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4.-TRIGONOMETRY.

13.-Determine x in the equation

5 sin x + 3 cos x = 7.

14. Is there a rapid solution of the following general equation? a sin x+b cos x = C.

5.-DESCRIPTIVE GEOMETRY.

15.-Having given, two right lines, of which one is perpendicular to the horizontal plane and the other to any line whatever, it is required to find the shortest distance between them.

16.-Are there several methods of finding the shortest distance between two right lines!

6.-FRENCH.

DICTATION.-Ce fut dans cette place qu'il conçut le dessein de détrôner le roi de Pologne par les mains des Polonais mêmes. Là étant un jour à table, tout occupé de cette entreprise, et observant sa sobriété extrême, dans un silence profond, paraissant comme enseveli dans ses grandes idées, un colonel allemand, qui assistait à son dîner, dit assez haut pour être entendu, que les repas que le tsar et les rois de Pologne avaient faits au même endroit, étaient un peu différents de ceux de Sa Majesté.--(Voltaire.)

Continue the reading of the extract with explanations.

7.-GEOGRAPHY.

Draw a map of the basin of the river Po, describing its northern tributaries.

8.-HISTORY.

1.—The Visigoths: Their origin; their manners and customs; their wars.

2. The government of Saint Louis: Give an account of everything bearing on the subject.

1.-ENGLISH VERSION.

9.-ENGLISH.

Un astrologue un jour se laissa choir

Au fonds d'un puits; on lui dit: "Pauvre bête,

Tandis qu'à peine à tes pieds tu peux voir,

Penses-tu lire au-dessus de la tête ?"

2.-Dictation at the blackboard of a passage from Irving's Columbus, with explanation. 3.-Give the meaning of the verb get; name its derivatives.

Give the meaning of next.

10.-LATIN.

1.-Translate and explain Book I, chapter 49, of Caesar's Gallic War, from Ubi eum castris se tenere to ad eum locum venit.

2.-Explain delegit, intellexit. Give the French noun and adjective derived from the

verb prohibere. Explain acie.

11.-GREEK.

Translate Book I, chap. 10, of Xenophon's Anabasis from 'Evravda dy Kúpov to στρατόπεδον.

Give the French derivatives of Kɛpaλǹ.

EXAMINATION OF CANDIDATE B.

1.-ARITHMETIC.

1. Show that when a number divides the product of two factors and is prime to one of them, it divides the other.

2-A number, N, has as many divisors above the square root as below. If the number of divisors is odd, N is a perfect square.

3-Extract the square root of a whole number.

2.-GEOMETRY OF SOLID BODIES.

1-Determine the volume generated by a triangle turning about an axis which passes through one of its vertices.

2-Prove that two triangular pyramids of equivalent bases and of the same altitude are equivalent.

-Two tetrahedrons are similar when they have equal dihedral angles comprised between two similar faces.

4.-The property of the tangent to a parabola. Draw a tangent (1) through a point

on the parabola; (2) through an exterior point.

5-The generation of a helix and the property of a tangent to this curve.

3.-ALGEBRA.

1-Discuss the equation

ax2 + px + c = 0.

What value dor and r" approach when x approaches 0?

2-Determine the rectangular parallelopiped of maximum volume having a given surface.

4.-TRIGONOMETRY.

Resolve a triangle having given two sides and the angle opposite one of them.

5.-DESCRIPTIVE GEOMETRY.

1-Find the angle between two planes whose traces are in a given right line. 2.-Determine the intersection of two planes.

3-How many lines are there perpendicular to the ground-line?

6.-FRENCH.

DICTATION.-Un fanfaron, amateur de la chasse, venant de perdre un chien de bonne race, qu'il soupçonnait dans le corps d'un lion, vit un berger. "Enseignemoi, de grâce, de mon voleur,” lui dit-il, “la maison, que de ce pas je me fasse raison." Le berger dit, "C'est vers cette montagne. En lui payant de tribut, un monton par chaque mois, j'erre dans la campagne comme il me plaît, et je suis en repos."

Continue the reading of the extract with explanations.

7.—GEOGRAPHY.

L-Give a sketch of the French shore of the Channel.

2-Draw a map of Russia. Give an account of its physical geography and of the cities in the southern part of the country.

8.-HISTORY.

1-Give an account of the form of government and of the legislation of the Teutonic nations that invaded the empire in the fifth century. State the principal differences between the Teutonic and Roman laws. Give an account of the Salic law. 2-Name the first six or seven kings of France. Give the dates and duration of their

reigns.

3-Give an account of the enfranchisement of the communes, stating the causes which led to it. Why were there no communes in the royal domain?

9.-ENGLISH.

ENGLISH VERSION.-Les montagnes voisines étaient couvertes de pampres verts qui pendaient en festons; le raisin, plus éclatant que la pourpre, ne pouvait se eacher sons les feuilles et la vigne était accablée sous son fruit.

Dictation at the blackboard of a passage from Irving's Columbus, with explana

tions. Explain rather. Give the plural of gulf. Give the rules for the formation of the

plural of nonns. Name the nouns in f which take re in the plural. Conjugate standing.

10 – LATIX.

Translate Book I, verses 740-746, of the Eneid.
Explain geminosque Triones. Give the derivation of (the French word) septentrion ;

the gender, number, and case of cythara.
Give the construction and force of docuit, canit, pecudes. Decline imber.

11.-GREEK.

Anabasis, Book I, chapter 6, from Oitos Kípo to drazzeiaul.
Decline ίππος, ίππε'ις, βασιλεί. Inflect the last word.

EXAMINATION OF CANDIDATE C.

1.-ARITHMETIC.

1.- Two irreducible fractions having the same denominator have the same number of

decimal figures in the period when the fractions are reduced to a decimal form.

Example: sir and 15. 2.-Give the rule of simple interest.

Ait Derive the forinula 1 = and resolve the equation, taking A aud t successively

as the unknown quantities. Find these two unknown quantities by analysis.

100'

2.-GEOMETRY OF SOLID BODIES.

1. —The volume generated by a triangle turning about an axis passing through one of

its vertices. Place upon the surface of the triangle the perpendicular let fall upon the axis through the center of the side opposite to the axis. Determine

the position of the axis in order that the volume may be a maximum. 2.-The definition of an ellipse. 3.-How is a tangent to the curve to be drawn (1) through a point on the curve (de

termine the locus of the foot of the perpendicular let fall from the tangent from a focus), (2) through an exterior point.

3.-ALGEBRA.

1.- What is to be understood by a polynomial, rational and entire in r?
2. — How would you ascertain whether this polynomial is divisible by I-a?
3.-In what cases is rm-am divisible by x+a?
4.-Decompose the function

y =ax+bx+c
into two factors of the first degree.
5.-Find the sum of the first n odd numbers.

4.-TRIGONOMETRY.

1.- What does the fraction

r sin r 1- -COS X

become when x=

=0? 2.-Show how a right line may be determined beyond an obstacle. Suppose, for ex

ample, that one is placed at a point A in AC, whence AC may be readily determined. Between C and D is an intervening obstacle. How may DB, the prolongation of AC, be determined ?

-DESCRIPTIVE GEOMETRY.

Find the projections of the intersection of two given planes.

6.-FRENCH.

DICTATION.-Auguste aima mieux alors recevoir les lois dures de son vainqueur que de ses sujets. Il se détermina à demander la paix au roi de Suède, et voulut entamer avec lui un traité secret. Il fallait cacher cette démarche au sénat qu'il regardait comme un ennemi encore plus intraitable.-(Voltaire.) Continue the reading with explanations.

7.-GEOGRAPHY.

1-Draw a map of the Spanish peninsula. Give an account of its physical geography, and fix the position of the principal cities.

2-Give the political history of the county of Venaissin, and describe its physical characteristics.

8.-HISTORY.

1-Give an account of the Ostrogoths and their origin. Narrate the events of the reign of Theodoric, noting the system of government, the legislation, and the extent of Theodoric's kingdom.

2.-Give a full account of the foundation of the Kingdom of the two Sicilies. The Norman conquest of Sicily.

9.-ENGLISH.

1-ENGLISH TRANSLATION.-On exposait une peinture

Où l'artisan avait tracé
Un lion d'immense stature

Par un seul homme terrassé.

Les regardants en tiraient gloire.

Un lion en passant rabattit leur caquet:

"Je vois bien, dit-il, qu'en effet,

On vous donne ici la victoire,

Mais l'ouvrier vous a déçus;
Il avait liberté de feindre;

Avec plus de raison nous aurions le dessus,
Si mes confrères savaient peindre."

2-Dictation at the blackboard of a passage from Columbus.
-Construction and force of the words no, one, however, indulge, unknown, how, show,

blow, height.

10.-LATIN.

Translate Cæsar, B. G., I. 47, from Biduo post Ariovistus to aliquem ad se mitteret, giving explanations of allusions. Give the construction and force of perfectæ, agi, iterum; mode and tense of constitueret, vellet; force of cœpta. Decline aliquem, is, hic, suum.

11.-GREEK.

Translate Xenophon, Anabasis, I, 4, § 11, from "Evrevlev ¿že avvei to óvópari.
Conjugate and give construction of ἐξελαύνει. Decline εύρος, μεγάλη.

S. EX. 51-21

NOTE K.

COURSE IN ENGLISH NAUTICAL LANGUAGE ON BOARD THE BORDA.

(Extracts.)

A ship is said to be sailing before the wind when she has the wind right aft. Both sheets are then hauled aft, the sails are set at right angles with the keel; the staysails are hauled down, and the mainsail is drawn up in the brails, that the wind may act upon the foresail; the helm is put amidships, and the only thing the steersman has to do is to put the helm a little to starboard or larboard, in order to keep the vessel from yawing.

COMMANDS IN TACKING.
Ready about, or Ready all--Pare à virer.
Haul over the boom-Bordez le gui.

About ship-Envoyez.
Helm alee gently--Labarre dessous en douceur.
Ease off; or, Let go the jib sheets-Filez les focs.
Up tacks and sheets-Lère les lofs.
(Stand by, or Get to the) after braces- Aux bras de derrière.
Haul mainsail, haul-Derrière changez.
Belay- Amarrez.
(Stand by the) head braces-- Aux bras de derant.
Haul oft, haul; Let go and haul-Devant changez.
(Stand by the) head bowlines-Boulines devant.
after bowlines-

derrière.
or head and after bowlines-Boulines partout.
Haul-Holez; Belay- Amarrez.
Haul aft; or, Sheet the courses; or

Bordez les basses voiles.
Fore and main sheets.
Haul taut the weather braces- Appuyez les bras du vent.
Sheet the jibs; or
Haul att the jib-sheets. S

Bordez les focs.
Clear or coil the ropes-Parez les manquvres.

A compound engine is one that uses the same steam at both high and low pressure, the object being to take as much elastic force as possible out of the steam before condensing it.

Gun-cotton is easily exploded by percussion or ignition, and any weight of this preparation is a good deal more effective than the equivalent weight of gunpowder. It is well-suited to the working and blowing up of mines, but is not used for military purposes, on account of the facility with which it may be ignited by friction, percussion, and heat.

NOTE L.

SYLLABUS OF LECTURES ON MARINE ENGINEERING.-BORDA.

FIRST YEAR.

I.

Elementary study of the action of a marine engine. 1.-Steam.- Definitions; saturated steam, dry and wet steam, superheated steam; for

mation, superheating, and condensation of steam. Pressure. Latent heat of steam. Instruments for measuring the pressure and vacuum. Bourdon's manometer. Vacuum indicator. Density of dry saturated steam.

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