to which they are usually attached. These filaments do not exist, at least do not separately exist; they are all united-soldered, as the French say, and it is a very good word-to the support of the Ovary. This expression, "support of the ovary," is new to us; but if the reader looks at his dissected Passion-flower, or at our 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 little stem being called a stipes, the ovary is said to be stipitate. This term, the reader will remember, occurs in our list of characteristics of this natural order. Let the student now examine a little more in detail the anthers or pollen-forming heads of the stamens. These do not point towards the stigmas, but in the opposite direction, which is very unusual. Fertilisation of the ovule depends, as we need not repeat, upon contact between the pollen-dust and the stigmas; hence it would seem that the anthers should always point towards the stigmas. In most cases they do so point towards them, but in the Passion-flower tribe we find an exception to this rule.

Fig. 150 represents the transverse section of the ovary containing the seeds. The fruit, or ripened ovary, in all species of the Passion-flower is egg-shaped, differing in size according to the species. The blue Passion-flower produces a fruit about the 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 useful 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 agreeable, but medicinal. One species, Passiflora Rubra, 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-flower 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 Passiflora Amabilis (Fig. 152) is a hybrid or cross race between Passiflora Alata 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 Mollisima bears rosecoloured 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 three 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 purpose, when they were persuaded to refer their dispute to the arbitration of the King of 'England.

Now Edward saw his opportunity, and resolved to seize it. He claimed a right to decide the matter by virtue of his being lord paramount of Scotland, a dignity the value of which has

already been given. He ransacked the abbeys and other depositories of records for proof of his right, and though he found little encouragement by so doing, he none the less boldly advanced his pretensions. In answer to the reference made to him as referee, he directed the claimants to meet him at Norham, whither he marched with a large force, which was meant to overawe the Scotch Parliament or Council, assembled at the same place.

In May, 1291, the meeting took place accordingly at Norham, the Scots 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 Scotch camp went the English Lord-Chancellor Burnel, and asked in his master's name "whether they would say anything that could or ought to exclude the King of England from the right and exercise 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, allow what was just, or report what was said to the king and his council, 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 controversy as to the Scottish crown; and then the chancellor inquired 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 did 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 signed and sealed 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 reminding the English that the claim once recognised under duress had 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 Balio' 'ndolent 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 him against France, and to surrender certain strongholds as security 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, 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. Baliol was imprisoned and afterwards died in banishment, and Earl Warenne was appointed viceroy or lieutenant of Scotland.

the

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 of 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 hae 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.

The

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."

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 Parliament.

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; ard 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 down. wards 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.

W

Fig. 70.

P

We have supposed that there is equilibrium in the system, that is, that the power exactly balances the weight, being, in this case, just one-half of it. Now, let the power be slightly in

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 PF be, for instance, 10 feet, and F w 2 feet. Then & 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 w w'; and since F P is five times as great as FW, P P is also, by the laws of geometry, five times as great as ww'. Yon 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 th 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.

Of course, as before explained, when we speak of the power multiplied by the distance, we mean the product of the two numbers which represent the number of units of weight in the power, whatever they be, and the number of units of length in the distance.

In the case above let P P' be 5 inches, w w' will be 1 inch, and 3 (the number of pounds in the power), multiplied by 5 (the number of inches through which it has passed), is equal to 15 multiplied by 1. This equation, as it is called, is plainly true, each product being 15.

This principle, which is called the LAW OF VIRTUAL VELOCITIES, is the fundamental principle in mechanics, and holds good in all the mechanical powers. On account of its importance, it has been called the Golden Rule of Mechanics.

We will now trace its application to the wheel and axle, which is, in reality, only a modification of the lever, being an arrangement whereby an endless succession of levers may be brought into play, for any two radii of the wheel and axle in the same straight line may be considered as a simple lever.

If the power be slightly increased it descends, and, when the wheel has turned just once round, will have fallen through a space equal to the circumference of the wheel. In the same time, the weight will have been raised through a space equal to the circumference of the axle. But the circumference of circles always bear the same ratio to one another that their radii bear. If, then, the radius of the wheel be 12 inches, and that of the axle 3 inches, the power will pass through four times as great a space as the weight, but will only be one-fourth of it.

COMPOUND PULLEYS.

We are now in a position more clearly to understand the remaining mechanical powers. We have explained the principle of the simple pulley, and seen how to find out the advantage gained by it, both when the cords are parallel and when they are inclined at an angle. But there are various combinations of fixed and movable pulleys which are called compound pulleys, and are very frequently used in ships and in raising heavy weights, or exerting powerful strains. We must examine the principle of these, and see how to ascertain the advantages gained by using them.

They are usually classed in three systems.

In the first system, which is represented in Fig. 72, each pulley hangs by a separate cord, and all are movable, at least all that have any effect, the runner, D, being introduced merely for the sake of reversing the direction in which the power acts.

Now let us try and see what is the ratio the power bears to the weight when the system is in equilibrium. We will suppose, for the sake of simplicity, that the power applied to P is 1 pound. The strain or tension of the cord PG is the same throughout its entire length (we are not taking into consideration now friction and the imperfect flexibility of the ropes). The pulley c is therefore kept at rest by the tensions of the three cords, a C, D C, and B C, and as these are parallel forces, the strain on B C is equal to the sum of the other two, each of which is 1 pound. The tension of each part of the cord C F is therefore 2 pounds. In the same way we see that the tension of the next cord, B E, is double that of CF, that is, 4 pounds. But the weight, Fig. 72. w, is supported by the two cords, B A, A E, or rather by these two parts of the same cord, and as each has a strain of 4 pounds, the total weight supported is 8 pounds. In this case then, there is a gain of 8, a power of 1 pound balancing a weight of 8 pounds. Similarly, if another pulley were added, a power of 1 pound would balance a weight of 16 pounds, each additional pulley doubling the weight supported; and thus we have the following rule for determining the gain in the first system of pulleys:

W

Multiply 2 by itself as many times as there are movable pulleys; the result will show the mechanical gain.

Thus, if there are five pulleys, the gain is 2x2x2×2×2, that is, 32. You must be careful, in calculating this, not to count the fixed pulley, as that has no effect.

In the second system of pulleys, instead of each having a separate cord, the same one passes round all, and they are arranged in two blocks, one of which is fixed and the other (usually the lower) is movable. Fig. 73 represents this system. One end of the cord is here fastened to the hook A on the fixed block, and it then passes in succession round the pulleys B, C, D, E, F, and G. In this case the weight is supported by six folds of the same cord, and each bears an equal part, the cord being equally strained throughout. Each part, therefore, sustains a portion of the weight equal to P, and w is therefore six times as great as P.

If we take away one pulley or sheave, as it is called, from the lower block, leaving two only, the weight will be divided between four folds of the cord, and thus only four times the weight of P will be supported. Similarly, were we to add another sheave to each block, we should have a mechanical advantage of 8. We see then that, in this system, the advantage is always twice as great as the number of pulleys in the movable blocks.

We have in this calculation supposed the cords to be parallel. They are not, however,

strictly so, still the difference

Fig. 73.

on

is so slight we need not notice it. A trifling loss of power, however results from it. Now there is one disadvantage about this system when made as shown in our illustration, and that is, that the weight must, on account of the length of the blocks in which the pulleys are set, be a long way below the point to which the upper block is fixed. If we are using it, for instance, to strain a telegraph wire or to tighten a rope in the rigging of a ship, purposes for which blocks are constantly employed, we should fasten our rope to the hook from which w hangs, and fasten the fixed block to the "dead eye the side of the ship; but then we should not be able to bring the rope within some considerable distance of the eye. Another form of this same system has therefore been contrived which obviates this difficulty. This is shown in Fig. 74. Here the required number of sheaves, three in the present case, are fixed side by side in each block, and the cord is fixed to a hook or staple in the upper one, and then passes in succession over each sheave. The weight is, of course, as before, divided between the six ropes. In all these cases it must be remembered that, as the lower block is suspended from the cords, it forms a part of the weight lifted, and the weight w is therefore less by this amount than our calculation makes it appear.

W

Fig. 74.

There is a third plan for arranging this system of pulleys which has the advantage of greatly reducing the amount of friction, there being only one sheave to turn on the axis instead of several. This will be understood from Fig. 75. Each sheave is here a compound one, as if several simple sheaves increasing in size were laid on each other. A little attention will show that for every inch the weight is raised 1 inch of cord will pass over the smallest pulley, and as the cord from this to No. 2 must also be shortened an inch, 2 inches will pass over No. 2. In like manner 3 inches must pass over No. 3. Their sizes must therefore be in the proportion of the numbers 1, 2, 3, etc., or else the cord will grate on the pulleys. This is another illustration of our fundamental law; and we see further that, if the weight is to be raised 1 inch, each of the cords supporting

Fig. 75.