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thee.

(our) father. 17. Thou well contendest with thyself. 18. God is with 19. Often the mind is in discord (disagrees with itself). 20. The enemies fight earnestly with us. 21. Thy speech is not in unison with thyself. EXERCISE 52.-ENGLISH-LATIN.

1. Omnia mea mecum porto. 2. Secumne omnia sua portant sapientes? 3. Tu me amas, ego te amo. 4. Vita tua mihi est cara, mea tibi. 5. Mali semper secum discordant. 6. Tractatio literarum gratissima est nobis. 7. Amant sese homines. 8. Amantne sese mulieres? 9. Pessime amant sese mali. 10. Per se pulchra est virtus. 11. Propter te ipsum te amo. 12. Mea patria gratior est mihi quam

tua tibi.

LESSONS IN BOTANY.-XV. SECTION XXVII.-CRUCIFERA OR BRASSICACEE, THE CRUCIFEROUS (CROSS-BEARING) OR CABBAGE TRIBE. ALREADY, in an early lesson, we have had occasion to make a statement respecting the cross-bearing flowers that we hope the reader has not forgotten. We mentioned that a strange plant being referred to this natural order, such plant might at once be considered harmless, and probably very good to eat.

Let us now go a little more minutely into the characteristics of these cross-bearers. They are these: Sepals, four, free; petals, hypogynous, four, free, cruciform; stamens, six, tetradynamous; ovary, bilocular, placenta parietal; fruit, ordinarily a pod; seed, dicotyledonous.

Let us now proceed to the application of such of the preceding characters as may be necessary. Firstly, the propriety of the term cruciferous will be rendered evident from an examination of the representation of the flower of a plant termed Shepherd's Purse, one of the cruciferous family (Fig. 147).

This same individual, the Shepherd's Purse, shall also serve to teach us yet something more regarding the peculiarities of the natural order Cruciferæ.

Let us now examine a branch of the plant (Fig. 146). Directing our attention at first to the flowers, we find them to be arranged after the manner of a raceme, and totally devoid of bracts. This absence of bracts pervades the whole natural order Cruciferæ, which is the only natural order in which the bracts are uniformly absent. Hence by this sign a cruciferous vegetable may be as readily known as by the structure of the flower; indeed, the sign of absence of bracts has a wider sphere of application. The flowers of the Crucifera are at the best very small, but perhaps they might not yet have fully developed themselves at the period of observation. Consequently, if the cruciferous shape of flowers were the only guide, the student might not be able to wait for the sign of discrimination; whereas by noticing the absence of bracts, he would know the plant under consideration to be cruciferous, and knowing this, he would be assured of its harmlessness at least. Most probably it would be good to eat, either in the form of salad or cooked.

The advantages of being thus able to refer an unknown plant to a harmless and useful order we need not specially indicate. They will be self-apparent. Let the reader consider the bearing of this anecdote. It is related that, when during Anson's voyages his crews disembarked in unknown places, the surgeon, fearful of poisons, would not suffer them to partake of any vegetables except grasses, notwithstanding the scurvy was making great ravages amongst them. Now the reader must be informed, if he does not already know, that the scurvy is a disease almost entirely dependent upon too exclusive a diet of salt meat, without accompaniment of vegetables, more especially vegetables of succulent character. Formerly the scurvy made great ravages in our navy; at present it is scarcely known, having been banished, partly by the administration of fresh preserved provens, but chiefly by the administration of lime-juice, which nstitutes a portion of the rations of every sailor. If

146. SHEPHERD'S PURSE.

Anson's crew had been provided with fresh vegetables to eat, their scurvy would have been cured; and they knew it. How great, then, must have been the fear of the surgeon, and how valuable is the knowledge of Botany!

Returning to our investigation of the distinctive signs by which cruciferous plants may be known, we shall merely call which two are more spreading and shorter than the others; your attention to the fact that each flower has six stamens, of hence the denomination Tetradynamia (or four-powered) in the Linnæan or artificial classification, and this is another essential characteristic of cruciferous plants. The other characteristic signs being for the most part microscopic, we pass them over without notice.

The Crucifera are dispersed all over the surface of the globe; the greater number, however, inhabit the northern temperate zone, more especially of the Old World; between the tropics they are rare, and when they exist, are found on mountain elevations; beyond the Tropic of Capricorn they become less fre- 147. FLOWER OF THE SHEPquent, even more so than beyond the Tropic of Cancer.

[graphic]

HERD'S PURSE, ENLARGED.

When we mention that cabbages, sea-kale, mustard, cress, and radishes belong to this order, we shall have stated enough to demonstrate the utility of its species. When we state again that wall-flowers (Fig. 149) and stocks are cruciferous plants, the reader will see that utility is not the only claim which the Crucifera present to our notice.

The Crucifera are imbued with an acrid volatile principle dispersed throughout all their parts, and frequently allied with sulphur. To this volatile principle cruciferous plants owe their piquancy and their peculiar odour, which, after putrefaction, is ammoniacal; thus proving the Crucifera to contain the simple body, nitrogen, ammonia being a compound of nitrogen with hydrogen. In many species of Crucifera there exists in connection with the odorous principle also a bitter material and a fixed oil; the latter is chiefly developed in the seed. The active principles of annuals belonging to this order reside in the leaves, those of the perennials in the root. Certain species, the leaves of which are inoperative, produce very acrid seeds. Many Cruciferæ grow mild by cultivation, which augments their amount of sugar and mucilage. The anti-scorbutic properties of many Crucifera have been known from times of great antiquity; the species which possesses the greatest fame in this respect being the Scurvy Grass (Cochlearia Officinalis), a drawing of which is represented in Fig. 148.

SECTION XXVIII.-PASSIFLORACE, OR THE PASSIONFLOWER TRIBE.

The beautiful Passion-flower, now so common in England, is a native of the forests of Central America, where it grows on large stems which hang like festoons from the boughs of forest trees, interleaving them in a network of gorgeous leaves and flowers. The term Passion-flower was applied by the Spaniards, owing to the supposed resemblance presented in various parts of the floral whorls to the accessories of Christ's crucifixion. The conspicuous ray-like appendages, sprinkled with blood-like spots, were compared to the crown of thorns; the stigma is cruciform; nor were the ardent Spaniards slow to discover other fancied resemblances, which eyes less prejudiced than their own in favour of a dominant idea can scarcely recognise.

Characteristics: Perianth free, petaloid, biserial (in two rows), tubular, urceolate (like a pitcher, from the Latin urceus, pitcher), ordinarily furnished at its throat with one or more series of filaments. Stamens sometimes inserted upon the throat of the perianth, or upon its base; sometimes hypogynous, attached to the support of the ovary; ordinarily equal in number to that of the external divisions of the perianth. Ovary stipu late; three or five placentae; three or four styles terminated by club-like stigmas; ovules reflexed; fruit, a berry, indehiscent (not splitting), or capsular, three or five valved; seed, dicotyledonous; embryo straight, central.

We shall be able to individualise the Passion-flower order

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are not green, but coloured like the petals of mostflowers. We have already stated, however, that amongst the other transformations of parts which occasionally ensue, the transformation of the calyx into theappearance of a corolla is

150

149

Passion-flowers. The term petaloid means resembling a petal; the termination oid being derived from the Greek word eidos (ei-dos), likeness, which word, in composition, changes eid into oid. Directing the eye to the lower part of the sepals, they will be observed to rise from a shallow cup-like body, to which also are attached the petals and other portions of the flower.

152. SCARLET PASSION-FLOWER (PASSIFLORA AMABILIS).

not unfre-
quent. So fre- 148. SCURVY GRASS (COCHLEARIA OFFICINALIS). 149. THE WALL-FLOWER. 150. TRANSVERSE SECTION OF OVARY
quently, in- OF PASSION-FLOWER. 151. OVARY OF PASSION-FLOWER.
deed, does this

occur, that mere green colour is not to be regarded as more
than a collateral circumstance. The external floral whorl is
always considered by botanists as a calyx, whatever its colour
may be. That colour is often very brilliant, as in the fuchsia,
for example, where the gay-looking part of the flower is not
corolla or aggregation of petals, but calyx, or aggregation of
sepals. This assumption by the parts of the calyx of the
appearances usually presented by the corolla gives rise to what
botanists term a petaloid perianth. The student will find this
term comprehended in the list of characteristics peculiar to

As regards the petals themselves, they are COloured similarly to the colour of the inside of the sepals, and are of the same colour on both sides, by which circumstance they may be distinguished from the sepals, as also by the circumstance of their not having a little horn, which may be found on examination springing from each of the sepals.

We next arrive at the filamentary rays which the imaginative Spaniards compared to the crown of thorns! What are those rays? Theyare petals so modified in shape that they almost present the appearance of stamens. This modification, and yet more frequently its converse, stamens modified into petals, is not at all unfrequent in many flowers, as the result of cultivation. In the Passionflower tribe, however, it exists as the usual condition of the flower. Let

[graphic]
[graphic]
[graphic]

us now proceed to examine the reproductive, or fruit and seedproducing portions of the flower, which are very peculiar. We have already mentioned a cup-like body in connection with the structure of a Passion-flower. It corresponds with the part lettered c in Fig. 151. In the centre of this cup a column-like body is observed rising aloft in the centre of the flower, to which certain appendages are attached. The nature of these appendages will at once be obvious. Externally, we easily recognise five anthers, and internally we recognise the club-headed pistils; but looking again at the stamens, we search in vain for the filaments

to which they are usually attached These laments do not exist
at least do not separately exist; they are au muted—a se
the French say, and it is a very good word-to the support dé tue
Ovary. This expression, "support of the ovary.

24 new to: bat if the reader looks at his dissected Puma-Émer, or at diagram in Fig. 151, he will recognise the propriety of the expression; for in this tribe the ovary is supported within the flower by means of a little stem. Now this unde man ben called a stipes, the ovary is said to be stist-te This term the reader will remember, occurs in our list of chara teration of this natural order. Let the student now examine a little more in detail the anthers or pollen-forming his of the stamens. These do not point towards the stigmas to in the opposite direction, which is very unusual. Fertallestion of the evile depends, as we need not repeat, upon contact between the pollen-dust and the stigmas; hence it would even that the anthers should always point towards the stigmas. Let cases they do so point towards them, but in the Passion-dower tribe we find an exception to this rule.

Fig. 150 represents the transverse section of the ovary taining the seeds. The fruit, or ripened ovary, in all species of the Passion-flower is egg-shape 1, differing in size averring to the species. The blue Passion-dower provinces a fruit about thi size of a hen's egg; but in other species the fruit is much larger, and contains a delicious pulp.

Passion-flowers, we have seen, are both agreeable and neful from the beauty of their flowers and the flavour of their fruits: many species are medicinal. The pulp surrounding their seeds is in some cases sweet, in others acid; the latter serve as the basis for the preparation of acidulated drinks, not only gnisable, but medicinal. One species, Passiflora Rura, contains a narcotic principle which is sometimes employed as a substitute for opium. Passiflora Quadrangularis is cultivated for the refreshing pulp surrounding its seeds, but its root is very poisonous. In European gardens a large number of species of the Passion-dower are now cultivated, amongst which may be cited as the chief, Passiflora Carulea, or the blue Passion-flower; this being the commonest of all. Of this flower the Passitora Amalias (Fig. 152) is a hybrid or cross race between Passiflora Ata and Passiflora Princeps. Its flowers are scarlet, and exhale a delicate odour. The Murucuja Ocellata is a hot-house species, bearing deep-red flowers. Tactonia Malisi na bears rose-, coloured flowers, and is a climbing plant, requiring a greenhouse for its culture.

HISTORIC SKETCHES.-XV.

HOW ENGLAND AND SCOTLAND BECAME ONE.-PART II.

MANY competitors, as might be supposed, appeared to contest
so great a prize as the crown of Scotland; but the question really
lay between two, John Baliol and Robert Bruce, noblemen of
Norman extraction. The ground on which they founded their
respective claims to the Scottish throne was as follows: William
the Lion died, leaving a brother David, who was created Earl of
Huntingdon on his marriage with King Edward's sister. This
earl had three daughters: the first, Margaret, who married Alan,
Lord of Galloway; the second, Isabella, who married Robert
Bruce, of Annandale; the third, Adama, who married Lord
Hastings. At the time of the death of Alexander III., John
Baliol, the grandson of Margaret, Lady Galloway, claimed the
crown, as nearest descendant of the elder branch; and Robert
Bruce claimed it by what he asserted to be a better title, in
that he was the son of Isabella, the second daughter of David,
and was thus one generation nearer to the original stock. Lord
Hastings claimed, somewhat absurdly, a third of the kingdom,
on the assumption that it must be divided equally between the
tree branches, as private property might have been. The last
claim was never seriously entertained by any one; but though
modern law and custom would have found no difficulty in
deciding in favour of John Baliol, the question between him
and Bruce was, in the then state of law, by no means an easy
one to answer. Both claimants determined to support their
pretensions by force of arms, and were gathering their friends
for that Y
when they were persuaded to refer their dis-
on of the King of England.

his opportunity, and resolved to seize it.
decide the matter by virtue of his being
tland, a dignity the value of which has

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already been given. He ransacked the abbeys and other depo- stories of reccris for proof of his right, and though he found Little excitragement by so doing, he none the less boldly advanced his pretensions. In answer to the reference made to him sa referee, he directed the claimants to meet him at Norham, whither he marched with a large force, which was meant to overswe the Scotch Parliament or Council, assembled st the same place.

In May. 1231, the meeting took place accordingly at Norham, the sorts being drawn up in a green plain opposite the castle, in pursuance of the demand they made to be allowed to deli berate in their own country; the English king and his followers being stationed on the English side of the Tweed. To the Setch camp west the English Lord-Chancellor Burnel, and asked in his master's name "whether they would say anything that call or caght to exclude the King of England from the right and encrise of the superiority and direct dominion over the kingdom of Scotland, which belonged to him, and that they would there and then exhibit it if they believed it was expedient for them-protesting that he would favourably hear them, all w what was just, or report what was said to the king and his ecuncil, that what justice required might be done." No dissentient voice having been raised, a notary who was present formally registered the right of the King of England to decide the octroversy as to the Scottish crown; and then the chanelle inired of all the competitors, beginning with Robert Bruce, whether, in demanding his right, he would answer and receive justice from the King of England as superior and direct lord over the kingdom of Scotland." Bruce answered, "that he dil acknowledge the King of England as superior and direct lord of the kingdom of Scotland, and that he would before him. as such, demand, answer, and receive justice." In like words the other claimants answered the chancellor's question, and simel and scaled a solemn instrument to the same effect. Commissioners were then appointed to represent the competitors, and sittings were held forthwith at Berwick, where the whole matter was solemnly gone into.

Judgment was given in favour of John Baliol, who was ready to acknowledge himself the vassal of the English king; but the Scottish lords of parliament, who attended the conference, expressly declined to do this, saying that they would not answer such a question until they had a king, at the same time remin ling the English that the claim once recognised under duress Lad been expressly and solemnly renounced, and that on several occasions their kings had refused to lend the help which as feudatories of English honours they really owed, unless their independence so far as Scotland was concerned was formally and distinctly recognised. Eventually, however, their unwillingness was overcome; they swore fealty to Edward as lord paramount, and acquiesced in the surrender of the principal Scotch fortresses into his hands. English domination was complete, and to show that it was so, King John was six times summoned to the English Parliament as one of the vassal peers.

Even Baliol, indolent and wanting in self-reliance as he was, rebelled at this, and the Scotch people, chafing under the idea of being in bondage, resolved to back him on the first opportunity that he should attempt to throw off the English yoke. This oppor tunity presented itself in 1294, when war broke out between France and England. That war had raged for some time with varying success, when in 1296 Edward called on John to help hi against France, and to surrender certain strongholds as securit for his doing so. John refused both demands, and Edward immediately marched with a strong army to the north, glad of the pretext he had long sought of bringing Scotland under his own personal sway by conquest. At Berwick and Dunbar the Scots were beaten with dreadful slaughter, after which Stirling, Edinburgh, Roxburgh, and all the southern part of the king dom, fell into Edward's hands. Bruce and his son, with many more of the Scotch nobles, were in the English camp, the unhappy country was divided against itself, and it fell with a great fall. Everywhere submission was made to the conqueror, the hare-hearted Baliol resigned his crown to Edward, who returned to the south undisputed lord of the whole of Great Britain. Isaliol was imprisoned and afterwards died in banish ment, and Earl Warenne was appointed viceroy or lieutenant of Scotland.

For eighteen months things went on drearily in Scotland;

the people lacked leaders; those who should have led them were afraid, incapable, or actually on the enemy's side; the iron heel of English dominion pressed heavily on the land, and entered into its soul. But there was a secret determination to make use of the first opportunity for throwing off the oppressor's yoke. Men bided their time, nursing up their wrath against the day of slaughter, waiting as patiently as they might for their natural leaders to come to their aid. At the end of eighteen months the opportunity came. King Edward was absent with his army in Flanders, and Earl Warenne was obliged by ill health to leave Scotland. The strong men were away, and the tyrannical conduct of the under rulers, especially that of Cressingham and Ormesby, served to irritate the Scots into taking advantage of the circumstance.

In the mountains and forests there had lived ever since the English came a number of so-called outlaws-men of independent spirit, trained to rough life, and imbued with the freedom of the air they breathed-men who never would acknowledge the English rule. Chief of them was William Wallace, a man of whom probably his friends have said too much, as his enemies undoubtedly have said more than enough; a rough soldier, in whose breast the unrefined spirit of liberty had a home, and who acted both according to his roughness and according to his love of liberty. This man put himself at the head of the malcontents, and issuing from his cover, raised the standard of revolt against the foreign king. Hundreds and thousands flocked to the rallying post, and in a few days after he had declared himself Wallace was at the head of an army respectable for its numbers, and for the thoroughly good stuff of which it was composed. Availing himself of his intimate knowledge of the country, Wallace effected a series of surprises on the English garrisons, which fell before him like huts before an avalanche. Ormesby, Earl Warenne's deputy, fled from Scone on hearing that an attempt would be made to take him there, and he carried to his chief the news of the rising of the Scots.

With 40,000 men Earl Warenne marched northwards, and meeting Wallace at Cambuskenneth, near to Stirling, thought to crush him by sheer weight; but the Scotch captain, who had meantime been joined by Sir William Douglas and many other noblemen, so skilfully conducted himself that he was able to fall on the English piecemeal, and utterly to defeat them ere their whole strength could be displayed. The hated Cressingham was among the slain, and report has it that his body was flayed, and that the Scots made saddle-girths of his skin. Earl Warenne retreated across the border, and Wallace, flushed with victory, carried the war into England, and ravaged and plundered the whole bishopric of Durham. Edward, on receiving this news, came over from Flanders, and hastily marched to the north with an army computed at 100,000 men. At Falkirk, on the 22nd of July, 1298, he encountered the Scots' army under Wallace, and entirely routed it, with an enormous loss in killed and wounded. So exhausting, however, was the effort, that Edward retreated instead of following up his success, and the Scots employed the interval in trying to get help both from the French king and the pope. The former refused the slightest assistance, but the pope, Boniface VIII., took up the matter by ordering Edward to refer his claims to the papal arbitration, seeing that the pope was lord paramount of all the kingdoms in the world. The English king, however, quickly disposed of this claim by informing the pope that "neither for Zion nor Jerusalem would he depart from his just rights while there was breath in his nostrils ;" and the English Parliament, before whom the pope's bull was laid, resolved with one voice, "that in temporal matters the King of England was independent of Rome, and that they would not permit his sovereignty to be questioned."

The war with Scotland went on for two years with changeable fortune, the Scots on the whole getting the best of it, when in 1302-1303, Edward took the matter in hand himself, and entering Scotland with a powerful army, applied himself vigorously to the campaign. Town after town succumbed to him, the magic of his skill made the strong places yield, and the heart of Scotland became chilled, as stroke after stroke of his heavy sword fell upon her devoted children. The English dominion was re-asserted in almost every part, and when in 1304 William Wallace was betrayed by Sir John Monteith, and subsequently beheaded in London as a traitor, hope itself seemed to be dead within the Scottish breast.

In 1305-6, however, Robert Bruce, Earl of Carrick, grandson of the competitor of Baliol, and one of those to whom Edward chiefly looked to secure his Scotch conquests for him, awoke to a sense of his duty, and entered into a plot for the overthrow of the Anglo-Scotch tyranny. Accident suddenly compelled him to declare himself, and when he did so as the would-be liberator of the kingdom and claimant of the crown, he was promptly joined by many of those "wha hao wi' Wallace bled." The principal Scotch nobles espoused his cause, and so strong did Bruce find himself that in March, 1306, he caused himself to be crowned king at Scone, the ancient coronation-place of the Scottish kings.

Overwhelming were the preparations made by Edward to crush the rebellion, as he called it. The Earl of Pembroke and other commanders invaded the country, and defeated Bruce and his friends in many encounters; so that by the winter of 1306 many of the chiefs were taken and executed, and Bruce himself was a wanderer. Bloody was the vengeance taken by Edward; the nearest and dearest of the principal actors in the field were cruelly put to death, and every circumstance of indignity was made to accompany their punishment. Nevertheless, in the spring of 1307, Bruce with a small band of followers appeared in Arran, and, passing into Ayrshire, was soon enabled to show a front. Sir James Douglas joined him, and his success became so marked and signal, that Edward found himself under the necessity of marching in person against him.

How Edward did march, and how he died on his way in sight of the Scottish border, and how before he died he made his son promise to carry his unburied corpse with the army till Scotland should have been subdued, are matters of history. So is it matter of history how, six years afterwards, in 1313-14, that son marched with an enormous army, and how at Bannockburn, on the 25th of June, 1314, Bruce overthrew him, and routed with irretrievable loss, both of men and prestige, the whole English army, inflicting a greater blow than the English arms had suffered since the conquest, and establishing once and for ever the independence of the kingdom of Scotland. Several futile attempts were subsequently made, as on the occasion referred to at the beginning of this article, to assert the English supremacy over Scotland, and the English kings for some time consoled themselves with the barren comfort of refusing to recognise the kings of Scotland as independent; but since the well-won battle of Bannockburn was fought, the question was never put practically to Scotland, as it had been done before, which of the realms should be the greater. same inconveniences which the policy of Edward I. sought to remove continued to present themselves; Scotland remained a source of danger, a thorn in the side, to England; national antipathies, aggravated by constant provocations, and finding vent perennially in border warfare, were fostered between the two countries, till the death of Queen Elizabeth opened the way to a community of interest, and a unity of state policy. Whenever, after Bannockburn, there was fighting between England and Scotland, it was always conducted on the principle of equality in status in the belligerents; the words "lord paramount" and "vassal" were no longer heard; and the Scots, jealous of any, the slightest dictation, whether from Southron or any other, were always ready to "fight for the liberty which was dearer to them than life."

The

It is a common error to suppose that when James VI. of Scotland and I. of England ascended the English throne, the crowns of the two countries resting upon one head, united the two kingdoms. England and Scotland remained separate and distinct in every respect, save as to their king; they had sepa rate parliaments, separate laws, a distinct religion, different social customs. There was not, of course, the same danger to either country as there had been before the power of peace or war centred in one man; but the national antipathies and prejudices became probably stronger for being brought more closely into contact. All through the English civil war the Scots acted as an independent people, and refused to meet the English in a common council, though they were engaged in a common cause. It was not till 1707, when Queen Anne was on the throne, that the union of England and Scotland into one kingdom under the name of Great Britain, was accomplished. Not without much difficulty, much delicate negotiation, much giving and taking, was the union effected; the Scots were jealous of the people who proposed to absorb them: the English were impatient and

huffy at the touchiness and susceptibility of the Scots. But the conditions, contained in twenty-five articles, having been agreed to, the two realms were so inseparably united that nothing short of successful revolution could ever sunder them again. The principal conditions of the union are appended, not only in justification of this assertion, but because they are not themselves generally known.

The Parliaments of the two countries agreed that

1. On the 1st of May, 1707, and for ever after, the kingdoms of England and Scotland shall be united into one kingdom, under the name of Great Britain.

2. The succession to the monarchy of Great Britain shall be the same as was before settled with regard to that of England. 3. The united kingdom shall be represented by one Parlia ment.

4. There shall be a communication of all rights and privileges between the subjects of both kingdoms, except where it is other wise agreed.

5. When England raises £2,000,000 by a land-tax, Scotland shall raise £48,000.

16, 17. The standards of the coin, of weights, and of measures, shall be reduced to those of England throughout the united kingdoms.

18. The laws relating to trade, customs, and the excise, shall be the same in Scotland as in England. But all the other laws of Scotland shall remain in force, although alterable by the Parliament of Great Britain.

22. Sixteen peers are to be chosen to represent the peerage of Scotland in Parliament, and forty-five members to sit in the House of Commons. [The Reform Act of 1832 added eight members, and Mr. Disraeli's Bill of 1868 proposed to add seven more.]

23. The sixteen representative peers of Scotland shall have all privileges of Parliament; and all peers of Scotland shall be peers of Great Britain, and rank next after those of the same degree at the time of the union, and shall have all privileges of peers, except sitting in the House of Lords, and voting on the trial of a peer.

MECHANICS.-XI.

PRINCIPLE OF VIRTUAL VELOCITIES THE THREE SYSTEMS OF PULLEYS.

In our last lesson we noticed the two kinds of single pulleys, the fixed and the movable. In the fixed pulley there is no gain at all in power, a force of 1 pound will only support a weight of the same amount. What, then, is the advantage of it? Simply this, that it enables us to change the direction in which any force acts; this is, however, very often as great an advantage as an increase of power would be.

Suppose, for instance, a man wants to raise a heavy bale to the top of a warehouse. He might go to the upper story, and lift it by pulling in a rope tied round it; but this would be a very bad way of applying his force, and would soon tire him, and, at the same time, there would be a great danger of his overbalancing himself and falling. Instead of this, the rope is passed over a pulley fixed to an arm which projects from the

warehouse, and he stands within, or on the ground, and by pulling downwards raises the bale.

In the single movable pulley there is, as we saw, an actual gain, a power of one pound balancing a weight of two pounds. The single fixed pulley, or runner, is often used with this, not that it increases the advantage gained, but merely to change the direction, it being usually more convenient for the power to act downwards than upwards. Now, if we turn our attention to the figure, we shall learn from it a new and very important principle, which, though it strictly belongs to dynamics, time being taken into account, we had better inquire into now, as it will help us more clearly to understand our subject. We have supposed that there is equilibrium in the system, that is, that the power exactly balances the weight, being, in this st one-half of it. Now, let the power be slightly in

Fig. 70.

creased so that P falls; the weight, w, will then be raised; and let this continue till it has been raised through a space of, say, two inches. Now, since it is supported by the cords, or rather the two parts A B, A C of the same cord, it is plain that each must be shortened by the same quantity-namely, two inches-and to effect this, P must move through four inches, or double the space passed over by w. Thus while, on the one hand, a power of one pound will balance a weight of two, the power must, on the other hand, be moved through four inches in order to move the weight through two, or, in other words, the power is only one-half the weight; but in order to raise the weight any given distance, it must move over twice that distance. This rule is frequently expressed as follows:

Whatever is gained in power is lost in time; that is, if by any of the mechanical powers we are enabled to overcome a larger resistance than the power could if directly applied, in just that proportion will the space through which the power moves be larger than that through which the weight moves, and therefore the time occupied will be proportionally longer.

This simple principle applies to all the mechanical powers, and, when fully understood, clears up many difficulties, and removes apparent paradoxes. It is, therefore, important for us to be clear about it. A machine cannot create force; it merely modifies the force or motion of the power, so as to cause it best to produce the resistance or motion required. The power must be supplied by some "prime mover," as it is called, such as the force of the wind or the tide, the strength of men or animals, or the force of heat, which converts water into steam. But when we have the force we can store it up, as is the case in a clock or watch, where the real driving power, which is the force of the hand exerted in winding it up, is laid up in the spring and used gradually; the spring not being, as it is commonly called, the moving power, but merely a kind of reservoir in which it is stored up for future use. Or we can modify and change the mode of action of our force, as in a water-mill, where the onward force of the stream is changed into the circular motion of the millstone, or applied in any other way that may be desired.

If by the movable pulley a man can lift a weight of two hundred-weight to any given height-say, for instance, four feet -when without it he can only lift one hundred-weight, it will take him twice as long to do it, and the practical result will be the same as if he divided the weight into two of one hundred-weight each, and lifted each separately; the only difference being one of convenience, for by it he can lift a weight which otherwise would be too heavy for him to move.

If we for a moment retrace our steps, and see the application of this principle to the mechanical powers we have already considered, we shall perceive more distinctly its full meaning and importance.

Let us take again the case of a lever of the first kind.

Fig. 71.

Suppose the power to act at a distance from the fulcrum, F, five times as great as the weight does; let Pr be, for instance, 10 feet, and F w 2 feet. Then a power of 3 pounds will balance a weight of 15 pounds. If P be now slightly increased, w will be raised that is, a weight of 15 pounds will be lifted by a force only slightly greater than 3 pounds. This at first sight seems very strange, and a contradiction of our principle that a machine cannot create force. But let us suppose that P has moved to P', so that the lever is now in the position of the dotted line P'w', w having likewise moved to w; P will have passed over the arc PP', and w over ww; and since F P is five times as great as FW, PP' is also, by the laws of geometry, five times as great as ww'. You can easily satisfy yourself of this by actual measurement. And so, though the power has lifted a weight five times as great as itself, in order to do so, it has had to pass over a space five times as large as that passed over by the weight.

We thus get another way of expressing our principle, which should be carefully remembered:

The power multiplied by the space through which it moves is equal to the weight multiplied by the space through which it moves.

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