Six in 56 (in the scale of 8) is six in 5 × 8 + 6, or 46, that is, 7 and 4 over. Six in 44 (in the scale of 8) is six in 4 × 8+ 4, or 36, that is, 6 and 0 over. Six in 3 is 0 and 3 over.

Six in 35 (in the scale of 8) is six in 3 × 8 + 5, or 29, that is, 4 and 5 over. And similarly for the other lines.

This operation, in fact, proves that

5 × 8+ 6 × 83 + 4 × 82 + 3x8 +5

= 3 × 63 +0 × 6 + 2 × 63 + 2 × 6a +0 × 6 + 5.

6. One application of the duodecimal scale is very useful in ordinary practice.

In finding areas and cubical contents, as we showed (Lesson XVIII, Arts. 7 and 8, Vol. I., page 292), we have to multiply the numbers indicating the dimensions together. Now, since 1 foot is 12 inches, any dimension given in feet and inches can be at once written down in the duodecimal scale. Thus, 5 feet 9 inches would be written 5.9, putting a point after the 5 to express that the 9 is of the unit, for the same reason that, in the decimal notation, we place a decimal point before the tenths' place.

Now suppose we have to find the dimensions of a board, the length of which is 5 feet 9 inches, and breadth 4 feet 5 inches, we should have to multiply 5.9 by 4.5 in the duodecimal scale. This would be done as follows:

5.9

4.5

24.9

180

21.49

We say 5 times 9 are 45; that is, 3 x 12 + 9. Write down the 9, and carry 3. 5 times 5 are 25, and 3 are 28, which is 2 x 12+ 4, and we therefore write down 24. Again, 4 times 9 are 36; that is, 3 x 12, or in the duodecimal scale, 30. Write down the cipher, and carry the 3. 4 times 5 are 20, and 3 are 23, which is 1 x 12+11; or, in the duodecimal scale, le, which we write down.

Adding, we get 9; 4; e and 2 are 13; that is, 1 x 12 +1. Write down 1 and carry 1; 1 and 1 make 2.

The result, therefore, is 21:49 in the duodecimal scale.

Now, 21 is 2 x 12 + 1, or 25 in the decimal scale; and 49 is

4 X 129, or 57 in the decimal scale.

Hence, the answer is 25 sq. feet 57 sq. inches.

7. We can verify the process by fractions :

96

259

240

19 144

48) 2736

240

336 336

ft.

sq. ft. = 1212 sq. ft.

N.B. It will assist the learner,
in multiplying, adding, etc., in
the duodecimal scale, to re-
collect that it is exactly the
same process as multiplying and
adding pence, and reducing
them to shillings. Thus, in the
above example, we might say:
5 nines are 45, that is, 3 and
9 pence;

5 fives are 25 and 3 are 28,
that is, 2 and 4 pence.
And so on.

8. EXAMPLE 2.-Find the cubical contents of a room which

is 25 ft. 9 in. long, 14 ft. 4 in. broad, and 16 ft. 4 in. high.

25 ft. 9 in. 21.9 in the duodecimal scale.

14 ft. 4 in. = 124

16 ft. 4 in. = 144 ""

21.9

12.4

870

436

219

269.10

14.4

t 3040

t 3040 26910

35t4-4406028 cub. ft. 624 cub. in.

SECTION LXXXIX.-IDIOMS RELATING TO TENIR. 1. THE verb tenir [2, ir.], to hold, often corresponds in signification to the English verb to keep:-Tenir un hôtel, to keep an hotel; tenir table ouverte, to keep open table; tenir sa chambre propre, etc., to keep one's room clean; tenir la porte, les fenêtres ouvertes, to keep the door, the windows open; tenir les yeux ouverts, fermés, to keep one's eyes opened, shut; tenir la tête droite, etc., to keep one's head upright; tenir sa parole, to keep one's word; tenir compagnie à quelqu'un, to stay or remain with

RÉSUMÉ OF EXAMPLES.

M. L. tient un hôtel superbe. Votre petite fille ne tient pas sa chambre bien propre. Pourquoi tenez-vous les portes ouvertes ?

Il fait si chaud que nous tenons toutes les fenêtres ouvertes. Tenez la tête droite et les yeux

ouverts. Pourquoi ne tenez-vous pas votre parole ?

Tenez compagnie à votre sœur; elle est malade.

Votre ami tient des propos bien singuliers.

Vous tenez des discours bien légers. La couleur de votre drap tiendrat-elle ?

Lui avez-vous fait tenir ce livre ?
À quoi vous en tiendrez-vous ?
Je m'en tiendrai à ce que j'ai dit.
Pourquoi se tient-il toujours de-
bout?

L'incrédule s'en tiendra-t-il au présent, qui doit finir demain?

Cocher, m., coachman.
Debout, standing.
Défend-re, 4, to forbid.
De près, closely.
En dehors, out, outside.
S'enrhum-er, 1, ref., to
get a cold.

Mr. L. keeps a superb hotel. Your little girl does not keep her room very clean.

Why do you keep the doors open?

It is so warm that we keep all the windows open.

Keep your head upright and your

eyes open.

Why do you not keep your word?

Stay with your sister; she is ill.

Your friend makes use of very singular expressions.

You use very light language.
Will the colour of your cloth be fast?

Have you sent him that book?
What will be your decision?

I shall abide by what I have said. Why does he always remain standing?

Will the unbeliever be satisfied with the present, which is to end to-morrow?

1. Quel hôtel votre frère tient-il? 2. Il tient l'Hôtel de l'Europe, rue 3. Votre petit garçon se tient-il bien propre? 4. Il se tient bien propre. 5. A quoi vous en tiendrezvous ? 6. Je m'en tiendrai à ce que je vous ai dit. 7. Ne savez-vous pas à quoi vous en tenir ? 8. Je sais parfaitement à quoi m'en tenir. 9. Pourquoi vous tenez-vous debout? 10. Parceque nous n'avons pas le temps de nous asseoir. 11. N'avez-vous point défendu à ces jeunes gens de tenir de tels propos ? 12. Je le leur ai défendu. 13. Votre cocher n'a-t-il pas tenu un langage bien insolent? 14. N'avez-vous pas peur de vous enrhumer, en tenant les portes ouvertes ? 15. Nous préfèrerions les tenir fermées. 16. Votre maître vous recommande-t-il de tenir la tête droite? 17. Il me recommande de tenir les pieds en dehors. 18. Pourquoi votre ami ne vous tientil pas compagnie? 19. Sa sœur est indisposée; il est obligé de rester avec elle. 20. Votre oncle ne vous a-t-il pas tenu lieu de père? 21. Il m'a tenu lieu de père et de mère. 22. Regarderez-vous de plus près à cette affaire ? 23. Non, Monsieur; je m'en tiendrai à ce que j'en sais. 24. Ce médecin ne tient-il pas à son opinion? 25. Il y tient plus qu'il ne tient à la vie de ses malades.

EXERCISE 174.

4.

1. Does that gentleman keep open table? 2. He keeps an hotel in Paris. 3. Why do you keep the windows open? We keep them open because we are too warm. 5. Has not your friend kept his word ? 6. He has kept his word; he always keeps his word. 7. Have you not told your scholar to keep his head upright? 8. I have told him to keep his head upright and his eyes open. 9. Why do you not stay with your sister? 10. Because I have promised to go to my cousin's this morning. 11. Have you forbidden your little boy to make use of these expressions? 12. I have forbidden him. 13. Does he make use of insolent language? 14. He does not. 15. What will be your decision? 16. I will abide by what I told your father. 17. Have you forwarded that money to your friend? 18. I have not yet forwarded it to him. 19. Will you forward it to him to-morrow? 20. I will forward it to him if I have an opportunity. 21. Why do you not keep standing? 22. Because I am tired. 23. Do you think that the colour of your coat is fast? 24. I think that it is fast; it (elle) appears very good. 25. Will you not look closely into your brother's affairs? 26. I shall not look closely into them. 27. I will be satisfied with your opinion. 28. Are you not tenacious of your opinion? 29. I am not too tenacious of it. 30. Does not

your physician adhere too tenaciously to his opinion? 31. He adheres to it. 32. Does that lady hold your mother's place? 33. She is a mother to me. 34. Our cousin is a father to us. 35. That physician does not value the life of his patient. SECTION XC.-IDIOMS RELATING TO ÊTRE.

1. The verb être enters into a great many idioms besides those which we have already mentioned:-Être en retard, to be late, to tarry; être en état, à même de, to be able to; être en peine de, to be uneasy about; être en vie, to be alive, to live; être en chemin pour, to be on the way to; être au fait, au courant de, to be familiar with; être à la veille de, to be on the eve of; être de trop, to be unnecessary, to be in the way; être bien avec, to be on good terms with; être brouillé avec, to be on bad terms with; être aux prises avec, to be in open rupture, quarrel, or battle with; être d'avis, to be of opinion, etc.

2. Être, as already said [Sect. XLVI. 5], is used in the sense of appartenir, to belong. It is also employed in the sense of to behove, to become. In the latter sense, it takes generally the preposition de before another verb.

Nous sommes d'avis que vous
alliez lui faire des excuses.
Ce n'est pas à lui de nous re-
procher notre bonté.

A qui est-ce à lire ?
C'est à ma sœur à lire ce matin.

Cette maison est à lui et à moi.
Elle est à moi, elle est à lui.
Ces souliers ne sont pas à nous.
Ils appartiennent à notre frère.
Ils lui appartiennent.
Monsieur n'y est pas.
Madame y est.

Achet-er, 1, to buy.
Arriv-er, 1, to arrive.

Correspondant, correspondent.

riage.

It is our opinion that you should go and apologise to him.

It does not become him to reproach us with our kindness. Whose turn is it to read?

It is my sister's turn to read this morning.

That house is his and mine.
It is mine, it is his.

These shoes are not ourS.
They belong to our brother.

They belong to him.

The gentleman is not at home.
The lady is in.

Craind-re, 4, ir., to fear, Mois, m., month. to dread.

Dev-oir, 3, to owe, be
obliged.
Gravure, f., engraving.

Montre, f., watch.
Mort, p. p., from mou-
rir, to die.
Mort, f., death.
EXERCISE 175.

set out.

Propriétaire, m.,

land

lord. Punir, 2, to purish. Veille, f., eve, day before. Veill-er, 1, to watch.

2. Il y a

10.

1. Y a-t-il longtemps que vous êtes brouillés ? plus d'un mois que je suis brouillé avec lui. 3. Votre ami estil encore en vie? 4. Non, Monsieur; il y a dix ans qu'il est mort. 5. Votre correspondant est-il en chemin pour Paris? 6. Je crois qu'il doit être arrivé. 7. Ce jeune homme n'est-il pas en retard? 8. Oui, Monsieur; il ne vient jamais à temps. 9. Ces gravures sont-elles à vous ou à votre libraire? Elles sont à moi; je viens de les acheter. 11. Ne craignezvous pas d'être de trop ici? 12. Nous sommes trop bien avec notre hôte pour craindre cela. 13. À qui est-ce à aller chercher les livres ? 14. C'est à moi à les aller chercher. 15. Est-ce à vous de le punir, quand il le mérite? 16. C'est à moi de le punir, car je lui tiens lieu de père. 17. Ces maisons n'appartiennent-elles pas à notre propriétaire? 18. Elles ne lui appartiennent pas. 19. Elles sont à notre correspondant. 20. À qui

* Monsieur, Madame, not followed by a name, are generally understood to mean the master and mistress of the house, the heads of the family.

and 4 feet above it. Anywhere upon the HL mark the PS (point of sight). From PS as a centre, and with the distance of 6 feet in the compasses, draw the semicircle DE', DE2. Before we go any farther we will examine this. To assist in understanding the position and meaning of this semicircle we refer back to Fig. 21, Lesson IV., Vol. II., page 360. There it will be seen that E represents the eye, and its distance from the PP from E to PS. Of course PS is opposite the eye E, and a line between the two would form right angles with. the PP. Now it is necessary to set off on the HL the distance of the eye from the PP, that is, the distance from E to PS, for a reason to be explained presently; therefore, the proper way to do that is to draw a semicircle, and mark the extremities meeting the HL as DE1 and DE2. In the eidograph (Fig. 21), the dotted semicircle through the eye E (ending on one side at DE' and the other at DE) is in an horizontal position; it is afterwards supposed to be turned up, or rabatted, upon the PP passing through E2 (to the same points). This

E

Fig.49.

vanishing line the length required, in the same way that we used the DE2 for cutting off the point d in the line b Ps. From DVP through d draw a line to meet the PP in e, make e ƒ equal to the length of the pole, 6 feet, and from ƒ draw another line back to the DVP, cutting the vanishing line from d in h; hd will then be the perspective length and representation of the pole. We must dwell upon this for a minute or two, as this cutting (as we term it) a vanishing line is important. Our pupils will have observed that we drew a line, commencing from the DVP, through d to e, and after we had marked the given length eƒ on the PP, we drew from ƒ back again to DVP; in other words, in order to determine the space upon the PP which is to contain the length of the pole, and at the same time secure the perspective position, Wa brought the nearest end, d, of the pole to the PP at e, measured its length, ef, and then ruled back again, to the distance point. This may be summed up in very few words, in the form of a rule to be rememberedthat every vanishing line is cut by its own distance point. The ability to draw an object in perspective upon this lineal system depends principally upon a clear understanding of the above rule in the several ways in which it may be applied. We advise our pupils to get this first problem well up, by doing it again at other angles, and other given distances and proportions. Afterwards they will have very little difficulty in understanding all that is to follow.

VP

DE1

H

DIVP

f

с

will be the position in which we shall place it for the future, and as seen in the figures which immediately follow Fig. 21. To proceed with Fig. 49: draw a line x x tangential to the semicircle, and parallel to the HL or PP. Our problem states that the inclination of the pole to be represented is at an angle of 40° with the PP. Therefore, from E draw a line at that angle with xx, meeting the HL in VP. There will be no difficulty in comprehending this, if we consider that because a a is parallel with the PP, therefore if the plan of an object is known to be at a certain angle with the PP (as in the ground-plan method), it will form the same angle with xx. This, then, is the way a VP is found without the necessity of a plan. From PS draw the perpendicular

PS a, and mark one foot to the right of a, viz., a b, because the nearest end of the pole is 1 foot to the right of the eye. Draw b Ps, and somewhere upon b Ps will be found the position of the nearest end of the pole, to be determined in the following manner :-From

set off b c equal to 2 feet, draw a line from c to DE2, cutting b Ps in d, the point required. This, with the exception of the pan, is precisely the same that was done with the line A в in Fig. 23,

Vpl

이

ae

PP

DER

PROBLEM XXVIII. (Fig. 50).-Two lines, each 3 feet long, form a right angle; one of the lines is at an angle of 40° with the PP, nearest point 2 feet to the left of the eye, and 1 foot within the

VP2

that is, by making C D equal to CA, a was found to be the nearest end of the line A B. We now come to a stage of the proceedings which will demand the closest attention of our pupils. It is that of cutting off a portion of a vanish ing or retiring line, to give the perspective length of the object, in this case the pole. From d, the nearest end of the pole, draw a line to the VP (the vanishing line of the pole); upon this line will be cut off the perspective length, as follows:From VP, with the radius VP E, draw the arc E DVP; DVP is the distance of the eye from the VP, and is set off upon the HL upon the same principle as the other distance points are placed; the use of this distance point is to enable us to cut off upon the

Fig.50.

DE2

picture; height of eye, distance, and scale as in the last problem.

Draw the PP, horizontal line, and semicircle through E at the given distance as before, make E VP at an angle of 40° with xx, and draw E VP2 at a right angle with it. From each of the vanishing points draw arcs from E to the HL for the respective distance points; produce E PS to a, and make a b equal to 2 feet; join b Ps, make b c equal to 1 foot, and draw a line from c to DE'; where this last line cuts b rs in d will be the position of the angle; draw a line from d to Vpl. Now we must remember the rule given in the last problem, every vanishing line is cut by its own distance point; consequently, as DVP' is the distance point of vP, we must draw a line from DVP1 through d to the PP at e, make e f equal to 3 feet, the length of one of the lines forming the right angle, and from ƒ rule back again to DVP', cutting d vp1 in h; d h will be the length of the line. The other line of the right angle must be similarly treated; as it vanishes at VP2, the distance point of VP2 must be used for cutting off its perspective length, by bring ing a line first from DVP2 through d to the PP at m; make mn equal to the length of the line, and draw from n back again to determine o in the vanishing line; h do will be the perspectiv0 representation of the right angle as required.

RECREATIVE NATURAL HISTORY.

THE OX FAMILY.

OUR common ox, the pride of every Smithfield Cattle Show, is so well known that any notice of such a quadruped may seem superfluous; but as a study of the most familiar forms of life is sure to disclose some peculiarity of structure, or to recall some important historical fact, we may be certain that this will be the result in the present case. If one were to ask what animal has most aided man in his progress to civilisation, the answer must probably be the ox. In the first stage of savage life, when food is procured by hunting wild beasts, the dog may be the most valued servant. But when this rude state has been passed, the ox becomes man's trusted friend, providing him with food and clothing, drawing the plough, and moving the wagon. It was not, therefore, wonderful that the early races of men should exalt this animal to the rank of a deity. Thus we see the wisdom of Egypt and the might of Assyria bowing before the symbolic bull; and even the chosen people of Hea

bling in these two particulars

those of the sheep,

goats,

bison or aurochs has fourteen. Many other anatomical peculiarities completely separate the bison from our oxen. Some writers, despairing of finding the parent race in Europe, trace it to the buffalo of Asia, while Cuvier himself inclined to the belief that the ancestors of our farm-oxen have become extinct. We must, therefore, look for the primary types of our Devons and Herefords in those fossil bones so often found in the upper deposits of the tertiary formations. Nor shall we probably go far wrong if we regard the wild cattle of Chillingham Park as very closely allied to some of our existing breeds. brief remarks may suggest to the reader some notions of the difficulties encountered in tracing the history of our most common animals.

These

We must not pass on without at least indicating some of the more remarkable species of the bovine family. No reader will wish us to lose time in technical descriptions of the various improved breeds reared for the market-topics suited to an agricultural journal, but out of place in these pages. Nor can

and antelopes. A vehement dispute has long raged respecting the origin of our common ox. One naturalist sees the original breed in the wild cattle still kept in Chillingham Park, Northumberland. Another regards the formidable urus, or wild bull of ancient Germany, as the ancestral type. But if we may trust the description given of these by Cæsar, they could scarcely have been the fathers of our present cattle. The great Roman says these ancient bulls of the German forests were nearly as large as elephants, and that their horns were capacious enough to form drinking vessels.t We shall have a word to say about these large horns hereafter. At present it may suffice to remark, that the existing breed of oxen cannot well be traced from the fierce and gigantic uri of Cæsar. The European bison, which is thought to be still wandering in the wild regions of the lower Danube, has been regarded by a few as the parent stock. The examinations of Cuvier and other anatomists show this to be almost impossible. He mentions one structural difference only in proof of this. Our oxen have thirteen pairs of ribs, but the

This term is derived from bovis, the genitive of bos, the Latin for C. The real root is the Greek Bous (bous). "De Bello Gallico," lib. vi., cap. 28.

VOL. III.

we describe all the widely-extended species of this family, but only those which are most remarkable for peculiarities of form, habits, or historical

associations.

The Chillingham wild cattle, to which reference has been already made, demand a few words more. It is probable that we see in these the descendants of the wild bulls which in the reign of King Henry II. roamed in the wide forests then extending far around London. They are cream coloured, but have black muzzles, and ears of a reddish tint. The horns are short,

black on the tips, and have

a slight curve upwards. Some of the bulls possess a short mane. Those who have seen them for the first time in the solitudes of Chillingham, have been struck by their peculiarly wild habits. No sooner does the herd behold a strange visitor than the whole body dash away, as if in fright. After running for about a hundred yards they stop, turn round, and advance, as if to charge the intruder, then suddenly pause at some distance, scrutinising the object before them. Should the man wave his arms, off they dart again, but to a shorter distance; then turning, dash forwards as before, coming nearer than at first. Thus, by a succession of retreats and advances, the animals at last come so near that the visitor receives warning to retire, lest the wild herd should finish by a fatal charge. Here is indeed a splendid zoological study for all who can gain an admission to such a collection. Once or twice the herd has been on the point of perishing from disease; but the care now taken will, it is hoped, long preserve these few remains of the wild forms of nature. Readers who have seen Landseer's famous picture of the Chillingham wild bull are able to form some notion of the force and beauty of the living animal.

Far different from these wild cattle of Britain is the bison of America, with its huge lion-like mane, humped back, and vindic70