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15. Did you (Art. 54).

- 46

+12

+ 286

them thon, and paid him. 13. Have you not seen your eldest sister write the terms of the subtrahend after those of the minuend. during your stay in Lyons? 14. I have not seen her. not go to bed too soon last night? 16. I went to bed late. 17. At what hour did you rise this morning! 18, I rose at five o'clock; I

Otherwise.Put the quantity to be subtracted in brackets, generally rise early. 19. Did you not seek to escape from your prison and write it after the quantity from which it is to be subtracted, last year! 20. I have never tried to escape. 21. Have you sold your with the sign between them; then apply the Rules of property? 22. I have not sold it. 23. What have you given to the Addition. soldier! 24. I have given him nothing. 25. During his stay at B.,

EXAMPLES we gave him all that he wished.

(1.) From 6a +96, take 3a + 4b. EXERCISE 96 (Vol. II., page 42).

Here, change the signs of the subtrahend, but not those of the 1. Que reçútes-vous la semaine dernière ? 2. Nous reçûmes cinquante

minnend, thus :

4b. francs de votre ami, et vingt-cinq de votre frère.

6a + 9b — 3a 3. Menâtes-vous

Next reduce these terms, by Art. 52, votre fils à l'église hier? 4. Je ne l'y menai pas. 5. Que perdites and you have the answer, 3a + 56. vous l'année dernière? 6. Nous perdimes notre argent, nos habille (2.) From 166 (3.) 14da (4.) - 28 (5.) -- 16b (6.) — 14da ments et nos chevaux. 7. Les avez-vous cherchés ? 8. Je les ai

Take 12b

6da
16
12b

6da cherchés, mais je ne les ai pas trouvés. 9. Parla-t-on de votre frère, hier? 10. On parla de lui et de vous. 11. Qu'est-ce que le médecin

Answer, 46 8da

- 12

46

8da vous a donné? 12. Il ne m'a rien donné. 13. À quelle heuro votre (7.) 16b (8.) 12b (9.) 6da (10.) -- 16 (11.) — 120 (12.) 6da scur se leva-t-elle hier? 14. Elle se leva à cinq heures. 15. Vous

286 166 14da - 28 - 166 - 14da êtes-vous levé de bonne heure ce matin? 16. Nous nous sommes levés å six heures et demie. 17. Votre cousin a-t-il vendu toutes ses pro - 125

-8da

+ 4b

+ 8da priétés? 18. Il ne les a pas vendues, il les a données à sa sœur aînée. 19. Le voyageur vous a-t-il raconté ses aventures? 20. Il me les a

(13.) + 166 (14.) + 14da (15.) — 28 (16.) - 166 (17.) - 14da racontées. 21. Cet homme a-t-il cherché à parler à votre père? 22.

- 126

6da
+ 16

+ 120 + 6da Il a cherché à lui parler. 23. Le professeur a-t-il parlé de votre frère, pendant son séjour chez vous ? 21. Il a parlé de lui. 25. Votre ami

+ 20da

- 286

- 20da a-t-il porté son habit neuf ? 26. Il ne l'a pas encore porté. 27. Avez- (18.) From 8ab, take 6xy. Ans. Sab - 6xy. vous remercié votre frère! 28. Je l'ai remercié. 29. Qu'avez-vous donné à votre sour ainée ! 30. Je ne lui ai rien donné, jo n'ai rien (19.) From baay

(20.) 16aazz à lui donner. 31, Quand M. votre frère vous donna un livre, l'année Take 17ay

20ax dernière, le remerciâtes-vous ? 32. Je ne le remercini pas. 33. Est-il tard! 34. Il n'est pas tard, il n'est que six heures. 35. Fait-il beau Answer, baay -- 17ay 16aaex - 20ax temps ou mauvais temps? 36. Il fait très-beau temps.

(21.) 6dd + 3d - 4ddd

10dc + 2dddd + 4dy LESSONS IN ALGEBRA.-IV.

6dd + 3d --- 4ddd - 10dc -- 2dddd 4dy

61. From these examples, it will be seen that the difference SUBTRACTION.

between a positive and a negative quantity may be greater than 56. SUBTRACTION is the finding of the diference between any two either of the two quantities. In a thermometer, the difference quantities or collections of quantities.

between 28 degrees above zero, and 16 degrees below, is 44 EXAMPLES.-(1.) Charles has 5a pears, and James has 3a degrees. The difference between gaining 1,000 pounds in trade, pears. How many more pears has Charles than James ? and losing 500 pounds, is equivalent to 1,500 pounds. In this example, we wish to take 3a pears from 5a pears.

62. Proof.-Subtraction may be proved, as in arithmetic, by But subtraction is denoted by the sign . Henco the expresadding the remainder to the subtrahend. The sum ought to be sion 5a - 3a pears represents the answer. But 5a - 3a = 2a equal to the minuend, upon the obvious principle, that the difpears; which is the answer.

ference of two quantities added to one of them, is equal to the (2.) A gentleman owns a house valued at £4,500, but he is in other. debt £800. How much is he worth?

EXAMPLES.-(1.) From 2ay - 1, subtract --- xy + 7.
Here we have £4,500 – £800 = £3,700. Ans.

Operation.

Proof. 57. Let us now attend to the principle upon which these Here, Minuend 2xy - 1 Add — xy + 7 Subtrahend. operations are performed. Let us suppose that you open a

Subtrahend – y + 7

To 3xy-8 Remainder. book account with your neighbour, and that when cast up, the debtor side, which is considered positive, is £500, and the credit

Remainder 3xy - 8

2xy --1 Minuend. side, which is considered negative, is £300. On balancing the

(2.) From h+ 3bar (3.) hy oh (4.) nd -- 7by account, you find that he owes you £500 - £300 = 200. Now, Take 3h - 9ba 5hy -- 6ah

5nd

by if you take £50 from the positive or debtor side, it will have the same effect on the balance, as if you added $50 to the negative Answer 2h + 12b3 4hy + 5ah

- And - bby or credit side; and on the other hand, if you take £50 from

(5.)
(6.)
(7.)

(8.) the negative or credit side, it will have the same effect on 3abm wy 17 + 4ax ax + 76

3ah + axy the balance, as if you added £50 to the positive or debtor - 7 abm + 6xy - 20

4ax + 156

- 7ah + axy side. 58. In like manner, if, in the expression 12a --5a, you take 10abm - 7:ey

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+3+ 5av + 5ax — 86 3a from 12a, it will have the same effect on the expression, as if you added 3a to 5a, and retained the negative sign in the sum; they may be united and their sum be used. Thus,

63. When there are several terms alike in the subtrahend, thus, 9a -- 5a is the same as 12a -- 8a. Again, if in the expression 12a -- 5a, you take 3a from 5a, and retain the negative sign

EXAMPLES.-(1.) From ab, subtract 3am + am + 7am in the difference, it will have the same effect on the expression, + 2am + bam, as if you added 3a to 120 ; thus, 12a---2a, is the same as

Here ab - 3am - 7am -- 2am - Cam = ab-19am. 15a --5a.

Answer. 59. Hence universally, taking away a positive quantity from an

(2.) From y, subtract a tata +- a. Ans. y - 4a. algebraic expression is the same in effect as adding an equal

(3.) From ax -bc + 3ax +7bc, subtract 4bc-2ar+he + 4ax. negative quantity; and taking away a negative quantity is the

Answer. 2ax + bc. same as adding an equal positive one.

(4.) From ad + 3dc- bæ, subtract 3ad + 76x -- dc + ad. 60. Upon this principle is founded the following

Answer. 4dc-8bx - 3ad. GENERAL RULE FOR SUBTRACTION.

64. The sign —, placed before the marks of parenthesis which

include a number of quantities, requires that, when these marks Change the signs of all the quantities to be subtracted, i.e., of are removed, the signs of all the quantities thus included should the subtrahend, or suppose them to be changed from + to -, and be changed.' Thus a - (b-c+d) signifies that the quantities from -- to +; then if the quantities are ALIKE, unite the terms 6-c and + d are to be subtracted from a. Remove the as in addition (Arts. 49, 50); but if the quantities are unlike, parenthesis, and the expression will then become a −6+o—,

+ 10ah

+y*.

an expression which has exactly the same meaning as the land if not King of France," had died away, and there was former.

neither rhyme nor reason in keeping up a ridiculous delusion. EXAMPLE.–From xy + d, take 7ad -- æy + d + hm. Here, Time was, however, when the assumed title represented a ty+d-(7ad - ay + d + hm) -7ad + 2xy - hm. Answer. reality; when, though not without dispute, the Kings of Eng

65. On the other hand, when a number of quantities are to be land were acknowledged to be also Kings of France. Let us introduced within the marks of parenthesis, with - immediately look for a while upon a scene whereon the mark of the English preceding it, their signs must be changed. Thus, -m +% domination was stamped with such indelible plainness that all -de + 3h=-(m-b + dx-3h).

the waters of oblivion that have flowed past it since have not EXERCISE 5.

sufficed to wash it away-a scene which will remain as an

historical memory to the end of time, and which showed, inci. 1. From bab + 75y + 18dfg, take 3xy + 4b + 8dfg.

dentally at least, this, that the English were wholly unworthy of 2. From - 35az 21ab - 37m, take - 30m - 15ab 10ax.

their position as lords of France. 3. From 9ay + 196. + 226c, take 12ay + 31bc + 50bx. 4. From xy - 10ab + 6d, take 12ab + 100 + 24xy.

At daybreak on the 30th of May, 1431, a priest entered the 5. From 7a + 6x + dy + xyz, take 3x - 4a - 389 - 17xys.

cell of a young woman at Rouen, and announced that he was 6. From 18be – 2y + 22gh, take 41xy - gh + bc.

come to prepare her for death. Not that the prisoner was ill7. From 21ax + y + ac - ay, take 4a - be + x - yz - de.

she was young, healthy, and in the full possession of her facul. 8. From 21x + 40xy - 13a, take 42 + 10ab - 5bc.

ties; the death she was to suffer was a violent one-she was to 9. From 5ay, take 2ab + 30ab + ab 4ab.

be burned alive! Burned alive at one-and-twenty! What could 10. From 5ax + 16ay, take fax - ay + 3ax + 4ay.

the poor wretch have done? She had shivered the power of 11. From a +b, take - (c + d-f+g-h-æy).

the English in France; she had, by means of an enthusiasm 12. F:om 7ab + 16xy - 7ad, take (hab - 12xy + ad).

which rendered her obnoxio":s to the clergy, roused the French 13. Introduce the following quantities within a parenthesis with immediately preceding, without altering their value; viz.,

nation from the torpor into which it had been thrown by the

- q + 8 -0-d + f + gh.

stunning blows dealt to it by Henry V. of England, and she 14. Also, ab -- cdx + df - x - y + ghf - be + xyz.

had dared to thwart the purposes and brave the anger of vin15. From 4tx + 6bbb, take Sax + 4bbb.

dictive churchmen like the Bishop of Beauvais, and the Bishop 16. From 20yy - 2y + 12aaa, take 15yy - 2y - 12aaa.

of Winchester, Cardinal Beaufort. The prisoner's name was 17. Froin – 8 (a + b) + 10 (x + y), take 2 (a + b) - 6(x + y). Jeanne Darc, or as she has been more commonly, but erro18. From 4 (a + b) 16 (x - y), take 17 (a + b) + 36 (x - y). neously, called, Joan of Arc. 19. From 2a - aa + ba, take a -4aa 6ba.

The priest's announcement took the poor maiden entirely by 20. From 2x + 3.x - xx, take 2x + 3xx + 10xxx.

surprise. A week before she had been led ont into a public 21. From 18 - 25ab + 20x + 3y, take 3x + 3y - 25ab + 1. 22. From 6 (a - y) - 17 (a + y), take 3 (a + y) - 7(a - y).

place in Rouen, and compelled in a moment of weakness, when 23. From ax - my-my-6, take bax - 6xy - ay + 46 - 709.

surrounded by enemies--not one kindly face among the crowd24. From 660 - 4b, take 20a - b - 30a - 16a - 3b + 5a.

and under circumstances of great excitement, to sign a docu25. From 6x** -a, tako 2x42% - 16.

ment disavowing and solemnly abjuring certain charges of 26. Fromx* + 4.23y + 6x?y2 + 4273 + y4, take at - 4k’y + 6x=y2 - 4xys heresy which were preferred against her; and she had been told

on that occasion that her life would now be spared, though she 27. From 4a3 - 8a* + 16a5, take 3as 4q+ + 5a".

must resign herself to a sentence of perpetual imprisonment. 28. From a + b + c, take - a + b + c.

The excuse for breaking faith with the poor girl was this, that 29. From 4a3 - 3a'x + ax - 203, take 2a3 402. - ar? - 23.

since her abjuration she had said that St. Catherine and St. 30. Take as - 31* + 3x - 1 from x3 + 3x2 + 3x + 1. 31. From ax? + by?, take rx2 – dya.

Margaret, with whom she asserted she was frequently in direct communion, had appeared to her, and rebuked her for her weak

ness in yielding to the threats of violence. KEY TO EXERCISES IN LESSONS IN ALGEBRA.

On first hearing the announcement of the priest, Jeanne's EXERCISE 4.

firmness gave way; she wept and gave vent to piteous cries, tore 1. hab + cd-4m + 7.

her hair, and appealed to "the great Judge” against the cruel 18. 7y + 9yy + 5xy 6x. 2. Sy -- die + hm - 1. 19. Saaa.

wrongs done to her; but by degrees her self-possession returned, 3. cbm + bm - 5y + x + 16. 20. 7yyyy + 12 xx.

and she listened to the ministrations of the priest, received the 4. Sam + 3xy - 11. 21. - 6 (a + b) - 12(x - y) - 13.

last sacrament from him, and announced herself ready to sub5. Jahy + 16.

22. 4(a - b) + 9a (x + y) - 6y. mit to the will of God. At nine o'clock in the morning she G. llad + 23. 15axy + 3bed.

was carried away in the hangman's cart to the market-place of 7. by + 3 (b-a) + sa.

24. 17 (x + y) 9. (a - b). Rouen, where had been already laid the funeral pyre on which 8. 6ax + xy. 25. 15abc + 2 (x + y).

the young victim was to be sacrificed. The Bishop of Beau9. 66 + 41cdf – 3xy. 26. 24x7 babe + 4mn 25a.

vais, Cardinal Beaufort, and several other prelates, with the 10. 180 + 4ax - 56x + c3cx + 363 27. ta (x + y) + 76 (x + y) = (ta English military commanders, were there, and a vast crowd had - 17xy.

+76) (x + y). 11. Sab

come out to see "the Maid of Orleans" die. - 6be + 4cd – 7y + 17mn 28. axa + a*x + xy + 3y2 + y8. + 1899 - 2ax. 29. llas - 10990 - 14ab2 + 1663.

In the centre of the market-place, about the spot where now 12. Sabe + 25abd + 5xyz. 30. 1023 - 2x + 3x - 2

stands a fountain surmounted by a figure of Jeanne Darc, the 13. 3df + 4ax + 74y + 30. 31, 2q + 2 + 2c + 2d,

stake was reared, and around it were piled the fagots. Soldiers 14. 55a + 686. 32. a

guarded the place of execution. The ceremonial of death was 15. 7(a + b). 33. 698

begun on that beautiful May morning by a sermon in which the 16. Qy (a + b).

34. (a + b + c) 23 + (b -c + d) z* crime of heresy was vehemently denonnced, then the sentence 17. 2ax + 5aa + 3x + 3xxx. 35. (m + n + 2) 22 - (n + p +1) •.

pronounced by the shepherds of the flock on the ewe lamb before them was published, and the signal was given to proclaim

the last act of the tragedy. A soldier's staff was broken and HISTORIC SKETCHES.-XXIX.

formed into a rough cross which “ the Maid” clasped to her

breast. She was then bound to the stake, the fagots were THE ENGLISH IN FRANCE.-JOAN OF ARC.

lighted, the fire leaped up around her, and after suffering the UNTIL some time after George III, had been on the throne agony indispensable to death by burning, her spirit returned to the style and title of onr kings was “ King of Great Britain, God who gave it. The English cardinal watched the whole France, and Ireland.” Even when James II. was a fugitive proceedings with unmoved face, and when his victim's life was from his kingdom, and was magnificently entertained by Louis beyond his reach he ordered her ashes and bones to be XIV. at St. Germains for a series of years, he still retained the gathered up and to be cast into the Seine. empty title of king of the country where he was dwelling as a Was it really heresy for which this poor girl suffered? Ostenguest. To be sure he was virtually as much King of France sibly it was, but had Jeanne's heresy stood alone, it would scarcely as he was King of England, but to the latter title he had much have provoked the interference of potentates like those who more than a mere pretension, and the title of King of France was “ did her to death." Upon her head, when bound to the stake, historically bound up with it. Yet in James's time (1685-1688), they fastened a cap on which was written her accusation, "reeven the echo of the old shoat of Henry V., “No King of Eng. I lapsed heretic, apostate, idolatress," but they did not write the

true cause of their unholy zeal in setting the church's law in motion against her, that cause being the crushing defeat Jeanne Darc had inflicted upon the English political influence in the country. But how came the English in the country at all P Was it by way of revenge for the conquest by William the Norman, or did it spring out of some after-born political entanglements?

The claim of the English kings to be kings also of France began to be seriously mooted when Edward III. was Prince of Wales, and when he came to the throne, the question was taken up with ardour when once he was aroused from the lethargy which in the earlier days of his reign seemed to be the forerunner of an inglorious era. In 1337, ten years after he had been on the throne, Edward lacked occupation, and manifesting a desire to let his energies find vent in true Plantagenetfashion, listened to the advice and remonstrance of some of those about him, who urged him to assert his right to the crown of France.

The way in which he claimed was almost too barefaced to be written down; and while it is certain that few of those who fought on his side so valiantly and well, knew the real merits of the case, it is likely that he himself was not very expert in tracing his genealogy. Those who had motives of their own for the war, and who hoped to win fortune and rank for themselves out of it, told him he had a righteous cause, and he, gladly convinced, believed them. It was the custom in France, borrowed from the Salian Franks, who had become absorbed in the nation, to exclude women from the succession to the throne, and when a woman came in the direct line of succession her place was taken by the male heir nearest related to the late king. This custom had been sanctioned by the approval of several hundred years, during which time no one who founded his title through a female had mounted the throne. When Philip the Fair died in 1314, he was succeeded by his son, Louis the Stubborn, who died without male issue, and Louis's brother, Philip the Long, succeeded him, being himself followed in 1322 by his younger brother, Charles the Fair.

Philip the Long had died without issue, and on the birth of a daughter to Louis the Stubborn, the estates of France decreed

her exclusion, and the exclusion of all females in future.

Charles the Fair's only child was a daughter, and with Charles

was extinct the direct male line of Philip the Fair. Philip's fourth child was a daughter, Isabella, married to Edward II. of England, and it was taken for granted that the law of exclusion which applied to Louis the Stubborn's daughter, married to Charles, King of Navarre, and which applied to the daughter of Charles the Fair, applied also to Isabella, their aunt. So thoroughly did this opinion prevail, that when Philip of Valois, nephew of Philip the Fair, claimed the throne on the death of his last male cousin, his claim was allowed as reasonable and unquestionable by the whole nation, and no one so much as thought of a claim being made on behalf of Isabella by her son. The exact position of affairs may be best seen from the annexed diagram.

Charles of

Valois—younger brother to-Philip * Fair. .

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homage to him, as his liege lord, for the province of Guienne, which belonged to Edward as feudal tenant of the French king. Edward obeyed, rendered homage, and thus virtually acknowledged Philip's right to be king. But he did so only because it was not convenient to have a quarrel on his hands at the time. He had a Scotch war to fight, troublesome subjects at home to curb, and there was a plentiful lack of that sinew of war— money—without which it is useless to back even the strongest claim. When these troubles were over he listened to the suggestions of Robert of Artois, a renegade French nobleman, who,

having been treated badly by Philip the Fair, took an ignoble revenge by giving his services to the foes of his country. Edward looked about for allies before launching forth on a great war with France, and he secured the friendship of the Counts of Flanders, Brabant, Namur, Gueldres, and Hainault, and the powerful assistance of the rich citizens of Ghent, repre: sented by the brewer, Jacob van Artevelde. Having gained these allies, and coaxed Parliament to give a large supply in aid of the war, Edward proceeded to pick a quarrel. He complained that Philip had helped the Scots in the late war between Scotland and England, and that he still protected the Scotch king, a personal enemy of his. Finally, he renounced his homage, and defied the French king, who, knowing that the contest must come, buckled to with a will, determined to suffer anything rather than admit Edward's claim to the French crown. At first matters did not go happily; the English king, who elected to attack from the side of Flanders, had great difficulty in keeping his allies together; and though he did advance with 50,000 men into French territory, he did not fight, and return. ing into Flanders, disbanded many of his troops. Charges to the extent of £300,000 had been incurred; the money given by Parliament, and that raised by pawning the crown jewels and the personal effects of the king, was all gone, and not a foot of French land had been won. The Parliament, in the king's absence, refused supply except on the condition of redress a grievances, and it seemed as if the royal expedition after thi French crown must end in an inglorious fiasco. Suddenly Edward appeared in London, wrung a heavy grant out of thi Parliament, and proceeded to fit out a fresh force agains Philip, notwithstanding that the Parliament told him it owe him no allegiance as King of France, and that if won, Franc must ever remain a separate part of the kingdom. On June 24, 1340, Edward's fleet, well manned and sound came up, off Sluys, with the French fleet of four hundred sai which Philip had prepared to intercept Edward's army in it descent on the coast. A bloody battle ensued. The Englis were the better sailors, and manoeuvred so as to take ever advantage of the enemy, who lost the greater part of the ships and upwards of 25,000 men. This crushing victor of which Edward was not prepared at the moment to tak advantage, fixed an unbridgeable gulf between the goo will of the two nations. National prejudice, national hatro had their birth in it, and from the battle of Sluys datest dreadful animus which existed down to quite recent tim between the English and French. From the same event, how ever, dates the welding of the English nation into one hom geneous whole; the lords ceased to affect French ways and ti French language—which, historically speaking, was theirs—at identified themselves with the country which was their me home. After the battle of Sluys the word “Englishman” ceas to be a term of reproach. The battle of Sluys, the first brilliant victory of the Engli navy, was barren of immediate result so far as Edward's clai to the French crown was concerned. As usual, when a Fren war broke out, the King of Scotland broke the peace by way diversion on his side, and Edward had to turn the whole of 1 strength against his northern enemy, who was, necessarily, be crushed before a foreiga war could be carried on. In 18 however, Edward, with the English nation at his back, set." on the campaign which ended on the field of Cresy, and wh |o followed some years afterwards by the rout of Poio (1356), where the French king, John, was captured by the Bla

Prince, and brought prisoner to London. The exhausting to made during the campaign were such as to prevent Edward fr following up his splendid successes, and he was glad to arro by the Treaty of Bretigni, for a long truce. Various reas conspired to prevent the resumption of hostilities on "...o scale during the rest of Edward's long reign. The English mained masters of large portions of French territory: * the claim of the English king to the crown was not abandon but kept as a sword in the scabbard, for use at a to nient season. The son of the Black Prince, Richard of B deaux, who succeeded to his grandfather's crown, did not * ceed to his energy or his ability, and the English claim virtually dormant during the whole of his reign, while French were employing the time in recovering from the effe of Edward's blows, and from the disastrous results of the

rgency which continued all the years King John was in captivity. Henry IV. had not leisure from home troubles to pursue the war, though he seems te have been desirous of doing so, not only as King of England, but by way of paying out the French king for his something more than neglect of him at the time he was in exile as Henry of Bolingbroke. When Henry W. succeeded, he had a large stock of energy to expend, squiet kingdom, and a fairly stocked treasury; he had plenty of brave spirits about him, and within him was an ambition which would have taken him to Constantinople or to the capital of the Great Mogul. He determined to assert his claim to the crown of France. To a king in his frame of mind an occasion of declaring war could not long be wanting, and there were several causes which allowed of his choosing his own time and opportunity. He set about his work deliberately, sent a special embassy to France to demand his right, and when that embassy returned from its bootless errand, he prepared with diligence and the utmost circumstance to enforce his claim with the sword. In the month of August, 1415, he sailed from Southampton with one of the inest armies ever mustered in England, landed at Harfleur, which he besieged and captured, and then prepared to advance on Paris. An enemy worse than all the French armies put together came into his camp. Dysentery smote down hundreds of his men, including some of the bravest and wisest, and so wakened the remainder that they could scarcely walk. Henry was obliged to abandon the idea of going to Paris, and gave orders for a march to Calais, whence he proposed to embark his afeebled army for England. At Agincourt, the French army, which had been hanging about him, barred his advance. It consisted of full three times the number of the English, and was ommanded by the Dauphin, the French king's eldest son, and of the flower of the French nobility. The French were confident of victory, the English were in a desperate case, and the battle * joined with an amount of fury seldom witnessed even in onse days. The French were utterly routed (October 25, 1415), not nminbers of them were slain, and the shattered remains of the English army pursued its march unmolested to Calais. In the next campaign, which was not undertaken till two jars afterwards, Henry met with but little resistance in the on country of Normandy, though Rouen was stoutly defended. He reduced Rouen and other towns, and marched to Paris, * he mastered, and dictated terms in the capital of his ony. The French king, Charles WI., was imbecile, and the Raty of Troyes, to which the Dauphin refused to be a o, provided that Charles should be called King of France *ing his lifetime, but that Henry should really administer the *rnment, and that after Charles's death he and his suc** should be acknowledged as kings of France. Henry *gthened the band by marrying Catherine, daughter of the * king, and during the rest of his life he did actually rule * France and receive the homage of her vassals. in the height of his power Henry was struck down with fistula,

governor of Orleans—the men fought with a courage which increased in proportion as her fame as a prophetess grew, and struck fear into the ranks of the English. Orleans was relieved by “the Maid” in person, and the garrison, now strong enough to attack its besiegers, sallied forth and drove the English from several of their positions. Subsequently another sally was made, a bloody battle was fought, the English lost 2,000 men, and Lord Talbot, afterwards Earl of Shrewsbury, was made prisoner. The Duke of Suffolk raised the siege, retiring to Paris, and Charles was crowned King of France with great solemnity at Rheims. With these signs of returning prosperity many wavering nobles and towns declared for Charles, and the Duke of Bedford had enough to do to hold Paris and the strictly English parts of France. Jeanne, believing her mission to be over, was anxious to return to herformer home in Lorraine, but was over-persuaded by Dunois to remain with the army till the English should be driven out of France. She remained, and in a sortie made by the garrison of Compiègne, was captured and given over to the English authorities. The English, partly from superstition, partly to excuse the disgrace of their defeats, said that “the Maid” had a devil, and that she had done her work through magic. They hoped also by punishing their prisoner not only to take revenge, but to show the French that their prophetess was a woman after all. The Duke of Bedford handed her over to the Church, with what effect we have seen already; and from the moment of her death the English power seemed to be stricken with mortal sickness. Place after place was wrested from them, Paris drove them out, the Duke of Burgundy forsook their alliance, and when in 1435 the Duke of Bedford died, their influence in France was at a very low ebb. A war of reprisals was carried on till 1443, and then a truce was agreed upon which either side broke or kept as it suited their convenience. Then came the English Wars of the Roses, during which disastrous period the claims to France were not thought of, and it never happened to any prince after Henry VI. to have power or opportunity to pursue the right which was never

formally renounced. Kings of England continued, neverthe

less, to write themselves down kings of France, even after

the loss, in Mary's reign, of their last remaining possession, . | Calais. Indeed, it was not, as stated at the beginning of this

paper, until George III. ascended the throne that the title ap

peared to those interested so ridiculous that it was ordered to

be expunged from the style and description of his Majesty of Great Britain.

GEOGRAPHY. —XXIX. ASIA. Position on the Earth's Surface.—Asia, the cradle of the human race, and the original seat of the Garden of Eden, lies within the northern and eastern hemispheres, and to the east

LESSONS IN

* the doctors could not cure. He died, still a young man, and and south-east of Europe. The greater part of this continent ***on, an infant of nine months old, to the guardianship of lies within the north temperate zone; the exceptions being part * Duke of Bedford and the Earl of Warwick. This was in of Siberia, which lies within the north frigid zone, and parts of ol. For five years Bedford, who managed with singular tact Arabia, Hindostan, Further India, and China, which lie within * Prudence, succeeded in keeping things pretty straight, in the torrid zone.

* of numerous causes of trouble and disturbance, including, Boundaries.—Asia is bounded on the north by the Arctic Ocean; **rse, the efforts of the Dauphin, who in the meantime had on the south by the Indian Ocean and the Chinese Sea; on the * Charles VII, to regain his father's throne. Charles had east by the Pacific Ocean; and on the west by the Ural Moun*ge following. especially in the south-east of France, and he tains, Ural River, Caspian Sea, Mount Caucasus, Black Sea, *able to possess himself of a few towns of strength and | Sea of Marmora, the Mediterranean Sea, the Isthmus of Suez, *tance. Orleans was of the number, but it was closely , which connects it with Africa, and the Red Sea or Arabian Gulf,

*ged by the English under the best of their generals, and ories despaired of relieving it, and thought of going to *redoc, there to make a final stand. Then arose Jeanne Darc, a peasant girl, who saw, or believed **, visions of the saints, especially of St. Catherine, who * to her and told her she must deliver France from the onee of the English. Her “voices,” as she called them, * her don man's attire, and directed her to fetch a certain * from a neighbouring church dedicated to St. Catherine. ***permitted by the authorities to follow her bent, and was - with armour and a horse. At first the regular soldiers *d other, but soon they got to regard her as a prophetess, **ent for the deliverance of France. Under her guidance T**ictly military operations she was assisted by Dunois,

Ectent, Length, Breadth, etc.—This continent extends from lat. 78° 25' N., to lat. 19 20° S.; and from long. 26° 4' E., to long. 170° W. This shows that a very small portion of this

continent lies in the western half of the northern hemisphere.

Its length, from the Strait of Bab-el-Mandeb, at the entrance to the Red Sea, to Behring Strait, between Asia and North America, is about 7,000 miles, measured across the continent in a straight line, as the crow flies. Its breadth, from Cape Severo, also called Cape Tcheliuskin, and North East Cape, in Siberia, in a straight line from north to south, almost identical with the 102nd meridian of east longitude, to Cape Romania, at the extremity of the Malay Peninsula, is about 5,250 miles. This continent is connected with that of Africa, at the Isthmus of |so, which is about 80 miles wide. The surface of Asia, in

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