8. Describe the eye as an optical instrument. What defects of the eye are corrected by eye-glasses? When should the eye-glass be convex and when concave?

9. What is the fundamental law of magnetism? What differences as regards magnetic properties are there between soft iron and steel?

10. How may the intensity of the earth's magnetism in two different places be compared?

11. Describe the electrophorus, and show how by its means we may charge a Leyden jar.

12. What properties of an electric current are utilized in telegraphy?

LATIN.

(Time allowed, 3 hours.)

1. Translate into English the following passages, parsing the words in italics: (a.) Et conversus ad simulacrum Jovis, "Audi, Juppiter, hæc scelera,” inquit; "audite jus Fasque. Peregrinos consules et peregrinum senatum in tuo, Juppiter, augurato templo, captus ipse atque oppressus, visurus es? Hæcine fœdera Tullus, Romanus rex, cum Albanis, patribus vestris, Latini, hæc L. Tarquinius vobiscum postea fecit? Non venit in mentem pugna apud Regillum lacum? Adeo et cladium veterum vestrarum et beneficiorum nostrorum erga vos obliti estis?" Quum consulis vocem subsecuta patrum indignatio esset, proditur memoriæ, adversus crebram implorationem deum quos testes fœderum sæpius invocabant consules, vocem Annii spernentis numina Jovis Romani auditam.

(b.) Vicit tamen pars, quæ in præsentia videri potuit majoris animi quam consilii; sed eventus docuit, fortes fortunam juvare. Bellum ex auctoritate patrum populus adversus Vestinos jussit. Provincia ea Bruto, Samnium Camillo sorte evenit. Exercitus utroque ducti, et cura tuendorum finium hostes prohibiti conjungere arma. Ceterum alterum consulem L. Furium, cui major moles rerum imposita erat, morbo gravi implicitum fortuna bello subtraxit; jussusque dictatorem dicere rei gerendæ causa longe clarissimum bello ea tempestate dixit, L. Papirium Cursorem, a quo Q. Fabius Maximus Rullianus magister equitum est dictus, par nobile rebus in eo magistratu gestis, discordia tamen, qua prope ad ultimum dimicationis ventum est, nobilius.

(c.) Fabius contione extemplo advocata obtestatus milites est, ut, qua virtute rem publicam ab infestissimis hostibus defendissent, eadem se, cujus ductu auspicioque vicissent, ab impotenti crudelitate dictatoris tutarentur; venire amentem invidia, iratum virtuti alienæ felicitatique; furere, quod se absente respublica egregie gesta esset; malle, si mutare fortunam posset, apud Samnites quam Romanos victoriam esse; imperium dictitare spretum, tanquam non eadem mente pugnari vetuerit, qua pugnatum doleat.

2. (a.) Give the derivations of the words: simulacrum, numen, provincia, auspicium, egregius.

(b.) Give some particulars of the battle at the lake Regillus.

(N. N.-Dictionaries are permitted for the remainder of the paper.)

3. Translate into English:

Cum in omnibus locis, consumpta jam reliqua parte noctis, pugnaretur, semperque hostibus spes victoriæ redintegraretur, eo magis quod denstos pluteos turrium videbant, nec facile adire apertos ad auxiliandum animum advertebant, semperque ipsi recentes defessis succederent, omnemque Galliæ salutem in illo vestigio temporis positam arbitrarentur, accidit inspectantibus nobis, quod, dignum memoria visum, prætermittendum non existimavimus. Quidam ante

portam oppidi Gallus, qui per manus sevi ac picis traditas glebas in ignem e regione turris projiciebat, scorpione ab latere dextro trajectus exanimatusque concidit. Hunc ex proximis unus jacentem transgressus, eodem ille munere fungebatur; eadem ratione ictu scorpionis exanimato altero, successit tertius, et tertió quartus; nec prius ille est a propugnatoribus vacuus relictus locus, quam, restincto aggere atque omni ex parte submotis hostibus, finis est pugnandi factus.

4. Translate into Latin:

(a.) The love of money is so great that not even the fear of death can altogether quell it.

(b.) After that battle they sent Pausanius to Cyprus, to drive out the barbarians from that island.

(c.) Perseus showed his enemies the head of the Medusa, by the sight of which
all were changed into stones.

(d.) Cicero warned the conspirators to conceal nothing from the judges.
(e.) We pity our fellow-citizens, who have lost all in the conflagration.

The first corps raised in England in accordance with our present system, and in fact the first germ of an English standing army, was the Coldstream Guards, raised by General Monk at Coldstream. In the course of a few years several others were added, and by 1665 the British infantry consisted of four regiments besides the Guards. Before the close of the century, a grenadier company, furnished with hand grenades, had been added to each regiment; bayonets had been introduced; several regiments of fusiliers, originally intended to protect artillery, had been raised; and the principle of a standing army of considerable numbers fairly established. Light horse were introduced in 1745, and lancers in the reign of George III. It is within the last few years, however, that the greatest changes have taken place in the British army. But the advancement and elevation of the soldier himself only render him more capable of appreciating the traditions of his corps.

II. Translate into English:

UN ÉPISODE DEVANT SÉBASTOPOL.

Je m'étais arrêté, et je regardais avec une émotion profonde tous ces hommes qui, un instant auparavant, étaient pleins d'audace et de courage; tous étaient immobiles. Cependant, sur l'un des brancards les plus rapprochés de moi se soulevait faiblement une capote, et le bras du blessé cherchait à atteindre le brancard que l'on avait placé à côté du sien; un instant après, deux mains se touchaient. Celui qui le premier avait cherché cette étreinte fraternelle, rejeta tout-à-coup la capote dont on l'avait couvert, et aux premières lueurs du jour je le vis lever la tête, essayer de se soulever, puis retomber.-Je me penchai sur lui; le pauvre soldat était mort.-Cette main étendue, qui voulait presser une autre main, avait été le dernier adieu du mourant à un frère d'armes.-CINQ MOIS AU CAMP DEVANT SÉBASTOPOL, PAR LE BARON DE BAZANCOURT.

III. GRAMMAR:

1. Write down the present participle and past participle of each of the following verbs: Savoir, voir, mouvoir, pouvoir; rire, dire, écrire; manger, placer, régler, mener. Give also the present subjunctive 2d person singular and plural of each.

Give the future, first person singular, of savoir, voir, pouvoir.

2. Give the feminine form of each of the following adjectives: Sec, grec; malin, marin; aigu, perdu; net, complet; vif, royal, formel.

3. Translate and write in full: "16 July, 1878; 200 men; 220 men; 2,220 men; 80 pounds; 84 pounds; 12,000 pounds; thousands of pounds." Explain the rule about vingt, cent, and mille.

4. "Cherchait à atteindre"; "je le vis lever la tête, essayer de se soulever." Why are these verbs in the infinitive? State the rule, or rules.

5. "Le brancard que l'on avait placé"; "celui qui avait cherché"; "le pauvre soldat était mort". With what part of the sentence do the participles placé, cherché, mort, agree? State the rule of agreement of the participle conjugated with avoir.

NOTE F.

Apportionment of naval instructors, midshipmen, and naval cadets among sea-going ships and otherwise, January 1, 1879.

* Exclusive of the class that entered in the preceding November, whose admission to the Britannia dated from January 15, 1879.

NOTE G.

EXAMINATION PAPERS: ROYAL NAVAL COLLEGE, JUNE, 1878.
EXAMINATION FOR RANK OF LIEUTENANT, R. N.

2. Prove the rule for finding the L.C.M. of two algebraical expressions. Find the L.C.M. of

6a4

3. Simplify

- a3b — 3a2b2 + 3ab3 — b1 and 9a1 — 3a3b — 2a2b2 + 3ab3 — b4.

xn -1 x2+1 xn+1 xn

1

1.

4. (a) Explain the terms: Surds, surds of the same order.

Express as surds of the same order 5 and 7.

6. A railway train 66 yards long, traveling at the rate of 50 miles an hour, met another train traveling at the rate of 22 miles an hour, which it passed in 5 seconds. Find the length of the second train.

8. If a and ẞ are the roots of the equation ax2 + bx + c=0, find the value of at + c2 (32 + ß1.

9. Explain the terms: Ratio, Ratio of less inequality.

If a b be a ratio of less inequality, and x a positive quantity, show that the ratio x: b x is less than the ratio a: b.

a

10. (a) Prove that the ratio of the sum of the latter half of 2n terms of any arithmetical series is to the sum of 3n terms of the same series as 1 to 3.

(b) Sum the series-+-&c. to 7 terms.

11. Having given two numbers and the difference of their logarithms, show how the base of the system may be determined.

In what system does the logarithm of 40 exceed that of 5 by 3?

II.-GEOMETRY.

(Time allowed, 3 hours.)

1. Describe an equilateral triangle upon a given finite straight line.

If a second equilateral triangle be described on the other side of the given line, what figure will the two triangles form?

2. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, namely, either the sides adjacent to the equal angles, or sides which are opposite to equal angles in each, then shall the other sides be equal, each to each, and also the third angle of the one equal to the third angle of the other.

3. The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.

4. On the sides AB, BC, CD of a parallelogram are described equilateral triangles ABE, CDF without the parallelogram and BCG within it; prove that EG, FG are equal to the two diagonals respectively.

5. Describe a square equal to a given rectilineal figure.

6. Define a circle.

If two circles touch one another internally, the straight line which joins their centers, being produced, shall pass through the point of contact.

7. Define the segment of a circle.

On a given straight line describe a segment of a circle containing an angle equal to a given rectilineal angle.

8. In a given circle, inscribe a triangle equiangular to a given triangle.

If the inscribed triangle be equilateral, show that the distance of any point in the circumference of the circle from the most remote angle of the triangle is equal to the sum of the distances from the other angles.

9. Enunciate the axioms of Euclid's Fifth Book.

Find a mean proportional between two given straight lines.

10. In equal circles, angles, whether at the centers or circumferences, have the same ratio which the arcs on which they stand have to one another; so also have the sectors.

III.-TRIGONOMETRY.

(Time allowed, 3 hours.)

1. What are the methods of measuring angles commonly made use of?

If the radius of a circle be 20 feet, find to four places of decimals the length of the arc subtending an angle of 7° at the center of the circle.

2. Trace the changes in the sign and magnitude of the fraction

6. Investigate a formula giving the value of the sine of half an angle of a plane triangle in terms of the sides.