Egyptian
Contribution: Since different people have different
lengths of arm, the Egyptians developed a standard royal cubit, which was
preserved in the form of a black granite rod against which everyone could
standardize their own measuring rods.
To measure smaller lengths required subdivisions of the royal
cubit. Although we might think there is
an inescapable logic in dividing it in a systematic manner, this ignores the
way that measuring grew up with people measuring shorter lengths using other
parts of the human body.
The
digit was the smallest basic unit, being the breadth of a finger. There were 28 digits in a cubit, 4 digits in
a palm, 5 digits in a hand, 3 palms (so 12 digits) in a small span, 14 digits
(or a half cubit) in a large span, 24 digits in a small cubit, and several
other similar measurements. Now one
might want measurements smaller than a digit, and for this the Egyptians used
measures composed of unit fractions.
Egyptian
Papyri: It is not surprising that the earliest
mathematics, which comes down to us, is concerned with problems about weights
and measures, for this indeed must have been one of the earliest reasons to
develop the subject. Egyptian papyri,
for example, contain methods for solving equations, which arise from problems
about weights and measures.
Babylonian
Contribution: A later
civilization whose weights and measures had a wide influence was that of the
Babylonians around 1700 BC. Their basic
unit of length was, like the Egyptians, the cubit. The Babylonian cubit (530 mm), however, was very slightly longer
than the Egyptian cubit (524 mm). The
Babylonian cubit was divided into 30 kus, which is interesting since the kus
must have been about a finger's breadth, but the fraction ^{1}/_{30}
is one, which is also closely connected to the Babylonian base 60 number
system. A Babylonian foot was ^{2}/_{3}
of a Babylonian cubit. Now we commented
in the previous paragraph about a subdivision of a Babylonian unit, which was
closely related to their number system.
This presents a problem as we look at developing systems of measures.
Many
early number systems tended to be based on ten for the obvious reason that we
have ten fingers on which to count.
Most such systems were not positional systems, so the reason to use
multiples of ten in measurement subdivision was less strong. Also ten is an unfortunate number into which
to divide a unit of measurement since it only divides naturally into ^{1}/_{2},
^{1}/_{5}, ^{1}/_{10}. Basing subdivisions on 12, mean that ^{1}/_{2},
^{1}/_{3}, ^{1}/_{4}, ^{1}/_{6},
^{1}/_{12} are natural subdivisions, giving much more range for
trading quantities. However, since most
measuring systems seem to have grown up as a combination of different
"natural" measures, no decision about a number to subdivide by would
arise. One exception, and the earliest
known decimal system of weights and measures, is the Harappan system.
Harappan
System: The Harappan civilization flourished in
the Punjab between 2500 BC and 1700 BC.
The Harappans appear to have adopted a uniform system of weights and
measures. An analysis of the weights
discovered in excavations suggests that they had two different series, both
decimal in nature, with each decimal number multiplied and divided by two. The main series has ratios of 0.05, 0.1,
0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500. Several scales for the measurement of length were also discovered
during excavations. One was a decimal
scale based on a unit of measurement of 1.32 inches (3.35 centimeters), which
has been called the "Indus inch".
Of course ten units is then 13.2 inches (33.5 centimeters) which is
quite believable as the measure of a "foot," although this suggests
the Harappans had rather large feet!
Another
scale was discovered when a bronze rod was found to have marks in lengths of
0.367 inches. It is certainly
surprising the accuracy with which these scales are marked. Now 100 units of
this measure are 36.7 inches (93 centimeters), which is about the length of a stride. Measurements of the ruins of the buildings
that have been excavated show that the Harappans in their construction
accurately used these units of length.
European
System of Measurement: European systems of measurement were
originally based on Roman measures, which in turn were based on those of
Greece.
Greek
Contribution: The Greeks
used as their basic measure of length the breadth of a finger (about 19.3 mm),
with 16 fingers in a foot, and 24 fingers in a Greek cubit. These units of length, as were the Greek
units of weight and volume, were derived from the Egyptian and Babylonian
units. Trade, of course, was the main
reason why units of measurement were spread more widely than their local
areas. In around 400 BC. Athens was a
center of trade from a wide area. The
Agora was the commercial center of the city, and we know from the plays of
Aristophanes the type of noisy dealing that went on there. Most disputes would
arise over the weights and measures of the goods being traded. Therefore, a standard set of measures was
kept in order that such disputes might be settled fairly.
The
size of a container to measure nuts, dates, beans, and other such items, had
been laid down by law, and if a container was found which did not conform to
the standard, its contents were confiscated and the container destroyed.
The
Romans Adapted the Greek System: The
Romans adapted the Greek system. They
had as a basis the foot that was divided into 12 inches (or ounces for the
words are in fact the same). The Romans
did not use the cubit but, perhaps because most of the longer measurements were
derived from marching, they had five feet equal to one pace (which was a double
step that is the distance between two consecutive positions of where the right
foot lands as one walks). The 1,000
paces measured a Roman mile, which is reasonably close to the British mile as
used today. This Roman system was
adopted, with local variations, throughout Europe as the Roman Empire
spread. However, if one looks at a
country like England, it was invaded at different times by many peoples
bringing their own measures. The
Angles, Saxons, and Jutes brought measures such as the perch, rod and
furlong. The fathom has a Danish origin
and was the distance from fingertip to fingertip of outstretched arms, while
the ell was originally a German measure of woolen clothed.
British
Contribution: In England
and France measures developed in rather different ways. We have seen above how the problem of
standardization of measures always presented problems, and in early 13^{th}
century England a royal ordinance Assize of Weights and Measures gave a
long list of definitions of measurement to be used. On one hand it was an extremely successfully attempt at
standardization for its definitions lasted for nearly 600 years. The Act of Union between England and
Scotland decreed that these standards would hold across the whole of Great
Britain.
Locally,
however, these standards were not always adhered to and districts still
retained their own measures. Of course,
although an attempt had been made to standardize measures, no attempt had been
made to rationalize them and Great Britain retained a bewildering array of
measures that were defined by the ordinance as rather strange subdivisions of
each other. Scientists had long seen the benefits of rationalizing measures,
and those such as Wren had proposed a new system based on the yard defined as
the length of a pendulum beating at the rate of one second in the Tower of
London.
France
Contribution: In France,
on the other hand, there was no standardization and as late as 1788 Arthur
Young wrote in "Travels during the years 1787, 1788, 1789"
published in 1793: “In France the infinite perplexity of the measures
exceeds all comprehension. They differ
not only in every province, but in every district and almost every town.”
In
fact it has been estimated that France had about 800 different names for
measures at this time, and taking into account their different values in
different towns, around 250,000 differently sized units. To a certain extent this reflected the
powers, which resided in the hands of local nobles who had resisted all
attempts by the French King over centuries, to standardize measures. Some French scientists had proposed uniform
systems at least 100 years before the French Revolution. Gabriel Mouton, in 1670, had suggested that
the world should adopt a uniform scale of measurement based on the mille, which
he defined as the length of one minute of the Earth's arc. He proposed that decimal subdivisions should
be used to determine the lengths of shorter units of length.
Lalande,
in April 1789, proposed that the measures used in Paris should become national
ones, an attempt at standardization but not rationalization. This proposal was put to the National
Assembly in February 1790, but in March a different suggestion was made. Talley
Rand put to the National Assembly a proposal due to Condorcet, namely that a
new measurement system be adopted based on a length from nature. The system should have decimal subdivisions;
all measures of area, volume, weight etc should be linked to the fundamental
unit of length. The basic length should
be that of a pendulum, which beat at the rate of one second, was adopted. This proposal was not designed to bring in a
French system of measurement but to design an international system of
measurement, so agreement was sought from other countries.
An
immediate problem was that the pendulum length depended on the latitude at
which the experiment was performed so a latitude had to be chosen. The French proposed 45,
which conveniently fell in France. The
British proposed London, and the United States proposed the 38th parallel which
was conveniently close to Thomas Jefferson's estate. Diplomatic wording allowed
an international agreement to be reached, but in March 1791 Borda, as chairman
of the Commission of Weights and Measures, proposed using instead of the length
of a pendulum, the length of ^{1}/_{10,000,000} of the distance
from the pole to the equator of the Earth.
They
might have obtained international agreement on this had they not declared that
this distance would be determined by an accurate survey of the distance between
Dunkerque and Barcelona. The Royal
Society in London declared this was based on a measurement of France, the
Americans were not prepared to accept the word of the French mathematicians for
its length. and even in France it was claimed that the whole project was really
proposed in order to gain information on the shape of the Earth. Indeed, probably Laplace and others were
more interested in finding the shape of the Earth rather than the length of the
meter.
Impact
of the French Revolution: Delambre
and Méchain measured the meridian from
Dunkerque and Barcelona between 1792 and 1798.
However between these dates the French Revolution progressed to the
stage where the Académie des Sciences was abolished in August 1793, but before
that Borda, Lagrange and Laplace had computed a provisional value for the meter
based on the survey carried out by Cassini de Thury in 1740.
United
States Approval: The
National Assembly passed the metric system into law and a meter bar together
with a kilogram weight was dispatched to the United States in the expectation
that they would adopt the new measures.
Congress hesitated because the standards were provisional. Britain became hostile to the meter, as did
Germany, which wanted a standard based on the pendulum.
International
Commission: An
International Commission began work in September 1798 to replace the
provisional values with precise ones computed from the data collected by
Delambre and Méchain. By June of the
following year the Commission had produced a platinum bar, which became the
official definition of the meter, and in September 1799 the meter was required
by law to be used in the Paris region.
However, as one might expect, introducing the new measure was easier
said than done. Part of the problem was
that Greek and Latin prefixes like kilo and centi had been proposed to help
make the new system internationally acceptable but were strongly disliked in
France. It was also a law, which was
essentially impossible to enforce, and, again as one might expect, many traders
took the opportunity to cheat their customers.
Teaching the metric system became compulsory in schools and the hope was
that at least the next generation would accept it even if the current
generation would not.
Napoleon
Repeals the Standards: In
November 1800 an attempt was made to make the system more acceptable by
dropping the Greek and Latin prefixes and reinstating the older names for
measures but with new metric values. In
September of the following year it became illegal to use any other system of
weights and measures anywhere in France, but it was largely ignored. It did not last long for, on 12 February
1812, Napoleon returned the country to its former units. The meter standard was still used in the
sense that a fathom was declared to be 2 meters; there were 6 feet in a fathom
and 12 inches in a foot.
Now,
despite this retrograde move, Napoleon had a major effect on the spread of the
metric system. French conquests of the
Low Countries had seen the metric system introduced there and, on the defeat of
Napoleon and the restoring of monarchy in those countries, they retained the
system. The decimal metric system was
passed into law in 1820.
Belgium
Controversy: In 1830
Belgium became independent of Holland and made the metric system, together with
its former Greek and Latin prefixes, the only legal measurement system. Perhaps the fact that the French had
scrapped the system they invented helped its acceptance in other European
countries. In 1840 the French
government reintroduced the metric system but it took many years before use of
the old measures died out.
British
Empire Adoption of the Metric System: In
the 1860s Britain, the United States and the German states all made moves
towards adopting the metric system. It
became legal in Britain in 1864 but a law, which was passed by the House of
Commons to require its use throughout the British Empire, never made it through
its final stages on to the statute books.
Similarly in the United States it became legal in 1866, although its use
was not made compulsory. The German
states passed legislation in 1868, which meant that on the unification of these
states to form Germany, use of the metric system was made compulsory.
British
Opposition: It is
interesting that many leading British scientists were opposed to the
introduction of the metric system in Britain in 1864, which is one reason it
only became legal but not compulsory.
George Airy and John Herschel argued strongly against it, as did William
Rankine who composed the poem The ThreeFoot Rule:
Some
talk of millimeters, and some of kilograms,
And some of deciliters, to measure beer and drams;
But I'm a British Workman, too old to go to school,
So by pounds I'll eat, and by quarts I'll drink, and I'll work by my three foot
rule.
A
party of astronomers went measuring the Earth,
And forty million meters they took to be its girth;
Five hundred million inches, though, go through from Pole to Pole;
So lets stick to inches, feet and yards, and the good old three foot rule.
International
Conference: In 1870 the
French in Paris convened an International Conference. Invitations had been sent to scientists from countries around the
world with the aim of improving international scientific cooperation by having
the metric system as the worldwide standard.
War broke out between France and Prussia just before the delegates were
due to arrive, however, and the German delegation did not attend. Wishing that
any decision be a truly international one, the conference was postponed and met
again in 1872. The outcome was the
setting up of the International Bureau of Weights and Measures, to be situated
in Paris, and the Convention of the Meter of 1875, which was signed by
seventeen nations. Further countries
signed up over the following years.
International
Bureau of Weights and Measures: In
1889, the International Bureau of Weights and Measures replaced the original
meter bar in Paris by a new one, and at the same time had copies of the bar
sent to every country that had signed up to the Convention of the Meter. The definition now became the distance
between two lines marked on a standard bar made from 90 percent platinum and 10
percent iridium. This remained the
standard until 1960 when the International Bureau of Weights and Measures
adopted a more accurate standard for international science when it defined the
meter in terms of the wavelength of light emitted by the krypton86 atom,
namely 1,650,763.73 wavelengths of the orangered line in the spectrum of the
atom in a vacuum. The meter was
redefined again in 1983, this time as the distance which light travels in a
vacuum in ^{1}/_{299,792,458} seconds. This remains the current definition. In all redefinitions, the length of the
meter was always taken as close as possible to the value fixed in 1799 by data
from the DelambreMéchain survey.
Notice
that the current definition defines the meter in terms of the second. Now Borda had argued against using the
length of a pendulum, which beats at the rate of one second to define the meter
in 1791 on the reasonable grounds that the second was not a fixed unit but
could change with time. Indeed the
second, then defined as 1/86,400 of the mean solar day, does change but the
International Bureau of Weights and Measures introduced a fixed definition in
1956, as ^{1}/_{31,556,925.9747} of the length of the tropical
year 1900. Although this fixed the value, it was seen as an unsatisfactory
definition since the length of the year 1900 could never be measured after
1900.
It
was changed in 1964 to 9,192,631,770 cycles of radiation associated with a
particular change of state of the caesium133 atom. By 1983 when the meter was defined in terms of the second,
Borda's objection was no longer valid as the definition of the second by then
did not have the astronomical definition, which was indeed variable.
Metric
System: The Metric
System, is
a decimal system of physical units based on a unit of length
known as the meter (Greek metron, “measure”). Introduced and adopted by law in France in
the 1790s, a majority of countries subsequently adopted the metric system as a
common system of weights and measures.
Scientists in all countries use the metric system in their work.
The meter (m), which is
approximately 39.37 in, was originally defined as one tenmillionth of the
distance from the equator to the North Pole on a line running through
Paris. From 1792 to 1799, French
scientists measured part of this
distance. Treating the Earth as a
perfect sphere, they then estimated the total distance and divided it into
tenmillionths. Later, after it was
discovered that the Earth is not a perfect sphere, the standard meter was
defined as the distance between two fine lines marked on a bar of
platinumiridium alloy. In 1960 the
meter was redefined as 1,650,763.73 wavelengths of the reddishorange light
given off by a form of the element krypton.
The measurements of modern
science required still greater precision; however, and in 1983 the meter was
defined as the length of the path traveled by light in a vacuum during a time
interval of 1/299,792,458 of a second.
The United States uses
inches, feet, miles, pounds, tons, and gallons as units of length, weight, and volume for common measurements. Today, however, within the framework of the International System
of Units, these Englishsystem units are legally based on metric standards.
Using the Metric System: The metric system is known
for its simplicity. All units of measurement in the metric system are based on
decimals—that is, units that increase or decrease by multiples of ten. A series of Greek decimal prefixes is used
to express units of ten or greater; a similar series of Latin decimal prefixes
is used to express fractions. For example, deca equals ten, hecto
equals one hundred, kilo equals one thousand, mega equals one
million, giga equals one billion, and tera equals one
trillion. For units below one, deci
equals onetenth, centi equals onehundredth, milli equals
onethousandth, micro equals onemillionth, nano equals
onebillionth, and pico equals onetrillionth. For conversion of metric system units to Englishsystem units, see
Weights and Measures.
Length: People who were taught the
English system of measurements in
schools in the United States often have difficulty visualizing metric
units. One way to visualize a meter is
to think of the distance from the floor to the top of a doorknob, or the
distance from the edge of an adult’s shoulder to the end of the opposite
outstretched arm. Smaller things are measured in centimeters and millimeters. A millimeter is quite small, about the thickness
of a dime.
A
centimeter is ten times bigger, about the height of a stack of ten dimes. Thereafter meters are used until one reaches
distances about the length of five city blocks when kilometers are used. One kilometer is the approximate distance
that an adult can walk in 12 minutes in a straight line and on a level
road. Kilometers are used to measure long distances within cities or
between cities.
Volume: Small volumes, such as the
contents of a drinking glass, are measured
in cubic centimeters, and large volumes, such as the contents of industrial
fuel tanks, are measured in
liters. A liter is 1,000 cubic
centimeters—also known as 1,000 milliliters.
Strictly speaking a cubic centimeter and a milliliter are not exactly
the same. However, the difference is so
slight that it may be ignored for everyday use.
Weight: Small volumes, such as the
contents of a drinking glass, are measured
in cubic centimeters, and large volumes, such as the contents of industrial
fuel tanks, are measured in liters. A liter is 1,000 cubic centimeters—also
known as 1,000 milliliters. Strictly
speaking a cubic centimeter and a milliliter are not exactly the same. However, the difference is so slight that it
may be ignored for everyday use. A
normalsized drinking glass contains about 300 milliliters. The size of a liter is increasingly well
known in the United States because of the many oneliter beverage bottles found
in grocery stores or supermarkets. Very
large volumes are measured in cubic
meters. Freight containers used in the
shipping industry, including railroad, truck, and ocean shipping, have a
capacity of about 70 cubic meters.
The basic unit of weight in the metric system is called a gram,
and it is equal to the weight of one
cubic centimeter of water. This is a
very small amount, but it is easy to comprehend. Just pick up a U.S. dollar bill (or any bank note), and its weight is one gram. Because the gram is too light to be a convenient standard of weight, a larger unit has been chosen. This unit is 1,000 grams. Following the regular pattern of metric
naming, it is called one kilogram. One
thousand grams of water occupy a volume of 1,000 cubic centimeters or one
liter. Therefore, a person need only
pick up a plastic oneliter bottle of water to understand how heavy a kilogram
is. Very heavy objects are weighed in
tons of 1,000 kilograms each. One
thousand kilograms is equal to one metric ton and is not the same as the usual
American ton of 907.2 kg.
Adoption
of the Metric System: In the United States several
attempts were made to bring the metric system into general use. In 1821 Secretary of State John Quincy
Adams, in a report to Congress, advocated the adoption of the metric system. In 1866 Congress legalized the use of the
metric system, and the system was increasingly adopted, notably in medicine and
science, as well as in certain sports, such as track and field. In 1893 the Office of Weights and Measures
(now the National Institute of Standards and Technology) of the United States
adopted the metric system in legally defining the yard and the pound.
In 1965 the United Kingdom
became the first of the Englishspeaking countries to begin an organized effort
to abandon the older units of measurement. Canada, Australia, New Zealand, and South Africa
quickly followed and adopted the changeover more rapidly than the United
Kingdom.
In 1971, after an extensive
study, the U.S. secretary of commerce recommended that the United States
convert to metric units under a tenyear voluntary plan. In 1975 President Gerald R. Ford signed the
Metric Conversion Act. It defines the
metric system as being the International System of Units as interpreted in the
United States by the secretary of commerce.
The act called for voluntary adoption of the metric system. In 1988 a provision in new federal
legislation called for all federal agencies to use the metric system in
business transactions starting in 1992, but this was never implemented. Lack of public interest and support has
prevented the metric system from being adopted in the United States.
Summary: Ancient
measurement of length was based on the human body, for example the length of a
foot, the length of a stride, the span of a hand, and the breadth of a thumb.
The Egyptian cubit was developed around 3000 BC. The Egyptians developed a standard royal cubit, which was
preserved in the form of a black granite rod against which everyone could
standardize their own measuring rods. A
later civilization whose weights and measures had a wide influence was that of the
Babylonians around 1700 BC.
The Harappans appear to have adopted a uniform system of
weights and measures with two options.
One was a decimal scale based on a unit of measurement of 1.32 inches
(3.35 centimeters), which has been called the "Indus inch." The Harappans had rather large feet! Another scale was discovered when a bronze
rod was found to have marks in lengths of 0.367 inches. Now 100 units of this measure are 36.7
inches (93 centimeters), which is about the length of a stride.
European systems of measurement were originally based on
Roman measures, which in turn were based on those of Greece. The Greeks used as their basic measure of
length the breadth of a finger (about 19.3 mm), with 16 fingers in a foot, and
24 fingers in a Greek cubit. Athens was
a center of trade from a wide area. The
Romans adapted the Greek system. Then
1,000 paces measured a Roman mile, which is reasonably close to the British
mile as used today. The fathom has a
Danish origin, and was the distance from fingertip to fingertip of outstretched
arms.
The Act of Union between England and Scotland decreed that
these standards would hold across the whole of Great Britain. British Scientists proposed a new system
based on the yard defined as the length of a pendulum beating at the rate of
one second in the Tower of London. The
basic length of a pendulum, which beat at the rate of one second, was
adopted. Britain and Germany became
hostile to the meter, which wanted a standard based on the pendulum. In 1830, Belgium became independent of
Holland and made the metric system, together with its former Greek and Latin
prefixes, the only legal measurement system.
The Metric System was adopted in Britain 1864. In 1866, the system became legal in the
United States, although its use was not made compulsory. The German states passed legislation in 1868
to adopt the Metric System. In 1889,
the International Bureau of Weights and Measures replaced the original meter
bar in Paris by a new one and at the same time had copies of the bar sent to
every country which had signed up to the Convention of the Meter. Note that in all these redefinitions, the
length of the meter was always taken as close as possible to the value fixed in
1799 by data from the DelambreMéchain survey.
The current definition defines the meter in terms of the
second. In 1866 Congress legalized the
use of the metric system, and the system was increasingly adopted, notably in
medicine and science, as well as in certain sports, such as track and field. In 1893 the Office of Weights and Measures
(now the National Institute of Standards and Technology) of the United States
adopted the metric system in legally defining the yard and the pound. In 1965 the United Kingdom became the first
of the Englishspeaking countries to begin an organized effort to abandon the
older units of measurement. In 1971,
after an extensive study, the U.S. secretary of commerce recommended that the
United States convert to metric units under a tenyear voluntary plan. In 1975 President Gerald R. Ford signed the
Metric Conversion Act.
Introduction: The
purpose of this section is to outline the definitions of the second and the
meter as influenced by the Egyptians, Babylonians, Greeks, British, Danish,
French, and the International Community:
Egyptian Concept (3000 BC): The Egyptians developed a standard royal cubit, which was
preserved in the form of a black granite rod against which everyone could
standardize their own measuring rods.
There were 28 digits in a cubit, 4 digits in a palm, 5
digits in a hand, 3 palms (so 12 digits) in a small span, 14 digits (or a half
cubit) in a large span, 24 digits in a small cubit, and several other similar
measurements:
28 digits = one cubit
24 digit = small cubit
14 digits = large span
12 digits or 3 palms = small span
4 digits = one palm
5 digits = one hand
Babylonian Concept (25001700):
Babylonian cubit = 530 mm = 30 kus
Babylonian foot = 2/3 Babylonian cubit
Kus = finger breadth (1/30)
Egyptian cubit = 524 mm
Harappan System (25001700):
Indus Inch = 1.32 inches = 3.35 cm
Foot = 13..32 inches
36.7 inches (93 centimeters) = length of a stride.
Greek Concept (400 BC):
Foot = 16 fingers
Finger Breadth = 19.3 mm (Greek)
Greek Cubit = 24 finger breath
Romans Adopted the Greek System:
1 foot = 12 inches
Roman Mile = 1000 paces
Danish Concept (400BC):
The fathom has a Danish origin and was the distance from
fingertip to fingertip of outstretched arms while the ell was originally a
German measure of woolen clothed.
Fathom = the distance from fingertip to fingertip of
outstretched arms.
Fathom = 2 meters, 6 ft in one fathom, and 12 inches in a
foot.
British Concept (13th Century):
Definition of the second = the length of a pendulum beating
at the rate of one second in the Tower of London.
One second = Instead of the length of a pendulum, the
length of 1/10,000,000 of the distance from the pole to the equator of the
Earth.
France Concept (16701800):
Mille = he defined as the length of one minute of the
Earth's arc.
Second = the basic length should be that of a pendulum
which beat at the rate of one second.
Redefinition of the second = Indeed the second, then
defined as 1/86,400 of the mean solar day.
Redefinition of the second = British Scientists proposed
using instead of the length of a pendulum, the length of 1/10,000,000 of the
distance from the pole to the equator of the Earth.
Platinum Bar = A platinum bar which became the official
definition of the meter.
Redefinition of the Fathom: The meter standard was still
used in the sense that a fathom was declared to be 2 meters; there were 6 feet
in a fathom and 12 inches in a foot.
The original meter bar definition was replaced by the
distance between two lines marked on a standard bar made from 90 percent
platinum and 10 percent iridium.
Meter Bar defined = Became the distance between two lines
marked on a standard bar made from 90 percent platinum and 10 percent iridium.
International Standards:
Redefinition of the Meter (1960) = The meter was redefined
in terms of the wavelength of light emitted by the krypton86 atom, namely
1,650,763.73 wavelengths of the orangered line in the spectrum of the atom in
a vacuum.
Redefinition of the meter (1956) = as 1/31,556,925.9747 of
the length of the tropical year 1900.
Although this fixed the value, it was seen as an unsatisfactory
definition since the length of the year 1900 could never be measured after
1900.
Redefinition of the meter (1964) = It was changed in 1964
to 9,192,631,770 cycles of radiation associated with a particular change of
state of the caesium133 atom.
Redefining of the meter (1983) = as the distance which
light travels in a vacuum in 1/299,792,458 seconds.
Metric Weights and Measures: A
millimicron is one thousandth of one millionth of one meter. Most of the world uses the metric
system. The only countries not on this
system are the U.S., Myanmar, and Liberia.
The metric system is based on 10s.
For example, 10 decimeters make a meter (39.37 inches).
Units smaller than a meter have Latin prefixes:
Units larger than a meter have Greek prefixes:
The
International System (Metric)
Source: Department of
Commerce, National Bureau of Standards.
The International System of Units is a modernized version of the metric
system, established by international agreement that provides a logical and
interconnected framework for all measurements in science, industry, and
commerce. The system is built on a
foundation of seven basic units, and all other units are derived from
them. (Use of metric weights and
measures was legalized in the United States in 1866, and our customary units of
weights and measures are defined in terms of the meter and kilogram.)
Length (Meter): Up
until 1983, the meter was defined as 1,650,763.73 wavelengths in a vacuum of
the orangered line of the spectrum of krypton86. Since then, it is equal to the distance traveled by light in a
vacuum in 1/299,792,45 of a second.
Time (Second): The
second is defined as the duration of 9,192,631,770 cycles of the radiation
associated with a specified transition of the cesium133 atom.
Mass (Kilogram): The
standard for the kilogram is a cylinder of platinumiridium alloy kept by the
International Bureau of Weights and Measures at Paris. A duplicate at the National Bureau of
Standards serves as the mass standard for the United States. The kilogram is the only base unit still
defined by a physical object.
Temperature (Kelvin):
The kelvin is defined as the fraction 1/273.16 of the thermodynamic temperature
of the triple point of water; that is, the point at which water forms an
interface of solid, liquid, and vapor.
This is defined as 0.01°C on the Centigrade or Celsius scale and 32.02°F
on the Fahrenheit scale. The
temperature 0 K is called “absolute zero.”
Electric Current (Ampere):
The ampere is defined as that current that, if maintained in each of two long
parallel wires separated by one meter in free space, would produce a force
between the two wires (due to their magnetic fields) of 2 × 107 Newton for
each meter of length. (A newton is the
unit of force that when applied to one kilogram mass would experience an
acceleration of one meter per second per second.)
Luminous Intensity (Candela): The candela is defined as the luminous intensity of
1/600,000 of a square meter of a cavity at the temperature of freezing platinum
(2,042°K).
Amount of Substance (Mole): The mole is the amount of substance of a system that
contains as many elementary entities as there are atoms in 0.012 kilogram of
carbon12.
Zero on the Fahrenheit scale represents the temperature
produced by the mixing of equal weights of snow and common salt.

°Fahrenheit 
°Celsius 
Boiling point of water 
212° 
100° 
Freezing point of water 
32° 
0° 
Absolute zero 
273.1° 
459.6° 
Absolute zero is theoretically the lowest possible
temperature, the point at which all molecular motion would cease.
Measuring Motion: Speed
is the measure of motion. You can find it by dividing the distance covered by
the time it takes to travel that distance.
Speed of Light: If a
star is 10 lightyears away, it is about 60 trillion miles distant. Light travels through space at 186,000 miles
per second.
LightYear: A light ray travels 5.88 trillion miles a year in space.
Star Distance: The
star Sirius is 9 lightyears away from the solar system.
More Earthly Speeds:
Horsepower: A
workhorse can lift 550 pounds 1 foot in the air in 1 second; that is 1
horsepower. Engines are measured in
horsepower. A 10horsepower engine can
do the work of ten horses.
Manpower: An average
man lifts 55 pounds 1 foot high in 1 second.
Candlepower: The
amount of light given off by a candle of a specific size, shape, type of
tallow, and type of wick. The
brightness of an electric light is measured in candlepower.
Megaton: A megaton is
the blasting power of a hydrogen bomb. One megaton has the power of 1 million
tons of TNT.
Nautical Measurement:
A fathom is 6 feet, the length of rope a man can extend
from open arm to open arm. The rope was
lowered into the sea to measure depth.
A cable length is the length of a ship's cable, about 600
feet. A nautical mile is 10 cable
lengths, or 6,076 feet.
1 nautical mile = 1.1508 miles
A knot is the measure of speed on water. One knot is 1 nautical mile per hour.
How Early Measures Made Their
Mark: Dividing things into units is an ancient task. Here are four basic units and the people who
first used them. You will recognize how
they are still used today.
Binary: This Hindu
unit divides things into halves, quarters, and eights. Modern computer programs are based on binary
code.
Decimal: The Chinese and the Egyptians were the first to use decimals, which are tenths. The metric system is based on decimal units. The decimal system of writing numbers was introduced into Europe in the 1300s and is now widely used.
Duodecimal: The Romans
used units of 12. Today we have 12
inches in a foot, 12 months in a year, 12 in a dozen.
Sexagesimal: The
Babylonians used units of 60. Time is
measured in 60s: 60 seconds in a minute, 60 minutes in an hour.
Miscellaneous Units of Measure:
Acre = An area is
43,560 square feet. Originally, it was
the area a yoke of oxen could plow in one day.
Agate = Originally a
measurement of type size (51/2 points), now equal to 1/14 inch. Used in
printing for measuring column length.
Ampere = Unit of
electric current. A potential
difference of one volt across a resistance of one ohm produces a current of one
ampere.
Astronomical Unit (A.U.)
= 93,000,000 miles, the average distance of the earth from the sun. Used for astronomy.
Bale = A large bundle
of goods. In the U.S., the approximate weight of a bale of cotton is 500
pounds. The weight varies in other
countries.
Board Foot (fbm) = 144
cubic inches (12 in. × 12 in. × 1 in.).
Used for lumber.
Bolt = 40 yards. Used for measuring cloth.
Btu = British thermal
unit. Amount of heat needed to increase
the temperature of one pound of water by one degree Fahrenheit (252 calories).
Carat (c) = 200
milligrams or 3.086 grains troy.
Originally the weight of a seed of the carob tree in the Mediterranean
region. Used for weighing precious
stones.
Chain (ch) = A chain
66 feet or onetenth of a furlong in length, divided into 100 parts called
links. One mile is equal to 80
chains. Used in surveying and sometimes
called Gunter's or Surveyor's chain.
Cubit = 18 inches or
45.72 cm. Derived from distance between
elbow and tip of middle finger.
Decibel = Unit of
relative loudness. One decibel is the
smallest amount of change detectable by the human ear.
Ell, English = 11/4
yards or 1/32 bolt. Used for measuring
cloth.
Freight = Ton (also
called measurement ton).
40 Cubic Feet of Merchandise = Used for cargo freight.
Great Gross = 12 gross
or 1728.
Gross = 12 dozen or
144.
Hand = 4 inches or
10.16 cm. Derived from the width of the
hand. Used for measuring the height of
horses at withers.
Hertz = Modern unit
for measurement of electromagnetic wave frequencies (equivalent to “cycles per
second”).
Hogshead (hhd) =
Liquid barrels or 14,653 cubic inches.
Horsepower = The power
needed to lift 33,000 pounds a distance of one foot in one minute (about 11/2
times the power an average horse can exert).
Used for measuring power of steam engines, etc.
Karat (kt) = A measure
of the purity of gold, indicating how many parts out of 24 are pure. For example: 18karat gold is 3/4 pure. Sometimes spelled carat.
Knot = Not a distance
but the rate of speed of one nautical mile per hour. Used for measuring speed of ships.
League = Rather
indefinite and varying measure, but usually estimated at 3 miles in English
speaking countries.
Light Year =
5,880,000,000,000 miles, the distance light travels in a vacuum in a year at
the rate of 186,281.7 miles (299,792 kilometers) per second. (If an astronomical unit were represented by
one inch, a lightyear would be represented by about one mile.) Used for measurements in interstellar space.
Magnum = Twoquart
bottle. Used for measuring wine, etc.
Ohm = Unit of
electrical resistance. A circuit in
which a potential difference of one volt produces a current of one ampere has a
resistance of one ohm.
Parsec = Approximately
3.26 lightyears or 3.08 × 1013 km (1.92 × 1013 mi). Term is combination of first syllables of parallax and second,
and distance is that of imaginary star when lines drawn from it to both Earth
and the Sun form a maximum angle or parallax of one second (1/3600 degree). Used for measuring interstellar distances.
pi (p)=3.14159265+.
The ratio of the circumference of a circle to its diameter. For practical purposes, the value is used to
four decimal places: 3.1416.
Pica = 1/6 inch or 12
points. Used in printing for measuring
column width, etc.
Pipe = 2
hogsheads. Used for measuring wine and
other liquids.
Point = .013837
(approximately 1/72) inch or 1/12 pica. Used in printing for measuring type
size.
Quintal = 100,000
grams or 220.46 pounds avoirdupois.
Quire = Used for
measuring paper. Sometimes 24 sheets
but more often 25. There are 20 quires
to a ream.
Ream = Used for
measuring paper. Sometimes 480 sheets,
but more often 500 sheets.
Roentgen =
International Unit of radiation exposure produced by Xrays.
Score = 20 units.
Sound, Speed of =
Usually placed at 1,088 ft. per second at 32°F at sea level. It varies at other temperatures and in
different media.
Span = 9 inches or
22.86 cm. Derived from the distance
between the end of the thumb and the end of the little finger when both are
outstretched.
Square = 100 square
feet. Used in building.
Stone = Legally 14
pounds avoirdupois in the U.K.
Therm = 100,000 btu's.
Township = U.S. land
measurement of almost 36 square miles.
The south border is 6 miles long.
The east and west borders, also 6 miles long, follow the meridians,
making the north border slightly less than 6 miles long. Used in surveying.
Tun = 252 gallons, but
often larger. Used for measuring wine
and other liquids.
Watt = Unit of
power. The power used by a current of
one ampere across a potential difference of one volt equals one watt.
Origins of Measurements: In ancient times, the body ruled when it came to measuring. The length of a foot, the width of a finger, and the distance of a step were all accepted measurements.
Inch = At first an
inch was the width of a man's thumb. In
the 14th century, King Edward II of England ruled that 1 inch equal 3 grains of
barley placed end to end lengthwise.
Hand = A hand was
approximately 5 inches or 5 digits (fingers) across. Today, a hand is 4 inches and is used to measure horses (from the
ground to the horse's withers, or shoulder).
Span = A span was the
length of the hand stretched out, about 9 inches.
Foot = In ancient
times, the foot was 111/42 inches. Today it is 12 inches, the length of the
average man's foot.
Yard = A yard was
originally the length of a man's belt or girdle, as it was called. In the 12th century, King Henry I of England
fixed the yard as the distance from his nose to the thumb of his outstretched
arm. Today it is 36 inches, about the
distance from nose to outstretched arm of a man.
Cubit = In ancient
Egypt, a cubit was the distance from the elbow to the fingertips. Today a cubit
is 18 inches.
Lick = A Lick was used
by the Greeks to measure the distance from the tip of the thumb to the tip of
the index finger.
Pace = The ancient
Roman soldiers marched in paces, which were the length of a double step, about
5 feet; 1,000 paces was a mile. Today,
a pace is the length of one step, 21/2 to 3 feet.
Measurements:
Near and Far:
Cooking Measurement Equivalents (see the Infoplease.com conversion calculator):
1 tablespoon (tbsp) = 3
teaspoons (tsp)
1/16 cup = 1 tablespoon
1/8 cup = 2 tablespoons
1/6 cup = 2 tablespoons + 2 teaspoons
1/4 cup = 4 tablespoons
1/3 cup = 5 tablespoons + 1 teaspoon
3/8 cup = 6 tablespoons
1/2 cup = 8 tablespoons
2/3 cup = 10 tablespoons + 2 teaspoons
3/4 cup = 12 tablespoons
1 cup = 48
teaspoons
1 cup = 16 tablespoons
8 fluid ounces (fl oz) = 1 cup
1 pint (pt) = 2 cups
1 quart (qt) = 2 pints
4 cups = 1 quart
1 gallon (gal) = 4 quarts
16 ounces (oz) = 1 pound (lb)
1 milliliter (ml) = 1 cubic centimeter (cc)
1 inch (in) = 2.54 centimeters (cm)
Source: United States Dept. of Agriculture (USDA)
US to Metric:
Capacity Weight
1/5 teaspoon 1
milliliter 1 ounce 28 grams
1 teaspoon 5
ml 1 pound 454 grams
1 tablespoon 15
ml
1 fluid oz 30
ml
1/5 cup 47
ml
1 cup 237
ml
2 cups (1 pint) 473 ml
4 cups (1 quart) .95 liter
4 quarts (1 gallon) 3.8
liters
91 gallon
Metric to US:
Capacity Weight
1 milliliter 1/5
teaspoon 1 gram .035 ounce
5 ml teaspoon 100
grams 3.5 ounces
15 ml 1
tablespoon 500 grams 1.10 pounds
100 ml 3.4
fluid oz 1 kilogram 2.205 pounds
240 ml 1
cup 35
ounce
1 liter 34
fluid oz, 4.2 cups, 2.1 pints, 1.06 quarts, 0.26 gallon
Linear Measure:
12 inches (in.) =
1 foot
3 feet = 1 yard
51/2 yards = 1 rod, pole, or
perch (161/2 ft.)
40 rods = 1 furlong (fur) = 220
yds = 660 ft.
8 furlongs = 1 statute mile (mi.)
= 1,760 yds = 5,280 ft
3 land miles = 1 league
5,280 feet = 1 statute or land
mile
6,076.11549 feet = 1
international nautical mile
Area Measure:
144 square inches = 1 sq ft.
9 square feet =1 sq yd = 1,296 sq
in.
301/4 square yards = 1 sq rd =
2721/4 sq ft.
160 square rods = 1 acre = 4,840
sq yds = 43,560 sq ft.
640 acres = 1 sq. mi.
1 mile square = 1 section (of
land)
6 miles square =1 township = 36
sections = 36 sq mi.
Gunter's or Surveyor's Chain
Measure:
7.92 inches = 1 link (li)
100 links = 1 chain (ch) = 4 rods
= 66 ft.
80 chains = 1 statute mile = 320
rods = 5,280 ft.
The meridian distance of a traverse
line is equal to the length of a line running east to west from the
midpoint of the traverse line to
a reference meridian. The
reference meridian is the meridian that passes through the most westerly
traverse station. In Figure #1 (Plot), the dotted lines indicate
the meridian distances of the traverse lines to which
they extend from the reference meridians.
The following rules for determining meridian distance are outlined
below:
1. For the initial
traverse line in a closed traverse, the meridian distance equals one half of
the departure.
2.
For each subsequent traverse line, the meridian distance
equals the meridian distance of the preceding course line, plus one half of the departure of the preceding line, plus one half of the departure of the line itself.
If the rules have been followed correctly, the BMD of the last
course will be equal to the departure of the last course with its sign changed.
The altitude is the latitude of the course, and the average of the
bases of the several courses is equal to the perpendicular distance to each
course of the meridian.
Methodology (Equipment Required):
One transit with a Tripod, Stadia Rod, and Data Collection forms shown in Figure #1.
Measurements: The Transit operator will be assisted by one individual to position the Stadia Rod under the command of the Transit Operator. The Transit will measure the range and bearing of the points. It is envisioned that a minimum of ten readings from each side will be taken. Figure #1 illustrates the necessary data elements that must be recorded during the surveying. Columns #1is the station number, Column #2 is the Slant Range, Column #3 Bearing Angle, and Column #4 the elevation angle. Columns #5 thru #10 are the elements of data calculated from the recorded measurements. The analytical results will be calculated before the measurements. The algorithm has been tested and verified  it works.
Calculations: Table #1 illustrates the series of calculations based on the following measurements: Distance, Bearing, and Altitude. For this project, it is assumed to be in two dimensions excluding the topography and elevation or altitude considerations. The recorded measurements are used to calculate the Latitude, Departure, Double Meridian Distance, and Double Areas. At the end of the calculations, the DMD of the last course should be the same or approximated to the departure of the last course except a different sign.
If they are not the same, a truncation error may have occurred. Figure #1 depicts the geometry of the plot, and Table 1 illustrates the calculations of the plot. A test case has been used to define the area in Distances and Bearing to calculate the Latitude and Longitude of each course line. In essence, the table data elements are the basis to determine the acreage of the land. A table of the liner measure and area measure standards are provided for information only.
The following is a summary of the formulas used to calculate the area of the farm:
St = Slant Distance in yards.
Bo = The azimuth angle to the course line referenced to North.
Latitude = (St)*Sine Bo (Theta)
Departure = (St)* cosine Bo (Theta)
DMD of the first course = Departure of the first course
DMD (1) = (DMD of the first course)+(departure of the preceding point)+(the departure of the current point) Note #1.
Double Areas = (Latitude) * (DMD). Multiply the latitude of the course line by the DMD of the course line. The results will be either positive or negative.
Note#1: The subsequent courses are calculated in the same fashion.
Appendix # 1Standard Measurement Used In Surveying:
U.S. Weights and Measurements
Linear Measure:
12 inches (in.) = 1 foot (ft.)
3 feet = 1 yard (yd)
51/2 yards = 1 rod (rd), pole, or
perch (161/2 ft.)
40 rods = 1 furlong (fur) = 220
yds = 660 ft.
8 furlongs = 1 statute mile (mi.)
= 1,760 yds = 5,280 ft.
3 land miles = 1 league
5,280 feet = 1 statute or land
mile
6,076.11549 feet = 1
international nautical mile
Area Measure:
144 square inches = 1 sq ft.
9 square feet = 1
sq yd = 1,296 sq in.
301/4 square yards = 1 sq rd =
2721/4 sq ft.
160 square rods = 1 acre = 4,840
sq yds = 43,560 sq ft.
640 acres = 1 sq mi.
1 mile square = 1 section (of
land)
6 miles square = 1 township = 36
sections = 36 sq mi.
Gunter's or Surveyor's Chain Measure:
7.92 inches = 1 link (li)
100 links = 1 chain (ch) = 4 rods
= 66 ft.
80 chains = 1
statute mile = 320 rods = 5,280 ft.
Table 1: Calculations of Plot #1
Course # 
Distance (Yards) 
Bearing (Degrees) 
SineƟ 
COS
Ɵ 
Latitude 
Departure 
DM
Ɵ 
Double + 
Areas  
AB 
360 
122 
.53 
.85 
191 
306 
306 

58,446.0 
BC 
220 
63 
.45 
.89 
+162 
196 
808 
130,896 

CD 
150 
45 
.71 
.71 
+106 
106 
1,110 
117,660 

DE 
250 
309 
.63 
.78 
+157 
195 
1,021 
160,297 

EF 
200 
282 
.21 
.98 
+ 42 
196 
630 
26,460 

FA 
290 
225 

.71 
.71 
206 
206 
228 

47,010 






TOTAL
DIFF
= 

435,313 329,857.00 YARDS 
105,456.0 
TOTAL
DOUBLE AREA (TDA)
TDA
= (DIFF) =
329,857.0 =
68.15 ACRES
4840 YDS.(SQ)/ACRE 4840
Cosine
Law:
COS A = b˛ + c˛  a˛
2bc
COS B = a˛ + c˛  b˛
COS C = a˛ + b˛ c˛
2AB
Sine
Law:
a = √ b˛ + c˛ = (A˛ + b˛) ˝
25001700
BC: Harappan
civilization flourished in the Punjab between 2500 BC and 1700 BC. The Harappans appear to have adopted a
uniform system of weights and measures.
1700
BC: Later civilization
whose weights and measures had a wide influence was that of the Babylonians
around 1700 BC. Their basic unit of
length was, like the Egyptians, the cubit.
The Babylonian cubit (530 mm), however, was very slightly longer than
the Egyptian cubit (524 mm). The
Babylonian cubit was divided into 30 kus, which is interesting since the kus
must have been about a finger's breadth, but the fraction ^{1}/_{30}
is one that is also closely connected to the Babylonian base 60 number
system. A Babylonian foot was ^{2}/_{3}
of a Babylonian cubit.
400
BC: Around 400 BC Athens
was a center of trade from a wide area.
The Agora was the commercial center of the city and we know from the
plays of Aristophanes the type of noisy dealing that went on there.
13^{th}
Century England: England
and France measures were developed in rather different ways. We have seen above
how the problem of standardization of measures always presented problems, and
in early 13^{th} century England a royal ordinance Assize of Weights
and Measures gave a long list of definitions of measurement to be used.
1670: Gabriel Mouton, in 1670, had suggested
that the world should adopt a uniform scale of measurement based on the mille,
which he defined as the length of one minute of the Earth's arc.
1700: The French, in fact, had more than 1,000
units of measurement by the late 1700s
with approximately 250,000 variations in size from one town to another.
1788: In France, on the other hand, there was
no standardization and as late as 1788 Arthur Young wrote in "Travels
during the years 1787, 1788, 1789" published in 1793: “In France the
infinite perplexity of the measures exceeds all comprehension. They differ not only in every province, but
in every district and almost every town.”
1789
Lalande, in April 1789, proposed that the measures used in Paris should
become national ones, an attempt at standardization but not rationalization.
1790: This proposal was put to the National
Assembly in February 1790, but in March a different suggestion was made. Talleyrand put to the National Assembly a
proposal due to Condorcet, namely that a new measurement system be adopted
based on a length from nature.
The meter (m), which is
approximately 39.37 in, was originally defined as one tenmillionth of the
distance from the equator to the North Pole on a line running through Paris.
1791: Diplomatic wording allowed an
international agreement to be reached, but in March 1791 Borda, as chairman of
the Commission of Weights and Measures, proposed using instead of the length of
a pendulum, the length of ^{1}/_{10,000,000} of the distance
from the pole to the equator of the Earth.
Notice
that the current definition defines the meter in terms of the second. Now Borda had argued against using the
length of a pendulum, which beats at the rate of one second to define the meter
in 1791, on the reasonable grounds that the second was not a fixed unit but
could change with time.
17921798:
Delambre and Méchain measured the meridian from Dunkerque and Barcelona
between 1792 and 1798. Later, after it
was discovered that the Earth is not a perfect sphere, the standard meter was
defined as the distance between two fine lines marked on a bar of
platinumiridium alloy.
1793:
French Revolution progressed to the stage where the Académie des Sciences
was abolished in August 1793 but before that Borda, Lagrange and Laplace had
computed a provisional value for the meter based on the survey carried out by
Cassini de Thury in 1740.
1798: An International Commission began work
in September 1798 to replace the provisional values with precise ones computed
from the data collected by Delambre and Méchain. By June of the following year the Commission had produced a
platinum bar, which became the official definition of the meter.
1799: The
meter was required by law to be used in the Paris region. However, as one might expect, introducing
the new measure was easier said than done.
Part of the problem was that Greek and Latin prefixes like kilo and
centi had been proposed to help make the new system internationally acceptable
but were strongly disliked in France.
1800:
An attempt was made to make the system more acceptable by dropping the
Greek and Latin prefixes and reinstating the older names for measures but with
new metric values.
1801: It
became illegal to use any other system of weights and measures anywhere in
France, but that was largely ignored.
1812:
Napoleon returned the country to its former units.
1820: The decimal metric system was required
to be used by law in the Low Countries in 1820.
1821: In 1821 Secretary of State John Quincy
Adams, in a report to Congress, advocated the adoption of the metric system.
1830: In 1830 Belgium became independent of
Holland and made the metric system, together with its former Greek and Latin
prefixes, the only legal measurement system.
1840: In 1840 the French government
reintroduced the metric system but it took many years before use of the old
measures died out.
1860=
In the 1860s Britain, the United States and the German states all made moves
towards adopting the metric system.
1864: It became legal in Britain in 1864, but
a law that was passed by the House of Commons to require its use throughout the
British Empire never made it through its final stages on to the statute
books. It is interesting that many
leading British scientists were opposed to the introduction of the metric
system in Britain in 1864, which is one reason that it only became legal but
not compulsory.
1866: In 1866 Congress legalized the use of the
metric system, and the system was increasingly adopted, notably in medicine and
science, as well as in certain sports such as track and field. The
Metric System became legal in the United States.
1868: The German states passed legislation in
1868, which meant that on the unification of these states to form Germany, use
of the metric system was made compulsory.
George Airy and John Herschel argued strongly against it, as did William
Rankine who composed the poem The ThreeFoot Rule:
Some
talk of millimeters, and some of kilograms,
And some of deciliters, to measure beer and drams;
But I'm a British Workman, too old to go to school,
So by pounds I'll eat, and by quarts I'll drink, and I'll work by my three foot
rule.
A
party of astronomers went measuring the Earth,
And forty million meters they took to be its girth;
Five hundred million inches, though, go through from Pole to Pole;
So lets stick to inches, feet and yards, and the good old three foot rule.
1870:
In 1870 an International Conference was convened by the French in Paris.
Invitations had been sent to scientists from countries around the world with
the aim of improving international scientific cooperation by having the metric
system as the world wide standard. War
broke out between France and Prussia just before the delegates were due to
arrive, however, and the German delegation did not attend.
1872: Wishing that any decision be a truly
international one, the conference was postponed, and it met again in 1872.
1875: The outcome was the setting up of the
International Bureau of Weights and Measures, to be situated in Paris, and the
Convention of the Meter of 1875 that was signed by seventeen nations. Further countries signed up over the
following years.
1889: In 1889 the International Bureau of
Weights and Measures replaced the original meter bar in Paris by a new one and
at the same time had copies of the bar sent to every country which had signed
up to the Convention of the Meter. The
definition now became the distance between two lines marked on a standard bar
made from 90 percent platinum and 10 percent iridium.
1893:
In
1893 the Office of Weights and Measures (now the National Institute of
Standards and Technology) of the United States adopted the metric system in
legally defining the yard and the pound.
1900:
All metric units were
originally derived from the meter, but by 1900 the metric system began to be
based on the meterkilogramsecond (makes) system.
1901:
The unit of volume, the liter, was originally
defined as 1 cubic decimeter (dm^{3}), but in 1901 it was redefined as
the volume occupied by a kilogram of water at 4°C and 760 mm of mercury.
1956: Indeed the second, then defined as
1/86,400 of the mean solar day, does change but a fixed definition was
introduced in 1956 by the International Bureau of Weights and Measures, as ^{1}/_{31,556,925.9747}
of the length of the tropical year 1900.
1960: This remained the standard until 1960
when the International Bureau of Weights and Measures adopted a more accurate
standard for international science when it defined the meter in terms of the
wavelength of light emitted by the krypton86 atom, namely 1,650,763.73
wavelengths of the orangered line in the spectrum of the atom in a vacuum.
1964: It was changed in 1964 to 9,192,631,770
cycles of radiation associated with a particular change of state of the
caesium133 atom. The original
definition (dm^{3}) was restored.
1965:
In 1965 the United Kingdom became the first of the
Englishspeaking countries to begin an organized effort to abandon the older
units of measurement. Canada, Australia, New Zealand, and South
Africa quickly followed and adopted the changeover more rapidly than the United
Kingdom.
1971:
In 1971, after an extensive study, the U.S. secretary of
commerce recommended that the United States convert to metric units under a
tenyear voluntary plan.
1975: In 1975
President Gerald R. Ford signed the Metric Conversion Act.
1983: The meter was redefined again in 1983,
this time as the distance which light travels in a vacuum in ^{1}/_{299,792,458}
seconds. This remains the current
definition. Note that in all these
redefinitions, the value fixed in 1799 by data from the Delambre Méchain
survey always has been used as the baseline.
1983:
By 1983 when the meter was defined in terms of the second, Borda's
objection was no longer valid as the definition of the second by then did not
have the astronomical definition that was indeed variable.
1988: In 1988 a provision in new federal
legislation called for all federal agencies to use the metric system in
business transactions starting in 1992, but this was never implemented.
BIBLIOGRAPHY
Weights
and Measures Article by: J J
O'Connor and E F Robertson
MacTutor History of Mathematics, April 2003
[http://wwwhistory.mcs.standrews.ac.uk/HistTopics/Measurement.html]
The Metric System, Microsoft
® Encarta ® Reference Library 2004. © 19932003 Microsoft Corporation. All rights reserved.
History of Mathematics by Michael S. Pilant, Microsoft ® Encarta ® Reference Library 2004.
© 19932003 Microsoft Corporation. All
rights reserved.