The standard of length of the système ancient was the toise of 6 pieds,
divided into 12 pouces of 12 lignes each.
The origin of the toise is not known, but it was probably legally
established by Philip Le Bel, about 1300, as he first appears to have
taken steps toward a uniform system of measures in France. In the 13th
century the toise is mentioned by Ch. Le Rains. In the 14th century
Menongier writes that, in marching, the sight should strike the ground 4
toises in front. In the fifteenth century Pereforest brings in the toise,
and in the sixteenth century the Contume de Berry says, “We use in this
country two toises; one for carpenters of 5 pieds and a half, the other
for masons of 6 pieds.”
Picard used the toise in his measurement of an arc of meridian from
Malvoisin to London in 1669.
The meridians measured by the Academy in 1735 to settle the question of
the figure of the earth were made by means of two standard toises, known
as the “Toise du Nord,” and the “Toise du Sud.”
The first, used by Maupertuis, Clairault, and Le Monnier, in Lapland, was
destroyed by immersion in sea-water, when their ship was wrecked on the
return voyage.
The second, with which La Condamine, Bourgner, and Godin operated in
Peru, was the original of the toise Canivet made in 1768, and of the
standards used in determining the mètre.
The commencement of the move for a scientific standard of length in
France which resulted in the mètre was in 1790, when the revolutionary
government proposed to England the formation of a commission of equal
numbers from the English Royal Society and the French Academy, for the
purpose of fixing the length of the seconds pendulum at latitude 45° as
the basis of a new system of measures. This proposal was not favorably
received, and the Academy, at the request of government, appointed as
a commission Borda, Lagrange, Laplace, Monge, and Condorcet, to decide
whether the seconds pendulum, the quarter of the equator, or the quarter
of a meridian, should be used as the natural standard for the new system
of measures. They settled on the last as best for the purpose, and
resolved that the ten millionth of the meridian quadrant, or distance
from equator to pole, measured at sea level, be taken for basis of the
new system, and be called a mètre.
Delambre and Mechin were at once charged with re-measurement of the
meridian surveyed in 1739 by La Caille and Cassini, from Dunkirk to
Perpignan, and its extension to Barcelona.
Operations were commenced in 1792, and carried on with great accuracy
to completion in 1799; Delambre working between Dunkirk and Paris, and
Mechin between Paris and Barcelona.
The distance measured from Dunkirk to Barcelona was 9° 40´ 24·24´´ of
arc, or 1,075,059 mètres, as reduced to the new standard.
The “toise de Peru” was the standard used in the work at a temperature of
13° R.
Two base-lines were measured with Borda’s compensating bars of brass and
platinum; one at Melun, near Paris, 6076 toises long, and the second at
Perpignan, 6028 toises long, and though over 900,000 mètres apart, the
calculated length differed by only 10 pouces.
This meridian was afterward, in 1806, extended by Gen. Roy to Greenwich,
on the north, and by Biot and Arago to Formentera, on the south. The
results, as given by Laplace in centesimal degrees and mètres, are as
follows:
Greenwich 57·19753° ·0 mètres.
Pantheon, Paris 54·27431° 292,719·3 “
Formentera 42·96178° 1,423,636·1 “
The middle of the arc being 50·079655° Cent., or 45° 4´ 18·0822´´ Sexa.,
and the middle degree centesimal being very nearly 100,000 mètres.
The determination of the final result of these geodetic measurements was
referred to a committee of 20 members; 9 named by the French Government,
and the others by the governments of Holland, Savoy, Denmark, Spain,
Tuscany, and of the Cisalpine, Ligurian, and Swiss republics, on the
invitation of France.
This committee established the meridian quadrant at 5,130,740 toises;
making the mètre 0·513074 of the toise, or 36·9413 pouces, or 443·296
lignes, and the toise 1·94903659 mètres.
Iron standard mètre bars, 12 in number were made by Borda, also 2 of
platinum and 4 standard toise bars.
The 12 standard iron mètre bars were sent to different countries, after
being verified by the French Government, and on the 2d of November, 1801,
the mètrical système was legalized by France, and the standard unit of
length declared to be the ten millionth part of a meridian quadrant of
the earth, as defined by the distance at a temperature of 0° Centigrade
(32° F.) between two points on a platinum bar in the keeping of the
Academy of Science at Paris. This standard bar is used only once every
ten years for exact comparisons, as stated by Dr. F. A. P. Barnard.
About 1837 Bessel, by a combination of 11 measured arcs of meridian,
deduced the quadrant of meridian as 5,131,179·81 toises instead
of 5,130,740 toises, as fixed by law. This would make to quadrant
10,000,565·278 legal mètres, or would increase the mètre length from
443·296 lignes to 443·334 lignes, agreeing very nearly with result
obtained by Airy in 1830, from a combination of 13 measured arcs.
The following are the measured arcs used by Bessel and Airy; the
combinations being indicated by initial letters, A and B.
_Measurer._ _Mid. Lat._ _Arc._ _Length._
B.--Svanberg, Sweden +66° 20´ 10·0´´ 1° 37´ 19·6´´ 593,277 feet
A.--Maupertuis, Sweden +66° 19´ 37·0´´ 0° 57´ 30·4´´ 351,832 “
A.--Struve, Russia +58° 17´ 37·0´´ 3° 35´ 5·2´´ 1,309,742 “
B.--Struve and Tenner,
Russia +56° 3´ 55·5´´ 8° 2´ 28·9´´ 2,937,439 “
B.--Bessel and Bayer,
Prussia +54° 58´ 26·0´´ 1° 30´ 29·0´´ 551,073 “
B.--Schumacher, Denmark +54° 8´ 13·7´´ 1° 31´ 53·3´´ 559,121 “
A, B.--Ganss, Hanover +52° 32´ 16·6´´ 2° 0´ 57·4´´ 736,425 “
A.--Roy and Kater, England +52° 35´ 45·0´´ 3° 57´ 13·1´´ 1,442,953 “
B.-- “ “ “ +52° 2´ 19·0´´ 2° 50´ 23·5´´ 1,036,409 “
A.--Lacaille and Cassini,
France +46° 52´ 2·0´´ 8° 20´ 0·3´´ 3,040,605 “
A, B.--Delambre and Mechin,
France +44° 51´ 2·5´´ 12° 22´ 12·7´´ 4,509,832 “
A.--Boscovich, Rome +42° 59´ ·0´´ 2° 9´ 47·0´´ 787,919 “
A.--Mason and Dixon,
America +39° 12´ ·0´´ 1° 28´ 45·0´´ 538,100 “
A, B.--Lambton, India +16° 8´ 21·5´´ 15° 57´ 40·7´´ 5,794,598 “
A, B.--Lambton and Everest,
India +12° 32´ 20·8´´ 1° 34´ 56·4´´ 574,318 “
A, B.--Lacondamine, Peru - 1° 31´ 0·4´´ 3° 7´ 3·5´´ 1,131,050 “
A.--Lacaille, Cape Good
Hope -33° 18´ 30·0´´ 1° 13´ 17·5´´ 445,506 “
B.--Maclear, “ “ -35° 43´ 20·0´´ 3° 34´ 34·7´´ 1,301,993 “
A.--Plana and Cartessi,
Piedmont -------------- 1° 7´ 31·1´´ ------------
The following different lengths of the mètre have been obtained:
As adopted by France, 1801 443·296 lignes.
According to Delambre 443·264 “
“ Bessel 443·33394 “
“ Airy 443·32387 “
“ Clarke 443·36146 “
From Peru Meridian 443·440 “
The length of a pendulum vibrating 100,000 times in a mean solar day was
determined in numerous careful experiments by Biot, Arago, and Mathieu,
in mètres of 443·296 lignes, as follows:
Dunkirk 56·67 lat. Cent. 0 above sea 0·7419076 mètres.
Paris 54·26 “ 65 “ 0·7418870 “
“ by Borda 54·26 “ 0 “ 0·7416274 “
Bordeau 49·82 “ 0 “ 0·7412615 “
Formentera 42·96 “ 196 “ 0·7412061 “
Borda also determined the length of the seconds pendulum at Paris, in
vacuo:
First result 440·5595 lignes = 0·9938267 mètre.
Second result “ “ = 0·9938460 “
As given by Ganot “ “ = 0·9935 “
In 1812 the système usuelle was established, of which the unit was one
third of the mètre, with the old name of pied, and duodecimally divided
into pouces and lignes.
This system continued in use till 1840, when it was abolished by law, and
the names of pied, pouce, and ligne forbidden under penalties. So the
mètre, decimally divided, remains the only legal measure of length in
France.