misconceptions of Reid on the point. 3. State clearly the Idealism in Perception of Locke, Berkeley, and Hume, shewing that each view follows inevitably from the preceding. Reid charges these philosophers with an error persona." Explain this. 66 4. Distinguish between sensation and perception, and between the primary and secondary qualities of body. How are the latter related to the former ? 5. Explain and illustrate natural and artificial signs. How does Reid make use of these in his doctrine of perception ? 6. Analyse Reid's perception by touch. Does he succeed in establishing a doctrine of immediate perception? Give reasons. 7. How, according to Reid, is extension perceived? How, in their relation to the real qualities, do the visible appearances of figure and colour differ? Add your own remarks. 8. State Reid's theory regarding our seeing objects erect by inverted images. How does this view differ from Berkeley's? 9. Take memory and imagination, and examine Reid's account of the knowledge and belief involved in these. Abercrombie's Intellectual Powers. 1. How does Abercrombie meet the argument that the mind is a function of the brain? On what does he base the belief of the soul's immortality? 2. Explain the process by which, according to Abercrombie, we acquire a knowledge of external things. Can there be any knowledge without attention ? 3. Distinguish between the primary and secondary qualities of body. In foggy air objects seem to be further away than they really are. Explain this. 4. What elements are involved in probability? What in credible testimony? How does Abercrombie distinguish between a marvellous event and a miracle ? 5. Explain, according to Abercrombie, tion, reverie, and voluntary suggestion. 5 6 5 6 5 6 6 5 6 5 6 5 6 recollection, concep 5 5 6 6. State clearly the nature of the dispute between nominalism and realism. What is conceptualism? 7. Explain the nature of first truths, and enumerate the chief of them. How does Aercrombie interpret what is called necessity in moral phenomena ? 8. Define reason, and explain what constitutes truth, in collecting facts, in tracing causation and in generalisation. What is inventive genius ? 6 |