Doch gehn sie aus der Welt ganz still, Ihr Leben war verloren. Wer etwas Treffliches leisten will, Der sammle still und unerschlafft Im kleinsten Punkte die höchste Kraft. SCHILLER. DR. ATKINSON. I. Translate into English : (a). Ich habe nie etwas thun können, mich mit einem manne abzufinden, der sechs jahre ehre und gefahr mit mir getheilt. (b). Die naseweise hat sie zum besten. (c). Franziska, ich glaube, wir werden vernommen. (d). (Der ring) ist seine fünfzehnhundert thaler unter brüdern werth. (e). Inwärts auf dem kasten muss der fräulein verzogener name stehen. 2. (a). Write a short essay on the importance of the drama "M. von Barnhelm" from a political point of view. (b). Lessing's chief aim in the Laokoon? (c). Purport of the essay "On the Education of Mankind"? 3. In the "Oberon" three distinct stories are welded into a unity? 4. (a). Winckelmann's theory of Greek sculpture in antiquity? (b). He notices certain external causes of the excellence of Greek art? 5. J. Möser's great political maxim? 6. Breitinger's suggestion as to the true object of all poetry? 7. (a). Gottsched's three propositions ? (b). Contrast the theories of Gottsched and Bodmer. 8. Write a notice on Hans Sachs. 9. Judging from the literature of the period immediately preceding the Reformation, what feelings seem to have been mainly prevalent throughout the land ? SENIOR FRESHMEN. Mathematics. A. MR. CATHCART. 1. Find the pole of the line joining the points 7, 8: 5, -3 in reference to the circle x2 + y2; = 100. 2. Find tangent of the angle between the lines, and also their point of intersection, 3. In a right-angled spherical triangle, the sine of the perpendicular on the hypotenuse is a mean proportional between the tangents of the segments into which it divides the hypotenuse ? 4. If the sides of a triangle A B C be a, b, c, and the distances from a point P to A, B, and C be related by the equation find the Cartesian equation of the locus of P. 5. In any spherical triangle, prove that sin a cos B + sin b cos e cos A: = cos b sin c. 6. Calculate to five places of decimals the limit of becomes infinite. MR. BURNSIDE. 7. Resolve into its simple factors the expression a1 (B2 — y2) + B1 (y2 — a2) + y2 (a2 — 82). 8. Eliminate x, y between the equations 2x + y = a, x2 + 2xy = b, x2 y = c. 9. Find the co-ordinates of the radical centre of the three circles 10. Find the area of the triangle formed by the lines x cos (8+ y) + y sin (8+ y) = r, x cos (y + a) + y sin (y + a) = r, x cos (a + B) + y sin (a + B) = r. II. Determine the radius of the circle circumscribing a quadrilateral whose sides are given in length. 12. If A be the area of a plane triangle, prove the formula 4A (cot A+ cot B + cot C) = a2 + b2 + c2. MR. PANTON. 13. Find the area of the quadrilateral whose vertices are the points (2, 2), (-2, 3), (3, 3), (1, 2). 14. Given a number of circles, find the locus of a point such that m' times the square of the tangent from it to the first + m" times the square of the tangent to the second + &c. = a constant. 15. Express the cosine of an angle of a spherical triangle in terms of the sides. 16. State Napier's rules for the solution of right-angled spherical triangles; and prove the resulting formulæ in the case of a triangle whose sides a, b are given, and whose base and base angles are to be expressed in terms of these. 18. Prove that the perpendicular let fall from the vertical angle C of a triangle on the base is equal to a+b+c cot A+ cot B and find in terms of A, B, and c an expression for the distance between the foot of the perpendicular and the middle point of the base. B. MR. CATHCART. 1. Prove the relation between the values of a function, and of its first two derived functions, denoting by e a positive proper fraction: 3. The chord drawn through a given point, so as to cut off the minimum area from a given curve, is bisected at the point. 4. Apply Boole's method to reduce the general equation of a parabola to tangent and diameter as axes. 5. Four fixed tangents to a conic cut any fifth in points whose anharmonic ratio is constant? prove that sin (8+ y) + sin (y + a) + sin (a + B) = o. 8. Prove the following relation between the determinants: 9. Find the locus of the intersection of normals to a parabola at the extremities of a focal chord. 10. A triangle ABC circumscribes a given circle; the angle C is given, and B moves along a fixed line. Find the locus of 4. 13. If two arcs through the same point intersect the circumference of a small circle on a sphere, and if the segments of these arcs be s, s', and σ, σ', respectively; prove the relation tans tan s′ = tan σ tan σ'. 14. Find the condition that two conics given by the general equations should be similar and similarly placed. (a). Prove that, for two concentric and similar ellipses, if any chord AB of the outer touch the inner in T, then any chord of the inner through Tis equal to half the algebraic sum of the parallel chords of the outer through A and B. 15. Calculate the symmetric function a3ß of the roots of the equation pass through the point P, (x'y'), having the values A1, A2 for A; express by means of A1, A2 the angle between tangents from P to the curve 3. Determine the quotient by the product of all the differences of a, B, y, d of B2 g2 + a2 82 I By + ad I I |