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3. The area of the surface described by a straight line revolving about another straight line in the same plane with it as an axis, is the product of the revolving line by the circumference described by its middle point. Give proof in each of the cases to which this theorem applies.

4. The cubic contents of two similar polyedrons are respectively 3 cubic inches and 24 cubic inches, and one side of the first is 5 inches; what is the homologous side of the second ?

5. Prove that the angles of a spherical triangle are respectively supplements of the sides of the corresponding polar triangle.

6. Prove that, of two sides of a spherical triangle, that is the greater which is opposite the greater angle, and the converse.

ANALYTIC GEOMETRY.

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1. What is the locus of each of the following equations : (1) 3x + y -2=0,

(2) 2y2 + 3x = 0, (3) y - 2*+1=0,

(4) y=0, (5) 2x2 — x+2y— 3y-2=0,

-2 the system of coördinates being rectangular ?

How is each of these loci situated with respect to the coördinate axes ?

2. The vertices of a triangle are A=(-1, 2), B= (2, -3), C=(-3,-1); find the equations of the sides AB and BC, and some trigonometric function of the angle B.

3. Deduce the equation of the parabola referred to its principal vertex.

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4. Deduce the equation of the tangent to an ellipse at the point (ac', y') of the curve.

5. The equation of a curve referred to a certain rectangular system is x2 - y2 = 1; what is the equation of the same curve referred to a second rectangular system, having the same origin as the first, and in which the axis of x makes an angle of 45° with the old axis of x? Sin 45o = cos 45° = .

PLANE TRIGONOMETRY.

1. TRACE the changes in the value and sign of the cosine, tangent, and cosecant of y when y increases from 0° to 360°. 2. Deduce the fundamental formula

cos (x + y)= 3. Deduce the formulae

1+ ctn (2; — y) =

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cosa x =

sin x + sin y=2 sin } (x + y) cos } (x - y). 4. Given the three sides of a plane oblique triangle. Show how to find the three angles giving the necessary formulae.

5. A ladder 51.42 ft. long, placed with its foot 10 ft. from a house, just reaches the top of the house. How high is the house? What angle does the ladder make with the vertical?

ENGLISH COMPOSITION.

You are required to write a short English composition, correct in spelling, punctuation, grammar, and expression. This composition must be at least fifty lines long, and be properly divided into paragraphs. One of the following subjects must be taken:

Moses at the Fair.
The Story of Ariel.
The Character of Flora MacIvor.

FRENCH.

1. TRANSLATE INTO ENGLISH :

DE ma position présente, il ne faut pas conclure que j'ai eu la Fortune pour marraine. Mes ancêtres, si le mot n'est pas bien ambitieux, étaient des pêcheurs; mon père était le dernier de onze enfants, et mon grand-père avait eu bien du mal à élever sa famille, car dans ce métier-la plus encore que dans les autres le gain n'est pas en proportion du travail; compter sur de la fatigue, du danger, c'est le certain, sur un peu d'argent, le hasard.

A dix-huit ans, mon père fut pris par l'inscription maritime; c'est une espèce de conscription, au moyen de laquelle l'État peut se faire servir par tous les marins pendant trentedeux ans, — de dix-huit à cinquante. Il partit ne sachant ni lire ni écrire. Il revint premier maître, ce qui est le plus beau grade auquel parviennent ceux qui n'ont point passé par les écoles du gouvernement.

Le Port-Dieu, notre pays, étant voisin des îles anglaises, l'État y fait stationner un cutter de guerre, qui a pour mission d'empêcher les gens de Jersey de venir nous prendre notre poisson, en même temps qu'il force nos marins à observer les règlements sur la pèche: ce fut sur ce cutter que mon père fut envoyé pour continuer son service. — MALOT, , Romain Kalbris.

2. State the tense of the italicized verbs in the above, and give it in full.

3. Give the principal tenses of connaitre, faire, recevoir, sentir (thus, Inc., étre; PRES. PART., étant ; PAST PART., été ; Ind. PRES., je suis ; PRET., je fus).

4. TRANSLATE INTO FRENCH :

(a) Where are you going to-morrow? (6) I do not know yet, I think I shall go to my uncle's. (c) How do you wish me to do this?

GERMAN.

1. TRANSLATE INTO ENGLISH :

Ariosto baute sich ein kleines Haus. Ein Freund fragte ihn, wie er sich mit einem so tieinen Hause begnügen könne, da er so schöne Paläste in seinem Orlando beschreibe. Der Dichter antwortete : Worte sind billiger als Steine.

2. Parse or explain the grammatical forms and relations of words in the first sentence of the above.

3. TRANSLATE INTO GERMAN :

Diogenes saw a youth blushing, and said to him: Well done, my son, that is the color of virtue.

4. Write out a short extract of some story that you have read in German

5. TRANSLATE INTO ENGLISH :

Verschwunden ist die finstre Nacht
Die Lerche schlägt, der Tag erwacht
Die Sonne kommt mit Prangen %
Am Himmel aufgegangen
Sie scheint in König's Bruntgemach
Sie scheinet durch des Bettlers Dach
Und was in Nacht verborgen war
Das macht sie kund * und offenbar.

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1. DESCRIBE the preparation of hydrogen, and give its two most striking properties.

2. Define the terms, acid, base, salt.

3. What is coal ? Deseribe the method of preparing gas from it.

4. How can pure water be obtained? What parallel process occurs in nature ?

PHYSICS.

5. Describe the Leyden jar and the Grove battery.
6. In what three ways can heat be distributed ?
7. What is the action of a prism on light?

8. What is the acoustic distinction between noise and music?

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