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without giving ourselves the trouble to appeal to all the charac- | Greek word e18os (ei-dos), likeness, which word, in composition,
teristics mentioned. Nevertheless, botanists who penetrate more changes eid into oid. Directing the eye to the lower part of in deeply into the study of plants find it necessary to examine all the sepals, they will be observed to rise from a shallow cup-like the characters present.
body, to which also are attached the petals and other portions Many species of Passion-flower are now common enough in of the flower. As regards the petals themselves, they are our gardens. For the purpose of examination we shall select coloured similarly to the inside of the sepals, and are of the an individual
same colour on of the species
both sides, by termed amo
which circumbilis, the repre
stance they sentation of
may be distin which we sub
guished from join (Fig. 152).
the sepals, as The student
also by the cirwill first ob
cumstance of serve, on glanc
their not hav. ing at the
ing a little broad charac
horn, which teristics of the
may be found specimen, that
on examination the flower is
springing from supplied with
each of the sethree large
pals. bracts, which
We next arconstitute
rive at the filawhat botanists
mentary rays term an invo
which the lucrum.
imaginative ceeding in
Spania r ds ward, we next
compared to arrive at
the crown of what ? The
thorns! What calyx ? It
are those rays? should be the
They are petals 15 calyx, judging
so modified in from its posi
shape that tion, but the
they almost appearance of
present the its separate
appearance of parts (sepals)
stamens. This is different
modification, from the ap
and yet more pearance of
frequently its those sepals
converse, stawe have al
mens modified ready met
into petals, is with. They
not at all un149 are not green,
frequent in but coloured
many flowers, like the petals
as the result of most flowers.
of cultivation. We have al
In the Passionready stated,
flower tribe, however, that
however, it amongst the
exists as the other trans
usual condi. formations of
tion of the parts which oc
flower. Let us casionally en
now proceed to sue, the trans
examine the reformation of
productive, or the calys into
fruit and seedthe appearance
producing porof a corolla is 150
tions of the not unfre
flower, which quent. So fre. 148. SCURVY GRASS (COCHLEARIA OFFICINALIS). 149. THE WALL-FLOWER. 150. TRANSVERSE SECTION OF OVARY
are very pequently, inOF PASSINN-FLOWER. 151. COLUMN OF PASSION-FLOWER. 152. SCARLET PASSION-FLOWER (PASSIFLORA AMABILIS).
We deed, does this
have already occur, that mere green colour is not to be regarded as more mentioned a cup-like body in connection with the structhan a collateral circumstance. The external floral whorl is ture of a Passion-flower. It corresponds with the part always considered by botanists as a calyx, whatever its colour lettered c in Fig. 151. From the centre of this cup a may be.
That colour is often very brilliant, as in the fuchsia, column-like body is observed zising aloft in the centre of for example, where the gay-looking part of the flower is not the flower, to which certain appendages are attached. The corolla or aggregation of petals, but calyx, or aggregation of nature of these appendages will at once be obvions. Extersepals. This assumption by the parts of the calyx of the nally, we easily recognise five anthers, and internally we appearances usually presented by the corolla gives rise to what recognise the club-headed styles; but looking again at botanists term a petaloid calyx. The term petaloid means the stamens, we search in vain for the filaments, which are, resembling a petal; the termination oid being derived from the lin fact, united to the stalk which elevates the ovary,
to which they are usually attached. These filaments do not exist, already been given. He ransacked the abbeys and other depoat least do not separately exist; they are all united-soldered, as sitories of records for proof of his right, and though he found the French say, and it is a very good word—to the support of the little encouragement by so doing, he none the less boldly ovary. This expression, “support of the ovary," is now to us; advanced his pretensions. In answer to the reference made to but if the reader looks at his dissected Passion-flower, or at our him as referee, he directed the claimants to meet him at diagram in Fig. 151, he will recognise the propriety of the Norham, whither he marched with a large foroe, which was expression ; for in this tribe the ovary is supported within the meant to overawe the Scotch Parliament or Council, assembled flower by means of a little stem. Now this little stem being at the same place. called a stipes, the ovary is said to be stipitate. This term, the In May, 1291, the meeting took place accordingly at Norham reader will remember, occurs in our list of characteristics of the Scots being drawn up in a green plain opposite the castle, this natural order. Let the student now examine a little more in pursuance of the demand they made to be allowed to deli. in detail the anthers or pollen-forming heads of the stamens. berate in their own country; the English king and his followers These do not point towards the stigmas, but in the opposite being stationed on the English side of the Tweed. To the direction, which is very unusual. Fertilisation of the ovule Scotch camp went the English Lord-Chancellor Burnel, and depends, as we need not repeat, upon contact between the asked in his master's name " whether they would say anything pollen-dust and the stigmas; hence it would seem that the that could or ought to exclude the King of England frorn the anthers should always point towards the stigmas. In most right and exercise of the superiority and direct dominion over cases they do so point towards them, but in the Passion-flower the kingdom of Scotland, which belonged to him, and that they tribe we find an exception to this rule.
would there and then exhibit it if they believed it was expedient Fig. 150 represents the transverse section of the ovary con. for them;--protesting that he would favourably hear them, taining the seeds. The fruit, or ripened ovary, in all species of allow what was just, or report what was said to the king and the Passion-flower is egg-shaped, differing in size according to the his council, that what justice required might be done." No species. The blue Passion-flower produces a fruit about the dissentient voice having been raised, a notary who was present size of a hen's egg; but in other species the fruit is much larger, formally registered the right of the King of England to decide and contains a delicious pulp.
the controversy as to the Scottish crown; and then the chanPassion-flowers, we have seen, are both agreeable and useful cellor inquired of all the competitors, beginning with Robert from the beauty of their flowers and the flavour of their fruits ; Bruce, " whether, in demanding his right, he would answer and many species are medicinal. The pulp surrounding their seeds receive justice from the King of England as superior and direct is in some cases sweet, in others acid ; the latter serve as the lord over the kingdom of Scotland.” Bruce answered, " that he basis for the preparation of acidulated drinks, not only agreeable, did acknowledge the King of England as superior and direct but medicinal. One specios, Passiflora Rubra, contains a nar. lord of the kingdom of Scotland, and that he would before cotic principle which is sometimes employed as a substitute for him, as such, demand, answer, and receive justice." In like opium. Passiflora Quadrangularis is cultivated for the refreshing words the other claimants answered the chancellor's question, palp surrounding its seeds, but its root is very poisonous. In and signed and sealed a solemn instrument to the same effect. European gardens a large number of species of the Passion-flower Commissioners were then appointed to represent the competitors, are now cultivatod, amongst which may be cited as the chief, and sittings were held forth with at Berwick, where the whole Passiflora Cærulea, or the blue Passion-fower; this being the matter was solemnly gone into. commonest of all. Of this flower the Passiflora Amabilis (Fig. Judgment was given in favour of John Baliol, who was ready 152) is a hybrid or cross race between Passiflora Alata and to acknowledge himself the vassal of the English king ; but the Passiflora Princeps. Its flowers are scarlet, and exhale a deli- Scottish lords of parliament, who attended the conference, cate odour. The Murucuja Ocellata is a hot-house species, expressly declined to do this, saying that they would not answer bearing deep-red flowers. Tactonia Mollisima bears rose- such a question until they had a king, at the same time coloured flowers, and is a climbing plant, requiring a green reminding the English that the claim once recognised under house for its culture.
duress had been expressly and solemnly renounced, and that on
several occasions their kings had refused to lend the help HISTORIC SKETCHES.-XV.
which as feudatories of English honours they really owed,
unless their independence so far as Scotland was concerned HOW ENGLAND AND SCOTLAND BECAME ONB.-PART II.
was formally and distinctly recognised. Eventually, however, MANY competitors, as might be supposed, appeared to contest their unwillingness was overcome ; they swore fealty to Edward so great a prize as the crown of Scotland ; but the question really as lord paramount, and acquiesced in the surrender of the lay between two, John Baliol and Robert Bruce, noblemen of principal Scotch fortresses into his hands. English domination Norman extraction. The ground on which they founded their was complete, and to show that it was so, King John was six respective claims to the Scottish throne was as follows: William times summoned to the English Parliament as one of the vissa the Lion died, leaving a brother David, who was created Earl of peers. Huntingdon on his marriage with King Edward's sister. This Even Balio! 'ndolent and wanting in self-reliance as he was, rsearl had three daughters : the first, Margaret, who married Alan, belled at this, and the Scotch people, chafing under the idea of Lord of Galloway ; the second, Isabella, who married Robert being in bondage, resolved to back him on the first opportunity Bruce, of Annandale; the third, Adama, who married Lord that he should attempt to throw off the English yoke. This opporHastings. At the time of the death of Alexander III., John tunity presented itself in 1294, when war broke out between Baliol, the grandson of Margaret, Lady Galloway, claimed the France and England. That war had raged for some time with crown, as nearest descendant of the elder branch; and Robert varying success, when in 1296 Edward called on John to help him Bruce claimed it by what he asserted to be a better title, in against France, and to surrender certain strongholds as security that he was the son of Isabella, the second daughter of David, for his doing so. John refused both demands, and Edward and was thus one generation nearer to the original stock. Lord immediately marched with a strong army to the north, glad of Hastings claimed, somewhat absurdly, a third of the kingdom, the pretext he had long sought of bringing Scotland under his on the assumption that it must be divided equally between the own personal sway by conquest. At Berwick and Dunbar the three branches, as private property might have been. The last Scots were beaten with dreadful slaughter, after which Stirling, claim was never seriously entertained by any one ; but though Edinburgh, Roxburgh, and all the southern part of the king modern law and custom would have found no difficulty in dom, fell into Edward's hands. Bruce and his son, with many deciding in favour of John Baliol, the qnestion between him more of the Scotch nobles, were in the English camp, the and Bruce was, in the then state of law, by no means an easy unhappy country was divided against itself, and it fell with a one to answer. Both claimants determined to support their great fall. Everywhere submission was made to the conqueror, pretensions by force of arms, and were gathering their friends the hare-hearted Baliol resigned his crown to Edward, who for that purpose, when they were persuaded to refer their dis- returned to the south undisputed lord of the whole of Great pute to the arbitration of the King of 'England.
Britain. Baliol was imprisoned and afterwards died in banishNow Edward saw his opportunity, and resolved to seize it. ment, and Earl Warenne was appointed viceroy or lieutenant of He claimed a right to decide the matter by virtue of his being Scotland. lord paramount of Scotland, a dignity the value of which has For eighteen months things went on drearily in Scotland;
the people lacked leaders; those who should have led them were In 1305-6, however, Robert Bruce, Earl of Carrick, grandson afraid, incapable, or actually on the enemy's side; the iron of the competitor of Baliol, and one of those to whom Edward heel of English dominion pressed heavily on the land, and chiefly looked to secure his Scotch conquests for him, awoke to entered into its soul. But there was a secret determination to a sense of his duty, and entered into a plot for the overthrow of make use of the first opportunity for throwing of the oppressor's the Anglo-Scotch tyranny. Accident suddenly compelled him yoke. Men bided their time, nursing up their wrath against to declaro himself, and when ho did so as the would-be libethe day of slaughter, waiting as patiently as they might for rator of the kingdom and claimant of the crown, ho was their natural leaders to come to their aid. At the end of promptly joined by many of those "wha hae wi' Wallace bled.” eighteen months the opportunity came. King Edward was The principal Scotch nobles espoused his cause, and so strong absent with his army in Flanders, and Earl Warenne was did Bruce find himself that in March, 1306, he caused himself obliged by ill health to leave Scotland. The strong men were to be crowned king at Scone, the ancient coronation-place of away, and the tyrannical conduct of the under rulers, especially the Scottish kings. that of Cressingham and Ormesby, served to irritate the Scots Overwhelming were the preparations made by Edward to into taking advantage of the circumstance.
crush the rebellion, as he called it. The Earl of Pembroke and In the mountains and forests there had lived ever since the other commanders invaded the country, and defeated Bruce and English came & number of so-called outlaws--men of indo. his friends in many encounters; so that by the winter of 1306 pendent spirit, trained to rough life, and imbued with the many of the chiefs were taken and executed, and Bruce himself freedom of the air they breathed-men who never would acknow. was a wanderer. Bloody was the vengeance taken by Edward; ledge the English rule. Chief of them was William Wallace, a the nearest and dearest of the principal actors in the field were man of whom probably his friends have said too much, as his cruelly put to death, and every circumstance of indignity was enemies undoubtedly have said more than enough; a rough made to accompany their punishment. Nevertheless, in the soldier, in whose breast the unrefined spirit of liberty had a spring of 1307, Bruce with a small band of followers appeared home, and who acted both according to his roughness and in Arran, and, passing into Ayrshire, was soon enabled to show according to his love of liberty. This man put himself at the a front. Sir James Douglas joined him, and his success became bead of the malcontents, and issuing from his cover, raised the so marked and signal, that Edward found himself under the standard of revolt against the foreign king. Hundreds and necessity of marching in person against him. thousands flocked to the rallying post, and in a few days after How Edward did march, and how he died on his way in sight ho had declared himself Wallace was at the head of an army of the Scottish border, and how before he died he made his son respectable for its numbers, and for the thoroughly good stuff promise to carry his unburied corpse with the army till Scotof which it was composed. Availing himself of his intimate land should have been subdued, are matters of history. So is knowledge of the country, Wallace effected a series of surprises it matter of history how, six years afterwards, in 1313-14, that on the English garrisons, which fell before him like huts before son marched with an enormous army, and how at Bannockburn, an avalanche. Ormesby, Earl Warenne's deputy, fled from Scone on the 25th of June, 1314, Bruce overthrow him, and routed on hearing that an attempt would be made to take him there, and with irretrievable loss, both of men and prestige, the whole he carried to his chief the news of the rising of the Scots. English army, inflicting a greater blow than the English arms
With 40,000 men Earl Warenne marched northwards, and had suffered since the conquest, and establishing once and for meeting Wallace at Cambuskenneth, near to Stirling, thought ever the independence of the kingdom of Scotland. to crush him by sheer weight; but the Scotch captain, who Several futile attempts were subsequently made, as on the had meantime been joined by Sir William Douglas and many occasion referred to at the beginning of this article, to assert other noblemen, so skilfully conducted himself that he was the English supremacy over Scotland, and the English kings able to fall on the English piecemeal, and utterly to defeat for some time consoled themselves with the barren comfort of them ere their whole strength could be displayed. The hated refusing to recognise the kings of Scotland as independent; but Cressingham was among the slain, and report has it that his since the well-won battle of Bannockburn was fought, the quesbody was flayed, and that the Scots made saddle-girths of his tion was never put practically to Scotland, as it had been skin. Earl Warenne retreated across the border, and Wallace, done before, which of the realms should be the greater. The Aushed with victory, carried the war into England, and ravaged same inconveniences which the policy of Edward I. sought to and plundered the whole bishopric of Durham.
remove continued to present themselves; Scotland remained a Edward, on receiving this news, came over from Flanders, source of danger, a thorn in the side, to England; national antiand hastily marched to the north with an army computed at pathies, aggravated by constant provocations, and finding vent 100,000 men.
At Falkirk, on the 22nd of July, 1298, he en- perennially in border warfare, were fostered between the two countered the Scots' army ander Wallace, and entirely routed countries, till the death of Queen Elizabeth opened the way to a it , with an enormons loss in killed and wounded. So exhausting, community of interest, and a unity of state policy. Whenever, however, was the effort, that Edward retreated instead of after Bannockburn, there was fighting between England and following ap his success, and the Scots employed the interval Scotland, it was always conducted on the principle of equality in trying to get help both from the French king and the pope. in status in the belligerents; the words “lord paramount” and The former refused the slightest assistance, but the pope, “ vassal” were no longer heard ; and the Scots, jealous of any, Boniface VIII., took up the matter by ordering Edward to refer the slightest dictation, whether from Southron or any other, were his claims to the papal arbitration, seeing that the pope was always ready to "fight for the liberty which was dearer to them lord paramount of all the kingdoms in the world. The English than life.” king, however, quickly disposed of this claim by informing the It is a common error to suppose that when James VI. of pope that “neither for Zion nor Jerusalem would he depart Scotland and I. of England ascended the English throne, the from his just rights while there was breath in his nostrils ;" and crowns of the two countries resting upon one head, united the the English Parliament, before whom the pope's bull was laid, two kingdoms. England and Scotland remained separate and resolved with one voice, " that in temporal matters the King of distinct in every respect, save as to their king; they had sepaEngland was independent of Rome, and that they would not rate parliaments, separate laws, a distinct religion, different permit his sovereignty to be questioned.”
social customs. There was not, of course, the same danger to The war with Scotland went on for two years with changeable either country as there had been beforo the power of peace or fortune, the Scots on the whole getting the best of it, when in war centred in one man; but the national antipathies and preju. 1302-1303, Edward took the matter in hand himself, and entering dices became probably stronger for being brought moro closely Sotland with a powerful army, applied himself vigorously to into contact. All through the English civil war the Scots acted the campaign. Town after town succumbed to him, the magic as an independent peoplo, and refused to meet the English in a of his skill made the strong places yield, and the heart of Scot. common council, though they were engaged in a common cause. land became chilled, as stroke after stroke of his heavy sword It was not till 1707, when Queen Anne was on the throne, that fell upon her devoted children. The English dominion was the union of England and Scotland into one kingdom under the -258erted in almost every part, and when in 1304 William name of Great Britain, was accomplished. Not without much Wallace was betrayed by Sir John Monteith, and subsequently difficulty, much delicate negotiation, much giving and taking, beheaded in London as a traitor, hope itself seemed to be dead was the union effected; the Scots were jealous of the people within the Scottish breast.
who proposed to absorb them; the English were impatient and
huffy at the touchiness and susceptibility of the Scots. But the creased so that p falls; the weight, w, will then be raised; and let conditions, contained in twenty-five articles, having been agreed this continue till it has been raised through a space of, say, two to, the two realms were so inseparably united that nothing short inches. Now, since it is supported by the cords, or rather the of successful revolution could ever sunder them again. The two parts A B, A C of the same cord, it is plain that each must principal conditions of the union are appended, not only in jus- be shortened by the same quantity-namely, two inches—and to tification of this assertion, but because they are not themselves effect this, P must move through four inches, or double the spaco generally known.
passed over by w. Thus while, on the one hand, a power of The Parliaments of the two countries agreed that,
one pound will balance a weight of two, the power must, on the 1. On the 1st of May, 1707, and for ever after, the kingdoms other hand, be moved through four inches in order to move the of England and Scotland shall be united into one kingdom, weight through two, or, in other words, the power is only one-half under the name of Great Britain.
the weight; but in order to raise the weight any given distance, 2. The succession to the monarchy of Great Britain shall be it must move over twice that distance. This rule is frequently the same as was before settled with regard to that of England. expressed as follows :
3. The united kingdom shall be represented by one Parlia- Whatever is gained in power is lost in time; that is, if by any ment.
of the mechanical powers we are enabled to overcome a larger 4. There shall be a communication of all rights and privileges resistance than the power could if directly applied, in just that between the subjects of both kingdoms, except where it is other proportion will the space through which the power moves be wise agreed.
larger than that through which the weight moves, and therefore 5. When England raises £2,000,000 by a land-tax, Scotland the time occupied will be proportionally longer. shall raise £48,000.
This simple principle applies to all the mechanical powers, and, 16, 17. The standards of the coin, of weights, and of mea- when fully understood, clears up many difficulties, and removes sures, shall be reduced to those of England throughout the apparent paradoxes. It is, therefore, important for us to be united kingdoms.
clear about it. A machine cannot create force; it merely 18. The laws relating to trade, customs, and the excise, shall modifies the force or motion of the power, so as to cause it best be the same in Scotland as in England. But all the other laws to produce the resistance or motion required. The power must of Scotland shall remain in force, although alterable by the Par- be supplied by some "prime mover,” as it is called, such as liament of Great Britain.
the force of the wind or the tide, the strength of men or 22. Sixteen peers are to be chosen to represent the peerage of animals, or the force of heat, which converts water into steam. Scotland in Parliament, and forty-five members to sit in the But when we have the force we can store it up, as is the case House of Commons. "[The Reform Act of 1832 added eight in a clock or watch, where the real driving power, which is the members, and Mr. Disraeli's Bill of 1868 proposed to add seven force of the hand exerted in winding it up, is laid up in the more.]
spring and used gradually; the spring not being, as it is 23. The sixteen representative peers of Scotland shall have commonly called, the moving power, but merely a kind of all privileges of Parliament; ard all peers of Scotland shall be reservoir in which it is stored up for future use. Or we can peers of Great Britain, and rank next after those of the same modify and change the mode of action of our force, as in a degree at the time of the union, and shall have all privileges of water-mill, where the onward force of the stream is changed peers, except sitting in the House of Lords, and voting on the into the circular motion of the millstone, or applied in any other trial of a peer.
way that may be desired.
If by the movable pulley a man can lift a weight of two MECHANICS.—XI.
hundred-weight to any given height-say, for instance, four feet
-when without it he can only lift one hundred-weight, it will take PRINCIPLE OF VIRTUAL VELOCITIES—THE THREE SYSTEMS
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 In our last lesson we noticed the two kinds of single pulleys, each, and lifted each separately; the only difference being one the fixed and the movable. In the fixed pulley there is no gain of convenience, for by it he can lift a weight which otherwise at all in power, a force of 1 pound will only support a weight of would be too heavy for him to move. the same amount. What, then, is the advantage of it? Simply If we for a moment retrace our steps, and see the application this, that it enables us to change the direction in which any of this principle to the mechanical powers we have already force acts; this is, however, very often as great an advantage considered, we shall perceive more distinctly its full meaning as an increase of power would be.
and importance. Suppose, for instance, a man wants to raise a heavy bale to Let us take again the case of a lever of the first kind. the top of a warehouse. He might go to the upper story, and
Suppose the power to act lift it by pulling in a rope tied round it; but this would be a
at a distance from the ful. very bad way of applying his force, and would soon tire him,
crum, F, five times as great and, at the same time, there would be a great danger of his
as the weight does; let PT overbalancing himself and falling. Instead of this, the rope is
be, for instance, 10 feet, passed over a pulley fixed to an arm which projects from the
and Fw 2 feet. Then & warehouse, and he stands within, or
power of 3 pounds will on the ground, and by pulling down.
balance & weight of 15 wards raises the bale.
pounds. If P be now In the single movable pulley there slightly increased, w will be raised that is, a weight of 15 is, as we saw, an actual gain, a power pounds will be lifted by a force only slightly greater than 3
of one pound balancing a weight of pounds. This at first sight seems very strange, and a contraI two pounds. The single fixed pulley, diction of our principle that a machine cannot create force.
or runner, is often used with this, not But let us suppose that p has moved to p', so that the lever is that it increases the advantage gained, now in the position of the dotted line P W', w having likewise but merely to change the direction, it moved to w; P will have passed over the arc PP', and w ofer being usually more convenient for the ww'; and since Fp is five times as great as Fw, PP is also, by power to act downwards than upwards. the laws of geometry, five times as great as ww. Yon can
Now, if we turn our attention to the easily satisfy yourself of this by actual measurement. And so,
figure, we shall learn from it a new though the power has lifted a weight five times as great as Fig. 70.
and very important principle, which, itself, in order to do so, it has had to pass over a space five
though it strictly belongs to dynamics, times as large as that passed over by th weight. time being taken into account, we had better inquire into now, We thus get another way of expressing our principle, which as it will help us more clearly to understand our subject. should be carefully remombered :
We have supposed that there is equilibrium in the system, The power multiplied by the space through which it moves is that is, that the power exactly
balances the weight, being, in this equal to the weight multiplied by the space through which it case, just one-half of it. Now, let the power be slightly in. moves.
Of course, as before explained, when we speak of the power Thus, if there are five pulleys, the gain is 2x2x2x2x2, that multiplied by the distance, wo mean the product of the two is, 32. You must be careful, in calculating this, not to count the numbers which represent the number of units of weight in the fixed pulley, as that has no effect. power, whatever they be, and the number of units of length In the second system of pulleys, instead of each having a in the distance.
separate cord, the same one passes round In the case above let P Pl be 5 inches, w w' will be 1 inch, all, and they are arranged in two blocks, and 3 (the number of pounds in the power), multiplied by 5 (the one of which is fixed and the other (usually number of inches through which it has passed), is equal to 15 the lower) is movable. Fig. 73 represents multiplied by 1. This equation, as it is called, is plainly true, this system. One end of the cord is here each product being 15.
fastened to the hook A on the fixed block, This principle, which is called the LAW OF VIRTUAL VELO- and it then passes in succession round the CITIES, is the fundamental principle in mechanics, and holds pulleys B, C, D, E, F, and g. In this case good in all the mechanical powers. On account of its import the weight is supported by six folds of the ance, it has been called the Golden Rule of Mechanics.
same cord, and each bears an equal part, We will now trace its application to the wheel and axle, the cord being equally strained throughout. which is, in reality, only a modification of the lever, being an Each part, therefore, sustains a portion of arrangement whereby an endless succession of levers may be the weight equal to P, and w is therefore six brought into play, for any two radii of the wheel and axle in times as great as P. the same straight line may be considered as a simple lever. If we take away one pulley or sheave, as
If the power be slightly increased it descends, and, when the it is called, from the lower block, leaving wheel has turned just once round, will have fallen through a two only, the weight will be divided bespace equal to the circumference of the wheel. In the same tween four folds of the cord, and thus only time, the weight will have been raised through a space equal to four times the weight of P will be supported. the circumference of the axle. But the circumference of circles Similarly, were we to add another sheave to always bear the same ratio to one another that their radii bear. each block, we should have a mechanical ad. If, then, the radius of the wheel be 12 inches, and that of the vantage of 8. We see then that, in this axle 3 inches, the power will pass through four times as great a system, the advantage is always twice as space as the weight, but will only be one-fourth of it.
great as the number of pulleys in the
movable blocks. COMPOUND PULLEYS.
We have in this calculation supposed the We are now in a position more clearly to understand the cords to be parallel. They are not, however, remaining mechanical powers. We have explained the principlo
strictly so, still the difference Fig. 73. of the simple pulley, and seen how to find out the advantage
is so slight we need not notice gained by it, both when the cords are parallel and when they
it. A trilling loss of power, however results from it. are inclined at an angle. But there are various combinations
Now there is one disadvantage about this sys. of fixed and movable pulleys which are called compound pulleys,
tem when made as shown in our illustration, and and are very frequently used in ships and in raising heavy
that is, that the weight must, on account of the weights, or exerting powerful strains. We must examine the
length of the blocks in which the pulleys are set, principle of these, and see how to ascertain the advantages
be a long way below the point to which the gained by using them.
upper block is fixed. If we are using it, for They are usually classed in three systems.
instance, to strain a telegraph wire or to tighten In the first system, which is represented in Fig. 72, each
a rope in the rigging of a ship, purposes for pulley hangs by a separate cord, and all
which blocks are constantly employed, we should are movable, at least all that have any
fasten our rope to the hook from which w hangs, effect, the runner, D, being introduced
and fasten the fixed block to the “dead eye" on merely for the sake of reversing the direc
the side of the ship; but then we should not be tion in which the power acts.
able to bring the rope within some considerable Now let us try and see what is the
distance of the eye. Another form of this samo ratio the power bears to the weight when
system has therefore been contrived which ob4 the system is in equilibrium. We will
viates this difficulty. This is shown in Fig. 74. 2 2
suppose, for the sake of simplicity, that Fig. 74. Here the required number of sheaves, three in the power applied to p is 1 pound. The
the present case, are fixed side by side in each B
strain or tension of the cord PG is the block, and the cord is fixed to a hook or staple
kept at rest by the tensions of the three lower block is suspended from the cords, it
cords, QC, DC, and BC, and as these are forms a part of the weight lifted, and the
C F, that is, 4 pounds. But the weight, several. This will be understood from Fig. 75.
A E, or rather by these two parts of simple sheaves increasing in size were laid on the same cord, and as each has a strain of 4 pounds, the each other. A little attention will show that total weight supported is 8 pounds. In this case then, there for every inch the weight is raised 1 inch of cord is a gain of 8, a power of 1 pound balancing a weight will pass over the smallest pulley, and as the of 8 pounds. Similarly, if another pulley were added, a power cord from this to No. 2 must
also be shortened of 1 pound would balance a weight of 16 pounds, each additional an inch, 2 inches will pass over No. 2. In like
Fig. 75. pulley donbling the weight supported; and thus we have the fol- manner 3 inches must pass over No. 3. Their lowing rule for determining the gain in the first system of sizes must therefore be in the proportion of the numbers 1, 2, 3, pulleys :
etc., or else the cord will grate on the pulleys. This is another Multiply 2 by itself as many times as there are movable pal. illustration of our fundamental law; and we see further that, it leys; the result will show the mechanical gain.
the weight is to be raised 1 inch, each of the cords supporting