« 前へ次へ »
Er ist nach zehn Uhr zu mir gekom'. He came to me after ten
EXERCISE 74 (Vol. I., page 324). o'clock. (He is come to me
1. What is that servant gone for ? 2. She is getting water at the aftor ten o'clock.)
well, wood from the forest, and meat from the market. 3. Has she Er ist wegen seiner Krankheit nicht On account of his illness he did already gone for my trunk at the railway station ? 4. Yes, she went gegan'gen.
not go. (He is on account for it directly after she got up. 5. We sent for a physician for the of his illness not gone.)
sick man. 6. He got me to copy the letter, and then to carry it to the
post. 7. I neglect nothing to bring your son to a better course. EXERCISE 140.
Let us not be deluded by this event. 9. One should suffer the dead to 1. Wissen Sie nicht, an was für einer Krankheit Ihre Nichte gestorben rest. 10. He kept me waiting, although I was in a hurry. 11. Why did ift? 2. So viel ich gehört habe, ist sie an der Auszehrung gestorben. 3. afternoon at school. 13. Do you let your children learn French ?
you not let your little brother come? 12. Because he was all the Stele find in diesem Jahre an der Chelera gestorben. 4. Weiß man nicht, 14. No, because I consider the English language more useful. 15. The met die filbernen Löffel gestohlen hat? 5. Nein, aber man þat Verdacht major ordered his servant to show me the way to the village. 16. The auf einen Betienten des Hauses. 6. Man hatte zuerst eine alte Aufrår- gentleman whom you ask for bad the captain driven into the country. terin im Berdacte. 7. Er hat mich im Verdachte
, ihn vorsäßlich beleitigt 17. For whom do you send for the books ? 18. I send for them for it haben. 8. IH weiß wirklich nicht, auf wen ich meinen Verdacht werfen, my youngest sister, in order to teach her Italian, 19. He had me in. unt worauf ich ihn ftüßen soll. 9. Nachtem ich mich angefleitet, und vited to travel with him next week. nachdem ich gefrühstückt haben werte, will ich ihn besuchen. 10. Nach.
EXERCISE 75 (Vol. I., page 324). tem e zu Mittag gespeist þatte, las er die Zeitung. 11. Nachdem er sich gebatet hatte, machte er einen Spaziergang. 12. Nach zehn ihr des
1. Welchen von diesen Aerzten werden Sie holen lassen? 2. Ich werbe bente besuchte er mich noch. 13. Nach Mitternacht werden wir unsere keinen von Beiden holen lassen. 3. laß mich zufrieden, tenn ich bin nicht Meiße weite: fortseßen. 14. && giebt Menschen, welde nach diesem Leben wohl. 4. Nur feige Solbaten lassen ihren Anführer im Stiche. 5. Warum kein enteres erwarten. 15. Ich freue mich seinetwegen mehr, als meinet. ließen Sie Ihre kleine Schwester nicht kommen? 6. Sie konnte nicht, denn wegen. 16. Ihretwegen ħabe ich die Ncise unternommen. 17. Guret sie war den ganzen Morgen in ter Schule. 7. Er þat einen Zahnarzt holen segen ift ter Bater so betrübt. 18. linsertwegen brauchen Sie fich nicht zu lassen, um einen Zahn herauszuziehen. 8. Was lassen Sie Ihr Dienstmät: fhamen. 19. Mein Bruder war seiner selbst nicht mehr mächtig. 20. chen holen? 9. Ich lasse sie Papier und Dinte holen. 10. Laßt uns Hafi Du Herrn N. selbst, oder seine Frau gesehen? 21. Id habe ihn menschlich yanteln. 11. Laßt uns doch nach der Schule gehen. 12. Laßt kelbft nicht nur gesehen, sondern auch gesprochen. 22. Ein treuer Soldat uns nicht den Beispielen der Gottlosen folgen. ftirbt lieber, als taß er zum Verräther wird.
EXERCISE 76 (Vol. I., page 347).
1. What kind of weather is it to-day? 2. It is beautiful weather to1. Are we obliged to wait for our friend? 2. No, not on his day, but it is somewhat colder than yesterday. 3. What opinion does
he entertain concerning this thing? 4. His opinion of it is not the account. 3. This man is detested on account of his perfidy. best.
5. My society is for him the most agreeable in the world. 6. 4. Do not grieve on account of us! 5. On my account you may what kind of fish are these? 7. They are sea-fish. 8. In what kind of do what you like. 6. My brother died of consumption in the work does he occupy himself ? 9. He occupies himself partly in Tineteenth year of his age. 7. Do you know who has stolen writing, partly in reading. 10. What a power music has over the mind your gold watch? 8. No, but I am suspicious of that man who of man! 11. What a great delight it is to see the world! 12. What came to our house yesterday. 9. At first I suspected a servant a glorious aspect the firmament, with its innumerable stars, presents ! of the house. 10. After I had performed my last voyage, I ap- 13. Every star in the heavens forms a world of its own. 14. The plied myself to the study of the living languages. 11. After really virtuous man devotes every day of his life to laying aside his faults we had dined, we took an airing on horseback. 12. After he 16. No, every one has a different one.
15. Has not every one of your friends such a hat?
17. Such men are necessary, in had breakfasted, he visited his brother-in-law. 13. This lady order to save their native land. 18. Have you seen that blind man wants eighteen ells of muslin for a dress. 14. That youth be- who possesses a delicacy of touch, which is astonishing? 19. Yes, came a doctor, 15. That speculation made our neighbour a I have seen him. 20. The giver of such a gift is to be praised. rich man. 16. He told me he should on his own account speak 21. The hardships of such a journey strengthen the body. 22. Such to his father.
actions will call forth the admiration of posterity. 23. I have not had such agreeable hours for a long time. 24. Among the inhabitants
there are many very opulent. 25. Have you not too lived to see KEY TO EXERCISES IN LESSONS IN GERMAN.
many strange things ? 26. O yes, I have already seen many remark
able things. 27. Many a brave soldier had to lose his life in the EXERCISE 72 (Vol. I., page 324).
battle. 28. Has not this author written many good works ? 29. Cer
tainly, many of them are excellent. 30. Have both friends come to 1. It is questionable whether we shall have fine weather to-morrow.
an understanding about this thing ? 31. Yes, in some points they 2. It is proper to keep holy the Sabbath. 3. It is proper to esteem
have agreed with one another. 32. Some English ships were sunk in older people. 4. One works more joyfully when one has the conscious
this storm. 33. A few prudent men retired from the meeting. 34. ness that one is doing something good. 5. It is not proper to decline All the inhabitants of the town fled at the enemy's approach. 35. the invitation. 6. The really prudent man will labour to adapt him- Many persons pass their whole life in idleness. 36. Was that your self as much as possible to the times. 7. It affords great pleasure brother who was the whole of yesterday in your society? 37. No, it to further what is good. 8. It is proper that every foreigner should was my nephew, who visits me once every year.
38. What a magniadopt the good, but not the evil customs of a people. 9. This man's tude the earth has, and how much smaller, notwithstanding, is it than wealth increases visibly. 10. It is not proper for children to be dis
the sun! 39. What advantages has man over the beast ? 40. What obedient. 11. It is questionable whether this man has done his duty, bird's feather is this? 41. If the scholar is industrious, he learas 12. It sometimes happens that the considerations connected with a something. sportive occurrence are very serious. 13. It often happens that small
EXERCISE 77 (Vol. I., page 347). circumstances occasion great events. 14. Who has met you this morning ? 15. My friend the captain has met me. 16. Did anything 1. Mandyer Gelehrte ist missverstanten worden. 2. O, was für Thordisagreeable happen to him on his last journey ? 17. Yes, a great Þeiten begeht der Mensch in seinem Leben! 3. Mit was für Gesellschaft misfortane befell him. 18. What has happened to you ? 19. Nothing hatten Sie Umgang ? 4. Manch fleißiger Kaufmann ist durch eine unvor, has happened to me. 20. This punishment serves him right.
Fichtige Speculation zu Grunde gerichtet worden. 5. Manche Blume ist EXERCISE 73 (Vol. I., page 324).
geboren, im Verborgenen zu blühen. 6. Jedes Blatt, jeder Zweig, und jeder
Tropfen Wasser zeugen von unendlicher Weisheit und Macht. 7. Jeder 1. Gå gehört sich, daß Kinter ihre Eltern achten. 2. Es schickt sich muß Rechenschaft von sich selbst geben. 8. Die ganze Umgegend von Coblenz nicht für einen weisen Mann, ter Menge zu folgen.
9. Alle sind wohl zu Hause. 10. Die Unterhaltung mit jungen Leute wünschen gros in der Welt zu scheinen. 4. Sie sollten unter solchen Menschen ist beschrend. 11. Ich habe nie von solch einem Unglücke olim llmftanben die Wahrheit sagen. 5. Es frägt sich, ob wir Ihre Ein- gehört. 12. Es ist heute schönes Wetter
, aber etwas fälter als gestern. lating annehmen werden. 6. && frägt sich, ob Sie Recht oder Unrecht 13. Ich habe schon manche Freude gehabt. 14. Idy wünsche einige Citronen
7. Gs trägt sich zuweilen zu, tak ter beste Mensch irrt. 8. Die zu haben. 15. Er kam etwas zu spät. Regierung forrett Gehorsam von ihren Unterthanen. 9. Die Bevölkerung Sentend nimmt jered Jahr ungeheuer zu. 10. Mein Bruder witmete fich
EXERCISE 78 (Vol. I., page 382). mebr ter Wifisenschaften, als dem Bergnügen. 11. Wissen Sie, wie weit 1. He defended himself with an umbrella instead of a stick. 2. InIhr Freunb 3hnen gerathen hat? 12. Er hat Ihnen gerathen das zu thun, stead of going with friends, he was always in the society of strangers. meron a gestern sprach.
3. They had a great chest in the room instead of a bed. 4. In Ger
3. Die meisten ist romantisch.
many they are very polite to foreigners. 5. The roots of the forest Oxides of Sulphur.-All the oxides of sulphur which are known were his only nourishment. 6. Water, on this occasion, took the possess acid properties :place of wine. 7. A scholar has taken the place of teacher. 8. They use pencils instead of pens. 9. Travelling gives me very much plea- Hydric Sulphite or Sulphurous Acid, H,50z. sure. 10. My children have learnt writing and reading of me. 11.
Hydric Sulphate or Sulphuric Acid, H,80.. Let us go; this long waiting is disagreeable to me. 12. They gene- Hydric Hyposulphite or Hyposulphurous Acid, H,8,0,. rally prefer sitting to standing. 13. He learnt to labour in his youth. Hydric Dithionate or Dithionic Acid, H,S,06. 14. We learnt to write together. 15. I hate writing; on the contrary, Hydric Trithionate or Trithionic Acid, H,8,0,. I like painting so much the more. 16. He understands drawing better Hydric Tetrathionate or Tetrathionic Acid, H,S.O. than painting. 17. We heard the bells pealing and the cannons thun. Hydric Pentathionate or Pentathionic Acid, H,8,0,. dering. 18. The howling of the storm, and the wild raging of the waves, heightened still further the courage of the brave captain and
Sulphurous Acid (symbol, SO,; combining weight, 64; density, his crew, instead of depressing it. 19. Thinking God more benevolent 32).-Sulphur burns in oxygen with a lilac-coloured flame, and than just, is equivalent to dishonouring him (Gellert). 2). This scho- the sole product of the combustion is the permanent gas, so,, lar's inexcusable behaviour vexed the teacher.
which has a density exactly double that of oxygen, for the gas occupies the same volume as the oxygen from which it is made,
S + 0, = 50,
- + 2 = 2. SULPHUR :—SYMBOL, S-ATOMIC WEIGHT, 32– DENSITY OF VAPOUR AT
The gas may be procured more easily by cautiously heating 1,000° CENT., 32.
in a flask a mixture of 3 parts of sulphur and 4 of manganese SULPHUR is a yellow solid which is found mixed with the soil dioxide; the reaction is thus expressed :in many volcanic districts. It also appears in combination with
Mn0, + 8, =MnS + 80g. metals forming a large class of ores named sulphides ; and moreover it takes some part in the animal economy, for it is found A third process consists in heating sulphuric acid with copper in albumen, hair, garlic, etc. The localities from which the or mercury in an ordinary flaskgreater part of the sulphur of commerce is procured are the
Hg + 2H,50, = HgSo, + 2H,0 + 50g. valleys of Noto and Mazzaro, in Sicily. Here it is mixed with clays and breccia. Some sulphur is derived from metallic sul. The gas is well known for its suffocating odour. It cannot phides, particularly iron pyrites, Fes, but this is liable to support combustion. Water at 0° Cent. dissolves 68-8 volumes contain arsenic. The pyrites is heated in conical clay tubes, of the gas, but this solution gradually absorbs oxygen from FeS remains behind, while the other atom of sulphur is the air, and becomes converted into sulphuric acid.
By liberated. The Sicilian sulphur undergoes partial purification causing the gas to traverse a tube surrounded by a mixture at the mines by being submitted to a rough sublimation that of salt and ice, or by submitting it to a pressure of 2 atmois, when heated to 490° Cent. the sulphur begins to boil
to spheres, it liquefies into a colourless limpid Auid. come off in vapour. This is passed into a chamber in which it Fig. 46 shows the arrangement. The gas, to purify it, is is cooled, the vapour condensing into a fine yellow powder sent through a "wash bottle," w, which contains concentrated flowers of sulphur. Sometimes the melted sulphur is run into sulphuric acid, by which the gas is dried. The liquefied sul. wooden moulds, by which it is converted into cane sulphur, or phurous acid collects in the tube on the jar s, and is preserved brimstone.
Properties.-Sulphur is a brittle solid without taste or smell. When rubbed it emits a peculiar odour, and becomes negatively electrified. It is a very bad conductor of heat, and when a stick of brimstone is held in the hand in contact with the ear it crackles and frequently falls to pieces from the unequal expansion. It is quite insoluble in water, as may be easily seen by examining a piece of brimstone which has been for years in a vessel of water from which a lady's lap-dog drinks. The edges of the roll will be found as sharp as the day when it was first put into the water. Alcohol and ether have but a slight solvent action upon it, but the bisulphide of carbon, CS,, dissolves it freely. Sulphur exists in three modifications. The sulphur which appears in nature when crystallised, is in rhombic octohedra. This same shape is assumed when the bisulphide of carbon, which holds sulphur in solution, is evaporated. These latter crystals, however, are transparent. To procure the second modification, sulphur is melted, and when it is covered with a film
w on cooling, a hole is broken through the crust, and the sulphur which is still liquid is poured out; the under surface of the film and
*** the sides of the crucible will be found covered with long needleshaped transparent crystals belonging to the oblique prismatic form, and having a specific gravity of 1.98, whereas that of the native sulphur is 2:07. These crystals soon become opaque, and when touched crumble into powder, the particles of which are found to be crystals similar to those of native sulphur. Thus sulphur is “ dimorphous," or capable of crystallising in two different systems. The third and more remarkable variety is produced by heat. At 115° sulphur begins to melt, forming a pale yellow mobile liquid. Upon raising the temperature its colour
Fig. 46. becomes darker, and at 250° it is an opaque mass, so viscid as to be poured from the vessel with difficulty ; 20° higher it by hermetically sealing its neck. Of course, when exposed to again resumes its fluid condition, and if it be poured into cold the air, the liquid evaporates rapidly, and by this means a temwater when in this state, it becomes a soft and plastic mass of perature of 60° Cent. may be obtained. This experiment may an amber-brown colour, and so tenacious that it can be drawn be easily shown by wrapping the bulb of an alcohol thermometer out into fine threads. It is in this condition that casts of in muslin and pouring some of the liquid upon it. medals, etc., are taken for electro-plating. After a lapse of Sulphurous acid possesses great bleaching powers, and also sorze time it returns to its yellow colour. In passing from one antiseptic properties. If a red rose be held over the fumes of of these conditions to another, there is invariably a remarkable ignited sulphur its colour will be immediately changed. Chlorine alteration in temperature.
cannot be used in bleaching silk, wool, and especially straw, as it
leaves them with a yellowish tinge. In these cases this gas is be bluish (Marsh's test). One of the oxides of nitrogen is zised. It seems simply to combine with the colouring matter, generally present—this may be ascertained by the test given for thus bleaching it. The gas is sometimes used for checking nitric acid. rinous fermentation when it is proceeding too rapidly. This is The presence of other salts may be determined by evapodone in the manufacture of cider, by burning sulphur over the vessel in which the fermentation is proceeding.
ILE Sulphuric Trioxide (symbol, sog; combining weight, 80; density, 40).—This substance may be prepared by passing a mixtare of sulphurous acid gas and oxygen through a tube containing spongy platinum heated to 180° Cent. In the pores of the platinum the sulphurous gas becomes oxidised into sog, which passes out of the tube in white vapours, and condenses in a recaiver into fine silky needles.
This substance possesses no acid properties until it combines with water, which it does with violence, forming sulphuric acid.
When the vapour of sulphuric trioxide is passed through a red-hot tube it is decomposed into 2 volumes of sulphic dioxide and 1 of oxygen, thusSo, = SO + 0.
Fig. 47. + 1. Nordhausen Sulphuric Acil (H,0.250g).-At Nordhausen, a
rating some of the acid in a platinum crucible; if any be pre
sent, they will remain. town in Sarony, a fuming acid of the above name and formula, has long been made by distilling green vitriol, which is iron afinity for water, of which it can take up fifteen times its
Properties.—This acid forms sulphates. It has a great sulphate, thus
weight if exposed long enough to the atmosphere. In com4 (FeSO.) + H,0 = 280, + 2Fe,0, + 1,0.250g. bining with water, the temperature is greatly increased, and the This acid, when heated, gives off sulphuric anhydride, and volume of the mixed liquids is less than the sum of their leaves British oil of vitriol behind, thus :
volumes. The maximum condensation, 3 per cent., is reached
when 3 volumes of acid are mixed with 2 of water. The 1,0.250, = sos + 1,0.50..
best test for sulphuric acid is barytic water, or a chloride or It is capable of dissolving sulphur, but its great use is to dissolve nitrate of barium; the barium displaces any other base from indigo, which property gives it its commercial value.
its combination with the acid, and forms the insoluble barium Sulphuric Acid, or Oil of Vitriol (H,$0.).-No chemical com sulphate, which falls in a white powder; thuspound is of such use in the arts and manufactures as this; indeed, the commercial prosperity of a country may be very
Caso, + BaNO,= CaNO, + Baso, accurately measured by the quantity of sulphuric acid it con The remaining five oxides of sulphur are not of sufficient sumes.
interest to require a notice here. The mode of preparing the acid is to oxidise sulphurous acid
COMPOUNDS OF SULPHUR AND HYDROGEN. gas, by means of nitric trioxide, thusSO, +1,0 + 1,0, = H,80,+N,Og.
Sulphuretted Hydrogen, or Hydric Sulphide (Symbol, H,S; com
bining weight, 34; density, 17).-This gas is always procured Here it will be seen that the nitric trioxide gives one atom of by treating some metallic sulphide with sulphuric acid. The its oxygen to the SO,, which thus becomes S03; this combines with sulphide of iron may be convoniently made by heating a rod an atom of water, forming H,OSOs, which is usually written of iron, such as that from which nails are made, to a strong red H,SO, The N, O, is now 1,0,, nitric oxide ; but in the presence heat, then touching it with a stick of brimstone; the sulphur of steam this gas is capable of combining with oxygen and and the iron combine, forming ferric sulphide, Fes. In the returning to its former state, thus
same bottle in which hydrogen or carbonic acid gas was made, N10, + 0 = 8,0,6
place this sulphide, and add diluted sulphuric acid and it is again in a condition to oxidise another atom of Soc.
FeS + H,80, = Feso, + H, S; Thus it appears that the nitric trioxide merely acts as a carrier that is, iron sulphate (green vitriol) and sulphuretted hydrogen of oxygen between the air and the sulphurous acid gas. Theo- are the results of the reaction. retically, a definite quantity of the trioxide can transform an Properties.-It is this gas which imparts to rotten eggs their indefinite quantity of the sulphuroas into sulphuric acid. Prac-offensive odour. In the decomposition of the albumen, the sultically, however, this is impossible, for reasons which will be phur which it contains unites with the hydrogen-another of its sufficiently apparent. Fig. 47 shows the arrangement by which constituents-producing the gas. When passed through a redthe manufacture of sulphuric acid is carried on. A chamber made hot tube, it is decomposed into sulphur and hydrogen ; the of wood, sometimes 300 feet long and 15 broad by 15 high, is lined latter having a volume equal to that of the undecomposed gas, with sheet lead; water a few inches in depth covers the bottom; as this equation would indicate :at one end there is a furnace in which sulphur is burning, and the flames of the sulphur heat a crucible containing sodium
H,S = H, +S nitrate and sulphuric acid, which produce the fumes of nitric acid ; at the other end is a boiler in which large quantities of The gas is very poisonous, but when largely diluted with air, it steam are generated, and ejected into the chamber by means of aots as a powerful narcotic. pipes. There is an opening at F to admit air and produce a It burns with a feebly luminous flame into water and sulphucurrent through the chamber; sometimes, thoronghly to mix the rous acid, a quantity of sulphur being deposited in the jar from racions vapours, several partitions divide the chamber, having incomplete combustion. Water, at ordinary temperatures, abtheir openings alternately at the top and near the floor. The sorbs three volumes of the gas, and in this manner it may be SO, as soon as formed fails and combines with the water; this kept for laboratory purposes;
only oxygen must be excluded, for process generally proceeds until the acid reaches a density of otherwise the hydrogen will be separated to form water and the 1:50. This is removed from the chamber and boiled in shallow sulphur deposited. This solution reddens litmus, and is thereleaden pans; when it reaches a density of 1.750 it corrodes the fore sometimes called hydro-sulphuric acid ; whenever an oxide lead, and therefore a further condensation is carried on in pla- of a metal is presented to it, the metal becomes a sulphide, timum vessels. The oil of vitriol of commerce is generally impure, and the hydrogen of the gas with the oxygen forms water, containing lead sulphate, as well as sulphates of any bases, lime, thus :04., which the water may contain, and if the acid has been
CuO + HQS = CuS + H,O. made from iron pyrites, which is the case with all English acid, From the variety of colours which sulphides exhibit, and their it is sure to contain arsenio. To decide if this be the case, behaviour under certain circumstances, this gas becomes a valuderelop hydrogen with the acid, ignite it, and the flame will able test agent. By consulting the following table the tests
will be apparent. Sulphuretted hydrogen liquefies under pres Or the discount may be found independently, as follows :sure of 17 atmospheres.
Find the interest on £100 for the given time, at the given METALS PRECIPITATED BY SULPHURETTED HYDROGEN.
rate per cent. Multiply the given amount by this interest, and
divide by the number formed by adding this interest to £100. In an acid solution.
Bismuth, the precipitate is Brown. Arsenic, the precipitate is Yellow. Cadmium
This will be seen at once, by stating it in the form of a Rule Antimony
Orange. In a solution neutralised by am- of Three question. Gold „Black Brown. monia.
We will take a particular case. Platinum
Iron the precipitate is Black. EXAMPLE.Find the discount upon £1031 178., due six Tin Brown or Yellow. Uranium
„Black Brown. months hence, at 3 per cent. (The above precipitates dissolve in Chromium*
Green. ammonia sulphide.)
In 6 months £100 would amount to £101; at 3 per cent.
Hence £1) is the discount on £101; due 6 months hence.
Therefore at the same rate per cent., and for the same time, we
shall have-as £101: £1; : : £1031 178.
= £15 58, very nearly. The Persulphide of Hydrogen (Symbol, HS«). — The cxact
BILLS, ETC. amount of sulphur in this compound has not been determined; it is obtained by acting on calcium persulphide (CaS, ) with hydro
15. In commercial transactions, when one man engages to pay chloric acid. It is a yellow oily liquid, and possesses bleaching another a certain sum of money at the expiration of a certain properties.
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 LESSONS IN ARITHMETIC.--XXXVII. amount of the debt, and tables of these stamps are given in DISCOUNT.
most of our almanacks and pocket-books. Such a document is
called a Bill. 11. Discount is the abatement made from a debt in consideration of its being paid before it is due.
A bill may be either what is called a Promissory Note, which If A owes B a sum of money (£500 suppose) which is to be
contains a promise on the part of the undersigned to pay the paid at the end of a given time (say six months), and instead of money at the end of a certain time; or it may be a Draft, which waiting until the six months have expired, discharges the debt also sometimes called a Bill of Exchange,
contains a request or order to the debtor to pay. A draft is now, it is evident that he ought not to pay the whole amount
We give the forms of both kinds :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
FORM OF A PROMISSORY NOTE. 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
£783 12s. 6d. sterling. plain that A ought to pay B such a sum as, put out to interest,
London, Oct. 5, 1862
Six months after date I promise to pay to Mr. Henry Jenkins, would amount in six months to £500. The sum so paid is, for
or Order, the sum of seven hundred and eighty-three pounds an evident reason, called the present worth of the debt; and the
twelve shillings and sixpence sterling, value received. interest upon it which added to it makes up the amount of the
WILLIAM JOHNSOX. debt, is the true discount.
The true discount, then, is the interest of the present worth for FORM OF A DRAFT, BILL OF EXCHANGE, OR ACCEPTANCE. 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. £783 125. 6d, sterling. 12. In mercantile transactions, where short periods of time
London, Oct. 5, 1862. are concerned, it is customary to deduct from the amount due
Six months after date, pay to my Order seven hundred and the interest upon the amount, and not the interest upon the
eighty-three pounds twelve shillings and sixpence sterling, value
received. present worth. This mode of reckoning is manifestly inaccurate, and it is for this reason that we have used the expression true
Mr. William Johnson,
HENRY JENKINS. discount, meaning thereby to distinguish it from the ordinary Accepted, payable at Messrs. Smith, Payne, Smith, and Co., discount of commerce.
London. The discount upon £105, due one year hence, at 5 per cent.,
WILLIAM JOHNSON, is £5, because in 12 months £100 would amount to £105. The interest on £105, however, is £5 5s, at the same rate.
The above are two different forms by which William Johnson N.B.-Observe that the difference between the interest and places himself under the obligation to pay £783 12s. 6d. to the true discount is the interest upon the true discount for the Henry Jenkins at the end of six months. given time.
The draft is called an Acceptance, after William Johnson has 13. To find the present worth of a given sum at a given rate what is called " accepted” the bill--that is, written across it per cent., due at the expiration of a given time.
“Accepted,” etc., and signed his name. The acceptance (placed, This is exactly the same question as that explained in Art. 7 in the above example, for convenience at the foot of the bill) (Vol. II., page 403), viz., to find what principal will with its is written across it by the Drawee. The person who makes out interest amount to the given sum in the given time at the given the bill (in this case Henry Jenkins) is called the Drawer. William rate per cent.
Johnson, upon whom the bill is drawn, is called the Draute, EXAMPLE.—Find the present worth of £6812 178., due until he has accepted it, and then he is called the Acceptor. 12 years 4 months hence, at 74 per cent.
Sometimes the bill is made out to be paid to a particular person, By the rule (see Art. 7) we have (since the interest of £100 who is called the Payee. at 75 per cent. for 12 years is £74 x 12, or £195, i.e., £92 10s. 16. Such bills, before they become due, are passed about x (£6812 17s.) as the required answer.
from hand to hand instead of money. The person in possession 1924
of the bill at any time is called the Holder, and when he pays it £6812 178. = £6812-85. Therefore present worth is fi * £681,285 £229344, which, when away to another person, he writes his name on the back, which reduced, gives £3,539 28. 103d.
is called endorsing the bill. The acceptor is always liable to the The discount upon £6812 178., being the difference between that holder, who can also recover from the drawer and endorser, sum and £3539 2s. 1094., is £3273 14s. 1 d.
This transference of a bill from one hand to the other is called 14. To find the DISCOUNT upon a given sum, due at the negotiating the bill. expiration of a given time, at a given rate per cent.
It is evident from what we have said about discount that the This may be done by finding the present worth, as in the last value of such a bill continually increases, up to the time at article, and then subtracting it from the amount.
which the debt is payable, the present worth being manifestly
greater the shorter the time it has to run. These are not precipitated as sulphides. The rest of the metals 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 LESSONS IN BOTANY.-XXVII.
SECTION LX-JASMINACEÆ. 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 monopetalous, saucer-shaped, five to eight partite ; stamens two,
Characteristics : Calyx free; corolla hypogynous, regular, monthe only to £496 2s. 6d. He would thus be a gainer of inserted upon the tube of the corolla; ovary two celled, uni. or 23 178. 6d. by the transaction. It is on this principle of discounting a bill at a higher rate of sule; seeds erect, dicotyledonous, exalbuminous.
bi-ovulate; ovules collateral, ascendant; fruit a berry or capinterest than that at which money can be borrowed, that bankers
The members of the family Jasminaceæ are usually trees and bill-discounters make their profits. 17. In calculating the day upon which a bill becomes due, stipules ; flowers complete; calyx persistent; corolla imbricated
or shrubs, often climbing, leaves ordinarily opposite, without a certain number of days, which varies in different countries, in æstivation ; anthers attached by their bases ; albumen at called Days of Grace, are added to the time specified. In Great first abundant, but towards maturity reduced to a very fine Britain, three days is the time allowed. Calendar months are
membrane; radicle inferior. always reckoned. Thus, a bill drawn on Feb. 15th at three
The Jasminaceæ are nearly allied to the Oleacex, from which 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 such as the number of their sepals and petals, the æstivation
they, however, differ in certain well-marked characteristics, 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 the erect seeds, and albumen almost absorbed.
of their corolla, the ascendant ovules, the endocarp never hard, of the month is taken, and the three days of grace added.
The principal region of this natural family is tropical Asia ; Thus a bill drawn on Jan. 31st at three months would (without the days of grace) be due on April 30th, and therefore would region. The greater number of the Jasminaceæ possess a
a few species, however, are indigenous to the Mediterranean be actually due on May 3rd.
volatile oil in the tissue of their corolla, not obtainable by EXERCISE 57.-EXAMPLES IN DISCOUNT, ETC.
distillation. The so-called oil of jasmine is the product of Calculate the True Discount upon
stratifying jasmine flowers with some fixed non-odorous oil, 1. £45, due 1 year hence, at 5 per cent.
generally oil of ben. This oil, which is used by watchmakers 2. £325 10s., due 18 months hence, at 3) per cent.
because it does not freeze so readily as other oils, is expressed 3. £1000 for 10 months, at 4 per cent.
from the ben nut, the seed of the Moringa pterygosperma, 4. What is the present worth of £450, payable in 6 months, at 6 per or winged-seeded horse-radish tree, a tree which grows in
Arabia and India, and the roots of which are used as wo 5. What is the present worth of £840 16s. 8 d., due 3 months hence, use horse-radish. The volatile oil of jasmine, to which allaat S) per cent ? 6. Find the present worth of £819 4s., due 9 months hence, at of the Jasminum officinale, or common white jasmine, or
sion has just been made, is obtained chiefly from the flowers 3) per cent. 7. Find the difference between the True and the Commercial discount those of the Jasminum grandiflorum, or large-flowered jasupon £3500, dne 10 months hence, at 6 per cent.
mine. The last-named is a greenhouse evergreen climber, 8. Find the discount upon £430, due 18 months hence, at 3) per cent. and not suitable for culture in the open air, like the common 9. Compare the cash and credit price of the same article ; credit hardy deciduous climbers. being given for one year, and simple interest at 4) per cent. per annum
SECTION LXI.-VACCINIACEÆ AND ERICACEÆ. being allowed. Find the cash price of articles, the credit price of which amounts to £114 ls, 7d.
Characteristics : Calyx free or adherent to the ovary; corolla 10. The difference between the interest and the true discount for a inserted upon an annulus or disc, either hypogynous or epigycertain sum for 2 years at 45 per cent. is £2 14s. 81.d.; find the sum. nous, monopetalous, regular; number of stamens equal to that [See N.B., Art. 12, in the preceding page.]
of the lobes of the corolla, alternating with them, or double 11. If the discount on £567 be £34 148. 39d. at 4; per cent., when is their number; anthers bilocular, separate celled; ovary one to the sum due ?
five celled, with central placentæ; seeds inverse; embryo dico12. Two men owe equal debts to a third, both due at the end of tyledonous, straight, in the axis of a fleshy albumen.
years; the one pays at once the equitable sum; the other leaves th3 The plants which compose these two families are united into amount of the debt in the bank for the benefit of the creditor, who one, under the name Ericaceæ, by some authors : they are thus receives sums in the ratio of 640,000 : 844,561. At what rate is shrubs or evergreen trees. The leaves, ordinarily narrow, are the interest calculated ?
articulated with the stem, and without stipules; flowers comIn the following questions the Mercantile Discount is to be plete; calyx four to six partite; corolla five or six partite ; calculated.
the lobes varying as to depth, sometimes almost free, imbricated Find the present worth of the following Bills :
in æstivation; ovules pendent or reflexed. 13. £235 88. 6d., drawn 5th April, at 6 months; discounted 31st Ericaceæ. Corolla generally persistent; ovary free; fruit May, at 6 per cent.
generally capsular. 14. £240, drawn 16th December, at 3 months ; discounted 28th
Vacciniaceæ. Corolla caducous; ovary inferior; fruit bacci. January, at 3 per cent.
13. £1000, drawn 31st December, at 4 months; discounted 2nd form or drupaceous; leaves plane ; buds ordinarily covered February, at 5 per cent.
with imbricated scales. 16. £1250 10s, 6d., drawn 29th November, at 3 months ; discounted
The Ericaceæ or heaths are dispersed over all the globe; 21st December, at 6 per cent.
they are especially abundant in the cold regions of the northern 17. £850 178. 6d., drawn 31st July, at 8 months ; discounted 15th hemisphere, and at the Cape of Good Hope. The heaths are September, at 4 per cent.
altogether wanting in Asia, America, and Australia. Some 18. £325, drawn 25th October, at 9 months; discounted 15th species of this genus are gregarious, covering immense tracts January, at 8 per cent.
in western and central Europe, where their presence indicates 19. 2755 5s. 9d., drawn 17th March, at 3 months ; discounted 31st the soil to be unadapted to the culture of cereals. The greater May, at 6 per cent.
20.2537 58. 22., drwn 29th August, at 3 months; discounted 27th number of species belong to the Mediterranean region. The October, at 3. per cent.
Vacciniacex, a family which takes its name from the vaccinium,
or whortleberry, grow for the most part on this side of the KEY TO EXERCISES IN LESSON XXXVI.
Tropic of Cancer, and in North America, chiefly inhabiting EXERCISE 55.
the temperate and cool regions of the northern hemisphere, 1. £26 28. 84.
erpecially the elevated mountains and hilly districts of America. 4. £2 0s. 5 d.
6. £21 28. 27d. 5. £19 175. 1 d. 7. £111 78. 5d,
Beyond the Tropic of Capricorn they altogether disappear. Most 8. £43 19s. 7.d.
of the Ericaceae contain bitter astringent principles, sometimes EXERCISE 56.
also a venomous balsam. The berries of certain species aro 1. £35 39. 4jd. 4. £1 158. 61 a. 7. £51.
edible. The Vacciniacou are especially valuable for yielding a * £51 29. 4. 5. £20 10s. 9.9.d. 8. £195 6s. 3d.
refreshing acidulated fruit. Their leaves are slightly astringent. 3. £512s.43d, to the 6. £129 178. 21d. 9. I lose £1 4s. 3311. The Thibaudia Microphylla produces berries which the inhabi. nearest farthing.
tants of Pasto, in Columbia, submit to fermentation, and produce
2. £33 08. 9 d.