The Circle of Knowledge: A Classified, Simplified, Visualized Book of Answers

Part 222

Chapter 2223,903 wordsPublic domain

The globe is divided into zones of 15 degrees or one hour breadth, the Greenwich meridian being in the center of the zero zone. Thus Belgium and Holland (since 1892) keep Greenwich time; Denmark, Sweden, Switzerland (1894), Austrian railroads, Germany, and Italy (1893) keep the time of longitude 15 degrees East--i.e. one hour earlier than Greenwich. In North America again five zones are distinguished. The corresponding times are distinguished as Eastern (67-1/2 to 82-1/2 degrees), Central (82-1/2 to 97-1/2 degrees), Mountain (97-1/2 to 112-1/2 degrees), and Pacific (112-1/2 to 127-1/2 degrees) times.

New York people are in the Eastern Time Belt. If they rise at six o’clock in the morning, they will be up a whole hour before Chicago people, who get up at the same hour.

Thus, each day begins an hour sooner in New York than in Chicago, two hours before Denver, and three hours before San Francisco.

Standard time in Japan is nine hours earlier than Greenwich time.

In the western parts of Canada the twenty-four hour system has been adopted, under which four P. M. becomes sixteen o’clock and so on. Steps are being taken to introduce it generally in India, Belgium, and the United States. It is of special convenience in the construction of railroad time tables; and it has long been used by the Italians and by astronomers.

THE CALENDAR

The reckoning of time among the ancients was very inaccurate. This was owning to their ignorance of astronomy, and also to changes that were made from time to time for political reasons. The calendar was reformed by Julius Cæsar, 46 B. C., who made the year consist of 365-1/4 days, adding one day every fourth year. In 1582, the error in the calendar established by him had increased to 10 days; that is, too much time had been reckoned as a year, until the civil year was 10 days behind the solar year. To correct this error, Pope Gregory XIII. decreed that 10 days should be stricken from the calendar, that the day following the 3d day of October, 1582, should be made the 14th, and that henceforth only those centennial years should be leap years which are divisible by 400.

Most Catholic countries adopted the Gregorian Calendar soon after it was established. Great Britain did not adopt it until 1752, when the error amounted to 11 days. By Act of Parliament, the 3d of September was called the 14th. The civil year by the same act was made to commence on the 1st of January, instead of the 25th of March, as was previously the case.

Dates reckoned by the Julian calendar are called Old Style (O.S.), and those reckoned by the Gregorian calendar are called New Style (N.S.). The difference now amounts to 12 days.

PERPETUAL CALENDAR

To find the day of the week for any given date.

1. Take the last two figures of the year, add one-fourth of them (neglecting remainder). Thus: 1949 = 49 + 12 = 61.

2. Add for the month, if for January or October, 1; May, 2; August, 3; February, March, or November, 4; June, 5; September or December, 6; April or July, 0; if leap year (that is, if it be divisible by 4 without remainder) January 0; February 3.

3. Add day of month.

Divide the sum of these three by 7, and remainder gives the number of the day of the week.

Thus:--What day of the week is 15th July, 1908?

1. 8 + 2 = 10 2. July = 0 3. 15th = 15 -- 25 = 7 × 3 + 4

4th day of the week = Wednesday.

What day of the week was December 25th, 1905?

1. 5 + 1 = 6 2. Dec. = 6 3. 25th = 25 -- 37 = 7 × 5 + 2

2nd day of the week = Monday.

The above only applies to 20th Century. For 19th Century, add 2; for 21st Century, add 6; 18th Century, 4; but before 1752 the “old style” was used.

WHERE THE DAY BEGINS

The day begins earlier as you go east until you meet the 180th meridian. This is where the day begins. Starting here, it travels westward, giving the whole world a new day. The 180th meridian is called the _International Date Line_ (_I. D. L._) but in reality, the date line is a crooked line which zigzags across the 180th meridian.

From the time the day starts at the International Date Line, until the sun again reaches that line, the same day is in progress the world over.

As marked now, the International Date Line passes southward through Behring Sea, then westerly, then returns to the 180th meridian at about 40 degrees north. It then follows the 180th meridian to 10 degrees south, where it swerves east but returns again to the 180th meridian at about 50 degrees south. It then follows that meridian.

TIME ON SHIPBOARD.--The twenty-four hours are divided on board ship into seven parts, and the crew is divided into two parts or watches, designated port and starboard watches. Each watch is on duty four hours, except from four to eight p. m., which time is divided into two watches of two hours each, called dog watches, by means of which the watches are changed every day, and each watch gets a term of eight hours’ rest at night. First watch, eight p. m. to midnight; middle watch, midnight to four a. m.; morning watch, four to eight a. m.; forenoon watch, eight a. m. to noon; afternoon watch, noon to four p. m.; first dog watch, four to six p. m.; second dog watch, six to eight p. m. The bell is struck every half-hour to indicate the time, as follows:

1 bell 12:30 A.M. 1 bell 12:30 P.M. 2 bells 1:00 A.M. 2 bells 1:00 P.M. 3 bells 1:30 A.M. 3 bells 1:30 P.M. 4 bells 2:00 A.M. 4 bells 2:00 P.M. 5 bells 2:30 A.M. 5 bells 2:30 P.M. 6 bells 3:00 A.M. 6 bells 3:00 P.M. 7 bells 3:30 A.M. 7 bells 3:30 P.M. 8 bells 4:00 A.M. 8 bells 4:00 P.M. 1 bell 4:30 A.M. 1 bell 4:30 P.M. 2 bells 5:00 A.M. 2 bells 5:00 P.M. 3 bells 5:30 A.M. 3 bells 5:30 P.M. 4 bells 6:00 A.M. 4 bells 6:00 P.M. 5 bells 6:30 A.M. 1 bell 6:30 P.M. 6 bells 7:00 A.M. 2 bells 7:00 P.M. 7 bells 7:30 A.M. 3 bells 7:30 P.M. 8 bells 8:00 A.M. 4 bells 8:00 P.M. 1 bell 8:30 A.M. 1 bell 8:30 P.M. 2 bells 9:00 A.M. 2 bells 9:00 P.M. 3 bells 9:30 A.M. 3 bells 9:30 P.M. 4 bells 10:00 A.M. 4 bells 10:00 P.M. 5 bells 10:30 A.M. 5 bells 10:30 P.M. 6 bells 11:00 A.M. 6 bells 11:00 P.M. 7 bells 11:30 A.M. 7 bells 11:30 P.M. 8 bells 12:00 noon 8 bells 12:00 night

HOW THE MONTHS GOT THEIR NAMES

January, from Janus, was the sacred month of the year to the Romans. To them, Janus was the god of the year. During the 18th century, the Europeans started to recognize it as the first month, but previous to this, March was considered the first.

February comes from februa, the name of a Roman festival celebrated on the 15th of the second month.

March is from Mars, the god of war. March was the first month of the year to the Romans.

April, from the Latin _aperire_, “to open,” was probably so called because during this month buds begin to open.

May is from Maia, the mother of Mercury. The Romans offered sacrifices to this goddess on the first day of May.

The sixth month in our calendar, June, got its name from Juno, the wife of Jupiter.

July was so named in honor of Julius Cæsar, who was born in this month.

Emperor Augustus Cæsar commanded that the eighth month be named August after him.

September is from the Latin septem, meaning seven. At the time when March was the first month of the year, September was the seventh.

October, November, and December were originally the eighth, ninth and tenth months. _Octo_, _novem_, and _decem_ are Latin numerals for eighth, ninth, and tenth.

HOW THE DAYS GOT THEIR NAMES

Sunday (that is, day of the sun, like Monday day of the moon), the first day of the week, the Lord’s day, was sacred to Sol or the Sun.

Monday (that is, moon-day; Anglo-Saxon, _Monandæg_, German, _Montag_), the second day of our week, was formerly sacred to the moon.

Tuesday, the third day of the week, is so called from _Tiwesdæg_, the day of Tiw or Tiu, the old Saxon name for the god of war. The day bears a corresponding name in the other Germanic dialects.

Wednesday, the fourth day of the week, the _Dies Mercurii_ of the Romans, the _Mittwoch_ of the modern Germans. The name Wednesday is derived from the Northern mythology, and signifies Woden’s or Odin’s day. The Anglo-Saxon form was _Wôdanesday_, the Old German _Woutanestac_. The Swedish and Danish is _Onsdag_.

Thursday, (Swedish _Thorsdag_, German _Donnerstag_), the fifth day of the week, is so called from Donar, or Thor (see Dictionary of Myths), who, as god of the air, had much in common with the Roman Jupiter, to whom the same day was dedicated. (Latin _Jovis dies_, French _Jeudi_).

Friday, the sixth day of the week, from the Anglo-Saxon _Frige-dæg_, is the day sacred to _Frigga_ or to _Freya_, the Saxon Venus.

Saturday (Anglo-Saxon _Sæterdæg_, _Sæterndæg_--_Sæter_, _Sætern_, for Saturn, and _dæg_, a day--the day presided over by the planet Saturn), is the seventh or last day of the week; the day of the Jewish Sabbath.

MEASURES OF VALUE

The common measure of value is _Money_.

It is also called Currency, and is of two kinds, viz.: coin and paper money.

Stamped pieces of metal having a value fixed by law are _Coin_ or _Specie_.

Notes and bills issued by the government and banks, and authorized to be used as money, are _Paper Money_.

All moneys which, if offered, legally satisfy a debt are a _Legal Tender_.

UNITED STATES MONEY

The unit of United States or Federal money is the Dollar.

The dollar mark is probably a combination of U. S., the initials of the words “United States.”

The standard of United States money is the gold dollar. Gold is used because in itself it has great worth and little bulk, and because it varies very little in value.

NAMES OF UNITED STATES COINS

_Bronze_: One-cent piece

_Nickel_: Five-cent piece

_Silver_: Dollar = $1.00 Half-dollar = 0.50 Quarter-dollar = 0.25 Dime = 0.10

_Gold:_ Double eagle = $20.00 Eagle = 10.00 Half eagle = 5.00 Quarter eagle = 2.50

It may be interesting to know that the word _dollar_ is supposed to have come from _Dale_, the name of a small town where dollars were first coined.

_Dime_ is from the French word _disme_, which means tenth.

_Cent_ comes from the Latin word _centum_, meaning hundred.

_Mill_ is also from the Latin, coming from _mille_, a thousand.

_Eagles_ were named after our national bird.

WEIGHTS OF THE UNITED STATES COINS

And the Amounts for Which They are Legal Tender

GOLD

====================+=======+================ DENOMINATIONS |WEIGHT |AMOUNT FOR WHICH |GRAINS | A LEGAL TENDER --------------------+-------+---------------- Double eagle, $20 | 516. |Gold coins of Eagle, $10 | 258. |denomination Half eagle, $5 | 129. |are legal Three dollars | 77.4 |tenders for Quarter eagle, $2.50| 64.5 |any amount. Dollars | 25.8 | --------------------+-------+----------------

SILVER

MINOR COINS

Besides the coins there is paper money, founded on credit. It represents value, but in itself has no value.

This paper money is made up of paper promises to pay the amounts named, in gold or silver, on demand.

It includes bank bills, United States treasury notes, government bonds, etc. They represent the values $1, $2, $5, $10, $20, $50, $100, $500, $1,000 and $10,000.

NOTATION OF UNITED STATES MONEY

Dollars and cents are written together. Thus, two dollars and sixteen cents is written, $2.16.

The dollars are separated from the cents by a period. If the number of cents is less than ten, the tens’ place is filled by a 0. Thus, we write twenty dollars and two cents, $20.02.

Mills, or tenths of a cent, are written to the right of the cents. Five dollars, six cents, four mills is written, $5.064.

NOTE.--The rules and processes of decimals apply to the addition, subtraction, multiplication, and division of United States money.

ENGLISH OR STERLING MONEY

_Sterling Money_ is currency of Great Britain and Ireland.

Table of Sterling Money

4 farthings (far.) = 1 penny (d.) 12 pence (not pennies) = 1 shilling (s.) 20 shillings = 1 pound (£), or sovereign 5 shillings = 1 crown 21 shillings = 1 guinea

The standard unit of Sterling Money is 1 pound or sovereign, whose value in our money is $4.8665.

The coins of Great Britain in general use are:--

_Gold_: Sovereign, half-sovereign, and guinea, which is equal to 21 shillings.

_Silver_: The crown (equal to 5 shillings), half-crown, florin (equal to 2 shillings), shilling, six-penny and three-penny pieces.

_Copper_: Penny and half-penny.

EXAMPLE: I have £5 sterling. What is the value in United States money?

SOLUTION:

The value is 5 × $4.8665, or $24.33

FRENCH MONEY

In France the currency is decimal. The unit is the _Franc_.

TABLE

10 centimes (ct.) [pronounced _son-teems_] = 1 decime (de.) 10 decimes [pronounced _des-seems_] = 1 franc (fr.)

_Scale._--Decimal

The value of the franc, as determined by the Secretary of the Treasury, is $.193 in United States money.

The coins of France are of gold, silver, bronze, and copper. The gold coins are the _hundred_, _forty_, _twenty_, _ten_, and _five_ franc pieces; the silver coins are the _five_, _two_, and _one_ franc pieces; also the _fifty_ and _twenty-five_ centime pieces. The bronze coins are the _ten_, _five_, _two_, and _one_ centime pieces. There are also copper coins in _ten_ and _five_ centime pieces.

EXAMPLE: When in France, I bought goods as follows:--

3 books at 2 francs,

1/2 dozen pipes at 1 franc,

2 pictures at 4 francs.

What was the cost in United States money?

WORK:

3 books at 2 francs cost 6 francs 1/2 dozen pipes at 1 franc cost 6 francs 2 pictures at 4 francs cost 8 francs ----------------------------------------- Cost of all 20 francs

20 francs = 20 × 19.3 cents, or $3.86

GERMAN MONEY

German money is legal currency of the German Empire.

TABLE

100 pfennigs = 1 mark

_Scale._--Decimal

1. The unit is the _mark_. Its value is $.2385 in United States money.

2. The coins of the German Empire are of gold, silver, nickel, and copper. The gold coins are the 20-mark piece, the 10-mark piece, and the 5-mark piece. The silver coins are the _two_ and _one_ mark pieces; the nickel coins are the _ten_ and _five_ pfennig pieces; and the copper coins are the _two_ and one _pfennig_ pieces.

PHILIPPINES WEIGHTS AND MEASURES

1 pulgada (12 linea) = .927 inch 1 pie = 11.125 inches 1 vara = 33.375 inches 1 gantah = .8796 gallon 1 caban = 21.991 gallons 1 libra (16 onzo) = 1.0144 pounds average 1 arroba = 25.360 pounds average 1 catty (16 tael) = 1.394 pounds average 1 pecul (100 catty) = 139.482 pounds average

PAPER MEASURE

24 sheets = 1 quire (qr.) 20 quires = 1 ream (rm.) 2 reams = 1 bundle 5 bundles = 1 bale

Although a ream contains 480 sheets, 500 sheets are usually sold as a ream.

NUMBER TABLE

12 units = 1 dozen 12 dozen = 1 gross 12 gross = 1 great gross 20 units = 1 score

PERCENTAGE AND ITS BUSINESS APPLICATIONS

The expression “per cent,” which is an abbreviation of the Latin words “per centum,” means “for each hundred.”

The symbol % is often used to denote “per cent.” Thus, 7 per cent, or 7%, means 7 parts out of every 100 parts, _i.e._, 7/100 of the whole.

Since per cent means hundredths, we may write any fraction whose denominator is 100 as so many per cent. In some cases the corresponding common fractions are so simple that it is advisable to remember them. For example:

25 1 25% = --- = -, 100 4

50 1 50% = --- = -, 100 2

75 3 75% = --- = -, 100 4

33-1/3 1 33-1/3% = ------ = -, 100 3

66-2/3 2 66-2/3% = ------ = -, 100 3

5 1 5% = --- = --, 100 20

2-1/2 1 2-1/2% = ----- = --, 100 40

12-1/2 1 12-1/2% = ------ = -, 100 8

and so on.

The _number_ per cent is called the _rate_ per cent.

TABLE OF ADDITIONAL VALUES

SYMBOL DECIMAL COMMON FRACTION 1% = .01 = 1/100 2% = .02 = 2/100 = 1/50 3% = .03 = 3/100 4% = .04 = 4/100 = 1/25 5% = .05 = 5/100 = 1/20 6% = .06 = 6/100 = 3/50 7% = .07 = 7/100 8% = .08 = 8/100 = 2/25 9% = .09 = 9/100 10% = .10 = 10/100 = 1/10 20% = .20 = 20/100 = 1/5 25% = .25 = 25/100 = 1/4 50% = .50 = 50/100 = 1/2 100% = 1.00 = 100/100 = 1

Here are a few others that should be learned:--

6-1/4% = 1/16 of 100% 16-2/3% = 1/6 of 100% 8-1/2% = 1/12 of 100% 33-1/3% = 1/3 of 100% 12-1/2% = 1/ 8 of 100% 66-2/3% = 2/3 of 100%

A DECIMAL AS PER CENT

Write the decimal as hundredths, and the number expressing the number of hundredths is the per cent.

EXAMPLES:

40 .4 = .40 = --- = 40% 100

80 .8 = .80 = --- = 80% 100

25 .25 = --- = 25% 100

33-1/3 .33-1/3% = ------ = 33-1/3% 100

50 .50 = --- = 50% 100

87-1/2 .87-1/2 = ------ = 87-1/2% 100

If the decimal has more than two decimal places, the figures after the second one are written as a fraction of a per cent, as,--

25-1/2 .255 = ------ = 25-1/2%. 100

16-3/10 .163 = ------- = 16-3/10%. 100

To change a common fraction to per cent:

1. _Change the fraction to a decimal._

2. _Express the decimal as hundredths._

3. _The result is the per cent desired._

EXAMPLES:

1/ 2 = .5 = .50 = 50% 3/ 4 = .75 = 75% 2/ 3 = .66-2/3 = 66-2/3% 9/10 = .90 = 90% 8/ 9 = .88-8/9 = 88-2/9% 7/ 8 = .87-1/2 = 87-1/2% 25/26 = .96-2/13 = 96-2/13%

Or, they may be written this way:

100 75 3/4 = 3/4 of --- = ------ = 75% 100 100

100 66-2/3 2/3 = 2/3 of --- = ------ = 66-2/3 100 100

100 50 1/2 = 1/2 of --- = ------ = 50% 100 100

TERMS USED IN PERCENTAGE

In _Percentage_, there are five terms or quantities considered; namely, the _Base_, _Rate per cent_, _Percentage_, _Amount_ and _Proceeds_ or _Difference_; any two being given, a third one may be found.

The base and rate given, to find the percentage.

RULE.--_Multiply the base by the rate per cent expressed decimally._

EXAMPLE: How many dollars is 6% of $50?

$50, the _Base_, or number on which percentage is computed. .06, the _Rate_, or term denoting number of hundredths taken. ------ $3.00, the _Percentage_, or the product of the base and rate per cent. $53.00, the _Amount_, or the base increased by the percentage. $47.00, the _Proceeds_, or _Difference_, the base less the percentage.

_Ans._ $3.00.

When the rate per cent is an aliquot part of 100, the percentage is readily found by taking such a part of the base as the rate per cent is part of 100. Thus, at 10%, take 1/10 of base; at 12-1/2%, 1/8; at 16-2/3%, 1/6, etc.

The base and percentage given, to find the rate.

RULE.--_Divide the percentage by 1% of the base_

EXAMPLE: Bought a watch for $15 and sold it for $18; what per cent did I make?

.15)3.00 ----- 20

_Ans._ 20%

Here, $15.00 is the base, and ($18 - $15) $3.00, the gain or percentage. Now, as 1% of 15.00 is .15, it is evident that 3.00 is as many per cent of 15.00, as .15 is contained times is 3.00, which is 20.

Proof: 20% or 1/5 of $15 = $3.

The percentage and rate given, to find the base.

RULE.--_Divide the percentage by the rate per cent expressed decimally_.

EXAMPLE: Received $6.40, percentage or interest, for money loaned at 4%, what was the base or principal?

.04)6.40 ----- _Ans._ $160

If $1 produces .04 (4 cents) in a certain time, $6.40 must be the percentage of as many dollars as .04 is contained times in $6.40, which is 160.

Proof: 4% of $160 (160 × .04) = $6.40.

The amount and rate given, to find the base.

RULE.--_Divide the given amount by 1.00 plus the rate per cent_.

EXAMPLE: Bought a horse at a certain price, and sold him for $84, making 12% on cost; what did he cost?

1.12)84.00 ------ _Ans._ $75

If I made 12% on cost, every dollar invested gained 12 cents; hence, the horse cost as many dollars as 1.12 is contained times in 84.00, which is 75.

Proof: 12% of $75 (75 × .12) = $9; $75 + $9 = $84.

The proceeds and the rate given, to find the base.

RULE.--_Divide the given proceeds by 1.00 minus the rate per cent_.

EXAMPLE: Sold a wagon for $51, which is 40% less than it cost; what did it cost?

.60)51.00 ------ _Ans._ $85

If I lost 40%, or 40 cents on the dollar, I received only 60 cents for every dollar the wagon cost; hence, it cost as many dollars as .60 is contained times in 51.00, which is 85.

Proof: 40% of $85 (85 × .40) = $34; $85 - $34 = $51.

NOTE.--The principles of percentage, in one form or another, enter into nearly all commercial calculations, besides many others. It is therefore of the utmost importance to business men, clerks, accountants, bookkeepers, and others, to become expert in percentage, and to adopt the easiest, simplest and shortest methods in computing interest, partial payments, trade discount, profit and loss, commission, insurance, stocks, bonds, taxes, exchange, etc.

PROFIT AND LOSS

When a thing is sold for more than it cost the seller, it is said to be sold at a profit. If it is sold for less than the cost, it is sold at a loss. Hence,

Profit = Selling Price - Cost Price.

Loss = Cost Price - Selling Price.

A profit or loss is generally reckoned as a percentage.

It is always understood that the percentage is reckoned on the cost price.

EXAMPLE: I buy wheat at 60 cents and sell it for 75 cents. What per cent do I gain?

SOLUTION: I gain the difference between 75 cents and 60 cents, or 15 cents. 15 cents is 25% of the cost. Hence, I gain 25%.

WORK:

75 cents - 60 cents = 15 cents.

15 cents ÷ 60 cents = .25, or 25%.

EXAMPLE: I bought flour at $3.50 per barrel. For what must I sell it to gain 20%?