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Can you do the Colonial Math?

The Math Book of Minerva Hutchinson
Middle Island

Minerva Hutchinson was born on February 18, 1798. She was one of six children born to Benjamin & Betsy Hutchinson. The family home was across from where the Longwood Public Library now stands. The Hutchinson homestead served the community as a store, later as the post office and stage stop. Minerva was an intelligent young lady, who kept a diary of her activities when she helped run the home as a stage stop. Following, is a copy of Minerva's math work book.  It is dated 1811, which would make her about 13 years old.

Think that colonial math was easy? Then try to do some of the math that a middle school aged student was expected to know almost 200 years ago.

This math book comes from the collection of the late Davis Erhardt.  Mr. Erhardt was a local historian who resided in Coram.  He took great interest in collecting original manuscripts, many of which appear on this site.  This math exercise is dedicated to his memory.


The definitions of terms come from the web site of Russ Rowlett. Director of the center for Mathematics and Science Education, at the University of North Carolina at Chapel Hill.

 

Troy Weight

Troy weight, system of weight used in the United Kingdom, and the United States, used for the weighing of precious metals (Gold). The name comes from the city of Troyes, France, where the system is believed to have originated.

Conversion table

480 grains = 1 oz.
5,760 grains = 1 lb.
24 grains = 1 dwt (penny weight)
20 dwt = 1 oz
 

1. In 47 lb. 10 oz. how many grains?

2. In 47128 grains of gold how many lb.

3. In 4560 grains of gold, how many spoons each half an ounce.

hints

Question 1

    47   Troy lbs.
 x 12   oz in 1lb
564 0z
+10 oz
574 oz.

   574  (# of Troy ounces)
x 480  ( grains in a Troy pound)

oz.   1  =  574     cross multiply  = 275, 520 grains
gr.  480      ?

Question 2

47128  grains                     = 8.2  oz.
5760    grains in a lb.

Question 3

4560   gr.
480     grains in an ounce      = 9.5 oz.

9.5 divided 1   = 9.5  x 2  = 19 teaspoons
                  2       1       1

grain (gr) [1]
a traditional unit of weight. The grain, equal to 1/480 troy ounce was the legal foundation of traditional English weight systems, with various pounds being defined as a specified number of grains: 5760 grains in a troy pound and 7000 grains in an avoirdupois pound.
pennyweight (dwt or pwt)
a unit of weight in the traditional troy system equal to 24 grains.  The d in the traditional symbol dwt is from the Latin word denarius for the small coin which was the Roman equivalent of a penny. (The letter d is also the traditional symbol for the penny in the English monetary system.)

Original math book page


Avoirdupois Weight
Conversion table

16 drams =  1 ounce
16 ounces = 1 pound
24 ounces = 1 Great pound
112 pounds = 1 hundredweight
4 quarters = 1 hundredweight
20 hundredweight = 1 ton
2,240 pounds = 1 ton

abbreviations
c = hundredweight
Qr. = quarters

1. In 3 tons of iron, how many c (hundredweight), c (quarters) & lb.

2. In 14,048 oz. how many C. (hundredweight)

3. In 461 Great Pounds of Morea silk, how many Oz. & drams

hints
How many hundredweight (C)

Question 1

1 ton = 20 hundredweight
   
    ton      1    =  3          =   60 c
     c        20      ?
How many Quarters (Qr.)

     4 qtr  =  1 c
    
     Qr.   4   =    ?      =  240 Qr
      C     1        60

    How many pounds

     lb.    2240    =   ?     = 6720 pounds
     ton     1             3
     
   

Question 2 

16 ounces = 1 pound
     14, 048  = ?  pounds
      
     14,048  = 878 pounds
        16

      C      1    =   ?        =  878 divided by 112   =   7.83
      lbs    112     878

Question 3 

24 ounces = 1 Great pound

    1 Great Pound  =  461 Great Pounds   = 11064 ounces
       24 ounces              ?

     16 drams = 1 ounce
     11064  x  16  =  177024  drams

dram (dr) [1]
a unit of weight in the traditional avoirdupois system , equal to 1/16 ounce or 1/256 pound. One dram equals about 1.7718 gram. The word dram comes from a Latin weight unit, the dragma, and derives ultimately from the Greek drachme, meaning a handful. The word is usually spelled "drachm" in Britain and "dram" in the United States, but both spellings are pronounced "dram." The avoirdupois dram is sometimes abbreviated dr. av. to distinguish it from the apothecaries' dram

Reduction Ascending and Descending

Conversion Table
1 shilling  = 12 pence
half crown  = 30 pence
1 crown  = 60 pence
half guinea  = 126 pence
guinea  = 252 pence
5 shilling  = 1 crown

abbreviations
L = pound
S = shilling
D = pence
C= hundredweight
CR = crown

1. In 720 S how many D and Crowns

2. In 120 S how many Cr. & half Crowns

3. In 612 half Cr. how many Cr. & D

4. Reduce 63 Crowns into S & guineas

hints

Question 1

1 shilling = 12 pence
   720 x 12   = 8640 pence

Question 2

 5 Cr. = 1 shilling  =  120 divided by 5  = 24 Crown

Question 3

612 half Crowns = 306 Crowns   612 divided by 2

     60 pence = 1 Crown  
     306 x 60 = 18360 pence
 

Question 4

1 Crown = 5 shilling
    63 x 5 = 315 shilling

1 Guinea = 21 shilling
315 divided by 21 = 15 Guinea


     Long Measure
conversion table
1 Furlong = 220 yards
= 660 feet
= 1/8 mile
= 40 poles
8 Furlongs = 1 mile = 5,280 feet

Pole = 16 1/2 feet = 5 1/2 yards
40 poles = 660 feet
1 " = 1 Barley Corn
12" = 36 Barley Corns

1 League = 3 miles

1. In seventy miles how many furlongs and poles

2. In 40 yards how many feet Inches and Barley Corns

3. How many Barley Corns in one mile

4. In a League how many yards

 

Hints;

Question 1

    1 mile = 8 Furlongs
    70 miles x 8 Furlongs  = 560 Furlongs

    1 Furlong = 40 poles
    560 Furlongs x 40 poles = 22400 poles

Question 2

a. 1 yard = 3 feet
    40 yards x 3 = 120 feet

b. 1 foot = 12 inches
    120 feet x 12 = 1440 inches
c. 1 inch = 3 Barley Corns
    1440 inches x 3 = 4320 Barley Corns

Question 3

     5,280 feet = 1 mile
     1 foot = 36 Barley Corns
     5280 x 36 = 190,080 Barley Corns

Question 4

      1 League = 3 miles
      4 Leagues x 3 miles  = 12 miles
      3 feet = 1 yard
      1 mile = 5280 feet  divided by 3 = 1760 yards
      1760 yards x 12 = 21,120 yards

definitions

League - Adopted by the Romans as the Leuga, it was supposed to represent the distance a person could walk in an hour. It became equal to 3 miles . In the united States, leagues have never been used on land only as 3 nautical miles at sea.

barleycorn - An old English unit of measure equal to 1/3 of an inch. The custom of using seeds is very common in farming societies. In England, where barley was a basic crop, barleycorns played this traditional role. The weight of a barleycorn, later renamed the grain is the original basis of all English weight systems.

furlong (fur)
a traditional unit of distance. Long before the Norman Conquest in 1066, Saxon farmers in England were measuring distance in rods and furlongs and areas in acres. The word "furlong", from the Old English fuhrlang, means "the length of a furrow"; it represents the distance a team of oxen could plow without needing a rest. A furlong equals 40 rods, which is exactly 10 chains, 220 yards, 660 feet, or 1/8 mile. One furlong is exactly 201.168 meters, so a 200-meter dash covers a distance very close to a furlong. The length of horse races is often stated in furlongs

pole also known as a rod

a traditional unit of distance equal to 5.5 yards. The rod and the furlong were the basic distance units used by the Anglo-Saxon residents of England before the Norman conquest of 1066. The Saxons generally called this unit the gyrd, a word which comes down to us as the name of a different unit, the yard. "Rod" is another Saxon word which meant just what it means today: a straight stick. The Normans preferred to call the gyrd a pole or a perch . The length of the rod was well established at least as early as the eighth century. It may have originated as the length of an ox-goad, a pole used to control a team of 8 oxen (4 yokes). Scholars are not sure how the rod was related to shorter units. It may have been considered equal to 20 "natural" feet. In any case, when the modern foot became established in the twelfth century, the royal government did not want to change the length of the rod, since that length was the basis of land measurement, land records, and taxes. Therefore the rod was redefined to equal 16.5 of the new feet. This length was called the "king's perch" at least as early as the time of King Richard the Lionheart (1198). Although rods and perches of other lengths were used locally in Britain, the king's perch eventually prevailed. The relationship between the rod and the other English distance units was confirmed again by the Parliamentary statute of 1592, which defined the statue mile to be either 320 rods or 1760 yards, thus forcing the rod to equal exactly 5.5 yards or 16.5 feet.

Cloth Measure
conversion table
1 nail = 2.5 inches
 Quarter (Qr) = 1/4 yard = 9 inches
20 nails = 1 Ell
4 Quarters = 1 yard

1. In 14 yards how many Quarters & Nails

2. In 7000 Nails of Holland (cloth) how many Ells

Hints

Definitions

Nail - an old English unit of length equal to 1/20 ell Like the ell, the nail was used for measuring cloth; traditionally, it represented the length of the last two joints (including the fingernail) of the middle finger. The nail is equivalent to 1/16 yard, 1/4 span,2.25 inches, or exactly 5.715 centimeters

ell
a traditional unit of length used primarily for measuring cloth. In the English system, one ell equals 20 nails, 45 inches, or 1.25 yards;; in metric terms, an English ell equals exactly 1.143 meters. The word comes from the Latin ulna, which originally meant the elbow and is now the name of the bone on the outside of the forearm. Unfortunately, the same word ulna was also used for the yard, creating frequent confusion between the two units in medieval documents. Probably the ell originated through a custom of measuring lengths of cloth using two forearms, with the hands touching or overlapping. The ell was used with a similar length in France (where it was called the aune). In Scotland, the ell was practically the same as the yard, being equal to 37 Scots inches or 37.2 English inches (94.5 centimeters). This Scottish length appears to reflect an old practice of cloth merchants in giving an extra inch with each yard, to allow for any irregular cutting at the ends of the piece. In eastern Europe, the ell was a shorter distance: see next entry.
elle

Land Measure
4 rods = 1 acre
40 perches = 1 acre

1. In 40 acres how many Roods (Rods) and Perches

2. Reduce 2850 Perches into Acres

perch
a unit of area equal to one square perch [1]. A perch of area covers exactly 272.25 square feet or about 25.292 85 square meters. There are 40 perches in a rood and 160 perches in an acre.
rood
an old unit of distance, used in several ways. Rood (or roede) is an old Dutch word meaning a rod or pole. So the rood is in some cases another name for a rod, a traditional unit of area used to measure land. The rood is defined to be 40 square rods (or perches), which equals 1210 square yards, or 10 890 square feet, or exactly 1/4 accre.. That would be the area of a lot 22 yards wide and 55 yards deep, about the size of many suburban lots.

 


Liquid Measurement
conversion table
2 pints = 1 quart
4 quarts = 1 gallon
2 gallons = 1 peck
4 pecks = 1 bushel
8 bushels = 1 Quarter
36 bushels = 1 chaldron
ale
Anchor = 10 gallons
1 barrel = 36 gallons
54 gallons = 1 hogshead
Before 1824 - 63 wine gallons = 1 hogshead

1. In 17 gallons how many Quarts and pints

2. 10 Barrels of beer, how many gallons & quarts

3. In 72 Hogsheads of beer, how many barrels


4. If a bark (ship) contains 30 barrels of beer, how many gallons doth it hold

5. In 3 Hogshead of Brandy (wine) how many half anchors

Hints:

Question 1

    17 gallons  x 4 (quarts in a gallon)  = 68 quarts
    68 quarts x 2 (pints in a gallon)  = 136 pints

Question 2

     36 gallons = 1 barrel
     36 ( # of gallons in a barrel)  x 10 (number of barrels  = 360 gallons
     360 gallons x 4 (# of quarts in a gallon) = 1440

Question 3

      72 Hogsheads of beer x 54 (number of gallons of beer in a Hogshead)   

      =  3888 gallons
      3888 divide by 36 ( # of gallons in a barrel) = 108

Question 4   

      30 )# of barrels)  x 36 (# of gallons per barrel)  = 1080 gallons
 

Question 5

      63 (# of gallons of wine in a Hogshead)
     63 (# of gallons in a Hogshead)  x 3 (# of Hogsheads)  = 189
     189 (# of gallons) divided by 5 (# of gallons in a half anchor) = 37 1/2   

     anchors - 4 gallons

 
chalder or chaldron (chd)
a traditional British unit of volume or weight used for dry commodities such as coal or lime. As a volume measure, the chaldron is equal to 36 bushels. The words "chalder," "chaldron," and "cauldron" are English spellings of the same old French word, which originally meant a large kettle.
hogshead (hhd)
a traditional unit of volume for liquids. Originally the hogshead varied with the contents, often being equal to 48 gallons of ale; 54 of beer; 60 of cider; 63 of oil, honey, or wine; or 100 of molasses. In the United States, a hogshead is defined to hold 2 barrels, or 63 gallons; this was the traditional British wine hogshead.  No one seems to know for sure how this unit got its unusual name.
quarter (qtr or Q)
a traditional unit of volume used for measuring grain. A quarter of grain is 8 bushels (about 281 liters, based on the U.S. bushel, or 291 liters, based on the British imperial bushel), presumably because this quantity of grain weighs roughly 1/4 ton.

 


Dry measure
conversion table
8 bushels = 1 quarter
1 bushel = 4 pecks
36 bushels = 1 chaldron

1. In 40 quarters of wheat, how many bushels & Pecks

2. Reduce 1280 pecks of wheat into Quarters

3. In 30 chaldrons of coals, each 36 bushels - is how many Pecks

Hints:

Question 1

     40 (# of quarters) x 8 (# of bushels in a quarter)  = 320 bushels
     320 (# of bushels)  x 4 (# of pecks in a bushel)  = 1280 Pecks

Question 2

    1280 (# of pecks) divided by 4 (# of pecks in a bushel)  = 320 bushels

     320 (# of bushels) divided by 8 (# of quarters in a bushel)  = 40 quarters

Question 3

     30 (# of chaldrons) x 36 (# of bushels in a chaldron)  = 1080 bushels
     1080 (# of bushels)  x 4 (# of pecks in a bushel) = 4320 Pecks


Motion
 

sign - An informal unit of angle measure in astrology. The sun's annual path through the sky, called the Zodiac, id divided into 12 parts called signs, each sign corresponds  to one of the classic twelve constellations through which the sun passes.

1 sign = 1/12 circle, or 30 degrees.

1. in half a years time the sun made his progress through 6 signs of the Zodiac, how many Degrees, Minutes, & Seconds doth that amount to-

Hint:

Question 1

   6 (# of signs) x 30 (# of degrees in a sign)  = 180 Degrees
  180 (# of Degrees) x 60 (# of minutes in an hour) = 10800 Minutes
   10800 (# of minutes)  x 60 (# of seconds in a minute)  = 648000 Seconds



Inverse Proportion

1. If 48 men can build a wall in 24 days, how many Men can do the same in 192 days -

2. How many yards of matting that is half a yard wide, will cover a Room that is 18 Feet wide, and 30 Feet long

3. Suppose 800 soldiers were placed in a garrison and their provisions were computed sufficient for 2 months; how many soldiers must depart, that the Provisions may serve them 5 months.

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