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place in the choroid of pigment of metallic brilliancy. This

may be well seen at the bottom of the eye of the ox inside; in THE EYE (Continued).

others, the sclerotic is coloured, as any visitor at the Zoological THROUGHOUT those classes of animals which are called verte- Gardens may see to be the case in the eye of the chimpanzee. brate, because they have an internal skeleton, the main central These diversities, with many others, such as the contraction portion of which consists of a back-bone of pieces jointed to one of the iris of the cat, so as to leave a slit instead of a circular another in a long row stretching from one end of the body to opening, are interesting, but by no means so functionally im. the other, the eye is essentially of the same structure as in man. portant as others to be mentioned hereafter, when we describe It is true there are differences in the proportion and shape of eyes suited to conditions altogether different, such, for instance, the parts, an some cases additional parts are found, while as the fish's eye, which is constructed to see in water. in others the eye is so reduced and degraded as to be of little Birds, some of which are almost exclusively denizens of the

air, and most of which have the power of betaking themselves to flight occasionally to escape pursuit, to hunt active prey, to search for new feeding-grounds, or to select a more genial climate at the change of the seasons, must have eyes suited to

distant vision. Hence the lens is of a very flattened form, and 7

does not increase in density from the outside to the inside as it does in mammalia, and more strikingly in fish. The distance from the lens to the back part of the eye is small, and to the

cornea large relatively; in other words, they have a larger 1

amount of aqueous and a smaller amount of vitreous humour' 179

than brutes have. The back part of the eye too is flatter, and 12

is a portion of a larger sphere in relation to the rest of the eye than in animals. The shape will be best seen by the aid of the diagram of the vertical section of the eye of a soaring bird.

When the eye is spherical and distended with fluid, as in man, there is no tendency of the pressure within to alter the shape of the ball; but when, as in the case of birds, it has any other form, the internal pressure would strain the elastic capsule of the eye in some parts more than in others. This strain can

only be prevented by rendering those parts of the capsule which VERTICAL SECTION OF THE EYE OF A SOARING BIRD.

are exposed to the extra pressure more solid. In the case of 1, Sclerotic; 2, Choroid ; 3, Retina ; 6, Pecten ; 4, Vitreous humour; the bird, this is effected by means of a series of bony plates

5, Bony support of sclerotic or hard coat; 6, Iris ; 7. Cornea ; which encircle the sclerotic, bedded in its substance, and & Lens ; 9, Aqueous humour ; 10, Lens ligament; 11, Ciliary pro- stretching from the rim of the cornea to the circumference of cesses; 12, Optic nerve.

the large segment of the eye, on the inside of which the retina or no nse; but in the majority of cases in brutes, reptiles, and is spread out. fishes, and in all birds, the eye is well developed, and even where The structures described above, conducive to long sight in a it can be of no use, still indications of it are found.

thin medium, are more especially to be remarked in soaring, Our English mole is an instance of an animal with a degraded raptorial birds, like the eagles, vultures, and hawks. These, as condition of eye. It is in this animal smaller than a pin's head, they wheel round at great height, survey a large extent of and has to be looked for carefully in the midst of the velvet fur. Of course, to an animal which lives underground, burrowing continually is soft earth, an eye would be useless, and even in. convenient; yet the rudiment of an eye is found.

Besides man, only apes (and some lizards, such as the chameleon, and perhaps some fish) have the yellow spot of distinct vision. Vision in some apes must be very powerful, for it is

8 suid a gentleman who owned a baboon used to ride away across the plain until he could only just see his dog-ape with the naked sye; then using his telescope, he made a number of gestures, which were immediately mimicked with precision by the animal.

In looking into the open eye the white is part of the opaque sclerotic. The coloured part is the iris seen through the transparent cornea and aqueous humour, while the pupil is the hole through the middle of this, which seems black because of the

TI dark non-reflecting choroid at the back of the eye.

The iris gives the colour to the eye. When there is only a layer of pigment on the back part of this, the eye is blue ; but when, in addition, specks or sheets of pigment are distributed through the substance of the iris, eyes of various colours are

VERTICAL SECTION OF THE EYE OF A FISE. produced. Thus, fair people have usually blue eyes, and black eyes accompany an olive complexion and dark hair. In other 1, Sclerotic ; 2, Choroid , 2, Inner layer of Choroid; 3, Retina ; Qg words, people that have a surplus of internal paint elsewhere

Choroid gland; 4, Vitreous humour; 5, Bony support of sclerotic have it in the iris too.

or hard coat; 6, Iris ; 7. Cornea; 8, Lens; 9, Aqueous humour;

10, Lens ligament; 11, Ciliary processes ; 12, Optic nerve. Again, the lack of pigment is sometimes so great that even the choroid has none, and then the pupil looks red because the country; yet their sight is so keen at that elevation that no blood-vessels of the choroid can be seen through its front layer. young unprotected animal, or maimed and disabled prey, escapes Albinos, as individuals with the last peculiarity are called, are their sight. So keen is the sight of the condor of the Andes, foand among rabbits, mice, cats, and many other species, and that if a carcase be exposed where the naked eye can detect are especially prone to occur under domestication. These none of these creatures in the horizon, yet in a few minutes creatures present an appearance which is very ethereal and they are seen streaming in from all directions straight towards fairy-like, so that artists have often intoduced them into their their hoped-for meal. fanciful pictures, as in Landseer's “Bottom and Titania.” But But though birds be long-sighted, it is also highly necessary however they may grace the ideal creation of the painter, they that they should see minute objects at a short distance. No are less suited to this working-day world than their coarser entomologist will deny that an insectivorous bird must have brothers.

keen eyes for short distances, if it is to get its living with On the other hand, in some species a further deposit takes ease. A microscopic sight is scarcely less requisite for a grain.

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feeding bird. The swallow, which plunges with such reckless in small quantity, and the result of this is that the fish can see impulse through the air, will nevertheless seize a small insect distant objects as well through the air as through the water ; as it dashes along with almost unerring certainty. Usually the and this is important, because almost all fish are surface fish; prey is so small, that the wonderful powers of the bird dis many feed on flies, and most have to be on their guard against played in the chase cannot be observed ; but sometimes, when aerial foes. The reader, then, need not be surprised when the the insect has large wings, this dexterity may be seen.

sun-loving shoals of carp or chub all plunge headlong into the The writer has seen a swallow seize, while in headlong flight, depths when he appears on the river bank. the beautiful, scarce swallow-tail butterfly, and shear out its As a singular instance of the adaptation of means to ends, sapid body from between the wide wings, and let them float it is found that all animals, whether reptiles, birds, or brutes, severally down; and then, not satisfied with a feast so little which are amphibious, or which spend much time in the water, proportioned to the splendour in which it was dished up, glance lave eyes which, though they differ from those of fish, in some round and seize again the several pieces before they had time things have the same relation of the cornea and lens. Thus to reach the ground. How, then, is a long sight and a keen the whale and the dolphin (which are but brutes which have short sight to be obtained from the same eye? This is done taken to the sea), the cormorant and diver, the frog and the mainly by the aid of the bony plates already described. These crocodile, have all spherical lenses and flat corneæ. are so disposed that the edge of one is capable of sliding over Fish and frogs have on the outer layer of the choroid a layer the edge of its next neighbour, so that when the fibres of the of silvery or golden crystals, and this layer, which is continued muscle which unites them contract they compress the eye all round till it occupies the front layer of the iris, gives to the round and make it more tubular, while the humours of the eye, toad so metallic and bright an eye as to countenance the legend thus subjected to pressure, cause the cornea to protrude more, that it has a jewel in its head. So Shakespeare — and also the retina to be removed further from the lens. These

The toad, ugly and venomous, motions are, in addition to the adjustment for distance, found

Wears yet a precious jewel in its head," in mammals.

Intimately connected with this pressure upon and alteration of the dimensions of the humours of the eye, is another pecu

LESSONS IN GERMAN.-IV. harity in the eye of a bird. This is a puckered, purse-like membrane, which is attached to the optic nerve, which in this

SECTION VIII.-INDEFINITE ARTICLE. class enters into the eye by a slit-like opening. This membrane The indefinite article is less varied than the definite, having for is sometimes called å marsupium, from its resemblance to a the masculine and neuter nominative but one form, aspurse, and sometimes a pecten, from its supposed likeness to a comb. It stretches to the interior of the eye to a different

Masculine : ein Mann, a man. Neuter : ein Glas, a glass. extent in different birds, and is composed of a tangled mass of DECLENSION OF THE INDEFINITE ARTICLE MASCULINE AND blood vessels, mixed with pigment granules. Whether this is

NEUTER WITH NOUNS. simply an erectile organ, which can rapidly contract and enlarge


Neuter. suddenly as it is deprived of or injected with blood, or is capable 9. Ein Mann, a man; ein Kind, a child; of feeding the vitreous humour with liquid strained by it from

8. Gines Mannes, of a man; eines Kindes, of a child ; the blood, and draining it off again as circumstances require, is

D. Einem Manne, to, fora man; einem Kinde, to, for a child; not known.

A. Ginen Mann, a man ;

ein Kind, child. The eyes of reptiles are so different from one another, ranging in structure between the eye of the bird and that of the fish,

OF THE COMPOUNDING OF NOUNS IN GERMAN. that it is better at once to pass on to a description of an eye 1. Nouns are more frequently compounded in German than adapted to sight in water.

in English ; and accordingly one word in German often requires A fish, living as it does in an atmosphere which is many hun- for its full translation several in English, as :dred times denser than air, and by no means so transparent,

Wirkungsfreie, sphere of action (action sphere); must have an eye suited to look at near objects. It must

Schwimmvogel, web-footed bird (swimming fowl); therefore be able to concentrate the rays of light rapidly; yet

Laftthier, beast of burden (burden animal); it is under this disadvantage, that as it is only when passing

Bugthier, draught animal (2. 7); from a rare into a dense transparent convex substance that

Haustbier, domestic animal (house animal). diverging rays are bent towards one another, and the original rays pass through a dense medium, the cornea and aqueous

VOCABULARY. humours can play no part in the bending of the rays towards Band, n. ribbon. Kaufmann, m. mer! Schmied, m. black. one another, for they are of about the same density as water. Gin, a, an.


smith. The whole duty of refraction must thus be done by the lens. Eisen, n. iron. Lastthier, n. beast of Schwert, n. sword. This is very dense, and of the sheets of which it is made up the Empfeh'lungsbrief, m. burden.

Stoc,' m. stick, cane. inside are denser than the outside, while it is so convex both

letter of recom- Oberhof'richter, m. Tuch, n. cloth. before and behind as to become a perfect globe.


judge of the supe- Tuch'handler, m. draBoth the consistence and shape of the round lens may be Feind, m. enemy. rior court.

per. seen by squeezing it out of the eye of a cooked fish, even by Geset bucy, law. Papier'handler, m. pa. Wagner, m. carriagethose whose taste for comparative anatomy is only stimulated book.


maker. at the dinner-table.

Geivehr', n. gun. Pflug, m. plough. Zugthier, n. draught In connection with this kind of lens we have a shallow eye. Kameel', n. camel.

animal. In other words, if the cornea, through which light enters, be turned upwards, tho back of the eye on which the retina is

RÉSUMÉ OF EXAMPLES. spread resembles a saucer, and not a cup as it does in animals Der Wolf ist ein Raubthier.

The wolf is a beast of prey. and birds.

Der Zim'mermann ist ein Hands The carpenter is a mechanic. This is so much the case, that even though the hard capsule werker. is shallower than in brutes, there is still left a large space Der Hammer ist ein Werkzeug. The hammer is a tool (an ir between this and the choroid, and even this latter has between

strument). two of its layers a horse-shoe shaped “gland” composed of Dan Bin'dewort ist ein Redetheil. The conjunction is a part of blood vessels, something like the pecten of a bird, though in a

speech. different place, and with exactly a converse function.

Der Name eines Dinges ist ein The name of a thing (substance) The hard outer coat is strengthened and held to its form by Dingwort.

is a substantive. a cup-shaped bone or cartilage, which occupies the parts which Das Kind liebt den Großvater. The child loves the grandfather. are left unoccupied by the bird's eye-bones; because while the

EXERCISE 9. latter are used to elongate the eye this maintains a shortened is.

1. Hat ein Mann, oder ein Kind der. Stock dieses Freundes? 2. Dieser The cornea, or window, and the watery fluid behind it being Mann hat ein Sawert eines Feindes, und dieses Kind hat den Stod eines useless to collect the rays are left, the one flat and the other | Freundes. 3. Wa8 bat der Jäger ? 4. Er hat cinen Hund und ein


Gevebr. 5. Wer hat den Pflug des Bauert ? 6. Der Bater dieses Attributive. Predicative. Kindes hat den Pflug. 7. Hat dieser Schmied das Geld bes Kaufmanns ? Das hart-e Eisen ist nüßlich. The hard iron is useful. 8. Nein, er hat nur Eifen von einem Kaufmanne. 9. Haben Sie den Dieser schön-e Vogel ist weiß. This beautiful bird is white. Bagen des Bädero? 10. Nein, ich habe diesen Wagen von einem Wag. Dieses weiß-e Papier ist dön. This white paper is beautiful net. 11. Haben Sie das Band dieses Mädchens ? 12. Nein, ich habe Einiger roth-e Wein.

Some (a little) red wine. Tut von einem Tuchhändler. 13. Haben Sie den Red dieses Freundes ? Einiges roth-e Papier.

Some (a little) red paper. 14. Nein, ich habe diesen Rock von einem Schneider. 15. Haben Sie das Ieder zufriedenee Mann ist Every contented man is happy. Papier des Sehrers ? 16. Nein, ich habe diejes Papier von einem Papier- glüdlich. häntler, und einem Empfehlungsbrief von dem Lehrer. 17. Ist das Pferd Jedes glūdlich-r Kind ist 31. Every happy child is contented. ein Zugthier? 18. Ja, und es ist auch ein lapthier? 19. Ist das Kameel frieden. auch ein Zugthier? 20. Nein, es ist nur ein Lastthier ? 21. Wessen Iener schön-e Baum ist groß. Yonder (that) beautiful tree is Gelegbuo hat der Sohn des Goelmanng? 22. Er hat das Gescßbuch des

large. Obersofrichters.

Jenes groß-e Pferd ist schön. Yonder (that) large horse is


Mancher gut-e Mann ist arm. Many a good man is poor, The adjective has thus far been employed only predicatively, Manches schön-e Mädchen ist eitel. Many a beautiful girl is vain. in which use it is unvaried in form, as

Solder fein-e Stahl ist fostbar. Such fine steel is costly.

Solches fostbar-e Tuch ist fein. Such costly cloth is fine. Staħt ift hart, steel is hard ; Blei ist weich, lead is soft.

Welcher alt-e Mann ist glüdlich? Which old man is happy? The terms attributive and predicative have, in grammar, a Welches Flein-e Kind ist zu. Which little child is contented ? strictly conventional sense, and should be distinctly understood. frieden? If we say, The deep river is here (der tiefe Fluß ist hier), the adjec

EXERCISE 10. tive deep is attributive: for the quality, depth, is there referred

1. Ist dieser junge Mann der Sohn des Capitains ? 2. Nein, er ist der to as a known and recognised attribute of the river. If we say, The river is deep here (ver Fluß ist hier tief), the adjective is pre-Sohn des aften Webers. 3. Wer hat das Nadelfiffen dieses kleinen Mäd.

5. Wer hat das dicative, for we then merely affirm or predicate of the river that heng?, 4. Dieses fleine Kind des guten Freundes hat es.

schöne Pferd des guten Dheims ? 6. Der junge Goldschmied hat es. it has the quality, depth.

7. When used attributively, the adjective is varied by the addi. Wer hat den großen schwarzen Hund des Jägers? 8. Der junge Bruder tion of suffixes.

des Kaufmanns hat ihn. 9. Hat das fleine Kind das scharfe Messer des 1. When not affected by a preceding word, the adjective is guten Bruders ? 10. Nein, es hat den neuen Kamm des guten Mädchens. inflected according to

11. Hat der junge Freund des alten Uhrmachers das schöne Pferd des 4".

Knechtes? 12. Nein, er hat das Pferd des reichen Engländert. 13. THE OLD DECLENSION.

Haben Sie den Frac des guten Schneiders ? 14. Nein, ich habe diesen Masculine.


neuen Frad von dem guten Schneider. 15. Saben Sie das Tuch diefes N. Gut-er Stahl, good steel ; gut-es Eisen, good iron;

armen Webers ? 16. Nein, ich habe Tuch von dem Weber. 17. If 6. Gut-e8 Stahls, of good steel ; gut-es Eisens, of good iron,

aller alte Wein Start ? 18. Nein, und nicht aller, neue Wein ist schwach. D. Gut-em Stahle, to good steel; gut-em Eisen, to good iron;

19. Der neue Frad ist von Schwarzem Tuche. 1. Gut-en Stahl, good steel; gut-es Eisen, good iron.

SECTION X.-DECLENSION OF ADJECTIVES (continued), The genitive of the old form is now seldom used; that of the

When preceded by any one of the following words
new form being preferred. Thus, guten Stah18; guten
Eisens, x., instead of gutes Stahls ; gutes Eisens, a.

Masculine. Neuter. Masculine. Neuter.
ein (a or an);

unser, unser (our); 2. When preceded by any of the following words

Mein, mein (my);

Ihr, Ihr (your);
Neuter. Masculine. Neuter.

Dein, dein (thy);


euer (your); tas (the) ; jeder, jedes (every);

Sein, sein (his, its);

ihr, ihr (their); Dieser, dieses (this); jener, jenes (that);

Shr, ihr (her);

tein, fein (no, or not any); alles (all); mancher, manches (many a);

the adjective has, in the nominative masculine and in the Giniger, einiges (some); solcher, solches (such);

nominative and accusative neuter, the terminations of the old Grlicher, aliches (some); welcher, welches (which);

declension, and, in all the other cases, those of the new, and is the adjective adds, in the nominative masculine and in the said to be of nominative and accusative neuter, the letter c, and in all the

THE MIXED DECLENSION. other cases en ; and is inflected according to


N. Mein gut-er, my good; mein gut-ed, my good;

6. Meines guten, of my good; meines guten, of my good;


D. Meinem guten, to, for my good; meinem guten, to, for my good; N. Der gut-e, the good ; das gut-e, the good;

A. Meinen guten, my good; inein gut-e8, my good. . Des guten, of the good; des guten, of the good ; D. Dem guten, to, for the good; dem guten, to, for the good;

1. In the preceding list of words, ein, mein, dein, a., it will 1. Den guten, the good; das gut-e, the good.

be seen that their form for the masculine and neuter is the same;

and hence that they do not (like the previous class, der, dieser, VOCABULARY.

2., and like adjectives of the old declension) indicate the gender ald, all.

of the nouns which they precede. The adjective, therefore, by Jung, young.

Schön, beautiful, fine. Engʻländer, m. Eng. Klein, small, little.

taking the characteristic terminations (er for the masculine and

Schwach, weak, feelishman.

es for the neuter) assumes the office of pointing out the gender Melser, n. knife.


of its noun, as
frad, . dress-coat. Na'delfifsen, n. pin. Schwarz, black.
Celtichmiet, m. gold-

Starf, strong.

Masculine : Gin großer Stein, a great stone.
Neu, new.
Uhrómacher, m. watch.

Neuter : Ein groß-e8 Schiff, a great ship.
Brok. great, large.

Dheim, m. uncle. maker.
Gut, good, well.
Scharf, sharp. Weber, m. weaver.


Aber, but.
Lamm, n. lamb.

Steil, steep

, n. roof. Nicht, not.

Stets, always.

Faul, lazy, idle. Schaf, n. sheep. Thier, n.animal, beast
Fett, fat.

Schuß. m. protection, Tief, deep.

Hol'länder, m. Dutch. defence.

Treu, true, faithful. · ulet hart-e Stahl ist nüßlich. All hard steel is useful.

Schwein, n. swine. Zufrieden, contented. alles nüßlich-e Gisen ist hart. All useful iron is hard.

Ihr, your.
Sein, his.

satisfied. Der nušlide Stahl ist hart.

The useful steel is hard. Keller, m, cellar. Sopha, n, sofa, Weiß, white.









Attributive. Predicative. ADJECTIVES IN THE NOMINATIVE AFTER THE MIXED | Ihr groß-es Feld ist grün. Their large field is green. DECLENSION.

Kein gut-er Stahl ist gelb. No good steel is yellow. Attributive. Predicative.

Rein gut-e8 Silber ist gelb. No good silver is yellow. (ComGin warm-er Rod ist gut. A warm coat is good.

pare Sect. IX. 3.) Gin warm-e$ Kleid ist gut. A warm garment is good.

Mein Hund ist alt. My good dog is old.
Mein alt-e8 Pferd ist gut. My old horse is good.

1. 3ft Ihr guter Freund, der Capitain, noch ein junger Mann? 2. 3a, Dein schön-er Vogel ist weiß. Thy beautiful bird is white. er ist noch jung, aber sein guter Freund, der Holländer, ist alt. 3. Haben Dein weiß-e8 Papier ist schön. Thy white paper is beautiful. Sie einen schönen, großen Sund? 4. Nein, ich habe ein schönes, großes Sein hart-er Stahl ist gut. His hard steel is good.

Pferb. 5. Hat Ihr kleines Kind mein neues Messer ? 6. Nein, aber Ihr Sein gut-es Eisen ist þart. His good iron is hard.

guter Sohn hat Ihren neuen Stoc. 7. Hat der Fleischer ein fettes Soaf? Shr gut-er Bruder ist Ilein. Her good brother is small. 8. Ja, und sein guter Sohn hat ein schönes, weißes Lamm. 9. Ift Ihr Ihr klein-e8 Kind ist gut. Her little child is good.

Freund, der junge Holländer, reich oder arm? 10. Er ist nicht reich, aber Unser groß-er Baum ist ídon. Our large tree is beautiful. er ist zufrieden. 11. Ein zufriedener Mann ist auch reich. 12. Ein reicher Unser schön-es Haus ist groß. Our beautiful house is large. Mann ist nicht stets ein zufriedener Mann. 13. Ihr großes Haus hat ein Guer alt-er Roffer ist schwarz. Your old trunk is black.

fteiles Dach und einen tiefen Keller. 14. Von wem haben Sie Ihr neues Quer schwarz-e8 Band ist alt. Your black ribbon is old. Sopha ? 15. Ich habe es von einem guten Freunde. 16. Das Schwein Ihr grün-er Garten ist groß. Their green garden is large. ist ein faules, fettes Thier. 17. Ein treuer Freund ist ein starter Souß.

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It is needful, therefore, for the learner to become acquainted

with a third elementary stroke before he can proceed to the HITHERTO the attention of the learner has been confined to formation of any new letters, and this he will find in the top letters based on the elementary stroke called the "pot-hook” and bottom-turn shown in Copy-slip No. 12. This stroke enters or "bottom-turn." He may now proceed to copy the next into the composition of six letters of the writing alphabet, as elementary stroke, called the "top-turn” or “hanger,” as shown the learner will find in future lessons. It consists of a fine in Copy-slip No. 11.

hair-stroke, commenced at the central line c c, brought upwards This stroke will be found to enter into the composition of towards the right in a gentle curve, and turned at the upper three letters only, and therefore plays by no means so important line a a into a broad down-stroke, which is again narrowed as it a part in the formation of the writing alphabet as the bottom-approaches the lower line bb into a fine hair-stroke that is turn, which, as it has been already said, enters into the turned and carried upwards towards the right. It may be de composition of no less than nine. It consists of a fine hair- scribed as being formed of the upper half of the top-turn and stroke, commenced on the central line c c, and carried upwards the lower half of the bottom-turn, joined together on the line in a direction bending gradually towards the right, as far cc. Examples of all these elementary strokes will be found in as the upper line a o, where it is turned and changed into No. 1 of “Cassell's Graduated Copy-Books.” When the learner labe broad down-stroke, which is brought downwards, with an can make these strokes with ease, he will fird that he is in a qual pressure of the pen throughout, as far as the lower position to form two more letters of the writing alphabet with. ne bb.

out any difficulty whatever, while he has also advanced more The top-turn may be described as being precisely the reverse than half-way towards the formation of the seven other letters of the bottom-turn; or, in other words, the bottom-turn reversed, that are partly made by the aid of these strokes. He may now as may be seen by turning the page upside down, and examin. proceed to copy the letters n and m, as shown in Copy-slips ing the stroke in this position. It is only used in combination Nos. 13 and 14, observing that the letter n consists of a comwith other elementary strokes in forming letters, for unlike the bination of these two strokes only, the top-turn being made first, bottom-turn, there is no letter of the writing alphabet which is and the top-and-bottom-turn added to it, while in the letter m formed of this stroke alone, or even by its repetition or any the top-turn is repeated twice, and the letter is then completed modification of it.

by the addition of the top-and-bottom-turn.


is contained 3 times and 1 over. Write the quotient 3

under the second figure in the dividend, and prefixing the reDIVISION

maining 1 to the 5, say, 4 in 15 is contained 3 times and 3 over. 1. The process of finding how many times one number is con- Write the quotient 3 under the third figure in the dividend, and tained in another is called Division.

prefixing the remaining 3 to the 6, say, 4 in 36 is contained 9 The number to be divided is called the Dividend.

times, with no remainder, and write down the 9 under the last The number by which we divide is called the Divisor.

or unit's figure of the dividend. The result-viz., the number of times which the Dividend

It will be seen that when, to get the first figure of the contains the Divisor—is called the Quotient (Latin quoties, quotient, we say 4 in 5 is contained once, with remainder 1, we * how often").

really indicate that 4 is contained in 5000 1000 times, with reThe sign • placed between two numbers means that the first mainder 1000, which 1000 we carry on to add to the next three is to be divided by the second. Thus, 19 = 5 means 19 divided of the dividend, which really indicates 300, and so on; as will by 5.

be seen by comparing the process with the analysis of the method If the Dividend does not contain the Divisor an exact number in Article 4. of times, it will contain it a certain number of times (the 6. To divide 7499 by 9. Quotient) with a number left over, which will be less than the

9)7499 Divisor. The number left over in this case is called the Remainder.

833-2 Thus, when we say that 5 is contained in 19 3 times and 4 over, 19 is the dividend, 5 the divisor, 3 the quotient, and 4 the Here, since 7, the first figure of the dividend, is less than the remainder.

divisor, 9, we take two figures of the dividend, and say, 9 in 74 This fact may be exhibited in the following form :

is contained 8 times, with a remainder 2, and put down the 8 19 = 3 x 5 + 4

under the second figure of the dividend (reckoning from the left 2. It will readily be perceived that division is, in reality, only 9 in 29 is contained 3 times and 2 over; and again, 9 in 29 is

hand). Then, proceeding as in the previous example, we say, a short method of performing a series of subtractions, in the contained 3 times and 2 over. This last 2 is 2 units, and is same way as multiplication is a convenient method of perform therefore the remainder left after dividing 7499 by 9. It is ing a series of additions. For instance, to find how many times generally written after the quotient, as above. 5 is contained in 19, subtract 5 (the divisor) continually from 19 (the dividend), until the number is exhausted, or a number divisor is a small number (generally one figure), is called Short

This method, which is only conveniently applicable when the less than 5 is left; then, counting the number of these subtrac

Division. tions, we shall get the quotient. Thus, 5 from 19 leaves 14, 5 from 14 leaves 9, 5 from 9 leaves 4. Since 5 has been sub

EXERCISE 8. tracted 3 times from 19, leaving 4 as a remainder, we see that (1.) Divide 658 by 2; 537 by 3; and 7891011 by 6. 19 divided by 5 has 3 for its quotient, leaving 4 as a remainder. (2.) Divide 4389127 by 8; 407792 by 11 ; and 5349279 by 9.

N.B.—It is evident, from the nature of division, that the (3.) Divide 41239789 by 12; and 54937862 by 5. product of the quotient and divisor, added to the remainder, is (4.) Divide each of the numbers contained in the square in equal to the dividend.

Ex. 4, page 23, successively by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 3. Method of Division.—The method we are about to explain (5.) Divide each of the numbers contained in the square in depends upon the truth of the following principle :

Ex. 4, page 23, sncce

ccessively by 2, 3. 4, 5, 6, 7, 8, 9, 10, 11, 12. If the dividend be split up into any number of parts, of (6.) Divide each of the numbers 1010421690, 7689768432134, which the sum is equal to the dividend, then, if we divide each 54932684736856, and 428571428571496, by all the numbers part separately by the divisor, the sum of all the quotients so from 2 to 12 inclusive. obtained will be the quotient required.

7. To divide 9298 by 35. For instance, 18 is equal to the sum of 9 and 6 and 3. The quotients of these, divided respectively by 3, are 3, 2, and 1, namber of times which 35 is contained

Arrange the figures as in the margin; then say, the largest

92 is 2 which, added together, make 6, the quotient of 18 divided by 3.

Similarly, 36 is 28 +8, and therefore 36 divided by 4 is the times. Write the 2 on the right, to form the first 35)9298(265 sum of the separate quotients of 28 and 8 by 4, which are 7 and figure of the quotient, and subtract 2 x 35—i.e., 2 respectively. Hence 7+2, or 9, is the required quotient.

Annex to this remainder

70-from 92, leaving 22. It must be observed that if, the quotient of a given dividend the next figure (9) in the dividend, thus making

it 229. and divisor being known, the dividend be increased by annexing any number of ciphers to it, the new quotient is obtained by contained in 229 is 6 (which must be found by trial).

Then say, the greatest number of times that 35 is

175 annexing the same number of ciphers to the quotient. Thus, 28 divided by 4 has the quotiont 7; and 28000 divided by 7 Put down the 6 to form the next figure in the 13 4000.

quotient, and subtract 6 times 35-i.e., 210—from 4. To divide 5356 by 4.

229, leaving a remainder 19. To this annex the last figure (8)

of the dividend, making it 198. 5356 - 5 thousands + 3 hundreds + 5 tens + 6 units.

Then say, the greatest number of times which 35 is contained Now 5 contains 4 opce, with remainder 1; therefore 5 thousands in 198 is 5. Write down the 5 to form the next figure in the contain 4 one thousand times, with remainder 1 thousand.

Add this remaining 1 thousand to the 3 hundreds, thus making 13 quotient, and subtract 5 times 35–i.e., 175—from 198, leaving hundreds

23. 265 is the required quotient, and 23 is the remainder. Now 13 contains 4 three times, with remainder 1; therefore 13 hun.

Hence 9298=265 x 35 + 23. dreds contain 4 three hundred times, with remainder 1 hundred.

8. A careful examination of the above process will show that Add this remaining 1 hundred to the 5 tens, thus making 15 tens. what we have really done is equivalent to saying: 35 is conNow 15 contains 4 three times, with remainder 3 : therefore 15 tens tained in 92 hundreds two hundred times, with a remainder 22 contain 4 thirty times, with remainder 3 tens, or 30.

hundred; then, subtracting 200 times 35—i.e., 7 thousandAdd this remaining 30 to the 6 units, thus making 36 units.

from 9298, we have 2298 left. Now 36 units contains 4 nine times. Therefore 1 thousand, 3 hundreds, three tens, and 9 units are the remainder of 19 tens ; then subtracting 60 times 35—i.e., 2100

Next we say : 35 is contained in 229 tens sixty times, with a number of times the parts into which 5356 has been divided contain the divisor 4 respectively. Their sum, therefore, is the required

-- from 2298, we have 198 left. guotient: this is

Next we say : 35 is contained five times in 198, with a re1 thousand + 3 hundreds + 3 tens + 9 units, i.e. 1339.

mainder 23. 5. The above is the analysis of the following shorter process, the dividend, again, 60 times from what is left, and again, 5 times

Hence we see that after taking away 35, first, 200 times from and will be seen fully to explain it :

Write down the dividend and divisor as in the margin; 4)5356 from what is left, we have 23 anits over, a number which is less then say 4 in 5 is contained 1 time, with 1 over. Write

than 35. the quotient 1 under the 5, and placing the remaining

Hence we see that 35 is contained in 92981 before the next figure of the dividend 3, say, 4 in 13

200+60+5—1,8., 265 times--with a remainder 23.


229 210




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