3. Translate into English, extracts from Thucydides, Books VII. and VIII. 4. Translate, with notes— (α) οὔκουν βούλεσθαι αὐτός γε ἐπιστάμενος τὰς Αθηναίων φύσεις ἐπ' αἰσχρᾷ τε αἰτίᾳ καὶ ἀδίκως ὑπ' Αθηναίων ἀπολέσθαι μᾶλλον ἢ ὑπὸ τῶν πολεμίων, εἰ δεῖ, κινδυνεύσας τοῦτο παθεῖν ίδια. (1) καὶ ὁ ̓Αλκιβιάδης προσκείμενος ἐδίδασκε τὴν Δεκέλειαν τειχίζειν καὶ μὴ ἀνιέναι τὸν πόλεμον. (ε) καίτοι οὐ πώποτε Αθηναίους διὰ τὰς στρατείας καὶ τὴν ὑπερόριον ἀσχολίαν ἐς οὐδὲν πρᾶγμα οὕτω μέγα ἐλθεῖν βουλεύσοντας ἐν ᾧ πεντακισχιλίους ξυνελθεῖν. (α) Ἐν δὲ τούτῳ τά Ἴσθμια ἐγίγνετο, καὶ οἱ ̓Αθηναῖοι, ἐπηγγέλθησαν γάρ, ἐθεώρουν ἐς αὐτά, καὶ κατάδηλα μᾶλλον αὐτοῖς τὰ τῶν Χίων ἐφάνη. GREEK-JUNIOR CLASS. HISTORY AND GENERAL QUESTIONS. PASS. ONE HOUR AND A HALF. Not more than SIX questions to be attempted. 1. Compare the Greeks and the English in respect of their powers of colonisation. 2. To what causes of character and circumstance do you attribute the Athenian rise to supremacy? 3. How far is it true to say of Sparta that she produced no great men? 4. Give some account of the confederacy of Delos, and of the process by which it passed into an Athenian Empire. 5. To what extent was Alcibiades responsible, as enemy and as friend, for the defeat of Athens? 6. What right had Sparta to call herself the champion of Greek freedom? 7. Is it in any sense justifiable to expect ethical theory of a poet? 8. What elements in early Greek religion were due to the influence of physical nature? 9. What was the main achievement of the Greek world during the four centuries between Hesiod and Aeschylus ? 10. Explain and criticise the Socratic dictum that "Virtue is knowledge." 11. Are the attacks of Aristophanes upon Euripides founded upon any genuine grievance? 12. "Plato gave permanent assertion to all that had been truest in the thought and faith of Greece." Explain and illustrate. LOGARITHMS AND TRIGONOMETRY. TWO HOURS AND A-HALF. PASS. 1. State and prove the rules relating to the characteristics of common logarithms. 2. Find the values of 3 ⚫0097321 (i.) (-152x0871 (ii.) logu 17. 3. Assuming that the population of a country increases by the same percentage every year, and that the population was 973,220 on December 31st, 1880, and 1,231,700 on December 31st, 1894, compute the population on December 31st, 1900. 4. Solve the triangle in which A=73° 25', b=623·42, c=711.91. 5. The shadow of a cloud at noon is cast in a spot 2,000 feet due W. of an observer. At the same instant he observes that the cloud is at an altitude of 25° in a direction W. 16° N. Find the height of the cloud, and the altitude of the sun. 6. Find the present value of an annuity of £150, consisting of eight payments, the first due one year hence, compound interest being allowed at the rate of 4 per cent. per annum. (ii.) sin 6A+ sin 6B+sin 6C = 4 sin 3A sin 3 B sin 3C. 8 Find an expression for the radius of a circle which touches one side of a triangle and the other two sides produced. With the usual notation prove that 9. If a'b'e' are the sides of the triangle formed by joining the points of contact of the inscribed circle with the sides of a triangle, shew that 1. Enunciate the proposition known as the parallelogram of forces. If forces acting on a particle are represented in magnitude and direction by the sides AB, BC, CD, DE of a polygon ABCDE, shew that their resultant is represented by AE. 2. Having given the magnitudes of two component forces, and of their resultant, state and prove a formula giving the cosine of the angle between the components. From this formula prove that the resultant cannot be greater than the sum of the components. If the components be 140 and 171, and the resultant 221 pounds' weight, find the angle between the components. 3. A weight of 50 pounds suspended freely from a fixed point A is drawn aside from the vertical through an angle of 45° by a force acting horizontally. Determine this force and the reaction at A. 4. If two parallel forces act in the same direction along the opposite sides AB, DC of a parallelogram, and another force act along the diagonal BD, and if these three forces. be respectively proportional to AB, DC and BD; find the magnitude and position of a fourth force which will keep the parallelogram at rest. 5. Prove that the moments of any two forces about any point in the line of action of their resultant are equal. 6. Define the centre of gravity of a body. Find the centre of gravity of three equal masses placed with their centres of gravity (i.) in the same straight line, (ii.) not in the same straight line. 7. Three particles A, B, C, whose weights are proportional to 3, 2, 1 respectively, are placed so that AB 5 feet, BC=4, CA=2; find the distance of their centre of gravity from C. 8. A uniform beam, 18 feet long, rests in equilibrium upon a fulcrum two feet from one end, having a weight of 5 pounds at the further end and one of 110 pounds at the nearer end to the fulcrum. Find the weight of the beam. 9. What are the requisites for a good balance? Shew that a balance is (other things being equal) more sensitive as its own weight is smaller. If the arms of a false balance be without weight, and one arm longer than the other by one-ninth part of the shorter arm, and if in using it the substance to be weighed is put as often into one scale as the other, shew that the seller loses five-ninths per cent. on his transactions. ANALYTICAL GEOMETRY. TWO HOURS AND A-HALF. PASS. 1. Find the length of the perpendicular from e', y' to the straight line acosa+ysin a=p. Determine a point on the straight line 3x+2y=4, whose perpendicular distance from the straight line 4x+3y-2=0is. 2. Find the points of intersection of the straight lines x+2y-5=0, 2x+y-7=0 and y-x-1=0; and shew that the area of the triangle formed by these lines is 3. 3. Obtain the equation of a circle whose centre lies on the straight line y=3, and which touches the straight lines x=1 and y=0. 4. Prove that the sub-normal is constant in a parabola. The normal PG at any point of a parabola is produced to Q, so that QG PG. Find the locus of Q. 5. Find the equation of the tangent at any point of an ellipse. 6. Find the equation to the normal at any point of an ellipse. If the normal at the point (a', y') meets CA in G, and CB' in g, find the coordinates of G, g. Prove that the locus of the middle point of Gg is an ellipse of the same shape as the original ellipse, but with the directions of its axes interchanged. 7. Find the equation of the conic section whose directrix is x+y=0, focus (1, 1) and eccentricity 2. SENIOR FRENCH I. COMPOSITION, TRANSLATION AT SIGHT, ETC. PASS. 1. Translate into French Although Lord Randolph certainly had never made a study of finance, he was not, when he became Chancellor of the Exchequer, so ignorant of it as Charles Fox, if the story be true which reports him to have said that he never could understand what Consols were he knew they were things that went up and down in the City; and he was always pleased when they went down, because it so annoyed Pitt. Lord Randolph possessed many of the qualities which had always won for Mr. Gladstone so high a reputation as a departmental chief-indefatigable assiduity, that energy which Dr. Arnold said is of more value than even cleverness, a strong intellectual force, which, while it in no way interferred with his attention to |