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.