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LESSONS IN PENMANSHIP.-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 which combine to form what we have given, these peculiarities are least noticeable in Specimay be properly termed a writer's peculiar style of writing. mens No. 2 (page 33) and No. 3, and most conspicuous in SpeciThese 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 not a single letter, except perhaps the letter T at the commenceimitate in every

ment, which de minor detail,

parts from the consist chiefly of

normal form of the peculiar mode

the letters of the of formation

writing alphabet. adopted for some

In Specimen No. of the letters and


2 the chief de the general ap

partures from the pearance of the

usual form are writing as

found in the letwhole, which last

ter k in the word will depend in a ad

acknowledge, and great measure on

the letter p in the temperament

the word receipt. and habits of the

In Specimen No. writer. On this, tor 012

1, the letter g in indeed, hinges the

the words give whole system of

and large shows & those persons

considerable de who seem to pos

parture from the

usual mode of of minutely de

making this let. lineating a man's

ter, while the let character from an

ters, thrice re. inspection of his

peated in the handwriting. It

word successful is unlikely that a

in each case looks slovenly person's


like the writing will pre

symbol f in writsent a series of clear and neatlySPECIMEN OF HANDWRITING APPROVED BY HER MAJESTY'S CIVIL SERVICE

ing than the let

ter it is intended formed letters; COMMISSIONERS.NO. 3.

to represent. In or, vice versa, 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 forwrite a coarse, sprawling hand, stretching across the page in an mation, as well as the g in given and the y in formality, irregular line of thick 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 cases out of ten, show the character of the writer by the firm handwriting. On a further inspection of the specimens before ness of the down-stroke, and the sharp, clean manner in which us, especially Specimen No. 3, it will be noticed that the writing each letter is defined; while a nervous, timid, irresolute man, is beautifully straight and regular in the first place; thet the who is

letters always ready to

shaped be led by

and clearothers in stead of

in the next taking

place; the lead, generally betrays

compact his constitutional

neatnesa failingsby

mee the irre. gularity of

the writhis writing, which,

shortness however,

of the must not be con.


that es irregularity caused by impetuosity of temper or rapidity of tend above or below the body of the letters in the centre of each thought, either of which will make a man write at such speed line. In these three points lie the principal requisites that the that his letters seem to run into one another, and are jumbled Examiners will look for in the handwriting of candidates for the together in an almost indistinguishable mass.

Civil Service, and our readers may rest assured that no candiWe place before our readers, in the present lesson, two more date who, in forming his handwriting and acquiring a style specimens of official handwriting approved by Her Majesty's peculiarly his own, has succeeded in making it compact, clear, Civil Service Commissioners, and an inspection of these may and legible, need entertain the slightest fear of rejection as far enable us to point out examples of what we have already spoken as his writing is concerned.


are well

ly defined

and, third ly, that

The Medical Certificate appears to me to be sometimes

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The most ancient monuments of Egypt ornamented with

columns are situated in the Heptanomis, an old division of the PROGRESS OF 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 rade 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 speciat last made its appearance. The great nations of

mens of the greatest simplicity, and strongly analoactiquity, 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 sich 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 bad of the elevated architeo

same flower. This ture into an art.

first idea 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. 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 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, Abousambul, Edfou, ternal and external galleries.

Memphis, and others; and large These single pillars could only be

public buildings, decorated with connected at the top by architraves

numerous columns, immense pil. of 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

tion would fail placed platforms

to convey any or ceilings of flat

idea to the
stones, which, by

their thickness,

In India, as
formed a new di-

in Egypt, isomension above the former; and upon these lated columns and pillars appear to have platforms were formed terraces or flat roofs, 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 tha cavern are fifty colossal statues from twelve to fifteen feet





high. The face of the great bust is five feet long, and the breadth image of Juggernaut, or Mahadeo, stands in the contre of the across the shoulders twenty feet. At the west end of this pagoda, building, upon an elevated altar. The idol is described as or temple, is a dark recess twenty feet square, without ornament; being an irregular pyramidal black stone, and the temple lit up the altar is in the centre, and there are two gigantic statues at only with lamps. each of the four doors by which it is entered. On entering In the ancient Hindoo writings, another kind of temple is Elephanta, there is a piazza extending sixty feet from east to described, of which now no vestige is to be found. The Ayeen west, and baving a breadth of sixteen feet; indeed, the body of Akberry relates that near to Juggernaat is the temple of the the cavern is surrounded on every side by similar piazzas. The sun, in the erection of which the whole revenue of the province caves of Kenneri, on the larger island of Salsette, in the same of Orissa, for twelve years, was entirely expended; that the vicinity, and those of Carli, on the opposite shore of the conti- wall which surrounded the whole was 150 cubits high, and nent, are equally remarkable. The mountain of Kenneri appears nineteen cubits thick; that there were three entrances : at the to have had a city hewn out of its rocky sides, capable of con- eastern gate were two elephants, each with a man on its trunk; taining many thousand inhabitants. The front is hewn into on the west, two figures of horsemen completely armed ; and four storeys or galleries, in which there are 300 apartments; over the northern gate, two tigers sitting over two dead elethese have generally an interior recess or sanctuary, and a phants. In front of the gate was a pillar of black stone, af small tank for ablution. The grand pagoda is forty feet high an octagonal form, fifty cubits high; and after ascending nine to the soffit of the arch or dome; it is eighty-four feet long, flights of steps, there was an extensive enclosure with a large and forty-six broad. The columns of the portico are finely cupola constructed of stone, and decorated with sculpture. decorated with bases and capitals; and at the entrance are two Such are the ancient monuments of which India can boast, long colossal statues, each twenty-seven feet high. Thirty-five pillars before architecture had reached that proud eminence on which of an octagonal form, about five feet in diameter, support the it stood in ancient Greece. In our next lesson we shall glance arched roof of the temple; their bases and capitals are com- at those of Persia. posed of elephants, horses, and tigers, carved with great exactness. Round the walls are placed two rows of cavities for receiving lamps. At the farther end is an altar of a convex

LESSONS IN GREEK.-III. shape, twenty-seven feet high, and twenty feet in diameter; GENERAL REMARKS ON THE NOUN, THE ADJECTIVE, AND round this are also cavities for lamps; and directly over it is a

THE PREPOSITIONS,-THE DEFINITE ARTICLE. 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. Nouns or Substantives are names of objects or things which The cave-temple at Carli is even on a greater scale than now exist in space or in the mind. There are, in Greek, three described. But the temples of Ellora, near Dowlatabad, are genders ; the masculine, to denote the male sex; the feminine, reckoned the most surprising and extensive monuments of to denote the female sex; and the neuter (Latin neuter, neither), ancient Hindoo architecture. They consist of an entire hill to denote objects which are neither male nor female. The excavated into a range of highly-sculptured and ornamented genders are distinguished partly by the sense and partly by temples. The number and magnificence of these subterranean the terminations of the nouns. There are terminations, for edifices, the extent and the loftiness of some, the endless diver- instance, which denote the feminine gender, as n; there are sity of the sculpture of others, the variety of curious foliage of other terminations which denote the masculine gender, as as in minute tracery, the highly-wrought pillars, rich mythological the first declension; and, again, there are others which denote designs, sacred shrines and colossal statues, all both astonish the neuter gender, as ov. This is a peculiarity to which we and distract the mind of the beholder. It appears truly wonder- have nothing similar in English adjectives. Those who have ful that such prodigious efforts of labour and skill should studied Latin are already familiar with it. In regard to gender remain, from times certainly not barbarous, without a trace to as denoted by the meaning, let the ensuing rules be committed tell us the hand by which they were designed, or the populous to memory. and powerful nation by which they were produced. The courts 1. Of the masculine gender are the names of male beings, of of Indra, of Juggernaut, of Parasu Rama, and the Doomar winds, of months, and of most rivers, as :-Matwv, Plato; Leyna or nuptial palace, are the names given to several of Zepupos, the west wind; Exatoubaiwy, the month Hecatombæon ; these great excavations. The greatest admiration has been Evpwras, the river Eurotas. excited by the one called Keylas, or Paradise, consisting of a 2. Of the feminine gender are the names of female beings, of conical edifice, separated from the rest, and hewn out of the trees, of lands, of islands, and of most cities, as :-Kopn, a girl

; solid rock, 100 feet high, and upwards of 300 feet in circum- spus, an oak; Apradia, Arcadia ; neobos, Lesbos ; Konopa, ference, entirely covered with mythological sculptures.

Colophon. Besides the excavated temples of India, there are several 3. Of the neuter gender are the names of fruits, the diminuothers of different forms which may here be noticed. First, those tive in ov (except the female proper name ý neortlov), the names composed of square or oblong enclosures ; secondly, temples in of the letters of the alphabet, the infinitives, all words not de the form of a cross; and thirdly, temples of a circular form. clinable in the singular and the plural, and every word used

Of temples of the first kind, the largest one remaining is that merely as the sign of a sound. of Seringham, near Trinchinopoly. The circumference of the

4. Of the common gender are personal nouns which, like our outward wall is said to extend nearly four miles. The whole child, may be applied to male or female ; thus, eos may be edifice consists of seven square enclosures, the walls being 350 used of a male or female divinity, and so be rendered either god feet distant from each other. In the innermost spacious square

or goddess. are the chapels. In the middle of each side of each enclosure This common gender" is a grammatical phrase used to wall there is a gateway under a lofty tower ; that in the outward denote such nouns as are common to both males and females ; wall, which faces the south, is ornamented with pillars of that is, are sometimes masculine and sometimes feminine. precious stones, thirty-three feet long, and five feet in diameter. Of temples of the second kind—namely, those in the form of order to indicate the gender. The definite article, nominativa

In Greek grammar it is usual to employ the definite article, in a cross-the most remarkable is the great temple in the city of singular, is 8, n, to, the ; & is masculine, feminine, and to Benares, on the banks of the Ganges, which has been devoted neuter;' , therefore, put before a noun, intimates that the to the religion and science of the Hindoos from the earliest noun is of the masculine gender; , that the

noun is of the periods of their history. The form of the temple is that of a feminine gender; and to, that it is of the nenter gender

. great cross with a cupola in the centre, which towards the top If both o and ń are put before a noun, it is done to show that becomes pyramidal. At the extremity of each branch of the the noun is of the common gender : thus, d amp, the man; crogs, all of which are of equal length, there is a tower with n yuvn, the woman; to epyov, the work ; d, , Deos, the male or balconies, to which the access is on the outside.

female) divinity; o, ý, mais, the child, whether boy or girl. 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 Number is a distinction of nouns founded on the circum. lived, according to their chronology, 4,800 years ago. The stance whethor they denote one or moro. If a noun denotes

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Ev, in.

one object, it is in the singalar number; if a noun denotes woman, being changed into nouxoy before the neuter tekvov,
more objects than one, it is in the plural number. The Greek child. An adjective of three terminations may be seen in this
tongue has a third number, called the dual (Latin duo, two), example :-
which denotes two objects; thus, Loyos is a word (singular);


Aoyou, words (plural) ; doyw, two words (dual); where os is the

και αγαθος ανήρ,

η αγαθη γυνη, singular termination, or the plural termination, and w the dual

το αγαθον τεκνον, termination,

the good man. the good woman. the good child. CASE.

Some adjectives have only one termination, as uakpoxeup, longThese terminations, os, oi, w, undergo changes according to handed; anatwp, without a father. In declension, adjectives, the relation in which they staní to a verb, to another noun, or with a few exceptions, follow the forms of the substantives. to a preposition. Thus os may become ov, and ou may become ous. Any word which is changed in form, to express a corresponding change in sense, is said to be inflected. Such inflexions relation which the nouns bear to the affirmation or negation

Prepositions are words which go before nouns, and show the or variations in the endings of nouns are termed cases. There

made in the sentence, or the member of the sentence in which are in Greek five cases, namely 1. The Nominative, the case of the subject; as, ó ratne present some knowledge of them must be communicated, in

they stand. Of prepositions I shall treat in full hereafter. At Ypaper, the father writes. 2. The Genitive, the case indicative of origin, whence; as, & Tou the words

order to prepare the beginner for the following instructions. In Tatpos úros, the father's son.

πορευομαι προς 3. The Dative, the case indicative of place, where, and of the

πατερα, ,

the father, manner, and instrument; as, TW TOU natpos viv, to the father's

the word mpos, to, is a preposition. 4. The Accusative, the case of the object, or whither; as, ó In Greek, prepositions govern either one case, two cases, or TATTP TOV úlov ayana, the father loves the son.

three cases, and may accordingly be classified thus :-
5. The Vocative, the case of invocation, or direct address; as,
αγαπα, πατερ, τον υιον, father, love thy son.

One Case.
Two Cases.

Three Cases. In Greek there is no ablative case ; the functions of the abla

tive case are discharged, partly by the dative, and partly by the
genitive. The nominative and the vocative are called recti, Ayti, in presence of, | Ara, through. Audi, about.
direct; the other cases are called obliqui, indirect.

instead of.
Kata, down.

Eri, upon.
Substantives and adjectives of the neuter gender have the Ato, from.

Υπερ, for.

Meta, with. nominative, the accusative, and the vocative alike, in the singu. Ex, out of.

Mapa, from. lar, the plural, and the dual.

Eveka, on account of.

Teps, concerning. The dual has only two case-endings; one for the nominative, mpo, before, for the

Mpos, with or from. accusative, and vocative, the other for the genitive and dative.

good of.

"Tло, by.


Apoi, around.
Declension is the classification of nouns and adjectives agree- Zuv, with.

Emi, on. ably to the variations of their case-endings. There are, in

Meta, amidst. Greek, three declensions; called severally, the first, the second,

Hapa, by, near (of and the third declension. The learner will do well in regard to

rest). every noun and adjective, to ask himself, What is its nomina

Περι, around. tive? What is its case ? What is its number? What is its

Npos, at (of rest). gender? What is its declension ?: For instance, Tpareçats is

"TTO, under (of rest). from the nominative apareca, a table, is in the plural number,

Accusative. dative case, feminine gender, and of the first declension. In

Αμφι and Περι, about order to practise and examine himself fully, he should also form Ava, up.

Ala, because of.

Eni, to. OF "go through" every noun, adjective, tense, mood, and indeed Eis, into.

Kara, down, through. Meta, after. every word capable of declension or conjugation, according to 'ns, toward.

Υπερ, over.

llapa, by the side of. the several models or paradigmas given in the successive lessons.

Npos, to (of motion).

Tro, under (of moTHE ADJECTIVE. An adjective denotes a quality. This quality may be con

tion). sidered as being connected with, or as being in an object, as "the A glance at this table will show that the case which in any red rose;" or as ascribed to an object, as the rose is red." In example a preposition is connected with, has much to do in both cases the adjective in Greek, as in Latin, is made to agree modifying its signification. Only by constant practice can the in form, as well as in sense, with its noun. A change takes exact meaning and application of the several prepositions be place in the adjective, conformably to the change in the signifi-known. The Latin student will, in this list, recognise words cation, thus, a good man is ayados amp, but a good woman is with which he is familiar; thus ek is the Latin ez; ev is the ayaon porn. Observe the os of the masculine is for the feminine Latin in; apo is the Latin pro; ano is the Latin ab; útep is the changed into n.

Not only in gender, but in number and in case Latin super; and ino is the Latin sub. does the adjective in Greek, as in Latin, conform to its noun : Before I treat of the declension of nouns, I must give the 6.9., 8 ayados av pwros, Latin, bonus homo, the good man; o definite article, as it is so intimately connected with nouns that ex@pwros COTIV ayados, homo bonus est, the man is good; ý kann the latter cannot well be set forth without the former ; and as Movoa, pulchra Musa, the beautiful Muse; À Movớa eÓTI ran, the article is often used as indicative of the gender of the noun. Musa pulchra est, the Muse is beautiful; to kalov cap, pul

THE DEFINITE ARTICLE, ,, ý, to, the. chrum ver, the beautiful spring ; to eap COTI kalov, ver pulchrum est, the spring is beautiful.

Singular. The adjective, then, like the substantive, has a threefold

Mas. Fem. Neut. English. gender-the masculine, the feminine, and the neuter. But many Nom. d

the. adjectives, such as compound and derivative, have only two ter- Gen.


of the. minations ; one for the masculine and feminine, and another for Dat.

τη To

to or by the


Nom. de åt

ή ήσυχος γυνη,
το ήσυχον τεκνον, ,

of the. the quiet man, the quiet woman. the quiet child.

to or by the. Here houxos remains the same with amp, man, and youn,

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the neuter; e.g.:



και ήσυχος ανήρ,














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Mont Cenis, the trains go along a series of zigzags, which are Nom. Acc. TW


really a succession of inclined planes, and thus the mountain Gen. Dat.

of or to the. chain is crossed. A driver, too, in driving a heavy load up a There is no form for the vocative; w, which is commonly steep incline will frequently cross from side to side of the road, used, is an interjection. The way to learn the article (as well

as he goes up a less steep incline, and thus spares the horses. as the adjective) is to repeat the parts first perpendicularly, d,

How comes it, then, that this advantage is gained, and what Tou, T4, Tov, etc., and then horizontally, as 8, ý, ro, until you proportion does the load bear to the power that raises it? We are perfectly familiar with the whole. When you think you

will try and solve these questions. Let A c represent a plane have mastered the task, examine yourself by asking, What is inclined at the angle c AB; W

Як the accusative singular, feminine gender? What is the nomina- is a weight resting on the plane tive plural, mascaline gender ? etc.; and when you have given and fastened to a cord which an answer from memory alone, consult the book, to ascertain passes over the pulley D, and whether you are correct. Finally, write out the article in full is kept stretched by a power, from memory.

The cord we will first supIndeed, spare no pains to make yourself master P. of the article. There is a special reason for this advice, since pose to be parallel to the sur.

Fig. 77. the terminations of the article are, in the main, the same as the face of the plane, and the terminations of the noun and the adjective.

power therefore acts in this

direction. Friction has, in practice, a great influence in a KEY TO EXERCISES IN LESSONS IN GREEK.-II,

case like this ; as, however, we shall speak about that shortly,

we will neglect it now, and suppose that the plane is perEXERCISE 1.-GREEK-ENGLISH.

fectly smooth, and that the weight is just kept in its position 1. Always be true. 2. Rejoice ye (xapw, I rejoice). 3. Follow, 4. by the action of P. We found in our third lesson that, if we Do not complain. 5. I live pleasantly. 6. I am well educated. 7.

draw a line, G E, downwards from G, the centre of gravity of w, Thou writest beautifully. 8. If thou writest ill, thou art blamed.

and make it of such a length as to represent the weight of w, 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.

and then through E draw E F parallel to G D, and just long If we flee, we are pursued. 15. You flee badly (like cowards). 16. If enough to meet the line G F, which is perpendicular to the you are idle, you are blamed. 17. If you fight bravely, you are ad- surface of the plane, that then EF represents in magnitude the mired. 18. If they flatter, they are not true. 19. It is not well to power P. We have, in fact, a triangle of forces, the three sides fee. 20. It is well to fight bravely. 21. If thou art pursued, do not of which represent the three forces which act on the weight and flee. 22. Fight bravely. 23. If they are idle, they are blamed. 24. If keep it at rest. But the angles of the triangle E F G are equal thou speakest the truth, thou art believed. 25. Always excel.

to those of the triangle C B A. This is easily seen, for the Eat and drink, and play, moderately.

angle E F G is equal to C B A, each being a right angle. GEF EXERCISE 2.-ENGLISH-GREEK.

is also equal to A C B; for, if we continue E F till it meets 1. Αληθενω. 2. Αληθευεις. 3. Αληθευει. 4. Αληθευομεν. 5. Αληθευετε. | B C, we shall have a parallelogram, and these will be opposite 6. Αληθευουσι. 7. Ει αληθενω πιστευομαι. 8. Mn Maxeobe. 9. Maxovta.. angles, and so must be equal; the third angles are equal too, 10. Επεσθε. 11. Επη. 12. Επεσθε. 13. Παιζει. . 14. Devyovor. 15. Es since G F and E G are perpendicular to a C and A B. The angles φευγουσι διωκονται. 16. θαυμαζομαι. 17. θαυμαζονται. 18. Ει βλακευουσιν | of one triangle are equal, then, to those of the other, and thereου θαυμαζονται. 19. Εν εχει ανδρειως μαχεσθαι. 20. Μετριως εσθιε και πινε. | fore the sides of the triangle EFG bear the same proportion to 21. Ου σπευδoυσι. 22. Ε: κολακευεις ον θαυμαζα. 23. Καλως γραφει. 24. one another that those of C B A do. Of this you can satisfy Γραφονσι κακως. . 25. Ευ εχει αει αριστενειν. 26. Metplws Biotevete. 27. yourself by actual measurement, and you will find the rule Αγαν εσθιουσι. .

always hold good. The proper mode of proving it, you will

learn from Euclid. MECHANICS.-XII.

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 INCLINED PLANE-THE WEDGE-THE SCREW.

the resistance of the plane, or the part of the weight which is THE mechanical powers are usually said to be six in number :- supported by it. Hence we see that if the incline be 1 foot in the lever, the wheel and axle, the pulley, the inclined plane, 20, a man in rolling a weight up will only have to support the wedge, and the screw. On examination, it will be found of it. that any machine whatever consists of various combinations or We can easily arrive at this result in another way. Suppose modifications of these. If, however, we look more closely, we a person wants to lift a weight of 200 pounds to a height of shall find that these six may really be reduced to three, namely, one foot, he will have to exert a force of that amount if he lift it the lever, the pulley, and the inclined plane.

straight up,

and will then move it through just one foot. But These, then, are the three fundamental mechanical powers; if, instead of this, he moves it up this incline, when he has the wheel and axle being, as we saw in our last lesson, a suc- passed over one foot in length of its surface, he will only have cession of levers coming into play one after another; and the raised it be of a foot, and will have to move it over the whole wedge and the screw, as we shall soon find, merely modifica- twenty feet of the plane in order to raise it the one foot

. tions of the inclined plane. To this, then, we must now turn That is, he will have to move it twenty times the space be our attention, and see how the inclined plane may be used as a would if he lifted it direct, and will therefore sustain only mechanical power, and what is the advantage gained by its use. of the weight at any moment. Still, he must sustain this

A horizontal plane is one that has an even surface, like a portion twenty times as long. This supplies us with another portion of the surface of a lake

on a calm day, every

part being illustration of the low of virtual velocities which we explained at the same level. If this plane be now tilted or lifted at one in the last lesson. end, so as to make an angle with the horizon, it is called an The general rule for the gain in the inclined plane when the inclined plane, and the angle which it makes with the level power acts in a direction parallel to it, may be stated as follows: surface is called its angle of inclination. Hence we speak of The power bears the same ratio to the weight it will sustain a plane inclined at an angle of 30, or any other number of that the perpendicular elevation of the

plane does to the length degrees. There is also another way of speaking of the inclina- of its surface. tion, as, for instance, when we say a road has an ascent of one If the power, instead of acting along the plane, acts at an angle foot in twelve, meaning that for every twelve feet of length to it, whether it be parallel with the base or in any other direc

: measured along its surface there is a vertical rise of one foot. tion, as G K, we have merely to draw i parallel to the line of These modes of expressing the same fact may be used indis-action of the force, instead of parallel to the plane, and, az criminately.

before, we shall obtain a triangle of forces, the three sides of Now we can easily soe that some advantage is gained by the which represent the three forces, and thus we can calculate the use of the inclined plane. If a drayman wishes to raise a heavy power required to support the weight. barrel into his dray, he does not attempt to lift it vertically, for If we have two inclined planes meeting back to back, like the he knows he could not do it; but he lays a ladder or plank letter V inverted, and a weight resting on each, the weights sloping from the ground up to the dray, and rolls the barrel up being connected by a cord which passes over a fixed pulley at this incline. So in the railway which has been formed over the summit, we can see, from this principle that there will be

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