1. How can the different conditions of royalty in England, France, and Germany be accounted for? 2. How does Guizot explain the transitory character of Cromwell's Protectorate ? 3. How does he criticise Scott's Quentin Durward? 4. What was the Ligue de Cambrai ? 5. Write a note on Racine's treatment of Greek subjects, and compare some of his characters with their Greek originals. 6. What did Racine attempt in comedy? 7. Explain cultorisme and euphuisme, as technical terms in literature. GERMAN. MR. MAHAFFY. Translate the following passages: I. Wenn ich doch so schön wär’ Sie tragen gelbe Hute Mit rosenrothem Band. Glauben, dass man schön sey, Dacht' ich, ist erlaubt In der Stadt ach! ich hab' es Dem Junker geglaubt. Nun im Frühling, ach! ist's Um die Freuden gethan; Ihn ziehen die Dirnen, Die ländlichen, an. Und die Taill' und den Schlepp Verändr' ich zur Stund'; Das Leibchen ist länger, Das Röckchen ist rund. Trage gelblichen Hut, Und ein Mieder wie Schnee Und sichle, mit andern, Den blühenden Klee. II. Im kühlen Gewolbe Gährt ihr der kräftige Kohl, und reifen im Essig die Gurken; Aber die luftige Kammer bewährt ihr die Gaben Pomonens. Gerne nimmt sie das Lob vom Vater und allen Geschwistern, Und misslingt ihr etwas, dann ist's ein grösseres Unglück, Als wenn dir ein Schuldner entläuft und den Wechsel zurücklasst. Immer ist so das Mädchen beschäftigt und reiset im Stillen Wünscht sie dann endlich zu lesen, so wählt sie gewisslich ein Kochbuch, Deren Hunderte schon die eifrigen Pressen uns gaben. 1. What is the origin of the phrase Sturm und Drang in German Literature? 2. Write a note on the plot and style of Goethe's Werther. 3. Describe the Lenore of Bürger, and quote from it, if you can. 4. Describe the character of Wagner in Goethe's Faust. 5. What scenes in this play have been omitted in the opera of Gounod? 6. Write a note on Herder as a poet, and as a philosopher. 7. Give a sketch of the contents of the Sixth Book of Wilhelm Meister. 1. Berlin is 11°.3' east of Paris: find the area of the portion of the Earth's surface between their meridians, Earth's radius being taken 3963 miles. 2. In a right-angled spherical triangle, if the hypotenuse be c, and b+c=π, show that cos A = cos2 a. 3. Determine the co-ordinates of the intersection of perpendiculars in the triangle whose vertices are (1, 2), (9, 9), (11, 3). 4. Find the lengths of the pair of tangents from the point (9, 9) to the circle x2+ y2 = 2x+4y, and find their points of contact. 5. Two couples in the same plane, whose moments are equal and opposite, balance each other? 6. A uniform bar 12 feet long is supported by two men, one of them is at one end: where must the other be in order that he may support three-fifths of the whole weight? MR. BURNSIDE. 7. Find the equation of the tangents from the origin to the circle (x − a)2 + (y-B)2 — p.2 = 0. 8. Find analytically the locus of the intersection of tangents to a circle, at the extremities of a chord of constant length. 9. In a spherical triangle, prove the formula cos a. sin B-cos b. cos C sin A= cos A. sin C. 10. The sides of a quadrilateral inscribed in a circle are a, b, c, determine the lengths of the diagonals. 11. A heavy particle, whose weight is W, is sustained on a smooth in W 3 clined plane by three forces applied to it, each equal to one acting vertically, another horizontally, and the third along the plane; find the inclination of the plane. 12. If O be any point in the plane of a triangle A, B, C, and D, E, F the middle points of the sides, prove that the system of forces ОA, OB, OC is equivalent to the system OD, OE, OF. MR. PANTON. 13. Find the area of a triangle whose angular points are the origin of co-ordinates and the feet of the perpendiculars from the origin on the lines 4x+5y-20=0, 2x + y −4=0. 14. Find the condition that the general equation of the second degree should represent a pair of right lines. Verify that the equation 3x2-5xy-2y2-x-5y-2=0 represents right lines, and find them. 15. Given log 5 = .69897, find the logarithm of (6.25)*. 16. If three arcs, drawn from any point perpendicular to the sides of a spherical triangle, divide these sides into segments a, a′; ß, B′; Y, Y' ; prove the relation cos a cos B cos y = cos a' cos B' cos y'. 17. The inscribed circle is removed from an isosceles triangle, find the distance of the centre of gravity of the remaining figure from the base. 18. If two forces acting at a point O are represented in direction by two lines OP, OQ, and in magnitude by OP, nOQ, and if a point R be taken on PQ such that PR = nQR; prove that the resultant of the forces is in the direction OR, and is represented in magnitude by (n + 1) OR. A. MR. CATHCART. 1. Three forces acting along the bisectors of the angles of a triangle equilibrate; find their relative magnitudes. 2. Three parallel forces P, Q, R, acting at the vertices of a weightless triangular plate, will balance three opposite forces Q+R-P, R+P-Q, P+Q-R acting parallel to them through the corresponding middle points of the sides of the triangle. 3. Calculate the integrals dx dx sin2 x (a + b cos x)' { x + √ a2 + x2 } } 4. The chord drawn through a given point to cut off the minimum area from a given curve is bisected at the point. 5. Find the envelope of the base of a triangle inscribed in a given conic, and whose sides pass through two given points. MR. BURNSIDE. 6. Find the envelope of a line such that the sum of the squares of the perpendiculars on it from two fixed points be constant. 7. Find the co-ordinates of the intersection of the perpendiculars of a triangle formed by three tangents to a parabola. 8. A heavy sphere is placed upon three other spheres which rest in contact on a smooth horizontal plane, all the spheres being equal: find the pressure on each, and the horizontal force which must be applied to each to preserve equilibrium. 9. An isosceles right-angled triangle rests in a vertical plane, with the right angle downwards between two pegs at a given distance apart in the same horizontal line; determine its positions of equilibrium. 10. Perform the integration 12. Find the equation of the nth pedal, and also that of the reciprocal polar, of the curve rmam cos me. 13. Find an expression for the tangent of the angle between the tangents from the point x', y' to the ellipse 14. Draw a tangent to an ellipse so that the distance intercepted on it between the axes shall be a minimum; and express in terms of the axes this distance and the radius-vector from the centre to the point of contact. 15. A heavy particle is placed inside a smooth parabolic tube whose axis is vertical, and is acted on by a horizontal force proportional to the distance of the particle from the axis; find the position of equilibrium. When will the particle rest in all positions? B. MR. CATHCART. 1. Determine the equation of the circle circumscribed to the common self-conjugate triangle of two conics u = o, v=o given by the general equations, the axes being rectangular. 2. If u, v, w be three cubics of the form u = ax3 + 3bx3y + 3cxy2 + dy3, &c., show that if they have a common factor its cube is proportional to d2u d2u d2u 3. An elliptic cylinder is placed with its axis horizontal on a rough plane inclined to the horizon; find under what conditions it may remain in equilibrio. 4. Explain how a point of inflexion on a curve may be found, and prove that from a point of inflexion on a cubic only three tangents can be drawn to the curve. 5. A heavy beam moves round a horizontal axis fixed at its lowest point; to its other end a weight is attached by a string passing over a fixed point vertically above the fixed end of the beam; the weight is to be supported on a curve in the vertical plane so that the system may be in equilibrium in all positions. Find the curve. MR. BURNSIDE. 6. Determine the polar reciprocal of the curve rm cos me = am. 7. If two chords c and c' of an ellipse, at right angles, touch a confocal ellipse, prove that 8. If a chord I с + I = a constant. of the circle whose equation is aß -ydo touch any conic laß + mydo, prove that the upper sign for internal contact, and lower sign for external contact. |