Second part. A Produce the line AB to C so that the square on AC-3 times the square on AB (Euclid I. 47. Cor.) Then make BD=BC, and the line AB is divided in D, so that the rectangle BA.AD=} BD2. = Proof.-AC or (Cons.), 3.4B, AB+24B. BC+BC (Euc. II. 4). Take AB2 from each, and substitute BD for BC, ... 2AB2=2AB.BD+BD2; Or 2(AB.BD+AB.AD)=2AB.BD+BD2, 7. First part. A segment of a circle is the figure contained by the straight line joining any two points in the circumference of the circle and the part of the circumference cut off by this lice (Euclid III. 21). Second part. PM, PN, are perpendicular respectively to 0.4, OB. Then MN is parallel to BL. Proof. Since the angles PMO, PNO are right angles, the quadrilateral PMNO could have a circle described about it, therefore the angle LMN the angle BOP, for each is the supplement of the angle PMN. But the angle BOP is the supplement of the angle BLM. Therefore the angles BLM, LMN are together equal to two right angles; wherefore BL is parallel to MN. NOTE.-PL may intersect OB and PN may not fall on OB, but on BO produced through 0. In each case the proof is similar to that given above, and can present no difficulty. Since the angles OAD, OBD are right angles the quadrilateral AOBD could have a circle described about it, therefore the angle BOD=the angle BAD; but (Cons.) the angles OAB, OBC, OCB are together equal to a right angle, because they are the respective halves of the angles of the triangle ABC. Therefore, the angles BAD, BAO are together equal to the angles BAO, OBC, and OCB. Consequently, BAD=OBC +OCB. But BOD BAD; ... BOD=OBC +OCB. To each add BOC. Therefore BOD +BOC OBC+OCB+BOC. That is, BOD+BOC=two right angles. (Euc. I. 32.) Wherefore OC, OD are in the same straight line. (Euc. I. 14.) Similarly, it may be proved that AO, OE are in the same straight line, as also BO, OF. 10. First part. Euclid IV. 10. Second part. Let O be the centre of the circle described about the triangle BCD. Then, since DB=DC, DO bisects the angle BDC and cuts BC at right angles in the point P. Therefore DO contains the centre of the circle described about the triangle ABC. But this centre lies in CE, the perpendicular from C on AB; therefore N, the point of intersection of the lines DO, CE, is the centre of the circle described about the triangle ABC. What is required, therefore, is to prove CN=CO. Since AB touches the circle described about the triangle BCD, the angle ABO is a right 6. A house is supplied with water from an open cistern find how many pounds of pressure to the square inch will have to be resisted by apipe at a depth of 30 feet below the cistern, being given that a cubic foot of water weighs 62 pounds. ANSWERS. Every particle of matter attracts every other particle of matter with a force which is directly as the product of the masses of the particles, and in-versely as the square of the distance between them. It was inferred by Kepler from observation that the planets revolve round the sun in accordance with certain laws, which have since been known as Kepler's laws. Newton subsequently proved that the fact of the planets performing their revoIntions in accordance with these laws showed that the planets are attracted towards the sun as a centre with a force which varies inversely as the square of the distance. Newton further demonstrated that the moon is kept in its orbit by a similar force, which force is the same as the force of gravity, supposing it to decrease as the square of the distance from the centre of the earth increases. He also showed how the most important of the motions in the solar system might be accounted for by the theory of universal gravitation. The proof on which this theory rests is briefly this: The motions of the various members of the solar system may be accurately determined in accordance with theory, and their positions calculated for any time past or present. The positions of the various members of the solar system as observed are the same as those determined by observation. Hence the truth of the theory is inferred. 2. Boyle's law is that while the temperature remains the same the volume of a given quantity of gas is inversely as the pressure which it bears. Thus, if the pressure on a cubic foot of air is increased from 15 lbs. per square inch to 30 lbs. per square inch, the volume is decreased to half a cubic foot. If v and p be the volume and pressure of a given weight of gas at a given temperature and v, and P1 be any other volume and pressure, then we have vp=v1Pi Also if d and d, be the corresponding densities we have P P1 d d = MILITARY ENTRANCE EXAMINATION. ENGLISH LITERATURE. (1.) Time, 3 hours. CHAUCER: Knight's Tale. 1. Write out, as much as possible in Chaucer's words, his description of one of the following-the fight of Palamon and Arcite in the wood, the temple of Mars, the funeral of Arcite. Remark on any points in the description that seem to you noteworthy. 2. Explain the following words grammatically and etymologically, and quote the context where you can; freten, paranentes, liche-wake, meth, couthe, stevene. 3. Illustrate from this poem (1) Chaucer's conception of chivalry, (2) his knowledge and treatment of classical ideas. SHAKESPEARE: Richard II. and Julius Cæsar. 4. Contrast in these two plays, the characters of the two rulers and the motives of the conspirators against them. Illustrate from them the difference between the political life of Rome and England. OF, (1) Blank verse makes some approach to that which is called the lapidary style. (2) The rights of nations sink into questions of grammar if grammarians discuss them. (3) While the people are not inclined to condemn me, I shall not fear the highflyers at Button's. (4.) Friendship has no tendency to secure veracity. (5) The sound should seem an echo to the sense. (6) In these verses the words "night" and "light" are too nearly allied. ANSWERS. 1. We take the description of the Temple of Mars. It is unnecessary to quote here; at the examination all the lines possible should be given. Similarly, in the other answers quotations will be sparingly made. In this description we may note how various are the characters and scenes which, in the poet's opinion, may fairly claim the patronage of "Mars Omnipotent." The desolation surrounding the temple is what might be expected. Chaucer's description of it is short but apt. But when we read further, we find many things which we are not apt to consider as part of the "pride, pomp, and circumstance of glorious war." We have the "pike-purse," "Woodnesse (i.e. madness) laughing in his rage," "The sow freting the child right in the cradel," "The coke yscalled," and "The carter overridden with his carte." 2. " Freten," the perfect participle of the verb "to fret." It had a more energetic signification in Chaucer's time than now, as the context shows : "I saw how that his houndes have him caught, And freten him for that they knew him naught." And in the passage describing the Temple of Mars, "The sow freting the child right in the cradle." "Paramentes," trappings, embroideries, suitable to their rank: "Lordes in paramentes on his courseres, Knights of retenue, and eke squieres." So in the "Squire's Tale" we have, "Till he come to his chambre of paraments." "Lichewake," the wake or watch kept over the dead; a custom more prevalent among the Celtic than other nations. Chaucer seems to confound the funeral games of the ancients with the "wake" of the moderns. "Meth," honey, afterwards "mead.” The latter form occurs frequently in Chaucer; it is a Celtic root. "Couthe," the perfect participle of conned, knew, by transposition of the d, and softening the n into u. "Stevene," a time for performing any action previously fixed by message. 3. It was the characteristic of chivalry to seek adventures, and above all, those which had fɔr their object the relief of the distressed, or the avenging of injuries done to the helpless. Thus Theseus turns away from the gates of Athens, on his triumphal entry, to punish Creon of Thebes for his cruelty to the wives of the conquered king and nobles. Thus, also, most of those who aided Palamon and Arcite in their final contest, wished to distinguish themselves in a quarrel in which they had personally no concern. Again, to keep the knightly word was of the strictest obligation. Thus Palamon says to Arcite : "For which thou art ybounden as a knight, And Arcite retorts. Deference to the fair sex, and unbounded devotion of the lover to his mistress, are also chivalric features painted strongly by Chaucer. Thus Theseus spares the lives of the lovers at the request of his queen and Emelie; and each of the former is willing to undertake any labour, and undergo any risks, to be even near the beloved one. Finally, we have the “ trial by wager," and the determination of disputed claims by the ordeal of battle. The description of the "jousts" leads us naturally to the second part of the question. It is evident Chaucer transferred the ideas of his own time to the classic ages. The knights appear in the lists, attended by their squires. Though called Licurge, Emetrius, &c., they are facsimiles of the best of the warriors of the fourteenth century. When the spears are shivered the swords are drawn, "But as a justes or a tourneying." Another example of "mixed" association of ideas in the poem is the introduction of Solomon's "folie" into the pictures in the Temple of Venus. And it is the same with the remainder of the pcem. Chaucer shows his knowledge of that portion of mythology in which the classic poets and dramatists sought their materials; and he introduces the Deus ex machina: Mars, Venus, and Saturn interfere for their earthly favourites ; the invocations of the latter, however, have only a faint resemblance to those of their antique prototypes. One idea of the ancients, viz., the sacredness they attached to the duty of burying the dead, is finely illustrated; another, the indifference regarding human life, was, unfortunately, also a feature of the time of Chaucer. decrees, he shortens Hereford's term of banishment at the intercession of his father; yet he dreads him more than he does Norfolk, and afterwards determines to violate his word. He notes Bolingbroke's designs to captivate the hearts of the people, yet makes him an object of their sympathy by unjustly seizing on his heritage; and then, by his voyage to Ireland, leaves England open to the attempts of him whom he considers his most dangerous foe, and whom he had furnished with such weapons against himself. His treatment of Gaunt on his death-bed exhibits a mixture of frivolous impatience and cruelty of which his expressions, when he hears his illness, are an anticipation : "Now put it, heaven, in his physician's mind, To help him to his grave immediately.” Towards the conclusion of the play, his character, softened and purified by affliction, is comparatively elevated. The scene where he delivers his throne to Bolingbroke shows the first stage of this improvement; he is irresolute, almost flatters his deposer, and yet cannot conceal his detestation. This is an example of Shakespeare's skill in developing character, and prepares us for the resignation and introspective repentance of the later scenes. In these we forget the tyrant of the first part of the play, and compassion takes the place of disgust. Julius Cæsar, as delineated in his own speeches in Shakespeare's play, is not the Julius Cæsar of history. In these, he is a boaster who contradicts himself; in the most important action of his life, judging from its consequences, he is led alternately by Calpurnia and Decius, while professing loudly his unchangeableness of resolve. To the former he says: 66 'Danger knows full well That Cæsar is more dangerous than he." Yet a speech of half a dozen lines from his wife, and he changes his mind. A few sarcastic sentences from Decius Brutus, and we have another fluctuation : "Give me my robe, for I will go." But there is no dissimulation; his irresolution, disguised only to himself, is apparent to the other actors; in his own imagination, he is loftily immutable. Cæsar, as painted by his bitter enemy Cassius, and by the magnanimity of Brutus, is more heroic. He is greater in the depreciatory speeches of the former than in his own; and the latter acknowledges freely his noble qualities. In "Richard II.," we find that the ruling forces in England were an aristocracy and a king, the latter depending on his personal qualities for his political weight. Richard falls by a combination of the nobles; Bolingbroke takes his place through their support, and through his descent from Edward III. Neither of these qualifications would suffice by itself, nor both combined, unless aided by his political skill. But the commonalty But the commonalty have to be reckoned with; nothing must be done which will offend the national sentiment, and above all, which presses upon them pecuniarily: "And that's the wavering commons; for their love Lies in their purses; and whoso empties them, By so much fills their hearts with deadly hate." In "Julius Cæsar," we have the aristocracy and the Commons; the former unable to tolerate the supremacy of a single individual-a supremacy naturally the aim of every able and ambitious man, like Cæsar or his nephew; the latter accustomed to decide the contests which personal rivalry and the struggle for power engenderedaccustomed, that is, to decide them for the moment in the city, the ultimate arbiter being the sword. Their fluctuating opinions are swayed by the appeals of the orators to their passions, prejudices, and their self-interest; the power of the senate, as such, is very little felt; the old order of things in the Roman commonwealth has passed, and the new commences. 5. In Act II. Scene 2, the Queen bewails her position to Bushy and Bagot, and afterwards to Green; York enters, complains of the troubles which are heaped upon him, and expresses his opinion impartially of the merits and demerits of the King's cause, and of Bolingbroke's; and then leaves with the Queen to support the former. In the next scene of the same act he meets Bolingbroke an his principal supporters, ani denounces most vigorously and eloquently their attempts. Bolingbroke answers temperately, exposes his wrongs, appeals to York's paternal feelings, and says he means only to claim his lawful inheritance. York answers that he is aware of the injustice inflicted upon Bolingbroke, but that the attempts to rectify it in such a manner amount to rebellion. As, however, he is powerless to oppose these attempts, he expresses his intention to remain neuter in the coming struggle. In Act V. Scene 2, York tells pathetically to his Duchess the entrance of Bolingbroke, now King, into London, with the deposed monarch in his train; Aumerle enters, his father finds out that he is a member of a conspiracy to kill the King at Oxford. He denounces his treason violently, and determines to set off and reveal all to Henry. The Duchess appeals, but in vain, to his feelings as a father; she then, after the departure of York, urges Aumerle to forestall him, confess his guilt to the King, and obtain his pardon. In the next scene, Aumerle obtains a private interview with Henry, gets a promise from him of pardon, and is interrupted by York in his confession. The father reveals all, and urges the King to do justice. The Duchess appears next upon the scene, and almost clamorously appeals to the King's clemency for her son, and obtains it, Henry, however, vowing vengeance on the other conspirators. We may add that in this scene, Shakespeare incurs the censure of Hallam for putting into York's mouth the phrase, 66 'Speak it in French, King; say pardonnez moi.” There are no scenes exactly parallel to these in "Julius Cæsar," but we may contrast York with Brutus and with Cæsar. When the conspiracy is revealed to the former, he joins; and then reveals it to his wife. Cæsar, again, yields to Calpurnia; York is proof against the entreaties of his friends and of his Duchess; his loyalty is stubborn, almost unnatural. 6. (1) This phrase is used by Gaunt on his death-bed, when lamenting the condition of his country under Richard : "This blessed plot, this earth, this realm, this England, Is now leased out (I die pronouncing it) Like to a tenement, or pelting farm." A tenement that can be passed from one to another, by the condition of holding; and a pelting farm, a petty, mean one, such as might form appropriately an article of traffic. (2) This extract is from a speech of Richard's, after receiving the information that Bolingbroke has rebelled, and that his own cause is well nigh hopeless. The full context affords the best explanation: "For within the hollow crown That rounds the mortal temples of a king An antic, or antique, a term applied to those (3) This is an exclamation from the servant in the scene between the Queen and the gardener. He asks, why should they keep order, extirpate weeds, model the beds, trim the plants, &c., within a space of ground paled or enclosed, when the kingdom is in such disorder. Is (4) This extract is from Portia's speech, where she reproaches Brutus for concealing his designs, and is an apt answer to his question. it physical," i.e., wholesome to the body, "to walk unbraced, i.e., with garments loose and frame exposed." "Suck up the humours, &c." It was considered hurtful to face the morning air without a draught, or some similar preservative; the humours or vapours of the dank or moist air were deemed very prejudicial to the health. (5) The citizens meet Cinna the poet in their excitement, after burning the houses of the conspirators. When he tells them his name, they think he is one of Cæsar's murderers, who had the same appellation, and cry out to destroy him. He exclaims, "I am Cinna the poet." The quo |