ist," antwortete Amrei, und die Köchin rief aus der Küche: "Das Barfüssele hat Recht, man darf ein Kind nicht bei seinem Namen nennen, eh'es getauft ist; das ist lebensgefährlich." Amrei lachte, und Rosel, ganz ausser sich, riss ihr das Halsband ab, warf sie zu Boden, und schlug sie in's Gesicht. "Lass mich los," schrie Barfüssele, "ich will mich ja ausziehen." In diesem Augenblicke liess Rosel ab, denn Johannes stand vor ihr. Er war leichenblass, er konnte kein Wort hervorbringen und legte die Hand schützend auf Barfüssele, welche noch knieend ihre Herrin zu entschuldigen suchte. "Komm," rief Johannes, "du sollst mit mir dies Haus verlassen; du bleibst bei mir, als meine Frau." 9. Ach, könnt' ich Molly kaufen, Man rühmt wol viel vom Golde, Mein liebes Leben enden DR. ATKINSON. 1. Chief works of Tauler (omitting his sermons)? (b.) "Der Franckforter" gives a concise account of Tauler's teaching: viz. ? 2. Give an account of the satires written [or edited] by Murner. 3. What is the general meaning of the term "romantic," as used by German literary historians? 4. An intimate acquaintance with the popular literature of the Third Period [1350-1525] is of great importance in one respect? 5. There were two men, the one the best of popular preachers, the other, the best speculative thinker of the thirteenth century: give some account of the leading tendencies of their teaching. 6. Two men represent respectively the lights and the shadows of the higher social life of the times [of the minne-singers]? Who were these, and what do you know of their writings? 7. One of these minne-singers protests against the current mediæval pessimism? 8. What are the two great romances of the thirteenth century? their authors ?—they contrast curiously? 9. The Nibelungenlied develops two admirable "motives"? (b). It is divisible into two stories ? 10. The prevailing sentiment in the other great Epic? Translate into English : (a.) Ja, der erste verdruss, an dem ich verworrene schuld war, Sei der letzte zugleich ! (b.) Wer fest auf dem sinne beharrt, der bildet die welt sich. (c.) Nicht das treffliche mädchen als magd, die fremde, zu dingen, Kam ich zum brunnen; ich kam, um deine liebe zu werben. (d). Nein, es hülfe mir nichts, wenn selbst mir verstellung gelänge. (e.) Und ich gehe nun wieder hinaus, wie ich lange gewohnt bin, Von dem strudel der zeit ergriffen, von allem zu scheiden. Und er sagte darauf zu ihr mit versuchenden Worten: Das ist schwer zu ertragen, und doch die Pflicht zu erfüllen SENIOR FRESHMEN. Mathematics. A. MR. CATHCART. 1. It is required to solve the following system of equations (a − a') x + (b − a) y + (c — a') z = a′′, 2. Determine the vertices of equilateral triangles on the line joining the points 5, 4 to 7, -1. 3. Find the co-ordinates of the point cutting the line joining the point 7, 8 to 15, -3 in the same ratio as the point - 38, - 2 cuts the line joining 7, 8 to 11, 4. 4. Eliminate between the equations a cos 30+ b cos 20+ c cos + d = 0, a sin 30+ sin 24 + c sin + d = 0. 5. Co-ordinate axes being inclined at 60°, find the co-ordinates of the vertices of the square inscribed in the triangle bounded by them and by the line x + y = 6, and having its base along the axis of x. 6. Find the equation of the circle inscribed in the same triangle. MR. BURNSIDE. 7. Solve the equation (1 + x)3 + (1 − x)3 = (1 − x2)3. 8. Solve the system of simultaneous equations (x + y) (x3 − y3) = 2616, (x − y) (x3 + y3) = 936. 9. Find the area of the triangle formed by joining the points of con tact of the inscribed circle of a triangle in terms of the sides. 10. Find the locus of the centre of a circle cutting off given intercepts from two given lines. II. Given the base of a triangle, and one base angle double the other find the locus of the vertex. 12. Prove that the area of a dodecagon inscribed in a circle is equal to that of a square on the side of an equilateral triangle inscribed in the same circle. MR. PANTON. 13. Find the co-ordinates of the point of intersection of the line joining the points (3, 1) and (− 2, 3) with the line drawn through the origin perpendicular to 2x + 3y 6 = 0. 14. Form the equation of the circle through the points (3, 0), (0, 2), (-1, -1); and find the value of the constant rectangle under the segments of all chords through the origin. 15. Find the length of the chord cut off by the circle 16. Prove that the area of a plane triangle is equal to (a+b+c)2 tan A tan B tan C. 17. Prove the following trigonometrical formulæ :— 2 sec 2° =tan 46° + cot 46°, 18. Given sin 5° = sin 41° + sin 67° – sin 31° – sin 77o. log 2 = 30103, log 3 = 47712, calculate the logarithm of 3888. B. MR. CATHCART. 1. Exhibit the product of two numbers, each of which is the sum of four squares, as the sum of four squares. 2. If a, B, y be perpendiculars let fall from the vertices of triangle of reference on any line; p, q, r be the perpendiculars of that triangle; and x, y, z co-ordinates of any point; the perpendicular from the point on that line 3. Find the equation of the circle on the line joining the centres of similitude of two given circles as diameter, and show that it is coaxial with them. 4. Form for the cubic ax3 + 3bx2 + 3cx + d = 0 the equation whose 5. Find the sine of the arc of a sphere joining two points, in terms of the six cosines of the arcs from those two points to the vertices of an equilateral quadrantal triangle. 6. Given the base of a triangle, and that the sides are the segments of a line cut in extreme and mean ratio; the locus of the vertex is a pair of circles. Determine their equations, centres, and radii. MR. BURNSIDE. 7 Find analytically the locus of the centre of a circle cutting three circles at equal angles. 8. Determine the lines represented by the equation a2 + B2 + y2 + 2By cos (B-C) + 2ya cos (C − A) + 2aß cos (A – B) = 0. 9. Prove the formula 10. Given the three perpendiculars of a spherical triangle, construct it. II. Given tan (x + y √ − 1) = cos a + √ I sin a, find general values of x, y in terms of a, satisfying the equation. 12. An ellipse moves about touching two given lines at right angles, find the locus of its centre. MR. PANTON. 13. Find the condition that the equation `ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 should represent a pair of right lines: and find, in that case, an expression for the tangent of the angle between the lines. 14. A perpendicular is let fall from the origin on the line and through its point of intersection with the line parallels to the axes are drawn; it is required to find the equation of the harmonic conjugate of the first line with respect to the latter pair. 15. In the determinant of the nth order find the sign of the diagonal term anbn-1 ........ li. |