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Of, course, as before explained, when we speak of the power Thus, if there are five pulleys, the gain is 2x2x2x2x2, that multiplied by the distance, we mean the product of the two is, 32. You must be careful, in calculating this, not to count the numbers which represent the number of units of weight in the fixed pulley, as that has no effect. power, whatever they be, and the number of units of length In the second system of pulleys, instead of each having a in the distance.
separate cord, the same one passes round In the case above let p p' be 5 inches, w w' will be 1 inch, all, and they are arranged in two blocks, and 3 (the number of pounds in the power), multiplied by 5 (the one of which is fixed and the other (usually number of inches through which it has passed), is equal to 15 | the lower) is movable. Fig. 73 represents multiplied by 1. This equation, as it is called, is plainly true, this system. One end of the cord is here each product being 15.
fastened to the hook A on the fixed block, This principle, which is called the LAW OF VIRTUAL VELO- and it then passes in succession round the CITIES, is the fundamental principle in mechanics, and holds pulleys B, C, D, E, F, and G. In this case good in all the mechanical powers. On account of its import the weight is supported by six folds of the ance, it has been called the Golden Rule of Mechanics.
same cord, and each bears an equal part, We will now trace its application to the wheel and axle, the cord being equally strained throughout. which is, in reality, only a modification of the lever, being an Each part, therefore, sustains a portion of arrangement whereby an endless succession of levers may be the weight equal to P, and w is therefore six brought into play, for any two radii of the wheel and axle in times as great as P. the same straight line may be considered as a simple lever.
If we take away one pulley or sheave, as If the power be slightly increased it descends, and, when the it is called, from the lower block, leaving wheel has turned just once round, will have fallen through a two only, the weight will be divided bespace equal to the circumference of the wheel. In the same tween four folds of the cord, and thus only time, the weight will have been raised through a space equal to four times the weight of P will be supported. the circumference of the axle. But the circumference of circles Similarly, were we to add another sheave to always bear the same ratio to one another that their radii bear. each block, we should have a mechanical ad. If, then, the radius of the wheel be 12 inches, and that of the vantage of 8. We see then that, in this axle 3 inches, the power will pass through four times as great a system, the advantage is always twice as space as the weight, but will only be one-fourth of it.
great as the number of pulleys in the
movable blocks. COMPOUND PULLEYS.
We have in this calculation supposed the We are now in a position more clearly to understand the cords to be parallel. They are not, however, remaining mechanical powers. We have explained the principle
_strictly so, still the difference Fig. 73. of the simple pulley, and seen how to find out the advantage
is so slight we need not notice gained by it, both when the cords are parallel and when they
it. A trifling loss of power, however results from it. are inclined at an angle. But there are various combinations
Now there is one disadvantage about this sysof fixed and movable pulleys which are called compound pulleys,
tem when made as shown in our illustration, and and are very frequently used in ships and in raising heavy
that is, that the weight must, on account of the weights, or exerting powerful strains. We must examine the
length of the blocks in which the pulleys are set, principle of these, and see how to ascertain the advantages
be a long way below the point to which the gained by using them.
upper block is fixed. If we are using it, for They are usually classed in three systems.
instance, to strain a telegraph wire or to tighten In the first system, which is represented in Fig. 72, each
a rope in the rigging of a ship, purposes for pulley hangs by a separate cord, and all
which blocks are constantly employed, we should are movable, at least all that have any
fasten our rope to the hook from which w hangg, G F E effect, the runner, D, being introduced
and fasten the fixed block to the “ dead eye” on merely for the sake of reversing the direc
the side of the ship; but then we should not be tion in which the power acts.
able to bring the rope within some considerable Now let us try and see what is the
distance of the eye. Another form of this same ratio the power bears to the weight when
system has therefore been contrived which obthe system is in equilibrium. We will
viates this difficulty. This is shown in Fig. 74. suppose, for the sake of simplicity, that Fig. 74. Here the required number of sheaves, three in the power applied to P is 1 pound. The
the present case, are fixed side by side in each
CF, that is, 4 pounds. But the weight, several. This will be understood from Fig. 75.
A E, or rather by these two parts of simple sheaves increasing in size were laid on the same cord, and as each has a strain of 4 pounds, the each other. A little attention will show that total weight supported is 8 pounds. In this case then, there for every inch the weight is raised 1 inch of cord is a gain of 8, a power of 1 pound balancing a weight will pass over the smallest pulley, and as the of 8 pounds. Similarly, if another pulley were added, a power cord from this to No. 2 must also be shortened of 1 pound would balance a weight of 16 pounds, each additional an inch, 2 inches will pass over No. 2. In like
Fig. 75. pulley doubling the weight supported; and thus we have the fol. manner 3 inches must pass over No. 3. Their lowing rule for determining the gain in the first system of sizes must therefore be in the proportion of the numbers 1, 2, 3, pulleys :
etc., or else the cord will grate on the pulleys. This is another Multiply 2 by itself as many times as there are movable pul- illustration of our fundamental law; and we see further that, if leys; the result will show the mechanical gain.
| the weight is to be raised 1 inch, each of the cords supporting
it must be shortened by that amount, so that in this case Pl Some of these adjectives are also used with the accusative mast fall 6 inches to raise w 1 inch; but a power of 1 ( 124. 2. Obs.), as :-30 bin tas Ochen nicht gewohnt, I am not. pound will balance a weight of 6 pounds; therefore, here also, accustomed to walking. Gr ift es mekbe, he is tired of it. the power multiplied by the distance through which it moves is equal to the weight multiplied by its distance.
VOCABULARY. These two systems are those in most general Ad'erbau, m. agricul. ! Fromin, devont, pious. Schulb, f. fault, guilt. use. We must, however, just look at the third ture.
Geizig, covetous. Schuldig, guilty. system, which is represented in Fig. 76. B is a An'flagen, to accuse. | Geschmit', n. gossip. | Summe, f. sum. pulley fastened to the cord B D, which passes Bar, m. bear. Gefin vig, confess-i That, f. deed. over the runner A, and is made fast to the Deparf'tig, wanting, ing.
Thron, m. throne. weight at the other end; c is likewise fixed to needy.
| Handwert, n. handi-' Lüchtig. well quali2 cord which passes over B to the weight; Begleitten, to accom- craft, trade.
fied. a third cord passes over c, and p acts at the pany, guide. Haut, f. skin, hide. Ueberbrüssig, weary, extremity of this. Each cord is thus fastened Benö'thigt, in want of. Gelfen, to help. disgusted. to the weight. Now in this case it is rather Beute, f. booty, prey. Kundig (sein), (to be) Un'gewohnt, unaocusmore diffonlt to find the advantage gained, as Bevor', before.
acquainted (with). ! tomed. the weight is not shared equally by the three Bewußt, conscious lantgut, n. farm, es- Un'fundiz, unac1 2 L cords. The first cord is stretched by P, which, (of).
quainted with. as before, we will call 1 pound; the part c F, Boden,m. ground, soil. Land'leben, n. country Un'werth, unworthy. therefore, supports 1 pound of the weight. The | Vije, m. wicked (pez- life.
Verbådy'tig.snspected. next cord is stretched by the tension of the son).
Nachste, m. neighbour. Vertrin'ten, to spend two parts of the first, and its strain is there. Dienft, m. assistance, ! Niemals, never, at no (for drink). fore 2 pounds, which is the portion of the service.
Berüben, to commit. weight it gustains. Similarly the tension of Freundschaft, f. friend. Richter, m. judge. Werth, worthy. Fig. 76. the cord which passes over the pulley A is 4 ship.
| Schießen, to shoot. Zukunft, f. future. pounds, and therefore the entire weight supported by p is the sum of 4, 2, and 1, that is, 7 pounds. Were
RÉSUMÉ OF EXAMPLES. another pulley added, p would in like manner support 8+4 Die der Regerei' an'geflagten Per. The persons accused of heresy +2+1, or 15 pounds.
so'nen mußten in der Vorzeit ben were compelled in (the) for. This, then, completes the description of the different systems Feu'ertod erleiften.
mer times to suffer death by of palloys. Try now and work out the following examples of the
fire. different mechanical powors as far as we have gone. In me- | Der Arme, ter einer Sache bedürftig The poor (man) who is destitute chanics, as well as in everything else, practice makes perfect, ist, ist gewöhn'lich auch einer an- of one thing is commonly also and the only way to become fully acquainted with its principles dern benö'thigt.
(needy) in want of another. is to try their application to the various cases in which you Wenn das Pfert fich seiner Stärfe If the horse were conscious of meet with them. You can easily find plenty of examples to try beivußt' wäre, fönnte es Niemand his strength, none could con. in addition to those given hore.
Nur ber'jenige, welcher tüchtig in Only he (the one) who is well EXAMPLES.
seinem Beruf' istfann seines qualified for his calling can 1. With what force must a man press on a lever, the total length of 1 Lebeno froh werden.
(be glad of) enjoy his life. which is 4 feet 4 inches, in order to raise a weight of 888 pounds, the 3ch bin meiner Sacbe gewiß' und bed I am sure of my cause, and acfulcrum being 4 inches from the end ?
Weges fundig. 2. Two boys are on a sec-9aw, one weighs 72 pounds, the other 51
quainted with the road. pounds; if the plank be 14 feet long, where must the fulcrum be placed
| An tas Fahren gewöhnt', werde ich Accustomed to ride, I soon befor them to balance each other?
balt bes Gebens müte.
come tired of walking. 3. Three men are weighing an anchor with a capstan. Two have Schuldig oter nicht schuldig eines Guilty or not guilty of a crime, spokes 4 feet long, the third has one 5 feet 6 inches long. The radius Verbrechend, feber wurde vers every one was condemned. of the axle is 6 inches. How much strain do they exert on the cable urtheilt. when each presses with a force of 100 pounds ?
Der Jäger ift seines Zieles ficher. The hunter is sure of his aim. 4. A man with a winoh 18 inches long turns a pinion with 6 teeth,
Ich bin jeßt meines Lebens über. I am now weary of my life. this works in a wheel of 60 teeth, carrying another pinion with 8, which drives & wheel with 54; round the axle of this the cord passes.
If ner sich it bed Diebftabte der A thief is guilty of (the) ther, the radius of the axle be 4 inches, what force must be exerted to raise a weight of 2 tons !
Mörter des Mortes, und in einem a murderer of (the) murder, (The radii must here be considered as proportional to the number
tempo'tischen Lande, cine frei beite. and, in a despotic country, of teeth.)
liebende Seele des Hochverrathể liberty-loving soul of high 5. In the simple pulley (Fig. 69), if the angle a ubis 90 degrees, | schulrig.
treason. and the power is 49 pounds, what weight can be supported ?
Mancher Mensch verbringt' sein le Many a man wastes his life um6. In the second system, when there are four movable pulleys, how ben un'eingetenfreiner e'
wigen mindful of his eternal des many pounds must I pull with to overeome a resistance of 7 hundred.
tiny. weight, and how far must the power move to raise the weight 6 inches?
Wenn er nur seiner Schuld gestän'. If he would only confess (wers 7. In the third system, with 5 pulloys, what weight will 5 pounds support; and how strong must the middle rope be ?
tig wäre, ich wollte ihm gern ver. confessing, etc.) his guilt, I 8. If a cask weighing 150 pounds be suspended from a pole 8 feet zei'ben.
would gladly pardon him. long, and carried between two men on their shoulders, if the point of suspension be 3 feet from the front man, how much of the weight will
EXERCISE 90. ench bear?
1. Ich bin einer solchen Arbeit ungewohnt und würde sie nicht thun, WEIR
ich nicht tes Velbed bedürftig wäre. 2. 3d bin einer großen Summe LESSONS IN GERMAN.-XXV.
Feltes benöthigt; helfen Sie mir, ich bin 3brer Gilfe gewiß nicht unwertp.
3. Wenn er eingebent meiner Wohltbaten wäre, würde er nicht so handia. SECTION XLVII.-ADJECTIVES REQUIRING THE
4. Dieser Mensch ist so schlecht, daß ich ihn jeter That fåbig halte. 5. GENITIVE.
Glauben Sie, daß ein Geiziger seines Lebens frob sein fann? 6. Id will ADJECTIVES in German that require the genitive, generally
German that require the genitive, generally gern meiner That geständig sein, laß mich nur laufen! 7. Der Jager with answer to our adjectives followed by the preposition "of” ($ 124), seiner Beute so gewig, daß er die Haut des Bären vertranf, bevor er ibn go 88 -3 bin der Sache gewiß, I am sure of the matter. Er ist seiner schossen hatte. 8. faß mich jekt gehen, ich bin seines Gestwäres berzha Blir eingebent, he is mindful of his duty. Sie find beiner Freunt. müte. 9. Out, wenn Sie meiner überbrüifig find, werde ich gehen
bia, they are unworthy of thy friendship. They are Miemals werde ich mich einer That schuldig machen, welche midy ghe 1t rendered by adjootives followed by the preposi- freundschaft unwürdig machen würde. 11. 3ch befiße ein Lantgut,
"to," as:--Er ist tes Weges funcig, he is ac ungewohnt der Arbeit, und unfuntig tes Aderbaucs, bin ich dcjelben uit las knowledgo of) the road. Es ist nicht ter Mühe trüffig. 12. Giner ift des Andern werth, aber auch oft Giner bes vorth the trouble.
| unwerth. 13. Ein König, der das Bolt nicht liebt, ist der Thrones us
man's horse. 13. Have you the good tailor's dress-coat? 14. No, I I can.
have this new dress-coat from the good tailor. 15. Have you this Der Hund ist seinem Herrn gehorsam The dog is obedient to his
poor weaver's cloth ? 16. No, I have cloth from the weaver. 17. Is and tankbar; warum will ber master, and thankful; why all old wine strong ? 18. No, and not all new wine is weak. 19. The Mensch ihn nicht gleich sein ? will man not resemble him ? new dress-coat is of black cloth.
LESSONS IN PEYVANSHIP_XXVIII. of as peculiarities in the formation of certain letters-peculiari.
ties so called, because they differ from the ordinary method OFFICIAL HANDWRITING.-11.
adopted for forming the letters in question. In our last lesson we spoke of peculiarities that lend a distinc. Of the four specimens of approved official handwriting that tive character to handwriting, and whieh combine to form what we have given, these peculiarities are least noticeable in Speci. may be properly termed a writer s peculiar style of writing. mens No. 2 (page 33) and No. 3, and most conspicuous in Speci. These peculiarities into which every one instinctively falls when mens No. 1 (page 33) and No. 4. In Specimen No. 3 there is he has no longer a copy-slip before him, which he is compelled to l not a single letter, except perhaps the letter T at the commenceimitate in every
ment, which de minor detail,
parts from the consist diedy of
normal form of the pecular mode
the letters of the of formatın
writing alphabet. adopted for some
In Specimen No. of the letters and
2 the chief de the genera un
partures from the pearance of the
usual form are
found in the letwhole warà asa
ter k in the word wall depensi una as were
acknowledge, and real measure 12
the letter p in the temporument
the word receipt. and habits of the
In Specimen No. water that cun
1, the letter g in vel, anges the
the words give wavio vyston
and large shows & ho person
considerable de who seem to pomen zo were
parture from the usual mode of
making this letbinoating a man's
ter, while the let character trom an
ters, thrice reimapeotion of his
peated in the handwriting It
in each case looks slovonly poreon's
more like ihe writing will pre
unu symbol & in writson sovios of SPECIMEN OF HANDWRITING APPROVED BY HER MAJESTY'S CIVIL SERVICE
ing than the letclear and weatly COMMISSIONERS.—NO. 3.
ter it is intended formod lottora i
to represent. In 06. vice verad, that
Specimen No. 4, any one who is neat in his person and precise in his habits will in the word easily, the letters e and y present differences of for writo a oarao, sprawling hand, stretching across the page in an mation, as well as the g in given and the y in formality. nromulus line of thiok and heavy up-strokes and down-strokes. From what we have pointed out, it will be readily seen how The writing of a steady, resolute, self-reliant man will, in nine these peculiarities combine to give a distinctive character to
os out of ton, show the character of the writer by the firm handwriting. On a further inspection of the specimens before was of the down stroke, and the sharp, clean manner in which us, especially Specimen No. 3, it will be noticed that the writing wok letton is defined; while a nervous, timid, irresolute man, is beautifully straight and regular in the first place; that the
The casual poor have been disa
wuch as were relieved by the Inspecs sarilor ste de store on his own responsib
such as were relieved by order of
the Parochial Board, but whose wovonly korean settlements are still undetermined.
ready to De led by
. The Medical Certifuate 19 appears to me to be sometimes
ly defined in the next place; and third ly, that compactness and neatness are im parted to the writing by the s hortness of the loops and the tailsof
NPWOIMEN OF HANDWRITING APPROVED BY HER MAJESTY'S CIVIL SERVICE COMMISSIONERS.-NO. 4. the letters
tbat er aused by impetuosity of temper or rapidity of tend above or below the body of the letters in the centre of eac af which will make a man write at such speed line. In these three points lie the principal requisites that I
one another, and are jumbled | Examiners will look for in the handwriting of candidates for the able mass.
Civil Service, and our readers may rest assured that no cand. the present lesson, two more date who, in forming his handwriting and acquiring a style upproved by Her Majesty's peculiarly his own, has succeeded in making it compact, clear, an inspection of these may and legible, need entertain the slightest fear of rejection as far what we have already spoken | as his writing is concerned.
LESSONS IN ARCHITEC
LESSONS IN ARCHITECTURE.—IV.
The most ancient monuments of Egypt ornamented with
columns are situated in the Heptanomis, an old division of the PROGRESS OR ARCHITECTURE IN EGYPT AND INDIA—THE
country which corresponded pretty nearly with the district COLUMN
called Middle Egypt by modern geographers, and which was After the rude style of building practised in early times had situated between the Delta and the Thebaid, extending from spread itself in various forms over the ancient world, true art | 24° N. lat. to 30° N. lat. These monuments exhibit speci. at last made its appearance. The great nations of
mens of the greatest simplicity, and strongly analoantiquity, as they advanced in civilisation, created a
gous to those of the Doric order. The monuments national architecture, each with a feeling and expres.
of India excavated in the rock present the same sion peculiarly its own. As soon as the stones used
principles of these primitive orders. In these two in buildings began to assume a cubical, prismatic, or
countries, which are the cradles of architecture, cylindrical form, and the square and compasses gave a
artists at first decorated their columns and their new direction to stone-cutting, architects gave wing
capitals with ornaments of which the ideas were to their imagination, because they now had the
taken from the local vegetation, to which were somemeans of realising its creations. Symmetry was
times added others borrowed from animal nature. studied in the ground-plan of their edifices; their Thus in Egypt, after having set up the simple architraves were raised upon pillars and columns; cylindrical shaft for their column, they sculptured and experience ere long taught them the strength upon it branches of the lotus, meeting each other of every stone, and the proper height of every and fastened together by fillets. The capital part of a building. Hence arose that harmony and which crowned the column was at first composed proportion which
of the bud of the elevated architeo
same flower. This ture into an art.
first id a was afterWe shall not at
wards developed in tempt to decide the
the application of question whether pillars and
vegetation of every kind to the columns were first formed in ex
ornamentation of the columns of cavations, or in separate construc
the temples and of the great tions; but it is evident that they
public edifices. Among the six were the first elements of a regular
examples of Egyptian capitals architecture that is to say, of
given in this page there is one the orders which constituted the
composed of the leaves of the first basis of architectural har
palm-tree.de mony. To the pyramidal con
Egypt, thus adorned with orders structions of Egypt and of Asia
of architecture, had its national speedily succeeded the erection
style. The numerous works upon of palaces and other edifices, in
the history and antiquities of which square and cylindrical pil.
Egypt published during the last lars formed a most essential
half-century have made us acpart: the great weight of the
quainted with its archæological materials employed requiring that
treasures, such as the temples and they should be supported at short
palaces of Thebes, the Isle of distances for the formation of in
Philæ, Karnac, Abougambul, Edfou, ternal and external galleries.
Memphis, and others; and large These single pillars could only bo
public buildings, decorated with connected at the top by architraves
numerous columns, immense pilof such dimensions as combined
lars, obelisks, and sphinxes, which the ratio of their breadth with
give to this style a peculiar chathe proportions of the supporting
racter of antiquity and grandeur, power of the co
of which mere lumns. Upon these
verbal descriparchitraves were
tion would fail placed platforms
to convey any or ceilings of flat
idea to the
In India, as
in Egypt, isomension above the former; and upon these lated columns and pillars appear to have platforms were formed terraces or flat roofs, i had their origin in subterranean excava
which were surrounded by another row of tions for architectural purposes; of these stones forming a border, and having an outward projection numerous examples are seen at Ellora, in the palace or temple which preserved the façade from the effects of the rain. I of Indra. These pillars are much shorter than those of Egypt, These were the origin of cornices and entablatures.
their bases and capitals occupying a considerable The column, in preference to the square pillar, be
portion of the height of the column, and the entacame the type of architectural proportion. Simple
blature, or rather the corona, is less accurately at first, it presented nothing but a cylindrical shaft,
traced. In cases where the Indians cut out the without ornament, and only expressing the purpose
rock for the purposes of decoration, and sculptured it for which it was originally intended. The oldest
over with various ornaments, the column assumes a specimens in Egypt are of this description; Asia
lighter appearance, and the principle of an order of presents similar specimens; and Greece, with the
architecture can be traced. whole of the West, follows the same track: thus
The excavated temples of India are numerous and proving that everywhere there is an invariable simi
extensive; the principal ones are those of Elephanta, larity in the origin of the arts. The simplicity,
Salsette, and Vellore, or Ellora. Elephanta is situated elegance, and utility of the column engaged the attention of near Bombay, on a small island of the same name, which received architects, and concentrated all the efforts of their imagination. this appellation from the figure of an elephant being cut out upon Thus it became their architectural type or model, and formed the rocks on the southern shore. The grand temple is 120 feet the nucleus of the different characteristic styles of building square, and is supported by four rows of pillars; along the side that were adopted by the great nations of antiquity.
of the cavern are fifty colossal statues from twelve to fifteen feet VOL. II.