46 



will be apparent. Sulphuretted hydrogen liquefies under pres- 

 sure of 17 atmospheres. 



METALS PRECIPITATED BY SULPHURETTED HYDROGEN. 



In. an acid solution. 



Arsenic, the precipitate is Yellow. 



Antimony Orange. 



Gold Black Brown. 



Platinum 



Tin Brown or Yellow. 



(The above precipitates dissolve in 



ammonia.) 



Silver the precipitate is Black. 

 Mercury 



Lead 



Copper 



The PersulpJiide of Hydrogen (Symbol, HSa;). The exact 

 amount of sulphur in this compound has not been determined ; it 

 is obtained by acting on calcium persulphide (CaS 5 ) with hydro- 

 chloric acid. It is a yellow oily liquid, and possesses bleaching 

 properties. 



Bismuth, the precipitate is Brown. 

 Cadmium Yellow. 



In a solution neutralised by am- 

 monia. 



Iron the precii tate is Black. 



Uranium 

 Chromium 

 Aluminium 

 Cobalt 

 Manganese 

 Nickel 

 Zinc 



Black Brown. 



Green. 



Colourless. 



Black. 



Flesh Bed. 



Black. 



White. 



LESSONS IN ARITHMETIC. XXXVII. 



DISCOUNT. 



11. Discount is the abatement made from a debt in con- 

 sideration 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 d5, 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 1\ x 121, or ,if5, i.e., .92 10s. 



192J x (6812 17s.) as the required answer. 



6812 17s. = 6812-85. 



Therefore present worth is -^ x 681,285 = fi^ff", which, when 

 reduced, gives 3,539 2s. 10? d. 



The discount upon 6812 17s., being the difference between that 

 um and 3539 2s. 10?d., is 3273 14s. Ifd. 



14. To find tlie DISCOUNT upon a given sum, due at the 

 expiration of a given time, at a given rate per cent. 



This may be done by finding the present worth, as in the last 

 article, and then subtracting it from the amount. 



* These are not precipitated as sulphides. The rest of the rnctils 

 form sulphides soluble in water, and therefore do not give precipitates. 



Or the discount may be found independently, as follows : 



Find the interest on <100 for the given time, at the given 

 rate per cent. Multiply the given amount by this interest, and 

 divide by the number formed by adding this interest to .100. 



This will be seen at once, by stating it in the form of a Rule 

 of Three question. 



We will take a particular case. 



EXAMPLE. Find the discount upon .1031 17s., due six 

 months hence, at 3 per cent. 



In 6 months 100 would amount to 101?; at 3 per cent. 

 Hence 1} is the discount on 101} due 6 mouths hence. 

 Therefore at the same rate per cent., and for the same time, we 

 shall have as 101} : 1} : : 1031 17s. 

 1031-85 309-555 



The result is 1'5 x ;;jpjr = -jTrrz- = 15 5s. very nearly. 



1U1 O 4U o f 



BILLS, ETC. 



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. 



783 12s. 6d. sterling. 



London, Oct. 5, 18G2. 



Six months after date I promise to pay to Mr. Henry Jenkins, 

 or Order, the sum of seven hundred and eighty-three pounds 

 twelve shillings and sixpence sterling, value received. 



WILLIAM JOHNSON. 



FORM OF A DRAFT, BILL OF EXCHANGE, OR ACCEPTANCE. 



783 12s. 6d. sterling. 



London, Oct. 5, 1862. 



Six months after date, pay to my Order seven hundred and 

 eighty-three pounds twelve shillings and sixpence sterling, value 

 received. 



Mr. William Johnson, ) 

 London. f 



Accepted, payable at Messrs. Smith, Payne, Smith, and Co., 

 London. 



WILLIAM JOHNSON. 



HENRY JENKINS. 



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. 



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 months 

 before it is due, and ask him to give me money for it ; he will 



