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I advise you to prosecute your studies now on your own basis, while at the same time you go forward with me. The way in which you may assist yourself is this: procure a Latin dictionary, and write out lists of connected words according to the models just given. With a little care you will be able to find the words in the dictionary. If you use a good dictionary you will make few mistakes. Having made a list, commit it to memory. Then make and learn others in succession. In this way you will learn not only the Latin but a good deal of philology or the science of language; and your progress will be rapid as well as sure.

66

You may perhaps be thinking what dictionary to purchase? Ainsworth's Latin dictionary in several forms is very common, and may often be met with at old book-stalls. But I advise you to leave the copies where they are, for like very many old books, they are not worth purchasing. Far preferable is Riddle's Latin dictionary, and in his Young Scholars English-Latin and Latin-English Dictionary," you would find a manual no less trustworthy than useful. The price of this book is twelve shillings. Should this be beyond your means, you may procure Riddle's "Diamond Latin-English Dictionary," which is an abridgment of the former work.

LESSONS IN BOTANY.-No. VII.

CLASS VI.-HEXANDRIA.

Plants bearing flowers with Six Stamens. ORDER I. MONOGYNIA. One Pistil.

STORES of wild hyacinths appear in almost every woodland towards the close of April. Some of the old herbalists call this beautiful flower the harebell. It is a native not only of every county of England, but of every land in Europe. The roots contain a great quantity of starch, which, in former times, was used for pasting books, and setting feathers on arrows, as well as by the laundress. The flower has a sweet scent, but the chief claims of the wild hyacinth are its early appearance and its great beauty.

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The wild tulip appears in April, in various parts of England and Scotland, and is naturalised in chalk-pits and quarries. The flower, of a bright yellow, and externally greenish, is rather drooping, the stem is about a foot high, and leafy at the middle, the leaves are lance-shaped, smooth, and clasp the stem. The bulb is egg-shaped, and the stamens are hairy at the base. The gaudy tulip, with its striped corolla of various hues, produced by the art of the florist, from the single colour of its natural state, was at one period the object of a passion, unmatched in the annals of the world. At Alcmaer, about twenty-three miles from Amsterdam, it is said there were sold publicly by auction, in the year 1637, one hundred and twenty tulips for 90,000 guilders, a sum equal to £8,437 10s. Nor was this a solitary instance, the tulip becoming associated with a kind of dealing like that of gambling in stocks.

The Wild Hyacinth.

Very nearly allied to the hyacinth is the vernal squill. Its leaves are numerous, its flowers of a deep blue, and its stalk three or four inches high. It flowers in April, May, and June; growing in sandy pastures by the sea. It is common on the sandy shores of Portugal, and the Levant. The bulb has been known as a medicine from the earliest ages, it is still held in high estimation, and is in very frequent use.

The flowers of the autumnal squill are rose-coloured. It grows in dry pastures in the south of England, the stalk is about three inches high, and flowers in September.

The lily of the valley, with its delicate bells growing half-hidden in the shade of their two broad leaves, appears in May. It is found in woods, but has probably been introduced there. Hurdis says truly of this flower:

"She ne'er affects The public walk, nor gaze of midday sun; She to no state nor dignity aspires,

But silent and alone puts on her suit,
And sheds a lasting perfume, but for which
We had not known there was a thing so sweet
Hid in the gloomy shade. So when the blast
Her sister tribes confounds, and to the earth
Stoops their high heads that vainly were exposed,
She feels it not, but flourishes anew,

Still sheltered and secure. And as the storm,

That makes the high elm crouch, and rends the oak,
The humble lily spares,-a thousand blows
That shake the lofty monarch on his throne,
We lesser folk feel not. Keen are the pains
Advancement often brings. To be secure,
Be humble; to be happy, be content!"

By the side of the lily of the valley may sometimes be seen the wax-like drooping blossoms of the Solomon's seal; so called because it was superstitiously supposed that the wise king of

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to five flowers on each stalk; the segments are white, tipped with green. There are, besides the common Solomon's seal, the narrowleaved, and the angular; the former flowering in June, the latter in May and June.

We give an illustration of one of the family of lilies, frequently met with in our gardens. It has the upper leaves oval, and the petals spotted. It is often known under the names of Turk's turban, or Turk's head. In colour it resembles that of the tiger, whence its name of the tiger lily.

Of the rushes there is a great variety. Their long, thin leaves, form islets on the stream, or fringe its border with its greenness. The soft rush and the common rush are used, in many parts of the country, for plaiting into mats and chair-bottoms, and for constructing small toy-baskets. The wicks of the candles, called rush-lights, are made from the pith, as also the wicks of some lamps. The soft and the common rush grow in wet meadows and pastures, and flower in July.

The sweet flag is abundant in the fenny districts of England, and was much prized when rushes were used instead of carpets. On festival days, the old cathedral of Norwich has its floors still profusely strewn with this fragrant plant. The Turks make a sweetmeat of the root, and consider it a preservative from plague. Our native species is aromatic like that brought from the Levant. It is one of the oldest medicines known, and is still much used.

Such are the only specimens our limits allow us to give of this large class. DIGYNIA, contains only the mountain sorrel. It grows in moist rocks and by rills, on the higher mountains of Scotland, Wales, the north of England and of Ireland, where it is abundant. Its stem is from six inches to a foot high; it is almost leafless; and the flowers, which appear in June, are small and drooping. From the order TRIGYNIA, we select the docks, which are very various. The meadow dock grows in marshy ground, and flowers in June and July. The Alpine dock grows by road-sides, but is not indigenous. It flowers in July. The fiddle dock, so called from the shape of its leaves, flowers in the same month. The petals of its flowers are egg-shaped, and very deeply toothed, of a green colour, with a large spot of scarlet in the centre of each. The stamens are large and yellow, adding to the brilliancy of the flower; the stem is light green, striped with red; each whorl of flowers is attended by a single leaf.

The fifth order, POLYANDRIA, has the water-plantains, which are found in ditches and other shallow waters. They may be known by a cup of three leaves, and a greatly-expanded corolla of three proportionally large, flat, circular petals.

CLASS VII.-HEPTANDRIA.

Plants bearing flowers with Seven Stamens.
ORDER I. MONOGYNIA. One Pistil.

The cup of the winter green, or chickweed, has seven spearshaped leaves; the blossom is formed like a star, and, though divided into seven segments, is of one petal. Though seven is the general number of stamens in this plant, it sometimes deviates from it. In one species, the parts of the fructification are defended against the injuries of rain, by the closing of the petals, and the hanging down of the flowers at its approach. Our song-birds, especially the tribe of finches, are much indebted to this plant for food; as they eat not only its numerous seeds, but its young tops and leaves. CLASS VIII.-OCTANDRIA.

Plants bearing flowers with Eight Stamens.
ORDER I. MONOGYNIA. One Pistil.

The willowherbs are generally characterised by a superior cup of four tapering, coloured leaves; a corolla of four circular expanding petals; and the summit of the pistil divided into four clefts. In some species, the stamens and pistils are upright, but lean towards the lower side of the blossom in others. Another distinction that marks the different species, is the shape of the leaves. The small-flowered hairy willowherb has spear-shaped, woolly, toothed leaves, growing opposite to one another. The great-flowered willowherb has its leaves running along, and embracing the stem; the top shoots have a very delicate smell; but it is lost almost as soon as they are gathered. These plants are generally found in marshy places, or on the banks of rivers.

There are several species of heath. They generally have a calyx of four leaves upright, coloured, enclosing the germ; a blossom of one petal, cut into four segments, the figure of which varies between egg-shaped and oblong. The bell-heath is one of our prettiest

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&c.

The common heath is the badge of the clan Macdonell; the cross-leaved heath of the Macdonalds; and the fine-leaved heath of the Macallisters. Many other floral emblems are assumed by the different Highland clans, as the yew, holly, pine, cranberry, The heath tribe is said to be the largest genus of plants; all, except about a dozen, are from the Cape of Good Hope. It is a remarkable fact, that some have been found wild in America; and although in autumn our mountain-sides and moors are completely empurpled with heath-flowers, there are only five species in Britain. TRIGYNIA. Three Pistils. The reddish-white blossoms of the knot-grass constantly meet the eye in passing from the paved ways of the city in the month of May. Milton speaks of

"The knot-grass dew besprent;"

and Herbert mentions this among wholesome and medicinal herbs.
This little plant forms green patches by every wayside, on the
borders of the public highways, and shoots up under the walls of
the crowded city, or even between the stones of the street.
Several plants are found in the order TETRAGYNIA, but on them
we must not dwell.

LESSONS IN FRENCH.-No. XIII
By Professor LOUIS FASQUELLE, LL.D.

SECTION XXVIII.

USE OF THE ARTICLE (§ 77).

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The flowers of the gardens of this
villa.

Do you intend visiting France?
I intend visiting Italy.
Is captain Dumont here?
Major William is at home.
Do you see your mother?
I see your brother.

My brother is not fond of praises.
EXERCISE 55.

Aim-er, 1. to be fond of, Demeur-er, 1. to dwell, Légume, m. vegetable;
to like;
live;
Loin, far;

Etudi-er, 1. to study;
Fleur, f. flower;
Fraise, f, strawberry;
Framboise, f. raspberry;

Lundi, m. Monday;

Pêche, f. peach;
Prune, f. plum.

Apport-er, 1. to bring;
Bois, m. wood, forest;
Capitaine, m captain;
Caporal, m. corporal;
1. Aimez vous le pain ou la viande? 2. J'aime le pain, la
viande, et le fruit. 3. Avons nous des pêches dans notre jar-
din? 4. Nous y avons des pêches, des fraises, des framboises
et des cerises. 5. Monsieur votre frère aime-t-il les cerises?
6. Il n'aime guère les cerises, il préfère les prunes. 7. Avez
vous des légumes? 8. Je n'aime point les légumes. 9. Nous
n'avons ni légumes ni fruits [Sect. 6. 3, 4]. 10. Nous n'ai-
mons ni les légumes ni les fruits. 11. Allez vous tous les
jours dans le bois de Monsieur votre frère? 12. Je n'y vais
pas tous les jours. 13. Votre sœur apporte-t-elle les fleurs?
14. Elle les apporte. 15. Madame votre mère apporte-t-elle des
fleurs? 16. Elle en apporte tous les lundis. 17. Voyez vous
le général Bertrand? 18. Je ne le vois pas, je vois le caporal

1. THE article le, la, les, as already stated, is used in French Duchêne. 19. Mesdemoiselles vos sœurs sont elles fatiguées ? before nouns taken in a general sense :

Les jardins sont les ornements des villages et des campagnes.

Gardens are the ornaments of
lages and of rural districts.

20. Mes sœurs sont fatiguées d'étudier. 21. Monsieur le prévil-sident est-il chez lui? 22. Non, Monsieur, il est chez Monsieur le colonel Dumont. 23. Demeure-t-il loin d'ici? 24. II ne demeure pas loin d'ici. 25. Où demeure-t-il? 26. Il demeure chez Monsieur le capitaine Lebrun.

2. The article is also used in French, as in English, before nouns taken in a particular sense :

Les jardins de oe village sont su- The gardens of this village are su
perbes.
perb.

3. It is also used before abstract nouns, before verbs and adjectives used substantively:

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EXERCISE 56.

1. Does your sister like flowers? 2. My sister likes flowers, and my brother is fond of books. 3. Is he wrong to like books? 4. No, Sir, he is right to like books and flowers. 5. Have you many flowers in your garden? 6. We have many flowers and much fruit. 7. Is your cousin fond of raspberries? 8. My cousin is fond of raspberries and strawberries. 9. Is the captain fond of praises? 10. He is not fond of praises. 11. Has the gardener brought you vegetables? 12. He has brought me vegetables and fruit. 13. Is he ashamed to bring you vegetables? 14. He is neither ashamed nor afraid to sell vegetables. 15. Is your mother tired? 16. My mother is not tired. 17. Is your brother at colonel D's? 18. He lives at colonel D's, but he is not at home at present (à présent). 19. How many peaches have you? 20. I have not many peaches but I have many plums. 21. Does Capt. B. like peaches?

23. Are you going into (dans) your brother's wood? 24. I go 22. He likes peaches, plums, raspberries and strawberries. there every morning. 25. Is general L. here? 26. No, Sir, he is not here, he is at your cousin's. 27. Does your friend General H. live far from here? 28. He does not live far from here, he lives at his brother's. 29. Have you fine flowers in your garden? 30. We have very fine flowers; we are fond of flowers. 31. Do you give them to him? 32. I give them to you. 33. I give you some? 34. I give them some. 35. Give us some. 36. Do not give us any.

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dius.

noun.

3. The article is not used in French before the number | 4. He knows him very well. 5. Are you acquainted with which follows the name of a sovereign. This number, (unless it be first and second) must be the cardinal, and not the ordinal [§ 26 (3)] :

Vous avez l'histoire de Henri qua

tre.

You have the history of Henry the

Fourth.

4. A noun placed in apposition with a noun or pronoun is not in French preceded by un, une, a or an, unless it be qualified by an adjective or determined by the following part of the

sentence.

Votre ami est médecin.

Notre frère est avocat.

Votre ami est un bon médecin.
Notre frère est un avocat célèbre.

Your friend is a physician.
Our brother is a barrister.
Your friend is a good physician.
Our brother is a celebrated advocate.
5. PRESENT OF THE INDICATIVE OF THE IRREGULAR VERBS.
APPRENDRE, to learn; CONNAÎTRE, to know; SAVOIR, to know;
J'apprends, I learn, do Je connais, I know, or Je sais, I know, or do

learn, or am learning;

Tu apprends,

Il apprend,

Nous apprenons,

Vous apprenez,

Ils apprennent.

do know;

Tu connais,

Il connait,

Nous connaissons,

Vous connaissez,

Ils connaissent.

know; Tu sais, Il sait,

Nous savons,

Vous savez,
Ils savent.

that lady? 6. I am not acquainted with her. 7. Is she a
German or a Swede? 8. She is neither a German nor a Swede,
she is a Russian. 9. Do you intend to speak to her? 10. I
intend to speak to her in (en) English. 11. Does she know
English? 12. She knows several languages; she speaks
English, Danish, Swedish, and Hungarian.
13. Is your
brother a colonel? 14. No, Sir, he is a captain. 15. Is your
upholsterer a Dane? 16. He is not a Dane, he is a Swede.
17. Are you a Frenchman? 18. No, Sir, I am a Hungarian.
19. Do you know Chinese? 20. I know Chinese, Russian,
and modern Greek. 21. Are you wrong to learn languages?
22. I am not wrong to learn languages. 23. Do you know
the Englishman who lives at your brother's? 24. I am
acquainted with him. 25. I am not acquainted with him. 26.
Do you like books? 27. I am fond of books. 28. Have you
a desire to learn Russian? 29. I have no desire to learn Rus-
sian. 30. Have you no time? 31. I have but little time. 32.
What do you learn? 33. We learn Latin, Greek, French, and
German. 34. Do you not learn Spanish? 35. We do not
learn it.

[We have been so repeatedly asked questions by our students of French, relating to the pronunciation of certain syl

6. Connaître means to be acquainted with; savoir, to know, is lables, words, and phrases, in that language, that we take an

said only of things.

Connaissez vous ce Français, cet
Anglais, cet Allemand, et cet
Espagnol ?

Savez vous le français, l'anglais,
l'allemand, et l'espagnol?

RESUME OF

Le capitaine G. sait il le français?
Il ne le sait pas, mais il l'apprend.
Connaissez vous le Docteur L.

Je ne le connais pas, mais je sais
où il demeure.

Ce monsieur est il peintre ?
Non, il est architecte.

Ce monsieur est un architecte dis-
tingué.

Ce Français parle grec et arabe.

Il parle le grec, l'arabe et l'italien.

Avez vous vu Charles dix, frère de
Louis dix-huit ?

Allemand, e, German;

Ancien, ne, ancient;

Anglais, e, English;

opportunity here, once for all, to mention that this elementary department has been so thoroughly gone into in the pages of the "Working Man's Friend," and in the "French Lessons," price sixpence, reprinted from that work, that it would be a task of supererogation to reproduce them in the POPULAR Do you know French, English, Ger- EDUCATOR. On all questions of this kind, therefore, we must man, and Spanish?

Do you know that Frenchman, that
Englishman, that German, and
that Spaniard?

EXAMPLES.

Does captain G. know French?

He does not know it, but learns it.

Do you know Dr. L.

beg to refer our correspondents to the manual above mentioned. As to questions relating to grammar, such as the gender of nouns, the conjugation of verbs regular and irregular, and syntax in general, we must again refer our readers to the SECOND PART of the Lessons in French, which are to appear in the POPULAR EDUCATOR, when we hope that all their real diffi

I am not acquainted with him, but I culties will be solved, if they do not vanish beforehand.]

know where he lives,

Is that gentleman a painter?

No, he is an architect.

That gentleman is a distinguished
architect.

That Frenchman speaks Greek and
Arabic.

He speaks the Greek, Arabic, and
Italian languages.

Have you seen Charles the Tenth, a
brother of Louis the Eighteenth?

EXERCISE 57.

Hongrois, e, Hungarian; Quatre, four;
Langue, f. language; Russe, Russian;
Moderne, modern; Suédois, e, Swedish,
Swede;
Polonais, e, Polish, Pole;
Danois, e, Danish, Dane; Quatorze, fourteen;
Grec, que, Greek;

Chinois, e, Chinese;

Tapissier, m. upholsterer.

1. Connaissez vous ce Monsieur? 2. Oui, Madame, je le connais fort bien. 3. Savez vous de quel pays il est ? 4. Il est hongrois. 5. Parle-t-il allemand? 6. Il parle allemand, polonais, russe, suédois, et danois. 7. N'est il pas médecin? 8. Non, Monsieur, avant la révolution, il était capitaine., 9. Avez vous envie d'apprendre le russe? 10. J'ai envie d'apprendre le russe et le grec moderne. 11. Connaissez vous les messieurs qui parlent à votre sœur ? 12. Je ne les connais pas. 13. Savez vous où ils demeurent? 14. Ils demeurent chez le tapissier de votre frère. 15. N'avez vous pas l'histoire de Louis quatorze, dans votre bibliothèque? 16. Je n'ai ni celle de Louis quatorze, ni celle de Henri quatre. 17. Avez vous tort d'apprendre le chinois? 18. Je n'ai pas tort d'apprendre le chinois. 19. Vos compagnons apprennent ils les langues anciennes? 20. Ils savent plusieurs langues anciennes et modernes. 21. Parlez vous anglais? 22. Je sais l'anglais et je le parle. 23. Connaissez vous l'Anglais que nous voyons? 24. Je ne le connais pas. 25. Il ne me connait pas et je ne le connais pas.

EXERCISE 58.

1. Does our physician know French? 2. He knows French, English, and German. 3. Does he know the French physician?

LESSONS IN ARITHMETIC.-No. XII.

RULE OF SIMPLE DIVISION-Concluded.

IN our last lessons we simplified the process of division by the use of the table of the multiples of the divisor, so as to render it comparatively an easy matter to find the successive figures of the quotient. In many cases, however, it might be reckoned both tedious and unnecessary to find these multiples, because several of them are frequently not required in the operation, especially when the quotient is to consist only of a few figures. In such cases, the common method of finding the quotient figure by trial or guess, is more frequently resorted to in practice; and, therefore, we proceed to explain this method, as one which includes all the preceding rules, and completes the rule

of division.

Rule 5.-Write down the divisor and dividend, with a place for the quotient, as formerly directed in Rule 3. Count off from the left of the dividend the smallest number of figures which make a number greater than the divisor; and find how many times the divisor is contained in these figures, putting this number of times in the quotient as its first figure. Observe,. that in trying to discover without the table of multiples, how many times one number is contained in another, especially when the divisor is beyond the limits of the multiplication table, proceed thus: Mark off mentally that number of figures from the right of both, which will bring the rest of the figures to the left, within the limits of that table, and use the remainders as trial numbers; that is, as trial divisor and dividend, in order to find the first figure in the quotient. Having found this first quotient figure, multiply the whole divisor by it, and subtract the product from the whole of the number of figures counted off from the left of the dividend at first. To the right of the remainder, annex the next figure of the dividend, for a dividuum (that is, a number to be divided); if this number be greater than the divisor, find how many times the divisor is contained in it, and annex the number of times to the quotient figure already found, repeating the process just described with this quotient figure as with the first. If the

dividuum be not greater than the divisor, annex to it the next
figure of the dividend, and the next again, and so on, until the
dividuum be greater than the divisor, taking care to annex to
the figure in the quotient, a cipher for every figure of the divi-
dend annexed to the dividuum. Proceed in the same manner
with this and every successive dividuum, as above directed,
until all the figures of the dividend have been taken into the
operation, when the complete quotient is then obtained: the
last remainder is the complete remainder, which may be
treated as before directed, and annexed in its fractional form to
the quotient.

EXAMPLE 1.--Divide 35821649 by 764,
Divisor. Dividend. Quotient.

764) 35821649 (46886

3056

5261

4584

6776

6112

6644

6112

5329

4584

there is no remainder, the reason of this method of proof is plainly this: that every product which arises from the multiplication of two factors, when divided by one of the factors gives the other factor; because the product being the one factor repeated as many times as there are units in the other, it is evident that the product contains the former as many times as the latter denotes,-that is, the divisor is the one factor and the quotient is the other. In the case where there is a remainder it is plain that if the remainder were subtracted from the dividend the same relation would subsist between the divisor, the quotient, and the dividend as subsists in the preceding case; consequently, the addition of the remainder to the product of the two factors,-viz., the divisor and quotient, must necessarily reproduce the dividend.

EXAMPLE.—In the case of the preceding example in division, the quotient is 46886, and the remainder 745. Therefore, multiplying 46886 by the divisor 764, and adding the remainder, the operation will be as follows:

46886 quotient

764 divisor

187544

281316

328202

745 remainder.

MODE OF OPERATION.

Here, according to the rule, counting off the smallest number of figures from the left of the dividend, which will make a number greater than the divisor, we have 3582; and we are to find how many times this number 3582 will contain the divisor 764. Now marking off mentally two figures from the right of both in order to bring the rest within the limits of the multiplication table, we have divisor 7 and dividend 35; hence, we find that 5 ought in this case to be the quotient figure. On trial, we should find this figure too much; because 5 times 764, or 3820, is greater than 3582 the dividuum, or number to be divided. This leads us to consider a little the nature of the figures mentally cut off; these were in the divisor 64, and in the dividend 82; now 82 does not contain 64 as many times as 35 contains 7. We must, therefore, adopt some method to meet this difficulty as much as possible. The simplest practical method is this; when the next figure, mentally cut off to the right, is 5, or a figure above 5, consider the rest of the figures to the left in the divisor, or the dividend, or in both, as the case may require, to be increased by unity, or 1; and then find the quotient figure as before. Thus, the trial numbers 7 and 35, in the preceding case, will become 8 and 36; because the next figures mentally cut off to the right were 6 and 8 respectively; now the dividend 36, and the divisor 8 will give the quotient figure 4, which is the right one. The reason of increasing the rest of the figures by 1, when the next figure cut off to the right is 5, or above 5, is that the figures so increased are nearer to the true number, though above it, than the figures not increased are, though below it. Thus, in the preceding case 800 is nearer to 764, though above it, than 700 is, though below it; and 3600 is nearer to 3582, though above it, than 2500 is, though below it.

The same principle carried out and applied to the successive dividuums, will give the successive quotient figures in the preceding example, with great accuracy. Practice in this rule will render the student very expert at division, and will enable him to work without the use of the table of divisor-multiples; at the same time, let it be remembered that this table will explain the nature of division more clearly and simply to a learner. But if at any time, the preceding method of finding the true quotient figure should fail, and should give a quotient figure either too great or too small by unity, which will be the greatest limits in general; the remedy is easy, and is quite at hand, the student having only to put the next less figure, or the next greater figure in the quotient, as the case may require. PROOF OF DIVISION.

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In cases where there is no remainder, it is evident from what has been said, that the product of the quotient and the divisor will reproduce the dividend; so that an example of this kind is unnecessary.

Another ingenious mode of proof is the following:-Arrange all the products of the divisor by the several quotient figures, under each other in the order in which their figures stand in the operation, for in each case they have a very different value, as already explained, placing the remainder in its proper place under the last product; find the sum of these products and the remainder thus arranged, and it will be the same as the dividend, if the operation be correct. The reason of this method and arrangement is, that these successive products are those which would arise from multiplying the divisor by the quotient, instead of the quotient by the divisor; so that the product must be the same as in the latter case; and the addition of the remainder is explained on the same principle as before.

EXAMPLE. In the case of the example already referred to, the successive products and remainder, arranged according to the preceding observations, would stand as follows:

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Proof 35821649 dividend reproduced.
EXERCISES ON THE PRECEDING AND FORMER LESSONS.
1. Divide one thousand billions by eighty-one.
2. Divide the same number by 729.

3. Divide a thousand thousand millions by 111.
4. Divide a thousand millions of millions by 1111.
5. Divide 908070605040302010 by 654321.

6. Divide 4678179387300 by the following divisors, separately,
2100, 36500, 8760, 957000, 87700, 1360000, and 87000.
7. Prove all the preceding questions by one or both methods
above prescribed.

S. If the annual revenue of a nobleman be £37960, how much is that per day, the year being supposed to be exactly 365 days?

9. What is the nearest number to one thousand billions, that can be divided by 11111 without a remainder?

10. How often could 43046721 be subtracted from 22876792454961, and at last leave no remainder?

The best method of proving division is to multiply the
quotient by the divisor, and to the product add the remainder
if there be any; the result of this operation will in all cases
reproduce (bring forth again) the dividend. In cases where give a quotient of 826451, and a remainder of 70404.

11. How many times does 310314420 contain 39390.
12. What number is that which divided by 123456 would

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