Imágenes de páginas
PDF
EPUB

LESSONS IN ARCHITECTURE.-IV. PROGRESS OF ARCHITECTURE IN EGYPT AND INDIA-THE

COLUMN.

AFTER the rude style of building practised in early times had 'spread itself in various forms over the ancient world, true art at last made its appearance. The great nations of antiquity, as they advanced in civilisation, created a national architecture, each with a feeling and expressich peculiarly its own. As soon as the stones used in buildings began to assume a cubical, prismatic, or cylindrical form, and the square and compasses gave a new direction to stone-cutting, architects gave wing to their imagination, because they now had the means of realising its creations. Symmetry was

studied in the ground-plan of their edifices; their architraves were raised upon pillars and columns; and experience ere long taught them the strength of every stone, and the proper height of every part of a building. Hence arose that harmony and proportion which elevated architeoture into an art. We shall not attempt to decide the question whether pillars and columns were first formed in excavations, or in separate constructions; but it is evident that they were the first elements of a regular architecture-that is to say, of the orders which constituted the first basis of architectural harmony. To the pyramidal constructions of Egypt and of Asia speedily succeeded the erection of palaces and other edifices, in which square and cylindrical pillars formed a most essential part: the great weight of the materials employed requiring that they should be supported at short distances for the formation of internal and external galleries. These single pillars could only be connected at the top by architraves of such dimensions as combined the ratio of their breadth with the proportions of the supporting power of the columns. Upon these architraves were placed platforms or ceilings of flat stones, which, by their thickness, formed a new di

The most ancient monuments of Egypt ornamented with columns are situated in the Heptanomis, an old division of the country which corresponded pretty nearly with the district called Middle Egypt by modern geographers, and which was situated between the Delta and the Thebaid, extending from 24° N. lat. to 30° N. lat. These monuments exhibit speci

G MYM

mens of the greatest simplicity, and strongly analogous to those of the Doric order. The monuments of India excavated in the rock present the same principles of these primitive orders. In these two countries, which are the cradles of architecture, artists at first decorated their columns and their capitals with ornaments of which the ideas were taken from the local vegetation, to which were sometimes added others borrowed from animal nature. Thus in Egypt, after having set up the simple cylindrical shaft for their column, they sculptured upon it branches of the lotus, meeting each other and fastened together by fillets. The capital which crowned the column was at first composed of the bud of the same flower. This first idea was afterwards developed in the application of vegetation of every kind to the ornamentation of the columns of the temples and of the great public edifices. Among the six examples of Egyptian capitals given in this page there is one composed of the leaves of the palm-tree.

[graphic]

SCULPTURED GATEWAY AT KARNAC.

mension above the former; and upon these platforms were formed terraces or flat roofs, which were surrounded by another row of stones forming a border, and having an outward projection which preserved the façade from the effects of the rain. These were the origin of cornices and entablatures. The column, in preference to the square pillar, became the type of architectural proportion. Simple at first, it presented nothing but a cylindrical shaft, without ornament, and only expressing the purpose for which it was originally intended. The oldest

specimens in Egypt are of this description; Asia presents similar specimens; and Greece, with the whole of the West, follows the same track: thus proving that everywhere there is an invariable similarity in the origin of the arts. The simplicity, elegance, and utility of the column engaged the attention of architects, and concentrated all the efforts of their imagination. Thus it became their architectural type or model, and formed the nucleus of the different characteristic styles of building that were adopted by the great nations of antiquity.

Egypt, thus adorned with orders of architecture, had its national style. The numerous works upon the history and antiquities of Egypt published during the last half-century have made us acquainted with its archæological treasures, such as the temples and palaces of Thebes, the Isle of Phila, Karnac, Abousambul, Edfou, Memphis, and others; and large public buildings, decorated with numerous columns, immense pillars, obelisks, and sphinxes, which give to this style a peculiar character of antiquity and grandeur, of which mere verbal description would fail

to convey any idea to the reader.

In India, as in Egypt, iso

lated columns and pillars appear to have had their origin in subterranean excavations for architectural purposes; of these numerous examples are seen at Ellora, in the palace or temple of Indra. These pillars are much shorter than those of Egypt, their bases and capitals occupying a considerable portion of the height of the column, and the entablature, or rather the corona, is less accurately traced. In cases where the Indians cut out the rock for the purposes of decoration, and sculptured it over with various ornaments, the column assumes a lighter appearance, and the principle of an order of architecture can be traced.

The excavated temples of India are numerous and extensive; the principal ones are those of Elephanta, Salsette, and Vellore, or Ellora. Elephanta is situated near Bombay, on a small island of the same name, which received this appellation from the figure of an elephant being cut out upon the rocks on the southern shore. The grand temple is 120 feet square, and is supported by four rows of pillars; along the side of the cavern are fifty colossal statues from twelve to fifteen feet

[graphic]

high. The face of the great bust is five feet long, and the breadth across the shoulders twenty feet. At the west end of this pagoda, or temple, is a dark recess twenty feet square, without ornament; the altar is in the centre, and there are two gigantic statues at each of the four doors by which it is entered. On entering Elephanta, there is a piazza extending sixty feet from east to west, and having a breadth of sixteen feet; indeed, the body of the cavern is surrounded on every side by similar piazzas. The caves of Kenneri, on the larger island of Salsette, in the same vicinity, and those of Carli, on the opposite shore of the continent, are equally remarkable. The mountain of Kenneri appears to have had a city hewn out of its rocky sides, capable of containing many thousand inhabitants. The front is hewn into four storeys or galleries, in which there are 300 apartments; these have generally an interior recess or sanctuary, and a small tank for ablution. The grand pagoda is forty feet high to the soffit of the arch or dome; it is eighty-four feet long, and forty-six broad. The columns of the portico are finely decorated with bases and capitals; and at the entrance are two colossal statues, each twenty-seven feet high. Thirty-five pillars of an octagonal form, about five feet in diameter, support the arched roof of the temple; their bases and capitals are composed of elephants, horses, and tigers, carved with great exact

ness.

Round the walls are placed two rows of cavities for receiving lamps. At the farther end is an altar of a convex shape, twenty-seven feet high, and twenty feet in diameter; round this are also cavities for lamps; and directly over it is a large concave dome cut out of the rock. It is said that about this grand pagoda there are ninety figures or idols, and not less than 600 of these figures within the precincts of the excavations. The cave-temple at Carli is even on a greater scale than now described. But the temples of Ellora, near Dowlatabad, are reckoned the most surprising and extensive monuments of ancient Hindoo architecture. They consist of an entire hill excavated into a range of highly-sculptured and ornamented temples. The number and magnificence of these subterranean edifices, the extent and the loftiness of some, the endless diversity of the sculpture of others, the variety of curious foliage of minute tracery, the highly-wrought pillars, rich mythological designs, sacred shrines and colossal statues, all both astonish and distract the mind of the beholder. It appears truly wonderful that such prodigious efforts of labour and skill should remain, from times certainly not barbarous, without a trace to tell us the hand by which they were designed, or the populous and powerful nation by which they were produced. The courts of Indra, of Juggernaut, of Parasu Rama, and the Doomar Leyna or nuptial palace, are the names given to several of these great excavations. The greatest admiration has been excited by the one called Keylas, or Paradise, consisting of a conical edifice, separated from the rest, and hewn out of the solid rock, 100 feet high, and upwards of 300 feet in circumference, entirely covered with mythological sculptures.

Besides the excavated temples of India, there are several others of different forms which may here be noticed. First, those composed of square or oblong enclosures; secondly, temples in the form of a cross; and thirdly, temples of a circular form.

Of temples of the first kind, the largest one remaining is that of Seringham, near Trinchinopoly. The circumference of the outward wall is said to extend nearly four miles. The whole edifice consists of seven square enclosures, the walls being 350 feet distant from each other. In the innermost spacious square are the chapels. In the middle of each side of each enclosure wall there is a gateway under a lofty tower; that in the outward wall, which faces the south, is ornamented with pillars of precious stones, thirty-three feet long, and five feet in diameter. Of temples of the second kind-namely, those in the form of a cross-the most remarkable is the great temple in the city of Benares, on the banks of the Ganges, which has been devoted to the religion and science of the Hindoos from the earliest periods of their history. The form of the temple is that of a great cross with a cupola in the centre, which towards the top becomes pyramidal. At the extremity of each branch of the cross, all of which are of equal length, there is a tower with

balconies, to which the access is on the outside.

Of temples of circular form, the temple of Juggernaut is considered the most ancient in India; the Brahmins attribute its foundation to the first king on the coast of Orissa, who lived, according to their chronology, 4,800 years ago. The

image of Juggernaut, or Mahadeo, stands in the centre of the building, upon an elevated altar. The idol is described as being an irregular pyramidal black stone, and the temple lit up only with lamps.

In the ancient Hindoo writings, another kind of temple is described, of which now no vestige is to be found. The Ayeen Akberry relates that near to Juggernaut is the temple of the sun, in the erection of which the whole revenue of the province of Orissa, for twelve years, was entirely expended; that the wall which surrounded the whole was 150 cubits high, and nineteen cubits thick; that there were three entrances: at the eastern gate were two elephants, each with a man on its trunk; on the west, two figures of horsemen completely armed; and over the northern gate, two tigers sitting over two dead ele phants. In front of the gate was a pillar of black stone, of an octagonal form, fifty cubits high; and after ascending nine flights of steps, there was an extensive enclosure with a large cupola constructed of stone, and decorated with sculpture. Such are the ancient monuments of which India can boast, long before architecture had reached that proud eminence on which it stood in ancient Greece. In our next lesson we shall glance at those of Persia.

LESSONS IN GREEK.—III. GENERAL REMARKS ON THE NOUN, THE ADJECTIVE, AND

THE PREPOSITIONS.-THE DEFINITE ARTICLE.

GENDER.

The

NOUNS or Substantives are names of objects or things which exist in space or in the mind. There are, in Greek, three genders; the masculine, to denote the male sex; the feminine, to denote the female sex; and the neuter (Latin neuter, neither), to denote objects which are neither male nor female. genders are distinguished partly by the sense and partly by the terminations of the nouns. There are terminations, for instance, which denote the feminine gender, as 7; there are other terminations which denote the masculine gender, as as in the first declension; and, again, there are others which denote the neuter gender, as ov. This is a peculiarity to which we have nothing similar in English adjectives. Those who have studied Latin are already familiar with it. In regard to gender as denoted by the meaning, let the ensuing rules be committed to memory.

1. Of the masculine gender are the names of male beings, of winds, of months, and of most rivers, as :-Пλarov, Plato; Zepupos, the west wind; Exaтoußaiwv, the month Hecatombæon; Eupwras, the river Eurotas.

2. Of the feminine gender are the names of female beings, of trees, of lands, of islands, and of most cities, as :-Kopn, a girl; Spus, an oak; Apkadia, Arcadia; Aeoßos, Lesbos; Koλopwv, Colophon.

3. Of the neuter gender are the names of fruits, the diminutive in ov (except the female proper name AcovTLOV), the names of the letters of the alphabet, the infinitives, all words not declinable in the singular and the plural, and every word used merely as the sign of a sound.

4. Of the common gender are personal nouns which, like our child, may be applied to male or female; thus, eos may be used of a male or female divinity, and so be rendered either god or goddess.

This common gender" is a grammatical phrase used to denote such nouns as are common to both males and females; that is, are sometimes masculine and sometimes feminine.

In Greek grammar it is usual to employ the definite article, in order to indicate the gender. The definite article, nominative singular, is 8,, ro, the; 8 is masculine, feminine, and ro neuter; 8, therefore, put before a noun, intimates that the noun is of the masculine gender; , that the noun is of the feminine gender; and To, that it is of the neuter gender. If both and are put before a noun, it is done to show that the noun is of the common gender: thus, & avnp, the man; yuvn, the woman; To epyov, the work; 8, n, eos, the (male or female) divinity; ó, h, rais, the child, whether boy or girl.

NUMBER.

Number is a distinction of nouns founded on the circum. stance whether they denote one or more. If a noun denotes

one object, it is in the singular number; if a noun denotes more objects than one, it is in the plural number. The Greek tongue has a third number, called the dual (Latin duo, two), which denotes two objects; thus, Aoyos is a word (singular); Aoyo, words (plural); λoyw, two words (dual); where os is the singular termination, or the plural termination, and w the dual termination.

CASE.

These terminations, os, o, w, undergo changes according to the relation in which they stand to a verb, to another noun, or to a preposition. Thus os may become ov, and or may become ous. Any word which is changed in form, to express a corresponding change in sense, is said to be inflected. Such inflexions or variations in the endings of nouns are termed cases. There are in Greek five cases, namely—

1. The Nominative, the case of the subject; as, 8 TаTηр ypaper, the father writes.

2. The Genitive, the case indicative of origin, whence; as, & Tov TaTpos vios, the father's son.

3. The Dative, the case indicative of place, where, and of the manner, and instrument; as, Ty тоν яатроs vių, to the father's

son.

4. The Accusative, the case of the object, or whither; as, d TаTηρ TOV VLOν Ayama, the father loves the son.

5. The Vocative, the case of invocation, or direct address; as, αγαπα, πάτερ, τον υιον, father, love thy son.

In Greek there is no ablative case; the functions of the ablative case are discharged, partly by the dative, and partly by the genitive. The nominative and the vocative are called recti, direct; the other cases are called obliqui, indirect.

Substantives and adjectives of the neuter gender have the nominative, the accusative, and the vocative alike, in the singular, the plural, and the dual.

The dual has only two case-endings; one for the nominative, accusative, and vocative, the other for the genitive and dative.

DECLENSION.

Declension is the classification of nouns and adjectives agreeably to the variations of their case-endings. There are, in Greek, three declensions; called severally, the first, the second, and the third declension. The learner will do well in regard to every noun and adjective, to ask himself, What is its nominative? What is its case ? What is its number? What is its gender? What is its declension? For instance, тpareçais is from the nominative rpareja, a table, is in the plural number, dative case, feminine gender, and of the first declension. In order to practise and examine himself fully, he should also form or "go through" every noun, adjective, tense, mood, and indeed every word capable of declension or conjugation, according to the several models or paradigms given in the successive lessons.

THE ADJECTIVE.

An adjective denotes a quality. This quality may be considered as being connected with, or as being in an object, as "the red rose;" or as ascribed to an object, as "the rose is red. In both cases the adjective in Greek, as in Latin, is made to agree in form, as well as in sense, with its noun. A change takes place in the adjective, conformably to the change in the signification, thus, a good man is ayabos avnp, but a good woman is αγαθη γυνη. Observe the os of the masculine is for the feminine changed into n. Not only in gender, but in number and in case does the adjective in Greek, as in Latin, conform to its noun: e.g., 8 ayabos aveρwños, Latin, bonus homo, the good man; areparos eσtiv ayatos, homo bonus est, the man is good; n kaλn Movoa, pulchra Musa, the beautiful Muse; Movσa eσтi kaλn, Musa pulchra est, the Muse is beautiful; To кaλoν eαр, pulchrum ver, the beautiful spring; TO Eаρ EσтI KAλOν, ver pulchrum est, the spring is beautiful.

The adjective, then, like the substantive, has a threefold gender-the masculine, the feminine, and the neuter. But many adjectives, such as compound and derivative, have only two terminations; one for the masculine and feminine, and another for the neuter; e.g.:

[blocks in formation]
[merged small][ocr errors][merged small][merged small][merged small]

Prepositions are words which go before nouns, and show the relation which the nouns bear to the affirmation or negation made in the sentence, or the member of the sentence in which they stand. Of prepositions I shall treat in full hereafter. At present some knowledge of them must be communicated, in order to prepare the beginner for the following instructions. In the words πορευομαι προς τον πατέρα, I go TO the father,

the word "pos, to, is a preposition.

In Greek, prepositions govern either one case, two cases, or three cases, and may accordingly be classified thus:

[blocks in formation]

A glance at this table will show that the case which in any example a preposition is connected with, has much to do in modifying its signification. Only by constant practice can the exact meaning and application of the several prepositions be known. The Latin student will, in this list, recognise words. with which he is familiar; thus ex is the Latin er; ev is the Latin in; po is the Latin pro; aro is the Latin ab; πep is the Latin super; and vwo is the Latin sub.

Before I treat of the declension of nouns, I must give the definite article, as it is so intimately connected with nouns that the latter cannot well be set forth without the former; and as the article is often used as indicative of the gender of the noun. THE DEFINITE ARTICLE, &, n, To, the.

[merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small]
[ocr errors]
[blocks in formation]

you

There is no form for the vocative; w, which is commonly used, is an interjection. The way to learn the article (as well as the adjective) is to repeat the parts first perpendicularly, 8, TOU, TW, TOV, etc., and then horizontally, as 8, , To, until you When you think are perfectly familiar with the whole. have mastered the task, examine yourself by asking, What is the accusative singular, feminine gender? What is the nominative plural, masculine gender? etc.; and when you have given an answer from memory alone, consult the book, to ascertain whether you are correct. Finally, write out the article in full from memory. Indeed, spare no pains to make yourself master of the article. There is a special reason for this advice, since the terminations of the article are, in the main, the same as the terminations of the noun and the adjective.

KEY TO EXERCISES IN LESSONS IN GREEK.—II. EXERCISE 1.-GREEK-ENGLISH.

4.

7.

9.

1. Always be true. 2. Rejoice ye (xaupo, I rejoice). 3. Follow. Do not complain. 5. I live pleasantly. 6. I am well educated. Thou writest beautifully. 8. If thou writest ill, thou art blamed. He hastens. 10. He fights bravely. 11. If you flatter, you are not true. 12. If thou flatterest, thou art not believed. 13. We flee. 14. If we flee, we are pursued. 15. You flee badly (like cowards). 16. If you are idle, you are blamed. 17. If you fight bravely, you are admired. 18. If they flatter, they are not true. 19. It is not well to flee. 20. It is well to fight bravely. 21. If thou art pursued, do not flee. 22. Fight bravely. 23. If they are idle, they are blamed. 24. If thou speakest the truth, thou art believed. 25. Always excel. Eat and drink, and play, moderately.

EXERCISE 2.-ENGLISH-GREEK.

26.

1. Αληθεύω. 2. Αληθεύεις. 3. Αληθεύει. 4. Αληθευομεν. 5. Αληθευετε. 6. Αληθεύουσι. 7. Ει αληθένω πιστευομαι. 8. Mn Maxcode. 9. Maxovтai. 10. Έπεσθε. 11. Επῃ. 12. Επεσθε. 13. Παίζει, 14. Devyovai. 15. E φεύγουσι διώκονται. 16. Θαυμαζομαι. 17. Θαυμαζονται. 18. Ει βλακεύουσιν ου θαυμάζονται. 19. Εν έχει ανδρειως μαχεσθαι. 20. METρIWS EσDie Kai Rive. 21. Οι σπεύδουσι. 22. Ε: κολακεύεις ου θαυμαζῃ. 23. Καλως γραφει. 24. Γραφουσι κακως. 25. Εν έχει αει αριστεύειν. 26. METPIWS BLOTEVETE. 27.

Αγαν εσθίουσι.

MECHANICS.-XII.

THE INCLINED PLANE-THE WEDGE-THE SCREW.

THE mechanical powers are usually said to be six in number :the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw. On examination, it will be found that any machine whatever consists of various combinations or modifications of these. If, however, we look more closely, we shall find that these six may really be reduced to three, namely, the lever, the pulley, and the inclined plane.

These, then, are the three fundamental mechanical powers; the wheel and axle being, as we saw in our last lesson, a succession of levers coming into play one after another; and the wedge and the screw, as we shall soon find, merely modifications of the inclined plane. To this, then, we must now turn our attention, and see how the inclined plane may be used as a mechanical power, and what is the advantage gained by its use. A horizontal plane is one that has an even surface, like a portion of the surface of a lake on a calm day, every part being at the same level. If this plane be now tilted or lifted at one end, so as to make an angle with the horizon, it is called an inclined plane, and the angle which it makes with the level surface is called its angle of inclination. Hence we speak of a plane inclined at an angle of 30, or any other number of degrees. There is also another way of speaking of the inclination, as, for instance, when we say a road has an ascent of one foot in twelve, meaning that for every twelve feet of length measured along its surface there is a vertical rise of one foot. These modes of expressing the same fact may be used indiscriminately.

Now we can easily see that some advantage is gained by the use of the inclined plane. If a drayman wishes to raise a heavy barrel into his dray, he does not attempt to lift it vertically, for he knows he could not do it; but he lays a ladder or plank sloping from the ground up to the dray, and rolls the barrel up this incline. So in the railway which has been formed over

A

W

G

E Fig. 77.

1 к

Mont Cenis, the trains go along a series of zigzags, which are really a succession of inclined planes, and thus the mountain chain is crossed. A driver, too, in driving a heavy load up a steep incline will frequently cross from side to side of the road, as he goes up a less steep incline, and thus spares the horses. How comes it, then, that this advantage is gained, and what proportion does the load bear to the power that raises it? We will try and solve these questions. Let A c represent a plane inclined at the angle CAB; W is a weight resting on the plane and fastened to a cord which passes over the pulley D, and is kept stretched by a power, P. The cord we will first suppose to be parallel to the surface of the plane, and the power therefore acts in this direction. Friction has, in practice, a great influence in a case like this; as, however, we shall speak about that shortly, we will neglect it now, and suppose that the plane is perfectly smooth, and that the weight is just kept in its position by the action of P. We found in our third lesson that, if we draw a line, G E, downwards from G, the centre of gravity of w, and make it of such a length as to represent the weight of w, and then through E draw E F parallel to G D, and just long enough to meet the line G F, which is perpendicular to the surface of the plane, that then EF represents in magnitude the power P. We have, in fact, a triangle of forces, the three sides of which represent the three forces which act on the weight and keep it at rest. But the angles of the triangle E F G are equal to those of the triangle C B A. This is easily seen, for the angle E F G is equal to C B A, each being a right angle. GEF is also equal to A C B; for, if we continue E F till it meets BC, we shall have a parallelogram, and these will be opposite angles, and so must be equal; the third angles are equal too, since G F and E G are perpendicular to A C and A B. The angles of one triangle are equal, then, to those of the other, and there fore the sides of the triangle E F G bear the same proportion to one another that those of C B A do. Of this you can satisfy yourself by actual measurement, and you will find the rule always hold good. The proper mode of proving it, you will learn from Euclid.

The three sides of A B C represent, then, the three forces which act on w; A c representing the weight, B C the power, and A B the resistance of the plane, or the part of the weight which is supported by it. Hence we see that if the incline be 1 foot in 20, a man in rolling a weight up will only have to support of it.

We can easily arrive at this result in another way. Suppose a person wants to lift a weight of 200 pounds to a height of one foot, he will have to exert a force of that amount if he lift it straight up, and will then move it through just one foot. But if, instead of this, he moves it up this incline, when he has passed over one foot in length of its surface, he will only have raised it of a foot, and will have to move it over the whole twenty feet of the plane in order to raise it the one foot. That is, he will have to move it twenty times the space he would if he lifted it direct, and will therefore sustain only of the weight at any moment. Still, he must sustain this portion twenty times as long. This supplies us with another illustration of the law of virtual velocities which we explained in the last lesson.

The general rule for the gain in the inclined plane when the power acts in a direction parallel to it, may be stated as follows: The power bears the same ratio to the weight it will sustain that the perpendicular elevation of the plane does to the length of its surface.

If the power, instead of acting along the plane, acts at an angle to it, whether it be parallel with the base or in any other direc tion, as G K, we have merely to draw E H parallel to the line of action of the force, instead of parallel to the plane, and, as before, we shall obtain a triangle of forces, the three sides of which represent the three forces, and thus we can calculate the power required to support the weight.

If we have two inclined planes meeting back to back, like the letter V inverted, and a weight resting on each, the weights being connected by a cord which passes over a fixed pulley at the summit, we can see, from this principle that there will be

[ocr errors][ocr errors]

equilibrium when the weights bear the same proportion to each other as the lengths of the inclines on which they rest: for it is clear that, the steeper the plane, the less is the portion of the resistance borne by it. If, for example, one incline is 15 inches long, and the other 21 inches, a weight of 5 pounds on the former will balance one of 7 pounds on the latter. For, supposing the vertical height of the summit to be 6 inches, the portion of the force of 5 pounds which acts downwards, and tends to raise the other, is of 5 pounds, which equals 2 pounds; while the portion of the other which acts downwards is of 7 pounds, which is also equal to 2 pounds.

This system of two inclines is often used in mining districts, a train of loaded trucks running down from the pit's mouth to the staith, being made to drag a train of empty ones up the incline. Many familiar instances of the use of the inclined plane are met with every day, though they often escape notice, unless we are specially looking for them. Our knives, scissors, bradawls, chisels, needles, and nearly all cutting and piercing tools, act on this principle. Those immense blocks of stone placed across the top of upright pillars, which excite the surprise of all visitors to Stonehenge, are believed to have been raised in this way, by making an inclined plane and pushing them up on rollers.

THE WEDGE.

We pass on now to notice the wedge, which essentially consists of two inclined planes of small inclination placed with Sometimes one side only of the wedge is sloping, and it is then simply a movable inclined plane. In using this, it is so placed that it can only be moved in the direction of the length, and the weight to be raised is likewise prevented from moving in any direction except vertically. If pressure be applied to the head of the wedge, the weight will be raised. The gain is the same here as in the inclined plane.

their bases one against the other.

C

P

Fig. 78.

R The wedge, however, usually consists of a triangular prism of steel, or some very hard substance, and is used as shown in Fig. 78. The point is inserted into a crack or opening, and the wedge is then driven, not by a constant pressure, but by a series of blows from a hammer, or some similar instrument. It is usual to consider the wedge as kept at rest by three forces-first, a pressure acting on the head of the wedge, and forcing it vertically downwards, as at P; secondly, the mutual resistance of it, and the obstacle which acts at right angles to the surface of the wedge, as at R R; and thirdly, the force which opposes the motion, and acts at right angles to the direction in which the object would

move, as at c.

As, however, the resistance to be overcome varies very much from moment to moment, both in direction and intensity, and as the force is usually supplied by impact or blows, and not by pressure, such calculations afford very little help towards determining the real gain.

The other mechanical powers are usually employed in sustaining or raising a weight, or offering a continuous resistance; a continuous force is therefore used with them. In the wedge, the resistance to which it is applied is usually one which, when once overcome, is not again called into play. In splitting timber, for instance, when the wedge is driven in, the particles of timber are forced apart, their cohesion is overcome, and they do not join again. So in dividing large stones, when once a crack has been made through them, no continued application of force is needed to keep them from re-uniting. When continuous force is required, the wedge having been driven forward is kept from slipping back by friction.

As, then, we cannot calculate the force generated by a blow, we must be content with the general statement that the smaller the angle of the wedge the greater is the power gained.

THE SCREW.

This is the last of the mechanical powers, and, like the wedge, acts on the principle of the inclined plane. If we stretch a cord so as to represent the slope of an inclined plane, and then, holding a ruler, or some cylindrical body, vertically, we roll up the

cord upon it, we shall have a screw, the spiral line traced out by the cord being called its thread. It is easy to see that the thread has at every point the same inclination as the inclined plane, and that a particle in travelling up the screw will pass over the same distance as if it moved up the plane. A screw, then, is a cylinder with a spiral ridge raised upon it; this ridge is sometimes made with a square edge (Fig. 79 a), and then has more strength; but usually it is sharp, as seen in a common screw, and this way of making it reduces friction.

To use the screw, it is necessary to have a hollow cylinder with a groove cut on the inside of it (Fig. 79 b), so that the thread of the screw (Fig. 79 c) exactly fits into it, and the screw will rise or fall according to which way it is turned. This hollow cylinder is called the nut or female screw.

d

Fig. 79.

It is evident that, if we are to gain any power, the nut must not be allowed to turn together with the screw; and hence we have different modes of using the screw, according as the screw itself or the nut is fixed. When used to fasten the

beams of a house together, or to strain the wire of a fence, the screw is prevented from rotating, and the nut turned by a wrench; the screw is thus drawn forward, and the required strain applied. In a carpenter's vice, on the other hand, the nut is fixed, and the pressure applied by turning the screw. The gain is in each case just the same, the difference being merely one of convenience in applying it.

Now we shall easily be able to see the amount of power gained. If a particle be placed at the point of a screw and prevented from turning with it, it will, after one revolution of the screw, have been raised through a distance equal to that between two threads of the screw, while any point in the circumference of the screw will have passed through a space equal surface of the screw, it will bear the same proportion to the to that circumference. If, then, the power be applied at the resistance that the distance between two threads of the screw

[graphic]

does to its circumference.

In practice, however, the power is nearly always applied at the extremity of a lever, as at d in Fig. 79 a, so that it becomes a combination of the lever and inclined plane. In a thumb-screw the flattened part acts as a lever, and when a screw is driven by a screwdriver we usually grasp it at the broadest part, and thus gain a leverage. More commonly, however, a long lever is put through the head of the screw.

fundamental principle of virtual velocities. Hence, we have the In all such cases we can easily ascertain the gain from the following rule:-Measure the circumference of the circle de

scribed by the power, and divide this by the distance between two threads of the screw; the result will be the mechanical gain.

Thus, if the power describe a circle whose circumference is 10 feet, and the distance between two threads be inch, we have a gain of 10 feet divided by inch, or 480. . There is, however, a difficulty here. We cannot easily measure the actual space through which the power passes, nor can we calculate it with absolute

[ocr errors]

accuracy. It is, however, usually near enough if we take the circumference as 3 times the diameter. but you may always use 34 without The fraction is more exactly 3.14159, being far wrong. Thus, if the radius of a circle be 2 feet 6

Fig. 80.

inches, its diameter is 5 feet, and its circumference 3 times 5 feet, or about 15 feet 8 inches. We see then, now, how to work a question like the following:-In the screw of a bookbinder's press there are 3 threads to an inch, and a force of 10 pounds is applied to a lever 14 inches long. What force are the books pressed with? The gain is 14 x 2 x 3 divided

« AnteriorContinuar »