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11. Discount is the abatement made from a debt in consideration of its being paid before it is due.

If A owes B a sum of money (£500 suppose) which is to be paid at the end of a given time (say six months), and instead of waiting until the six months have expired, discharges the debt now, it is evident that he ought not to pay the whole amount of the debt; for B could put out the £500 to interest, and then, at the expiration of the six months, he would be in possession not only of the £500, but also of the interest on £500 for that time.

In order that the transaction may be strictly equitable, it is plain that A ought to pay B such a sum as, put out to interest, would amount in six months to £500. The sum so paid is, for an evident reason, called the present worth of the debt; and the interest upon it which added to it makes up the amount of the debt, is the true discount.

The true discount, then, is the interest of the present worth for the time the debt has to run; or, what is the same thing, it is the difference between the amount of the debt and its present worth.

12. In mercantile transactions, where short periods of time are concerned, it is customary to deduct from the amount due the interest upon the amount, and not the interest upon the present worth. This mode of reckoning is manifestly inaccurate, and it is for this reason that we have used the expression true discount, meaning thereby to distinguish it from the ordinary discount of commerce.

The discount upon £105, due one year hence, at 5 per cent., is £5, because in 12 months £100 would amount to £105. The interest on £105, however, is £5 5s. at the same rate.

N.B.-Observe that the difference between the interest and the true discount is the interest upon the true discount for the given time.

13. To find the present worth of a given sum at a given rate per cent., due at the expiration of a given time.

This is exactly the same question as that explained in Art. 7 (Vol. II., page 403), viz., to find what principal will with its interest amount to the given sum in the given time at the given rate per cent.

EXAMPLE. Find the present worth of £6812 17s., due 12 years 4 months hence, at 7 per cent.

By the rule (see Art. 7) we have (since the interest of £100 at 7 per cent. for 12 years is £71 × 121, or £15, i.c., £92 10s.

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15. In commercial transactions, when one man engages to pay another a certain sum of money at the expiration of a certain time, a document is drawn up, according to an established form, upon a piece of paper, to which a government stamp of a certain value is affixed. The value of the stamp varies according to the amount of the debt, and tables of these stamps are given in most of our almanacks and pocket-books. Such a document is called a Bill.

A bill may be either what is called a Promissory Note, which contains a promise on the part of the undersigned to pay the money at the end of a certain time; or it may be a Draft, which contains a request or order to the debtor to pay. A draft is also sometimes called a Bill of Exchange, We give the forms of both kinds :—

FORM OF A PROMISSORY NOTE.

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The above are two different forms by which William Johnson places himself under the obligation to pay £783 12s. 6d. to Henry Jenkins at the end of six months.

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The draft is called an Acceptance, after William Johnson has what is called "accepted" the bill-that is, written across it Accepted," etc., and signed his name. The acceptance (placed, in the above example, for convenience at the foot of the bill) is written across it by the Drawee. The person who makes out the bill (in this case Henry Jenkins) is called the Drawer. William Johnson, upon whom the bill is drawn, is called the Drawee, until he has accepted it, and then he is called the Acceptor. Sometimes the bill is made out to be paid to a particular person, who is called the Payee.

16. Such bills, before they become due, are passed about from hand to hand instead of money. The person in possession of the bill at any time is called the Holder, and when he pays it away to another person, he writes his name on the back, which is called endorsing the bill. The acceptor is always liable to the holder, who can also recover from the drawer and endorser. This transference of a bill from one hand to the other is called negotiating the bill.

It is evident from what we have said about discount that the value of such a bill continually increases, up to the time at which the debt is payable, the present worth being manifestly greater the shorter the time it has to run.

Suppose I take such a bill for £500 to a banker three month form sulphides soluble in water, and therefore do not give precipitates. before it is due, and ask him to give me money for it; he will

offer to "discount" it at so much (say 8) per cent. This means that he will give me £490 for it-that is, £500 less the interest for three months at 8 per cent. Now if the banker can borrow money at a less rate than 8 per cent. (say 5 per cent.) he can at

once borrow £490 at 5 per cent. This would amount in three months only to £496 2s. 6d. He would thus be a gainer of 23 17s. 6d. by the transaction.

It is on this principle of discounting a bill at a higher rate of

interest than that at which money can be borrowed, that bankers and bill-discounters make their profits.

17. In calculating the day upon which a bill becomes due, a certain number of days, which varies in different countries, called Days of Grace, are added to the time specified. In Great Britain, three days is the time allowed. Calendar months are always reckoned. Thus, a bill drawn on Feb. 15th at three months becomes actually due on May 18th. If a bill be drawn on the 29th, 30th, or 31st of a month, and the month in which it becomes due (not reckoning the days of grace) does not contain 29, 30, or 31 days, as the case may be, then the last day of the month is taken, and the three days of grace added.

Thus a bill drawn on Jan. 31st at three months would (without the days of grace) be due on April 30th, and therefore would be actually due on May 3rd.

EXERCISE 57.-EXAMPLES IN DISCOUNT, ETC.

Calculate the True Discount upon

1. £45, due 1 year hence, at 5 per cent.

2. £325 10s., due 18 months hence, at 34 per cent.

3. £1000 for 10 months, at 4 per cent.

4. What is the present worth of £450, payable in 6 months, at 6 per cent.?

5. What is the present worth of £840 16s. 8d., due 3 months hence, at 3 per cent ?

6. Find the present worth of £819 4s., due 9 months hence, at 3) per cent.

7. Find the difference between the True and the Commercial discount upon £3500, due 10 months hence, at 6 per cent.

8. Find the discount upon £430, due 18 months hence, at 3 per cent. 9. Compare the cash and credit price of the same article; credit being given for one year, and simple interest at 43 per cent. per annum being allowed. Find the cash price of articles, the credit price of which amounts to £114 1s. 7d.

10. The difference between the interest and the true discount for a certain sum for 2 years at 4 per cent. is £2 14s. 8d.; find the sum. [See N.B., Art. 12, in the preceding page.]

11. If the discount on £567 be £34 14s. 3 d. at 4 per cent., when is the sum due ?

12. Two men owe equal debts to a third, both due at the end of 4 years; the one pays at once the equitable sum; the other leaves the amount of the debt in the bank for the benefit of the creditor, who thus receives sums in the ratio of 640,000: 844,561. At what rate is the interest calculated?

In the following questions the Mercantile Discount is to be calculated.

Find the present worth of the following Bills :

13. £235 8s. 6d., drawn 5th April, at 6 months; discounted 31st May, at 6 per cent.

14. £240, drawn 16th December, at 3 months; discounted 28th January, at 3 per cent.

15. £1000, drawn 31st December, at 4 months; discounted 2nd February, at 5 per cent.

16. £1250 10s. 6d., drawn 29th November, at 3 months 21st December, at 6 per cent.

; discounted

17. £850 178. 6d., drawn 31st July, at 8 months; discounted 15th September, at 4 per cent.

18. £325, drawn 25th October, at 9 months; discounted 15th January, at 8 per cent.

19. £755 58. 9d., drawn 17th March, at 3 months; discounted 31st May, at 6 per cent. 20. £537 5s. 2d., drawn 29th August, at 3 months; discounted 27th October, at 3 per cent.

LESSONS IN BOTANY.-XXVII.

SECTION LX-JASMINACEÆ.

Characteristics: Calyx free; corolla hypogynous, regular, monopetalous, saucer-shaped, five to eight partite; stamens two, inserted upon the tube of the corolla; ovary two celled, uni- or bi-ovulate; ovules collateral, ascendant; fruit a berry or capsule; seeds erect, dicotyledonous, exalbuminous.

The members of the family Jasminacea are usually trees stipules; flowers complete; calyx persistent; corolla imbricated or shrubs, often climbing, leaves ordinarily opposite, without in aestivation; anthers attached by their bases; albumen at first abundant, but towards maturity reduced to a very fine membrane; radicle inferior.

The Jasminacea are nearly allied to the Oleaceae, from which they, however, differ in certain well-marked characteristics, such as the number of their sepals and petals, the æstivation of their corolla, the ascendant ovules, the endocarp never hard, the erect seeds, and albumen almost absorbed.

The principal region of this natural family is tropical Asia; a few species, however, are indigenous to the Mediterranean region. The greater number of the Jasminacea possess a volatile oil in the tissue of their corolla, not obtainable by distillation. The so-called oil of jasmine is the product of stratifying jasmine flowers with some fixed non-odorous oil, generally oil of ben. This oil, which is used by watchmakers because it does not freeze so readily as other oils, is expressed from the ben nut, the seed of the Moringa pterygosperma, or winged-seeded horse-radish tree, a tree which grows in Arabia and India, and the roots of which are used as WO use horse-radish. The volatile oil of jasmine, to which allusion has just been made, is obtained chiefly from the flowers of the Jasminum officinale, or common white jasmine, or those of the Jasminum grandiflorum, or large-flowered jasThe last-named is a greenhouse evergreen climber, and not suitable for culture in the open air, like the common hardy deciduous climbers.

mine.

SECTION LXI.-VACCINIACEÆ AND ERICACEÆ. Characteristics: Calyx free or adherent to the ovary; corolla inserted upon an annulus or disc, either hypogynous or epigynous, monopetalous, regular; number of stamens equal to that of the lobes of the corolla, alternating with them, or double their number; anthers bilocular, separate celled; ovary one to five celled, with central placentæ; seeds inverse; embryo dicotyledonous, straight, in the axis of a fleshy albumen.

The plants which compose these two families are united into one, under the name Ericaceae, by some authors: they are shrubs or evergreen trees. The leaves, ordinarily narrow, are articulated with the stem, and without stipules; flowers complete; calyx four to six partite; corolla five or six partite; the lobes varying as to depth, sometimes almost free, imbricated in æstivation; ovules pendent or reflexed.

Ericacea. Corolla generally persistent; ovary free; fruit generally capsular.

Vacciniacea. Corolla caducous; ovary inferior; fruit bacciform or drupaceous; leaves plane; buds ordinarily covered with imbricated scales.

The Ericaceae or heaths are dispersed over all the globe; they are especially abundant in the cold regions of the northern hemisphere, and at the Cape of Good Hope. The heaths are altogether wanting in Asia, America, and Australia. Some species of this genus are gregarious, covering immense tracts in western and central Europe, where their presence indicates the soil to be unadapted to the culture of cereals. The greater number of species belong to the Mediterranean region. The Vacciniacer, a family which takes its name from the vaccinium, or whortleberry, grow for the most part on this side of the Tropic of Cancer, and in North America, chiefly inhabiting the temperate and cool regions of the northern hemisphere, especially the elevated mountains and hilly districts of America. Beyond the Tropic of Capricorn they altogether disappear. Most of the Ericaceae contain bitter astringent principles, sometimes also a venomous balsam. The berries of certain species aro edible. The Vacciniacea are especially valuable for yielding a refreshing acidulated fruit. Their leaves are slightly astringent. 9. I lose £1 48. 321d. The Thibaudia Microphylla produces berries which the inhabitants of Pasto, in Columbia, submit to fermentation, and produce

KEY TO EXERCISES IN LESSON XXXVI.

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a sort of wine. The flowers of Thibaudia Quereme are used by the Peruvians in the composition of an aromatic tincture useful in toothache.

The rhododendrons, which belong to the family Ericaceae, are remarkable for their narcotic property. The yellow flowered rhododendron (Rhododendron chrysanthum), a shrub growing in the Alps and Northern Asia, has bitter astringent leaves, employed occasionally in medicine.

Among the Vacciniaceae, the South American plant Thibaudia microphylla, a shrub which grows on the Andes in Peru, deserves to be mentioned. Its leaves contain a powerful narcotic, and if eaten by cattle they are fatal. Kalmia latifolia, if swallowed, causes a species of drunkenness and delirium, vomitings, convulsions, and frequently death. The intoxicating honey of the Euxine, so celebrated amongst the ancients from the date of the retreat of the ten thousand under the Greek historian Xenophon, derived its qualities from the

straight in the axis of a fleshy albumen; stem woody; leaves provided with caducous stipules, and ordinarily alternate.

The Celastraceae are usually shrubs, sometimes climbing. Their flowers are regular, axillary, disposed in cymes, small green, white, or purple in colour. The base of the calyx is surrounded with a fleshy disc, sometimes adherent to the ovary. The petals, enlarged towards the base, are inserted upon the border of the disc; imbricated in æstivation. The ovary is merged to a varying extent into the disc; ovules reflexed. Fruit, two to five celled, sometimes dehiscent, either drupaceous

or samaroidal, or, finally, capsular with loculicidal dehiscence, or mode of splitting in cells. The seeds are enveloped in a Leshy arillus. Radicle inferior.

The Celastraceae inhabit for the most part the sub-tropical regions of the southern hemisphere; towards either pole and the equator they become rare, and none are found in the two frigid zones. The greater number of Celastraceæ contain bitter

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flowers of the Azalea Pontica and Rhododendron Ponticum.

Most of the species already mentioned are cultivated in gardens as ornamental shrubs. The Vacciniaceae, in addition to the genera already mentioned, furnish to horticulture the Thibaudia and Macleania. Thibaudia pulcherrima was originally brought from Northern India; its flowers are disposed in umbels sessile upon the aged and leafless stems. The corolla of these flowers is tubular, campanulate, palishred in colour, verging occasionally towards greenish-yellow, marked longitudinally and transversely with lines of deep red.

SECTION LXII.-CELASTRACEE, OR SPINDLE-TREES. Characteristics: Calyx free, four or five partite; corolla perigynous, with four to five petals; stamens four to five, alternate with the petals; ovary two to five celled, ordinarily containing one or two ovules; ovules ascending; fruit capsular or drupaceous; seeds generally provided with an arillus, or exterior coating fixed to them at the base only; embryo dicotyledonous,

and astringent principles, united with others which are acrid, purgative, and emetic, or simply stimulant. The fruit of certain species is fleshy and edible, the seeds of others contain a fixed oil. The Celastrus scandens is termed by the French Bourreau des arbres (trees' hangman), because it winds so tightly around their trunk that they are strangled.

This species is indigenous to North America. Its bark is emetic. The Celastrus venatus, a spring shrub growing at the Cape of Good Hope, is dangerous on account of the wounds it causes. The Maytenus macrocarpus is a Peruvian shrub, the leaves of which are acid. The M. Chiliensis is an efficacious remedy against the poison oak. The decoction of its leaves is employed as a wash for application to parts injured by the former plant. The kat or gat (Catha edulis) is cultivated along with coffee in Arabia, and is in great repute amongst the Arabs as a preventive of sleep. They moreover pretend that localities where this plant grows are always free from the plague.

LESSONS IN BOOKKEEPING.—VII.

HOME TRADE.

26th.

Bought of Andrews and Co., London,
14 bags of Maranham Cotton (on credit),
Net 4350 lbs. at 7 d. per lb.

3,

39

31st.

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No. 2, Payable to their Order, due at 3 months
Smith and Co.
4 months
February 1st.

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Sold to Brown and Smith, London,
22 bags of Berbice Cotton (at 1 mo. credit),
Net 7280 lbs. at 10 d. per lb.
Discount at 1 per cent.

Lent to Thomas Watson, London

5th.

5th.

10th.

WHEN you see in a city, such as London, a space of ground
dug up to a certain depth, and surrounded by a hoarding, you
naturally conclude that a building is about to be commenced,
that a superstructure is about to be raised, and that its Accepted Two Bills drawn by Andrews and Co., London,
foundation is in the process of preparation. You are still
more convinced of the fact, when you see cartloads of stone,
brick, and lime deposited within the hoard, and workmen
proceeding to prepare the mortar and stones or bricks for
the foundation. So it is in the system of Bookkeeping by
Double Entry, which we are about to lay before you. We
must begin with a series of transactions in business, which are
arranged in the exact order of their occurrence, as the materials
to be employed in forming a system or superstructure which
shall constitute a model for your guidance in keeping the books Drew out of the London and Westminster Bank
of any mercantile house in which you may hereafter be engaged.
We have selected the supposed transactions of a particular
branch of home trade-namely, that of a cotton merchant, as
one well adapted, from its simplicity and generality, to exem-
plify the principles which we have explained in former lessons.
We have arranged these transactions in order from January,
when we suppose the business to be commenced, till June,
when we suppose a balance to be struck, and the merchant's
real worth ascertained. These six months' transactions in
the cotton trade are interspersed with various banking, bill,
and cash transactions, such as might be supposed to occur in
the business of a cotton merchant resident in the metropolis;
and the whole is afterwards entered in the various subsidiary
books which belong to such a business; then into the Journal;
and, lastly, into the Ledger. The General Balance is then
taken, and the difference between the Assets and Liabilities, or
the real worth of the merchant, is ascertained from the Ledger
alone. The remarks which it will be necessary to make con-
cerning the method of Balancing the Books-a process equivalent
to the taking of stock among tradesmen and others, who only
use Single Entry-we must postpone until we have shown how
to make up the Subsidiary Books of our system.

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Bought of White and Co., London,
24 bags of West India Cotton (at 1 mo. credit),
Net 7460 lbs. at 6d. per lb.
Discount at 1 per cent.

14th.

Sold to Williams and Co., London,

14 bags of Grenada Cotton (at 1 mo. credit),
Net 4312 lbs. at 94d. per lb.-
Discount at 1 per cent.

17th.

Bought of White and Co., London,

24 bags of West India Cotton (at 1 mo. credit),
Net 8476 lbs. at 6 d. per lb.
Discount at 1 per cent.

21st.

Sold to Williams and Co., London,

16 bags of Grenada Cotton (at 1 mo. credit),
Net 4928 lbs. at 94d. per lb.

Discount at 1 per cent.

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Received of Thomas Watson, London,
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Bought of Andrews and Co., London,

30 bags of Grenada Cotton (on credit),

Net 9240 lbs. at 8 d. per lb.

17th.

Drew out of the London and Westminster Bank

17th.

Bought £1000 of Stock in the Three per Cents. Consols, at 981 per cent.

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21st.

Drew out of the London and Westminster Bank
26th.

£120 0 0

Accepted a Bill drawn by Osmond and Co., London,
No. 1, Payable to their Order, due at 3 months

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22nd.

Drew out of the London and Westminster Bank

22nd.

Took out of Cash for my Private Account

VOL. III.

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LESSONS IN GREEK.—XV.

EXERCISES FROM THE BOOK OF PROVERBS.

1. Υίος σοφος ευφραίνει πατέρα, υἱος δε αφρων λυπη τῇ μητρι 2. Πενια ανδρα ταπεινοῖ, χειρες δε ανδρείων πλουτίζουσιν. 3. 6 Ευλογία Κυρίου επι κεφαλῇ δικαίου. 4. Μνημη δικαιων μετ' εγκωμίων (understand εστι), ονομα δε ασεβοῦς σβεννυται. 5. Μισος εγείρει νεικός. 6. Ος εκ χειλεων προσφέρει σοφίαν, ῥαβδῳ τύπτει ανδρα ακαρδιον. 7. Ανηρ διγλωσσος αποκαλύπτει βουλας εν συνεδριῳ, πιστος δε πνοῃ κρύπτει πραγματα. 8. Γυνη σπουδαία στεφανος τῳ ανδρι. 9. Λόγον αδικον μισει δικαιος, ασεβής δε αισχύνεται. 10. Σίδηρος σιδηρον οξύνει, ανηρ δε παροξύνει προσωπον ἑταιρου. 11. Ώσπερ δροσος εν αμητῳ, και ωσπερ ύετος εν θέρει, ούτως ουκ εστιν αφρονι τιμη. 12. Ακανθαι φύονται εν χειρι μεθυσμου, δουλεια δε εν χειρι των αφρόνων. 13. Σοφία και εννοια αγαθη εν πυλαις σοφων (understand εισιν)· σοφοι ουκ εκκλίνουσιν EK στόματος Κυρίου. 14. Αποθνησκει αφρων εν 1 ἁμαρτίαις. 15. Μη χαιρε επι κακοποιοις, μηδε ζηλου ἁμαρτωλούς. 16. Φοβού τον Θεον, υἱε, και βασιλεα. 17. Λογοις σοφων παραβαλλε σον οὓς, και ακουε εμον λόγον. 18. Ελεημοσυνη και αληθεια 4 φυλακη βασιλεῖ. 19. Κοσμος νεανίαις σοφία, δοξα δε πρεσβυτερων πολιαι. 20. Πας ανηρ φαίνεται ἑαυτῷ δικαιος, κατευθύνει δε Ο καρδιας Κυριος. 21. Ακολαστον οινος, και ὑβριστικον μεθη, πας δε αφρων τοιουτοις συμπλεκεται.

£257 12 1

£257 12

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VOCABULARY TO THE PASSAGES FROM THE PROVERBS. 1. Evopaivw, I rejoice (transitively); Avπn, -ns, ʼn, grief.

2. Пevia, -as, n, poverty; Tañεivow, I lower, degrade; avôpeios, -a, -ov, manly, excellent; λOUTI(w, I make rich (from what noun is the verb derived?)

3. Evλoyia, as, n, a blessing (what are the components of the noun ?) Kupios, -ov, ó, lord, master, the Lord-that is, the 8 Almighty, in the Old Testament; dikalov for Tоv dikaιov. The article is often omitted in the Greek version of the Hebrew Scriptures. This version is called the Septuagint, sometimes the Seventy," because said to have been made by that number s of learned Jews in Alexandria in Egypt; the translation was completed in the second century before Christ.

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4. Μνημη, ης, ή, memory, the memory ; εγκωμιον, -ου, το, praise, eulogy, our word encomium; aσeßns, -oûs, impious, compare σeBoμai, I worship; oßevvvμi, I extinguish; oßevvutai, is extinguished, that is, destroyed.

5. Midos, -oûs, To, hatred, connected with μoew, I hate; VELKOS, -OŪS, TO, strife; here is exemplified the remark that the Seventy are given to the omission of the article, for in Attic Greek this proposition would be το μισος εγείρει το νεικός.

6. 'Os, the relative pronoun he who; xeixos, -oûs, To, a lip; Ο ῥάβδος, ου, ή, a stick, staff, ακάρδιος, τον (from a, not, and Kapoia, the heart), heartless, senseless.

£600

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7. Atyλwooos (from dis, twice, and yλwτtα, -ns, ǹ, a tongue),

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