SECTION VI.

DENOMINATE NUMBERS.

237. A Denominate Number is a concrete number in which the unit is a measure; as 3 feet, 4 pounds, etc.

238. A Measure is a unit by which quantity of magni tude or continuous quantity is estimated numerically; as, a yard, a pound, etc.

239. A Compound Denominate Number is a number which expresses several different units of the same kind of quantity; as, 4 yd., 2 ft., and 11 in.

240. The Terms of a compound number are the num bers of its different units. Thus the terms in the example

given are 4 yd., 2 ft., and 11 in.

241. Similar Compound Numbers are compound numbers which express the same kind of quantity.

242. Denominate Numbers may be embraced under eight distinct classes, as follows:

1. Value.

2. Weight.

3. Length.

4. Surface.

5. Volume.

6. Capacity.
7. Time.

8. Angles.

NOTE.-Concrete numbers are of two classes: 1st, those in which the unit is natural; 2d, those in which it is artificial. Natural units are such as exist in nature, and artificial units are those which are agreed upon to measure quantity of magnitude. The latter are called denominate numbers.

MEASURES OF VALUE.

243. The Value of anything is its worth, or that property which makes it useful or estimable.

244. Money is the measure of the value of things. It is of two kinds, coin and paper money.

245. Coin, or Specie, is metal prepared and authorized by government to be used as money.

246. Paper Money consists of printed promises to pay the bearer a certain amount, duly authorized to be used as money.

247. Currency is whatever circulates as money. It is. of two kinds, specie currency and paper currency.

248. Legal Tender is a term applied to money which is required by law to be accepted in payment of debts.

249. An Alloy is a baser metal compounded with either gold or silver for the purpose of rendering it harder and more durable. In coinage, the alloy is considered as having no value.

UNITED STATES MONEY.

250. United States, or Federal Money, is the legal currency of the United States.

I. NAME.-United States money is so called because it is the money of the United States. It is called Federal Money because it was the money of the Federal Union. It was adopted by Act of Congress, Aug. 8, 1786. II. TERMS.-The term dollar is supposed to be from Dale or Daleburg, a town where it was first coined; dime is from the French disme, meaning a tenth; cent is from the Latin centum, a hundred; mill is from the Latin mille, a thousand; eagle is from the name of the national bird. The cent was proposed by Robert Morris, and named by Thomas Jefferson.

III. UNIT.-The unit is the gold dollar. The currency is founded upon the decimal system, dimes, cents, and mills being written as decimals. This gives great simplicity to the operations.

IV. COINS. The coins are of gold, silver, nickel, and bronze. The gold coins are the double eagle, eagle, half-eagle, quarter-eagle, three dollars, and one dollar. The silver coins are the trade dollar, half-dollar, quarterdollar, twenty-cent piece, and dime. The nickel coins are the three-cent and five-cent pieces. The bronze coin is the cent. The silver half-dime and

three-cent piece, the bronze two-cent piece, the nickel cent, and the old copper cent and half-cent, although still seen in circulation, are no longer coined. The mill has never been a coin; it is merely a convenient name for the tenth part of a cent.

V. COMPOSITION.-The gold and silver coins consist of 9 parts of pure metal and 1 part alloy. The alloy of the silver coin consists of pure cop per; the alloy of the gold coin consists of silver and copper, the silver not to exceed of the alloy. The nickel coins contain nickel and copper. The bronze coins consist of 95 parts copper, and 5 parts tin and zinc.

NOTE.-The Notes on the tables are not to be memorized or recited, unless otherwise directed.

VI. Gold coins are a legal tender for any amount; silver coins, of the present coinage, for any amount not exceeding $5 in any one payment; bronze and nickel coins for any amount not exceeding 25 cents in any one payment.

MENTAL EXERCISES.

1. How many cents in $? $? $I? $I? $‡? $? $?

2. What part of a dollar is 10 cts.? 12§ cts.? 20 cts.? 25 cts.? 16} cts.? 33 cts.? 37 cts.? 50 cts.? 62 cts.? 75 cts.? 83 cts.?

3. What part of 5 eagles is 15 dimes? what part of 12 cents is of a dime?

4. How many eagles in 60 dollars? in 400 dimes? in 8500 cents? in 25,000 mills?

ENGLISH, OR STERLING MONEY.

251. English, or Sterling Money, is the legal currency of England.

I. NAME.-The term Sterling is supposed to be derived from Easterling, the name given to early German traders, who came from the east to England. Their money was called Easterling Money, which was contracted into Sterling Money.

II. TERMS.-The term farthing is a modification of "four things," tl e old English penny being marked with a cross so deeply impressed that it could be broken into two or four pieces, called respectively half-penny and four things. The Pound, as a measure of value, was derived from the pound as a measure of weight, 240 pence formerly weighing a pound The guinea is so called because the gold of which it was first made came from Guinea, in Africa.

III. SYMBOLS.-The symbols £., s., d., qr., are the initials of the Latin words libra, solidus, denarius, and quadrans; signifying respectively, pound, shilling, penny, and quarter.

IV. UNIT.-The unit is the pound, represented by the sovereign and £1 bank note. Its value by late act of Congress is fixed at $4.8665.

V. COINS.-The coins are of three classes: gold, silver, and copper. The gold coins are the sovereign (=£1), and_half sovereign (=10s.), guinoa (=21 s.) and half guinea (=10 s. 6 d.). The silver coins are the crown (=58.), the half crown (=2 s. 6 d.), the florin (=2s.), the shilling, and the six-penny, four-penny, and three-penny pieces. The copper coins are the penny, half-penny, and farthing.

VI. COMPOSITION.-The standard for gold coins is 22 carats fine, that is, 11 parts pure gold, and 1 part alloy. The standard for silver is 37 parts pure silver and 3 parts alloy, hence the silver coins are 7 pure, and cop per. Pence and half-pence are made of pure copper.

7. What part of 2 pence is 6 farthings? What part of 3 shillings is 5 pence?

8. What part of 16 pence is of a shilling? What part of a guinea is of a pound?

WRITTEN EXERCISES.

1. How many pence in £16 11 s. 10 d.?

SOLUTION.-In one pound there are 20 shillings, and in £16 there are 16 times 20 shillings, which, increased by 11s., are 331 shillings. In one shilling there are 12 pence, and in 331 shillings there are 331 times 12 pence, which, increased by 10 pence, equals 3982 pence.

2. How many pounds, shillings, and pence in 4367 pence?

SOLUTION.-There are 12 pence in one shilling, hence in 4367 pence there are as many shillings as 12 is contained times in 4367, which are 363 shillings and 11 d. remaining. There are 20 shillings in one pound, hence in 363 shillings there are as many pounds as 20 is contained times in 363, which are £18 and 3 shillings remaining. Hence in 4367 d. there are £18 3 s. 11 d.

OPERATION.
d.
12)4367
2|0)363-11 d.
£18 - 3 s.

Ans. £18 3 s. 11 d.

3. How many farthings in 9 s. 8 d. 3 far.? Ans. 467 far. 4. Farthings in £19 17 s. 11 d. 2 far.? Ans. 19102 far. 5. Shillings, pence, and farthings, in 7859 far.?

Ans. 163 s. 8 d. 3 far.

6. Pounds, shillings, etc., in 58763 far.?

Ans. £61 4 s. 2 d. 3 far.

CANADA MONEY.

252. The Currency of Canada is nominally the same as that of the United States, the table and denominations being the same.

253. The decimal currency was adopted in 1858, the Act taking effect in 1859, previous to which their currency was the same as the English.

I. COINS. The coins consist of silver and copper. The silver coins are the 50-cent piece, the 25-cent piece, the shilling or 20-cent piece, the dime, the half-dime. The copper coin is the cent.

IV. VALUE.-The coins are nominally equal to the corresponding coins of United States money, but the intrinsic value is a little less. The eagle of the United States is the legal tender for sums of $10 and upwards.

III. COMPOSITION.-The silver coins consist of 925 parts silver and 75 parts copper; or 37 parts silver to 3 parts copper, the same as the English silver coins.

FRENCH MONEY.

254. French Money is the legal currency of France. The unit is the franc, whose value is 19.3 cents.

255. The Franc is divided into tenths and hundredths, called respectively decimes and centimes. The decime, like our dime, is not used in business calculations, but is expressed by centimes; thus, instead of 5 decimes we say 50 centimes.

GERMAN MONEY.

256. The German Empire has adopted a new and uniform system of coinage.

257. The Unit is the mark (Reichsmark) worth 23.85 cents, and this is divided into 100 pfennige.

WRITTEN EXERCISES.

1. How many dollars in 25.50 francs?

2. How many francs in $256?

Ans. $4.9215. Ans. 1326.42+fr.

3. How many dollars in 753 marks 15 pfennige?

Ans. $179.626+.

4. How many marks in $456.25? Ans. 1913. marks. 5. Bought an opera-glass for 20 francs; what did it cost in United States money? Ans. $3.86.

MEASURES OF WEIGHT.

258. Weight is the measure of the force by which bodies are naturally drawn towards the earth.

259. There are three kinds of weight in common use. Troy Weight, Apothecaries' Weight, and Avoirdupois Weight.