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war niemals in den Fehden seiner Nachbarn verwickelt, auch sah man ihn nur selten auszerhalb den Eingmauern seines klcinen Schlosses. Nur selten wurde Eckbert yon Gasten besueht, und wenn es auch geschah, so wurde ihretwegen fast nichts in dem gewohnlichen Gange dcs Lebens geiindert, die Maszigkeit wohnte dort, und die Sparsamkeit selbst schien alles anzuordnen. Eckbert war alsdann heiter und auf geraumt; nur wenn er allein war, bemerkte man an ihm cine gewisse Verschlossenheit, cine still© zuriickhaltende Melancholic. 2. State the genitive and plural of der Schwan, das Schaf, der Haken, der Pudel, das Lamm, die Nadel, die Maus, der Staat. 3. Give the genitive singular and nominative plural of the following substantives: Der Stern, der Burger, die Feder, das Segel, der Hase. 4. What is, in German, " the young bird," and " the young birds " ? 5. State the gender of Stufe, Zahn, Ton, Strom, Dinte, Gabel, Freiheit, Liebe, Malerei. 6. Translate into German— A young man who had paid great attention to his studies, and consequently had made rapid progress, was once taken by his father to dine with a company of learned men. After dinner the conversation turned naturally upon literature and the classics. The young man listened to it with great attention, but did not say anything. On their return home his father asked him why he had remained silent when he had so good an opportunity of showing his knowledge. " I was afraid, my dear father," said he, " that if I began to talk of what I did know I should be interrogated upon what I do not know." " You are right, my dear boy," replied the father: " there is often more danger in speaking than in holding one's tongue." *„* The abovo translation must be written in German characters. TEIGONOMETEY. 1. In any plane triangle show that the sides are proportional to the sines of the opposite angles. 2. Prove that— Sin(A+B) = SinA Cosß + CosA Sinß. Sin (A - B) = Sin A Cosß - Cos A Sinß. Cos(A+B) = CosA Cosß-SinA Sinß. Cos(A-B) = CosA Cosß+SinA Sinß. 3. Prove that— Sin^V^^* CosiA = VSj^Area of triangle = </s (s —a) (sb) — b) (s — c). Eadius of inscribed circle = /y — . 4. Express the limits of the numerical values, also the signs of the sine, cosine, tangent, cotangent, secant, and cosecant, of all angles from 0° to 360° in the first, second, third, and fourth quadrants. 5. Show that— Sin22y--= V(2-V2); Cos22f°*=^ 2+V2>; Tan 22i°= */2-l. 6. A circular pond covers an area of 4,840 square yards (one acre): what is the breadth, in yards, of a belt of plantation of uniform width surrounding it, and also containing one acre ? 7. What is the area of a triangle of which the three sides are respectively 700, 899, and 1,068 links? 8. The hypotenuse of a right-angled triangle is 420, and the angle opposite to the perpendicular 33° 45' 19": what are the base and perpendicular? 9. In the triangle ABC, let AB = 345 feet, BC = 232 feet, and the angle A = 37° 20': what are the other angles and the third side ? 10. In the triangle DEF, let DF=I,SBO links, EF = 1,228 links, and the angle F= 98° 40': what are the angles D and E and the third side DE ? ALGEBKA. 1. Find the value of , and prove your answer. 2. Find the G.C.M. of 2x*-xy-6f and 3x i-Bxy+4y\ and the L.C.M. of a?—l and a?-l. 3. mm is m* »-„ o. (*££2)(- !=?)(- «=f) ? 4. From fa+6c-|6 take 9c+fa- T %&. X a x V i n n ,• im? 12mn 9»> 5. Square §— §, and find square root of -^ — +-■&..* 6. Simplify V(1 ~X)+^) . + V(l-a* 2) 7. Besclve -77— into an infinite series.