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

Chapter I: The Anglo-Saxon Period, 449-1066 (14)

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===================+======+============================================
ARTICLE |WEIGHT| STATES
-------------------+------+--------------------------------------------
|Pounds|
Blackberries | 30|Iowa. Tennessee, 48 pounds; dried 28 pounds.
Blueberries | 42|Minnesota.
Canary seed | 60|Tennessee.
Cantaloupe melon | 50|Tennessee.
Cement | 80|Tennessee.
Cherries | 40|Iowa. Tennessee, with stems 56 pounds;
| |without stems, 64 pounds.
Chestnuts | 50|Tennessee. Virginia, 57 pounds.
Cotton seed, staple| 42|South Carolina.
Cucumbers | 48|Iowa, Tennessee, Missouri. Wisconsin,
| |50 pounds.
Currants | 40|Iowa and Minnesota.
Grapes | 40|Iowa. Tennessee, with stems, 48 pounds;
| |without stems, 60 pounds.
Hickory nuts | 50|Tennessee.
Hominy | 60|Ohio. Tennessee, 62 pounds.
Horse-radish | 50|Tennessee.
Kaffir corn | 56|Kansas.
Kale | 30|Tennessee.
Land plaster | 100|Tennessee.
Mustard | 30|Tennessee.
Plums | 40|Florida. Tennessee, 64 pounds.
Plums, dried | 28|Michigan.
Popcorn | 70|Iowa, Indiana, Tennessee. Ohio, in the ear,
| |42 pounds; Iowa, shelled, 56 pounds.
Prunes, dried | 28|Idaho; green, 45 pounds.
Quinces | 48|Florida, Iowa and Tennessee.
Rape seed | 50|Wisconsin.
Raspberries | 32|Iowa, Kansas, Tennessee, 48 pounds.
Rhubarb | 50|Tennessee.
Salads | 30|Tennessee.
Sand | 130|Iowa.
Spinach | 30|Tennessee.
Strawberries | 32|Iowa. Tennessee, 48 pounds.
Sugar-cane seed | 57|New Jersey.
Velvet-grass seed | 7|Tennessee.
Walnuts | 50|Tennessee, Iowa.
-------------------+------+--------------------------------------------

APOTHECARIES’ WEIGHT

Apothecaries’ Weight is used by apothecaries and physicians weighing medicines for prescriptions.

TABLE
20 grains (gr.) = 1 scruple (sc., or ℈)
2 scruples = 1 dram (dr., or ʒ)
8 drams = 1 ounce (oz., or ℥)
12 ounces = 1 pound (lb., or ℔)

Pound Ounces Drams Scruples Grains
1 = 12 = 96 = 288 = 5760

1. In writing prescriptions, physicians express the number in Roman characters, using j instead of i final. They also write the symbol first; thus: ℥v, ʒvj, ℈ij.

MEDICAL SIGNS AND ABBREVIATIONS

℞ (Lat. Recipe), take; āā, of each; ℔, pound; ℥, ounce; ʒ, drachm; ℈, scruple; ♏, minim, or drop; O or o, pint; f℥, fluid ounce; fʒ, fluid drachm; as, ℥ss, half an ounce; ℥i, one ounce; ℥iss, one ounce and a half; ℥ij, two ounces; gr. grain; Q. S., as much as sufficient; Ft. Mist., let a mixture be made; Ft. Haust., let a draught be made; Ad., add to; Ad lib., at pleasure; Aq., water; M., mix; Mac., macerate; Pulv., powder; Pil., pill; Solv., dissolve; St., let it stand; Sum., to be taken; D., dose; Dil., dilute; Filt., filter; Lot., a wash; Garg., a gargle; Hor. Decub., at bed time; Inject., injection; Gtt., drops; ss, one-half; Ess., essence.

COMPARISON OF WEIGHTS

TABLE

1 pound avoirdupois = 7000 grains
1 ounce avoirdupois = 437-1/2 grains
1 pound Troy, or apothecary = 5760 grains
1 ounce Troy, or apothecary = 480 grains

CIRCULAR MEASURES

_Circular or Angular Measures_ are used in surveying, navigation, astronomy, geography, reckoning latitude and longitude, and computing differences in time.

A _Circle_ is a plane figure bounded by a curved line, every point of which is equally distant from a point within, called the center.

The _Circumference_ is the bounding line of a circle.

The _Radius_ of a circle is a straight line drawn from the circumference to the center.

The _Diameter_ is a straight line drawn through the center, with the ends terminating in the circumference.

An _Arc_ of a circle is any portion of the circumference.

An _Angle_ is the difference in direction between two straight lines which meet.

If two diameters divide a circle into four equal parts, these diameters make _right angles_ with each other.

An angle less than a right angle is an _acute angle_.

The circumference of a circle may be divided into 360 equal parts, called _degrees_. If the circle is large, the degree is large, and if the circle is small, the degree is small, but the degree is always 1/360 part of the circumference, whatever the size of the circle.

An angle at the center of a circle is measured by the arc which bounds it.

If the angle is a right angle, it is measured by 1/4 of 360 degrees, or 90 degrees; hence, any angle of 90 degrees is a right angle.

An acute angle is always less than 90 degrees.

An obtuse angle is always more than 90 degrees.

TABLE OF CIRCULAR MEASURE

60 seconds (′′) = 1 minute (′)
60 minutes = 1 degree (°)
360 degrees = 1 circumference (cir.)

Circumference Degrees Minutes Seconds
1 = 360 = 21,600 = 1,296,000

A _quadrant_ is 1/4 of a circumference, or 90°; a _sextant_ is 1/6 of a circumference, or 60°.

The length of a degree of longitude on the earth’s surface at the Equator is 69.16 miles.

In astronomical calculation 30° are called a _sign_, and there are therefore 12 signs in a circle.

LONGITUDE AND TIME

The earth’s circumference (which has the form of a circle) at the equator is (3.1416 × 7926), 24900 miles; which divided by 360, gives 69.17 miles for 1 degree of longitude at the equator. Leaving the equator, degrees of longitude gradually diminish, since all meridians converge at the poles. Thus, 1 degree of longitude, at 10 degrees of latitude, is 68.1 miles; at 20 degrees 65 miles; at 30 degrees 59.9 miles; at 40 degrees 53 miles; at 50 degrees 44.5 miles; at 60 degrees 34.6 miles; at 70 degrees 23.7 miles; at 80 degrees 12 miles; at 90 degrees 0.

Imaginary lines running north and south, through these degrees, from pole to pole, are called _meridians_. Those east and west, _parallels_.

One meridian which runs through Greenwich, near London, England, is called the _prime meridian_, and all the other meridians are reckoned as east or west of it.

_Longitude_ is distance east or west of the prime meridian. When we say that the longitude of Paris is 2° 20′ East, we mean that the meridian running through Paris is 2° 20′ east of the prime meridian that runs through Greenwich, England. The longitude of Washington, D. C., is 77° 7′ West. That means that the meridian which passes through Washington is 77° 7′ west of the prime meridian.

The longitude of a place tells in degrees, minutes, and seconds, the distance it is east or west of the prime meridian.

RULE.--_To find the difference of time between two places, when the difference of longitude is known, or vice versa, multiply the given longitude, expressed in degrees, by 4. This gives the equivalent time in minutes. Dividing the given time, expressed in minutes, by 4, gives the equivalent longitude in degrees._

EXAMPLE: The difference of longitude between Boston and San Francisco is nearly 51-1/4°, what is the difference of time?

51-1/4 × 4 = 205. 205 minutes equal 3 hours and 25 minutes. _Ans._ 3 hours and 25 minutes.

The difference of time between London and New York is about 4 hours and 55-1/2 minutes, what is the difference of longitude?

4 hours and 55-1/2 minutes equals 295-1/2 minutes. 295-1/2 ÷ 4 = 73-7/8. _Ans._ 73-7/8°.

MEASURES OF TIME

The unit of time measurement is the same among all nations. Practically it is 1-86400 of the mean solar day, but really it is a perfectly arbitrary unit, as the length of the mean solar day is not constant for any two periods of time. There is no constant natural unit of time.

Time measures are used in telling the time of day, in problems in longitude and time, in figuring interest on notes and bills, and in numerous other ways.

TABLE OF THE DIVISIONS OF TIME

60 seconds (sec.) = 1 minute (min.)
60 minutes = 1 hour (hr.)
24 hours = 1 day (da.)
7 days = 1 week (wk.)
30 days = 1 commercial month (mo.)
52 weeks = 1 year (yr.)
12 months = 1 year
360 days = 1 commercial year
365 days = 1 common year
366 days = 1 leap year
100 years = 1 century

Century Years Months Days Hours Minutes
1 = 100 = 1,200 = 36,500 = 876,000 = 52,560,000

Centennial years exactly divisible by 400, and other years exactly divisible by 4, are _Leap Years_.

WHY WE HAVE LEAP YEAR

The average time it takes the earth to revolve once around the sun (_one_ year) is 365 days, 5 hours, 48 minutes, 47.8 seconds, or about 365-1/4 days.

The change in the length of the mean sidereal day, _i.e._, of the time of the earth’s rotation upon its axis, amounts to 0.01252 seconds in 2400 mean solar years.

Instead of reckoning this part of a day each year, it is disregarded, and an addition is made when this amounts to one day, which is very nearly every fourth year. This addition of one day is made to the month of February. Since the part of a day that is disregarded when 365 days are considered as a year, is a little less than one quarter of a day, the addition of one day every fourth year is a little too much, and, to correct this excess, addition is made to only every fourth centennial year.

STANDARD TIME

By this is meant time which differs from Greenwich mean time by whole hours.

The earth revolves on its axis from west to east, nearly 17.3 miles in 1 minute at the equator; at the latitude of New Orleans, nearly 15 miles in 1 minute; at Memphis, 14 miles; at Chicago, 13 miles; at London, 10.8 miles; at St. Petersburg, 8.6 miles. That is, a watch would gain one minute going west, or lose one minute going east that distance, in the latitudes of the respective cities.

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.

This diagram illustrates the curious fact that a telegram despatched from London may be delivered in New York apparently before the time it was sent off, and why a telegram apparently takes so long to reach Bombay.]

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%?

SOLUTION: I must sell it for 100% of the cost plus 20% of the cost, or 120% of the cost.

120% of $3.50 = $4.20.

∴ I must sell it at $4.20.

EXAMPLE: I sold my carriage for 80% of its cost and received $90 for it. What was the cost?

SOLUTION:

1% of the cost is 1/80 of $90, or $1.125.

100% of the cost = 100 × $1.125, or $112.50.

COMMISSION

is a percentage paid for buying or selling real estate, goods, etc. A consignment is a quantity of goods, sent to an agent, broker or commission merchant, for sale. The consignor is the one who sends the goods, the consignee the one to whom they are sent.

PRINCIPLES:

1. _The commission is some number or per cent of the price of what is bought or sold._

2. _The proceeds equal the selling price minus the commission._

3. _The amount equals the selling price plus the commission._

Commission presents two classes of problems. One of these classes may be called “buying problems.” The other may be called “selling problems.”

BUYING PROBLEM: I sent my agent $1977.60 to _buy_ wild farm lands in northern Wisconsin, at $3 per acre. He was to receive 3% for his work. How many acres did he buy?

WORK AND EXPLANATION:

3% of $3 = $.09.

Cost to me of 1 acre is $3 + .09 = $3.09

For $1977.60 he buys as many acres as $3.09 is contained times in $1977.60, or 640. Hence, he buys 640 acres.

SELLING PROBLEM: My agent _sells_ 360 pounds of butter for me at 20 cents. He pays $4.20 freight charges and $9.60 for storage. His commission is 5%. What does he send me?

WORK AND EXPLANATION:

360 pounds at 20 cents = $72.00
Freight is $4.20
Storage is 9.60
Commission is 5% of $72, or 3.60
Total charges = 17.40
------
He sends me the difference, or $54.60

TRADE DISCOUNT

is an allowance made by manufacturers and jobbers from their list or marking prices. When the market varies, they change the discount accordingly, or make several discounts instead of changing the list.

Trade discount is a certain per cent off, or from list or marking price; while profit and loss is computed on the cost or purchase price.

The amount of the discount allowed depends sometimes upon the amount of order, and sometimes upon the terms of settlement. Very often two or more discounts are deducted in succession. Thus, 10% and 5% off; or, as it is generally expressed in business, 10 and 5 off, means a discount of 10%, and then 5% from what is left; 20, 10, and 5 off, means three successive discounts. A retailer’s profit is smaller when he is allowed 10 and 5 off, than if he were allowed 15 off. The result is not affected by the order in which the discounts are taken.

EXAMPLE: I receive a bill of goods amounting to $100, 20% off. What is the net cost?

FIRST WAY:

20% of $100 =$20

$100 - $20 = $80

SECOND WAY:

100% - 20% = 80%

80% of $100 = $80

EXAMPLE: A merchant receives two bills of $200 each. On one there is a discount of 25%; on the other, 15% and 10%. What must he pay on each, net?

FIRST BILL:

100% - 25% = 75%, or 3/4

3/4 of $200 = $150.

SECOND BILL:

100% - 15% = 85%

100% - 10% = 90%

90% of 85% = 76.5%

.765 × $200 = $153.

PROMISSORY NOTES

A _note_ is a written promise to pay a specified sum at a certain time.

The person who promises is called the _maker_, and the person to whom he promises is called the _payee_.

The FACE of a note is the sum of money promised.

A _negotiable note_ is one which is made payable to the bearer, or to the order of the payee. A negotiable note can be sold or transferred.

A note is _non-negotiable_ when it is payable only to the person or persons named in the note.

An _indorser_ of a note is a person who writes his name on the back of it. The person who indorses, by so doing guarantees its payment. An _indorsement in blank_ is simply the signature of the indorser written across the back of the note or draft. When indorsed in this way the note or draft is made payable without further indorsement to any person holding.

A note or draft is _indorsed in full_ when the indorser states, over his signature, the person to whose order the note or draft is to be paid. If an indorser does not wish to guarantee the payment of a note or draft, he writes “Without recourse” over his name when indorsing it.

A _protest_ of a negotiable note or draft is a formal statement by a notary public that said note or draft was presented for payment or acceptance and refused.

A note, when due, must be presented at the place at which it is made payable. The _day of maturity_ is the day on which a note becomes due.

The _days of grace_ are the three days beyond the specified time for payment. Days of grace are now practically abolished throughout the United States.

KINDS OF NOTES.--There are three principal kinds of notes--_Time Notes_, _Joint Notes,_ and _Joint and Several Notes._

A _Time Note_ must be paid in a specified time.

A _Joint Note_ is one signed by two or more persons who are jointly liable for its payment.

A _Joint and Several Note_ is a note signed by two or more persons who are both jointly and individually liable for its payment. Each man who signs the note is as much responsible for the payment of the whole sum as if he had signed alone.

LEGAL RULES THAT APPLY TO NOTES

A note made out on _Sunday_ is void.

If a note does not state that _interest_ is to be paid, it does not bear interest until after it is due.

If anyone obtains a note _by fraud_ or from an _intoxicated person,_ he cannot collect.

_To be negotiable_ an instrument must be in writing and signed by the maker (of a note) or drawer (of a bill or check).

_It must contain_ an unconditional promise or order to pay a certain sum in money.

Must be payable on demand, or at a fixed future time.

Must be payable to order or to bearer.

In a bill of exchange (check), the party directed to pay must be reasonably certain.

Every negotiable instrument is presumed to have been issued for a valuable consideration, and want of consideration in the creation of the instrument is not a defense against a bona-fide holder.

_An instrument is negotiated_, that is completely transferred, so as to vest title in the purchaser, if payable to bearer, or indorsed simply with the name of the last holder, by mere delivery; if payable to order, by the indorsement of the party to whom it is payable and delivery.

One who transfers an instrument by indorsement warrants to every subsequent holder that the instrument is genuine, that he has title to it, and that if not paid by the party primarily liable at maturity, he will pay it upon receiving due notice of non-payment.

_To hold an indorser liable_ the holder upon its non-payment at maturity must give prompt notice of such non-payment to the indorser and that the holder looks to the indorser for payment. Such notice should be sent within twenty-four hours.

_When an indorser is thus compelled to pay_ he may hold prior parties, through whom he received the instrument, liable to him by sending them prompt notice of non-payment upon receiving such notice from the holder.

One who transfers a negotiable instrument by delivery, without indorsing it, simply warrants that the instrument is genuine, that he has title to it, and knows of no defense to it, but does not agree to pay it if unpaid at maturity.

_The maker of a note is liable_ to pay it, if unpaid at maturity, without any notice from the holder or indorser.

Notice to one of several partners is sufficient notice to all.

_When a check is certified_ by a bank the bank becomes primarily liable to pay it without notice of its non-payment, and when the holder of a check thus obtains its certification by the bank, the drawer of the check and previous indorsers are released from liability, and the holder looks to the bank for payment.

_A bona-fide holder_ of a negotiable instrument, that is, a party who takes an instrument regular on its face, before its maturity, pays value for it and has no knowledge of any defenses to it, is entitled to hold the party primarily liable responsible for its payment, despite any defenses he may have against the party to whom he gave it, except such as rendered the instrument void in its inception. Thus, if the maker of a note received no value for it, or was induced to issue it through fraud or imposition, that does not defeat the right of a bona-fide holder to compel its payment from him.

The dates and amounts of _partial payments_ on a note, before it is finally paid in full, are placed on the back.

The _place of payment_, if not mentioned, is at the maker’s place of business or residence, during reasonable business hours.

If a _note_ or a _check_ received in payment of a debt is _dishonored_, the debt revives.

_Ignorance_ of the law does not excuse anyone. No _contract_ is good unless there be a _consideration_. No consideration is good that is _illegal_.

The _maker_ of an _accommodation note_ is not bound to the person accommodated; but he is bound to any other person receiving the note for value.

BANK DISCOUNT

The sum charged by a _bank_ for cashing a note or time draft is called _bank discount_. This discount is the simple interest, paid in advance, for the number of days the note has to run. Wholesale business houses usually sell goods on _time_ and take notes from the retailers in payment. These notes are not often for a longer period than _three months_. Some are placed in the banks for collection, others are _discounted_. When a note is discounted at a bank the payee _indorses_ it, making it payable to the bank. Both maker and payee are then responsible to the bank for its payment. If the note is drawing interest the discount is reckoned on and deducted from the amount due at maturity. Most notes discounted at banks do not draw interest. The _time_ in bank discount is always the number of days from the date of discounting to the date of maturity.

EXAMPLE: A note of $250, dated July 7, payable in 60 days, is discounted July 7 at 6%; find the proceeds.

EXPLANATION: This note is due in 63 days, or September 8. The accurate interest of $250 for 63 days at 6% is $2.59. The proceeds, then, will be $250-$2.59, or $247.41.

The _Present Worth_ of a note or debt is a sum, which, if put at interest, will amount to that debt in the given time.

The _True Discount_ is the difference between the debt at maturity and its present worth.

REMEMBER:

1. _To allow three days of grace, if the debt discounted is a note._

2. _To add the interest due at maturity to the principal, before discounting, if the note bears interest._

EXAMPLES: Case I.--Note not bearing interest.

What is the present worth and true discount on a note of $200, if paid 6 months before due, the discount being 6%.

SOLUTION: Amount of $1 for 6 months at 6% = $1.03. If $1.03 = amount of $1, $200 is the amount of as many dollars as 200/1.03, or $194.17+.

$194.17 is the present worth. $200 - $194.17 = $5.83 true discount.

The following rule can be deduced from the foregoing solution:--

RULE: 1. _To find the present worth, divide the debt by the amount of $1 for the given time._

2. _To find the true discount, subtract the present worth from the debt._

Case II.--Note bearing interest.

What is the present worth of a note of $300, bearing 6% interest, due in 2 years 4 months, if money is worth 10%.

SOLUTION: Interest on $300 for 2 years 4 months at 6% = $42.

$300 + $42 = $342. Amount due at maturity.

Amount of $1 for 2 years 4 months at 10% = $1.23-1/3.

If $1.23-1/3 = amount of $1, then $3.42 is the amount of

342
$--------, or $277.29.
1.23-1/3

$277.29 = present worth.

INTEREST

If a person borrows money, he usually pays something for the loan.

The sum of money he borrows is called the _Principal_; the money he pays for the use of the principal is called _Interest_. Interest is generally reckoned at so much for the use of each $100 for one year. This amount is called the _Rate per cent per Annum_.

Thus, if we say that $200 is borrowed for three years at 4 per cent per annum, we mean that the borrower, at the end of each year, pays the lender $4 for each $100 borrowed--_i.e._, $8 interest for each year.

In the above example the interest is supposed to be paid to the lender at the end of each year. Interest thus reckoned is called _Simple Interest_.

The sum obtained by adding the interest for any given time to the principal is called the _Amount_ in that time.

COMMON INTEREST METHODS

If we were to find the interest on a sum of money for 3 years 4 months 5 days, we would find the interest for 1 year, then for 1 month (1/12 of a year), then for 1 day (1/360 of a year). Having the interest for 1 year 1 month 1 day, it is a simple matter of multiplication to get it for 3 years 4 months 5 days.

EXAMPLE:

What is the interest on $520 for 1 year 3 months at 6%?

WORK:

1 year 3 months = 1-1/4 year

$520 principal
.06
--------
4)$31.20 interest 1 year
--------
$7.80 interest 1/4 year
--------
$39.00 interest 1-1/4 year

THE 60-DAY INTEREST METHOD

In what is called the 60-Day Method, 360 days are considered one year, and 30 days one month. Upon this basis the interest for 60 days, or two months, at any rate, will be 1/6 of the interest for one year; and when the rate is 6% the interest for 60 days is one per cent or 1/100 of the principal. Thus, the interest of $247 for 60 days at 6% is $2.47.

EXAMPLE: Find the interest of $1728 for 80 days at 6%.

WORK:

$17¦28 = interest for 60 days.
5¦76 = interest for 20 days.
---+--
$23¦04 = interest for 80 days.

EXPLANATION:

The interest of $1728 for 60 days at 6% is 1% of $1728, or $17.28; and the interest for 20 days (1/3 of 60) is 1/3 of $17.28, or $5.76. Hence for 80 days it will be $17.28 plus $5.76, or $23.04.

METHODS OF RECKONING TIME

_The Common Method._--When the time is long, generally 30 days are considered a month.

_The Exact Method._--When the time is short, the exact number of days is generally counted but we sometimes find the exact number of days also when the time is long.

_The Bankers’ Method._--Bankers get the exact number of days between two dates, but each day is reckoned as 1/360 of a year.

PROBLEM, when the time is long.

Find the time between April 12, 1895, and September 22, 1899.

BEST METHOD

From April 12, 1895, to April 12, 1899, is 4 _years_.

From April 12, 1899, to Sept. 12, 1899, is 5 _months_.

From Sept. 12, 1899, to Sept. 22, 1899, is 10 _days_.

Time between dates = 4 years 5 months 10 days.

ANOTHER METHOD

1899 9 22
1895 4 12
----------
4 5 10

PROBLEM, when the time is short. Find the difference in time between April 12 and July 15, 1902.

WORK:

Number of days left in April = 18
in May = 31
in June = 30
in July = 15
--
Total number of days = 94

NOTE.--If the rate and principal are given, it is a simple matter to find the interest, now that we have the time.

Example of the use of Table: What is the time from February 10 to October 18, in the same year. February 10 is numbered 41, and October 18 is numbered 291; 291 - 41 = 250, _Ans._ This includes the last day, but not the first. If both days are taken, subtract 40 from 291 = 251, _Ans._ When February 29 occurs in a term, count an additional day. The day of the date of a note is not included in its term; thus, required the last day of grace of a note dated March 24, at 90 days. March 24 = 83; 83 + 93 = 176 = June 25, _Ans._

TABLE OF TIME, IN DAYS

The following table gives the exact time, in days, between two dates.

====+====+=====+=====+===+====+====+====+=====+====+====+====
Jan.|Feb.|March|April|May|June|July|Aug.|Sept.|Oct.|Nov.|Dec.
----+----+-----+-----+---+----+----+----+-----+----+----+----
1| 32| 60| 91|121| 152| 182| 213| 244| 274| 305| 335
2| 33| 61| 92|122| 153| 183| 214| 245| 275| 306| 336
3| 34| 62| 93|123| 154| 184| 215| 246| 276| 307| 337
4| 35| 63| 94|124| 155| 185| 216| 247| 277| 308| 338
5| 36| 64| 95|125| 156| 186| 217| 248| 278| 309| 339
6| 37| 65| 96|126| 157| 187| 218| 249| 279| 310| 340
7| 38| 66| 97|127| 158| 188| 219| 250| 280| 311| 341
8| 39| 67| 98|128| 159| 189| 220| 251| 281| 312| 342
9| 40| 68| 99|129| 160| 190| 221| 252| 282| 313| 343
10| 41| 69| 100|130| 161| 191| 222| 253| 283| 314| 344
11| 42| 70| 101|131| 162| 192| 223| 254| 284| 315| 345
12| 43| 71| 102|132| 163| 193| 224| 255| 285| 316| 346
13| 44| 72| 103|133| 164| 194| 225| 256| 286| 317| 347
14| 45| 73| 104|134| 165| 195| 226| 257| 287| 318| 348
15| 46| 74| 105|135| 166| 196| 227| 258| 288| 319| 349
16| 47| 75| 106|136| 167| 197| 228| 259| 289| 320| 350
17| 48| 76| 107|137| 168| 198| 229| 260| 290| 321| 351
18| 49| 77| 108|138| 169| 199| 230| 261| 291| 322| 352
19| 50| 78| 109|139| 170| 200| 231| 262| 292| 323| 353
20| 51| 79| 110|140| 171| 201| 232| 263| 293| 324| 354
21| 52| 80| 111|141| 172| 202| 233| 264| 294| 325| 355
22| 53| 81| 112|142| 173| 203| 234| 265| 295| 326| 356
23| 54| 82| 113|143| 174| 204| 235| 266| 296| 327| 357
24| 55| 83| 114|144| 175| 205| 236| 267| 297| 328| 358
25| 56| 84| 115|145| 176| 206| 237| 268| 298| 329| 359
26| 57| 85| 116|146| 177| 207| 238| 269| 299| 330| 360
27| 58| 86| 117|147| 178| 208| 239| 270| 300| 331| 361
28| 59| 87| 118|148| 179| 209| 240| 271| 301| 332| 362
29| --| 88| 119|149| 180| 210| 241| 272| 302| 333| 363
30| --| 89| 120|150| 181| 211| 242| 273| 303| 334| 364
31| --| 90| --|151| --| 212| 243| --| 304| --| 365
----+----+-----+-----+---+----+----+----+-----+----+----+----

COMPOUND INTEREST

Interest computed, at regular intervals, on the sum of the principal and any unpaid interest, is called _compound interest_. In other words, as soon as interest becomes due and is unpaid, it begins to draw interest at the same rate as the principal. Compound interest is generally paid on the deposits in savings banks and is used in calculating amortization and sinking funds.

Interest may be compounded quarterly, semi-annually, annually, or at the end of any other period agreed upon. In some States the collection of compound interest is not permitted.

EXAMPLE: Find the amount and the compound interest of $1200 at 6% for two years, interest compounded semi-annually.

SOLUTION:

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The Circle of Knowledge: A Classified, Simplified, Visualized Book of AnswersChapter I: The Anglo-Saxon Period, 449-1066 (14)

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