HISTORY. Examiner-MR. M. J. WHITE, M.A. 1. (a.) Draw a map of Ancient Greece, showing its various divi. sions, and marking the position of ten of the cities most famous in history, (6.) What connexion may be traced between the physical features of the country and the character of the people ? (c.) What did the Greeks understand by the terms Hellas and Hellenes ? In what sense were the Hellenes one nation ? 2. (a.) What were the laws and institutions of Solon ? How were these extended and improved by Clisthenes ? (6.) What induence had these reforms on the success of Athens against Persia ? 3. (a.) By what measures did Themistocles seek to establish the power and security of Athens ? Show the results of his policy by describing the state of Athens under Pericles. (6.) Mention (without entering into detail) the circumstances which led to the downfall of Athens and the supremacy of Sparta. 4. (a.) By what means did Epaminondas weaken the power of Sparta ? (6.) Write a narrative of the campaigns of Leuctra and Man. tinea. 5. (a.) Describe the character of Philip of Macedon as a general and a statesman, (6.) Give a few details with regard to the victories of Alexander the Great in Asia Minor and Phænicia. (c.) In his subsequent career of conquest, Alexander passed through the valleys of four great rivers. Which were these ? Men. tion a few of the principal places in each valley, and one important event which occurred at each during this expedition. (d.) What were the most striking results of Alexander's con. quests ? 6. (a.) What advantages did the Plebeians derive from the appointment of Tribunes, the Agrarian Law of Spurius Cassius, the Laws of the Decemviri, and the Laws of Licinius and Sextus ? (6.) What were the evils which existed in the Roman state at the time of the Gracchi? What was the result of their attempts at Reform ? 7. (a.) Mention, with a few details, the victories of Hannibal a in Italy. (6.) What circumstances led to his retreat and final defeat ? 8. (a.) What were the grounds of quarrel between Cæsar and Pompey ? (6.) Give an abstract of the principal events from the crossing of the Rubicon to the battle of Pharsalia. (c.) In what designs for the extension and improvement of the empire was Cæsar engaged at the time of his death? 9. (a.) What changes were introduced into the government of the empire by Diocletian and Constantine ? (6.) How did these changes affect the stability of the empire ? EUCLID, ARITHMETIC, AND ALGEBRA, Examiner-MR. A. M. Nash, M.A. 1. The rectangle contained by the diagouals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides. 2. Define the inclination of a plane to a plane. If a solid angle be contained by three plane angles, any two of them are together greater than the third. 3. Given four points not in the same plane; find the position of a point equidistant from them all. 4. ABCD is a square inscribed in a circle, E the middle point of BC; AE produced meets the circumference in F, and DF cuts BC in G : prove that BG is double of CG. 5. Find the present value of 4,8671. 4s. due two years hence, at 4 per cent. compound interest. 6. A man invests Rs. 1,200 in 4 per cents. at 80, and at the end of a year sells out at 90; what is his gain per cent. ? 3 + ✓ 18 7. Reduce to a decimal the fraction N 50 N98 N 72 - 1 8. What is meant by the G. C. M. of two algebraic expressions ? Find the L.C.M. of 6x4 7x2 + 2, and 208 + 613 3. 9. Solve the equations : X + 6 20 + 1 1 ; 4xy + 5y = 33, 4x2 - xy = 10; (3) x +y+z=3, yz + za + xy = -1, 1++ 10. If a, B be the roots of the equation x2 + 2ax + b = 0, form & quadratic equation with rational coefficients, one of whose roots is a + B + na+ B2. 11. If 28 = a + b + c, prove that (8 - a) + (8 - b) + (8 -c) - 3 (8-a) (8-5) (8 - c) = 1 2 (a® + 68 of c® — 3abc). 12. The sum of n terms of an A.P. is 2na ; find the first term and common difference. Sum to n terms, and, if possible, to infinity, the series 3 3 (1) 6 2 (2) 2 +7 + 14 + 23 + 34 +... 13. For what value of r is the number of combinations of n things taken r at a time greatest ? If Cr denote the number of n things taken r at a time, show that Co + C2 + C4 + ...=Ci+ C3 + C5 +. 3+ 14. Write down the coefficients of to and x1° in the expansion of (as + 362) –5, and the rth term of the expansion of (1 — x)*: measure TRIGONOMETRY AND STATICS. Examiner-MR. W. Griffiths, M. A. 1. State clearly what are the units of angular measurement in the centesimal, sexagesimal, and circular methods of measuring angles. Express the angle of a duodecagon in each of these modes of measurement. 2. Prove the following identities : (a.) Cos (A + B) = cos A cos B F sin A sin B. A 2 sin A · sin 2A 2 2 sin A + sin 2A (d.) Tan A = cot A - 2 cot 2A. 3. Prove the following identities in the case of a plane trie angle: (a.) Tan A + tan B + tan C tan A tan B tan C. (c.) Tan24 4. In a right-angled triangle, if the hypothenuse be divided into two segments (. y) by the line which bisects the right angle, and if t= the tangent of half the difference of the acute angles x:y=1 +t:1-t. 5. If two sides and the included angle are given, show how to solve the triangle. The two sides of a triangle are 876 feet, and 348 feet, and the included angle 53° 20'. Find the remaining triangles, given log 1.224 - 0877814, L tan 63° 20° 10-2991070, L tan 40° 40% = 9.9340559. 6. The bridge at Howrah subtends an angle of 45° at a given point at the edge of the river ; at a distance of 1,000 yards higher up it subtends an angle of 30° If the direction of the river in this portion of its course be straight, and the bridge is built at right angles to its direction, find the breadth of the bridge. 7. What is force ? Show that a force can be adequately represented by a straight line. 8. What is meant by the resultant of any number of forces ? Define the resolved part of a force in any direction. Three forces represented by the diameter of a circle, and two chords on the same side of it, and terminating in one extremity of the diameter, and inclined at angles of 30° and 60° to it respectively, act on a particle. Find the magnitude and direction of the resultant. 9. What are the necessary conditions that three forces should form a system in equilibrium ? A very thin conical stick is suspended by means of a string fastened to its ends, and passing round a smooth peg. Prove that in the position of equilibrium the peg divides the string into two por. tions in the ratio 3 : 1. 10. Two unlike parallel forces, P and Q, have a resultant R, which is distant from them & and y feet respectively. What are the relations connecting P, Q, R, & and y? 11. What is meant by the centre of gravity of a body ? Given the centre of gravity of a body and of part of it, find the centre of gravity of the remaining part. If OP, OQ, OR in one plane represent three forces which keep the point o at rest, show that o coincides in position with the centre of gravity of the triangle PQR. 12. A man is given an iron bar (12 feet long) and a fulcrum, and is required to lift a mass weighing 24 maunds. The greatest force he can exert is 60 lbs. Find where he ought to place the fulcrum (using the bar as lover) so as just to be able to move the mass. PSYCHOLOGY. Examiner-Rev. J. ROBERTSON, M.A. [N. B.-Candidates may answer either of the following series of questions. ] Reid's Inquiry. 1. Sensation and memory are simple, original, and perfectly distinct operations of the mind; and both of them are original principles of belief:-Explain this fully. State the corresponding doctrines of the ideal system, and show how Reid refutes them. What is the immediate object of memory ? It is contended that Reid was misled by the ambiguity of the term 'object.' Explain and discuss this. 2 State and contrast the views of Berkeley, Hume, and Reid as to the relation (1) between sensation and a sentient being, and (2) between sensation and the qualities of matter. State concisely Reid's theory of perception, and show how far he recognises an immediate knowledge of external things. By what senses do we obtain a knowledge of things at a distance ? 3. Reid asserts that “the wisdom of philosophy is set in opposition to the common sense of mankind,” as to the existence of a material world. Explain this fully, state how far it is correct, and show how Reid proposes to settle the points in dispute. 4. Reid argues that “sight discovers almost nothing which the blind may not comprehend.” Explain this, and show how he applies his conclusion to our notion of extension. Is there any sensation proper to visible figure ? 5. “Colour is a quality of bodies, and not a sensation of the mind." State the grounds on which Reid maintains this, and expound the inferences he draws from it. How does Reid account for the ambiguity of such terms as ' smell' and 'heat,' and how does he use this ambiguity in criticising the ideal system ? 6. How does Reid explain our seeing objects erect by inverted images ? Reproduce his criticism of the views of Berkeley. 7. “ There are two ways in which men may form their notions and opinions concerning the mind.” Explain and compare these and show, from the history of philosophy, how far and with what results they have been applied, 8. What are first principles, and how do we obtain our know. ledge of them ? Explain Reid's appeal to common sense, and show how far it is legitimate. Abercrombie's Intellectual Powers. 1. Explain the controversy in regard to the origin of onr ideas ;” and name and state the various views that have been held. What view is commonly held now? 2. “The deductions made from the ideal theory by Berkeley “ and Hume seem to have been applications of it which its former “advocates had not contemplated.” Explain the theory and the deductions referred to. What objections are urged against the theory? 3. “Mind is a function of the brain." Explain this doctrine fully, give the facts on which it rests, and show how far they support it. Explain and criticise the phrase “the independent existence of the thinking principle;" and state concisely the extent of our knowledge of mind and the means of acquiring it. 4. Name and describe fully the process by which we obtain onr knowledge of external things. What is the extent of this knowledge? What are false perceptions, and how are they corrected ? 5. Explain reflection, and state fully what knowledge we derive from it. Show how the knowledge thus obtained assists us in the investigation of truth. Name and explain the operation of the faculty that is mainly concerned in the investigation of truth. 6. Explain the connexion between memory, attention, and asso. ciation. State the principles of association and explain the various classes of associations. Explain the common use of the term 'con ception, and contrast it with Abercrombie's. 7. Describe the process of abstraction. Explain fully the controversy that arose in counexion with it, state clearly the points in debate, and name and describe the various views that have been held. Give Abercrombie's view. 8. On what does the validity of an argument depend, and how is its validity tested ? How do you account for varieties of opinion? “ There is one species of reasoning which is free from uncer. tainty." Name it, and account for its superiority. |