fertigt, der auf die erste Nachricht von dieser Belagerung zu verstehen gab, dass die spanische Macht an den Mauern Antwerpens sich zu Grund richten werde. Um jedoch nichts zu versäumen, was zur Erhaltung dieser Stadt dienen konnte, berief er, kurze Zeit vor seiner Ermordung, den Bürgermeister von Antwerpen, Philipp Marnix von St. Aldegonde, seinen vertrauten Freund, zu sich nach Delft, wo er mit demselben wegen Vertheidigung Antwerpens Abrede nahm.

(2) Unterdessen rückte der Zug immer näher, und die Dunkelheit der Nacht erhöhte noch den ausserordentlichen Anblick. So weit das Auge dem Strome folgen konnte war alles Feuer, und die Brander warfen so starke Flammen aus, als ob sie selbst in Feuer aufgingen. Weit hin leuchtete die Wasserfläche; die Dämme und Basteien längs dem Ufer, die Fahnen, Waffen und Rüstungen der Soldaten welche sowohl hier als auf der Brücke in Parade standen, glänzten im Widerschein. Mit einem gemischten Gefühl von Grauen und Vergnügen betrachtete der Soldat das seltsame Schauspiel, das eher einer Fête als einem feindlichen Apparate glich, aber gerade wegen dieses sonderbaren Kontrastes der äussern Erscheinung mit der innern Bestimmung die Gemüther mit einem wunderbaren Schauer erfüllte. Als diese brennende Flotte der Brücke bis auf zweitausend Schritte nahe gekommen, zündeten ihre Führer die Lunten an, trieben die zwei Minenschiffe in die eigentliche Mitte des Stroms und überliessen die übrigen dem Spiele der Wellen, indem sie selbst sich auf schon bereit gehaltenen Kähnen hurtig davon machten.-SCHILLER, Belagerung von Antwerpen.

B.-Grammatical Questions :

1. Write down the genitive singular with the respective definite article, and the dative plural of-Bürger, Stadt, Prinz (Passage 1); Auge, Strom, Soldat (Pass. 2).

2. Decline in the singular and plural-sein vertrauter Freund (Pass. 1); das seltsame Schauspiel; diese brennende Flotte (Pass. 2).

3. Write down the second person singular of the present indicative, and the infinitive, and past participle of gab, konnte, berief, nahm (Pass. 1); and warfen, betrachtete, glich (Pass. 2).

4. Decline the personal pronouns ich, du, er in the singular and plural, and the pronoun es in the singular only.

5. Give the rule on the formation of the comparative and superlative of German adjectives. Illustrate your answer by examples and state exceptions.

6. Explain the inversion in the clause: Unterdessen rückte der Zug immer näher (Pass. 2). Can you point out some similar inversions in the same passage?

C.-Translate into English :

Kronstadt, 5 Jan., 1880.-Vorige Woche ereignete sich in dieser Nachbarschaft ein Vorfall, welcher als ein neues Beispiel dienen kann von der Treue und dem Verstande der Hunde. Ein Bauer, der am Tage nach der Stadt gegangen war, um eine Kuh zu verkaufen, kehrte am Abend mit seinem Hunde nach seinem Dorfe zurück. Unterdessen war aber so viel Schnee gefallen, dasz er die Strasse kaum erkennen konnte. Plötzlich fiel der Mann in eine Grube voll Schnee. Als der Hund dies sah, lief er fort, und holte einen Wagen ein, dessen Führer er beim Arm packte. Derselbe dachte gleich, es müsse ein Unglück geschehen sein und folgte dem Hunde. Bald kam er zu der Stelle, wo der Bauer halbtodt im Schnee lag. Er legte ihn auf den Wagen und brachte ihn rasch nach einem. Dorfe, wo er sich nach einigen Stunden erholte.-Deutsche Volkszeitung.

D. Translate into German :

1. Our house is very large, but it is not too high. It has twenty-five rooms with high doors and forty windows. There is also a large garden behind the house, where there grow many flowers, and a few old trees.

2. The winter has been very cold, but now the weather is becoming warmer. I hope the summer will be fine, for we shall go to Germany as soon as the holidays begin.

3. The bridge which the Duke had built across the Scheldt was finished in the year 1585, when the siege had lasted seven months.

WEDNESDAY, MAY 26, from 2 to 4.30 P.M.

III. 6. Mathematics. (First Paper.)

[N. B. Candidates are reminded that in order to pass in this subject they must satisfy the Examiners in the first section of this Paper.

No credit will be given for any answer, the full working of which is not shewn.]

1. Find the value of

I. Algebra.

2. Multiply also divide

3. Simplify

x2-ax3+a3x-a4 by x2+ax + a2; p-9pq3+18q by p2-3pq+3 q2.

4

4. Find the G. C. M. of

x3-6x-4 and 3x3-8x+8;

also the L. C. M. of

(3a2-3ab)2, 18 (a3b2-ab1), and 24 (a3b3 —b®).

7. The sum of two numbers is 35; and their difference exceeds one fifth of the smaller number by 2; find the numbers.

8. After 127. has been divided equally among a certain number of men, an additional shilling apiece is given to them; and it is then found that each possesses as many shillings as there are men. Find the number of the men. 9. Prove that if b be a mean proportional between a and c, then a2+262: a :: 62+2c2: c.

10. Sum to 6 terms the series

+11 + 3 + ....

Also insert 12 arithmetic means between - and 5.

FRIDAY, MAY 28, from 2 to 4.30 P. M.

III. 6. Mathematics. (Second Paper.)

[N. B. Candidates are reminded that in order to pass in this subject they must satisfy the Examiners in Euclid I, II.]

Euclid I, II.

1. Define a line, a straight line, an angle, a right angle, a triangle, an acute-angled triangle, a parallelogram, and a rectangle.

What is Euclid's criterion of the equality of magnitudes ?

2. Make a triangle of which the sides shall be equal to three given straight lines, any two of which are greater than the third.

3. If a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square on the whole line.

4. The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel.

5. If a straight line be divided into any two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.

6. To a given straight line apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

7. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.

2. Euclid III, IV, VI.

8. Angles in the same segment of a circle are equal to one another.

9. Define-similar rectilineal figures, and reciprocal figures. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular to one another, and shall have those angles equal which are opposite to the homologous sides.

10. When is a rectilineal figure said to be described about a circle?

Describe an equilateral and equiangular pentagon about a given circle.

11. Define―ratio, proportionals, and ́ex æquali.’

If four straight lines be proportionals, the similar rectilineal figures similarly described on them shall also be proportionals.

In the quadrilateral figure ABCD, AB: BC:: CD: DA, and angle B angle D. Prove that ABCD is a parallelogram.

=

12. If from any point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it, and if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square on the line which meets the circle, the line which meets the circle shall touch it.

13. If two circles cut one another in A and B, and from B straight lines BEC, BFD are drawn cutting the circumferences in E, C and F, D; the triangles AEC, AFD are similar.

SATURDAY, MAY 29, from 2 to 4.30 P. M.

III. 6. Mathematics. (Third Paper.)

[N.B. No credit will be given for any answer, the full working of which is not shewn.]

1. Plane Trigonometry and use of Logarithms. 1. Obtain a formula connecting the circular measure of an angle with the measure of the same angle in degrees.

Assuming that π = 3, find the length of an arc of a circle of radius 3 yards 1 foot which subtends at the centre an angle of 6° 18′.

2. Prove that tan Atan (180°-4).

Determine the values of the trigonometrical functions for an angle of 30°; and find the values of cot 240° and cosec 600°.