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the oak and willow, for example-is hard and rough, while in the beech and birch it is smooth. The straight parts of the branches of some trees are short, from their slow growth, while others that increase more rapidly shoot forth their stems in one direction to a greater extent. The smaller twigs and shoots of some, like the birch, are very slender, numerous, and drooping; the horsechestnut has fewer shoots, but they are thicker, and grow upwards. Much more might be added to our consideration of this important subject, but we think enough has been said to point out the way, trusting our pupils will perfectly comprehend our intention by these remarks, and be prepared to accompany us in the consideration of foliage.

In our last lesson we mentioned that, in drawing foliage, the mode of treatment must in a very great measure be influenced by the light and shade. We propose now to proceed with this interesting part

of our subject, and show what is meant by the term "massing in the foliage." There are some who think that it is necessary to have for each kind of treesome distinct and especial touch,classifying them as "the oak touch," "the elm touch," "the beech touch," and numerous others, regardless of the fact that as the sun casts its light upon a tree it brings out the shape and individual character of its branches so definitely that even at a considerable distance, when it would be impossible to recognise the leaves, we can pronounce the tree to be an oak, or elm, or whatever else it may be, simply from the manner in which, as an artist would say, "the sun lights it up." The most important consideration in drawing a tree is

to devote much attention to the light, and the parts that are made out in light. There are two reasons why the lights are considered to have such special importance (this principle belongs not to trees only, but to every other object that claims the attention of the painter): the first is, because the details are more recognisable in the light than in the shade, and require particular care to represent them faithfully, for without the details in light there would be very little to show for our pains, as the shadows to a great extent absorb or obscure not only the colour but also the form; the other reason is, that the eye naturally rests upon the lights and all the brighter parts first-afterwards, when we make a further and closer examination, we see the parts in shadow. | Nor must we enter into laborious and painful detail, as in the practice of mere leaf-painting. As we have said before, we do not look at leaves singly, but at foliage collectively; therefore those branches of a tree, let its kind be what it may, which are!

in the light, will have their own especial forms in mass to characterise them, and it is those forms in masses which we must copy. But lest our pupil should suppose from these remarks upon generalising foliage that we intend him to stop here, and to represent nothing more than the breadth of light and shade, we must remind him of what has been said above respecting the details in light; we must remember also that, however broadly and definitely the light may fall upon a tree, since it is not a flat surface like a wall, there will be hundreds of minor shadows and semi-tones scattered all over the extent of light, and there is as much individuality amongst these as in the whole mass, and their characteristics in detail are not less striking and significant because they are small: in short, they are reduced repetitions of the general masses of light, and must be treated with the same feeling if we wish to make a faithful represen

tation. Here again is the point of difference between a first-rate and an inferior artist, mentioned in a former lesson- namely, the ability he possesses to represent the minor shades and semi-tones, both in regard to their number and expression, and his capability for doing this will determine his rank as an artist. Sir Joshua Reynolds mentions a landscape painter who was remarkable for his patience in what he considered "high finish," thought that the greatest excellence to be attained consisted in the representation of every leaf on a tree. "This picture," says Sir Joshua, "I never saw; but I am very sure that an artist who regards only the general character of the species, the order of the branches,

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and

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and the masses of the foliage, will in a few minutes produce a more true resemblance of trees than this painter in as many months." We must dwell for a few moments upon the principles here inculcated, and explain by what means a painter obtains the enviable power of making a faithful resemblance with comparatively slight labour: it is because he adopts the excellent practice of making separate studies of details, such as branches, trunks, stems, weeds, and foregrounds-in short, everything that may be deemed worthy of note. It is this method of copying parts of objects with close accuracy that gives him the power of representing them generally and yet faithfully, with the natural effect which they bear to one another as a whole. An eminent English landscape painter, whose manner was as remarkable for its freedom of execution as it was for the truthfulness of its results, once remarked to us:"The secret of my success is in having bestowed much time

upon the close examination of the anatomy of trees; how their branches spring from the trunks; the forms of their leaves, and the manner in which they grow or cluster in masses from the stems." When such labour and painstaking as this is the rule, we need not wonder at a successful result.

Having said thus much upon the theoretical part of our subject, we will now turn to the practical. We advise our pupils to make a drawing of Fig. 101, leaves of the lime tree, with an H B pencil. He must first make the arrangement of the whole of the stems, and then proceed with the leaves, beginning where the two stems join, arranging every leaf in succession, without passing over any, to the end, then faint the arrangement, and draw carefully every particular: it will be much better at first to make an enlarged drawing, say double the size; do the same also with Fig. 102. Fig. 103, the cluster of leaves, will require more time and attention, which must be especially bestowed on

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avoided. Here again we must introduce another caution respect ing the treatment of shadows amongst foliage-namely, never make the interior shadows too dark; a moderate, clear, and yet decisive tone will be enough, because there must be in all cases, but especially with regard to trees, sufficient opportunities left for marking in more forcibly any form which may be remarked in the shadows, observing that the making out details in shadows cannot be carried to the extent of making out details in the lights. Trees, as we have previously said, are not flat like walls, but their branches and leaves project and recede indefinitely, and consequently those leaves which come out nearer to the light will require a different tone to those which are in shadow; the pupil's own observation must be his guide in this matter as to which leaves must receive the minor tones and the depth of tint to be laid upon them. In Fig. 103 the light falls upon the right side, where less shading is required, but the whole of the leaves to the left, away from the light, must be toned down, though not to the extent of the deep shadow in the middle and interior of the branch. Fig. 100 we recommend should be copied double the size, and according to our old principle of

marking in. We were once asked by a pupil, "When shall I leave off marking in ?" We replied, never; it is not desirable that you should ever leave off the practice, because all who do mark in find that they make progress in drawing, and that it saves time, and produces a more satisfactory result. A young mechanic whom we know, who had very much improved his power of drawing from attending a night class at a Mechanics' Institute, offered himself as a candidate for a situation as draughtsman at a manufactory where drawing was essential. Having obtained it, one of his employers, after a few days, when he had become familiar with his work, brought him three or four subjects to draw for working purposes, telling him at the same time that they would, no doubt, occupy him four days at least: at the same hour on the following day he returned the whole finished. His master was agreeably surprised, and also much pleased with the excellence of the work, and asked him

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first,

and

always make marks to indicate the course of the outline; the consequence is I have

very little rubbing out and alteration, and that

has enabled me to finish the drawing so quickly." Therefore, in copying Fig. 100, note every angle, and the distances between each angle, and do the same respecting the positions of the branches as they grow from the trunk, the direction and inclination of the branches, and their extent, and you cannot fail to make a satisfactory drawing.

The illustrations that accompany the present lesson are representations of the stem, branches, blossom, and leaves of the Tilia Europea,

the European or common lime tree, which is the most valuable of the different varieties of this useful tree. It grows most extensively in the middle and northern parts of Europe, and is very common in England. Its large size, handsome appearance, and profusion of sweet flowers, make it a very general favourite throughout this country and most parts of the Continent, where it is extensively planted in parks and other places of public recreation. Its wood is well adapted for carving, being white, close-grained, and smooth. The carvings at Windsor Castle, those of Trinity College, Cambridge, and those at Chatsworth, are of limewood, as, indeed, are most of the other fine specimens of this branch of art in England. The fibres of the bark, which is tough, form the material of an extensive manufacture of cordage and matting in Russia and Sweden. Many specimens of this tree exist which are remarkable for their great age and size. At Neustadt, in Würtemberg, there is a prodigious lime tree, which adds its name to that of the town, this being called Neustadt an der Linden (Neustadt at the lime tree). The age of this enormous tree is said, probably with some exaggeration, to be one thousand years.

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EXERCISE 92.

1. How much is my house worth? 2. It is worth about twenty thousand francs. 3. Is that horse worth as much as this one? 4. This horse is worth two hundred dollars, and that one three hundred. 5. Is it worth the while to write to your brother? 6. It is not worth the while. 7. Is it worth the while to go out when one does not wish to walk? 8. It is not (n'en) worth the while. 9. Does it suit you to write to my brother to-morrow? 10. It does not suit me to write to him. 11. Does it become you to reproach me with my neglect? 12. It becomes me to blame you when you deserve it. 13. What is that man worth? 14. I cannot tell you exactly, about fifty thousand francs. 15. Is that cloth good? 16. No, Sir, it is good for nothing. 17. Is your gun worth as much as mine?

4. Ne rien valoir means to be good for nothing; ne pas valoir 18. Yes, Sir, it is worth more. 19. Will you go to my father's? grand'chose, to be worth little, not to be good for much.

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20. No, Sir, I have something else to do. 21. Is it better to go to market early than late? 22. It is better to go early. 23. How much may your horse be worth? 24. It is not worth much, it is very old. 25. Is your watch better than mine? 26. It is not worth much, it does not go. 27. Is that book worth two francs? 28. It is worth one, at most. 29. Have you asked your sister what that book is worth? 30. I have not. [Sect. XXIV. 1, 2; XLV. 4.] 31. What must I do? 32. You must speak to your father. 33. Must he have money? 34. He must have some. 35. Has he not sold his horse? 36. He has sold it, but it was

6. Valoir mieux, conjugated unipersonally, means to be better; not worth much. valoir la peine, to be worth the while.

Il vaut mieux travailler que d'être It is better to labour than to be idle. oisif,

Il ne vaut pas la peine de parler It is not worth the while to speak when one has nothing to say. EXAMPLES.

quand on n'a rien à dire,

RÉSUMÉ OF

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De combien votre oncle est-il riche? Il est riche de deux cent mille francs.

thousand francs.

How much is your uncle worth?

SECTION XLIX.-REGIMEN RELATING TO SOME VERBS. 1. When the verbs prendre [4, ir., see § 62], to take; voler, to rob, to steal; acheter, to buy; demander, to ask for; payer, to pay, are followed by one regimen only, or by several regimens in the same relation, these regimens, if nouns, must not be separated from the verb by a preposition; if pronouns, they take the form of the direct regimen, le, la, les.

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He is worth two hundred thousand J'ai payé le livre au libraire,
francs.

Ne vaut-il pas mieux lire que jouer? Is it not better to read than to play?

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3.

1. Vous sied-il de nous reprocher notre négligence P 2. П me sied de vous faire des reproches quand vous le méritez. Vous convient-il d'aller trouver mon frère ? 4. Il ne me convient pas d'aller le trouver, j'ai autre chose à faire. 5. Combien ce champ peut-il valoir? 6. Il peut valoir une vingtaine [§ 27 (2)] de mille francs. 7. Valez-vous mieux que votre frère ? 8. Mon frère vaut beaucoup mieux que moi. 9. Ce couteau ne vaut-il pas plus que le vôtre ? 10. Le mien est meilleur, il vaut davantage. 11. Combien votre montre vautelle ? 12. Elle ne vaut pas grand'chose, elle ne va pas bien. 13. De combien le négociant est-il riche? 14. Je ne puis vous le dire au juste, il est riche d'une centaine de mille francs. 15. Ne vaut-il pas mieux rester ici que d'aller au marché ? 16. Il vaut mieux aller au marché. 17. Votre chaîne d'or vautelle plus que la mienne? 18. Elle vaut tout autant. 19. Elle ne vaut pas grand chose, elle est cassée. 20. Cela vaut-il cinquante francs ? 21. Cela vaut tout au plus deux francs. 22. Avez-vous demandé au marchand ce que cela vaut? 23. Je ne le lui pas demandé. 24. Il m'assure que cela vaut une centaine de francs.

Je le lui ai payé, etc.,

I have paid the bookseller for the book.

I have paid him for it.

3. Demander is used also in the sense of to inquire for, to ask for. J'ai demandé ce monsieur,

I asked for that gentleman.

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Je ne connais pas celui qui me les a pris, mais je sais qu'il demeure ici. 5. Avez-vous demandé vos livres ? 6. Je les ai demandés à mon cousin. 7. Vous les a-t-il rendus ? 8. Il me les a payés. 9. Vous a-t-on volé beaucoup de fruit cette année? 10. On m'a volé des légumes, mais on ne m'a point volé de fruit. 11. Avez-vous payé votre chapeau au paysan? 12. Je ne le lui ai pas payé, je l'ai payé au chapelier. 13. A qui avez-vous demandé des renseignements? 14. J'en ai demandé au voya 16. geur. 15. Savez-vous qui vient de frapper à la porte ? C'est M. L., qui vous demande. 17. Qui avez-vous demandé? 18. J'ai demandé votre frère. 19. Votre frère a-t-il payé toutes ses dettes ? 20. Il ne les a pas encore payées, parce qu'il n'a pas reçu ses revenus. 21. Lui avez-vous payé ce que vous lui avez acheté ? 22. Je le lui ai payé. 23. Ne leur avez-vous pas payé votre loyer? 24. Je le leur ai payé. 25. Ils nous ont payé notre maison.

your brother.

EXERCISE 94.

1. Have you paid your landlord? 2. I have paid him my rent. 3. Have you paid him for the windows which you have broken ? 4. I have paid him for them. 5. Has the hatter paid for all his hats? 6. He has not paid for them, he has bought them on credit (à crédit). 7. Do you pay what you owe every day? 8. I pay my butcher every week. 9. Have you paid him for his meat? 10. I have paid him for it. 11. For whom did you inquire this morning? 12. I inquired for 13. Why did you not inquire for my father? 14. I know that your father is in England. 15. Has the hatter been paid for his hats? 16. He has been paid for them. 17. Has your money been taken from you? 18. My hat has been stolen from me. 19. Have you asked your brother for your money? 20. I have asked him for it, but he cannot return it to me. 21. Has he no money? 22. He has just paid all his debts, and he has no money left (de reste). 23. Have you asked your father for money? 24. I have not asked him for any, I know that he has none. 25. From what bookseller have you bought your books? 26. I bought them from your bookseller. 27. Are you wrong to pay your debts? 28. I am right to pay them. 29. Who is inquiring for me? 30. The physician is inquiring for you. 31. Who knocks? 32. Your shoemaker knocks.

KEY TO EXERCISES IN LESSONS IN FRENCH.

For the use of those who are studying our Lessons in French, we now give the first portion of a Key to the exercises contained in those lessons. We have deferred its commencement until the present time designedly, that we might not subject our readers to the temptation of consulting the Key until after they had written the Exercises to which it relates, and made such progress as will enable them to detect and amend any errors they may have made when beginning our course of lessons. The only way to acquire a thorough knowledge of a living language is to practise one's self in the use of it; and the best exercises will be of no service unless they are written without any other assistance than is supplied by general grammatical information. When, however, the selfteacher has thoroughly studied both lessons and exercises, it is useful for him to be able to turn to a key, such as we are now going to give him, for the purpose of comparison and the final correction of any mistakes he may not be able to perceive

himself.

It may be objected that we have given a Key to the exercises in each Lesson in Latin in the lesson that immediately follows it. It must, however, be remembered that Latin is a highly inflected language, and one which the learner will never attempt to speak; while the grammatical construction of the French language is less complicated; and that it should be the chief object of the learner to speak French; and, for this purpose, to drill himself thoroughly in the rules of which each lesson is composed. To induce him to rely as much as possible on his own resources, we have, therefore, deferred commencing a Key to the Exercises in Lessons in French until the present

time.

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11. The butcher has the meat. 12. The miller has the meat, and I have the coffee. 13. Have you the water and the salt? 14. Yes, Sir; we have the water, the salt, and the oats. 15. Have we the 16. No, Sir; the girl has the tea, the vinegar, and the salt. tea? 17. Have I the wine? 18. No, Madam, you have only the vinegar and the meat. 19. Have you the table? 20. Yes, Madam, I have the table. EXERCISE 2 (Vol. I., page 3).

1. Avez-vous le blé ? 2. Oui, Monsieur, j'ai le blé. 3. Qui a la viande ? 4. Le boucher a la viande et le sel. 5. A-t-il l'avoine ? 6.

Non, Madame, le cheval a l'avoine. 7. Avons-nous le blé? 8. Vous

avez le blé et la farine. 9. Qui a le sel ? 10. J'ai le sel et la viande. 11. Avons-nous le vinaigre, le thé, et le café ? 12. Non, Monsieur, le frère a le vinaigre. 13. Qui a le cheval ? 14. Le boulanger a le cheval. 15. Avons-nous le livre et la plume ? 16. Non, Mademoiselle, la fille a la plume, et le meunier a le livre. 17. Avez-vous la table, Monsieur ? 18. Non, Monsieur, j'ai seulement le livre, Qui a la table ? 20. Nous avons la table, la plume, et le livre. EXERCISE 3 (Vol. I., page 3).

19.

1. Have you the gold watch? 2. Yes, Madam, I have the gold watch and the silk hat. 3. Sir, have you the tailor's book? 4. No, Sir, I have the physician's book. 5. Have they the baker's bread ? 6. They have the baker's bread and the miller's flour. 7. Have you the silver pencil-case? 8. Yes, Sir, we have the silver pencil-case. 9. Have we the horse's oats? 10. You have the horse's oats and hay. 11. Who has the carpenter's cloth coat ? Have you the wooden table? 15. Yes, Sir, I have the carpenter's wooden table. 16. Have they the silver knife? 17. They have the silver knife. 18. The physician's brother has the silver watch. 19. The shoemaker's sister has the silk dress. 20. Has she the leather shoe? 21. No, Madam, she has the satin shoe. 22. Have we the woollen stocking? 23. No, Sir, you have the tailor's silk stocking. 24. Who has the cotton stocking? 25. The physician has the cotton stocking. 26. The lady has the satin shoe of the baker's sister.

12. The shoemaker has the tailor's silk hat. 13. The tailor has the shoemaker's leather shoe. 14.

ESSAYS ON LIFE AND DUTY.-V.
CHARITY.

CHARACTER can never be said to be complete without the
presence of the element of charity. So many false ideas, how-
ever, are current concerning the nature of charity, that it may
be well to preface this article by reminding the reader that
charity is not the synonym for a mere mawkish sentimentality.
To be charitable, according to some theorists, is to be indifferent
to the distinction between honour and dishonour, good and evil,
and to treat even the most flagrant faults with palliative excuse
and toleration. Charity, like each of the virtues, must exist in
harmony with others, or it loses its claim to be considered a
virtue. A charity which could exist apart from truth, righteous-
ness, and justice, would only serve to put a premium upon vice
and crime. What then, it may be asked at the outset, is
charity? It is the wise exercise of the affectionate side of our
nature; it is the letting love operate as a motive power in
all our varied relationships, as citizens and members of a
commonwealth in which each ought to consider the best
interests of the other. This can never be done by mere ex-
pediency, nor from a sense of utilitarian morality; it must be
the result of innate beneficence or kindness. Charity refers to
our estimates, as well as our actions; it considers the weakness
incidental to its own nature, and is therefore lenient in its judg-
ment about others, not as blind to their faults, but as looking
to the frailties of our common humanity, and finding in the
errors of others counterparts of the shortcomings which exist
in ourselves. Charity considers that there is a common weal, as
well as a private weal, and feels the claim of the outside world
upon its powers of help and sympathy: thus realising that with
all the distinctions which are evidently inherent in the system
of things, such as rich and poor, high and low, there is yet a
brotherhood of humanity, in which the stronger are expected to
Charity considers the terrible exigencies of
help the weaker.
life into which many are born, and in looking at the lamentable
phases of character continually brought to light, it is ever on the
alert to educate the masses and to ameliorate the condition of
their dwellings. Charity, moreover, is no spasmodic exercise of
generosity, no sudden surprise of human nature into an act of
startling goodness, but it is the spirit of the life, that which
underlies all our judgments of and our actions towards others.
Charity, thus interpreted, is the co-existence and exercise of

the affectionate with the intellectual and judicial faculties of our nature.

No character can claim to be complete without charity. It is possible to let one side of our nature overtop the other, and thus human nature, when love is eliminated, becomes hard, stern, and severe. Some men may be gigantic in intelligence, and dwarfish in affection, but they are monstrosities in human nature. Only the equable development of all our powers can be commensurate with our possibilities, and therefore our responsibilities.

A moral science which found no room for charity would develop character very much after the Roman type-hard, stern, and unbending-such as might exist with unflinching bravery and unyielding energy, but which effectually crushes the affectionate side of human nature. Moreover, it is necessary to guard against the great mistake that charity means, in some sort, weakness of character, for there is no such inspiration to acts of self-surrender, self-denial, and self-sacrifice, as is to be found in the influence of this virtue. In proportion to its power is the diminution of that selfishness which so often merges into cowardice, and cripples the exercise of the higher virtues. Το be charitable is, for the most part, to have that consideration for others which makes us set aside the comfort or discomfort, the rest or unrest of our own lives. Charity is a virtue which needs careful culture; men are so apt to be disheartened by ingratitude and base treatment, that they tire in acts of beneficence, and sometimes they catch that cynical tone of mind which helps to make them not only indifferent to the wants of others, but misjudgers of the race. We should never form our opinions of the baseness of men from one or two specimens of wrong-doers we may meet with, or charity will receive no encouragement for its culture, and we ourselves shall lose the sweet sensation which comes from its exercise. Let it be remembered that, if we were to argue from the score, not only of utility to others, but utility to ourselves, we should commend charity, as it ministers largely to human happiness, to think well of, and to act kindly towards, those around us.

It often happens that, as nations increase in the luxuries of civilisation, they become more petrified by selfishness. There is a tendency in the eager race to be rich, or to be successful, to forget the wants and claims of others, and to become isolated from them the fact that the poor are ever so charitable to the poor comes from this, namely, that they are not absorbed in successful ambitions for themselves.

:

Charity towards others in matters of opinion is much needed; the tendency of every age has been to institute some sort of inquisition or other, by which free thought may feel its penalties. Mankind have been far too ready to put gyves and shackles on the limbs of those whose opinions they disliked and scorned; and in no sphere has the exercise of charity been less experienced and more required than in the region of human judgment and opinion.

The exercise of charity towards others will prepare us for the enjoyment of it in return. There is a knowledge of ourselves which induces humility, and which, while it makes us conscious of our marvellous mistakes and errors, makes us deeply sensitive to the experiences of a charitable consideration. Most assuredly there is a punishment awaiting the uncharitable, as for the most part moral science teaches us that such vice is its own Nemesis, and that the stern and unforgiving in the end have meted out to them the same measure that they have meted out to others.

The virtue of charity is no foe to wisdom. Charity itself requires the exercise of judgment and forethought. Otherwise, charity is in no sense charity, so far as its outworking in acts of beneficence is concerned. Much as men may dislike the name of political economy, or political philosophy, it must be manifest that, were the practical workings of charity presided over by wisdom, as well as inspired by love, the blessedness of its results would be tenfold or twentyfold increased.

We have, however, kept in mind in this essay the fact that charity is a matter which affects our judgments, and criticisms of others, quite as much as our actual beneficence; and no one can claim to have mastered the first elements of moral science in any practical way, much less to have graduated in the high attainments of character, until, as a regulating faculty of the affectionate nature, Charity takes its place side by side with Justice and Truth.

MECHANICS.-X.

THE PULLEY.

IN the machines we have so far considered, the essential parts were rigid. It was a beam, or a spoke, or a complete wheel, or an axle we had to deal with; and if a rope was used, it was only with a view to connecting the power or resistance with these rigid parts. But it may have escaped your notice that, in using a rope for this purpose you had fallen on a veritable machine. Such is the case; a rope is a machine-a most convenient machine-which possesses the peculiar property of not only transmitting a force from one point to another in its original direction, but also sending it, very little D impaired, round any number of corners, into a correspond. ing number of successive new directions. This

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Fig. 67.

practical advantage everybody is familiar with; nobody more than the British sailor, whose daily work consists in no small degree in sending the muscular power of his arms round all manner of corners for the benefit of the good ship he navigates.

The Pulley, the third of the mechanical powers, is the instru ment by which this object is gained in practice. In its simplest form it consists of a rope which passes round a small solid wheel which is itself mounted in a block. In theory, neither wheel

a

Fig. 68.

nor block are indispensable parts of the machine; the single essential is the rope, which is supposed to be perfectly flexible, and to turn round a mere point without experiencing any resistance from rubbing against it, that is, from friction.

The theory of the pulley, thus based on the suppositions of perfect flexibility and absence of friction, may be understood from the upper part of Fig. 67. Let A, B, C, D be any number (say four) of rings, representing so many points, through which a rope passes, enabling a force, P, at one end to balance a resistance, w, at the other. The flexibility being perfect, and no friction between rope and ring, P is transmitted unimpaired, and we have therefore the power equal to the resistance, whether the rings are all fixed in position, or some be movable.

But in practice, the suppositions made do not hold good, neither is the rope perfectly flexible, nor the friction nothing. For the former reason each corner must be rounded off to relieve the rope from the sharp bends at A, B, C, D; and, for the latter, these rounded corners are made into small wheels, as at E, F, G, E, which move round with the rope, and prevent the power being diminished by the friction that would result, were the rope allowed to slide round them. Thus the theoretical pulley in the upper part of Fig. 67 becomes the practical one in the lower, where the rings are replaced by wheels ; and though some friction remains, and default of flexibility to impair P in its transmission, we say practically, as we did before theoretically, that still the power is equal to the resistance.

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W

Fig. 69.

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The relations of the power and resistance in the various forms and combinations of pulley can now be easily determined. There is first the Single Pulley, which is of two kinds, fixed and movable; and of these in various combinations, the more com

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