On 2007/09/30, at 11:29 AM, Pierre Abbat wrote:
One of the students' demonstrations was about the Gunter's chain.
One chain is
just over 20 m and is divided in 100 links. Has anyone made a
metric chain
which is 20.000 m instead of 20.1168 m?
Pierre
Dear Pierre and All,
I had the good fortune recently to visit Monticello in Virginia, the
home of Thomas Jefferson. There I discovered that he was a keen
surveyor (as were George Washington and Abraham Lincoln).
Here is an extract from the historical Reference at http://
celebrating200years.noaa.gov/theodolites/theodolitehead_zm.html
**
Several of our nation's early presidents spent time as surveyors.
Lawrence and Austin Washington inherited the most valuable of the
Washington lands when their father died in 1743, leaving younger
brother George (future first president of the United States) in need
of a profession. George did inherit Augustine Washington's surveying
equipment, and, at age sixteen, George embarked on his first career.
George headed across the Blue Ridge Mountains, then considered the
western frontier, to survey land for Thomas, Lord Fairfax.
Abraham Lincoln wrote of the time he spent as assistant to the
Sangamon County (Illinois) Surveyor as something that "procured bread
and kept soul and body together." Unfortunately, it apparently didn't
always pay the bills, as in 1834, Lincoln sold his surveying
equipment at auction to pay a debt.
While it may not be common knowledge that Presidents Washington and
Lincoln were practitioners of the science of surveying, it should
come as no surprise that Thomas Jefferson, the same President who
referred to freedom as "the first born daughter of science," sent the
Lewis and Clark Expedition west and established the Survey of the
Coast, was also fascinated by the mathematics and techniques of
surveying. Although he filled the post of Albemarle County (Virginia)
Surveyor for a short time, Jefferson primarily used his skills on his
own lands. However, in 1815, at the age of 72, Jefferson used the
theodolite shown here to determine the elevation of the Peaks of
Otter in the Blue Ridge Mountains.
**
This fascinated me as this piece of information provide the missing
link as to how the system of 'universal measure' -- now know as the
metric system or SI -- travelled from England in 1668 to France in
the 1790s. It looks like it travelled in large part through the USA
via two people, George Washington and Thomas Jefferson, who had both
had direct experience with the ease of use of decimal numbers in
their surveying calculations using Gunter's Chain.
This sounds odd so let me put this into context with a short chronology:
1585
Simon Stevin published his decimal arithmetic book in two languages
as Thiende (Of tenths in Flemish) and as Disme (Of tenths in French).
1620
Edmund Gunter (1581/1626) publishes his 'Canon Triangulorum'
describing several measuring instruments that he had invented
including what has become known as 'Gunter's Chain'. Gunter's Chain
was based on Simon Stevin's decimal arithmetic in that it had 100
links to facilitate the use of decimal arithmetic in making
relatively complex trigonometric calculations. It is interesting that
Gunter's base in London, Gresham College, was the same college where
John Wilkins worked in the 1660s. Presumably, Gunter was familiar
with Simon Stevin's work on decimal arithmetic that was translated
into English as 'Decimall Arthmetike' in 1608. At Gresham College in
the 1660s, John Wilkins would have been familiar with Gunter's
decimal work as he formulated his ideas for a 'universal measure'
based on decimal numbers.
1743
George Washington (1732/1799) inherited his father's surveying
equipment presumably so he was familiar with the ease of use of the
decimal measures made using Gunter's decimal chain.
1757
Thomas Jefferson inherited his father's (Peter Jefferson) surveying
equipment again presumably with a decimal Gunter's Chain.
1785
Federal legislation in the USA required that official surveys had to
be done using Gunter's chains made up of 100 links each 7.92 inches
long.
1785 to 1789
Thomas Jefferson served as Minister to France where he was in regular
contact with English and French intellectual leaders of the
Enlightenment as they formed their ideas about universal measurement.
For example, Charles Maurice de Talleyrand-Périgord (1754/1838),
Bishop of Autun, but usually known simply as Talleyrand, in France;
Sir John Riggs-Miller, in England; and Thomas Jefferson, USA Minister
to France, corresponded on a proposal for a universal 'decimal
système metrique' Essentially, Talleyrand, Riggs-Miller, and
Jefferson were proposing that their three nations should cooperate to
equalise their weights and measures, by the joint introduction of a
decimal metric system.
1790 January
George Washington (1732/1739), in his first message to Congress,
reminded the legislators of their responsibility on weights and
measures when he said:
A uniformity of weights and measures is among the important objects
submitted to you by the Constitution, and, if it can be derived from
a standard at once invariable and universal, it must be no less
honorable to the public council than conducive to the public
convenience.
The House of Representatives responded by asking Secretary of State
Thomas Jefferson (1743/1826) to make a special report on the subject.
Jefferson proposed a decimal measurement system to the USA Congress.
Jefferson's suggestion used some of the scientific investigations
aimed at reform of the French weights and measures but it varied in
the detail. Jefferson's proposals had a remarkable similarity to the
design for 'universal measure' outlined by John Wilkins in 1668.
Jefferson recommended a two-part plan.
The first part of the plan proposed the adoption of a unit based on
the seconds-pendulum, measured at 45 degrees north latitude at sea
level and the conversion of existing English units to that unit. To
give some flavor of Jefferson's recommendation, here is an excerpt of
his length measures:
Let the foot be divided into 10 inches; the inch into 10 lines; and
the line into 10 points. Let 10 feet make a decad; 10 decads one
rood; 10 roods a furlong; and 10 furlongs a mile.
The second part proposed the use of a decimal system as a basis for
the seconds-pendulum unit; to reduce:
Every branch to the same decimal ratio, thus bringing the
calculations of the principal affairs of life within the arithmetic
of every man who can multiply and divide plain numbers.
George Washington and Thomas Jefferson combined forces politically,
to propose the use of decimal currency for the USA. Decimal currency
became reality in the USA in 1792.
1790 March 29
Knowing that Sir John Riggs Miller had raised the question of weights
and measures in the British House of Commons during 1789, Talleyrand
wrote this private letter to him (This is Sir John Riggs Miller's
translation of the letter).
Sir,
I understand that you have submitted for the consideration of the
British Parliament, a valuable plan for the equalization of measures:
I have felt it my duty to make a like proposition to our National
Assembly. It appears to me worthy of the present epoch that the two
Nations should unite in their endeavour to establish an invariable
measure and that they should address themselves to Nature for this
important discovery.
If you and I think alike on this subject, and that you are of opinion
that much general benefit may be derived from it, it is through you
only that we can hope for its accomplishment; and I beg to recommend
it to your consideration. Too long have Great Britain and France been
at variance with each other, for empty honour or for guilty
interests. It is time that two free Nations should unite their
exertions for the promotion of a discovery that must be useful to
mankind.
I have the honour to be, Sir, with due respect, your most humble and
obedient servant,
The Bishop of Autun
Talleyrand's concept was for the adoption of a brand new basic
standard, 'derived from nature (pris dans le nature) and therefore
acceptable to all nations. Talleyrand further suggested that the
French National Assembly, the English Parliament, and the Royal
Society of London should undertake preliminary work towards this
objective jointly. He wrote:
Perhaps this scientific collaboration for an important purpose will
pave the way for political collaboration between the two nations.
1790 April 13
Sir John Riggs Miller reported on the receipt of the letter from
Talleyrand, and expressed himself in favour of the scheme. He then
made a speech to the British House of Commons proposing measurement
reform. He had been in contact with both Talleyrand and with Thomas
Jefferson, who was then the first Secretary of State of the United
States of America.
At about the same time Talleyrand, one of the foremost members of the
French National Assembly, introduced the subject and launched a
debate that resulted in a directive to the French Academy of Sciences
to prepare a report on a new system of measurement for France and for
the world. The French National Assembly sent delegates to Britain,
Spain and the United States to propose cooperation in units of
measurement.
1790 May 8
Talleyrand submitted a proposal to the National Assembly for a
decimal system of stable, unvarying and simple measurement units.
These were to be based on the length of the seconds pendulum at 45°
latitude beating a second. At Talleyrand's suggestion, the French
National Assembly adopted this new measuring system. Louis XVI
authorised scientific investigations aimed at a reform of all French
weights and measures and these investigations led to the development
of the 'metric system'.
The metric system as it was proposed was always intended as a
standard system understandable to everyone and it was:
an enterprise whose result should belong some day to the whole world.
1790 August 22
Talleyrand's proposal, having been referred to the Committee on
Agriculture and Commerce, was recommended to the king, who sanctioned
action on August 22. This was the French decree that led to the
further development of the metric system. The French Academy of
Sciences was made responsible, and appointed a committee that
included Lagrange and Laplace among its members; their first report,
in October, recommended the decimal division of money, weights, and
measures.
The National Assembly decreed that all measures in use throughout the
provinces of France should be sent to the Academy of Sciences who
would then issue new standard measures to all the parishes of France.
The idea was that by doing this the old measures could be dispensed
with altogether. However, it seems that the National Assembly had
little idea of the complexity and magnitude of this task as they
considered that the new standards could be adopted and copies of it
could be distributed, replacing all of the old measures with the new,
within six months.
1790 October 27
Later in the year the French Academy of Science issued a report that
recommended:
… that the length of a meridian from the North Pole to the Equator be
determined, that 1/10 000 000th of this distance be termed the metre
and form the basis of a new decimal linear system, and, further, that
a new unit of weight should be derived from the weight of a cubic
metre of water.
This report also recommended that the new system of weights and
measures should be decimal and it included a list of prefixes for
decimal multiples and sub-multiples. This system became the decimal
metric system that later became the International System of Units
that we now use in every nation in the world.
1790 November 11
Talleyrand urged that the preparation of a new system of weights and
measures should be a collaborative venture, with the French inviting
the participation of the English Parliament and the Royal Society of
London. Talleyrand also made efforts to establish contacts with other
countries. These included negotiations with Thomas Jefferson
concerning the definition of the metre. Jefferson initially favored
using a pendulum at the latitude of 38°N as this was close to the
centre of the territory of the United States of America, but
eventually he accepted the 45°N, proposed by the French National
Assembly as he felt that this was better suited to an international
destiny for the metric system.
Cheers,
Pat Naughtin
[EMAIL PROTECTED]
http://www.metricationmatters.com.html
PO Box 305 Belmont 3216, Geelong, Australia
Phone: 61 3 5241 2008
Pat Naughtin is manager of http://www.metricationmatters.com an
internet website that primarily focuses on the many issues, methods
and processes that individuals, groups, companies, and nations use
when upgrading to the metric system. You can contact Pat Naughtin at
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