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sont ces lettres ? 21. Elles ne sont point à moi, elles sont à ma ache? 8. Yes, Madam, she has the ear-ache and the tooth-ache. 9. cousine. 22. Cette montre est à lui. 23. N'étes-vous point à Is not your head cold? 10. No, Sir, but my fingers are cold. 11. Is la veille de partir pour Londres ? 24. Nous sommes à la veille not your face cold? 12. No, Sir, it is not cold. 13. Has that gentlede nous embarquer pour Cadix. 25. Il y a longtemps que mouth. 15. Has that young lady handsome teeth? 16. She has

man an aquiline nose? 14. He has an aquiline nose and a large nous sommes aux prises.

handsome teeth and handsome eyes. 17. Has that little boy small EXERCISE 176.

feet? 18. He has small feet, and large hands. 19. Has not your niece 1. Are you able to pay that person ? 2. I am not able blue eyes ? 20. No, Sir, she has black eyes. 21. Have your scholars to pay him; I have not received my money. 3. Are you on

hurt their faces ? 22. They have hurt their chest. 23. Have your good terms with your bookseller ? 4. I am not on good terms daughters a good memory? 24. They have an excellent memory. with him. 5. How long have you been on bad terms with 25. Those Italian ladies have not a fresh complexion. him! 6. It is more than a month. 7. Are you not able to

EXERCISE 126 (Vol. II, page 237). satisfy my friend's demand ? 8. I am able to satisfy it (d'y satisfaire). 9. Are you on your way to Naples? 10. No, Sir;! main. 3. M. votre frère a-t-il mal aux doigts ? 4. 11 a mal aux doigts

1. Qu'avez-vous à la main ? 2. Il y a dix jours que j'ai mal à la I am on my way to Rome. 11. Is not your physician on the ! et à la main. 5. M. votre frère qu'a-t-il à la main ? 6. Il a une plume fre of starting for Montpellier ? 12. He is on the eve of start- ! à la main. 7. Votre petit garçon a-t-il mal à la gorge? 8. Il a le ing for Paris. 13. Am I in the way here? 14. No, Sir; you | mal de gorge. 9. Votre sour ainée n'a-t-elle pas mal aux dents ? 10. are not in the way. 15. Whose turn is it to speak? 16. It is Elle n'a pas mal aux dents, mais elle a mal au doigt. 11. Pourquoi my turn to speak and to read. 17. Is it my place (à moi) le soldat ne marche-t-il pas ? 12. Il ne pent marcher, il a mal au to make apologies to him ? 18. It is your brother's place pied. 13. N'avez-vous pas mal aux pieds ? 14. Je n'ai pas mal aux to apologise to him. 19. Does it become you to punish that pieds. 15. Si vous aviez mal aux doigts, écririez-vous ? 16. Si j'avais child? 20. It behoves me to punish him. 21. Do you hold the mal aux doigts je n'écrirais pas. 17. Si votre frère avait mal à la place of a father towards him? 22. I hold the place of a tête, étudierait-il sa leçon ? 18. Il n'étudjerait pas sa leçon, s'il avait father towards him. 23. Is that coat yours ? 24. No, Sir; it 20. Il a des douleurs à la poitrine et au côté. 21. Votre petite fille

le mal de tête. 19. Ce monsieur n'a-t-il pas des douleurs à la poitrine ? is not mine ; it is my brother's. 25. Have you broken openly a-t-elle les yeux noirs ou bleus ? 22. Elle a les yeux noirs et le teint with him? 26. We have been quarrelling two months. 27. frais. 23. Mlle, votre fille n'a-t-elle pas le mal de dents? 24. Elle a Is not that large house yours ? 28. No, Sir; it is not mine; it mal aux dents et à l'oreille. 25. N'avez-vous pas froid aux mains et is my sister's. 29. Does it become your brother to reproach aux pieds ? 26. J'ai froid aux mains, mais j'ai chand aux pieds. 27. himn with his kindness ? 30. It does not become him to do it. Ces dames n'ont-elles pas le nez aquilin? 28. Elles ont le nez aquilin, 31. Whose turn is it to go and fetch the books ? 32. It is my et le teint beau. 29. Mlle, votre sour a-t-elle les mains grandes ? 30. place to go and fetch them. 33. Is the gentleman in ? 34. No, Non, Monsieur, ma sœur a les mains petites. 31. Ces petites filles ne Sir, the gentleman is not in; but the lady of the house is in.

se sont-elles pas fait mal à la tête ? 32. Elles ne se sont pas fait mal à la tête,'elles se sont fait mal au visage. 33. Ce petit garçon

a les cheveux noirs. KEY TO EXERCISES IN LESSONS IN FRENCH. EXERCISE 123 (Vol. II., page 202).

GEOMETRICAL PERSPECTIVE.-IX. 1. Why does that workman pretend to be ill? 2. He pretends to be in because he does not wish to work. 3. Does not that student Our previous lessons in Perspective have been upon the groundplay the learned man? 4. He does not play the learned man, he plays plan method ; we will now introduce to our pupils the lineal the fool. 5. Does it become that young man to play the master here ? method—we call it the lineal because its results depend upon 6. It becomes nobody to play the impertinent. 7. Does that matter the projection of planes and angles without the intervention 8. That is of no consequence whatever. 9. Can that concern those of a plan. It sometimes occurs that a perspective elevation vine-dressers ? 10. That does not concern them at all. 11. Are you of a house or other building is all that is required ; in this case Dot very much grieved at that? 12. We are very sorry for it, but we cannot help it. 13. Has not your partner become a jeweller? 14. convenient, as it saves the labour of making a plan for the sole

a plan would be useless, and the lineal method would be most No, Sir, he has turned painter. 15. Has not that mechanic turned glazier? 16. He has become a tanner, and his brother has become a purpose of raising an elevation from it. soldier. 17. Has not the milliner had her hair cut? 18. She has

The picture plane, the horizontal line, vanishing points, had it cut. 19. Do you not rise as soon as it is daylight ? 20. Yes, station point, line of contact, or measuring line for heights, and Sir, I rise very early. 21. Is it not moonlight ? 22. It is very light, point of sight, are common to both methods; therefore we need bat it is not moonlight. 23. Is the living good in America ? 24. not recapitulate our remarks upon them; that which will be The living is very good in America; provisions are cheap.

especially new to our pupils is that the angle of inclination EXERCISE 124 (Vol. II., page 203).

which an object makes with the picture plane is described, 1. Ce monsieur ne fait-il pas le savant; 2. Il fait le seigneur et le instead of drawing it in plan. Visual rays will not be required, fou à la fois. 3. Ce garçon ne fait-il pas le malade ? 4. Il fait le as the retiring length of an object is cut off the vanishing line by malade, il n'a pas envie d'étudier ses leçons. 5. Quand vous n'avez the help of its distance point, marked Dr. The nearest approach pas envie de travailler, faites-vous le malade ? 6. Je ne fais jamais' to this system which we have yet made is shown in Lesson IV., le malade. 7. Fait-il de la boue aujourd'hui? 8. Il ne fait pas de Vol. II., page 359. It is true we have there made use of a boue, il fait de la poussière. 9. Fera-t-il clair de lune ce soir? 10. plan, but there are no visual rays (see Figs. 22, 26). The plan Il ne fera pas clair de lune, il fera très-obscur. 11. Fait-il bon ici ? has been introduced solely for the purpose of obtaining by con12. Il y fait très-bon. 13. Fait-il trop chaud

ou trop froid ? 14. Il straction the positions of the extremities of the lines upon the les cheveux ? 16. Je me suis fait couper les cheveux hier matin. 17. picture plane. Let us take Fig. 23, and we shall here see that Ne voulez-vous pas aller à la maison, il commence à se faire tard ?

18. the position of the line I in the picture is ascertained by findSe fait-il pas très-obscur dehors ? 19. Il ne fait pas obscur, il fait ing the positions of the two extremities only. Thus the points h clair de lune. 20). Le vitrier ne s'est-il pas fait orfèvre ? 21. Il ne and i being determined as the perspective representations of u s'est pas fait orfèvre, il s'est fait soldat. 22. Cela fait-il quelque and 1, the completion of the line follows by drawing a line chose à M. votre frère ? 23. Cela ne lui fait rien. 24, N'êtes-vous between the two points. Now these positions can be given pas faché de cela ? 25. J'en suis fâché, mais je ne puis qu'y faire. ! without the necessity of a plan, as we are about to explain. 3. Pourquoi vous faites-vous raser? 27. Parceque je ne puis me mser moi-même. 28. N'avez-vous pas fait mal à ces enfants ? 29.

We think we shall be able to make our explanations clearer, Je ne leur ai pas fait mal. 30. Vous êtes-vous fait mal au bras 31. and better understood by our pupils, if we propose a problem at Non, Monsieur, mais je me suis fait mal à la tête? 22. Mlle. votre once, and during the process of drawing, accompany the explanakur ne s'est-elle pas fait mal à la main ? 33. Elle s'est fait mal à tions of the work with our observations upon the theory, at the la main, et ma mère s'est fait mal au coude. 34. Ne vous êtes-vous same time employing the figure as we draw it to illustrate our pas fait mal à la tête ! 35. Je ne me suis pas fait mal à la tête, mais remarks. je me suis fait mal à la main.

PROBLEM XXVII. (Fig. 49).- A pole 4 feet long is lying on EXERCISE 125 (Vol. II., page 237).

the ground, and is inclined to the picture plane at an angle of 1. Has that young man a sore throat? 2. Yes, Sir, he has had a

40°; its nearest enl is 2 feet within the picture, and 1 foot to the sore thront for two days. 3. Have you often the headache ? 4. I right of the eye ; distance of the eye from the pp is 6 feet and 4 have the headache almost every day. 5. Have you not a sore arm feet from the ground; scale 1 inch to the foot. 6. I have a sore arm and a sore hand. 7. Has your sister the ear Draw the picture plane, PP, and the El parallel with the PP

e

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and 4 feet above it. Anywhere upon the HL mark the ps (point vanishing line the length required, in the same way that we used of sight). From Ps as a centre, and with the distance of 6 feet the DEM for cutting off the point d in the line b Ps. From DVP in the compasses, draw the semicircle de', DE”. Before we go through d draw a line to meet the PP in e, inake e f equal to the any farther we will examine this. To assist in understanding length of the pole, 6 feet, and from f draw another line back to the position and meaning of this semicircle we refer back the DVP, cutting the vanishing line from d in h; h d will then be to Fig. 21, Lesson IV., Vol. II., page 360. There it will be the perspective length and representation of the pole. We must seen that E represents the eye, and its distance from the PP dwell upon this for a minute or two, as this cutting (as we term from E to PS. Of course Ps is opposite the eye E, and a line it) a vanishing line is important. Our pupils will have observed between the two would

that we drew a line, come form right angles with .

mencing from the DVP, the PP. Now it is neces

through d to e, and after sary to set off on the HL

we had marked the given the distance of the eye from

Fig.49. length e f on the pr, we the PP, that is, the dis

drew from f back again to tance from E to Ps, for a

DVP; in other words, in reason to be explained

order to determine the presently; therefore, the

space upon the PP which proper way to do that is

is to contain the length to draw a semicircle, and

of the pole, and at the mark the extremities meet

same time secure the pering the HL as Del and

spective position, DE. In the eidograph VP

DE?

PIS
DVP

brought the nearest end, (Fig. 21), the dotted semi

d, of the pole to the PP circle through the eye E

at e, measured its length, (ending on one side at

ef, and then ruled back DE' and the other at DEP)

again, to the distance is in an horizontal posi

point. This

may be tion; it is afterwards

summed up in very few supposed to be turned up,

words, in the form of a or rabatted, upon the

PP

rule to be remembered PP passing through E (to f f

that every vanishing line the same points). This

is cut by its own distance will be the position in which we shall place it for the future, point. The ability to draw an object in perspective upon this and as seen in the figures which immediately follow Fig. 21. To lineal system depends principally upon a clear understanding of proceed with Fig. 49 : draw a line x æ tangential to the semi- the above rule in the several ways in which it may be applied. circle, and parallel to the HL or PP. Our problem states that we advise our pupils to get this first problem well up, by doing the inclination of the pole to be represented is at an angle of 40° it again at other angles, and other given distances and proporwith the PP. Therefore, from E draw a line at that angle with tions. Afterwards they will have very little difficulty in under* *, meeting the HL in vp. There will be no difficulty in compre- standing all that is to follow. hending this, if we consider that because æ æ is parallel with the PROBLEM XXVIII. (Fig. 50).-Two lines, each 3 feet long, PP, therefore if the plan of an object is known to be at a certain form a right angle; one of the lines is at an angle of 40° with the angle with the PP (as in the ground-plan method), it will form PP, nearest point 2 feet to the left of the eye, and 1 foot within the the same angle with a x.

picture; height of eye, disThis, then, is the way a

tance, and scale as in the VP is found without the

last problem. necessity of a plan. From

Draw the Pp, horizonPs draw the perpendicular

Fig.50. tal line, and semicirelo Ps a, and mark one foot

through E at the given to the right of a, viz., ab,

distance as before, make because the nearest end

E vpl at an angle of 40° of the pole is 1 foot to

with a x, and draw E Vp the right of the eye.

at a right angle with it. Draw b PS, and some

From each of the vanishwhere upon 6 Ps will be

ing points draw arcs from found the position of the

E to the HL for the respecnearest end of the pole, DE1

DVFI

tive distance points; proto be determined in the

duce E PS to a, and make following manner :-From

a b equal to 2 feet; join 1 set off b c equal to 2

b Ps, make b c equal to 1 feet, draw a line from c

foot, and draw a line from to DE?, cutting b Ps in d,

c to Le'; where this last the point required. This,

line cuts b ps in d will be with the exception of the

the position of the angle; pian, is precisely the

PP

draw a line from d to same that was done with

vpl. Now we must rememthe line A B in Fig. 23,

ber the rule given in the that is, by making o D equal to C A, a was found to be the last problem, every vanishing line is cut by its own distance point; nearest end of the line A B. We now come to a stage of consequently, as pvpl is the distance point of vp!, we must draw the proceedings which will demand the closest attention of a line from ovpl through d to the PP at e, make e f equal to 3 our pupils. It is that of cutting off a portion of a vanish-feet, the length of one of the lines forming the right angle, and ing or retiring line, to give the perspective length of the from f rule back again to pvp, cutting d vpl in h; dh will be object, in this case the pole. From d, the nearest end of the the length of the line. The other line of the right angle must pole, draw a line to the VP (the vanishing line of the pole); upon be similarly treated; as it vanishes at vp?, the distance point of this line will be cut off the perspective length, as follows:- vp2 must be used for cutting off its perspective length, by bring From VP, with the radius VP E, draw the arc E DVP; DVP is the ing a line first from pvp through d to the pp at m; mako mu distance of the eye from the vp, and is set off upon the il upon equal to the length of the line, and draw from n back again to the same principle as the other distance points are placed; the determine o in the vanishing line; h d o will be the perspectivo use of this distance point is to enable us to cut off upon the representation of the right angle as required.

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RECREATIVE NATURAL HISTORY.

bison or aurochs has fourteen. Many other anatomical

peculiarities completely separate the bison from our oxen. THE OX FAMILY.

Some writers, despairing of finding the parent race in Europe, OUR common or, the pride of every Smithfield Cattle Show, is trace it to the buffalo of Asia, while Cuvier himself inclined to so well known that any notice of such a quadruped may seem the belief that the ancestors of our farm-oxen have become superfluous; but as a study of the most familiar forms of life extinct. We must, therefore, look for the primary types of our is sure to disclose some peculiarity of structure, or to recall Devons and Herefords in those fossil bones so often found in some important historical fact, we may be certain that this will the upper deposits of the tertiary formations. Nor shall we be the result in the present case. If one were to ask what probably go far wrong if we regard the wild cattle of Chillingham animal has most aided man in his progress to civilisation, the Park as very closely allied to some of our existing breeds. These answer must probably be the ox. In the first stage of savage brief remarks may suggest to the reader some notions of the life, when food is procured by hunting wild beasts, the dog difficulties encountered in tracing the history of our most may be the most valued servant. But when this rude state common animals. has been passed, the ox becomes man's trusted friend, pro We must not pass on without at least indicating some of riding him with food and clothing, drawing the plough, and the more remarkable species of the bovine family. No reader moving the wagon. It was not, therefore, wonderful that the will wish us to lose time in technical descriptions of the various early races of men should exalt this animal to the rank of a improved breeds reared for the market—topics suited to an deity. Thus we see the wisdom of Egypt and the might of agricultural journal, but out of place in these pages. Nor can Assyria bowing

we describe all before the sym

the widely-exbolic bull; and

tended species even the chosen

of this family, people of Hea

but only those ven were de

which are most luded into wor

remarkable for shipping the

peculiarities of golden calf, and

form, habits, listened with

historical out sign of hor

associations. for to the words,

The Chilling“These be thy

ham wild cattle, gods, O Israel."

to which referFew readers

ence has been need to be re

already made, minded that the

demand a few of belongs to

words more. It the order Ru

is probable that minantia (ru

we see in these minants), and

the descendants to the family

of the wild Bovidæ,* a term

bulls which in including the

the reign of ox, bison, buf.

King Henry II. falo, and all

roamed in the other species or

wide forests Farieties. The

then extending horns of all the

fararound Lonfamily are hol.

don. They are low and perma

cream coloured, nent, resem

but have black bling in these

muzzles, and two particulars

ears of a redthose of the

dish tint. The sheep, goats,

horns are short, THE AMERICAN BISON OR BUFFALO and antelopes.

black on the A vehement

tips, and have dispute has long raged respecting the origin of our common ox. a slight curve upwards. Some of the bulls possess a short mane. One naturalist sees the original breed in the wild cattle still Those who have seen them for the first time in the solitudes of kept in Chillingham Park, Northumberland. Another regards Chillingham, have been struck by their peculiarly wild habits. the formidable urus, or wild bull of ancient Germany, as the No sooner does the herd behold a strange visitor than the ancestral type.

But if we may trust the description given whole body dash away, as if in fright. After running for about of these by Cæsar, they could scarcely have been the fathers a hundred yards they stop, turn round, and advance, as if to of our present cattle. The great Roman says these ancient charge the intruder, then suddenly pause at some distance, bulls of the German forests were nearly as large as elephants, scrutinising the object before them. Should the man wave his and that their horns were capacious enough to form drinking arms, off they dart again,

but to a shorter distance;

then turn. vessels. +

We shall have a word to say about these large ing, dash forwards as before, coming nearer than at first. horns hereafter. At present it may suffice to remark, that Thus, by a succession of retreats and advances, the animals the existing breed of oxen cannot well be traced from the at last come so near that the visitor receives warning to retire, fierce and gigantic uri of Cæsar. The European bison, which is lost the wild herd should finish by a fatal charge. Here is thought to be still wandering in the wild regions of the lower indeed a splendid zoological study for all who can gain an Danube, has been regarded by a few as the parent stock. The admission to such a collection. Önce or twice the herd has examinations of Cavier and other anatomists show this to be been on the point of perishing from disease ; but the care now almost impossible. He mentions one structural difference only taken will, it is hoped, long preserve these few remains of in proof of this. Our oxen have thirteen pairs of ribs, but the the wild forms of nature. Readers who have seen Landseer's

famous picture of the Chillingham wild bull are able to form This term is derived from bovis, the genitive of bos, the Latin for some notion of the force and beauty of the living animal. 05. The real root is the Greek Bous (bous).

Far different from these wild cattle of Britain is the bison of * "De Bello Gallico," lib. vi., cap. 28.

America, with its huge lion-like mane, hamped back, and vindicVOL. III.

[graphic]

70

tive eye. It is singular that our common cattle, the aurochs or first swallow, and then, after some time, commence the chewing European bison, and the bison of America should each differ in process, called "ruminating" by the learned, and "chewing the the number of the ribs. The domesticated ox has but thirteen cud” by the peasant. Let us trace this process in our wellpairs, the aurochs fourteen, and the American bison fifteen pairs. known friend the cow. We see the tongue collecting a monthThese wild cattle of the New World are sometimes, though im- ful of grass into a small bundle, which is then nipped off by the properly, called buffaloes, but the name is of small importance, combined action of the teeth of the lower jaw and the grasping the chief fact calling for notice being the countless hosts which power of the muscular lips. It will be observed that the cox spread over the prairies. Some of these droves are estimated at does not pause to masticate the grass, but swallows, or, as 20,000 head of majestic cattlo, many being eight feet long, and some would say, "bolts" the whole. The matter, thus speedily weighing nearly eighteen hundredweight each. No wonder is disposed of, is deposited for awhile in the first stomach or it that the fiercest wars between the Indians and the white races rumen, which serves as a kind of cupboard or store-room, in should arise from the intense desire of the red men to keep the which the food is kept till wanted for further operations. It magnificent hunting-grounds of the bison regions for them- consists of four small sub-divisions, and the coat is covered selves. If the white man should advance, as he surely will, the with thousands of little elevations, which doubtless produce bison will depart or perish, for the European slaughters them by some chemical change on the newly-received food. The tens of thousands for the hides and tallow only. Nor will this diseases of this stomach often demand the attention of be matter for wonder, when it is remembered that 150 pounds the rustic “cow doctor," and even of the skilled veterinary weight of fat are obtained from the best animals, and that the surgeon. Here are frequently formed dangerous concretions of hides are go valuable as to have been called “ Californian bank hardened vegetable or even mineral matters. The once famous notes.” Then the white man is grieved at the dearness of meat bezoar stones, supposed to be universal remedies against in the crowded homes of civilisation, and is forming societies for poisons, were simply formed by disease in the stomach of preserving bison beef, and transporting it to the meat market the wild goat of Persia. These masses of phosphate of England. The red man has heard of this, and is gloomily of lime have been sold for five or six times their weight of pondering over the one great article of his creed, “If white man gold! From this first large stomach the food descends into comes, bison goes.” But the departure or destruction of these the second, much smaller, but exceedingly complex in structure. wonderful herds means the annihilation of the red tribes. It is covered with multitudes of small cells, from which it is often Therefore is it that, even while we are reading these lines, the called the honeycomb bag. The food is so acted upon in this rifles are flashing along the Indian frontiers. The bison is the receptacle as to take usually the form of compact and rounded main cause of the contest. “Why don't the red men plough masses, which are returned from this second stomach, by a pecuthe ground? then there would be lots of food, and to spare," liar muscular action, through the gullet into the mouth. Then cries the exasperated white settler, whose house has been burnt begins the process properly called ruminating, during which the by the savages. There is just the difficulty. The Indian will cow seems to enjoy the very perfection of animal bliss. As not plough ; therefore he must hunt; therefore he relies on the each portion of the food is re-masticated, it is passed from the bison; and therefore he tries, but all in vain, to stop, even mouth direct into the third stomach. This is accomplished by with rifle and tomahawk, the white man's resistless march. the closing of the tube which leads to the first and second Such is the importance of one member of the ox family in the stomachs. This third receptacle is very small, and is called the far West. Every poor man in England has an interest in the manyplus, from the numerous folds, arranged like the leaves of matter. If the Indian would become à tiller of the soil, then a book, of which it is composed. Between these active folds science would soon find means for sending to Europe the fine the food rests a short time, and is then passed into the fourth bison meat now left on the prairies for the wolves and vultures. or true stomach, where the final processes of digestion are Some of the flesh has for years been imported, but its appear- completed. This short description will perhaps suffice to show ance does not, as hitherto presented, attract the ordinary how exceedingly complex is the organisation by which grass purchaser.

is gradually changed into beef. Many other peculiarities of Another American animal, the musk-ox (Ovibos muschatus), structure must be passed over for the present, our only reason is remarkable for three peculiarities—the shape and size of its being want of space to treat such topics satisfactorily. singular horns, the great length of the fine hair, and the fond Allusion has been already made to the gigantic horns of some ness of the animals for the wild deserts of the North American ancient oxen; and many readers will doubtless recollect those wastes. These herds wander far within the Arctio circle, dis- famous historical drinking horns, still held as heir-looms by puting for the lichens and northern herbage with their rivals, the some old families, especially those of Aubrey and Pusey. The reindeer. Often is a solitary Esquimaux tribe roused from its Borstal horn was the symbol by which Edward the Confessor torpor by the appearance of a herd of musk-oxen, thirty or forty conveyed a large estate to one Nigel, who killed a savage boar in number, which thus offer to the wild people of the Arctic which had imperilled the person of royalty in the neighbourhood shores a prospect of high feasting and jollity. Clothing, too, of the palace at Brill. From the family of Nigel the treasured equal to the highest notion of an Esquimaux belle, is furnished horn has descended, with the Borstal estate, to that of Aubrey. by the beautiful hair of the musk-ox, which is twisted into The Pasey horn, above two feet long, has an inscription which many a curious form by the damsels of the frigid zone. The declares it was delivered by that descendant of Odin, King name given to this ox by the Cree Indians signifies " ugly bison,” | Canute, to “ Wyllyam Payse." Such ox-horns truly deserve and this, though not complimentary, is much more suitable their honours. than the absurd name of musk-ox. The designation of "little We must not, however, forget the extraordinary veneration bison,” given by some Indian tribes, is much more appropriate. for the ox in ancient days, the solemn worship paid to his The scientific name, Ovibos, assumes that the animal combines highness while living, the national mourning for him when dead, the qualities of the sheep (ovis) with those of the ox.

and the embalming of his venerable body, for the admiration of The buffalo of South Africa (Bos Coffer) is immediately dis- after ages. It was not, indeed, every ox which was thus tinguished from his American relative by the absence of the honoured, even in Egypt. That would have been too expensive shaggy mane, the large spreading horns, and the more massive even for the Pharaohs. But the homage paid to Apis at Mem

form of the body. These animals resemble the bisons in two phis, and his brother Mnevis at Heliopolis,* must have shed a respects—the tendency to associate in large herds, and their reflected splendour on all humble bovidæ. Nor must we forget Desperate courage when wounded.

the honours paid to the bull at Nineveh, where the figure of the We must omit any detailed description of the Abyssinian ox, animal was combined with the human and cherubie forms. The having its horns hanging as it were by hooks to the head; of the man-headed and winged bulls now in the British Museum attest zebu, or sacred bull of India, as gentle, and yet as impudent, as the extraordinary veneration for the ox " that eateth hay." a spaniel ; and of various other species, simply from want of Even at this day India regards the white bull as a symbol of space. The above references will suffice to suggest to the her great divinity, Siva. reader the wide extent of the ox family.

In all these rude, wild, and pagan customs we may trace the As these animals are classed among the Ruminants, a few feeling of great benefits flowing to mankind from the docility, remarks are necessary on the complex stomachs belonging to strength, and labours of the ox. each quadruped of the order. Every reader is probably aware that all ruminants masticate their food a second time; or rather, * Called Beth-shemesh, and also On, in the Old Testament.

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REDUCTION OF FRACTIONS.

LESSONS IN ALGEBRA.-IX.

Again, if all the signs of all the terms in the denominator of a

fraction are changed, the value of the fraction is also changed. FRACTIONS.

ab

ab 117. FRACTIONS in algebra, as well as in arithmetic, have

Thus,
6
ta; but

-6 reference to parts of numbers or quantities. The term is

125. If then the sign prefixed to a fraction, or the signs of all derived from the Latin word fractio, which signifies a breaking the terms of the numerator, or the signs of all the terms of the into parts.

denominator, be changed, the value of the fraction will be 2a Thus, is fa; is }; is ga; and

changed from positive to negative, or from negative to positive. 3 7

126. If the same change be made upon the numerator and 118. Expressions in the form of fractions occur more frequently denominator of a fraction at the same time, they will balance each in algebra than in arithmetic. Indeed, the numerator of every other, and the value of the fraction will not be altered. Thus, by fraction may be considered as a dividend, of which the denomi.

ab nator is a divisor.

changing the sign of the numerator, the fraction ta

b 119. The value of a fraction is the quotient of the numerator

- ab 6

becomes =-a. But by changing the signs of both the nudivided by the denominator. Thus, the value of

b
2
is 3; the

ab
ab

- bb
merator and the denominator, it becomes =+a, where the

b
To
is

is a +b.
6

original value is restored. By changing the sign before the frac120. From this it is evident, that whatever changes are made

ab

ab in the terms of a fraction, if the quotients be not altered, the tion, the expression y +7=y+a becomes y -c=y-a. But : value of the fraction remains the same. For any fraction, by changing the sign of the numerator also, it becomes therefore, we may substitute any other fraction which will give the same quotient.

where the quotient a is to be subtracted from y, or

b 4 10 4ba 8dru 6+2 Thus, 2 5 2ba

etc.; for the quotient in which is the same thing [Art. 58], + a is to be added, making the 4dra 3+1'

6 - 6

6 each of these instances is 2.

value yta as at first. In like manner,

2 2 121. It is also evident, from the preceding articles, that if the

6

6
6 6

6 numerator and denominator be both multiplied, or both divided,

3. 2 2

2 by the same quantity, the value of the fraction will not be altered. Hence the quotient in division may be set down in different ways Thus, *=, each term being multiplied

by 9; and = js = , and still have the same value. Thus (a — c) = 6 is either each term being divided by 3, and the result by 3 again.

abo 3bx Iba jabc So

b

гъ Б' b ab 3b 26 jab ; for the quotient in each case 7+ is.

122. Any integral quantity may, without altering its value, 127. A FRACTION may be reduced to lower terms, by dividing be expressed in the form of a fraction, by making unity or 1 thé both the numerator and denominator by any quantity which will denominator ; or by multiplying the quantity into any proposed divide them without a remainder; or by throwing out any factor denominator, and making the product the numerator of the fraction common to both. According to Art. 121, this process will not ab ad + ah hadh

alter the value of the fractions. required. Thus, a= ī

the quotient b dth odh

ab

EXAMPLE.—Reduce to lower terms. Ans. cf each of these being a.

cb Algo dth= dx +hx

2dry + 2dr ; and r+1=

128. If the same letter or combination of letters is in every 2dr

term, both of the numerator and denominator, it may be can..

celled, for this is dividing by that letter or combination of ON THE SIGNS OF FRACTIONS.

letters. [Art. 98.] 123. Each sign in the numerator and denominator of a fraction

3am tay

3m+y EXAMPLE.—Reduce

to lower terms. Ans. affects only the single term to which it is prefixed. The dividing

adtah

dth line answers the purpose of a parenthesis or vinculum, namely, to connect the several terms of which the numerator and de

129. If the numerator and denominator be divided by the Dominator may each be composed. The sign prefixed to it

, greatest common measure, it is evident that the fraction will be therefore, affects the whole fraction collectively and

every term reduced to the lowest terms. individually. It shows that the value of the whole fraction,

5a+

EXAMPLE.-Reduce to its lowest terms. and of course every term, is to be subjected to the operation

За2 denoted by the sign. Hence, if the sign before the dividing line

5a 5αααα Баа Here,

Ans. be changed from + to-, or from — to +, the value of the whole

3a" 3αα 3 fraction is also changed.

EXERCISE 13. ab Thus it is plain that the value of 7 is a. [Art. 111.] But this

Reduce the following fractions to lower terms : will become negative if the sign - is prefixed to the fraction.

B + bc

dry + dy

3.
ab

8dy
(a + bc) x m

dhy - daj Hence, y + z =y+a. But y =y-a,

am + ay 7mr*

bne + by 124. In performing fractional operations there is frequent occasion to remove the denominator of the fraction; also to

EXERCISE 14. incorporate a fraction with an integer, or with another fraction. In each of these cases, if the sign – is prefixed to the dividing

Reduce the following fractions to their lowest terms :line, the signs of all the terms of the numerator must be changed, as

3x5 + 20*3-*** + 2x + 3 1.

7. in Art. 64, where a parenthesis, having the sign before it, is

23 - 5 - 5x + 1 removed.

3a. + 4a

*** -- 2" - 2x +2.
Thusb
ad + ah

8.
ad -ah
=b-d-h; and b-
=b-dth. 8a3y - 12a”ya + bays

4.-1
ta'y + 4ay*

18.7* - 5.2 + 44-5 Next, if all the signs of all the terms in the numerator of a

9.

3* + 20x3 -5733 + 80x-50% fraction are changed, the value of the fraction is changed in the ab

- ab
*° + 2ax + aa

161* - 53.7% + 45.1 + 6 Thus,

10.
7
= + a [Art. 101]; but

30a8 + 3123-12x ab + bc

- 2763

- 22,4 - 1463 +26=a-c; but -a + c

11. b

a

a

C

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5.

ab

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3x5.

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And ab-bc

6.

1825 - 18* - 14.5 x 30x2 - 12.0*

4a 963

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